text:
Moderators

6792

47856

Moderators

5336

21013

3. ## iNow

Senior Members

5045

23764

Moderators

4265

25528

## Popular Content

Showing content with the highest reputation since 03/28/04 in Posts

12 points
2. ## Mike Smith Cosmos

I was reading through Mordred's long standing thread on space and I came across some posts from Mike in the early part. Members may wish to know that Mike passed away earlier this month after a long standing degenerative illness (not covid). Mike was an interesting character, an artist with a degree in Physics and the founder of a successful manufacturing business before retirement to Cornwall. His artistic (dreamy) side gave him an unusual and sometimes frustrating perspective on Physics, especially later in life when we knew him. But he was a genuine character and sometimes offered suprising insights as well.
8 points
3. ## Rules update: bad faith discussions

Staff have decided to update the forum rules to include the following: This is in response to a number of threads and certain members who have made threads here under the premise of 'just asking a question,' only to reveal that they are in fact trying to peddle conspiratorial or otherwise nonsense ideas. While covered to some extent by pre-existing rules, we have decided to make it explicit that we will not be hosting these sorts of threads, if for no other reason than the fact that they are a waste of everyone's time.
8 points
4. ## Matter creates gravity

OK let's clarify something here. First consider the following definitions. Mass is resistance to inertia change Energy the ability to perform work. Spacetime a geometric model system with 3 spatial dimensions with 1 time dimension. In physics dimension is an independent variable or value that can change without affecting any other mathematical object. So how does mass curve spacetime. Well GR models bodies in free fall that is without any force applied. Time is given units of length and can be called an interval. This is done by setting c which is constant to all observers and adding a unit of time. So the time coordinate is given units of length by ct. $(t,x,y,z)=(ct,x,y,z)=(x^1,x^2x^3x,x^4)$ the last is in four momentum form for convenience as its useful to model a particle trajectory along the x axis. Now what is spacetime curvature. Well space is just volume... (Very important ) it isn't a stretchable bendable fabric... Those are just analogy descriptive. What spacetime truly means by curvature is the worldline paths for light it us the null geodesic. If you shoot two laser beams in flat spacetime those beams stay parallel. If spacetime is curved then the beams converge for positive curvature and spread apart for negative curvature. This is a consequence of how the mass term affects the time it takes for a particle to go from emitter to observer. That whole resistance to inertia. So let's drop two objects toward a planet. You have the usual Centre of mass. As the objects free fall they do not stay parallel. They will converge upon one another as they approach the center of mass. That what is really meant by curvature the free fall paths are curved. Not the volume of space.
8 points
5. ## When did God put the soul in humans during evolution?

So looking at the image below, it appears that Galagidae have recognizable soles, but Cynocephalidae do not : and when we look at a primate phylogeny, we see the split between these two groups is around 65 million years ago: So soles originated about 65 million years ago, give or take. You meant soles as in soles of the feet, right?
8 points
6. ## So are quantum entangled or teleported particles instantly there

So if I change the charge of one plate, somebody can measure an instantaneous change at the other plate. Wouldn't that be a violation of special relativity? @Menan You show that you do not understand entanglement. Let's go one step at a time. First a classical example. I have a bag of balls, they are all red or green. Without looking I pick two balls, and I put them in separate boxes. I keep one, and send the other far away. Then I open my box, and see it is a green ball. What can I conclude about the colour of the ball in the remote box? Right, nothing. And why? Because there was nothing special with my picks. It could have been two reds, two greens, or one red and green. Now I pick, looking of course, one red and one green, and put them in two separate boxes. So what I did here is 'entangle' the balls. Now I shuffle the two boxes, so that I do not know which one is which. If I open one, and see that it is red, I immediately know that the ball in the other box is green. And of course, this is independent on the distance. If I send the second box lightyears away, and only then open my box, I still know immediately what some alien sees when he opens his box. I know it because the observations are correlated. And the correlation already happened at the moment of my picks. That is the moment of entanglement. It is not when the boxes are opened. Now in quantum physics, there are processes where two particles pop out, which have e.g in one aspect always opposite values. Say the direction of spin. So if I measure the spin e.g. in a vertical direction, say it is 'up', then I immediately know that the other one will measure spin 'down', when also measured in the vertical direction. But as with the balls, the 'moment of entanglement' is when these particles popped into existence. But in quantum physics a few things are different: first, it is impossible to say which particle has which spin without measuring (it is as if I created the green and red balls, including their boxes, without knowing which ball is in which box). But as the two particles are entangled, if I measure both, the measurements will always be correlated. And there is nothing special with correlation: if I send one particle far away, and then measure my particle in the vertical direction, and the alien measures his particle in the same direction, I will always know what he measures: the opposite of my measurement. The 'spooky' aspect comes in when we do not know from each other in which direction we measure the spin. It can be vertical, horizontal, 30o, 45o, 55.3977o. What we find is that the correlation is stronger than one would expect if we would assume that the particles already had a definite spin from the beginning. But it still is correlation, not causation. As with the red and green balls, there is no direct causal relationship between my and the alien's observation. The causal relationship goes back to the moment of 'entanglement'. Everything afterwards is just correlation, and therefore cannot be used to transfer information. And because there is no causal relationship between my measurement of the spin of my particle, and the alien's measurement, I cannot use entanglement for sending information. And all this is very well understood by all quantum physicists, and is no secret at all.
8 points

7 points
8. ## Can you be a scientist and still believe in religion?

Well, since Markus has expressed his desire to join a Monastery, I think that definitely answers the OP question. But, some words to Markus... ( no offence meant, just trying to lighten the mood ) A young monk arrives at the monastery. He is assigned to helping the other monks in copying the old laws of the church by hand. He notices, however, that all of the monks are copying from copies, not from the original manuscript. So, the new monk goes to the head monk to question this, pointing out that if someone made even a small error in the first copy, it would never be picked up! In fact, that error would be continued in all of the subsequent copies. The head monk, says, “You make a good point, my son.” He goes down into the dark caves underneath the monastery where the original manuscripts are held in a locked vault. Hours go by and nobody sees the head monk. The young monk gets worried and goes down to look for him. He sees him banging his head against the wall and wailing. “We missed the R! We missed the R! We missed the R!” “Father!” cries the young monk. “What’s wrong?” The head monk with tears in his eyes replies, “The word is CELEBRATE!"
7 points

7 points
10. ## My first thousand

Just did not want to let this pass without a party (Dutch treat...). You are all invited at the lakeside! (Just Click on the picture to see it full size.) Thank you to all from who I learned a lot, and also thank you all who understand less than I do about certain subjects, but force me me to rethink, or make my viewpoint clearer, or force me to read some book or article (again). I noticed that much of what I read is influenced by topics here in these fora. And thanks to those who make this forum possible, moderators, administrators, sponsors, etc. Up for the next 1000!
7 points
11. ## Special Relativity - simple questions?

SR does not claim that such an observer will always see the Earth clock run slow, if by see, you mean what his eyes or instruments directly record. In this usage of see, he will see it run at a rate of T = To ((1-v/c))(1+v/c))1/2 where v is positive if Earth and the Observer are receding from each other and negative if they are approaching each other. A factor contributing to this observation is the the distance and thus the propagation time for signals is constantly changing, getting longer when receding and getting shorter when approaching. This factor works out to be c/(c+v) When you factor this out of the first equation you are left with the time dilation equation. This means that there are two things to consider: what you see happening to the Earth clock, and what is happening to the Earth clock. So while while receding from the Earth, the observer will see the the 1000 Hz signal as being 500 hz and the Earth clock as ticking 1/2 as fast as his own,. Taking into account the effect of the increasing distance, he will determine that the Earth clock is ticking 0.8 as fast as his own. He will meet up with the object when his own clock reads 1.01.2022 (as the distance between Earth will be only 1.2 ly as measured by him and this is how long it takes to traverse this distance at 0.6c.) He will see the Earth clock reading 1.01.2021, but determine that it is 8.07.2021 on the Earth at that moment. Now at first, you might be tempted to think " But wait, if he sees 1.01.2021 on the Earth clock, and the Earth is, according to him, 1.2 ly away, wouldn't that mean that it should be 3.15.2022 on the Earth by his reckoning?" This is not the case. The light he is seeing at that moment left Earth at a time when the distance between them was less than 1.2 ly, so the time it took the light he is seeing took less than 1.2 years to reach him from the Earth. Now he accelerates in order to come start the trip back towards Earth. We will assume a minimal acceleration period. Now this is the part where people tend to get tripped up. After he is done and is now approaching the Earth and not receding, we will assume that he still reads 1.01.2021 on the Earth clock by visual means. However, he will no longer conclude from this that it is 8.07.2021 on the Earth. Instead he will conclude that it is 6.05.23. During the return trip he will see a frequency of 2000 hz from the signal and the Earth clock tick twice as fast as his own. But again, taking into account the decreasing distance effect, he will conclude that the Earth clock is ticking at a rate 0.8 as fast as his own. Thus he will see the Earth clock tick from 1.01.2021 to 1.01.2025, but conclude that it ticked from 6.05.23 to 1.01.2025 during his return leg. (see will see it tick off 4 years, but conclude that it ticked off 1.6 years. Again, it all come back to what happens during that acceleration period. As far as anyone at rest with respect to the Earth is concerned, nothing special beyond the standard SR effects take place. But for the observer actually undergoing the acceleration, things aren't this simple. For him, the rate at which clocks run depend on which direction they are from him relative to the acceleration he is undergoing and the distance from him in that direction. Clocks in the direction of the acceleration run fast, and those in the opposite direction run slow (beyond what he sees. This even effects clocks that share his acceleration. A clock in the nose of the Ship will run fast and one in the tail will run slow. ( in this case, since there is no changing distance between himself and the clocks, what he sees, will be in perfect agreement with what is happening to the clocks. While this may seem to be at odds with common sense, it is how a Relativistic universe works. A problem with your questions is that they only deal with particular points of the whole scenario without taking in the whole picture. It like comparing two men walking and only considering where they end up. Below we have the paths of two men, Red and Blue, over the same interval. If you just look at where they end up, you would conclude that Blue walked a shorter distance because he ends up closer to the starting point than Red does. But when you consider the whole interval, it is clear that Blue walked a further distance. The same thing is true with SR, if you only consider the end results, you are missing what is really going on.
7 points

