Introducing John Trevithick, from New Zealand.
Coming from a background in electronics and computing, John has an interest in systems dynamics. Part-time, he is:
Combination of interests centers around the definitions (and confusions) of positive/negative feedback.
Wikipedia:Subpages help section. Draft pages that trial different historical/example/terminology sections:
Edition 3 of The Encyclopedia Britannica, 1792:"He runs into what is termed by logicians a vicious circle."
www.etymonline.com: Inflation: Economics sense from 1844, Monetary sense of "enlargement of prices" ... first recorded 1838 in American English.Steele's "Popular Physics" schoolbook (1888) Ch1: "30. Why can not a man lift himself by pulling up on his boot-straps?"
www.etymonline.com: "chain reaction is from 1916 in physics, specific nuclear physics sense is from 1938; Chain letter recorded from 1892; usually to raise money at first..."
"St. Nicholas" magazine, vol. XXVI, April 1899: "Nine out of every ten givers are reluctant and unwilling, and are coerced into giving through the awful fear of 'breaking the chain,' so that the spirit of charity is woefully absent."
James Joyce, Ulysses, 1922:"There were others who had forced their way to the top from the lowest rung by the aid of their bootstraps."
Kunitz & Haycraft, British Authors of the Nineteenth Century, 1936:"A poet who lifted himself by his own boot-straps from an obscure versifier to the ranks of real poetry."
Jay (1865) [1]
Cole (1866) [2]
Maxwell (1868) [3]
...
Braun (1909)
[4]
Espenschied (1922) [5]
When the two one-way radio channels are merged at their two ends into a regular telephone circuit for connection to the wire network ... then there is a limit in the transmission equivalent which can be given over the radio part of the circuit ... imposed by the tendency of the two one-way channels to form a round-trip circuit by "feeding-back" from one to the other via the voice frequency connecting circuit. If the total amplification around the circuit including the voice-frequency line, exceeds the total losses in the circuit, "singing" will result. Were no line balance provided at the voice frequency terminals, then it would be impossible to operate the circuit at a zero equivalent. By setting up a balancing circuit at each end in the manner illustrated, a transmission loss is, in effect, inserted between the sending and receiving sides of the voice circuit which tends to prevent this sing-around action. : 130
King (1923) [6]
Use of a common grid battery, as shown, introduces a small feed-back from the second stage to the first. This feed-back may be either positive or negative, depending upon the phase relations in the intermediate transformer and may be eliminated by placing a condenser across the grid battery terminals. : 58
Singing, which is one of the most serious troubles in amplifiers, is always due to some form of feed-back. This may be magnetic, electrostatic, or in the form of mechanical vibrations as in an amplifier having a microphone attached to the input and a receiver to the output. ... The coupling which is responsible for feed-back may be difficult to locate, but when found can usually be removed. Both retard coils and transformers may afford an easy method of coupling due to stray fields. If the coupling induces voltages which are in phase with the input voltages, it may cause singing, and if out of phase, the amplification may be seriously reduced. : 63–64
The unequal amplification of various frequencies arises from the presence of resonant characteristics in the circuit. This may take the form of a feed-back which discriminates in favor[sp] of certain frequencies, the feed-back not being pronounced enough to cause singing. A negative feed-back may also occur, causing a loss of efficiency over some particular frequency range. : 66
The "feed back" or regeneration in a set is ... due to the coupling between the grid circuit and the plate circuit of the tubes through the grid-plate capacity...
If the "feed-back" action is positive, ... then the tube voltmeter reading will increase, and in order to bring it back to its former value, the resistance of the loop is increased by an amount R'... If on the other hand the "feed-back" action is negative, the resistance of the loop must be decreased in order to obtain the former value of the tube voltmeter reading.
The "feed-back" amplification K' is defined as the increase (or decrease) of signal voltage due the "feed-back" action between amplifier and its tuned input circuit. [Original emphasis. my note: Total amplification = ordinary amplification K + feedback amplification K']
Regeneration or feed-back is of considerable importance in many applications of vacuum tubes.
However, by building an amplifier whose gain is made deliberately ... higher than necessary ... and then feeding the output back to the input in such a way as to throw away the excess gain, it has been found possible to effect extraordinary improvement in constancy of amplification and freedom from nonlinearity.
