Talk:Memristor/Archive 2

656:" — emphasis added), and also previously ("Incidently I am a graduate student and have actually published papers on this subject"). Please do try to read what the other person is writing, and avoid bickering. The goal here is to try and improve the article. That said, I'm dubious of hyperbolic statements, e.g. that reading papers on a topic for a year earns one "expertise" — this seems to negate the role that research (especially the hands-on kind) plays in forming understanding of a complex subject that is nowhere near fully understood. I for one am very interested in reading about the latest research into the relationship between memristors, neurons, and artificial neural networks, whatever that might be. Sadly, this article has been tagged for updating and improvement, but the last debate on this discussion topic thread seems to have ended back in January 2009. I have no horse in this race, but if one of the other contributors to this thread who's done work in the field would care to contribute some sourced information to the article, I think that would be a great start. (I noticed one update from a 2011 IEEE Computer article regarding neural network applications, so it seems there's been some activity, but I'm really interested to see information included about memristors as compared to biological neurons.) 424:

seems like an important ingredient to AI and Greg Snider of HP Labs published an article in 2007 entitled "Self-organized computation with unreliable, memristive nanodevices" noting the potential for memristor circuit architectures for enhanced pattern recognition. Another article entitled "Memristive model of amoeba's learning" by Yu V. Pershin, S. La Fontaine, and M. Di Ventra identified memristive behavior in amoeba's learning and, as already pointed out, Chua and Kang's 1976 article note the connection between memristive systems and the Hodgkin-Huxley neuron model. At the 2008 Memristor and Memristive Systems symposium the connection between neurons and memristors was also discussed by Greg Snider. Thus there is verifiable evidence in the literature that there is a connection between neurons and memristors and, while it may be too early to tell how important this connection will turn out to be, the connection itself is what "Mlvlvr" originally questioned.

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humility in your postings rather than try to come off as an expert. From a study of the literature there is actually a stronger connection between memristors and neurons than between memristors and neural networks. Neural networks are more closely connected to the crossbar architecture which Greg Snider of HP Labs was looking at to implement molecular neural networks a few years back based on rotaxane switches. Greg Snider's research has moved on to the examination of memristors for neuromorphic architectures which go beyond the limitations of neural network architectures. If you are seriously interested in memristors I would consider educating yourself a little more in the literature. UC Berkeley has a series of videos covering the Memristor Symposium on YouTube and I would strongly recommend watching them, particularly the video covering Snider's work on memristive neuromorphic circuit architectures.

2933:) and have got a good intuitive notion about the essence of the memristor idea. It is extremely interesting for me to unriddle the mystery of the basic Chua's postulates about memristance not giving people peace as many as forty years. First, I will show what the problems with this formulation are; then, I will give some recommendations how to solve them. I would like to share my insights with you in a bit nontraditional emphatic manner by tracing back the evolution of Chua's idea and trying to guess how he was thinking when propounding his memristor theory. Of course, only the very Chua can say if the hypothetic story below is true. For concreteness, let's consider a current- (charge-) driven memristor although it can be voltage- (flux-) driven as well. Also, let's consider an integrating memristor although it can be differentiating or some else as well. 297:

mesh of them was neural, I learned a few things. One of them is that over the decade of enthusiasm beginning (in 1982) with Hopfield and Tank's seminal work, everyone in the (large) field learned that an artificial neural network is a mathematical object relevant to statistics, but not to neuroscience. Why then are neurons so prominent in this article and articles by others? No doubt it is because Stan Williams' and HP's documentation on memristors includes the topic, and maybe the memristor's theoretical inventor, Leon Chua, mentions them, too. In this sense, memristors' neuralness is a meme, but memes can mislead. I think these references should be removed, but I am new to the community and would like some input from other users.

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current giving dV/dI=R. Similar statements apply for C and L. The memresistance of a charge-controlled memristor, on the other hand, is defined as M = dΦ/dQ, and MUST depend on Q, to make it different from a regular resistor. If M did not depend on Q, then the memristor would just be a regular resistor, with a constant resistance that does not depend on the current or charge. Memresistance is not analogous to resistance, capacitance, and inductance. If you want to compare to resistance, capacitance, and inductance, then you must compare to Φ/Q, which is not the same as M. Φ/Q = ($ MdQ)/Q, the ratio you want is the integral of M over Q, divided by Q. I don't recall Chua giving a name to this ratio in his original paper.

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more generic dynamic systems. For example, there are dynamic circuit elements such as the thermistor which was identified in Chua and Kang's 1976 paper as a type of mem-resistive system in which the memory effect is volatile. The transient thermistor model plays a role in phase change memory resistor models when coupled to crystallization rate equations. There are also other mem-resistive systems models under development for different types of memory resistors such as ion doped chalcogenides which diverge significantly from HP's TiO2 memristor model and should not be lumped in with HP's memristor. There are also "mem-transistor" dynamic circuit models which I developed for application to modeling of the Widrow-Hoff

2844:: the resistor creates opposing voltage drop across itself while the capacitor and the inductor create opposing voltage. Resistors do this by throwing out (dissipating) energy while capacitors and inductors do it by taking energy from the excitation source, accumulating it into itself and setting it against the input source. In the first case there is a voltage drop while in the second case there is a voltage. This means that we can emulate these elements by other elements having the same but opposing voltage (having contrary to the excitation voltage polarity when travelling along the loop). So, we can emulate these elements by replacing them with some other elements producing the same voltage. 492:"We," Mlvlr and I, are both saying that H-H was state of the art long long ago but neuroscience has moved on. I'm not going to do research for you. The wiki attitude that a few Google searches makes one an expert is unfortunate, but I don't expect to sway you. Mlvlr claims to have been a researcher in the field for years, and I studied it for about a year in high school, mostly reading edited anthologies of influential papers. I think you still should re-read his post again. Let me repeat: simple artificial neural networks, while useful, are not the best analogues of neurons. The word "neuron" should not be used alone to describe an element of an artificial neural network. 741:

ion-beam-assisted electron beam deposition" (Applied Physics Letters, Vol. 78, No 7). I exchanged some E-mails with Prof. Chua about this topic after the symposium and the possibility exists for memristive system analogies to both capacitors (memacitors) and inductors (memductors) so it may possibly be said that there are six rather than four fundamental circuit elements. Alternatively, it could be more appropriate to say that there are still three basic circuit elements and that the memristor, memacitor, and memductor are more generalized versions of the three basic elements which exhibit the pinched hysteresis Lissoujous curves characteristic of memristive systems.

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First, we will supply a variable linear resistor (a rheostat) with constant current and will move uniformly the slider from zero to maximum resistance to obtain a memristor acting as a "resistive capacitor". Then, we will supply the variable resistor with constant voltage and will move irregularly the slider from maximum to zero resistance to obtain a memristor acting as a "resistive inductor". I intend to realize this computerized experiment by connecting the variable resistor in the place of the resistors R1 and R2 of an op-amp inverting amplifier so that the rest of the circuit acts as a perfect

3387:...not so, we can read the sources. A lot of this is clarified in Di Ventra et al. 2009, and apparently avoiding directly contradicting Chua at the same time. I have obtained this paper and I think you will probably like what it says, but I don't have time to go through it in detail right now. In the meantime, please don't make stuff up yourself to put in the article. You must surely know by now that the Knowledge way is to write from the sources. I strongly encourage you to read sources, then write; not to write, and then hope for a source to back it up. 794:

equivalent resistance of the memristor is equal to the charge that has passed through the device. I think the most confusing part is distinguish the memristor with RRAM. RRAM shows nonvolatile attribute which the memristor also has. However, the intrinsic resistive switching mechanisms are different. There are lots of technical papers about the switching mechanisms, most conceivable proposals include: ionic transportation, thermal effect, electrochemical effect. The memristor fabricated by Strokov et al. was mainly based on ionic transportation effect.

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model how were electrical engineers going to build systems based on these devices. Meanwhile papers were being published by circuit theorists based on the original charge vs. magnetic flux linkage concept of Chua even though this does not describe real memory resistive effects due to non-linear ionic mobility among other considerations. At this time it seemed to me that many of the material scientists who published on the "memristor" only had 2nd-hand knowledge of the theory while the circuit theorists did not understand the material considerations.

3218:"? And that this term should not be used in the literal sense here as it would duplicate the genuine magnetic variable? It can be used here only figuratively, as a metaphor; we should say "this variable is similar to magnetic flux" but not "this variable is a magnetic flux"... I will try to persuade you of this obvious truth by a simple example. Imagine an inductor driven by a constant voltage source. In this arrangement, the current through the inductor is proportional to the time integral of the voltage across it (i.e., to Chua's "magnetic flux Φ 681:

hardware. The issue is the ratio of neuronal units (neurons in wetware) to inter-unit connections (synapses) and their relative physical size. In wetware (which we must all admit does DR rather well), the synapes-to-neuron ratio is typically ≈ 1000:1 or more. Wetware synapses are tiny compared to wetware neurons so it all fits together well. However, in pre-memristor analogue CMOS hardware, the silicon area of each "synapse" has typically been as large - or often much larger - as the "neuron" making high density networks impractical.

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that this material is necessary to the article: the first part of the Theory section now says little more than various ways of restating Ohm's law for the case when resistance is a function of the charge that has passed through the device, and the second part of the Theory section is, at best, unclear, and tends to be misleading (since memristors are not magnetic devices). I didn't delete it, however, since I'm still hoping that somebody who understands the value of this particular formalism will come by and clarify the discussion.

2763:(a geared motor driving a rheostat connected in series with it) is even more expressive. If we change slowly enough the input current, the motor will manage to move the rheostat slider and the resistance will change depending on the current and time; the "memristor" will act as an electromechanical integrator (a "resistive capacitor"). If we change sharply (or wiggle) the current, the motor will not react to our intervention at all. The resistance will stay constant and the "memristor" will be just a humble ohmic resistor. 2544:). So, maybe it is better to separate the memristor as a particular element staying between resistors and capacitors (inductors) and to say that it is a mixed element combining the energy properties of resistors and time properties of reactive elements? Then passive elements will be four (resistor, memristor, capacitor and inductor) and even five (resistor, memristor acting as a capacitor, memristor acting as an inductor, capacitor and inductor)? Or, we have to place them into three groups in respect to energy and time: 474:

Also unless you can back up your opinions with verifiable evidence please refrain from making blanket statements about neuroscience or artificial intelligence and do not refer to your opinions in the plural ("We"). You are not the representative for all the neuroscientists and computer scientists of the world. Amoebas do not have neurons per se but they have been found to exhibit spatiotemporal oscillatory behavior which has been studied for neurocomputing (do a search for "amoeba-based neurocomputing" in GoogleScholar.

1174:- There needs to be a simpler, clearer description in words of what a memristor is, does and what it is used for. I don't see anything here that is logically so complex it can't be rendered in plain english. These sentences in the opening paragraph are most awkward, "There is no such thing as a generic memristor. Instead, each device implements a particular function. A linear time-invariant memristor is simply a conventional resistor." What is anyone meant to make of these unexplained facts if they just came here? 2528:). From this viewpoint, memristors, memcapacitors and meminductors are only varieties of the three basic passive elements; so, they are placed in an additional column of the table (memristor is a kind of a resistor as it dissipates energy; memcapacitor is a kind of a capacitor as it stores electric energy; meminductor is a kind of an inductor as it stores magnetic energy). In this way, I have refuted Chua's assertion that the memristor is fourth, the memcapacitor - fifth and the meminductor - sixth circuit element. 1273:

Kang) and which may be understood without a knowledge of calculus or differential equations. Incidently the equations used in this wikipedia article are not really the best. See my knol "An Introduction to Memimpedance and Memadmittance Systems Analysis" for a more complete analysis which integrates the memcapacitive with the memristor concept to form a more general mathematical foundation to explain the memory effects found in thin films due to oxygen vacancy drift and filament formation.

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represent a real device at the time. Chua and Kang extended the memristor concept to cover a larger class of memory circuits in 1976 and this is what HP's memristor basically represents. Several example of materials having memristive characteristics have been known for over 50 years in the form of both electrochemical and solid state thin film materials. I have some online articles which provides some additional info. Google "Widrow memistor" or go to the following link:

2426:(which is already cited in the article) which categorises memristors, memcapacitors and meminductors. By the way, the descripion of memresistors in this paper seems to be at odds with his description in the "fourth circuit element" paper, and more along the lines being proposed by Circuit dreamer. There would seem to be two distinct uses of the term memristor which we should make more clear than it currently is in the article. Perhaps there should even be two articles. 567:"Neuromorphic hardware has long been hindered by the difficulty of implementing “synapses” efficiently—they simply require too much area. Dynamical nanodevices, each no larger than 30 nm X 30 nm, can supply a multiplicative transfer function and implement correlational learning laws. Using conventional CMOS for neurons, nanowires for axons and dendrites, and memristive nanodevices for synapses, I'll present architecture for implementing fundamental cortical circuits." 1328:"Indeed, Chua’s original idea was that the resistance of a memristor would depend upon how much charge has gone through the device. In other words, you can flow the charge in one direction and the resistance will increase. If you push the charge in the opposite direction it will decrease. Put simply, the resistance of the devices at any point in time is a function of history of the device –- or how much charge went through it either forwards or backwards." 1465:

uncharged. This needs to be clarified "the integral of current that has flowed through the device," or "the total charge which has flowed through the device." I would personally delete this "theory" section completely, and rewrite it without ever mentioning magnetic flux. However, since apparently somebody thought it was appropriate to start here, so even though I don't know why they though it was appropriate, I am hesitant to delete their work.