7 points

6 points
14. ## autism brain connectivity

I’m on the autism spectrum myself. The problem here is that we can’t isolate a specific sensory stimulus at the exclusion of everything else. So in this particular example, the stimuli coming from eye contact and his spoken words are both present, and both equally prominent simultaneously, which makes it difficult to focus on the actual content of either one of them. Averting eye contact simply makes it easier to focus on the person’s speech, so a lot of autistics will do this unconsciously and automatically. A better example would be a room full of people all talking to each other; it is very hard for me to just focus on what the person in front of me is saying, since I am forced to equally register all the other conversations in the room at the same time. There is no functioning filter there to limit and focus sensory stimuli - which is why we get sensory overload in certain stimuli-rich environments. Note that this is a matter of degree - different environments affect different autistic people in different ways and degrees.
6 points
15. ## 1. Thermodynamic work

A question about a sign convention that leads to a lot of confusion. This is not the only instance multiple sign conventions in Science. In this case it is a result of History. Thermodynamics was originally developed by physical scientists and engineers. They were concerned with making machines (steam engines) for the industrial revolution. Steam engines are heat engines. That is they thought in terms of input (heat in the form of fuel) and output (work). Both of these were thought of as 'naturally being' positive quantities. So they wrote their version of the Law of Conservation of Energy (The First Law of Thermodynamics) as ΔU = q - w. Chemists came to the scene from a different point of view. They wanted all forms of energy to have the same sign, whichever side of the conservation appearance they appeared so they could present the equation as a sum on both sides of the equation. So they wrote their equation as ΔU = q + w. By then it was also realised that, although all the terms are energies, there is a difference between ΔU , which is a state variable of the system, and q and w which are exchange variables of the energies crossing the system boundary. So they tidied up by stating that all energies crossing the boundary from the system to the surroundings are negative and all energies passing from the surroundings to the system are positive. Now they could add them up, move them about in equations and between equations in other parts of Science in a consistent manner. It is an improved system But it shows the importance of knowing the sign convention in use and the equations that go with it. This last remark also applies to other such instances of multiple conventions such as those in Electricity, Elasticity and elsewhere.
6 points
16. ## Last post of the first 1000

This is my 1000th post! Time to celebrate, This is a fine moment to open the Islay Single Malt I got for Christmas. Cheers from Ghideon, to all new and old form members!
6 points

6 points
18. ## My grand daughter!

My son holding my grand daughter!
6 points
19. ## The Border Wall or Fence

Implicit here is a false suggestion of equivalence. That’s not the case. If a kid walks down the hallway in school and gets punched in the face and has his lunch money stolen, is it his fault for carrying lunch money or walking freely down a public hallway? No, of course not, but if you think “both sides” need to compromise here then that’s precisely what you’re saying... that the kid is equally guilty as the bully. Trump last year said send a bill to my desk and I’ll sign it. Republicans were in control so drafted their version. Democrats agreed to vote for it and provide billions of dollars for this wall last year, and the compromise was that dreamers would get status. Trump backed out. He moved the goalposts. He said I want more. Funding ran out in December and Democrats said, fine... we’ll sign the republican bill yet again... we’ll compromise... but want money allocated to smarter enforcement options. A wall is not smart, and even countless republicans across the nation and some on Fox News itself agree. Trump said no. Eff you, a wall or nothing. Democrats said, Republicans still control all 3 branches of government. Since they’re in control, they need to get their president onboard. They couldn’t. President had a tantrum. Paper tiger in the Oval Office. Said he wants a shutdown. Shutdown began. Democrats took control of the house in January and on Day 1 passed a bill to reopen the government. Senate leader McConnell would not even bring it to the floor. Democrats later said they’d give more money for border protection, just not a wall. They compromised. President still refused. Wall or nothing. Eff the workers. Democrats passed multiple other bills to reopen parts of the government and agreed to negotiate terms on border security. They AGAIN voted for the previously passed republican funding bill from December. McConnel AGAIN wouldn’t bring it to the floor. Today Democrat senators continued to pressure McConnell to bring the bills up for a vote. He refused. He said it was pointless because the president won’t sign. Democratic Senators reminded him that they had the votes to override a presidential veto... that they are a co-equal branch of government and need to act like it. McConnell left. He just walked off the floor. Still no vote. Democrats will again pass a bill tomorrow to reopen the government. The bill will be the one drafted and previously agreed to by republicans. I agree there’s a lack of compromise here, but to say it’s equal across the aisle is absurd. The bully is trying to steal the lunch money. The other side has already offered to share their sandwich with him and are not at fault merely for having lunch money in their pocket.
6 points
20. ## What if Einsteins Definition of Simultaneity is incorrect?

Right, he is saying that the speed of light in both directions is the same with respect to any inertial frame as measured from that frame. So in the following example we have two observers. One standing along the tracks and the other traveling along the tracks in a railway car. Two flashes are emitted from two points along the tracks that are equal distance from the track observer. the light from these flashes arrive at the midpoint observer at the same moment as the railway observer is passing him. Thus both observers detect the light from the flashes at the same time. Like this: For the midpoint observer ( or anyone at rest with respect to the tracks) these flashes were emitted simultaneously, as shown by the expanding circles: However, for the railway car observer, events have to occur differently. He still detects the light from both flashes simultaneously, and they arrive when he is adjacent to the track observer. But unlike the track observer he has not remained halfway between the emission points the entire time. He is not an equal distance from the emission points when either of the flashes was emitted. But he must also measure the speed of light for each of the flashes as being the same relative to himself. But since the distances each of these flashes travel relative to him are not the same, in order for the light of the flashes to reach him simultaneously, they must have left at different times. And the sequence of the events for him occur like this: For the track observer, the flashes are emitted simultaneously, but for the railway observer they are not. This is the relativity of simultaneity: Events that are simultaneous in one inertial frame are not so according to another which in relative motion with respect to the first frame.
6 points
21. ## SFN's New Moderators Thread

I am pleased to now add CharonY and Strange to the list of gullible fools wonderful people willing to sacrifice their time for the greater good here at SFN. Congratulations!
6 points

6 points
23. ## Stephen Hawking Passed Away 3/14/2018

Stephen Hawking has passed away at the age of 76 on Pi day, 3/14/2018. http://www.bbc.com/news/uk-43396008 https://www.theguardian.com/science/2018/mar/14/stephen-hawking-professor-dies-aged-76?CMP=fb_us
6 points
24. ## Trump Effects

This is the rhetoric pushed by billionaires who don't need the government the way most of us do. Isn't it pretty obvious that the billionaires in politics today are only interested in removing restrictions on themselves, and limiting the money spent on the rest of us? These folks have been hammering this message of "bad government" and "sleazy politicians" for decades, while actively being the representatives with the sleaziest behavior, doing everything they can to make the government bad. They don't care if you have access to libraries, museums, parks, swimming pools, or healthcare. They have all those things taken care of due to their massive wealth, and object to taxes that make these things available to the rest of us. They've chosen to ignore our efforts that brought them great wealth, and instead spend money convincing folks that government needs to be dismantled for OUR good. And now they have this blatant racist sexual assaulter-in-chief who is morally and economically corrupt, and happens to have a deluded following all chanting about bringing down the Fed. Working class folks who think this billionaire has their backs while he whittles away at the very thing that has the best chance of making all their lives a lot better. The wolves have tricked the sheep into removing restrictive fences, and the sheep are all praising the freedom.
6 points
25. ## Why doesn't truth matter & middle ground

Puerto Rico agrees. Black athletes agree. The anti-fascist movement agrees.
6 points
26. ## God and science

Why do you limit your options to 'god did it' or 'everything popped out of nothing'? What about it didn't start, i.e. it's always existed? What about 'we don't know'? Also, as i understand it physicists have found that things do simply pop into existence. And yes, i'm frequently astonished by existence. Why does that imply god? I like this question. Many people seem to question that the universe could either just pop into existence or that it has always existed - but are happy to ascribe these exact same properties to something they call 'god'. Either way something has this property - why not discard the middleman and simply ascribe it to the universe. Depends how god is defined. A god that set up the conditions for the big bang but does not intervene at all thereafter would be impossible to detect, at least with our current capabilities. A personal god that answers prayers and parts seas has been pretty well debunked. Such a god would be easy to detect - we would just look for instances where the laws of physics contradict themselves (i.e. the rules change) - seas start to part, lakes turn into wine, whatever other crazy stuff you think a god might do. There is no sign of such a god.
6 points
27. ## What taxes a billionaire?

There are several parallel issues here. One is that wealth acquired by the ultra wealthy tends to get put into tax shelters and nebulous investments so it grows (but remains outside the system), whereas that same money in the hands of the less fortunate goes IMMEDIATELY into the community around them. They spend it on groceries and vehicle repairs and school clothes for kids and paying the electricity bill so it’s not dark in their apartment anymore at night and their kids can read. The providers of those goods and services in that community where this money is being spent ALSO spend the money once received for THEIR groceries and THEIR service needs and on THEIR kids. Dollar for dollar / unit for unit… the money in the hands of the less fortunate does more net good than money in the hands of the already fortunate. Yes, spending from the wealthy also creates jobs and injects money back into the system, but very little relative to money used in “trickle up” stimulation packages. Also, a bit of extra money in the hands of someone who already has a bunch of it doesn’t tend to change their behavior or encourage extra spending. Getting $1,000 tax break when you’re sitting on$50M isn’t going to suddenly result in them finally making a call to a plumber or the purchasing a new dishwasher… but for the person living paycheck to paycheck that money literally changes lives, gets spent and injected back into the system quickly, and results in lasting reductions in poverty and suffering. When you’re living at the margins, every dollar counts. It also costs a lot to be poor. When the washing machine breaks, you can’t afford a new one but you can afford to pump quarters into the machine at the laundromat… but that ends up being more expensive on net. When the car breaks down, you don’t get to work on time and you get fired. The rich, however, have tax protected ways of growing their wealth and can afford tax attorneys to hide it. Paying more tax has more impact on their ego than on their lived experience. The anger at the rich is out of hand, though. We need better policies and enforcement mechanisms, not more hate and vitriol directed at those doing better than us. Sadly, the anger is probably in large part intentionally being amplified by the very people on the receiving end. If they can keep everyone mad and focused on the wrong things, then the status quo remains stable and no progress or change gets made. Like most issues in economics, we make a huge mistake by treating it as a moral failure when at its core it’s a policy failure. Fixing the policy is just super hard because the people with the power to change the laws tend to be the same ones benefiting the most from them… and also because focusing on wonky policy details is hard for a public who’s often just trying to survive through to tomorrow and who’d much prefer throwing stones and being distracted with us/them tribalism. Perhaps this thread could try focusing on wonky policy details instead of distractions like yachts and steel boats… or not.
5 points
28. ## Is Gravity a Force?