As a quantitative measure of the effect of feed-back 1/(1-μβ) will be used and the feed-back referred to as positive feed-back or negative feed-back according as the absolute value of 1/(1-μβ) is greater or less than unity. Positive feed-back increases the gain of the amplifier; negative feed-back reduces it. The term feed-back is not limited merely to those cases where the absolute value of 1/(1-μβ) is other than unity.
Black (1937) [10]
One improvement is in lowered distortion arising in the amplifier. Another improvement is greater constancy of operation, in particular a more nearly constant gain despite variable factors such as ordinarily would influence the gain.
Hendrik_Wade_Bode (1930-1940)
Rosenblueth, Wiener and Bigelow (1943) [11]
All purposeful behavior may be considered to require negative feed-back. If a goal is to be attained, some signals from the goal are necessary at some time to direct the behavior.
Positive feed-back adds to the input signals; it does not correct them. ...the behavior of an object is controlled by the margin of error at which the object stands at a given time with reference to a relatively specific goal. The feed-back is then negative...
[Feedback is] the chain of the transmission and return of information:: 96
Notice that the feedback [in a steam governor] tends to oppose what the system is already doing, and is thus negative.: 97
We do not will the motions of certain muscles, and indeed we generally do not know which muscles are to be moved to accomplish a given task; we will, say, to pick up a cigarette. Our motion is regulated by some measure of the amount by which it has not yet been accomplished. The information fed back to the control center tends to oppose the departure of the controlled from the controlling quantity, but it may depend in widely differnt ways on this departure.: 97
Ashby (1956). [13]
Skinner (1957) [14]
Haus and Adler 1959 [15]
Wilts (1960) [16]
Johnson(1963) [17]
Herold (1977) [18]
Bennett (1979) [19]
Mees (1981) [20]
Ramaprasad (1983) [21]
Sadler (1989) [22]
Senge (1990) [23]
Levine (1992) [24]
Richardson (1995) [25]
Bhattacharyya (2000?) [26]
Mindell (2000) [27]
Sterman (2000) [28]
Carver (2001) [29]
Mindell (2002) [30]
Allison & Hobbs (2006) [31]
Aström & Murray(2008) [32]
Beerei(2009) [33]
Impey(2011) [34]
Alternative definitions of feedback:
The terms positive/negative as applied to feedback have varying usage in different contexts:
Some possible reasons for the above: as a practicality of early control theory, measuring the mechanism was difficult - whereas the results tended to be clear and unambiguous. In psychology, it is the details of the mechanism that attracts much attention, and goal-seeking (*negative) feedback is often assumed. in performance evaluation, the reference value of "good" performance can be hard to pin down, and may differ between the assessor and the assessed - and again goal-seeking feedback* is often assumed.
System analysis of the feedback amplifier diagram. A system requires at least one of {input, process, output}. Looking at the diagram, I can see it as representing:
The overall system {A,B,+} has only one input and one output that cross the system boundaries. Most of the subsystems above have only one input and one output. We could argue that {A} has two outputs, but I don't think that distinction serves any useful purpose here, or it would have involved its own 'splitter' process.
Systems that include process {+} have two inputs. That makes these systems interesting, since this is where some sort of comparison is being made. In terms of semantics, it is important to note which input we mean: without qualification of some sort, I would understand input to mean the arrow leading in from the external environment, and output to mean the arrow that leads out to the external environment.
If we accept for now the idea that negative feedback is always about using a fed-back output to negate an input, it seems that the {+} process is the key point to this definition, and it highlights some of the confusion of terms: one of the inputs to {+} is the fed-back output, and the output from {+} is the modified input in question. It seems that input/output is expressed in terms of the system being controlled, and not in terms of the system doing the controlling. Yet it is the controlling system that defines feedback.
Another confusion is around gain. Black talked about using feedback to 'throw away some of the gain'. Actually the feedback throws away some of the input. The effective gain of the whole system (1) is reduced, but the actual gain of the amplifier component {A} is not changed. Only what it amplifies is changed.
So is it gain control? If we think of the diagram in terms of (3) above, then yes - the gain of the controlled system {A,+} is changed. Otherwise, we say that it is the input to {A} that is being controlled.
Ambiguity of the term "negative" is simply the converse of the above, except for the last definition. Here "negative" tends to mean null or empty; a non-result.
