janneman said:
Jan, perhaps one of the most astonishing examples of similar behavior of seemingly unrelated phenomena is the phase transition of a system between two or more very different macroscopic conditions.
The equations modeling phase transitions in water, magnetization in ferromagnetic materials, and volume of a gel in solution to name a few, are basically the same.
The underlying principle in this case is the statistical properties of a large amount of individual interacting entities.
Rodolfo
I would not put much practical stock into this. IF you degenerate any device enough, it will not behave as it would without degeneration.
It is true that a really starved FET will have the same distortion profile as a bipolar transistor, BUT this is not a good place to operate the device for analog audio.
It is true that a really starved FET will have the same distortion profile as a bipolar transistor, BUT this is not a good place to operate the device for analog audio.
ingrast said:
Rodolfo,
This is actually the type of thing I had in mind, but it was too fuzzy to articulate it as well as you did.
To go one step further (and more off-topic, please indulge me), sometimes you also have the feeling that the behaviour of say large groups of people closely mimic the behaviour of large groups of particles. That is why I find chaos theory so fascinating. I am convinced that there are strong parallells between chaos theory and evolution, in fact I think the latter is based on the former.
If you conclude that behaviour of large groups of people follows some universal law (and talk to crowd control specialists if you want a slant on that), it immediately brings great consequences to the question of free will and personal responsibility.
You know, I wish I had another 200 years to study all this!
Back to topic..
Jan Didden
Another off topic post
Another parallel between society and the micro world is the discovery that social networks and gene expression networks obey a power law distribution (log/log). They find, contrary to original belief, that people, the internet, and cells are not randomly connected. Instead, there are a few major "hubs" that are very connected and a lot of nodes that are "loosely" connected. This makes the internet, cells, etc. robust to random failures, but susceptible to malice "viruses" that expressly attack hubs. I'm just coming up to speed on this and yet could still draw parallels (in areas of finance, sexual behavior, and politics). This is one way to explain how the ecosystem survives the extinction of a few species... For anyone interested, I recommend, as a starting place, the following website: http://www.nd.edu/~networks/papers.htm. It looks like they use the term self organizing networks; however, power law, "small world", and scale free are terms also used... Albert-László Barabási authored a book titled "Linked" that is popular. In it, he describes the "six degrees of separation"--it's a small world--and how any two randomly selected web pages (of the billions) are connected by 17 clicks, etc.
JF
janneman said:
Another parallel between society and the micro world is the discovery that social networks and gene expression networks obey a power law distribution (log/log). They find, contrary to original belief, that people, the internet, and cells are not randomly connected. Instead, there are a few major "hubs" that are very connected and a lot of nodes that are "loosely" connected. This makes the internet, cells, etc. robust to random failures, but susceptible to malice "viruses" that expressly attack hubs. I'm just coming up to speed on this and yet could still draw parallels (in areas of finance, sexual behavior, and politics). This is one way to explain how the ecosystem survives the extinction of a few species... For anyone interested, I recommend, as a starting place, the following website: http://www.nd.edu/~networks/papers.htm. It looks like they use the term self organizing networks; however, power law, "small world", and scale free are terms also used... Albert-László Barabási authored a book titled "Linked" that is popular. In it, he describes the "six degrees of separation"--it's a small world--and how any two randomly selected web pages (of the billions) are connected by 17 clicks, etc.
An externally hosted image should be here but it was not working when we last tested it.
JF
OT (again)
Apparently, fractals (associated with chaos theory) are like self generating networks...
JF
Apparently, fractals (associated with chaos theory) are like self generating networks...
JF
Check out Michael Crichton's book "Prey" Yes, it's fiction.
It discusses this at length. How can a group of organisms like ants that have no individual intelligance build the homes that they do?
It discusses this at length. How can a group of organisms like ants that have no individual intelligance build the homes that they do?
The distinction between a self-organised collection of entities and a living organism becomes blurred, if you go this way (and I fully agree).
Is the sun, a self-organised collection of particles, alive?
Is earth, a self-organised collection of self-organised collections of self-organised cells of self-organised molecules alive (the Gaia theory)?
BTW, the remark about how any of the billions of webpages can be reached with just 17 clicks has also a parallel in brains, where the number of combinations of connections exceed the number of particles in the known universe. Which is, in round numbers, quite a bunch.
Yet within a fraction of a second, in reaction to an external event, the brain 'self-organises' these connections into a pattern that allows the organism to adequately react to the event. Makes you feel very small, doesn't it?
Jan Didden
Is the sun, a self-organised collection of particles, alive?
Is earth, a self-organised collection of self-organised collections of self-organised cells of self-organised molecules alive (the Gaia theory)?
BTW, the remark about how any of the billions of webpages can be reached with just 17 clicks has also a parallel in brains, where the number of combinations of connections exceed the number of particles in the known universe. Which is, in round numbers, quite a bunch.
Yet within a fraction of a second, in reaction to an external event, the brain 'self-organises' these connections into a pattern that allows the organism to adequately react to the event. Makes you feel very small, doesn't it?
Jan Didden
sorry, one more OT
hehehe... my above link just experienced a "random failure". It was working...