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signal processing and I was invited to speak at the 1st Memristor and Memristive Systems Symposium at UC Berkeley in 2008. I was somewhat surprised that the model they were using actually diverged from the original charge vs. magnetic flux linkage definition of Chua and that Stan Williams group was using a more generic memristive systems model. At the time this did not bother me too much and I was simply glad to have been invited to participate.

1837:, which you are) and it is not now clear over what surface you are defining flux. I don't know what the phrase "flux between the two terminals" means. The definition doesn't seem to have any meaning for a resistor, the case M(q)=constant. I put the "clarification needed" tag back on; but this is only the tip of the problems with the explanation; it needs to be thought out with the objective "how can this be clearly explained to a beginner?" 31: 1405:

does not disqualify it from conceptual meaningfulness. If some of the literature describes hypothetical power generating memristors (or even attempts to simulate them with power sources) then that restriction can be pushed into the but-in-the-real-world section, further cleaning up the theory area. If there's a solid theoretical basis for why memristive theory cannot tolerate power generation, it needs to be said.

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lacking any methodical study when I am the only one who is backing up my position with verifiable evidence and you have only provided your unverified opinions (Incidently I am a graduate student and have actually published papers on this subject). Below is the abstract from Greg Snider of HP Labs describing his neuromorphic architecture in which memristive nanodevices serve as neural synapses available at

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generic term which would create an artificial advantage for HP relative to competitors working on RRAM, CBRAM, and phase change memory. It is possible that one day in the future "memristor" might become a generic term but this should be based on market acceptance not because of a wikipedia article. It is premature to assume that this will be the case since no RRAM is available on the market yet.

1476:, the equivalent of nonlinear resistors) in which the memristance is a more complicated function of the history of the device. Chua moves very quickly to generalize the idea to nonlinear cases, but it is, I think, useful to start by just defining the simple memristor. (Chua apparently considers a diode to be just a nonlinear form of a resistor. ) So I tried to make this more explicit. 1245:, which is not short at all. The knol link (Programmable Electronics using Memristor Crossbars) doesn't attempt to define the memristor at all aside from as a device with a Lissajous I-V graph, and does not address a lay audience as it assumes knowledge of signal processing. Note that hysteresis is not a property of a pure memristor, but defines when the device 276:

some aspects of memristive metal oxide systems since the total volume is fixed and it is the distribution of oxygen vacancies (expressed in terms of charge) between different discrete regions that determines the resistance state. To avoid confusion in the future when you state that something is being varied you should specify if it is time or position.

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done in the 1960's by Argall "Switching Phenomena in Titanium Oxide Thin Films" and HP's memristor does not actually follow the original charge vs magnetic flux definition of Chua. A few weeks after ISCAS a representative from IEEE e-mailed my advisor at George Mason University and told him that it was bad for my reputation to give this presentation.

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memristor suggesting that any type of generic memristive system should now be referred to as a memristor. I had a little problem with this and noted to this person that I believed it would cause confusion with other forms of memory resistance materials being developed for Resistive RAM by other companies but I was not in a position to do anything.

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memory devices? Are there any that clearly state that the HP device does not conform to Chua's definition? Are there any that conclude that HP is using the memristor name as a marketing gimic? Can Chua's definition be said to be the mainstream definition - from what you have said above this appears to be rapidly becoming not the case.

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voltage-driven rheostat (I even planned to make a computer drive a digitally-controlled resistor). Then I did not know that we together (I and the humble rheostat:) actually emulated the Chua's memristor; "we" acted as a memristor:) I came to know about it a few days ago when Blm19732008 directed my attention to Pershin & Ventra's

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definition of the memristor and the term memristor is gradually being turned into a generic PR term so that HP can take control of the Resistive RAM market without consideration of whether it is truly justified. This is to the benefit of HP and to the disadvantage of HP's competitors and should be avoided.

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R doesn't have to be a constant. Even in a regular resistor, R changes depending on the voltage (or current), and only remains approximately constant within small intervals. You can write R(I) = V(I)/I or R(V) = V/I(V) to emphasize that R may depend on I or V. And for M, you may write M(Q) or M(Φ)

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You cannot post an uncited diatribe on the talk page and then start amending the article to comply with it over references in the article. I have reverted most of what you put in (I tried to undo specific edits but you had made too many changes to allow for this). As I said in the edit summary, the

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and the stray inductance inherent for every electrical element including resistor. The rest of them, relying on common sense and realizing that there was nothing magnetic here and the stray inductance is unrelated, began looking for some way of justifying the misleading denoting (to explain that, for

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idea in the late 60's when I (a schoolboy) wanted to make such an "integrating transistor" by bare pencil graphite. I remember also how in the middle 80's I tried to present to my students in the laboratory the time behavior of a capacitor and inductor by moving uniformly the slider of a current- and

2124:

The purpose of this page is to discuss improvements to the article. To put this analysis into the article we are obliged to reference it to published sources. Are there published papers you can point us to which make a clear distinction between charge/magnetic flux definition of memristor and other

2096:

Over time I began to notice an increase in scientific publications describing different types of materials as "memristors" without providing a proper dynamic systems model in accordance with the definition of memristive systems developed by Chua and Kang. This bothered me a lot because without such a

1873:

Looking at the first two sentences of the section as now written, it says "The memristance can be written as (equation). It can be inferred from this that memristance is simply charge-dependent resistance." ***No, it can't.*** It is now extremely confusing and off-putting right at the outset, because

1427:

Regarding the more general idea beyond magnetic flux this is usually associated with Chua and Kang's 1976 paper on memristive systems which used a dynamic systems definition rather then the "fourth fundamental circuit element" memristor definition. In reality most real materials exhibiting memristive

1393:

If that's the actual state of things, fine, but if you actually want to make the concept of a memristor accessible, an example is merited, and that means choosing an example M() so that a nice illustration or animation can be produced, even if no claims are made that it represents an "ideal" device.

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It is a good, lay, description of a memristor. One reason the lead isn't more like that right now is that the article was bombarded by cranks in its early development, who insisted the situation was more complicated than that and that they had some other math. Please feel free to add that, if you can

1139:

The memistor is a three electrode device. It is really a liquid state device. It uses electroplating to change resistance between two of its electrodes. Electroplating is caused by current flowing between the third electrode and the other two. The amount of electroplated metal depends on the integral

1074:

Horace Tharp Mann working for the National Security Agency and TRW makes reference to "The Persistor" in a 1966 report on associative memory. I have not been able to find any more about the Persistor, but the name sure sounds relevant to memistor. I found this as a result of investigating H.T. Mann

1027:

In the Widrow / Hoff patent, #3,222,654, devices in figures 1 through 15, the value of resistance is read to determine what value was stored. Figure 19 is a memory element in which the value of capacitance is electrically varied and stored. Figure 20 uses an alternating magnetic field from one coil

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However the link between electric charge and magnetic flux is only a more specific case of the definition given by Chua. In fact his definition was more general. More specifically, his definition first defines how the memristor's voltage depends on current and a "state variable". The "state variable"

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But to answer Mlvlvr's question, "Why then are neurons so prominent in this article and articles by others?", it is because the lack of nano-scale nonvolatile analogue memory has been just about the single biggest impediment to building practical large-scale distributed representation (DR) systems in

610:

Well if you think your admittedly high-school level knowledge is better than someone who has studied this on the graduate level and has published on the topic more power to you. There is a distinction between neural networks and neuromorphic systems. Memristors have not been applied to the former but

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Sign like this: ~~~~ . It sounds like you can add your expertise to the article, by drawing a distinction between a neuron (the complex physical object) and a neural network (the "learning graph"). Removing info is often considered inflammatory, but here "modeling the fire of neurons" looks certainly

3538:

Capacitance is C = Q/V, not dQ/dV, Inductance is L=Φ/I, not dΦ/dI, Resistance is R=V/I, not dV/dI. dV/dI has a name and is called differential resistance, which is not the same as resistance. Only when the resistance does not depend on the current, can we solve for V and take the derivative over the

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phenomenon like nonlinear resistance. This means that there is no matter if we drive a hysteretic element by slow (DC) or rapidly (AC) changing input quantity; it will show different forward/backward paths (what is the definition of hysteresis) of its IV curve in both the cases. This is not true for

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It is just superb! You have guessed right: I do not simply like it; I love it since it says what I would say! I only regret that I did not read it carefully a few weeks ago when Blm19732008 kindly directed my attention to it (sorry!) IMO this article is our salvation from the vicious circle where we

3300:

Yes, and this does not come under the heading of "obvious truth" anyway, at least to most mere mortals. Chua definitely speaks of magnetic flux in his original paper, and appears not to mean simply the time integral of voltage. It is not clear that the devices with V/I constitutive relations, such

2829:

It is worth to show the remarkable property of memristor to mimic (emulate, simulate) basic passive electrical elements (a resistor, capacitor and inductor) since it is convenient, for some reasons, to replace them by their circuit equivalents (a gyrator, multiplier, memristor...) It is important to

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device. For example, in the case of an integrating memristor, if we wiggle rapidly the input quantity (AC input signal), the memristor does not change its resistance; so it behaves as a linear (ordinary, ohmic, constant, steady) resistor. If we change slowly the input quantity, the memristor changes

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So one paper is all that is necessary to completely re-write a wikipedia article? I don't agree with Chua's assertion; although I do sympathize with his need to publish. He is considering a second order effect, hysteresis, to be a memory property. So what if some mem-resistors are found to have a

1543:

Since real resistors change with state variables such as length, area, and temperature, resistors provide a readily-available example of a more general class of memristors than the article suggests. The example can be made very general: temperature depends on heat dissipation and even heat capacity

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I'll add my voice to the people saying that this article is very unclear. The original start of the article ("theory") defined a memristor in terms of magnetic flux. Memristors aren't magnetic devices! There's no reason to define them in terms of magnetic flux; I can't see how this makes anything

1397:

The insistence on using "magnetic flux" and accompanying many of those references with explanation that no, it's more a general idea than "magnetic flux" is distracting. Would it be possible to get away with just "flux" -- is that term used alone in literature enough to justify doing that? In that

1226:

Stan Williams (of HPLabs) has a short Youtube video (available in the External Links section) which does a very good job for a layperson introduction. I also wrote a brief introduction to memristors in a knol entitled "Programmable Electronics using Memristor Electronics" which is also linked in the

552:

Please avoid personal attacks since this is against Knowledge policy. I am sorry if I appear rude to you but I am simply attempting to point out the facts related to the relationship between memristors and neurons which is the topic of this section. It seems bizarre to me that you are accusing me of

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I didn't say that they were unrelated. Mlvlvr doesn't either, if you read his post. The assertion of "modeling" is misleading because simple models of large neural networks have been around for a long, long time. However the behavior of a memristor can be creatively interpreted, it won't bring AI to

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In only the narrowest and antiquated sense do memristors have anything to do with neurons. Having spent several years developing artificial neural network technology at Intel in the late 1980s and early 1990s, motivated by the claims that EPROMs were an electrical analog of synapses and therefore a

2100:

Last summer I was invited to speak at a memristor session in the 2010 IEEE International Symposium on Circuits and Systems (ISCAS) and I attempted to raise issues such as whether it was correct to say that the memristor was a missing 4th fundamental circuit element found by HP when similar work was

1859:

Geoffrey, I just rewrote that section. Also, it appears the text had barely changed at all since I wrote it a couple years ago. You might as well address any issues to me. As I've already said on this page, someone who doesn't understand resistors, capacitors and inductors, and without knowledge of

1431:

Regarding negative memristance, one of the proven mathematical properties of memristive systems is that they are passive and do not produce energy. Thus if there are devices having some properties similar to a memristor but which produce (or amplify) energy it would not be formally describable as a

1272:

The Youtube video I was thinking of is entitled "6-minute memristor guide" which I thought was on the links page but is easy to find in any case. I was referring to the first section of the knol which uses the zero-crossing I-V curve which defines memristors (according to the 1976 paper of Chua and

1043:

If the term memistor is to have a broad definition, then I would expect it to include mercury coulombmeters. The only mercury coulombmeters I have seen were read optically, I am unaware of any being read by any other method. These devices remember the total NET couloumbs which have passed through

865:

I second you completely. Really, the memristor is extremely simple and intuitive device but its theory is too complex and abstract. This is a good example of how a theory makes the simple things complex... Thank you for the great Einstein's thought; let's try to put it into practice. A geared motor

793:

It seems to me that the memristor is one kind of resistance change memory (RRAM). The memristor was first introduced by Dr. Chua in UC Berkley in 1971. The definition of the memristor (flux linkage and electrical charge) was given at that time. The memristance has its own meaning, it means that the

717:

Dr Chu describes a "Memory Capacitor" that is a capacitor that is a function of flux. So it can be accurately called a "flux capacitor" or more accurately a "flux-based capacitor". I saw on many web sites that people were trying to call the memristor a flux capacitor which is not at all correct.

