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Part of the problem is that the machine is not physically secure. Best Price On Tramadol, The design makes it relatively easy to access the memory card slot, reboot the machine, and install new software, Tramadol Contain Morphine. Another major problem is that the system is designed to accept new software and firmware updates through the same memory card interface used for vote collection---with no authentication or code-signing. 180 Cheap Tramadol, One flaw that got my attention: on bootup, the machine emits a sound that might give you away, but this can be squelched in the obvious way, What Is Tramadol Used For, by plugging in a headphone jack.

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No rx tramadol bars, I came up with this surprising result thinking up probability examples for my class. It would be far too cruel to use in class, so I present it to you, dear reader.

Suppose we play a game called "I give you money." you repeatedly flip a fair coin until the first time it comes up tails. For every time you flipped heads, you win 25 cents.

Question 1: if Alice plays this game, what are her expected (average) winnings.

Answer: 25 cents, no rx tramadol bars.

Question 2: if Alice played this game and the tax-man took a fourth of her winnings, what's her expected net profit.

Answer: 80 cents.

So if we know the tax-man took some of her money, we expect she ends up with more. Tramadol Euphoria, Why. No rx tramadol bars, Believe it or not, the principle behind this question is actually useful in my line of work, which is reverse-engineering secret algorithms. Answer after the flip....

You might expect that this is some weird conditional probability scenario, and it is. The basic idea is that the probabilities change when you are given information. Here, the new information is that Alice's winnings must have been a multiple of four, or else the tax-man couldn't take exactly a fourth of her money.

You also know she hasn't won 0.00 dollars, which makes a big difference. You might dispute this based on the exact wording of the problem, no rx tramadol bars. We can work it out either way.

So prior to any extra information, Alice flips n heads with probability (0.5)^(n+1). The expected number of heads is 1, for 25 cents.

If I tell you that the number of heads was a multiple of 4 and greater than 0, Tramadol Hci Tablets, the probability of "most" numbers drops to zero, while the remaining probabilities are increased by a factor of 30 (so that all probabilities still add to 1.) Working out the sum gives you an expected value of 4*(16/15) heads, or 16/15 dollars won, and 12/15 dollars after the tax-man. No rx tramadol bars, 80 cents.

If instead you thought that Alice might have won 0 cents (and the tax-man took 0 cents, which is technically a fourth of her earnings,) then you end up dropping out a factor of 16, meaning her expected winnings are now 5 cents. Also counterintuitive, but not as dramatic.

Why is this interesting?

This is a phenomenon I call quantization leakage, meaning that you are given extra information by the fact that something in the real world tends to happen in whole numbers, or round numbers. What Is Ultram Used For, Sometimes this information is pretty significant. In reverse-engineering, we can often guess that the designer of a secret algorithm will pick round numbers for the sizes of certain things, no rx tramadol bars.

Here is a real-world example: we recently reverse-engineered a secret watermarking algorithm, as part of a contest that we won earlier this year (netting ourselves a digital camera and some great new theoretical results.) The watermark detector, it turns out, extracted roughly 50,000 statistical features from a computer image, and scanned them for a watermark. The watermark embedder tweaked these features in a detectable way---a pretty common approach to image watermarking. The images were standard monochrome test images of 512x512 pixels.

If you know enough about common techniques used in watermarking, "about 50,000" is a lot of information. No rx tramadol bars, First, 50,000 is not a round number in the computer world. That's round to human beings but not to machines. It is close to a common round number in hexadecimal, 49152 (C000 hex.) In some scenarios if you are told a number in a computer algorithm is "about 50, Overnight Tramadol Online,000," 49152 is a pretty good guess for the exact number.

The images used by the watermarking algorithm were 512 by 512, which have 4096 8x8 blocks. 49152 is 12x4096. Coincidence, no rx tramadol bars. 8x8 block transforms are quite common in image processing, particularly 8x8 DCTs. So you might guess that the watermark features are 8x8 block DCT coefficients, 12 per block, probably low-frequency AC coefficients. This was, in fact, the algorithm used. Tramadol Sent Cod, All this can be guessed from a rough estimate of the number of features.

I wish I could say that this was how we deduced the algorithm, and then you could all wow at our mad deductive abilities. In fact, we used different techniques to deduce the algorithm, which gave us a few papers worth of new ideas.

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