This one currently works:
http://www.nd.edu/~networks/
Thanks for your thoughts Jan! Unfortuantely, duty calls, but I'll get back to pondering your post. You drew the essential inference that I glossed over regarding the "17 clicks"...it's a relatively short path through a very large network... Take care.
JF
hehehe... my above link just experienced a "random failure". It was working...
This one currently works:
http://www.nd.edu/~networks/
Thanks for your thoughts Jan! Unfortuantely, duty calls, but I'll get back to pondering your post. You drew the essential inference that I glossed over regarding the "17 clicks"...it's a relatively short path through a very large network... Take care.
JF
Self organization and other meanderings
Just to steer back to the forum's topic (not the thread) without leaving altogether the current branch, I have high hopes on the marriage of neural networks with audio technologies.
A particular area I should like to investigate is the self adaptation of corrective feedback so as to effectively linearize an amplifying chain.
The way a neural network "learns" from stimuli and desired response is something not completely understood (in a deep sense I mean), and is a hot topic.
Rodolfo
Just to steer back to the forum's topic (not the thread) without leaving altogether the current branch, I have high hopes on the marriage of neural networks with audio technologies.
A particular area I should like to investigate is the self adaptation of corrective feedback so as to effectively linearize an amplifying chain.
The way a neural network "learns" from stimuli and desired response is something not completely understood (in a deep sense I mean), and is a hot topic.
Rodolfo
Rodolfo,
Interesting thought. There is some evidence that this 'learning' is related to evolutionary processes. For instance in the brain, patterns that solve a particular problems are stengthened and persist longer, and are staying quite close to the surface, the more they are succesfull. The particular theory is called 'neuronal group theory'. A particular connection pattern is called a group, and it has been shown that there is a kind of evolutionary battle between groups for survival. The pattern best fit for a particular purpose survives and remains available at short notice, while the 'less fit' disappear and never return.
This also partly provides an answer to the question how the blueprint for such a complex item as the brain can be crammed into our genes, which have totally unsufficient codes for that. Well, they are not in the genes. The genes provide the general layout and the inner workings and capabilities. These are shaped by evolution. Then, *after* you were born, evolution *continues* inside your head as the pressures of learning shape brain patterns that happen to cope with it. The ones that work stay.
One indication is that although certain activities like speaking or learning reside in the same general brain area for all humans, the actual brain connection patterns that activate the activity are often completely different from individual to individual.
Survival of the fittest, right between your ears, up to this very minute. Amazing. It also gives food to the thought that evolutionary processes are some kind of universal law or process within our universe.
Jan Didden
Interesting thought. There is some evidence that this 'learning' is related to evolutionary processes. For instance in the brain, patterns that solve a particular problems are stengthened and persist longer, and are staying quite close to the surface, the more they are succesfull. The particular theory is called 'neuronal group theory'. A particular connection pattern is called a group, and it has been shown that there is a kind of evolutionary battle between groups for survival. The pattern best fit for a particular purpose survives and remains available at short notice, while the 'less fit' disappear and never return.
This also partly provides an answer to the question how the blueprint for such a complex item as the brain can be crammed into our genes, which have totally unsufficient codes for that. Well, they are not in the genes. The genes provide the general layout and the inner workings and capabilities. These are shaped by evolution. Then, *after* you were born, evolution *continues* inside your head as the pressures of learning shape brain patterns that happen to cope with it. The ones that work stay.
One indication is that although certain activities like speaking or learning reside in the same general brain area for all humans, the actual brain connection patterns that activate the activity are often completely different from individual to individual.
Survival of the fittest, right between your ears, up to this very minute. Amazing. It also gives food to the thought that evolutionary processes are some kind of universal law or process within our universe.
Jan Didden
I have to agree that the fundamental equations used do describe the behavior of tubes, bipolars, and probably fets were developed from statistical analysis. Engineers are usually just given these equations (like Child's law) or the derivation of Gm in bipolars. Fets tend to be a degenerate form of bipolars, unless operated at unrealistically low operating currents when they merge into bipolar Gm behavior with current. In fact, most physical processes seem to behave in a similar way. Too bad that I hate statistics. 
FETs at unrealistically low currents...
Who would ever try that?
Oh, wait......I know......Bill Conrad would. In fact, he built a preamp that way. Some people even bought one. Oy.
Economists love statistics, too.
Jocko
Who would ever try that?
Oh, wait......I know......Bill Conrad would. In fact, he built a preamp that way. Some people even bought one. Oy.
Economists love statistics, too.
Jocko
Re: Self organization and other meanderings
Rodolfo,
You really got my attention with that one. Any further thoughts on this? Offline if you prefer?
Jan Didden
ingrast said:
Rodolfo,
You really got my attention with that one. Any further thoughts on this? Offline if you prefer?
Jan Didden
Re: Re: Self organization and other meanderings
Not really an original idea I guess, but have not devoted time to dig into it so I throw it here in the hopes someone else has read - done something related.
In the cannonical form of feedback control systems of which audio amplifiers are a branch, you have and input that is in this case amplified to obtain an output. This output is not an exact scaled copy of the input because of deviations introduced along the way in the form of amplitude and frequency dependent nonlinearities.