Yes @joigus, I lurk in the shadows and follow proceedings here whenever I get the opportunity At present I live in the jungles of Thailand, having recently been ordained as a monk, and do not have access to anything other than an old mobile phone with spotty and slow internet access, so I’m not really in a position to participate in discussions. It’s just too slow and painful to type this way. I will return once I get access to better infrastructure - perhaps some time next year. Satellites in orbit are in free fall - place an accelerometer into them, and it will show exactly zero at all times. No proper acceleration -> no force acting on them. And yet they don’t fly off into space, but remain gravitationally bound into their elliptical orbits. Clocks in them are also dilated wrt to far-away reference clocks, which is also a gravitational effect. Thus, no force, but still gravity. Newtonian forces are simply bookkeeping devices, and as such they often work well - but only in the right context. Their nature is descriptive, but not ontological. They are not very physical either, given that they are assumed to act instantaneously across arbitrary distances. The strong, weak, and EM interactions aren’t ‘forces’ in that sense at all, since they work in very different ways. They are only sometimes called ‘forces’ by convention, for historical reasons. They ultimately arise through the breaking of symmetries, with the particles involved being irreducible representations of symmetry groups. Finally, it should be noted that physics makes models, that’s what it sets out to do - and as such it is always descriptive rather than ontologically irreducible. So, asking whether gravity “really is” A or B, or whether A or B are “true” is fairly meaningless, since both A and B are descriptions of reality, but not reality itself. Like maps of a territory. The correct question is thus whether models A and/or B are useful in describing gravity, and in what ways and under what circumstances they are useful. So - Newtonian gravity is sometimes useful, but GR is more generally useful, as it gives more accurate predictions for a larger domain. So for now the best answer to “what is gravity” that we have is a purely descriptive one: it’s geodesic deviation, and thus a geometric property of space time. To put it flippantly, it’s the failure of events to be causally related in a trivial manner. Future advancements may upend this picture in the high-energy domain, perhaps radically. We’ll see. I’m sorry I can’t contribute much at the moment, but I’ll leave you with the above thoughts. I could have written much more, but it’s too much of a pain on a small mobile phone screen.
5 points
29. ## Transgender athletes

I watch MMA. Some women in the sport have raised concerns about transgender athletes, which is how it came to my attention. Some in the medical have put forward scientific reasons to legitimise this concern, others refute these reasons, and that debate continues within the medical community (links have been provided in the course of this thread). To have these concerns just brushed away as ridiculous, and to equate them with resistance against gay marriage is unhelpful at best. It's the sort of rhetoric that pushes people toward Trump and Brexit, as it exacerbates the us vs them attitude that precludes nuanced debate - the nuance here being that having concerns about transgender athletes does not automatically make you transphobic (although it's likely true that all transphobes oppose all trans athletes and will leverage legitimate concerns to muddy the waters). It may turn out that these concerns are unfounded, but i would hope, on a science forum of all places, that the concerns were addressed rather than being dismissed simply ridiculous. It is patronising.
5 points
30. ## I will no longer post on your forum for the following reasons.

Lol I’m reminded of this
5 points
31. ## A very tough (and possibly controversial) poll about sexual abuse and rape

While this thread is closed and (I think) being the only person who identifies as female in this thread, I just wanted to provide a little food for thought. Of all the women in my life with whom I am close to, I can't think of a single one who hasn't been sexually assaulted or raped by a man at some point in her life. I cannot say the same about the men I know wrt to false accusations. Anecdotal I know, but something to think about.
5 points
32. ## The Official JOKES SECTION :)

I can't unsee it. Eh?
5 points

5 points
34. ## FTL thought experiment

When you arrive at point C, you will see the same light coming from both stars as someone who never moved from point C; Light that left both stars 5 yrs ago. You see both stars as they were 5 yrs ago.
5 points
35. ## The Official JOKES SECTION :)

Three of those images imply too much power in the wrong place. The other is a horse.
5 points
36. ## Gravity

The 'bowling ball on a rubber sheet' is a two dimensional reduction of a 4 dimensional configuration. It has multiple problems, one of which is that you can observe it from an embedding third dimension. Space-time has no embedding dimension; both the bowling ball and you, the observer, would need to be intrinsic to the rubber sheet ( i.e. also two dimensional ). A three dimensional representation would already get rid of some problems, but not all. Picture a three dimensional grid, where x, y, and z axis divide up the space into cubic elements. A mass placed in this space would curve the x, y, and z lines such that the elements are moreskewed, and smaller, as you get closer to the mass. That is 'space' curvature, and one aspect of gravity, but already much harder to visualize than the two dimensional example of the bowling ball/rubber sheet. Actual gravity is four dimensional 'curvature' of space-time, and I can't help you visualize that as it is impossible. Some problems are just not suited to visualization, but understanding even just the basics of the math goes a long way to clarifying things.
5 points
37. ## The world has changed...

The 'economy' is not just a money making mechanism for the wealthy, Phi. It is the means by which most of us feed, clothe, house ourselves and our families; it's how we survive. I have no problem with the economy 'going for a sh*t' as long as it saves lives. But if it 'goes for a sh*t' for too long, people start losing their life for reasons other than the pandemic. That is the balance that has to be struck; dying by starvation is just as bad as dying by Covid-19. I believe that is what Danijel Gorupec meant.
5 points
38. ## Bob Lazar

Element 115 (moscovium) has a half life of about half a second, so is not very practical as a target. https://en.wikipedia.org/wiki/Moscovium (And I doubt that element 116 can be produced by firing protons at the nucleus.) "Immediately decays"? It is true that the half life of livermorium is less than that of mosocvium; but it is not immediate. Livermorium decays via alpha decay. In other words, it emits a helium nucleus (a pair of protons and a pair of neutrons bound together). https://en.wikipedia.org/wiki/Livermorium It does not emit anti-protons. That would violate all sorts of conservation laws. https://en.wikipedia.org/wiki/Conservation_law And anyway, what would be the point? This can only be of interest to people who think that antimatter=magic. What are you going to do with these anti-protons? Presumably combine them with some protons to generate energy. But you can't get any more energy out of that than you put in. So the whole process of accelerating some protons, transmuting 115 to 116, then capturing the anti-protons and then generating some protons for them to interact with, then controlling their interaction and directing the energy ... all takes energy. And must run at less than 100% efficiency. https://en.wikipedia.org/wiki/Laws_of_thermodynamics So you are going to get less energy out than just using shooting the original protons out the back of the rocket. Or using the heat from the rapid decay of the moscovium (you will be left with no useful fuel after a few minutes, anyway). There is nothing to critique here. This is just meaningless word-salad from a bad SF book. No references here because there is no such thing as "Gravity-A waves", "Gravity B waves" or "Gravity Amplifiers". Also, gravitational waves (which do exist) are not directly related to gravity. Gravitational attraction is not a wave phenomenon. Also, gravity is only attractive; there is no practical or theoretical reason to think that somehow causing gravitational waves (if that is what the ignorant author means) to interfere would cause any gravitational effect (either pull or push). Gravitational waves cause stress (stretching and shrinking) in directions orthogonal to their direction of travel. This effect is too small to be significant, unless you are a few miles from two merging back holes. https://en.wikipedia.org/wiki/Gravitational_wave Gravity waves are something completely different. They are a phenomenon in fluid dynamics and have nothing to do with gravity (in the sense implied here; they are caused by gravity, not a cause of gravity). https://en.wikipedia.org/wiki/Gravity_wave It is almost as if the author doesn't know what they are talking about. And are just stringing together a bunch of words they don't understand. See anyone can do it.
5 points
39. ## How can the cosmos be eternal?

A better question is why $10^{-43}$. Would it help to recognize that number is one unit of Planck time with our current observable universe to the volume of 1 Planck length. The temperature being equivalent to Planck temperature. The Planck units are in essence boundary conditions on which our ability to mathematically describe in essence breaks down into Infinities and nonsensical results. You often only hear the space and time axis in essence flipping roles for the GR descriptive but cosmology must also include both macro and quantum effects. So its good to understand how the limits of the macro and quantum theories apply. (String theory also recognizes these limits) One detail as mentioned in this thread is were describing our Observable portion in essence the limits of shared observable causality with our current universe. Time being a measure of rate of change or duration you in essence need a dimension in order to have something to measure or even something that must be able to change. However one must also realize that the t=0 represents the collective worldlines of all particles in our observable portion extrapolated from the closest we can mathematically describe and potentially measure. In the closest to pointlike we can describe. It does not represent any time outside our region of shared causality. In essence $10^{-43}$ is the origin of time for all potential worldlines in our observable universe that are extrapolated to the beginning of our observable universe (as the emitter event).
5 points
40. ## Space anchor idea

Thank you for all your feedback. I’m currently working on some mental health issues and cannot reply on give the answers the time that I would like to in regards to research and time and I struggle to express the concept fully and accurately, more to come but I have to work on my stability at this time kind regards David Wavish
5 points
41. ## Sorry about the downtime -- we're back!

