How exactly was the original coefficient for difficulty determined?


I'm not sure it was. When the network started operating (and Satoshi was pretty much the only one mining), blocks weren't found every 10 minutes. For example, the first 2016 blocks were found in 24 days rather than 2 weeks. Normally this would cause the target to go up but it can't go above the hardcoded max target, so only in block 32256 in December 30 2009 we started seeing the retarget mechanism kicking in and blocks arriving every 10 minutes.

However, seeing that it did come out close to 10 minutes, it's possible Satoshi figured out the hashrate of his own machine, and chose the parameter as a round number close to what it would take to find a block every 10 minutes on his hardware.

I think you did not understand this line of code correctly. Hash values are represented as 256-bit unsigned integers. uint256(0) gives the representation of 0 in this data type. ~ is logical not and ~uint256(0) inverts all bits, giving the highest possible integer, 2^256-1. Right...

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A stock's beta coefficient is a measure of its volatility over time compared to a market benchmark. A beta of 1 means that a stock's volatility matches up exactly with the markets. A higher beta indicates great volatility, and a lower beta indicates less volatility.

Calculating beta for a given stock is not too difficult, despite the intimidating jargon. To calculate it, all you need is some market data over a period of time and a spreadsheet program.

Why calculate beta yourself?
There are many online resources to find a given stock's beta over various time frames and compared to various market benchmarks. Those are great tools, but oftentimes they limit how much control you have over the calculation. For example, your stock may be highly concentrated in a foreign country. In that case, it may make sense to forgo the standard market benchmark, the S&P 500, and instead use an international market index.

Time frames are also highly important and should be...

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are two technical properties of a test that indicate the quality and usefulness of the test. These are the two most important features of a test. You should examine these features when evaluating the suitability of the test for your use. This chapter provides a simplified explanation of these two complex ideas. These explanations will help you to understand reliability and validity information reported in test manuals and reviews and use that information to evaluate the suitability of a test for your use.

Chapter Highlights

What makes a good test?Test reliabilityInterpretation of reliability information from test manuals and reviewsTypes of reliability estimatesStandard error of measurementTest validityMethods for conducting validation studiesUsing validity evidence from outside studiesHow to interpret validity information from test manuals and independent reviews.

Principles of Assessment Discussed Use only reliable...

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What are newsgroups?

The newsgroups are a worldwide forum that is open to everyone. Newsgroups are used to discuss a huge range of topics, make announcements, and trade files.

Discussions are threaded, or grouped in a way that allows you to read a posted message and all of its replies in chronological order. This makes it easy to follow the thread of the conversation, and to see what’s already been said before you post your own reply or make a new posting.

Newsgroup content is distributed by servers hosted by various organizations on the Internet. Messages are exchanged and managed using open-standard protocols. No single entity “owns” the newsgroups.

There are thousands of newsgroups, each addressing a single topic or area of interest. The MATLAB Central Newsreader posts and displays messages in the comp.soft-sys.matlab newsgroup.

How do I read or post to the newsgroups?

MATLAB Central

You can use the integrated newsreader at the...

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What is the 'Correlation Coefficient'

The correlation coefficient is a measure that determines the degree to which two variables' movements are associated. The range of values for the correlation coefficient is -1.0 to 1.0. If a calculated correlation is greater than 1.0 or less than -1.0, a mistake has been made. A correlation of -1.0 indicates a perfect negative correlation, while a correlation of 1.0 indicates a perfect positive correlation.

BREAKING DOWN 'Correlation Coefficient'

While the correlation coefficient measures a degree to which two variables are related, it only measures the linear relationship between the variables. Nonlinear relationships between two variables cannot be captured or expressed by the correlation coefficient.

A value of exactly 1.0 means there is a perfect positive relationship between the two variables. For a positive increase in one variable, there is also a positive increase in the second variable. A value of...

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Coefficient of correlation is “R” value which is given in the summary table in the Regression output. R square is also called coefficient of determination. Multiply R times R to get the R square value. In other words Coefficient of Determination is the square of Coefficeint of Correlation.

R square or coeff. of determination shows percentage variation in y which is explained by all the x variables together. Higher the better. It is always between 0 and 1. It can never be negative – since it is a squared value.

It is easy to explain the R square in terms of regression. It is not so easy to explain the R in terms of regression.

Coefficient of Correlation is the R value i.e. .850 (or 85%). Coefficient of Determination is the R square value i.e. .723 (or 72.3%). R square is simply square of R i.e. R times R.

Coefficient of Correlation: is the degree of relationship between two variables say x and y. It can go between -1 and 1. 1 indicates that the two...

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In statistics, the correlation coefficient r measures the strength and direction of a linear relationship between two variables on a scatterplot. The value of r is always between +1 and –1. To interpret its value, see which of the following values your correlation r is closest to:

Exactly –1. A perfect downhill (negative) linear relationship

–0.70. A strong downhill (negative) linear relationship

–0.50. A moderate downhill (negative) relationship

–0.30. A weak downhill (negative) linear relationship

0. No linear relationship

+0.30. A weak uphill (positive) linear relationship

+0.50. A moderate uphill (positive) relationship

+0.70. A strong uphill (positive) linear relationship

Exactly +1. A perfect uphill (positive) linear relationship

If the scatterplot doesn’t indicate there’s at least somewhat of a linear relationship, the correlation doesn’t mean much. Why measure the amount of linear...

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Regression analysis generates an equation to describe the statistical relationship between one or more predictor variables and the response variable. After you use Minitab Statistical Software to fit a regression model, and verify the fit by checking the residual plots, you’ll want to interpret the results. In this post, I’ll show you how to interpret the p-values and coefficients that appear in the output for linear regression analysis.

How Do I Interpret the P-Values in Linear Regression Analysis?

The p-value for each term tests the null hypothesis that the coefficient is equal to zero (no effect). A low p-value (< 0.05) indicates that you can reject the null hypothesis. In other words, a predictor that has a low p-value is likely to be a meaningful addition to your model because changes in the predictor's value are related to changes in the response variable.

Conversely, a larger (insignificant) p-value suggests that changes in the predictor are not...

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Re: Determine the damping coefficient

Hi Nagi,

Thanks for your reply.
1. Regarding the transient analysis, the reason that it is not possible because by default, defining an elastic material in COMSOL without damping, treats the material as undamped, and hence in the time domain analysis, at the point where voltage is applied, the displacement appears across the beam abruptly, without any damping response, which contradicts what happens physically (due to damping).
More about this issue can be found in this thread:

2. Would you elaborate more please on how to determine these coefficients, because as far as the documentation explains, it mentions that these parameters (alpha and beta) shall be computed using two known frequencies as well as their damping factors. My question is how to determine these damping factors, is it done analytically or can they be extracted through another simulation...

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