684:

Hence the excitement in the neuromorphic electronics community (of which I am a humble member) that we might finally see a device in the TiOx memristor that can store continuous-valued weights on tiny areas of silicon. Sure, memristors can also work wonders for digital (binary) storage density but

510:

From mlvlr's posting it seems he (or she) was not aware of the Hodgkin-Huxley model or at least the connection of the model with memristors so the grouping of "we" does not seem appropriate. For someone who admittedly has only a year of high school study on the subject I would display a little more

473:

I did initially read the entire post by Mlvlvr and it is reflective of the title. The original posting expressed ignorance of the connection between memristors and the Hodgkin-Huxley neuron model which you still do not seem to comprehend based on your statement that memristors do not model neurons.

275:

While I agree that charge density is used more often there are cases where it is more useful to talk about the difference of the total charge (not charge density) between two spaced apart regions of a semiconductor. One example is when determining capacitive effects. This may also have relevance to

220:

You are confusing yourself by thinking in terms of point charges and schematics. Circuit elements exist outside of schematics and are embodied by actual materials such as semiconductors. Semiconductors can be doped to produce a particular charge distribution in which different amounts of charge are

2901:

Thus we have made a connection between apparently different memristor, gyrator and multiplier. It is even more interesting to make a connection with the true (absolute) negative resistor. What is a true negative resistor? What does it do? Here, the ordinary ohmic resistor is replaced again with a

2583:

Chua's assertions. If there exist published papers disputing Chua's work, then they can be mentioned too, but no amount of argument on this talk page, however convincing, can result in a change to the article. If what you are proposing is based on sources, then please name them, otherwise please

2531:

Now, I would like to give hopes to Prof. Chua:) that it is still possible to present the "mem" elements as separate items if only we classify passive elements with respect not only to energy but to their behavior through time as well. From this viewpoint, the memristor is neither true resistor (as

2092:

I knew that there were several earlier examples of memory resitance materials and I started the timeline of this wikipedia page to provide some context with respect to HP's development. A few months after the Memristor Symposium I received an e-mail from one of the main figures associated with the

1969:

Why do you feel this is inappropriate? Indeed the term "magnetic flux", which is really only appropriate to inductors, is defined later, but that is the definition. Is it really right to override and reformulate Chua's definition? Or would it be better to add a note to the effect of, "This term is

1741:

I did one more pass through the article, separating the part of the "theory" section explaining memristance in terms of magnetic flux into a separate subsection, "Flux Forumulation of Memristance", which now follows (instead of preceding) the discussion of the I/V relationship. I'm still not sure

1404:

Finally, while it is certainly the case that memristors of interest operate with M(q(t)) never negative, the case for maintaining this restriction when discussing a hypothetical "ideal" device is not laid out convincingly, if it even exists. Just because a device would inject power into a circuit

591:

Reading the latest research is not methodical study. "Neuromorphic hardware" cannot be understood if you have not read the first few chapters of a biology or psychology textbook on neurons. It looks to me like you're jumping into popular science without background. If you had background, you would

385:

I agree that an analysis of neurons can be "really complicated" as you state. Nevertheless the Hodgkin-Huxley model is a fundamental model related to neurons and the paper by Chua and Kang make the connection between memristors and this model. Thus the statement "Memristors have nothing to do with

151:

Of course the amount of charge can vary with position. For example in the basic model of atoms there are a different number of electrons associated with different shells as determined by quantum physics. Electrets also demonstrate charge variation with position. Your distinction between charge and

3123:

I have a great idea about a colorful picture on the top of the article representing the situation: Prof. Chua, longing to convince his students of the magnetic nature of memristor and to evoke their interest in electrical phenomena, holds a big magnet in his hands and tries to gather a heap of HP

2678:

Now, 25 years later, I intend to repeat these empathy experiments (identifying with investigated objects with the purpose to understand them) in the laboratory to show to my students what a memristor actually is. The idea is the same as this one in 80's and as the Pershin & Ventra's emulator.

2372:

The table you present is representative of models developed by Yuriy Pershin and Max Di Ventra who are my fellow researchers in mem-electronic theory. However, perhaps better categories for the third column may be mem-resistive systems, mem-capacitive systems, and mem-inductive systems to address

2088:

I have been a researcher in memory resistance materials since 2006. When I first heard about HP's memristor I believed they had actually developed something new and I was enthusiastic about their device. I presented a short paper at a conference in Boston based on applications of the memristor in

1039:

Unless there is a term to describe memory resistors separately from memory capacitors, separately from memory inductors, then the definition of memistor at the beginning of this wikipedia page on the subject should start out with a more general definition of a device that stores an analogue value

852:

I would suggest some simple mechanical analogies: A geared motor driven by the current, which drives a potentiometer? A negative coefficient thermistor which is heated/cooled by a Peltier module? A simple electronic circuit which accurately simulates a Memrister? Some simple electronic oscillator

740:

Materials which could exhibit a memory capacitor effect to enable such a "flux capacitor" or "memacitor" (the term I prefer) are discussed in "Ultralarge capacitance-voltage hysteresis and charge retention characteristics in metal oxide semiconductor structure containing nanocrystals deposited by

676:

To go back to Mlvlvr's original assertion, "In only the narrowest and antiquated sense do memristors have anything to do with neurons", this is perfectly correct in that there's no titanium dioxide in wetware neurons or synapses. I could argue that it's not that "memristors are neurons" but that

423:

You seem to be providing a lot of opinion but not much fact. If "Mlvlvr" agrees that memristors are related to neurons than the choice of title for this section is very poor. Do you have any basis for your opinion that the next step in AI is not related to computing equipment? Pattern recognition

348:

In the paper "Memristive Devices and Systems" by Chua and Kang (1976) the model of memristive systems was shown to be applicable to the Hodgkin-Huxley model describing action potentials in neurons. Greg Snider at HP Labs is also working on designing a neuromorphic architecture based on memristors

3433:

are now. As I can see, after almost forty years, the authors corrected tenderly (not so rudely as me:) the "magnetic flux" problem and the very Chua approved this revision by the fact of his participation. So, here is the solution - we should mention the original Chua's article but we should use

2613:

Well, I agree with you about Knowledge aims and purposes and I will not insist on considering this topic any more. It seems this is just a question of taxonomy and it is not so important for the root of the matter. My aim was only to say something more about the nature of the memristor in a more

2474:

The significance of this is that it is Chua that first proposed the Q/Φ constitutive relation memristor, yet in this paper memristor becomes a V/I constitutive relation - ie, simply a variant resistor (one with hysterisis). It is also significant for our article that the HP device is of the V/I

2403:

This table doesn't make any sense and is just more imaginative taxonomy. Capacitors and inductors are non-linear. A varactor is not a fundamental component the same way as resistors, inductors and capacitors are. The memristor has a theoretical basis but the other elements of the table are

2164:

which are also 2-terminal passive resistive memory but which are not claimed to be memristors by the companies developing the technology. My main concern is that this page should maintain the charge vs. magnetic flux linkage definition in the introduction in order to avoid "memristor" becoming a

2151:

The original 1971 article of Chua "The missing memristor" defines the memristor as a 4th fundamental circuit element based on a relationship between charge and magnetic flux linkage (which can be equated to the time integral of voltage). That article along with the 2008 memristor article from HP

1301:

I don't think an IV curve or a Lissajous figure are more accessible to the average person than an integral. More people take calculus in high school than ever see an IV plot or hear a definition of hysteresis. Even undergrads have trouble interpreting that, particularly when the concepts are put

1149:

istor, as I understand it, is a two element solid state device whose resistance is changed by current through the device. HP is planning to use it for digital non-volitile memory, and possibly to use it for neural networks. The memistor was developed for neural networks and was used to implement

776:

If you don't know what a resistor, inductor, and capacitor are, and you don't have a specific question, you might just be out of luck. In particular, we can't point to a physical thing and say "this is what a memristor looks like." A memristor is any device with memristance, and memristance is a

3502:

If we assume that volatile "mem" elements possess hysteresis, we should accept that the ordinary ("not mem") capacitors and inductors possess hysteresis as well. For example, if we drive a capacitor with low frequency AC input current, measure the voltage across it as an output and draw its "IV

3044:

The results of this misleading denoting were tremendous. Any intuitive notion about this extremely simple device disappeared. People, knowing what such an integrating resistor was, ceased understanding it; they began trying to see something "magnetic" in this pure resistive device. Others began

2644:

I have the ambition to grasp the basic ideas behind "mem" elements by intuition and to explain them to people because the situation is very interesting and indicative. From one side, there are extremely simple and intuitive "mem" elements and circuits; from the other side, there is an extremely

2180:

My friend, I really have no disagreement with your sentiment and I do understand the difference to Chua's original description. The problem here is that it is not Knowledge's business to protect the purity of Chua's definition nor to campaign againt HP misusing the name in its marketing nor to

2108:

Meanwhile there are several companies developing competing Resistive RAM to HP's potential product. In many cases these companies have been developing these materials since before HP came on the scene. As this wikipedia page has evolved it seems to me that there is less reliance on the original

1574:

Resistors and memristors are both special cases of the more general state variable equations defining memristive systems described in a 1976 paper by Chua and Kang "Memristive Devices and Systems." These equations include a first equation (1) which is a generalization of Ohm's law which relates

1464:

that has passed through the device." As a general thing, the magnetic flux on a memristor will be zero if no charge is flowing through it, independent of how much charge has passed through it. The article also mentions the charge on the device; it's a little unclear here, since memristors are

201:

to represent charge density does not mean "the distinction is ridiculous." If the units are different, the concepts are different. It should be obvious that there is no such thing as position on a schematic diagram, and schematics are incapable of representing waves, which tie time and position

2104:

As time goes on I am seeing a greater number of articles written by researchers who appear to me are just trying to ride the coattails of the memristor meme without any understanding of the dynamic framework required in order for a system to be considered memristive. The original definition of

1810:

Thanks for your suggestion. I have once again switched the order of the theory section. I do understand that you want to start with the definItion you list as originating from Chua, but this is starting at a far too detailed level, not an introductory place to start beginners. Please note,

1757:

Perhaps you should read Chua's 1971 paper on the memristor before making all of these changes. In that paper the memristor is defined as a non-linear functional mapping between magnetic flux and charge based on a symmetry relationship with non-linear resistors, capacitors, and inductors. I can

1090:

Nice research (especially the NSA "persistor"). Widrow's memistor (1960) was a 3-terminal electrochemical device and he did not develop a mathematical model for it. Chua's memristor (1971) was based on a mathematical model for a fourth non-linear 2-terminal passive circuit element but did not

893:

I think a better analogy would be as R. Stanley Williams put it, consider a memristor as a pipe whose diameter changes as water flows through it. Getting narrower and therefore harder to traverse as the water flows in one direction, and easier and easier as it flows in the other. --TheRandom

2014:

after its first use, and some other minor changes, mostly trying to remove some of the implication that Φm represents the flux of physical magnetic fields, and instead make it clear that it's a generalization of the concept from inductors to general circuit elements. There's still a little

1199:

Part of the problem is that a particular kind of memristor has gotten a lot of popular coverage, so you expect this page to be simpler or entirely different. Typically when a laboratory invents a new device, they name it something unique, ie "micro-memristor" or "memristive memory," with an

651:

Yes, Blm19732008 did. If word choice is to be trusted, then he wrote more than one. He stated it once implicitly in the paragraph to which you just responded ("Well if you think your admittedly high-school level knowledge is better than someone who has studied this on the graduate level

2384:

I think your idea for the table is good but it might be better for a new wikipedia article on "mem-electronics" covering the wide variety of "mem" models that currently exist and are likely to emerge in the next few years. One reference discussing a variety of mem-systems is available at

1332:

Wouldn't something to this effect be a much better introduction? I don't have the knowledge to say if this is accurate, but something like this, or drawing analogies to analogue computing, or a comparison with transistors would go a long way to making this article more readable. David

1023:

It is my understanding that a memristor is an electronically variable analogue device which retains its value when no power is applied. The definition(s) of the electric charge and magnetic flux devices are memistors, but I believe that they are one type of memistor, not the definition

819:

I must say, the first sentence of the "Theory" section (even though it still cannot be understood by laypersons) is significantly easier to understand than the introduction of the entire article! Surely the introductions should be far simpler. Here is the first sentence of the "theory"

3085:

Chua reference talks about magnetic flux linkages so there is no justification in the article qualifying this unless there are other sources that can be quoted. Likewise, later edits have introduced concepts into sections cited to the HP reference which cannot be found in that source.