Fake news! It was a perfect renewal! Absolutely perfect. In a world where even my fridge can give me reminders, I still managed to forget. Luckily Capn was able to social engineer his way through my answering service who sent a page out to me stating "CAPN REFSMMAT - RE: WEBSITE". They even listed a hospital he was calling from 😂. I wasn't on call today so when I heard my answering service text me I about lost my mind until I saw who it was.
5 points
42. ## Idea for a rocket engine

I'll clarify for him. For the reaction mass to produce an upward force on the rocket, it has to be accelerated downward relative to the rocket. In order to return that mass to the top of the rocket, any downward velocity the mass has relative to the rocket has to be stopped and reversed. This is an acceleration just as much as the one producing the upwards force on the rocket (acceleration is either change in speed, direction or both). This action will exert a force on the rocket opposite to that caused by accelerating the fuel downward. The end result of this force will be counter any upward movement by the rocket. This ends up with the net movement of the rocket as being zero. There is no way around this. There is no "clever" way to "fool" the rocket into having net movement by recirculating the fuel/reaction mass.
5 points
43. ## Members in the Mod Queue

thethinkertank has been placed in the queue for spamming the forum with an impressive amount of nonsense.
5 points
44. ## Shamima Begum

Brevity and sarcasm. No wonder no-one knows WTF you're talking about half the time.
5 points
45. ## climate change intensified the amount of rainfall in recent hurricanes

Accusations of deliberate, widespread bias and falsification of results, across every major institution (in several different nations) doing climate science and climate modelling really does require evidence. Evidence of which, if this misconduct was really going on, would leave a much clearer trail than a couple of questionable phrases in one email exchange. There is no such evidence, just accusations or it would have come to light a long time ago. Does anyone really think successive governments across the developed world, many with demonstrated hostility to climate science's reports and studies, could not uncover that extent of deliberate bias and collusion? Or that level of incompetence not be noticed within long running non-secret institutions where high standards - with everything on the record - are essential to everything they do? The claims of bias and incompetence are all accusation and no evidence. We have agencies that can pick out guarded exchanges between anonymous terrorist conspirators but they can't catch out hundreds (thousands?) of published working scientists conspiring within and between legitimate government agencies? They haven't exposed this alleged conspiracy of incompetent science and world subjugation because it doesn't exist. Making casual accusations against ordinary people doing their job (better than some people like) is, itself, a serious kind of wrongdoing (slander), besides being very insulting to people who, so far as evidence goes, have been doing their jobs with all the appropriate care and attention and honesty. All that professional effort to work out how our climate system really works, only to be casually accused of being everything from colluding in incompetence to engaging in a global conspiracy! What upsets me almost more than anything else, is that climate scientists have given us an extraordinary gift in the forewarning and foresight they have given. The window of time to transform the way we do energy has been precious beyond price; that we have been squandering it is not the fault of climate scientists failing to communicate. The persistent counter-messaging by opponents and obstructors is indicative of a far more insidious conspiracy of biased incompetence than even their made up version of conspiratorial climate scientists and green-socialist-globalists. In the face of that kind of politicking, and given the seriousness of the climate problem it is climate scientist who do not resort to advocacy that I find questionable. Mistermack - I think you are too gullible and that you have been gulled. I don't expect you to believe anything from me even if you did give it due consideration. Or from Al Gore or from Greenpeace or whoever; however, I do think you should consider taking the Royal Society and National Academy of Sciences, the NOAA, NSIDC, NASA, CSIRO, Hadley CRU and so on, seriously.
5 points
46. ## Why doesn't the electron fall into the nucleus?

Because the electron is not a classical particle (“little ball of mass and charge”), but a quantum object. As a first approximation, you can picture an electron as a 3D standing wave around the nucleus - you can only get standing waves of a given wavelength in specific places, which is why orbitals come in discrete levels. Crucially, there is a lowest energy level, which corresponds to the minimum distance an electron can be with respect to the nucleus (let’s assume here there is only one electron) - and that lowest energy level is not zero. Therefore the electron cannot fall all the way to the nucleus, it can only fall into its lowest energy level, which corresponds to an orbital that is still some distance outside the nucleus. This is a direct consequence of the laws of quantum mechanics, and coincidentally one of the questions that motivated the development of quantum mechanics in the first place.
5 points

5 points

5 points
49. ## Time Does Not Exist

Ironically, under the title “time does not exist” it says “posted three hours ago”.
5 points
50. ## Banned/Suspended Users

scherado has been banned for multiple instances of rule-breaking in his quest to become the Troll King. We apologize that his interruption in the normal rational discourse was all noise and no signal whatsoever. Roger Dynamic Motion has been banned, NOT for incessant hijacking and almost daily irrationality, but for failing to respond to requests for clarity, EVER. Discussion requires that we express our ideas so others can understand. We wish him good luck with his ideas, whatever they were supposed to be.
5 points
×


text:
# HLSL mipmapping not working

I want to implement a mipmap filter in my 3D game, so that textures which are located far away are using a lower resolution than the original. For the shader I'm using hlsl version 4_0_level_9_1 or 4_0 depends on which one I will get this running. I have tried this:

texture Texture;
sampler diffuseSampler = sampler_state
{
Texture = (Texture);
MAGFILTER = ANISOTROPIC;
MINFILTER = ANISOTROPIC;
MIPFILTER = ANISOTROPIC;
};
[...]
{
return tex2Dlod(diffuseSampler, float4(input.TexCoord, 0.0, 0.0));
}

in vs_4_0 it still uses the full-res texture. And in vs_4_0_level_9_1 it won't even compile: "texlod not supported on this target"

I could manually generate the downscaled textures, but there must be a way to only input one texture and let hlsl do the rest.

In short: How to apply the mipmap filter in hlsl?

• tex2dlod is for accessing a specific level of the mipmap chain. You just use standard tex2d with the correct texture state objects set and you'll get mipmap filtering. As noted below, the sampler state you define in HLSL is not relevant to the vs profiles only fx. – Chuck Walbourn Oct 31 '16 at 7:07

You don't.

Unfortunately some online resources don't make this explicit, but the code you've given is actually not HLSL; instead it's part of the old (and deprecated) effects framework. What actually happens if you use the effects framework (which is nothing more than a wrapper around the D3D API) is that a shader object and a state object will be created and set for the current draw call.

In the absence of the effects framework (which I assume because you actually have to intentionally set out to use it these days) you need to create your own sampler state object and set it.

• See this post for some more background here. – Chuck Walbourn Oct 31 '16 at 7:06

That there is DX9 HLSL

You want something like this:

Texture2D Texture : register(t0);;
sampler diffuseSampler : register(s0);

{
float4 Position : SV_Position;
float2 TexCoord : TEXCOORD0;

};
// outputs a full screen triangle with screen-space coordinates
// input: three empty vertices
{
result.TexCoord = float2((vertexID << 1) & 2, vertexID & 2);
result.Position  = float4(result.TexCoord  * float2(2.0f, -2.0f) + float2(-1.0f, 1.0f), 0.0f, 1.0f);
return result;
}

{
// float3(UV,Mip)
float4 color = Texture.SampleLevel(diffuseSampler, float3(input.TexCoord, 0.0f));

return color;
}

then like Le Comte du Merde-fou said, set all state by hand.

like this:

  _Context.XXXXShader.SetSampler(0, yourSampler)

format: plain


text:
# How do you write the mathematical expression for "n more than 8"?

Dec 19, 2015

$8 + n$

#### Explanation:

$n$ more than $8$ means to add $n$ to $8$.


text:
Original post on Zemanta’s blog, reproduced here for posterity:

A covisitation graph of all websites with at least 100 unique visitors over a 3-day span and node size logarithmically proportional to number of visitors.

It’s every advertiser’s worst nightmare: advertising on a seemingly legitimate site only to realize that the traffic and/or clicks from that site are not the coveted genuine human interest in the ad. Instead they find fake clicks, unintentional traffic or just plain bots. In a never-ending quest for more ad revenue, website publishers scramble for ways to impersonate their more successful counterparts. However, not all approaches are as respectable as improving readability and SEO.

One pernicious tactic is sharing traffic between two or more sites. Of course, almost all websites share some of their visitors, but this percentage is small. Moreover, as the site accumulates more visitors, the probability of a large overlap occurring by chance becomes infinitesimal. This tactic is commonly used by botnets, so that the sites employing this traffic can also be unwitting targets of such schemes. For example, a botnet can, among the suspicious sites, add several well-known and respected websites, so that the apparent credibility of the malicious sites is artificially boosted.

The question is thus, can we identify these traffic-sharing websites? And if so, then how? The answer to the first question is yes, and to the second is this blog post.

Our problem lends itself nicely to a network approach called a covisitation graph [1]. We will construct a graph, such that the sites that share traffic will be tightly connected. Especially if visitors are shared between several sites, as is usually the case. We can represent all of the websites as vertices (nodes) in a graph. To encode the overlap between a pair or sites, we will use directed edges weighted between 0 and 1. This number will be the proportion of visitors from the source of the edge that were also seen on the target edge. Let A have 200 visitors, B have 1000 visitors, and the shared traffic be 100 visitors. The edge from A to B is the overlap divided by A’s visitors, or 100/200 or 0.5. Similarly, from B to A we have 100/1000 or 0.1. Of course, a network is no network if it’s completely connected. We must set an appropriate threshold to remove edges but keep the ones that are important. A simple threshold of 0.5 proved most useful in our case.

To get the full network, we must repeat this calculation for all pairs of edges. This network is useful for more than just computation, as a quick visual inspection reveals many interesting things. Tight clusters of websites that are only loosely connected to the core of the graph are precisely the aberrations we would expect when several sites band together. In graph theory, they are called cliques, and have been well researched. A well-known measure of “cliqueness” is the clustering coefficient: $C = \frac{\text{\# of actual triangles}}{\text{\# of possible triangles}}.$ It is a number between 0 and 1, with 0 meaning that none of the node’s neighbors are connected with each other, and 1 meaning the opposite (i.e. the node and its neighbors form a clique). We can combine this number with the probability of such a cluster occurring randomly to get a sensible measure of suspicion for each site. Thus, a small clique of 2-3 sites is somewhat likely to occur, but a clique of 20 nodes warrants a closer discerning look. The circled areas in the graph at the beginning indicate exactly these occurrences. We have several groups of websites with dissimilar content where they all share each other’s traffic. One of the suspicious cliques is completely detached from the rest of the graph.

On one hand, there are going to be a lot of naturally occurring edges in the graph. Overlaps as high as 50% are not uncommon between websites of similar content. On the other hand, sites should have very few outgoing edges, especially if they are popular and have many visitors. Popular sites may have many incoming edges, but as long the sources of these edges are not connected with each other it is not going to be predicted as fraud by our methods.

