To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
Languages
Recent
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

Correlation immunity

From Wikipedia, the free encyclopedia

In mathematics, the correlation immunity of a Boolean function is a measure of the degree to which its outputs are uncorrelated with some subset of its inputs. Specifically, a Boolean function is said to be correlation-immune of order m if every subset of m or fewer variables in is statistically independent of the value of .

YouTube Encyclopedic

  • 1/5
    Views:
    193 973
    17 166
    1 718
    153 819
    109 103
  • The lymphatic system's role in immunity | Lymphatic system physiology | NCLEX-RN | Khan Academy
  • Top 10 AMAZING Predictions By Using MATH
  • Beautiful Equations - Herd Immunity
  • How lymphatic vessels move fluid | Lymphatic system physiology | NCLEX-RN | Khan Academy
  • What is actually in lymph | Lymphatic system physiology | NCLEX-RN | Khan Academy

Transcription

We've talked about how the purpose of the lymphatic system is to collect fluid that's squeezed out of blood vessels like this one-- to collect that fluid and eventually bring it back into the blood so that we don't lose too much fluid. So this is a blood vessel. Around it, we have some cells that are maybe being fed by the blood vessel. And at the same time, we have these lymphatic vessels that kind of start out of nothing. And they're porous so that they can collect the fluid that was squeezed out of the blood vessels. And then eventually, they'll put that fluid back into the blood. But the lymphatic system actually has other purposes. It helps us in other ways. And we're going to talk about one of those other ways in this video. And to talk about that, we need to talk a little bit about infection. So infection is when your body gets attacked by a foreign invader. And that invader will usually be a bacteria or a virus. And in this case, let's talk about a bacteria. So let's say we get a bacteria that invades this tissue here. So the first thing you might ask is, why am I drawing the bacteria here? Why am I drawing it outside of the blood? Maybe I should be drawing it here inside the blood. And one reason why I might think that, why you might think that, is because think about when you get infected. Sometimes, you get infected when you cut yourself, right? When you cut yourself, you might get an infected wound. And when you cut yourself, you see blood. So you might think that you're getting infected because bacteria or viruses or whatever are getting into the blood. But actually, that's not quite true. Infections are usually not in the blood. And actually, there's a pretty simple, you could say, proof of that, which is that when you get infected, infections almost always stay localized. And by that, I mean that they usually stay in one place. So think about when you get an infected cut. Usually-- let's say, it's on your finger-- the infection will stay on your finger. Or let's say you get a UTI, which is a urinary tract infection. The infection usually stays in your urinary tract. Or maybe you get pneumonia. The infection stays in your lungs. So if the infection was actually in your blood, it would immediately go all over the body. And that does happen sometimes. But it's way more serious than the majority of infections. So really, the most accurate way to draw a typical infection is to draw the infection occurring in the tissues. Now, when we have this infection, there are going to be some local immune cells that your body has that's going to be fighting these bacteria and trying to kill them. But your body also has more powerful, really, defenses, which consist of B cells and T cells. And these guys are part of the adaptive immune system, which means that they actually sort of react to the specific invader that's there. So unlike these guys here-- which, for the most part are macrophages-- unlike these macrophages, who can fight lots of different kinds of bacteria, these B cells and T cells will react to the specific bacteria and end up having a much more powerful effect against them because of that. They're specially tailored to the invader. But the problem is that these guys don't just sit out there in the tissues where the infections start. And there are a few reasons for that. But probably the most important is that for these B and T cells to specialize against these invaders requires a very complex process that couldn't possibly occur just willy-nilly out here in the tissues. They require a special environment, which we can draw here, which is kind of like a training camp where they can develop in response to this specific invader. But now, we're faced with a problem, because we've already said that these bacteria stay here in the tissues. They're not swept into the blood and then carried to the B and T cells over there. They stay in the tissues. And these B and T cells are not out there in the tissues. So how can we get these B and T cells to see these bacteria and be able to react against them? And that is precisely what this lymphatic system does, because these bacteria are going to get swept in. And at the same time, these macrophages might gobble up some of these bacteria. And once they've done that, they might migrate into these lymphatic vessels. And it turns out that the way your body resolves all this is to sweep all these things directly to the nearest lymph node. And that's what this structure is called. It's called a lymph node. It's called a node because it's generally a smallish object in your body, and it looks somewhat circular. So it's like a node. And the word lymph has to do with the fact that we have B and T cells here. And it's also