1609:

I would like to consider adding this information on the history of development of the memistor. I am reading Dr. Buck's notebooks for this. I am an electronic engineer, not a chemist; for that reason I would like a chemist to review this for accuracy before we consider adding this.

405:

the next step because the current challenge is not related to the computing equipment. Proponents of exotic physical neuron analogues, particularly semiconductors, are mostly disingenuous. Therefore an alternative viewpoint is needed to stay NPOV, or the promotion should be toned down.

1210:

On the face of it, you can't begin to understand what a memristor is without knowing about current, voltage, and integrals (maybe throw electrons into the mix), because these are the symbols used to define the word. And a lay audience by definition knows about none of those things.

192:

To get from charge density to charge, you must integrate over a volume. This integration eliminates the position parameter. Electron wavefunctions vary probability with position, not charge. To say that a finite amount of charge exists at a single position would violate the

3499:

a volatile memristor, memcapacitor and meminductor that exhibit "hysteresis" only in the case of slow changing input. If we wiggle the input rapidly, their bizarre ("pinched") hysteresis loop will become a humble straight line (for example, imagine an inert thermistor).

2460:

second order hysteresis effect? This would mean there are mem-mem-resistors. Maybe there are mem-mem-inductors and mem-mem-capacitors as well. It is all very specious. The article should be restored to its earlier state, possibly with these speculative ideas added.

2152:

should be the primary references for this wikipedia entry and the definition in the introduction section of the article should not deviate from these original references or attempt to generalize the definition beyond this. There are already separate wikipedia entrys for

455:. The papers are nice, but keep in mind that research tends to occur at the crossroads of buzzwords. Research on neurons and artificial neural nets have advanced separately to the point where there is a definite distinction. Also, note that amoebas do not have neurons!! 2226:

passive elements). The rows of the table represent the three possible electrical properties and the columns represent the three variations of these properties. The obtained passive elements (generic or specific) are placed in the according table cells. Please, discuss.

3167:

Of course, this was only humor but the problem is serious and we have to solve it somehow. I suggest the simplest but effective solution - simply to not mention "magnetic flux linkage" in the lede; to revert the article to its old state without Blm19732008's insertion

3361:

I like your speculations about Q/Φ versus V/I constitutive relation memristor. IMO we have to arrange the lede and the introductory part of the background section according to these two viewpoints at the same element (now, the background section is quite scattered).

1674:

I will retract my suggestion to add this information on the early history. It has been pointed out to me that my suggestion is considered "original research" because it is not cited anywhere. (I learned something new! ). We may revisit this someday in the future.

3506:

It seems only nonvolatile "mem" elements (i.e., true memory elements) should possess hysteresis since their IV curve does not depend on the input rate? Please, discuss this extremely interesting topic; I would like to know if I am right. I have copied this text to

1170:

Coming to this page for the first time to find out what a memristor is, I feel I really couldn't get the whole picture without coming to the discussion page, and thence to the history pages. There are some complaints people already voiced which I think are valid:

2061:

In 1962, Hickmott observed a negative resistance in a thin anodic oxide film. The result shows that a current through this anodic film increases when the voltage across the film decreases. This negative resistance phenomenon may also relevant to the memristor

2902:

voltage source (exactly as in the case of gyrators and multipliers) but it is with reversed polarity. It has the same polarity as the input voltage source so that it adds the same energy that the equivalent "positive" resistor would consume. Please, discuss.

529:

No, he definitely is aware. Reading papers for a year earns expertise at any age, and if you had any methodical study yourself you'd know which papers are seminal. But you didn't study and you don't know. The point of describing my study that way is to

2532:

its resistance depends on time) nor true capacitor or inductor (as it dissipates instead to store energy). It resembles resistors (with respect to energy processing) and capacitors and inductors (with respect to time behavior); it may be defined as a

1860:

calculus (that is, a beginner) has no hope of understanding memristors, and would probably skip the theory section anyway. I don't think attempting to adjust this section to cater to the lowest common denominator will clarify or improve it for anyone.

1654:

I am very new here on wikipedia. I am lost trying to add the citation; Dudley A. Buck 1 July 1958, M.I.T. Computation Book - 3/28/58 - death, page 7 (If deserving of a separate citation, the tin-dendrite work was June 25 through 29, pages 3 to 5.)

923:

In the article the memristor is formally defined as: "The memristor is formally defined as a two-terminal element in which the magnetic flux Φm between the terminals is a function of the amount of electric charge q that has passed through the device"

3006:, expressed the right time integral of current as charge Q and began speculating how to express the left time integral of voltage. Inspired by his speculation about the existence of a 4-th passive element, he saw a connection with the magnetic flux Φ 1498:

100 gigabits (12.5 GB) per cm² maybe seemed amazing some years ago, but today I can purchase a 32 GB smart card using conventional transistor technology (I am assuming that is the case anyway) The chip inside is probably smaller than 1cm² as well.

1035:

The shortest way to describe the difference between the titanium device and 'all others' is that all the others (I think) use an electrolyte to aid in the change to the device. As I have interpreted the HP titanium device, there is no electrolyte

1389:

The article seems to go to lengths to expound that there is no such thing as an "ideal memristor" (basically because there seems to be no consensus what the ideal, most logical, M(q(t)) would be barring constant (in which case it's a resistor).)

329:

out of line, now that you point it out, and there is still another reference to "artificial neural networks. So you can probably delete the offending sentence and leave the properly qualified one. If you like add a disclaimer to that one, too.

2002:

indeed define it the first time that you use it (which you now do) and state that it "does not represent a magnetic field here" (which was never explicitly stated earlier). What the earlier draft had done was to link to the Knowledge article

2836:

The general property of passive electrical elements is taking (consuming) energy from the input excitation source; resistors dissipate this energy while capacitors and inductors store (accumulate, "steal") it. But how do they do it?

1930:

Can you be any more specific? Do you agree about my reasoning why your edit is even less clear? It's hard to do this all by myself. There's a lot of nonconstructive criticism here, and nobody else has edited it for two whole years.

1183:

In general, this is certainly not written for the layman, nor someone new to the concept. I hope someone with knowledge on the subject could take a stab at improving the clarity and the flow of information within the article. David

1031:

Perhaps these devices would not come under the definition of a "memory resistor", yet they, and the titanium device are all devices which retain an analogue value representing an integral of the signal applied to it over its entire

2940:) establishing a linear relation between voltage and current if only the resistance stayed constant. In the case of nonlinear resistance (depending from the input quantity - voltage or current), it is written in a derivative form ( 870:. It is even better than the 3-terminal Widrow's memistor:) since the output is completely isolated from the input. If you connect the motor and the rheostat in series, you will get a 2-terminal integrating memristor. Regards, 1428:

effects obey the 1976 dynamic system definition but have nothing to do with the 1971 magnetic flux definition. My opinion is that HP has used the 1971 definition more for marketing purposes then for any real technical merit.

1180:- It became apparent reading the history that there are some problems/controversies with the concept and the application of memristors that I would certainly like to have known about without trawling through article changes. 2015:

inconsistency over whether capital Q or small q is used to represent charge-- the theory section starts with Q but then when it gets to memristor characteristics, it uses q. This may be ok, though, so I left it as is.

3596:

to emphasize that it depends on the charge, or magnetic flux. The basic quantity of interest in resistors is their resistance, not differential resistance. Resistance is not a special case of differential resistance.

3568:

M = R = V / I (constant resistance) is not interesting here. As it was written, the table included the nonlinear quantities as well. R = V/I, C = Q/V and L = Φ/I are special cases of R = dV/dI, C = dQ/dV and L = dΦ/dI.

1824:

Nevertheless, a significant problem remains: the section discussing magnetic flux, as written, is incomprehensible. It needs to be clarified by somebody who understands the physics well enough to explain it clearly.

221:

located in different positions of the semiconductor providing a variation in the amount of charge with respect to position. In any case this argument is moot since I already changed the confusing section of the article.

2185:

becoming a generic term. Knowledge articles are encyclopedia articles and merely summarise what is in the sources. So we need published sources discussing this issue before we can make the points you want to make.

848:

This is an appallingly inaccessible article. The Memristor is a simple device, and needs a simple English explanation. "If you can't explain it to a six-year old, you don't understand it yourself". Albert Einstein.

3317:. I have searched for a simple analytic example of such a case but I am probably not a good enough mathematician to succeed. We definitely need sources discussing this issue before writing anything at all on it. 2894:

To emulate passive elements, we may replace elements behaving as resistors with sources and elements behaving as sources - with resistors (besides the more natural "sources - with sources" and "resistors - with

1758:

sympathize with you that the definition used by HP deviates from this and is not a magnetic device but I do not agree that it is a good idea to ignore Chua's definition since he was the originator of the idea.

1455:

I don't think that the magnetic flux section is well written, actually; magnetic flux is undefined for a two-terminal device (terminals are one dimensional). I don't even understand the statement "The magnetic

442:

It is a poor title, and you really should read his post before writing a longer post yourself. Pattern recognition is nice but, as we're pointing out, is understood in statistical terms not biological terms. We

1626:

to experiment, unsuccessfully, with tin dendrites as a means of using electrical current to form electrical connections. This work was quickly followed by an artificial synapse made from cuprous sulfide,

3490:

I do not share Chua's, Ventra's and others' (including this article) assertions about the (unconditional) existence of hysteresis in memresistive, memcapacitive and meminductive elements (see for example

866:

driving a rheostat is a very good electromechanical example. If you apply input voltage across or current through the motor and take the rheostat resistance as an output, you get a 4-terminal integrating

1423:

HP's 2008 memristor paper in Nature used M(q)=ROFF(1-mvRON/D^2 q) where ROFF, RON are the off and on resistances, mv is the ionic mobility of oxygen vacancies, D is the film thickness and q is charge.

3000: 2645:

complex theory that cannot explain them in a human friendly manner and even misleads and prevents understanding. All the debates on this talk page (including the archives) confirm this contradiction.

152:

charge density is ridiculous because there are many examples in electromagnetics textbooks of charge being written as a function of position (i.e. q(x,y,z)) such as in Gauss's law in integral form.

2850:

First, we may replace them with varying voltage sources and this is the most natural way of making emulated capacitors and inductors (as they behave as varying through time voltage sources). Op-amp

1575:

voltage (v) and current (i) except that the resistance R is dependent on a state variable w. The second equation (2) defines the rate of change of the state variable with respect to time (dw/dt).

1135:

I sent an inquiry by email to Dr. Widrow, requesting a clarification on memistor versus memRistor. This is his reply. The first paragraph is about the memistor, the second is about the memRistor.

823:"The memristor is formally defined as a two-terminal element in which the magnetic flux Φm between the terminals is a function of the amount of electric charge q that has passed through the device." 1966:

The memristor is formally defined as a two-terminal element in which the magnetic flux Φm between the terminals is a function of the amount of electric charge q that has passed through the device.

3626:

It seems clear from the more mathematical sections below that if M(q) is constant then it's the same as a resistor (and M=R), but if M(q) is a non-constant but linear function then it's not.

1203:

Perhaps there should be a separate page for HP's celebrated "invention." (And, as the timeline shows, a few predecessors.) But there isn't an agreed name besides "HP's memristor." I propose "

3441:"The memristor is characterized by a relation between the charge and the flux, defined mathematically as the time integral of the voltage, which need not have a magnetic flux interpretation" 2729:

with PTC fixed to a massive radiator (or simply a lamp with a thick filament, a solid heater, etc.) The constant current begins flowing through the thermistor; as a result, its temperature T

2737:

begin increasing slowly. So this arrangement acts as an integrator with current input and resistive output, as a "resistive capacitor". If we change slowly enough the input current, then T

3354:

No one knows what kind of ideas inhabit "beautiful minds"; we "mere mortals" can only guess... Chua is a theoretical genius and definitely he had good reason to name it "magnetic flux Φ

1028:

to another mounted in a parallel plane to measure the stored value. Figure 21 discloses a device that stores the variable as a function of mutual coupling between two orthogonal coils.

611:

have been applied to the latter. Both Mlvlr and your ignorance was established by your failure to note the connections between memristors and the Hodgkin-Huxley model or Snider's work.

1432:

memristor or a memristive system. This is one reason why it is unlikely for memristors to replace transistors since they are incapable of performing signal amplification on their own.