Thus, out of the vast interconnected graph that is the world wide web, we can, with precision, pick out the few bad apples that are trying to rake in revenue unfairly and at the detriment of everyone else. We mark all such sites as suspicious, and they are given one final personal look before the are added to a jailing list. This list is used to temporarily blacklist visitors that were seen multiple times on several of these malicious sites. Consequently, no bids for advertisements are placed and thus no ads are shown on our part to these users, since there is no return on investment for the cost paid by the clients. The whole approach outlined in this blog post is just one of the tools in Zemanta’s arsenal for combating malicious traffic, where the focus lies in bringing quality traffic for the best possible price.

The analysis was part of my 3-month internship at Zemanta, where I worked on how to detect this type of fraud, as well as implementing our approach at scale in the existing infrastructure. The implementation was a breeze with such awesome support from the whole team. It was a great learning experience and an invaluable opportunity to work on a codebase that scales to many thousands of requests in a second. Personally, I believe that this bridging of the gap between research and industry benefits both parties immensely, and I hope to do more such collaborations in the future.

[1] Stitelman, Ori, et al. Using co-visitation networks for detecting large scale online display advertising exchange fraud. Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 2013


text:
Art of Surface Interpolation-Chapter 5:Solving special tasks In the next sections there are examples of interpolation problems,

Chia sẻ: Thanh Cong | Ngày: | Loại File: PDF | Số trang:17

0
57
lượt xem
4

Art of Surface Interpolation-Chapter 5:Solving special tasks In the next sections there are examples of interpolation problems,

Mô tả tài liệu

Tham khảo tài liệu 'art of surface interpolation-chapter 5:solving special tasks in the next sections there are examples of interpolation problems,', công nghệ thông tin, kỹ thuật lập trình phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả

Chủ đề:

Bình luận(0)

Lưu

Nội dung Text: Art of Surface Interpolation-Chapter 5:Solving special tasks In the next sections there are examples of interpolation problems,