Confusion seems to arise around the use of "positive" to mean "beneficial", "desirable" or "higher", rather than the intended use of "accumulative/increasing". This is distinct from meaning 4, since we are talking about a gap or displacement, an absolute value. Negative feedback also has its confusions - here maybe due to a finer distinction between "reducing" and "negating", as well as the "undesired/harmful" implications. Also distinct from meaning 4 - a movement to close a gap is valid from either "direction".
Are these the same? In the first case, is the wall is stable, or the ladder?
Confusion arises as to whether a parameter influenced by positive feedback becomes stable when it comes up against a limit - like a ladder against a wall. Is this the same as a parameter that resists perturbations due to negative feedback? Does the limit count as negative feedback?
If this refers to the entire loop, it seems a useful definition. I break the loop somewhere arbitrarily, put a signal or input into one end and see what comes out the other. If it is inverted, the loop is "negative". If it is bigger, |gain| > 1. That seems to work. If this refers only to the feedback path, then there are issues... but maybe this only applies in cases where we can assume the forward path has gain=1. What about when we are interested in gain as the thing to be controlled? The (1-AB) formulation? Hmm.
Confusion from Assumptions about positive/negative:
Target-shooting example: where Bob the shooter is practising hitting the bullseye of a target, and being fed back a score based on each group of shots. Bob wants to get as high a score as possible, which means grouping the shots as close to the bullseye as possible. Let's assume Bob is improving.
Freezer-thermostat example: where a freezer is kept below (say) 10°C, not by monitoring output ("coldness" leakage?) but by measuring the internal state (temperature). If temp rises, the compressor is switched on (input increases) to lower it again. This is negative feedback, even though temp_increase = input_increase, because input_increase = temp_decrease. The loop as a whole is self-cancelling.
It seems that the use of "positive/negative" to mean pleasant/unpleasant is considered poor usage across many disciplines. In Reinforcement, which deals with the pleasant/unpleasant aspect, "positive/negative" is used to indicate the presence or absence of a stimulus, not its valence. In Management Theory, several authors are pushing for the Systems view (reinforcing/opposing change) and are openly critical of the valence usage. John_Sterman comes to mind, and maybe Jay_Wright_Forrester? Ramaprasad sort of avoids the issue.
Investigating the idea that all oscillation can be described as "hunting" or corrective overshoot.
Some counter-arguments involve phase-shift, or instability. User:Nigelj's example of a shaft position control system is very interesting. "The sense of an amplifier had been wired reversed - causing very strong positive feedback instead of the expected negative FB. ...[This] made the system oscillate violently"--Nigelj 22:58, 8 March 2012 (UTC)
Some points to ponder:
In the sense that PF can reinforce a very small existing oscillation until it is noticeable, we could say that PF "gives rise" to osc. Is that "causing" osc?
Looking a bit closer at what is meant by "causing": PF can be a contributory cause of the oscillation. What about being a necessary or sufficient cause? Necessary seems unlikely - oscillation doesn't necessarily imply PF (e.g., pendulums, hunting, etc). Sufficient? Well, no - PF doesn't guarantee oscillations.
Is there possible confusion between delayed NF and PF? Since both can be said to reinforce a value... Momentum pushes a pendulum past the equilibrium point. BUT not through feedback - a body in motion tends to stay in motion.
A possible counter-argument comes from the LC circuit. The circle of cause-and-effect seems to consist of 4 negative/inverting connections. Which means the net circuit is positive!
Aim is to (A) improve wikipedia article(s) related to oscillation. Needs are to (B) avoid ambiguous or unclear statements, and (C) include common & important phenomena.
The Core Conflict Cloud is an Evaporating Cloud that emerges from analysis of a Current Reality Tree (CRT), one of the Thinking Processes. The CRT provides a way for analyzing many system or organizational problems at once, treating them as symptoms of a single core problem. If an easy solution to such a core problem has not already been implemented, it is likely there is some conflict in the organization that is blocking implementation. [35]: 165 The role of the Core Conflict Cloud is to address the inherent conflict that prevents sorting the core conflict out. [36]: 710
"refered to by some as the Conflict Resolution Diagram (CRD)"(Handbook page635, refering to: [44])
he general process for applying an EC to problem solving is described by Cohen (2010) as follows:
{{
cite book}}
: CS1 maint: location missing publisher (
link)
[4]
Introducing John Trevithick, from New Zealand.