1200:

associated acronym. However, HP labs instead chose to claim they had "found the missing memristor" when in reality Chua had from the start illustrated the idea with everyday examples.

928:

in this case is a quantity that measures a physical property of a device. The second part expresses how the changing state variable depends on the charge flowing through the device.

174:

As a general rule any physical quantity that can vary with time can also vary with position. In any case the original phrasing was confusing so I changed it as suggested by Arnob1.

3002:), what gave nothing new if the resistance stayed still constant. Then he made the resistance be nonlinear (depend on the input quantity - the charge Q in this case) and name it 118:

Charge could vary with position without varying with time (as in a nonuniform charge density) so the statement "if charge varies with anything, it must vary with time" is false.

2830:

say, in the very beginning, that these circuits emulate only particular properties (e.g., time behavior) of the genuine elements. Let's first see what these properties are.

1047:

This question might have an answer in whatever document was the first to use the term memistor or memristor. Does anyone know when & where one of those terms was used?

1639:

in his notebook. From his notebook, 1 July 1958: "Cuprous Sulfide appears to be a good candidate for such a self-oranizing system component. By plating copper out of Cu

3226:". It turns out that there are two duplicated variables (one "synthetic" and another - genuine); we have denoted two absolutely different quantities by the same term... 2866:

circuits do it in this way. In these circuits, the op-amp output voltage represents the voltage across the according capacitor or inductor (see more about the topic in

1502:

Is this capacity theory understated, or has standard transistor technology surpassed it? What is the practical application of this? Am I comparing apples to oranges?

1590:

The case described by Ywaz in which the state variable w is based on temperature was also treated in the Chua/Kang paper and was used in the analysis of a thermistor.

79:

There is a statement in the article "Of course, nonzero current implies instantaneously varying charge.". Would it be better to say time varying charge here instead?

1401:

Another tact towards showing the relationship in a more layman-friendly format might be to try it out in the frequency/impedence domain and see if it is prettier.

931:

This means that a magnetic interaction is not necessary for memristance and linking electric charge and magnetic flux is only one way to satsify the definition.

1305:

The equations in this article were cherry picked from Chua's original paper. Your knol would not be a suitable reference. Note that there is still no article at

1785:

which also might shed some light on Chua's original argument of the memristor as a "4th fundamental circuit element" linking magnetic-flux linkage and charge.

2222:

I would like to show with the table below that the memristor, memcapacitor and meminductor are nothing else than kinds of resistors, capacitors and inductors (

1651:

S ..... CuBr or CuI is a good cathode for accepting the copper ions. Pt or graphite forms a suitable anode. Electronic conduction is primarily by holes."

1523:

article. Memristers can apparently go smaller than transistors. And could actually replace them, allowing for memory and processing to be done simultaneously.

959:

Read the section " Magnetic flux in a passive device" to see why "magnetic flux linkage" is an integral of voltage, unrelated to any "magnetic interaction."

2840:

Let's for concreteness imagine that the considered passive element is connected in series to the exciting voltage source. What does it do in this case? It

2423: 239:

Those "different amounts of charge" are still charge density, not eg Q(x,y,z) = 1.6*10^-6 Coulombs. Typically dopant density is measured in atoms per cc.

3358:". The problem is that this term is contrary to our notion about the constituents of this name and we "mortals" have to solve somehow this contradiction. 1177:- The article should more explicity explain why it is called a memristor (this is only addressed in passing, and a most unsatisfactory reason is given). 3138: 3142: 202:

together. Memristors (and the other 2-terminal components) exist only in schematic diagrams, where there is such a thing as a node or a terminal.

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For quick input changes the integrating memristor behaves as a linear (ohmic) resistor; for slow input changes it behaves as a nonlinear resistor

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How simple it was: first, to name the variable; then, to define it mathematically and finally, to distinguish it from the similar magnetic one.

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Memristance isn't variation with any variable, it's variation with Q(t), where reversing the direction of current reverses the change in Q.

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converter. To obtain the Pershin & Ventra's emulator, we have to make the computer drive a digitally-controlled resistor R1 or R2.

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think they're cool. (A discussion on all sorts of problems building neural networks in digital hardware doesn't belong here - try the

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simply made up. One reference is not sufficient. The earlier version of this article was more balanced and should be restored.

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them. Other applications were for non-volitile analog memory. Commercial applications existed but did not develop into big markets.

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as the HP device are in the same class as that defined by Chua. It may be that there is some class of constitutive relations of

3058:; it is written "flux" but it is not a "flux", etc.:) Memristor produced a sensation and media intensified all these problems... 1697:

Article needs updated, ReRam coming... two reuters articles and tons of other coverage; HP teamed up with Hynix to manufacture

1782: 1092: 98:. If charge varies with anything, it must vary with time… maybe cut it down to simply "implies varying charge" or "implies that 3249:

The way to persuade is to provide a source, not by endlessly delivering lectures on the talk page. Save it for your students.

2719:

its resistance; so it behaves as a nonlinear resistor. Let's see this phenomenon in a few simple and clear memristor examples.

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Superb-- the rewrite you just did makes is a lot clearer! Yes: if you're using the term "magnetic flux" to mean something

2579:

This is completely back-to-front. It is not for Knowledge to "refute Chua's assertion". The Knowledge article should be

1587:

In the case of a memristor f(w,i) = i and the memristance function is dependent on charge (the time integral of current).

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He denoted the new artificial quantity exactly with the same "magnetic" letter (Φ) and with the same "magnetic" subfix (

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is in respect to energy processing. It divides the passive electrical elements into three groups - dissipating energy (

1544:

of resistors, so that change in charge results in non-trivial change in flux (i.e. area under the voltage*time curve).

1834: 1040:(excluding potentiometers). Then proceed to describe the various analogue memory devices of differing technologies. 761:

seriously, i have no idea what this is all supposed to mean and all i wanted to know was what a memresistor was :(

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But I wanted to point out that he did invent a "flux capacitor", as the 5th possible element in basic circuits.

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Neurons are REALLY COMPLICATED. Being applicable to one very simple model does not equate to generally modeling.

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To second my university colleagues in their educational efforts, I give a promise to make a humble memristor of

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together with arrows, although it is more "visual." The assumption of sinusoidal input is particularly obscure.

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I read the article which was referred to by 98.218.144.3. I found it to be extremely helpful on this subject.

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I understand the controversy over whether a memistor is a neuron, but Dudley Buck clearly labeled the device

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S, as an electrolyte, with copper iodide, CuI, as a cathode and graphite as the anode in a quartz envelope.

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mathematical concept. As the article says, it is similar to variable resistance (yet very different). Sorry.

677:"wetware synapses behave like memristors" only I feel that's too philosophical for a cold February afternoon. 3503:

curve", we will probably see a "hysteresis" loop (I am not sure if it will be "pinched"; please, check it:)

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and synaptic floating gate transistors which I presented at ICECS 2010. This presentation is available at

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memristor is now so bastardized that some people seem to be applying it to any dynamic system with memory.

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Memristor is not simply a nonlinear device as this article and many other sources claim; instead, it is a

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variety and not the "fourth element" of Chua's original formulation, HP's marketing hype notwithstanding.

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of the current. The equivalent circuit of the memistor is that of a transistor with a built-in integrator.

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This draft is much clearer. I cleaned up the text a little; added a definition of Φm that follows more

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So the question to those who've been digging into the literature is: what would that expedient M() be?

943: 3170:"...and is expressable in terms of a functional relationship between charge and magnetic flux linkage" 3137:: Prof. Chung creates a negative resistance in front of her students by using a humble bridge circuit 556: 312: 3639: 3622:"However, as mentioned above, if it has no non-linearity then it is the same as a standard resistor." 3570: 3512: 3453: 3363: 3279: 3227: 3173: 3062: 2903: 2796: 2764: 2688: 2615: 2557: 2228: 2065: 2019: 1901: 1838: 1788: 1761: 1743: 1702: 1509: 1480: 1479:

In any case, I have now rewritten an introduction section in order to (I hope!) make it more clear.

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case, the clarification could be restricted just to the discussion of comparisons with an inductor.

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Have I misunderstood something, or is the following sentence from the Background section in error?

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Please, discuss and suggest remedies for correcting these misconceptions to improve the article.

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OK, I'll address coments to you: the section you wrote needs a lot of work. It is not clear.

1783:

http://knol.google.com/k/memistors-memristors-and-the-rise-of-strong-artificial-intelligence#

1093:

http://knol.google.com/k/memistors-memristors-and-the-rise-of-strong-artificial-intelligence#

2465: 2409: 2389: 2166: 2110: 1615: 1591: 1529: 1433: 1281: 1228: 742: 612: 574: 512: 475: 425: 387: 350: 277: 222: 175: 119: 84: 3222:"). But the current flowing through the inductor creates another (genuine) "magnetic flux Φ 2863: 2859: 2664: 349:

which was described at the 2008 Memristor and Memristive Systems Symposium at UC Berkeley.

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in an inductor and did three crucial actions changing the world for the next forty years:

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The definitions agree perfectly. Can you give an example of what you would like to see?

983:

Can a simple (non-technical) definition be added to the start of the article? Regards,

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I was emotionally connected with and fascinated by the elegant simplicity of Widrow's

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the memristance equivalent of a resistor) and more complicated nonlinear memristors (

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In the case of a resistor f(w,i)=0 and the memristance function R(w) is a constant.

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I have also a big idea about a funny top picture for another sensational article -

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Lol. So I suppose if you studied at the graduate level, you wrote a paper then?

80: 46:

If you wish to start a new discussion or revive an old one, please do so on the

3643: 3605: 3586: 3562: 3548: 3528: 3495: 3469: 3407: 3379: 3337: 3295: 3269: 3243: 3189: 3105: 3078: 3029:(time integral of voltage) exactly with the same name as the similar integral 2919: 2812: 2780: 2726: 2704: 2631: 2604: 2573: 2495: 2469: 2446: 2413: 2397: 2244: 2206: 2145: 2077: 2051: 2027: 1940: 1909: 1883: 1846: 1800: 1773: 1751: 1684: 1666: 1619: 1599: 1568: 1553: 1532: 1513: 1488: 1441: 1417: 1378: 1358: 1342: 1318: 1293: 1266: 1236: 1220: 1193: 1160: 1127: 1109: 1084: 1059: 1014: 992: 977:

Also, what is the difference between this definition and the definition here:

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External Links section and which is intended be accessible to the layperson.

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can vary with position. That is different from charge varying with position.

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if you want to see what the idea of such "apparent negative resistance" is:)

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which when differentiated yield hysterisis-like constitutive relations of

2876:

But a memristor can do the same by replacing these voltages by equivalent

1528:

Everyone else read the article because it's apparently new information. --

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To be more specific myself, I see now that you removed the lead sentence

1257:) 17:30, 10 July 2009 (UTC) Woops, I confused hysteresis and saturation. 867: 2037:

Third sentence in the Theory section: "where Q is defined by Q = dI/dt"

920:

I think there is a slight misunderstanding of the memristor definition.

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stop pushing for this, it will just cause a lot of grief for no gain.

1874:

you moved the introduction and the section now begins at the middle.

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between the terminals is a function of the amount of electric charge

534:

pose as an expert… you're really pretty rude… Have fun with YouTube.

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memristors scattered on the table in front of the curious students:)

1833:

across a two dimensional surface (typically a loop, if you're using

1468:

There also seems to be some confusion between the simple memristor (

253:

You'd be better off not using phrases like "confusing yourself" per

557:

http://memristor.ucmerced.edu/2.asp?uc=1&lvl2=6&contentid=6

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I have read with great pleasure and interest the talk (especially

2824:

revealing the connection between memristor, gyrator and multiplier

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An arrangement (IV curve tracer) for manual emulating a memristor

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make it not copyvio. Of course, it's not a substitute for math.

25: 3534:

Invalid Equations for Resistance, Capacitance, and Inductance

2745:

will change as well. If we change rapidly the current, then T

2379:

http://www.slideshare.net/blaisemouttet/memtransistor-systems

1813:

The material that you want to keep in the article still there

826:

Or are the two definitions different in some way? Regards,

3114:

And God said, "Let resistive elements be magnetic! Amen!":)

2552:

elements ("capacitive" and "inductive" memresistors) and

2520:), storing electric (potential or pressure-like) energy ( 1324:

This is taken from the Wired article in External Links:

978: 3210:

Blm19732008, how do I persuade you that "magnetic flux Φ

2995:{\displaystyle \int V\mathrm {d} t=R\int I\mathrm {d} t} 1369:

for advice and examples on writing the lead section. --

2556:

elements (capacitors and inductors)? Please, discuss.