To correct this situation, we sample the output and substract from the input in order to predistort the actual signal to be amplified in opposition to the distortion that will be introduced along the amplifier path.
For this to work we must allways accept the output contains an error, and we basically ignore the nature of the amplifier nonlinearities.
An alternative - unthinkable technologicaly a decade or two back - is to make the feedback path an intelligent and nonlinear one whereby we feed the system with a known signal, sample the output and let the feedback branch adapt its transfer function to effectively null the error.
This could be particularly suitable for mostly digital amplifying chains like the ones that will probably dominate both the portable devices (mp3, CD players) and high end / professional / high power systems featuring fully switching elements up to the output power stage.
Rodolfo
janneman said:
Not really an original idea I guess, but have not devoted time to dig into it so I throw it here in the hopes someone else has read - done something related.
In the cannonical form of feedback control systems of which audio amplifiers are a branch, you have and input that is in this case amplified to obtain an output. This output is not an exact scaled copy of the input because of deviations introduced along the way in the form of amplitude and frequency dependent nonlinearities.
To correct this situation, we sample the output and substract from the input in order to predistort the actual signal to be amplified in opposition to the distortion that will be introduced along the amplifier path.
For this to work we must allways accept the output contains an error, and we basically ignore the nature of the amplifier nonlinearities.
An alternative - unthinkable technologicaly a decade or two back - is to make the feedback path an intelligent and nonlinear one whereby we feed the system with a known signal, sample the output and let the feedback branch adapt its transfer function to effectively null the error.
This could be particularly suitable for mostly digital amplifying chains like the ones that will probably dominate both the portable devices (mp3, CD players) and high end / professional / high power systems featuring fully switching elements up to the output power stage.
Rodolfo
Right.
I have done something that goes in that direction. You know that normally the amp open loop gain Aol is nonlinear, but the feedback network beta is linear. I made a circuit where the amp feedback loop has Aol in it, and the total amp chain has beta in it, no longer Aol. There you have it, a feedback network that follows Aol and thus can be seen as "adapting" to Aol. In theory, Aol non-linearity was completely disappearing from the forward path. Not just getting very small, but getting zero, zilch, nada.
The problem was that it depended on the exact matching of resistor ratios to the gain (x1 in the simplest case) of a small auxiliary amplifier, and that only was good enough at a specific frequency. These are called null-networks (Thanks Ed Cherry for helping me stop dreaming) and have the property that they only work over small freq ranges and are extremely sensitive to mismatches.
Actually it worked great at low freqs with THD reductions of hundreds of dBs (simulated and calculated, no way to measure that).
Jan Didden
I have done something that goes in that direction. You know that normally the amp open loop gain Aol is nonlinear, but the feedback network beta is linear. I made a circuit where the amp feedback loop has Aol in it, and the total amp chain has beta in it, no longer Aol. There you have it, a feedback network that follows Aol and thus can be seen as "adapting" to Aol. In theory, Aol non-linearity was completely disappearing from the forward path. Not just getting very small, but getting zero, zilch, nada.
The problem was that it depended on the exact matching of resistor ratios to the gain (x1 in the simplest case) of a small auxiliary amplifier, and that only was good enough at a specific frequency. These are called null-networks (Thanks Ed Cherry for helping me stop dreaming) and have the property that they only work over small freq ranges and are extremely sensitive to mismatches.
Actually it worked great at low freqs with THD reductions of hundreds of dBs (simulated and calculated, no way to measure that).
Jan Didden
janneman said:
Jan:
Here you highlighted some of the problems I feel can be better addressed with adaptative learning.
You could in principle circumvent the resistor matching using a table lookup which reverses to a sufficiently high resolution the DC transfer characteristic of the amplifier to be corrected. That is, you digitize a DC sweep rail to rail and pass the incoming signal through an inverse function so as to obtain a stright total transfer. This works well at DC or more precisely, at the s plane origins and immediate surroundings.
Being input signals in principle represented by the whole s plane (OK in a general sense), something more than the former approach is required, that is, the possibility to construct an arbitrary C(s) transfer function that when multiplied by the actual A(s) amplifier transfer yields K, that is, perfection. C(s) is simply the reverse of A(s) scaled, I guess it can be better achieved intelligently on the fly than by design, among other things because it can compensate component tolerances, variations and environmental conditions by itself.
Rodolfo
Follow up
Oh, and a word of caution less someone scrambles merrily to build something and gets disappointed by results.
A(s) is a *NONLINEAR* function. Not the usual linear stuff we are used to deal with. C(s) will then be nonlinear obligingly.
It remains to be seen whether C(s) can be generated within practical constraints such as convergence in a finite time with reasonable computational resources.
Rodolfo
Oh, and a word of caution less someone scrambles merrily to build something and gets disappointed by results.
A(s) is a *NONLINEAR* function. Not the usual linear stuff we are used to deal with. C(s) will then be nonlinear obligingly.
It remains to be seen whether C(s) can be generated within practical constraints such as convergence in a finite time with reasonable computational resources.
Rodolfo
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