Coming from a background in electronics and computing, John has an interest in systems dynamics. Part-time, he is:
Combination of interests centers around the definitions (and confusions) of positive/negative feedback.
Wikipedia:Subpages help section. Draft pages that trial different historical/example/terminology sections:
Edition 3 of The Encyclopedia Britannica, 1792:"He runs into what is termed by logicians a vicious circle."
www.etymonline.com: Inflation: Economics sense from 1844, Monetary sense of "enlargement of prices" ... first recorded 1838 in American English.Steele's "Popular Physics" schoolbook (1888) Ch1: "30. Why can not a man lift himself by pulling up on his boot-straps?"
www.etymonline.com: "chain reaction is from 1916 in physics, specific nuclear physics sense is from 1938; Chain letter recorded from 1892; usually to raise money at first..."
"St. Nicholas" magazine, vol. XXVI, April 1899: "Nine out of every ten givers are reluctant and unwilling, and are coerced into giving through the awful fear of 'breaking the chain,' so that the spirit of charity is woefully absent."
James Joyce, Ulysses, 1922:"There were others who had forced their way to the top from the lowest rung by the aid of their bootstraps."
Kunitz & Haycraft, British Authors of the Nineteenth Century, 1936:"A poet who lifted himself by his own boot-straps from an obscure versifier to the ranks of real poetry."
Jay (1865) [1]
Cole (1866) [2]
Maxwell (1868) [3]
...
Braun (1909)
[4]
Espenschied (1922) [5]
When the two one-way radio channels are merged at their two ends into a regular telephone circuit for connection to the wire network ... then there is a limit in the transmission equivalent which can be given over the radio part of the circuit ... imposed by the tendency of the two one-way channels to form a round-trip circuit by "feeding-back" from one to the other via the voice frequency connecting circuit. If the total amplification around the circuit including the voice-frequency line, exceeds the total losses in the circuit, "singing" will result. Were no line balance provided at the voice frequency terminals, then it would be impossible to operate the circuit at a zero equivalent. By setting up a balancing circuit at each end in the manner illustrated, a transmission loss is, in effect, inserted between the sending and receiving sides of the voice circuit which tends to prevent this sing-around action. : 130
King (1923) [6]
Use of a common grid battery, as shown, introduces a small feed-back from the second stage to the first. This feed-back may be either positive or negative, depending upon the phase relations in the intermediate transformer and may be eliminated by placing a condenser across the grid battery terminals. : 58
Singing, which is one of the most serious troubles in amplifiers, is always due to some form of feed-back. This may be magnetic, electrostatic, or in the form of mechanical vibrations as in an amplifier having a microphone attached to the input and a receiver to the output. ... The coupling which is responsible for feed-back may be difficult to locate, but when found can usually be removed. Both retard coils and transformers may afford an easy method of coupling due to stray fields. If the coupling induces voltages which are in phase with the input voltages, it may cause singing, and if out of phase, the amplification may be seriously reduced. : 63–64
The unequal amplification of various frequencies arises from the presence of resonant characteristics in the circuit. This may take the form of a feed-back which discriminates in favor[sp] of certain frequencies, the feed-back not being pronounced enough to cause singing. A negative feed-back may also occur, causing a loss of efficiency over some particular frequency range. : 66
The "feed back" or regeneration in a set is ... due to the coupling between the grid circuit and the plate circuit of the tubes through the grid-plate capacity...
If the "feed-back" action is positive, ... then the tube voltmeter reading will increase, and in order to bring it back to its former value, the resistance of the loop is increased by an amount R'... If on the other hand the "feed-back" action is negative, the resistance of the loop must be decreased in order to obtain the former value of the tube voltmeter reading.
The "feed-back" amplification K' is defined as the increase (or decrease) of signal voltage due the "feed-back" action between amplifier and its tuned input circuit. [Original emphasis. my note: Total amplification = ordinary amplification K + feedback amplification K']
Regeneration or feed-back is of considerable importance in many applications of vacuum tubes.
However, by building an amplifier whose gain is made deliberately ... higher than necessary ... and then feeding the output back to the input in such a way as to throw away the excess gain, it has been found possible to effect extraordinary improvement in constancy of amplification and freedom from nonlinearity.