2524:) and storing magnetic (kinetic or flow-like) energy ( 3214:" used here is neither "magnetic", nor "flux", nor "Φ 2957: 2925:

Demystifying the circumstances about memristor rising

1728:

http://www.reuters.com/article/idUS111925223920100901

1717:

http://www.reuters.com/article/idUS254583059320100901

2880:

across dynamic time-dependent resistors. Transistor

2040:

Actually, I = dQ/dt therefore Q = integral of I dt.

447:

how neurons perform pattern recognition. Memristors

197:

and would be nonsense. Just because a textbook uses

3486:"Mem" elements do not obligatory possess hysteresis 2213:

What memristors, memcapacitors and meminductors are

2994: 2948:is the incremental resistance in the given point. 2791:. Shortly, an integrating memristor behaves as an 2725:Imagine we connect a constant current source to a 2218:A classification with respect to energy processing 2951:In 1971, Chua simply integrated Ohm's equation ( 1072:http://www.stormingmedia.us/48/4883/0488356.html 592:not have assumed mlvlr was ignorant. Clear now? 3158:and to investigate it in front of my students:) 2818:Memristor can emulate basic electrical elements 1075:in reference to Frank Rosenblatt's Perceptron 3278:Do we really need sources for obvious truths? 3135:Deborah Chung's "apparent negative resistance" 2508:A classification with respect to time behavior 3447:in quotes but I know you will not accept it). 2710:Memristor is a conditionally nonlinear device 1811:however, that I did not delete any content. 757:this page is way too technical for laypersons 8: 3202:" is neither "magnetic", nor "flux", nor "Φ 2083: 1066:And now for some more potential confusion: 715:http://www.youtube.com/watch?v=QFdDPzcZwbs 292:Memristors have nothing to do with neurons 94:Maybe. The intent is, time varying charge 2984: 2964: 2956: 2760: 1643:S, one can change the composition from Cu 2842:subtracts voltage from the input voltage 2640:Empathy can help understanding memristor 2248: 2007:, which had been completely misleading. 1605:add more early history of the memistor ? 1709: 1539:Resistors really are general memristors 685:it's the analogue storage that make me 3050:the purposes of theory, it is written 44:Do not edit the contents of this page. 3045:looking for some connection between Φ 3040:) as the genuine "magnetic" quantity. 2675:but let's discuss this topic later). 7: 2848:Emulating by varying voltage source. 3553:I have fixed the invalid equations 386:neurons" contradicts the evidence. 2985: 2965: 1242:The only YouTube external link is 713:At time point 46:40 of this video 24: 3139:hand-made by two pencil graphites 2936:In 1826, Ohm formulated his law ( 2733:, resistance R and voltage drop V 2874:Emulating by varying resistance. 2084:HP's memristor may be propaganda 29: 2387:http://arxiv.org/abs/1011.3053 2052:02:15, 19 September 2010 (UTC) 1207:memristor," maybe it'll stick. 916:Formal Definition of Memristor 654:and has published on the topic 1: 2868:Demystifying gyrator circuits 2078:01:41, 20 February 2011 (UTC) 2028:14:18, 7 September 2010 (UTC) 1941:05:37, 7 September 2010 (UTC) 1910:03:43, 7 September 2010 (UTC) 1884:02:42, 7 September 2010 (UTC) 1847:20:31, 6 September 2010 (UTC) 1801:22:13, 5 September 2010 (UTC) 1774:18:25, 5 September 2010 (UTC) 1752:20:35, 4 September 2010 (UTC) 1514:16:56, 22 December 2009 (UTC) 1489:15:40, 3 September 2010 (UTC) 1442:02:57, 18 December 2010 (UTC) 1418:18:59, 16 December 2010 (UTC) 910:14:42, 12 December 2011 (UTC) 810:01:35, 20 February 2011 (UTC) 703:15:27, 17 February 2012 (UTC) 666:02:16, 23 February 2011 (UTC) 3014:He denoted an integral of a 2546:dissipating time-independent 2018:This is good work; thanks! 1781:I have an online article at 1600:01:02, 4 February 2010 (UTC) 1569:01:18, 27 January 2010 (UTC) 1554:10:56, 26 January 2010 (UTC) 853:circuits using a Memrister? 751:16:08, 23 January 2009 (UTC) 734:04:56, 23 January 2009 (UTC) 639:19:22, 28 January 2009 (UTC) 621:14:52, 28 January 2009 (UTC) 602:19:17, 27 January 2009 (UTC) 583:16:11, 27 January 2009 (UTC) 544:19:22, 25 January 2009 (UTC) 521:14:59, 25 January 2009 (UTC) 502:19:06, 23 January 2009 (UTC) 484:15:45, 23 January 2009 (UTC) 465:01:06, 22 January 2009 (UTC) 434:22:36, 21 January 2009 (UTC) 415:21:52, 20 January 2009 (UTC) 396:19:20, 18 January 2009 (UTC) 377:19:12, 16 January 2009 (UTC) 359:18:51, 16 January 2009 (UTC) 339:13:15, 16 January 2009 (UTC) 321:23:57, 15 January 2009 (UTC) 286:19:59, 8 February 2009 (UTC) 267:23:49, 6 February 2009 (UTC) 249:23:46, 6 February 2009 (UTC) 231:22:48, 6 February 2009 (UTC) 212:16:27, 6 February 2009 (UTC) 184:15:14, 6 February 2009 (UTC) 168:03:25, 6 February 2009 (UTC) 147:04:52, 4 February 2009 (UTC) 128:14:33, 1 February 2009 (UTC) 112:20:00, 31 January 2009 (UTC) 89:17:42, 31 January 2009 (UTC) 3644:16:21, 28 August 2011 (UTC) 3661: 3529:09:36, 10 April 2011 (UTC) 3190:14:42, 29 March 2011 (UTC) 3172:. I have already done it. 3106:23:10, 27 March 2011 (UTC) 3079:11:11, 27 March 2011 (UTC) 3018:quantity (voltage) with a 2920:10:41, 24 March 2011 (UTC) 2813:22:16, 21 March 2011 (UTC) 2781:06:51, 22 March 2011 (UTC) 2705:13:06, 20 March 2011 (UTC) 2632:06:49, 20 March 2011 (UTC) 2605:00:47, 20 March 2011 (UTC) 2574:00:21, 20 March 2011 (UTC) 2550:dissipating time-dependent 2496:10:20, 20 March 2011 (UTC) 2470:02:37, 20 March 2011 (UTC) 2447:17:44, 19 March 2011 (UTC) 2414:17:24, 19 March 2011 (UTC) 2398:05:27, 18 March 2011 (UTC) 2245:22:40, 16 March 2011 (UTC) 2207:08:01, 15 March 2011 (UTC) 2175:04:07, 15 March 2011 (UTC) 2146:18:10, 14 March 2011 (UTC) 2119:06:34, 14 March 2011 (UTC) 1835:Faraday's law of induction 1015:08:03, 13 April 2010 (UTC) 993:17:54, 11 April 2010 (UTC) 969:19:29, 23 April 2009 (UTC) 952:17:02, 23 April 2009 (UTC) 836:17:50, 11 April 2010 (UTC) 787:02:00, 20 April 2009 (UTC) 771:18:23, 19 April 2009 (UTC) 3470:22:44, 9 April 2011 (UTC) 3408:18:37, 9 April 2011 (UTC) 3380:15:48, 9 April 2011 (UTC) 3338:16:22, 8 April 2011 (UTC) 3296:02:37, 8 April 2011 (UTC) 3270:00:20, 8 April 2011 (UTC) 3244:20:23, 7 April 2011 (UTC) 1533:11:27, 9 April 2010 (UTC) 1379:08:19, 13 July 2009 (UTC) 1359:03:55, 13 July 2009 (UTC) 1343:01:59, 13 July 2009 (UTC) 1319:03:55, 13 July 2009 (UTC) 1294:01:45, 13 July 2009 (UTC) 1267:19:07, 10 July 2009 (UTC) 1237:02:24, 10 July 2009 (UTC) 888:11:29, 8 March 2011 (UTC) 300:How do I sign this? Dan 3606:18:55, 26 May 2011 (UTC) 3587:04:14, 25 May 2011 (UTC) 3563:03:38, 25 May 2011 (UTC) 3549:21:16, 17 May 2011 (UTC) 2888:do it in a similar way. 2793:inert nonlinear resistor 2753:will not change at all. 2224:time-dependent nonlinear 1685:20:35, 9 June 2010 (UTC) 1667:17:29, 26 May 2010 (UTC) 1221:14:25, 9 July 2009 (UTC) 1194:02:32, 9 July 2009 (UTC) 1161:20:44, 9 June 2010 (UTC) 1128:14:33, 7 June 2010 (UTC) 1110:04:29, 5 June 2010 (UTC) 1085:17:14, 27 May 2010 (UTC) 1060:22:28, 26 May 2010 (UTC) 2860:memcapacitive (fig. 1b) 2716:conditionally nonlinear 2673:capacitance multipliers 2534:time-dependent resistor 2422:Actually, Chua himself 2033:Typo in Definition of Q 1249:the memristive regime. 3437:memristor definition: 2996: 2864:meminductive (fig. 1c) 2655: 2548:elements (resistors), 1968: 691:Von Neumann bottleneck 2997: 2651: 1964: 449:implement neural nets 195:uncertainty principle 96:at that point in time 42:of past discussions. 2955: 2886:multiplying circuits 2514:classification above 844:Inaccessible Article 3614:Linear vs. constant 3494:). Hysteresis is a 2795:. Please, discuss. 2538:resistive capacitor 2424:co-authored a paper 2162:phase change memory 2057:Negative resistance 1581:(2) dw/dt = f(w,i) 2992: 2757:Electromechanical. 2685:voltage-to-current 2681:current-to-voltage 2656: 2654: 2542:resistive inductor 2366: 2359: 2352: 2345: 2344: 2334: 2327: 2320: 2313: 2312: 2302: 2295: 2288: 2281: 2272: 2265: 2258: 1815:, just rearranged. 1614:1958 Interest in 75:Current and Charge 3385:we can only guess 3031:magnetic quantity 3027:electric quantity 2834:Genuine elements. 2652: 2370: 2369: 2362: 2355: 2348: 2343: 2339: 2330: 2323: 2316: 2311: 2307: 2298: 2291: 2284: 2277: 2268: 2261: 2254: 2068:comment added by 1791:comment added by 1764:comment added by 1624:Dudley Allen Buck 1297: 1280:comment added by 1205:solid electrolyte 1100:comment added by 955: 938:comment added by 900:comment added by 800:comment added by 724:comment added by 324: 307:comment added by 158:comment added by 72: 71: 54: 53: 48:current talk page 3652: 3647: 3496:rate-independent 3435:Di Ventra et al. 3404: 3401: 3400: 3397: 3396: 3334: 3331: 3330: 3327: 3326: 3266: 3263: 3262: 3259: 3258: 3198:"Magnetic flux Φ 3102: 3099: 3098: 3095: 3094: 3001: 2999: 2998: 2993: 2988: 2968: 2614:intriguing way. 2601: 2598: 2597: 2594: 2593: 2492: 2489: 2488: 2485: 2484: 2443: 2440: 2439: 2436: 2435: 2249: 2203: 2200: 2199: 2196: 2195: 2142: 2139: 2138: 2135: 2134: 2080: 1970:defined below"? 