Es crucial recordar que la estructura y el contenido particular de un acuerdo de compensación pueden cambiar según el negocio y sus regulaciones internas.  https://www.genera.cl/donde-debe-ubicarse-el-reloj-control-de-asistencia/sistemas-de-control-de-asistencia/

thanks for sharing awesome information as well to You have an interesting approach. I think that Karl Berg worked a little more with complexity, but it was some time ago here is

https://survivalop.com/how-long-does-spam-last-in-the-fridge/

The problems with these techniques likely come from attempting to determine complexity from data that is a mixture of signals. For this to work, you need to first separate the data into

component signals, then identify and measure complexity aspects of each separately.

For clarity of explanation, consider a simplistic view of EKG as a wavelet (the beat) periodically
added to white noise. Define "span" as the difference between the maximum and minimum value in the data.

The entropy of the data is the log of the span, which is the average number of bits needed to
store each data point. (The number of bits needed to store the data in exponential form is twice the number of bits of the average (expressed as a number), plus twice the number of bits of the span (expressed as a number), plus twice the encoding kernel length (expressed as a number), plus the log of the span times the number of samples. In the limit as the number of samples approaches infinity, the bits from the constant terms become negligible in comparison to the number of data bits, so the total approaches the number of bits in the exponential encoding: the log of the span times the number of samples. The average is that number divided by the number of samples, which is the log of the span.)

If you write an algorithm that subtracts the wavelet at points in the data stream and inserts a
token which has the value of (reduced span plus 1) as an indicator of "a heartbeat starts here", you decrease the span by a lot and increase it by 1 to represent the token. You also add tokens to the data as if they are extra samples.

The new encoding has extra constant bits added at the beginning (the wavelet subtracting algorithm) and this extra does not depend on the number of samples, so will be negligible as the samples goes to infinity.

If the new encoding uses fewer bits than the original encoding, then the number of bits saved tells the likelihood that the original data was actually composed of wavelets plus noise. The probability that the original signal was *not* so composed is 1/(2**saved-bits), so if the algorithm saves 6 bits the probability that this occurred by random chance is 1-in-64, and so on. It's not uncommon to save several tens of bits, making the new encoding astronomically likely to be the correct encoding.

Suppose the example data stream is 100 samples per second, and an AGC circuit automatically
amplifies the signal to 10 bits of span (supposing, for example, a 12-bit A/D converter with feedback to amplify the beat to span 10 bits of signal). The base data storage estimate is then 10
bits per sample for 100 samples per second, or 1000 bits for each second of data.

Now suppose an algorithm subtracts beat wavelets from the data and inserts an extra data point whose value is "reduced span +1" where it finds a beat. If this reduces the span of the data from 1024 (10 bits) to 1/4 of that value, the new span is 256 and the data can be stored as 8 bits per sample, and every 100 samples (once a second-ish) an extra token is added to indicate the beat. In this case the data storage is slightly more than 8 bits per sample (the reduction to 1/4 of the signal, plus 1 to indicate the token) times 100 samples, plus just over 8 bits to indicate the token. (8.0056 * 100 samples + 8.0056 ⇒ about 808 bits for 1 second). The algorithm saves almost 200 bits of storage per second of data, which is a very good indicator that the signal is real.

Once you have separated the data into component signals (noise and wavelet heartbeat in the simple example), you can take complexity measurements of the individual signals separately.

To continue the example, if the remaining data contains no other signals, then the entropy of the
noise is the log of the span (Shannon entropy). You can measure differences in timing between
individual beat tokens and might discover that the "jitter" between heartbeats is a normal distribution, which has an average and a variance. These numbers (average and variance) are
parameters of the entropy formula for a normal distribution, and are the results you want.

The complexity of your original data is therefore a mash-up of complexities derived from the
component signals in different dimensions of measurement. In the example given, the noise has
complexity of value, while the jitter has complexity in time.

For your application, you want to first separate the data into component signals, then determine
the complexity type and parameters for each.

New access to data allows application of  these methods  to determine how closely theory applies to real world observation. Beyond this, actual benefits may be derived with accepted interpretation. Manufacturing has obvious applications.

Panopticlick project can use this analysis to suggest how easily government may infer browser characteristics to identify individuals, possibly connecting by theory of socialization. These are strange times. On the day of a government official's retirement, a felon may see his home burned because of a browser configuration, and over-reaching theory.

I had read the paper in the link you had posted in response to my comment several months ago, and it has changed the way that I am looking at my power monitor project a little bit. Rather than trying to use the data as absolute, I want to treat the data as the probability to an event occuring, with the base being the resolution of the anolog signal + the resolution of the ADC, and then determin the probability of the desired event having occured. I believe that the probability will become closer to a certainity as an event occurs more often, and even more so with training. Additionally, I have been thinking of ways that this could be useful beyond the obvious.