1. Chapter 5 Solving special tasks In the next sections there are examples of interpolation problems, which need special pro- cedures to be solved. Most of the procedures are directly coded in the graphical user inter- face SurGe but some procedures are solved using stand-alone utilities. 5.1 Zero-based maps Certain types of maps (for example maps of pollutant concentration in some area, maps of precipitation, maps of rock porosity or permeability and so on) have a common feature – their z-values cannot be negative. Let us name these maps as zero-based maps. If a smooth interpolation is used for such types of maps, there is a real “danger” that the res- ulting function will be negative in some regions. As discussed in paragraph 2.4.1 Smooth- ness of interpolation and oscillations, undesired oscillations and improper extremes cannot be avoided in such cases. For this reason, the graphical user interface SurGe offers a possib- ility (using the menu item Substitute below) to substitute all z-values of the surface, which are less than a specified constant (for example zero) by this constant. Similarly, the menu item Substitute above enables to “cut off” values of the surface exceeding the specified constant. As an example of a zero-based map we will use the data set CONC.DTa containing sulphate concentration measured in a soil layer. An interesting comparison of results obtained using different interpolation methods provides an evaluation of how maximal and minimal z-val- ues of points XYZ were exceeded by the generated surface. As in all preceding examples, the Kriging method was used with the linear model and zero nugget effect, the Radial basis function method with the multiquadric basis functions and zero smoothing parameter and the Minimum curvature method were used with a tension of 0,1. These are summarized in the following table. interpolation method exceeding the exceeding the minimal value maximal value Kriging -18,8455 -4,4299 Radial basis functions -18,8455 -4,4299 Minimum curvature -46,4989 +0,7771 ABOS, q=0,5 -24,7731 +1,9323 ABOS, q=3,0 -16,6539 +1,8871 The difference between the surfaces created using the Kriging and Radial basis function methods is less than 1,0E-7 – that is why the results in the table are the same for these meth- ods. The next figure contains maps obtained using the ABOS and Kriging method. In both cases negative values were substituted with zero values. According to the opinion of many SurGe users, “pits” and “circular” contours in the surface generated by the Kriging method are un- desirable. 64
2. Fig. 5.1: Map of sulphate concentration created using the ABOS and Kriging method. 5.2 Extrapolation outside the XYZ points domain The extrapolation properties of the ABOS method was examined in paragraph 2.4.3 Con- servation of an extrapolation trend. Let us note that we only examined the domain determ- ined by points XYZ. In the next example (see figure 5.2a), aerodynamic resistance data measured at a small part of a racing car body was interpreted to obtain results outside the domain determined by points XYZ. Fig. 5.2a: Aerodynamic resistance data measured at a small part of a racing car body. As the picture indicates, the desired domain of the interpolation function set by the bound- ary (red rectangle) exceeds the domain defined by the points XYZ. The boundary was set so that the aerodynamic resistance could be estimated aside the data on the left and bottom. 65
3. The interpreter tested several interpolation methods available in the Surfer software but without satisfactory result. As explained in paragraph 4.2.3.10 Interpolation with a trend surface, SurGe implements a special procedure enabling to conserve the extrapolation trend. This procedure was imple- mented to the examined data with the result represented in figure 5.2.b. For comparison, figures 5.2.c and 5.2.d contains results from the Kriging and Minimum curvature methods, which were not accepted as satisfactory. Fig. 5.2.b: Aerodynamic resistance data interpolated by SurGe. Fig. 5.2.c: Aerodynamic resistance data interpolated by the Kriging method. 66
4. Fig. 5.2.d: Aerodynamic resistance data interpolated by the Minimum curvature method. 5.3 Seismic measurement The processing of seismic data is one of the most significant tasks for geologists if they have to create a geological map of some underground rock structure. The typical results of seismic measurement are times at which reflected sound waves return from a certain bound- ary between different types of rock. These times are, of course, measured from some datum level and they are usually recorded using a dense mesh covering the area of interest with a typical number of nodes between 10000 and 100000. Because the homogeneity of covering rocks cannot be assumed and the speed of sound waves in covering rocks is unknown or known only approximately, the measurement must be supported by precise depth values usually measured at exploration wells. In general, the interpreter has to work with two sets of data – the first one is the dense mesh of reflection times and the second one is the measurement of rock structure depth at wells. Let us note that the number of wells is usually small in comparison to the number of points at which the reflection time is measured. To demonstrate the interpretation of seismic measurement we will use the data set SEIS- M1.DTc containing reflection times – the corresponding grid is shown in the next figure. Fig. 5.3.a: Grid of reflection times created from the SEISM1.DTc data set. 67
5. The file SEISM1.DTc contains reflection times in the range from 1736 to 1875 seconds at 25853 points. It is obvious that the lower the value of reflection time, the higher the position of the rock structure boundary. The depth of the rock structure was also measured at 14 wells and the results were stored in the file containing the second data set SEISM1.DTa – see the next list of the file content. 1225.976 2339.511 -2246 W-01 837.871 2270.595 -2250 W-02 428.004 2118.255 -2271 W-03 859.634 1878.863 -2272 W-04 181.357 1519.776 -2292 W-05 1940.525 2187.171 -2277 W-06 2738.498 2292.358 -2255 W-07 2981.517 2375.783 -2238 W-08 3344.232 935.805 -2338 W-09 2121.882 812.481 -2317 W-10 493.292 500.547 -2309 W-11 1519.776 1733.777 -2267 W-12 3663.421 2143.645 -2264 W-13 2999.652 2172.662 -2252 W-14 As follows from the list, the range of depths is -2338 to -2238 meters. As a rule, the depth of a geological structure has a negative value measured from some datum plane (for ex- ample sea-level). The standard procedure of seismic data processing is the following: 1. The map of reflection times is created. 2. For all wells the sound speed is calculated from known structure depth and reflec- tion time at the well. 3. The velocities known at well positions are used for the creation of the so-called ve- locity map. 4. The velocity map is multiplied by the map of reflection times and thus the map of depths is obtained. The SURGEF offers another solution: to create a depth map directly from the structure depths at wells using the reflection time grid as an external grid. This means that the grid containing the map of reflection times SEISM1f.GRc is copied (renamed) into the file SEISM1f.GRa and this grid is read at the beginning of the interpolation process. It may seem to be strange especially if we realize that the reflection times are positive values while the structure depths are negative. Let us have a closer look at the procedures performed by SURGEF. Firstly, SURGEF is run for the data set SEISM1.DTa and it is instructed to read the external grid SEISM1f.GRa (which is a copy of SEISM1f.GRc and represents the map of reflection times) by answering Y to the prompt: READ FILE .GRD? (Y/N) [N] Y Then SURGEF changes this grid using the linear transformation a⋅P i , j b  P i , j , where n the constants a and b minimize the term ∑ a⋅f  X i , Y i b−DZ i 2 , as described in sec- i=1 tion 2.2.8 Iteration cycle. In this case the constant a was computed as the negative number -1.160139 and together with b (-217.38) changed the grid so that the sum of squared differences between the new 68
6. surface and structure depths at wells is minimal. As expected there were some differences between the new surface and the structural depths at wells because of heterogeneity of cov- ering rocks; however these differences were used in the next iteration cycle (cycles) as in the normal interpolation process. As a result, the new surface passes through negative z-coordinates of structural depths while conserving the morphology corresponding to the reflection times. Fig. 5.3.b: Surface created directly from the seismic reflection times. 5.4 Wedging out of a layer Construction of layer geometry is one of the basic tasks in reservoir engineering. The boundaries between individual layers are constructed as surfaces passing through structural depths (z-coordinates) measured in wells. As explained in section 5.3 Seismic measure- ment, layer construction may be combined with seismic measurement, if it is available. If there is a small layer thickness indicated in some wells, no algorithm for smooth interpol- ation can ensure that the bottom layer boundary will not exceed the top layer boundary. Fig- ures 5.4a and 5.4b illustrates such a situation – in figure 5.4a there is a top layer boundary (contained in the file GRES.DTa) and bottom layer boundary (contained in the file GRES.DTb) of a gas reservoir structure including the position of the cross-section A-A’, where the bottom layer boundary exceeds the top one (see figure 5.4b). Such a phenomenon suggests that a so-called wedging out of layer (which is common in geology) should be in- terpreted. 69
7. Fig. 5.4a: Maps of the top and bottom layer boundary. Fig. 5.4b: Cross-section A-A’ through the top and bottom layer boundary. This problem can be effectively solved in the SurGe graphical interface using mathematical operations offered in the dialog Math calculation with grids (see 4.2.3.8 Mathematical calculations with grids), where selected binary mathematical operation is performed for all z-values at nodes of grids representing the two surfaces. There are two mathematical operations represented by characters $and %, which can be utilized for solving the wedging out of layer problem. In the case of the first operation ($) the resulting value is the z-value of the first surface, but if the z-value of the second surface is greater, the resulting value is the average. In the case of the second operation (%) the res- ulting value is the z-value of the second surface, but if the z-value of the second surface is greater than the z-value of the first surface, the resulting value is the average. Both mentioned operations were applied for the presented surfaces and the resulting new surfaces were stored with new suffixes 1 and 2. Figure 5.4c contains the cross-section A-A’ through the new surfaces indicating that the wedging out of layer problem was properly solved. 70
8. Fig. 5.4c: Cross-section A-A’ through the top and bottom layer boundary after solving the wedging out of layer problem. 5.5 Maps of thickness and volume calculations To demonstrate this feature an example concerning the estimate of new snow volume in an avalanche field after an avalanche event is presented. Two data sets were available for solv- ing this problem – AVALAN.DT0 containing the measurement of snow surface before the avalanche event and AVALAN.DT1 containing the measurement of snow surface after the avalanche event. In figure 5.5a there are two maps of snow surfaces created from the above-mentioned files corresponding to the situation before and after the avalanche event; the white line is an as- sumed boundary of the avalanche field. Fig. 5.5a: Snow surface before (on the left) and after (on the right) the avalanche event. 71
9. There are no visible differences between both surfaces, but as soon as the first surface is subtracted from the second (using the menu item Interpolation / Math calculation with grids), the map of the new snow thickness is obtained (see figure 5.5b). Fig. 5.5b: Thickness of the new snow layer. It is obvious from figure 5.5b that snow also increased outside the assumed boundary of the avalanche field – it was probably caused by the additional snow precipitation, creation of snow drifts and so on. To calculate the volume of new snow, the VOLUME utility (see 4.4 Calculation of volumes) can be used: Fig. 5.5c: Calculation of new snow volume using the VOLUME utility. 72
10. From figure 5.5c the following results are obtained: The volume of the new snow layer in the avalanche field is 484424 m3, the horizontal area of the avalanche field determined by the boundary is 293144 m2 and the maximal thickness of the new snow layer is 3.73 m. 5.6 Digital model of terrain The digital model of terrain is a common term for computer processing of geodetic meas- urement. If the input data represents measurements from some terrain, it is usually suitable to use only linear tensioning with a small number for smoothing which is close to the Triangula- tion with linear interpolation method – compare digital models of a stone quarry (see [S8]) in figures 5.6a and 5.6b. As a rule, characteristic points of terrain are measured – this means that the person perform- ing such a measurement surveys only points where the slope of terrain changes (tops, edges, valleys and so on). For interpretation of such data, the triangulation with linear interpolation method is usually used, so the ABOS method is applicable as well. Fig. 5.6a: Digital model of the stone quarry created using the Triangulation with linear in- terpolation method. As pointed out in paragraph 1.2.1 Triangulation with linear interpolation, the domain of the triangulation method is restricted to the convex envelope of the points XYZ. To restrict the domain of the function constructed using the ABOS method by the same way, a bound- ary as a convex envelope was created (see 4.2.6.2 Boundaries) and nodes outside the boundary were set as undefined using the SurGe menu item Interpolation / Blank grid outside boundary. 73
11. Fig. 5.6b: Digital model of the stone quarry created using the ABOS method. 5.7 Digital Elevation Model Digital Elevation Model (DEM) is a standard (see [S9]) for the ASCII format of files con- taining digital geological and geographical data produced by the United States Geological Survey (USGS). It is supported by most GIS (geographic information system) applications such as Global Mapper, ARCGIS, GRASS, Geomatics, MapInfo, Intergraph, ERDAS and so on. The data is stored as arrays of regularly spaced elevation values referenced horizontally either to a Universal Transverse Mercator (UTM) projection or to a geographic coordinate system. The grid cells are spaced at regular intervals along south to north profiles that are ordered from west to east. In fact the DEM file is a grid file, because the elevation data (z-coordinates) are specified at nodes of a square grid (where the size of a grid square is 30 meters), but the format of this file is different from the format of a SurGe grid file. To display DEM files using SurGe, there is a stand-alone console utility DEMGRD (see 4.3.2 Conversion command line utilities) included in the SurGe software enabling to con- vert DEM files into ASCII Surfer grid files. Moreover, the DEMGRD utility creates the ba- sic data file, because SurGe cannot read a grid file without the basic data file. Then the user of SurGe has two possibilities – to import the grid file using the menu item File / Read grid from ASCII file or to create a new grid from the basic data file. As an example of a DEM file displayed by the SurGe software there is an elevation model of mount Shasta in Northern California. 74
12. Fig. 5.7: Digital elevation model of mount Shasta in Northern California. 5.8 Construction of model grid One of the most important applications of SurGe in my profession are projects of geological models of underground gas storages (UGS) in the Czech Republic. The geological models were implemented for these storages: • Dolni Dunajovice • Lobodice • Stramberk • 9.-11. sarmatian layer in Tvrdonice SurGe was used for the map creation of both geological surfaces of layers and maps of rock properties such as porosity, permeability or net to gross ratio. Geological models had to be transferred into a 3D grid for a mathematical model in EC- LIPSE (3D three phase model of fluid flow in porous media, see [S10]) which enables to work with so-called corner point geometry (CPG) grids. A corner point geometry grid is formed by general hexahedrons and makes it possible to adapt the grid to the shape of a reservoir structure including curved boundaries, tectonic faults and wedging out of layers. An important concept in the construction of grid data for corner point geometry is the idea of “coordinate lines”. Coordinate lines are straight lines upon which all the cell corners must lie. Thus if there are NX cells in the x-direction and NY cells in the y-direction, there will be (NX+1)*(NY+1) coordinate lines. Models of the above mentioned storages were created using vertical coordinate lines, but in more general grids they can be off-vertical to coincide with sloping faults (see the next figure). Fig. 5.8a: Construction of corner point geometry grids. 75
13. The ECLIPSE digital representation of corner point geometry grid consists of data follow- ing two keywords COORD and ZCORN, which have to be included in the input data file. The keyword COORD introduces the data describing coordinate lines and the keyword ZCORN introduces the data describing z-coordinates of cell corners. To construct a model grid for ECLIPSE, three utilities have been developed: • EGRID is a simple graphical utility for interactive creation of a model grid horizontal projection consisting of general quadrangles. • CPG is a console utility generating data for keywords COORD and ZCORN. As an in- put, the CPG utility uses the horizontal projection of the model grid created by the EGRID utility and surfaces of layers generated by SurGe. The surfaces of layers must be specified (using the suffix convention) in order of increasing depth beginning from the most top layer, and the top surface of each layer must be specified as the first. There may be interspaces between layers, which are considered to be impermeable and which are used for modelling of impermeable bands. • PROP is a console utility generating data for keywords, which describe rock proper- ties, for example PORO (porosity), PERMX (permeability in the x direction), NTG (net to gross ratio), SGAS (gas saturation) and so on. As an input, the PROP utility uses the horizontal projection of the model grid created by the EGRID utility and maps of layer properties created by SurGe. Layers must be specified (using the suffix con- vention) in order of increasing depth beginning from the most top layer. An example of a complicated ECLIPSE model grid with faults, which was created using named utilities, is in the next two figures. The model consists of ten layers having very het- erogeneous properties – porosity and permeability. As the geological model shows, there are “channels” with high porosity and permeability in the bottom layers where preferential fluid flow can be expected. Fig. 5.8b: Porosity of a geological model. 76
14. Fig. 5.8c: Permeability of a geological model. The previous two figures are hard-copies of screens displayed by GRIDV, an OpenGL ap- plication written as a post-processor for viewing and checking the ECLIPSE model results. 77
15. Conclusion The most important result of this work is the design and especially the computer imple- mentation of the new interpolation / approximation method ABOS for digital generation of surface passing through Z coordinates of points irregularly distributed in 3D Euclidean space. In contrast to sophisticated interpolation methods such as Radial basis functions, Kri- ging or Minimum curvature, the ABOS method does not fulfil any mathematical formula- tion such as linear combination of basis functions, statistical formulation of the best linear unbiased estimate or requirement of minimal curvature of the resulting surface. Instead, it provides tools for modelling the resulting surface based on numerical tensioning and smoothing enabling to create a broad range of surface shapes and to accommodate the res- ulting surface according to the user’s conception. Moreover, the ABOS method makes it possible to solve large problems without the necessity to search points in a specified sur- rounding of the grid nodes and without the necessity to solve a system of equations. As for computational speed, ABOS is up to twenty times faster than methods based on solving equation systems, for example the Kriging method. The computer implementation SURGEF.EXE and namely the implementation of user graphical interface SurGe extends the applicability of the ABOS method and enables to: - create and manage projects containing many maps - easily change interpolation parameters and to experiment with surface shapes - filter input data - transform coordinates of map objects (points, faults, polylines, boundaries) - digitise map objects using mouse and keyboard - model discontinuity in the generated surface - perform mathematical calculations with surfaces - blank the grid nodes outside the boundary - double the grid using cubic polynomial interpolation between grid nodes - output z coordinates of the generated surface at any set of points from domain - calculate isolines and display them - display a raster colour map and 3D view of the resulting surface - display a shadowed colour map and shadowed 3D view - define and display cross-sections through several surfaces - compute and display gradient lines - solve special tasks using special procedures such as - wedging out of layers - preserving extrapolation trend in areas without data - direct conversion of seismic reflection times into the structural depth of layer boundary - creating layer thickness maps and volume calculations One of the most important applications of SurGe in my profession are projects of geological models of underground gas storages (UGS) in the Czech Republic. The geological models were implemented for storages Dolni Dunajovice, Lobodice, Stramberk and 9th – 11th sarmatian layer in Tvrdonice, where in all cases the ABOS method was applied for the map creation of both geological surfaces of layers and rock properties such as porosity, permeab- ility and net to gross ratio. Furthermore, the method was used for model creation of aquifer structures while processing remediation projects in localities CHZ Sokolov, Stráž pod Ralskem and Licoměřice. 78
16. After more than three-years of publication through the medium of Internet WWW pages (see [13]) and through the medium of more than 300 software distributors (see List of selec- ted SurGe distributors in References), the ABOS method and SurGe software has proven wide applicability. Now thousands of people worldwide use the software not only in tradi- tional fields as reservoir engineering, geology and geophysics, but also in hydrology, geodesy, archeology, bathymetry, gravimetry, genetics, neurology, electronics, aerodynam- ics or nuclear physics; some people use SURGEF.EXE as an interpolation engine in their own mapping software. References Software and data source [S1] Generic Mapping Tools, http://gmt.soest.hawaii.edu/ [S2] Golden Software, http://www.goldensoftware.com/products/surfer/surfer.shtml [S3] K. L. Clarkson, http://cm.bell-labs.com/cm/cs/who/clarkson/2dch.c [S4] LandSerf, http://www.landserf.org/ [S5] Global Mapper, http://www.globalmapper.com/ [S6] ESRI Shapefile, http://www.esri.com/library/whitepapers/pdfs/shapefile.pdf [S7] Inno Setup, http://www.jrsoftware.org/ [S8] Atlas DTM, http://www.atlasltd.cz/ [S9] USGS, http://rockyweb.cr.usgs.gov/nmpstds/demstds.html [S10] Schlumberger, http://www.slb.com/content/services/software/reseng/index.asp [S11] Mathworld, http://mathworld.wolfram.com/VoronoiDiagram.html List of selected SurGe software distributors http://www.simtel.net/product.php[id]77464[sekid]0[SiteID]simtel.net http://www.downloadplanet.net/info37162.htm http://www.fileboost.net/directory/education/science/surge/029209/review.html http://www.softpicks.net/software/SurGe-8048.htm http://www.softpedia.com/get/Science-CAD/SurGe.shtml http://www.yankeedownload.com/software/surge-ilicp.html http://www.geologicresources.com/software.html http://www.forestpal.com/Toolbox_mappers.html#surge http://www.vterrain.org/Elevation/contour.html SurGe WEB pages http://surgeweb.sweb.cz/surgemain.htm http://surge.czweb.org/surgemain.htm 79
17. Bibliography [1] W.H.F. Smith, P.Wessel, Gridding with continuous curvature splines in tension, Geo- physics, Vol.55, No.3, p.293-305, 1990 [2] D.G. Krige, A statistical approach to some basic mine valuation problems on the Wit- watersrand, Journal of the Chemical, Metallurgical, and Mining Society of South Africa, vol. 52, pp. 119-139, Dec. 1951 [3] C. V. Deutsch, A. G. Journel, GSLIB. Geostatistical Software Library and User’s Guide. Oxford University Press, New York, NY, 1998 [4] T. H. Mayer, The Discontinuous Nature of Kriging Interpolation for Digital Terrain Model, Cartography and Geographic Information Science, Volume 31, Number 4, 2004, pp. 209-216(8) [5] C. de Boor, A practical guide to splines, Springer-Verlag., 1978 [6] Ch. Yang, S. Kao, F. Lee, P. Hung, Twelve Different Interpolation methods: A Case Study of Surfer 8.0, Geo-Imagery Bridging Continents, XXth ISPRS Congress, 12-23 July 2004 Istanbul, 2006 [7] N. Sukumar, A Note on Natural Neighbor Interpolation and the Natural Element Meth- od (NEM), Theoretical and Applied Mechanics, Northwestern University, 1997 [8] H. Mitasova, L. Mitas, Interpolation by Regularized Spline with Tension: I. Theory and Implementation, Mathematical Geology, 25, 641-655, 1993 [9] I.C. Briggs, Machine Contouring using minimum curvature, Geophysics, 39, 39-48, 1974 [10] M. Dressler, Computation and presentation of surface in geology, Zemní plyn a nafta, 40, 4, 317-323, 1996 [11] J. Hora, M. Dressler, V. Wasserbauer, Model Diamo for ground-water flow and trans- port of chemicals. Proceedings from Environmental Statistics and Earth Science, Brno, 1996. [12] V. Onderka, M. Dressler, STRAZ BLOCK GROUNDWATER POLLUTION - PHASE I, GeoGas Brno, 1995. [13] M.Dressler, Approximation / interpolation of surfaces based on numerical tensioning and smoothing, http://www.sweb.cz/M.Dressler/ABOS.htm 80