1803: 1776: 1730: 1725: 1719: 1714: 1616:Frank Rosenblatt 1296: 1274: 1112: 954: 932: 912: 812: 736: 323: 301: 170: 68: 56: 55: 33: 32: 26: 3660: 3659: 3655: 3654: 3653: 3651: 3650: 3649: 3637: 3616: 3571:Circuit dreamer 3536: 3513:Circuit dreamer 3509:hysteresis talk 3488: 3454:Circuit dreamer 3402: 3398: 3394: 3392: 3390: 3364:Circuit dreamer 3357: 3332: 3328: 3324: 3322: 3320: 3308: 3280:Circuit dreamer 3264: 3260: 3256: 3254: 3252: 3228:Circuit dreamer 3225: 3221: 3217: 3213: 3208: 3205: 3201: 3174:Circuit dreamer 3156:pencil graphite 3100: 3096: 3092: 3090: 3088: 3063:Circuit dreamer 3048: 3039: 3009: 2953: 2952: 2927: 2904:Circuit dreamer 2820: 2797:Circuit dreamer 2765:Circuit dreamer 2752: 2748: 2744: 2740: 2736: 2732: 2723:Electrothermal. 2712: 2689:Circuit dreamer 2642: 2616:Circuit dreamer 2599: 2595: 2591: 2589: 2587: 2558:Circuit dreamer 2510: 2490: 2486: 2482: 2480: 2478: 2441: 2437: 2433: 2431: 2429: 2229:Circuit dreamer 2220: 2215: 2201: 2197: 2193: 2191: 2189: 2140: 2136: 2132: 2130: 2128: 2086: 2063: 2059: 2035: 2020:Geoffrey.landis 1902:Geoffrey.landis 1839:Geoffrey.landis 1786: 1759: 1744:Geoffrey.landis 1739: 1734: 1733: 1726: 1722: 1715: 1711: 1695: 1656: 1650: 1646: 1642: 1630: 1607: 1578:(1) v = R(w) i 1541: 1496: 1481:Geoffrey.landis 1459: 1449: 1387: 1385:Ideal Memristor 1275: 1168: 1095: 933: 918: 895: 872:Circuit dreamer 846: 795: 759: 719: 711: 688: 302: 294: 153: 77: 64: 30: 22: 21: 20: 12: 11: 5: 3658: 3656: 3642:comment added 3630:89.204.153.129 3624: 3623: 3615: 3612: 3611: 3610: 3609: 3608: 3590: 3589: 3535: 3532: 3487: 3484: 3483: 3482: 3481: 3480: 3479: 3478: 3477: 3476: 3475: 3474: 3473: 3472: 3450: 3449: 3448: 3419: 3418: 3417: 3416: 3415: 3414: 3413: 3412: 3411: 3410: 3359: 3355: 3345: 3344: 3343: 3342: 3341: 3340: 3306: 3273: 3272: 3223: 3219: 3215: 3211: 3207: 3203: 3199: 3196: 3195: 3194: 3193: 3192: 3162: 3161: 3160: 3159: 3149: 3148: 3147: 3146: 3128: 3127: 3126: 3125: 3118: 3117: 3116: 3115: 3109: 3108: 3054:but it is not 3046: 3042: 3041: 3037: 3034: 3023: 3007: 2991: 2987: 2983: 2980: 2977: 2974: 2971: 2967: 2963: 2960: 2926: 2923: 2819: 2816: 2750: 2746: 2742: 2738: 2734: 2730: 2711: 2708: 2665:"mem-emulator" 2641: 2638: 2637: 2636: 2635: 2634: 2608: 2607: 2509: 2506: 2505: 2504: 2503: 2502: 2501: 2500: 2499: 2498: 2452: 2451: 2450: 2449: 2417: 2416: 2368: 2367: 2360: 2353: 2346: 2336: 2335: 2328: 2321: 2314: 2304: 2303: 2296: 2289: 2282: 2274: 2273: 2266: 2259: 2252: 2219: 2216: 2214: 2211: 2210: 2209: 2149: 2148: 2085: 2082: 2058: 2055: 2034: 2031: 1988: 1987: 1986: 1985: 1984: 1983: 1982: 1981: 1980: 1979: 1952: 1951: 1950: 1949: 1948: 1947: 1946: 1945: 1944: 1943: 1919: 1918: 1917: 1916: 1915: 1914: 1913: 1912: 1891: 1890: 1889: 1888: 1887: 1886: 1866: 1865: 1864: 1863: 1862: 1861: 1852: 1851: 1850: 1849: 1819: 1818: 1817: 1816: 1805: 1804: 1778: 1777: 1738: 1735: 1732: 1731: 1720: 1708: 1707: 1694: 1693:ReRam - Update 1691: 1690: 1689: 1688: 1687: 1653: 1648: 1644: 1640: 1633: 1628: 1612: 1606: 1603: 1572: 1571: 1540: 1537: 1536: 1535: 1525: 1524: 1495: 1492: 1457: 1448: 1445: 1386: 1383: 1382: 1381: 1367:Knowledge:LEAD 1362: 1361: 1322: 1321: 1303: 1270: 1269: 1224: 1223: 1208: 1201: 1167: 1164: 1133: 1132: 1131: 1130: 1088: 1087: 1068: 1049: 1048: 1045: 1041: 1037: 1033: 1029: 1025: 1021: 1020: 1019: 1018: 1017: 998: 997: 996: 995: 981: 972: 971: 917: 914: 891: 890: 845: 842: 841: 840: 839: 838: 824: 821: 814: 813: 790: 789: 758: 755: 754: 753: 726:24.214.120.227 710: 709:Flux Capacitor 707: 706: 705: 693:for a start.) 686: 682: 678: 673: 672: 671: 670: 669: 668: 655: 644: 643: 642: 641: 624: 623: 607: 606: 605: 604: 586: 585: 571: 570: 569: 568: 562: 561: 560: 559: 549: 548: 547: 546: 524: 523: 507: 506: 505: 504: 487: 486: 470: 469: 468: 467: 451:, they do not 437: 436: 420: 419: 418: 417: 399: 398: 382: 381: 380: 379: 362: 361: 344: 342: 341: 293: 290: 289: 288: 272: 271: 270: 269: 251: 234: 233: 217: 216: 215: 214: 187: 186: 160:129.174.74.102 131: 130: 115: 114: 102:is changing"? 76: 73: 70: 69: 62: 52: 51: 34: 23: 18:Talk:Memristor 15: 14: 13: 10: 9: 6: 4: 3: 2: 3657: 3648: 3645: 3641: 3635: 3631: 3627: 3621: 3620: 3619: 3613: 3607: 3603: 3599: 3594: 3593: 3592: 3591: 3588: 3584: 3580: 3576: 3572: 3567: 3566: 3565: 3564: 3560: 3556: 3551: 3550: 3546: 3542: 3533: 3531: 3530: 3526: 3522: 3518: 3514: 3510: 3504: 3500: 3497: 3493: 3485: 3471: 3467: 3463: 3459: 3455: 3451: 3446: 3443:(I would put 3442: 3439: 3438: 3436: 3431: 3430: 3429: 3428: 3427: 3426: 3425: 3424: 3423: 3422: 3421: 3420: 3409: 3406: 3405: 3386: 3383: 3382: 3381: 3377: 3373: 3369: 3365: 3360: 3353: 3352: 3351: 3350: 3349: 3348: 3347: 3346: 3339: 3336: 3335: 3316: 3312: 3304: 3299: 3298: 3297: 3293: 3289: 3285: 3281: 3277: 3276: 3275: 3274: 3271: 3268: 3267: 3248: 3247: 3246: 3245: 3241: 3237: 3233: 3229: 3197: 3191: 3187: 3183: 3179: 3175: 3171: 3166: 3165: 3164: 3163: 3157: 3153: 3152: 3151: 3150: 3144: 3140: 3136: 3132: 3131: 3130: 3129: 3122: 3121: 3120: 3119: 3113: 3112: 3111: 3110: 3107: 3104: 3103: 3083: 3082: 3081: 3080: 3076: 3072: 3068: 3064: 3059: 3057: 3053: 3035: 3032: 3028: 3024: 3021: 3017: 3016:pressure-like 3013: 3012: 3011: 3005: 2989: 2981: 2978: 2975: 2972: 2969: 2961: 2958: 2949: 2947: 2943: 2939: 2934: 2932: 2924: 2922: 2921: 2917: 2913: 2909: 2905: 2899: 2898: 2893: 2889: 2887: 2883: 2879: 2878:voltage drops 2875: 2871: 2869: 2865: 2861: 2857: 2853: 2849: 2845: 2843: 2838: 2835: 2831: 2827: 2825: 2817: 2815: 2814: 2810: 2806: 2802: 2798: 2794: 2790: 2787: 2783: 2782: 2778: 2774: 2770: 2766: 2762: 2758: 2754: 2728: 2724: 2720: 2717: 2709: 2707: 2706: 2702: 2698: 2694: 2690: 2686: 2682: 2676: 2674: 2670: 2666: 2661: 2650: 2646: 2639: 2633: 2629: 2625: 2621: 2617: 2612: 2611: 2610: 2609: 2606: 2603: 2602: 2582: 2578: 2577: 2576: 2575: 2571: 2567: 2563: 2559: 2555: 2551: 2547: 2543: 2539: 2535: 2529: 2527: 2523: 2519: 2515: 2507: 2497: 2494: 2493: 2473: 2472: 2471: 2467: 2463: 2458: 2457: 2456: 2455: 2454: 2453: 2448: 2445: 2444: 2425: 2421: 2420: 2419: 2418: 2415: 2411: 2407: 2402: 2401: 2400: 2399: 2395: 2391: 2388: 2382: 2380: 2376: 2365: 2361: 2358: 2354: 2351: 2347: 2342: 2338: 2337: 2333: 2329: 2326: 2322: 2319: 2315: 2310: 2306: 2305: 2301: 2297: 2294: 2290: 2287: 2283: 2280: 2276: 2275: 2271: 2267: 2264: 2260: 2257: 2253: 2251: 2250: 2247: 2246: 2242: 2238: 2234: 2230: 2225: 2217: 2212: 2208: 2205: 2204: 2184: 2179: 2178: 2177: 2176: 2172: 2168: 2163: 2159: 2155: 2147: 2144: 2143: 2123: 2122: 2121: 2120: 2116: 2112: 2106: 2102: 2098: 2094: 2090: 2081: 2079: 2075: 2071: 2067: 2056: 2054: 2053: 2049: 2045: 2044:GatesofDawn67 2041: 2038: 2032: 2030: 2029: 2025: 2021: 2016: 2013: 2008: 2006: 2005:magnetic flux 2001: 1997: 1996:magnetic flux 1993: 1977: 1973: 1972:Potatoswatter 1967: 1962: 1961: 1960: 1959: 1958: 1957: 1956: 1955: 1954: 1953: 1942: 1938: 1934: 1933:Potatoswatter 1929: 1928: 1927: 1926: 1925: 1924: 1923: 1922: 1921: 1920: 1911: 1907: 1903: 1899: 1898: 1897: 1896: 1895: 1894: 1893: 1892: 1885: 1881: 1877: 1876:Potatoswatter 1872: 1871: 1870: 1869: 1868: 1867: 1858: 1857: 1856: 1855: 1854: 1853: 1848: 1844: 1840: 1836: 1832: 1828: 1827:Magnetic flux 1823: 1822: 1821: 1820: 1814: 1809: 1808: 1807: 1806: 1802: 1798: 1794: 1790: 1784: 1780: 1779: 1775: 1771: 1767: 1763: 1756: 1755: 1754: 1753: 1749: 1745: 1736: 1729: 1724: 1721: 1718: 1713: 1710: 1706: 1704: 1700: 1692: 1686: 1682: 1678: 1673: 1672: 1671: 1670: 1669: 1668: 1664: 1660: 1652: 1638: 1632: 1625: 1621: 1617: 1611: 1604: 1602: 1601: 1597: 1593: 1588: 1585: 1582: 1579: 1576: 1570: 1566: 1562: 1561:Potatoswatter 1558: 1557: 1556: 1555: 1551: 1547: 1538: 1534: 1531: 1527: 1526: 1522: 1518: 1517: 1516: 1515: 1511: 1507: 1503: 1500: 1493: 1491: 1490: 1486: 1482: 1477: 1475: 1471: 1466: 1463: 1453: 1446: 1444: 1443: 1439: 1435: 1429: 1425: 1421: 1419: 1415: 1411: 1406: 1402: 1399: 1395: 1391: 1384: 1380: 1376: 1372: 1368: 1364: 1363: 1360: 1356: 1352: 1351:Potatoswatter 1347: 1346: 1345: 1344: 1340: 1336: 1330: 1329: 1325: 1320: 1316: 1312: 1311:Potatoswatter 1308: 1304: 1300: 1299: 1298: 1295: 1291: 1287: 1283: 1279: 1268: 1264: 1260: 1259:Potatoswatter 1256: 1252: 1251:Potatoswatter 1248: 1244: 1241: 1240: 1239: 1238: 1234: 1230: 1222: 1218: 1214: 1213:Potatoswatter 1209: 1206: 1202: 1198: 1197: 1196: 1195: 1191: 1187: 1181: 1178: 1175: 1172: 1165: 1163: 1162: 1158: 1154: 1151: 1148: 1142: 1141: 1136: 1129: 1125: 1121: 1117: 1116: 1115: 1114: 1113: 1111: 1107: 1103: 1099: 1094: 1086: 1082: 1078: 1073: 1069: 1067: 1064: 1063: 1062: 1061: 1057: 1053: 1046: 1042: 1038: 1034: 1030: 1026: 1022: 1016: 1012: 1008: 1007:Potatoswatter 1004: 1003: 1002: 1001: 1000: 999: 994: 990: 986: 982: 979: 976: 975: 974: 973: 970: 966: 962: 961:Potatoswatter 958: 957: 956: 953: 949: 945: 941: 