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That is to say with just those set of constructs, anything you can describe algorithmically you can compute with that set of constructs.
图灵完全化语言的特点，的例子之一,也就是说用这些结构。
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If its in Cartesian form I'll pass in an x and y and compute what a radius and angle is.
来得到的这个点,我都可以得到这个点的,全部的这种信息。
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Oil is a very important asset, ... so we want to compute what that-- so now we have lots of inputs.
石油是一种重要的资产，我们想计算-,现在我们有许多参数。
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If you looked at heteronuclear molecules and you wanted to compute the bond energy, you might start with the bond energies of the two constituents.
如果你看那些相同电子的分子,你想计算共享能，你也许会从,两个组成部分的总能量。
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You could then, for any actor or actress, compute the most connected one.
你也可以…,拿任何一个演员来作中心，算出连接性最强的一个。
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And I'm going to pause for a minute, before I run it, and ask each of you to compute in your head what you think the answer should be.
我将暂停一会儿，在我运行之前，我想问问你们你们,心算得出的答案应该是什么。
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If it's in polar form I passed in a radius and angle and I'll compute what the x- and y- value is.
以及半径和角度,但是现在是这样的,不管我是以哪种形式。
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It's the world portfolio, it's everything and we compute the expected return on that portfolio, rm that's rm.
这就产生了世界投资组合,然后我们在此基础上计算出预期收益，所得值就是。
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The algorithm doesn't know that it's going to take this long to compute, it's just busy crunching away, trying to see if it can make it happen.
这很可能会发生，但是你知道的,算法本身并不知道，计算这个问题需要多长的时间，它就一直忙碌的算啊算。
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Also, they don't have to actually--in the old days, they didn't actually have to compute the investment rate.
其实在过去人们不必,真正计算投资收益率
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For a couple of reasons. In some ways, this would be nicer, do expected cases, it's going to tell you on average how much you expect to take, but it tends to be hard to compute, because to compute that, you have to know a distribution on input.
关注最快的情况，在某种意义上来说，因为一些原因这样想挺不错的，当我们处理一个给定的问题,计算平均时间的时候,是很难计算的，因为你并不知道输入的分布情况,这些输入会是怎么样的呢？
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Once you've got them together, then you can compute the efficient portfolio frontier without the riskless asset.
当你明确了这些参数后，就可以算出没有无风险资产情况下的,有效边界了。
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As I said, what we want to do is, we want to count the number of basic steps it takes to compute a computation as a function of input size.
我刚才提到了，我们要建立，一个根据输入大小的方法来计算,一个计算过程需要的时间,建立这个方法需要几步呢？
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That's what we have to know to compute the efficient portfolio frontier with three assets.
这些都是计算三种资产的有效边界,所需要用到的。
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I've added the ability to have more complex data structures here. But I dropped a hint in the first lecture about what you could computer with things. In fact if you think for a second about that list, you could ask what can I compute with just that set of constructs?
我添加了使用更复杂的数据结构的能力,但是我在第一节课给大家了了一个,关于你可以用什么来做计算的暗示,实际上如果你思考,这个列表一会儿的话,你会问我可以用？
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This is how they actually compute the payments because you can take, if you want--if someone is borrowing -let's bring it up to today- they're borrowing $200,000.
这就是计算贷款偿还额的方法,比如,如果某人要借款,我们用现实的例子,假设要借20万美元
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This is boring. In fact, you can do some nice things to prove what is the class of functions you can compute with straight-line programs, and what you'd see if you did that is, it's not particularly interesting.
这很无聊，实际上，你可以通过做一些很有趣的事情,来证明你可以通过直线程序,来做很多功能，但是你也看到我们之前讲过的了，这不太有趣。
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Again, I could have some other functions to compute things, but this is typically the place where I'm going to put them in.
注意这个声明典型的行为,就是为了定义了内部变量，以及类的内部特性,在说一次，我可以写一些。
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Suppose I want to compute square roots a lot of places in a big chunk of code.
假设我想在一大段代码中,计算很多次平方根。
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Well, you'll know when it crashes, that doesn't help you very much, but you can't always tell whether something's stuck in an infinite loop or whether it's simply taking a long time to compute.
好，你将学到它在什么时候会崩溃，这对你帮助并不大，但是你不能辨别出到底是在一个循环中,有什么东西卡住了呢,还是程序需要很长的时间来计算一个结果呢。
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I want to compute the length of the hypotenuse of a right triangle.
我想计算下,直角三角形的斜边。
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I'm going to write a function to compute integer power exponents.
我要去写一个,计算一个整数幂指数的方法。
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It says that the forward rate, which you can compute from today's newspaper or from today's website--you can compute the forward rates for all future dates.
这些告诉我们,人们可以从今天的报纸,或网上的信息中计算出,未来任意时刻的远期利率
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Compute the angle the same way, just using the appropriate things.
用合适的计算来求，那么我们要说的概念是。
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Remember, this thing only runs for sixty days and you could compute your sixty-day return, but people like to compare annual returns-- once again, a tradition we have.
注意,这个债券期限只有60天,当然你可以计算60天的收益率,但是人们往往喜欢用年收益率进行比较,这也是一种传统
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Well, what I always do in anything like this is, the first thing I do is, I run it on something where I can actually compute the answer in my head. So I get a sense of whether or not I'm doing the right thing.
好的，我常常在,这种问题中会做的是，我会做的第一件事是我,会先带入我可以心算的值来运行,因此我能够知道我是否做对了。
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So I'm first going to compute something base move Think of this as kind of the basis from which we'll be computing the actual move.
所以我先计算叫,的东西，called，the，base，move。,它是我们计算实际值时,用到的初值。
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What we want to do now is compute the mean and variance of the portfolio-- or the mean and standard deviation, since standard deviation is the square root of the variance-- for different combinations of the portfolios.
我们现在要做的是,计算这个投资组合的均值和方差-,或者均值和标准差，因为标准差的平方就等于方差-,这对任何投资组合都是一样的。
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So we're to assume we can get to any piece of data, any instruction in constant time, and the second assumption we're going to make is that the basic primitive steps take constant time, same amount of time to compute. Again, not completely true, but it's a good model, so arithmetic operations, comparisons, things of that sort, we're all going to assume are basically in that in that particular model.
因此如果我们假设在恒定的时间内,我们可以取得任何一块数据,任何一种数据结构的话,我们要做的第二个假设就是,基本的原始操作计算花费的时间是恒定的,这个假设也不是完全正确的，但这个模型其实挺不错的，因此算法操作，比较，这一类的事情，我们在这个特定的模型中都假设是基本的,操作，花费的时间是恒定相同的。
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If it's not in the memo, I'll compute its value and put it in the memo.
如果值没有保留在memo中，我要计算它的值,并把这个值存在memo中。
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