text:
# How to Define my own Data Set with the Installer¶

The Akeneo PIM allows to prepare a data set to use during the installation.

You can configure the data set in the app/config/parameters.yml file:

 1 2 3 # /app/config/parameters.yml parameters: installer_data: PimInstallerBundle:icecat_demo_dev # use PimInstallerBundle:minimal for minimal data set

The following steps allow you to easily define your own basic entities when you install the PIM.

## Create a Bundle¶

Create a new bundle:

  1 2 3 4 5 6 7 8 9 10 # /src/Acme/Bundle/MyBundle/AcmeMyBundle.php

Register it into AppKernel.php:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 # /app/AppKernel.php

Create a directory Resources/fixtures/mydataset in your bundle.

Copy the *.yml and *.csv files from Installer bundle into the mydataset directory of your bundle.

Then edit the files, for example, to declare your own channels:

 1 2 3 4 5 6 7 8 9 # /src/Acme/Bundle/MyBundle/Resources/fixtures/mydataset/channels.yml channels: default: label: Default locales: - en_US currencies: - USD tree: default

Tip

Take a look at Pim/Bundle/InstallerBundle/Resources/fixtures/minimal to see what is the expected format and which fixtures are absolutely needed. All fixtures can be created in CSV or YAML.

## Install the DB¶

Update the app/config/parameters.yml to use your data set:

 1 2 3 # /app/config/parameters.yml parameters: installer_data: 'AcmeMyBundle:mydataset'

You can now (re)install your database by running:

> php app/console pim:install --force --env=dev --task=db

Fixture files can be loaded individually by using the pim:installer:load-fixtures command :
> php app/console pim:installer:load-fixtures src/Acme/Bundle/MyBundle/Resources/fixtures/mydataset/*


text:
## Research Collection Lee Kong Chian School Of Business

#### Title

Rate of Return under Re-Capitalisation: A Note

Journal Article

10-1988

#### Abstract

Conclusion The measure in (6) is suggested as the most appropriate measure when n is over a month or so for it explicitly takes into account time value. For small n (e.g. daily returns), we can assume k=0, n=1, and therefore, the time value is not an issue and we can simplify (6) as: $$1 + R_{t + 1} = {{[P_{t + 1} \{ 1 + ({1 \mathord{\left/ {\vphantom {1 N}} \right. \kern-\nulldelimiterspace} N})\} + D_{t + 1} ]} \mathord{\left/ {\vphantom {{[P_{t + 1} \{ 1 + ({1 \mathord{\left/ {\vphantom {1 N}} \right. \kern-\nulldelimiterspace} N})\} + D_{t + 1} ]} {[P_t ({I \mathord{\left/ {\vphantom {I N}} \right. \kern-\nulldelimiterspace} N})]}}} \right. \kern-\nulldelimiterspace} {[P_t ({I \mathord{\left/ {\vphantom {I N}} \right. \kern-\nulldelimiterspace} N})]}}$$ .

Finance

#### Publication

Asia Pacific Journal of Management

6

1

141

147

0217-4561

#### Identifier

10.1007/bf01732255

Springer Verlag

COinS


text:
Isomorphic simple groups - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T02:41:49Z http://mathoverflow.net/feeds/question/118417 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/118417/isomorphic-simple-groups Isomorphic simple groups Yu 2013-01-09T03:58:53Z 2013-01-10T18:29:54Z
It is known that \$SL_{4}(\mathbb{F}_2)\cong A_8\$. Obviously, this is equivalent to the existence of a subgroup of \$Sl_4(\mathbb{F}_2)\$ of index \$8\$. How to find such a subgroup?
 http://mathoverflow.net/questions/118417/isomorphic-simple-groups/118559#118559 Answer by Quang Hoang for Isomorphic simple groups Quang Hoang 2013-01-10T18:14:53Z 2013-01-10T18:29:54Z
An elementary answer in terms of symmetric groups.

Let \$V\cong\mathbb F^3\$ be a \$3\$-dim \$\mathbb F_2\$ space. Consider \$V\$ as a subgroup of \$S(V)\$. It is well-known that \$N_{S(V)}(V) \cong V\rtimes GL(4)\$. Then the isomorphism \$A_8\cong GL_4\$ because they are both even subgroups of \$S_8=S(V)\$.

Now the subgroup of index \$8\$ is the group \$A_7\$ which fixes the origin of \$V\$.

Edit: Apparently, I made a silly mistake along the way that \$N_{S(V)}(V) \cong V\rtimes GL(4)\$ (Should be \$GL(3)\$). Yet somehow I think it could be fixed and that the argument is somewhat equivalent to that of Elkies.


text:
# Distance to an ellipse surface

1. Jun 30, 2011

### Trenthan

Hey guys, this isn't a course work question more independent study to improve something i'm working on for my course, to increase computation time.

It may be in the wrong thread but the others state to post independent study in the homework section so its here. Placed it in maths since its seems most relevant but please feel free to move this thread if its in the wrong place!

Bit of background first
-I'm currently producing a path planning algorithm using potential flows to guide a non-holonomic robot through a field of obstacles.
-To model multiple obstacles we use a weighting function that determines which object is dodged first, and is dependent on the DISTANCE to the SURFACE of THAT OBSTACLE from our robots position in the field.

Now everything works fine, and i can produce smooth trajectories around multiple obstacles in a large field.

Issue is calculating the distance to the surface of an elliptical obstacle and plates (lets ignore plates for now).

This is currently done by generating the coordinates of the ellipse surface, and by searching for the smallest distance between the surface coordinate and robot position. Right away you can see this is inefficient and slow!