937: 929: 925: 921: 915: 913: 911: 907: 903: 902:144.173.5.197 899: 889: 885: 881: 877: 873: 869: 864: 863: 862: 860: 856: 850: 843: 837: 833: 829: 825: 822: 818: 817: 816: 815: 811: 807: 803: 799: 792: 791: 788: 784: 780: 779:Potatoswatter 775: 774: 773: 772: 768: 764: 763:99.245.16.164 756: 752: 748: 744: 739: 738: 737: 735: 731: 727: 723: 716: 708: 704: 700: 696: 692: 683: 679: 675: 674: 667: 663: 659: 653: 650: 649: 648: 647: 646: 645: 640: 636: 632: 631:Potatoswatter 628: 627: 626: 625: 622: 618: 614: 609: 608: 603: 599: 595: 594:Potatoswatter 590: 589: 588: 587: 584: 580: 576: 573: 572: 566: 565: 564: 563: 558: 555: 554: 551: 550: 545: 541: 537: 536:Potatoswatter 533: 528: 527: 526: 525: 522: 518: 514: 509: 508: 503: 499: 495: 494:Potatoswatter 491: 490: 489: 488: 485: 481: 477: 472: 471: 466: 462: 458: 457:Potatoswatter 454: 453:model neurons 450: 446: 441: 440: 439: 438: 435: 431: 427: 422: 421: 416: 412: 408: 407:Potatoswatter 403: 402: 401: 400: 397: 393: 389: 384: 383: 378: 374: 370: 369:Potatoswatter 366: 365: 364: 363: 360: 356: 352: 347: 346: 345: 340: 336: 332: 331:Potatoswatter 327: 326: 325: 322: 318: 314: 310: 306: 298: 291: 287: 283: 279: 274: 273: 268: 264: 260: 259:Potatoswatter 256: 252: 250: 246: 242: 241:Potatoswatter 238: 237: 236: 235: 232: 228: 224: 219: 218: 213: 209: 205: 204:Potatoswatter 200: 196: 191: 190: 189: 188: 185: 181: 177: 173: 172: 171: 169: 165: 161: 157: 149: 148: 144: 140: 139:Potatoswatter 136: 129: 125: 121: 117: 116: 113: 109: 105: 104:Potatoswatter 101: 97: 93: 92: 91: 90: 86: 82: 74: 67: 63: 61: 58: 57: 49: 45: 41: 40: 35: 28: 27: 19: 3628: 3625: 3617: 3552: 3537: 3505: 3501: 3489: 3444: 3440: 3434: 3389: 3384: 3319: 3314: 3310: 3302: 3251: 3209: 3169: 3087: 3060: 3055: 3051: 3043: 3030: 3026: 3025:He named an 3022:name (flux). 3019: 3015: 3003: 2950: 2945: 2941: 2937: 2935: 2928: 2900: 2896: 2891: 2890: 2877: 2873: 2872: 2847: 2846: 2841: 2839: 2833: 2832: 2828: 2823: 2821: 2792: 2788: 2785: 2784: 2759:The example 2756: 2755: 2722: 2721: 2715: 2713: 2684: 2680: 2677: 2657: 2643: 2586: 2580: 2553: 2549: 2545: 2541: 2537: 2533: 2530: 2525: 2521: 2517: 2511: 2477: 2428: 2383: 2371: 2340: 2332:Memcapacitor 2308: 2278: 2269: 2262: 2255: 2223: 2221: 2188: 2182: 2150: 2127: 2107: 2103: 2099: 2095: 2091: 2087: 2070:130.65.11.70 2060: 2042: 2039: 2036: 2017: 2011: 2009: 1999: 1991: 1989: 1965: 1830: 1812: 1793:98.218.144.3 1766:98.218.144.3 1740: 1723: 1712: 1696: 1657: 1636: 1634: 1613: 1608: 1589: 1586: 1583: 1580: 1577: 1573: 1542: 1504: 1501: 1497: 1478: 1473: 1469: 1467: 1461: 1454: 1450: 1430: 1426: 1422: 1410:140.232.0.70 1407: 1403: 1400: 1396: 1392: 1388: 1335:218.143.30.1 1331: 1327: 1326: 1323: 1271: 1246: 1225: 1186:218.143.30.1 1182: 1179: 1176: 1173: 1169: 1146: 1144: 1143: 1138: 1137: 1134: 1102:98.218.144.3 1089: 1065: 1050: 930: 926: 922: 919: 896:— Preceding 892: 855:Gutta Percha 851: 847: 802:130.65.11.70 760: 712: 658:151.151.16.9 531: 452: 448: 444: 343: 299: 295: 198: 150: 134: 132: 99: 95: 78: 65: 43: 37: 3638:—Preceding 3004:memristance 2895:resistors") 2892:Conclusion: 2856:multiplying 2786:Conclusion. 2390:Blm19732008 2364:Meminductor 2357:NL inductor 2309:Capacitance 2167:Blm19732008 2111:Blm19732008 2064:—Preceding 2012:immediately 1787:—Preceding 1760:—Preceding 1592:Blm19732008 1434:Blm19732008 1282:Blm19732008 1276:—Preceding 1229:Blm19732008 1096:—Preceding 934:—Preceding 796:—Preceding 743:Blm19732008 720:—Preceding 613:Blm19732008 575:Blm19732008 513:Blm19732008 476:Blm19732008 426:Blm19732008 388:Blm19732008 351:Blm19732008 303:—Preceding 278:Blm19732008 223:Blm19732008 176:Blm19732008 154:—Preceding 133:No, charge 120:Blm19732008 36:This is an 2727:thermistor 2522:capacitors 2341:Inductance 2279:Resistance 1699:R3ap3R.inc 1620:Perceptron 1519:Read this 1506:Mrrealtime 1307:mempacitor 1166:Needs work 695:P.r.newman 445:don't know 3511:as well. 3141:(see the 3020:flow-like 2942:dV = r.dI 2931:archive 1 2749:, R and V 2741:, R and V 2581:reporting 2526:inductors 2518:resistors 2318:Capacitor 2300:Memristor 2263:Nonlinear 2183:memristor 1677:AlanDewey 1659:AlanDewey 1637:Synapse 1 1452:clear. 1153:AlanDewey 1120:AlanDewey 1077:AlanDewey 1052:AlanDewey 1036:involved. 1032:lifetime. 985:telewatho 828:telewatho 66:Archive 2 60:Archive 1 3598:Humanoid 3579:contribs 3555:Humanoid 3541:Humanoid 3521:contribs 3462:contribs 3372:contribs 3288:contribs 3236:contribs 3182:contribs 3071:contribs 3056:magnetic 3052:magnetic 2944:) where 2912:contribs 2805:contribs 2773:contribs 2697:contribs 2669:gyrators 2660:memistor 2624:contribs 2566:contribs 2375:memistor 2350:Inductor 2325:Varactor 2293:Varistor 2286:Resistor 2237:contribs 2181:prevent 2066:unsigned 1789:unsigned 1762:unsigned 1494:Capacity 1371:Bcjordan 1290:contribs 1278:unsigned 1098:unsigned 948:contribs 936:unsigned 898:unsigned 880:contribs 868:memistor 820:section: 798:unsigned 722:unsigned 317:contribs 305:unsigned 255:WP:CIVIL 156:unsigned 3640:undated 2938:V = R.I 2882:gyrator 2852:gyrator 2554:storing 1831:defined 1647:S to Cu 1447:Unclear 1145:The mem 1024:itself. 940:Mvd1221 135:density 39:archive 2462:Zen-in 2406:Zen-in 2270:Memory 2256:Linear 2160:, and 1998:, you 1530:trlkly 1456:flux]Φ 1247:leaves 309:Mlvlvr 3583:email 3525:email 3466:email 3403:Spark 3376:email 3333:Spark 3305:and Φ 3292:email 3265:Spark 3240:email 3186:email 3101:Spark 3075:email 2916:email 2809:email 2777:email 2761:above 2701:email 2628:email 2600:Spark 2570:email 2491:Spark 2442:Spark 2241:email 2202:Spark 2158:CBRAM 2141:Spark 1994:than 1992:other 1645:1.996 1470:i.e., 1044:them. 884:email 687:drool 81:Arnob 16:< 3634:talk 3602:talk 3575:talk 3559:talk 3545:talk 3517:talk 3458:talk 3445:flux 3368:talk 3313:and 3284:talk 3232:talk 3178:talk 3143:talk 3067:talk 2908:talk 2884:and 2862:and 2801:talk 2769:talk 2693:talk 2683:and 2671:and 2620:talk 2562:talk 2512:The 2466:talk 2410:talk 2394:talk 2233:talk 2171:talk 2154:RRAM 2115:talk 2074:talk 2048:talk 2024:talk 2000:must 1976:talk 1937:talk 1906:talk 1880:talk 1843:talk 1797:talk 1770:talk 1748:talk 1737:Flux 1703:talk 1681:talk 1663:talk 1649:1.93 1622:led 1596:talk 1565:talk 1550:talk 1546:Ywaz 1521:news 1510:talk 1485:talk 1474:i.e. 1438:talk 1414:talk 1375:talk 1365:See 1355:talk 1339:talk 1315:talk 1286:talk 1263:talk 1255:talk 1233:talk 1217:talk 1190:talk 1157:talk 1124:talk 1106:talk 1081:talk 1070:See 1056:talk 1011:talk 989:talk 965:talk 944:talk 906:talk 876:talk 859:talk 832:talk 806:talk 783:talk 767:talk 747:talk 730:talk 699:talk 662:talk 635:talk 617:talk 598:talk 579:talk 540:talk 517:talk 498:talk 480:talk 461:talk 430:talk 411:talk 392:talk 373:talk 355:talk 335:talk 313:talk 282:talk 263:talk 245:talk 227:talk 208:talk 180:talk 164:talk 143:talk 124:talk 108:talk 85:talk 3636:) 2870:). 2826:) 2540:or 2381:. 1829:is 1618:'s 532:not 3604:) 3585:) 3581:, 3577:, 3561:) 3547:) 3527:) 3523:, 3519:, 3468:) 3464:, 3460:, 3399:ng 3395:ni 3393:in 3391:Sp 3378:) 3374:, 3370:, 3329:ng 3325:ni 3323:in 3321:Sp 3294:) 3290:, 3286:, 3261:ng 3257:ni 3255:in 3253:Sp 3242:) 3238:, 3234:, 3188:) 3184:, 3180:, 3097:ng 3093:ni 3091:in 3089:Sp 3077:) 3073:, 3069:, 2979:∫ 2959:∫ 2918:) 2914:, 2910:, 2858:, 2854:, 2811:) 2807:, 2803:, 2779:) 2775:, 2771:, 2703:) 2699:, 2695:, 2630:) 2626:, 2622:, 2596:ng 2592:ni 2590:in 2588:Sp 2572:) 2568:, 2564:, 2487:ng 2483:ni 2481:in 2479:Sp 2468:) 2438:ng 2434:ni 2432:in 2430:Sp 2412:) 2396:) 2243:) 2239:, 2235:, 2198:ng 2194:ni 2192:in 2190:Sp 2173:) 2156:, 2137:ng 2133:ni 2131:in 2129:Sp 2117:) 2076:) 2050:) 2026:) 1939:) 1908:) 1882:) 1845:) 1799:) 1772:) 1750:) 1705:) 1683:) 1665:) 1627:Cu 1598:) 1567:) 1552:) 1512:) 1487:) 1440:) 1420:) 1416:) 1377:) 1357:) 1341:) 1317:) 1309:. 1292:) 1288:• 1265:) 1235:) 1219:) 1192:) 1159:) 1126:) 1108:) 1083:) 1058:) 1013:) 991:) 967:) 950:) 946:• 908:) 886:) 882:, 878:, 861:) 834:) 808:) 785:) 769:) 749:) 732:) 701:) 664:) 637:) 619:) 600:) 581:) 542:) 519:) 500:) 482:) 463:) 432:) 413:) 394:) 375:) 357:) 337:) 319:) 315:• 284:) 265:) 247:) 229:) 210:) 182:) 166:) 145:) 126:) 110:) 87:) 3646:. 3632:( 3600:( 3573:( 3557:( 3543:( 3515:( 3456:( 3366:( 3356:m 3315:I 3311:V 3307:m 3303:Q 3282:( 3230:( 3224:m 3220:m 3216:m 3212:m 3206:" 3204:m 3200:m 3176:( 3065:( 3047:m 3038:m 3033:. 3008:m 2990:t 2986:d 2982:I 2976:R 2973:= 2970:t 2966:d 2962:V 2946:r 2906:( 2897:. 2822:( 2799:( 2767:( 2751:R 2747:R 2743:R 2739:R 2735:R 2731:R 2691:( 2618:( 2560:( 2536:( 2464:( 2408:( 2392:( 2231:( 2169:( 2113:( 2072:( 2046:( 2022:( 1978:) 1974:( 1935:( 1904:( 1878:( 1841:( 1795:( 1768:( 1746:( 1701:( 1679:( 1661:( 1641:2 1629:2 1594:( 1563:( 1548:( 1508:( 1483:( 1462:q 1458:m 1436:( 1412:( 1408:( 1373:( 1353:( 1337:( 1313:( 1284:( 1261:( 1253:( 1231:( 1215:( 1188:( 1155:( 1147:r 1122:( 1104:( 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