As a quantitative measure of the effect of feed-back 1/(1-μβ) will be used and the feed-back referred to as positive feed-back or negative feed-back according as the absolute value of 1/(1-μβ) is greater or less than unity. Positive feed-back increases the gain of the amplifier; negative feed-back reduces it. The term feed-back is not limited merely to those cases where the absolute value of 1/(1-μβ) is other than unity.
Black (1937) [10]
One improvement is in lowered distortion arising in the amplifier. Another improvement is greater constancy of operation, in particular a more nearly constant gain despite variable factors such as ordinarily would influence the gain.
Hendrik_Wade_Bode (1930-1940)
Rosenblueth, Wiener and Bigelow (1943) [11]
All purposeful behavior may be considered to require negative feed-back. If a goal is to be attained, some signals from the goal are necessary at some time to direct the behavior.
Positive feed-back adds to the input signals; it does not correct them. ...the behavior of an object is controlled by the margin of error at which the object stands at a given time with reference to a relatively specific goal. The feed-back is then negative...
[Feedback is] the chain of the transmission and return of information:: 96
Notice that the feedback [in a steam governor] tends to oppose what the system is already doing, and is thus negative.: 97
We do not will the motions of certain muscles, and indeed we generally do not know which muscles are to be moved to accomplish a given task; we will, say, to pick up a cigarette. Our motion is regulated by some measure of the amount by which it has not yet been accomplished. The information fed back to the control center tends to oppose the departure of the controlled from the controlling quantity, but it may depend in widely differnt ways on this departure.: 97
Ashby (1956). [13]
Skinner (1957) [14]
Haus and Adler 1959 [15]
Wilts (1960) [16]
Johnson(1963) [17]
Herold (1977) [18]
Bennett (1979) [19]
Mees (1981) [20]
Ramaprasad (1983) [21]
Sadler (1989) [22]
Senge (1990) [23]
Levine (1992) [24]
Richardson (1995) [25]
Bhattacharyya (2000?) [26]
Mindell (2000) [27]
Sterman (2000) [28]
Carver (2001) [29]
Mindell (2002) [30]
Allison & Hobbs (2006) [31]
Aström & Murray(2008) [32]
Beerei(2009) [33]
Impey(2011) [34]
Alternative definitions of feedback:
The terms positive/negative as applied to feedback have varying usage in different contexts:
Some possible reasons for the above: as a practicality of early control theory, measuring the mechanism was difficult - whereas the results tended to be clear and unambiguous. In psychology, it is the details of the mechanism that attracts much attention, and goal-seeking (*negative) feedback is often assumed. in performance evaluation, the reference value of "good" performance can be hard to pin down, and may differ between the assessor and the assessed - and again goal-seeking feedback* is often assumed.
System analysis of the feedback amplifier diagram. A system requires at least one of {input, process, output}. Looking at the diagram, I can see it as representing:
The overall system {A,B,+} has only one input and one output that cross the system boundaries. Most of the subsystems above have only one input and one output. We could argue that {A} has two outputs, but I don't think that distinction serves any useful purpose here, or it would have involved its own 'splitter' process.
Systems that include process {+} have two inputs. That makes these systems interesting, since this is where some sort of comparison is being made. In terms of semantics, it is important to note which input we mean: without qualification of some sort, I would understand input to mean the arrow leading in from the external environment, and output to mean the arrow that leads out to the external environment.
If we accept for now the idea that negative feedback is always about using a fed-back output to negate an input, it seems that the {+} process is the key point to this definition, and it highlights some of the confusion of terms: one of the inputs to {+} is the fed-back output, and the output from {+} is the modified input in question. It seems that input/output is expressed in terms of the system being controlled, and not in terms of the system doing the controlling. Yet it is the controlling system that defines feedback.
Another confusion is around gain. Black talked about using feedback to 'throw away some of the gain'. Actually the feedback throws away some of the input. The effective gain of the whole system (1) is reduced, but the actual gain of the amplifier component {A} is not changed. Only what it amplifies is changed.
So is it gain control? If we think of the diagram in terms of (3) above, then yes - the gain of the controlled system {A,+} is changed. Otherwise, we say that it is the input to {A} that is being controlled.
Ambiguity of the term "negative" is simply the converse of the above, except for the last definition. Here "negative" tends to mean null or empty; a non-result.