It works in real time since its generated step by step while the robot moves, but for simulation purposes its too slow. If it takes the robot in reality 20seconds to trace the path, its takes 20 seconds to generate the simulation for a fake environment of the computer. (if its 2 minutes, than its 2 minutes as well). This makes it difficult when coding and playing around with idea's since i loose a lot of time sitting around waiting to see the result. This section of the code takes up 95% of the computation time so if it can be reduced, it would be a big plus!!

I'm curious to know if there is a neat mathematical equation, or some geometric techniques that can easily allow me to find the shortest distance to an ellipse from a point in space**. (If it could be done with the ellipse at any orientation (45, 217 degrees etc) it would be better, but i can easily address this with other algorithms currently implemented).

Im happy to be pointed in the correct direction, i've hunted IEEE, gone through my old course work and nothing on this type of stuff. Searched the web without much luck; more alot of junk that isn't too useful.

Cheers Trent

2. Jun 30, 2011

### micromass

Hi Trenthan!

Let's get you on the way. The general equation for an ellipse is

$$\left\{\begin{array}{c} x=x_c+a\cos(t)\cos(\varphi)-b\sin(t)\sin(\varphi)\\ y=y_c+a\cos(t)\sin(\varphi)+b\sin(t)\cos(\varphi)\\ \end{array}\right.$$

where $(x_c,y_c)$ is the origin of the ellipse, where a and b describe the length of the major and minor axis and where $\varphi$ is the anlge of the major axis with the x-axis.

Let $(x_0,y_0)$ be the point in space. Your job is now to minimize

$$\sqrt{(x_c+a\cos(t)\cos(\varphi)-b\sin(t)\sin(\varphi)-x_0)^2 + (y_c+a\cos(t)\sin(\varphi)+b\sin(t)\cos(\varphi)-y_0)^2}$$

with respect to t. I.e. you need to find the t that makes the above expression minimal. OF course, the square root can be dropped, so you need to find the t that minimizes

$$(x_c+a\cos(t)\cos(\varphi)-b\sin(t)\sin(\varphi)-x_0)^2 + (y_c+a\cos(t)\sin(\varphi)+b\sin(t)\cos(\varphi)-y_0)^2$$

To do this, calculate the derivative of this expression and see when it equals 0. You may want to use a computer algebra system for that like wolfram alpha...


text:
IMP Manual  develop.691286d60a,2020/01/19
EMageFit: solution of a complex structure using subunit structures and EM class averages

# Introduction

In this example, EMageFit is used to build a model of porcine mitochondrial respiratory complex II (PDB id 3sfd), using crystal structures of its 4 constituent proteins and a number of electron microscopy (EM) class averages of the complex. For more information on the protocol employed during this example, see the EMageFit protocol page.

(See also the MultiFit example for building models using 3D EM maps instead of 2D class averages.)

All steps in the procedure use a command line tool called emagefit. For full help on this tool, run from a command line:

emagefit --help

# Setup

First, obtain the input files used in this example and put them in the current directory, by typing:

cp -r <imp_example_path>/EMageFit/3sfd/* .

(On a Windows machine, use xcopy /E rather than cp -r.) Here, <imp_example_path> is the directory containing the IMP example files. The full path to the files can be determined by running in a Python interpreter 'import IMP.EMageFit; print(IMP.EMageFit.get_example_path('3sfd'))'.

The input files are for modeling are the three simulated class averages of the complex located in the em_images directory, and the subunits to assemble: 3sfdA.pdb, 3sfdB.pdb, 3sfdC.pdb, and 3sfdD.pdb. A number of Python files are also present. These control the modeling procedure and are described below. For an extensive description of all the parameters see config_example.py.

Building a model requires 4 steps: pairwise docking between interacting subunits, SA-MC optimization, SA-MC model gathering, and DOMINO sampling.

# Pairwise docking

To do the dockings, run from the command line:

emagefit --exp config_step_1.py --dock --log dock.log

Open the file dock.log and search for the line:

INFO:buildxlinks:The suggested order for the docking pairs is [('3sfdB', '3sfdA'), ('3sfdB', '3sfdC'), ('3sfdB', '3sfdD'), ('3sfdD', '3sfdC')]

EMageFit has determined the dockings required, and the order recommended. The pairs are (Receptor,Ligand), so 3sfdA should be docked into 3sfdB, and so on. If HEXDOCK is installed, it is used to perform these dockings, and generates several sets of new files. These include PDB files of the initial docking solutions as estimated from the cross-linking restraints (ending in initial_docking.pdb); the PDB files with the best solutions from HEXDOCK (ending in hexdock.pdb); a set of text files starting with hex_solutions, containing all the solutions from HEXDOCK; and 4 text files starting with relative_positions, which contain the relative transformations between the subunits participating in each pairwise docking. This last set of files is used by the SA-MC optimization.

If HEXDOCK is not present, the relative positions files need to be generated using some docking algorithm. They have a simple format; each line is simply the transformation needed to dock the ligand to the receptor, given as the components of the rotation quaternion followed by the translation vector.

Next, the anchor component and the docking transforms need to be placed into the configuration file for the next step, by setting self.anchor and self.dock_transforms respectively. The anchor component is the component with most neighbors, and is the first receptor in the list of docking pairs printed in the log file (the second component, 3sfdB, in this case). (Anchored components are not moved during the SA-MC optimization.) The file config_step_2.py includes this information.

# SA-MC optimization

The next step is running a Monte Carlo optimization. There are several parameters to control this optimization, such as the profile of temperatures, number of iterations, cycles, maximum displacement and angle tolerated for the random moves, and also the parameter self.non_relative_move_prob. This last parameter indicates the probability for a component of undergoing a random move instead of a docking-derived relative move. For example, a value of 0.4 means that the component acting as ligand (e.g. 3sfdA) will prefer to do a random move with respect to its receptor (3sfdB) 40% of the time. A value of 1 ignores all the relative positions, and a random move is always chosen (i.e. all docking solutions are ignored). To run the optimization:

emagefit --exp config_step_2.py --monte_carlo -1 --log monte_carlo.log --o mc_solution1.db

Note that config_step_2.py sets Monte Carlo parameters to get a very short simulation, for demonstration purposes. For serious application, a longer Monte Carlo simulation is recommended; suitable parameters can be found in config_step_1.py.

The output is the file mc_solution1.db, an SQLite database with the solution. To generate multiple candidate solutions, simply run the command multiple times with different output file names.

# Model gathering

After generating a set of solutions, they must be gathered together into a single database, using a command such as:

emagefit --o monte_carlo_solutions.db --gather mc_solution*.db

For this example, a pre-built database is included in the outputs directory, containing the results of 500 Monte Carlo runs. To use this for subsequent steps in the example, run:

cp outputs/monte_carlo_solutions_500.db monte_carlo_solutions.db

# DOMINO sampling

The last part of the modeling is running DOMINO employing the configuration file config_step_3.py. This new configuration file has changes with respect to config_step_2.py in the classes DominoSamplingPositions and DominoParams. The parameters are:

• self.read is the file with the Monte Carlo solutions obtained before.
• self.max_number is the maximum number of solutions to combine. In this example, with 500 solutions and 4 components, strict enumeration would require 5004 combinations to be explored, which is unfeasible. This number allows you to reduce that. In this example, it is set to 5, and therefore only 54 combinations are explored.
• self.orderby is the name of the restraint used to sort the Monte Carlo solutions. Here the value is "em2d", so the best 5 solutions according to the em2d score will be combined with DOMINO. Another option is to use "total_score".
• self.heap_solutions. This is a rather technical parameter. It is the number of solutions that DOMINO keeps at each merging step. The larger the number, the better the space of 54 combinations is explored, at the cost of a larger running time. Here, a value of 200 is used.

The command to run is:

emagefit --exp config_step_3.py --log domino.log --o domino.db

The output domino.db is a database of solutions. For the actual benchmark used in the EMageFit publication, parameters of self.max_number=50 and self.heap_solutions=2000 were used, resulting in the file outputs/domino_benchmark.db.

# Analysis

The solutions can be written out as PDB files. To write out the 10 best models according to the value of the em2d restraint, run:

emagefit --exp config_step_3.py --w 10 --o domino.db --orderby em2d

The best solution, shown fitted in the density map of the complex, is shown below:


text:
Homework Help: Cl(U ^ A) = cl( U ^ cl(A) )

1. Nov 3, 2008

Unassuming

1. The problem statement, all variables and given/known data

Prove that cl(U^A) = cl(U^cl(A)).

2. Relevant equations

Theorems...

1.) cl(U^A) $$\subseteq$$ cl(U)^cl(A)
2.) cl(A)=cl(cl(A))

3. The attempt at a solution

My proof so far,

Let x be in cl(U^A). From #1, then x is in cl(U)^cl(A). From #2, x is in cl(U)^cl(cl(A)).

I am stuck there. I feel like I am one hair away from finishing but cannot.

EDIT: I realized I need to use neighborhoods for this proof. I am currently working on it and I think I might have something.

Last edited: Nov 3, 2008


text:
## Issue Tracker¶

If you have found an issue with the code or have a feature request, please see our issue tracker. If there is no issue yet that matches your inquiry, feel free to create a new one. Please make sure you receive the mails that github sends if we comment on the issue in case we need more information. For bugs, please provide all the information necessary, like the operating system you’re using, the full error message or any other logs, a description of what you did to trigger the bug and what the actual bug was, as well as anything else that might be of interest. Obviously, we can only help if you tell us precisely what the actual problem is.

## Mail¶

For users of our framework, there is a mailing list for support inquiries on the kivy-users Google Group. Use this list if you have issues with your Kivy-based app. We also have a mailing list for matters that deal with development of the actual Kivy framework code on the kivy-dev Google Group.

## Discord¶

Kivy on Discord at https://chat.kivy.org

Discord is great for real-time communication, but please make sure to wait after you asked your question. If you just join, ask and quit we have no way of knowing who you were and where we’re supposed to send our answer. Also, keep in mind we’re mostly based in Europe, so take into account any timezone issues. If you’re unlucky more than once, try the mailing list.

If you don’t have the Discord app, you can also use Discord’s web client, but please, don’t leave too soon. Just make sure to ask on the #support channel.