While my thinking may be naive or just foolish, but if I look at the home as an extension of a person and the usage as an extension of reasoning then I think that it could be used, at least at some level to determine aspects of mental or overall health. What brought me to this is that I have a number of older relatives and when I go to visit with them it is plain to see that they repeat the same tasks everyday with little variation, this is in stark contrast with my eradic behavior, and I would think that patterns would present themselves for someone with OCD, and if it were possible to look at data from those with know issues and compared with those with no known issues I am wondering if this would allow for the prediction of developing problems.

While this has not brought me back to the original intent of the project you have posted here, I appreciate that you have posted this, and would love to know if any of your students are able to follow up with any of the data collection in these areas..

You have an interesting approach. I think that Karl Berg worked a little more with complexity, but it was some time ago. https://www.cnr.berkeley.edu/~beis/BeissingerLab/labmemberbio.php?ecode=ksb39@cornell.edu
and

The Shannon paper is really fantastic. It actually prompted me to order James Joyce's "Finnegan's Wake" and take another look at his language expansion from the complexity standpoint. But the most tantalizing thing about this paper is that it ends with "To be continued". Do you know if it was?

Also, the project itself ends with: "The next two things to try are the second order entropy techniques and the Renyi entropy." Did you get to this part yet?

I did not. Moved on to another project.

I wish I could give this project a lot more skulls! Bravo!

Thanks! Any thoughts you have about the topic I would like to hear.

I think about this particular thing a lot. Are you familiar with the "How long is a coastline? It depends on the size of your ruler!" concept? Complexity is a lot like that. A lot of times you get what you are looking for, because you are looking for it in a particular way.

Variance plays into it too, because what does one mean by complexity? Variance has its own complexity, so does one include it or try to exclude it? It's an arbitrary decision. If you take data on something that should be a straight line, but has variance, you could best-fit the data points to the line you expect, and get a simple but perhaps "correct" view of the data. But if you were to exactly curve-fit the points to an arbitrary but totally "true" curve, you would get a very complex curve with a lot of coefficients. Technically, this would be more accurate than the line, which was an approximation. The situation is compounded with a complex signal.

Measurement error also has its own complexity, and such approximations are meant to offset some of that signal perturbation, but how much? Arbitrary again, and sure there are lots of techniques to characterize all this, estimate things properly. But a lot of times it just comes back to how well it fits the initial assumption, and how far you are willing to go, and how much it "matters".

Sampling rate enters into it, on a rolling basis, since you don't necessarily know how fast to sample something before you sample it, and it may not be periodic. It's good to sample more quickly where you expect more complexity, to be able to characterize it. But if you don't know ahead of time (again, assumptions) when that will be...

You cannot say anything about the complexity below the sampling threshold - but that does not mean it does not exist! Same with meta-levels you cannot detect until enough time has elapsed. The former may not be an issue with digital or discrete streams, but the latter certainly is. We can determine that the Phaistos disk (for instance) contains complexity in its signal stream, but we don't have enough units of complexity to decipher it.

Well, there are some thoughts... I better stop there, there's just so much interesting stuff with this topic!

Just wanted to give you a link for the coastline thing, if you weren't aware of it:
http://en.wikipedia.org/wiki/Coastline_paradox

If you think about complexity in terms of fractal dimensions, you can see how it is relevant. It's also one way to de-inifinity-ize self-similar complexity, which is naturally occurring.

I don't know if this occurs in man-made data streams like communication - I suspect it does, since language is organic. (That Bell paper is amazing, thanks so much for that link!)

This is a hard topic. I would start with Claude Shannon's 1948 paper on information content of a channel. http://www3.alcatel-lucent.com/bstj/vol27-1948/articles/bstj27-3-379.pdf

Some of your links are broken, but I didn't understand the math from what I saw any way. I found the following link looking for an introduction to the subject. I thought it may be useful to others who come across this project. My understanding is that the area of study where complexity is found is not as important as the complexity itself because the same questions arise. Is there any other material you could recommend ?

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=6&ved=0CGAQFjAF&url=http%3A%2F%2Fdis.unal.edu.co%2F~gjhernandezp%2Fsim%2Fhide%2FComplex%2520Adaptive%2520Systems%2520An%2520Introduction%2520to%2520Computational%2520Models%2520of%2520Social%2520Life%25200691127026.pdf&ei=LICGU6TfLcayyAT_2IDIBw&usg=AFQjCNFM-WTZ4jjqg1_ylWSC59iSDJ9O5w&sig2=DtnPdCWgW2EQJMQkkIK5CA&bvm=bv.68114441,d.aWw