Confusion seems to arise around the use of "positive" to mean "beneficial", "desirable" or "higher", rather than the intended use of "accumulative/increasing". This is distinct from meaning 4, since we are talking about a gap or displacement, an absolute value. Negative feedback also has its confusions - here maybe due to a finer distinction between "reducing" and "negating", as well as the "undesired/harmful" implications. Also distinct from meaning 4 - a movement to close a gap is valid from either "direction".
Are these the same? In the first case, is the wall is stable, or the ladder?
Confusion arises as to whether a parameter influenced by positive feedback becomes stable when it comes up against a limit - like a ladder against a wall. Is this the same as a parameter that resists perturbations due to negative feedback? Does the limit count as negative feedback?
If this refers to the entire loop, it seems a useful definition. I break the loop somewhere arbitrarily, put a signal or input into one end and see what comes out the other. If it is inverted, the loop is "negative". If it is bigger, |gain| > 1. That seems to work. If this refers only to the feedback path, then there are issues... but maybe this only applies in cases where we can assume the forward path has gain=1. What about when we are interested in gain as the thing to be controlled? The (1-AB) formulation? Hmm.
Confusion from Assumptions about positive/negative:
Target-shooting example: where Bob the shooter is practising hitting the bullseye of a target, and being fed back a score based on each group of shots. Bob wants to get as high a score as possible, which means grouping the shots as close to the bullseye as possible. Let's assume Bob is improving.
Freezer-thermostat example: where a freezer is kept below (say) 10°C, not by monitoring output ("coldness" leakage?) but by measuring the internal state (temperature). If temp rises, the compressor is switched on (input increases) to lower it again. This is negative feedback, even though temp_increase = input_increase, because input_increase = temp_decrease. The loop as a whole is self-cancelling.
It seems that the use of "positive/negative" to mean pleasant/unpleasant is considered poor usage across many disciplines. In Reinforcement, which deals with the pleasant/unpleasant aspect, "positive/negative" is used to indicate the presence or absence of a stimulus, not its valence. In Management Theory, several authors are pushing for the Systems view (reinforcing/opposing change) and are openly critical of the valence usage. John_Sterman comes to mind, and maybe Jay_Wright_Forrester? Ramaprasad sort of avoids the issue.
Investigating the idea that all oscillation can be described as "hunting" or corrective overshoot.
Some counter-arguments involve phase-shift, or instability. User:Nigelj's example of a shaft position control system is very interesting. "The sense of an amplifier had been wired reversed - causing very strong positive feedback instead of the expected negative FB. ...[This] made the system oscillate violently"--Nigelj 22:58, 8 March 2012 (UTC)
Some points to ponder:
In the sense that PF can reinforce a very small existing oscillation until it is noticeable, we could say that PF "gives rise" to osc. Is that "causing" osc?
Looking a bit closer at what is meant by "causing": PF can be a contributory cause of the oscillation. What about being a necessary or sufficient cause? Necessary seems unlikely - oscillation doesn't necessarily imply PF (e.g., pendulums, hunting, etc). Sufficient? Well, no - PF doesn't guarantee oscillations.
Is there possible confusion between delayed NF and PF? Since both can be said to reinforce a value... Momentum pushes a pendulum past the equilibrium point. BUT not through feedback - a body in motion tends to stay in motion.
A possible counter-argument comes from the LC circuit. The circle of cause-and-effect seems to consist of 4 negative/inverting connections. Which means the net circuit is positive!
Aim is to (A) improve wikipedia article(s) related to oscillation. Needs are to (B) avoid ambiguous or unclear statements, and (C) include common & important phenomena.
The Core Conflict Cloud is an Evaporating Cloud that emerges from analysis of a Current Reality Tree (CRT), one of the Thinking Processes. The CRT provides a way for analyzing many system or organizational problems at once, treating them as symptoms of a single core problem. If an easy solution to such a core problem has not already been implemented, it is likely there is some conflict in the organization that is blocking implementation. [35]: 165 The role of the Core Conflict Cloud is to address the inherent conflict that prevents sorting the core conflict out. [36]: 710
"refered to by some as the Conflict Resolution Diagram (CRD)"(Handbook page635, refering to: [44])
he general process for applying an EC to problem solving is described by Cohen (2010) as follows:
{{
cite book}}
: CS1 maint: location missing publisher (
link)
[4]