convenient, because what leads to it is the lymphatic vessel. So these bacteria and some of these macrophages carrying the bacteria will get swept along. And they'll be in contact with these B and T cells, who can then multiply and specialize and get ready to fight this infection over here. And we're not going to talk about how they ultimately do that, because that's a topic, really, for another video. But I just wanted to mention that, as we said, the primary purpose, really, of the lymphatic system, of these lymphatic vessels, is to carry fluid back into the blood. So obviously, by the time all this stuff gets here to this lymph node, that can't be the end of the lymph vessel. So lymph vessel is actually going to continue. It's going to continue, and it's going to eventually carry fluid and such back into the blood. So ultimately, the fluid is going to end up back in the blood. And so actually, another nice side effect of having these lymph nodes here interspersed throughout the lymphatic vessels is that they'll actually filter all this fluid that's gonna get put back into the blood. If you didn't have this lymph node here, you would still need the lymphatic vessels to get rid of the fluid that your blood is filtering. And what would happen is these bacteria would get just put directly back into the bloodstream. And that would be a problem, because as we said, infections of the blood are way more serious than local infections of tissues. So this lymph node acts as a filter for the lymph, which is passing through here. And actually, it also has some macrophages here that are going to help gobble up some of the bacteria that might be floating through. And so in sum, I think we're left with something that's really a very elegant system. What happens is we've developed a way to sweep all these bacterial invaders basically to the nearest police station. And at the same time, we've developed a system to filter the fluid that got squeezed out of these blood vessels, to filter it as it passes through here, so that by the time it gets to the end, it's free of bacteria and other debris. So before we finish, let's talk a little bit more about these lymph nodes so we have a sense of what they're like in reality. So they're generally fairly small. They're definitely much smaller than your average organ. And so they're not considered organs. And they're about 1 to 25 millimeters. And they're small enough that you can have lots of them in your body. And so you do. You have about 600. There are about 600 in the body. And some of them are located close enough to the skin that you can feel them. And those would obviously be the bigger ones. It would be hard to feel something that's 1 millimeter. And so let's look at where some of these are located on a human body. Let's actually give this guy a neck to be generous. So the lymph nodes are, obviously, located all along lymph vessels. But because there are 600 of them, they're located along the larger lymphatic vessels that have already collected many of the little lymphatic vessels and consolidated them. So let's start with places where you might actually feel lymph nodes on your own body. So often, you can feel the lymph nodes that are in the inguinal region there, kind of between your thigh and your abdomen. And as we know, there are kind of large lymphatic vessels that consolidate here and merge and rise up the body. And all along here, you might have lymph nodes, all along there. And then often, when a doctor gives you a check up, he'll feel for lymph nodes along your clavicles there. He might feel along your neck. And he might actually feel on your face and below your jaw. So all those are along lymph vessels that are coming down. And then the lymph vessels that are coming here from your arms-- those will have lymph nodes along them. And so in this way, you have about 600 of these lymph nodes sprinkled about in your body. And the cool fact to remember is that any lymph that's coming out of any tissue in your body will pass through at least one lymph node before it goes back to your blood. So even if it's out in your little pinky finger or something, the lymph vessels that carry that back will come and join a larger lymph vessel, which will pass through a lymph node. Or even if it's here in your stomach, it'll come and it'll join, and it'll pass, and it'll get into a larger one with a lymph node. So really, all the lymph that goes back into your blood is filtered.

Definition

A function is -th order correlation immune if for any independent binary random variables , the random variable is independent from any random vector with .

Results in cryptography

When used in a stream cipher as a combining function for linear feedback shift registers, a Boolean function with low-order correlation-immunity is more susceptible to a correlation attack than a function with correlation immunity of high order.

Siegenthaler showed that the correlation immunity m of a Boolean function of algebraic degree d of n variables satisfies m + d ≤ n; for a given set of input variables, this means that a high algebraic degree will restrict the maximum possible correlation immunity. Furthermore, if the function is balanced then m + d ≤ n − 1.[1]

References

  1. ^ T. Siegenthaler (September 1984). "Correlation-Immunity of Nonlinear Combining Functions for Cryptographic Applications". IEEE Transactions on Information Theory. 30 (5): 776–780. doi:10.1109/TIT.1984.1056949.

Further reading

  1. Cusick, Thomas W. & Stanica, Pantelimon (2009). "Cryptographic Boolean functions and applications". Academic Press. ISBN 9780123748904.


This page was last edited on 3 June 2017, at 09:13
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.