Memristor

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Memristor

Memristor developed by the University of Illinois at Urbana-Champaign and National Energy Technology Laboratory
Invented	Leon Chua (1971)
Electronic symbol

A memristor (/ˈmɛmrɪstər/; a portmanteau of memory resistor) is a non-linear two-terminal electrical component relating electric charge and magnetic flux linkage. It was described and named in 1971 by Leon Chua, completing a theoretical quartet of fundamental electrical components which also comprises the resistor, capacitor and inductor.

Chua and Kang later generalized the concept to memristive systems. Such a system comprises a circuit, of multiple conventional components, which mimics key properties of the ideal memristor component and is also commonly referred to as a memristor. Several such memristor system technologies have been developed, notably ReRAM.

The identification of memristive properties in electronic devices has attracted controversy. Experimentally, the ideal memristor has yet to be demonstrated.

As a fundamental electrical component

Conceptual symmetries of resistor, capacitor, inductor, and memristor

Chua in his 1971 paper identified a theoretical symmetry between the non-linear resistor (voltage vs. current), non-linear capacitor (voltage vs. charge), and non-linear inductor (magnetic flux linkage vs. current). From this symmetry he inferred the characteristics of a fourth fundamental non-linear circuit element, linking magnetic flux and charge, which he called the memristor. In contrast to a linear (or non-linear) resistor, the memristor has a dynamic relationship between current and voltage, including a memory of past voltages or currents. Other scientists had proposed dynamic memory resistors such as the memistor of Bernard Widrow, but Chua introduced a mathematical generality.

Derivation and characteristics

The memristor was originally defined in terms of a non-linear functional relationship between magnetic flux linkage Φ_m(t) and the amount of electric charge that has flowed, q(t):

${\displaystyle f({\mathrm{\Phi }}_{\mathrm{m}}(t),q(t))=0}$

The magnetic flux linkage, Φ_m, is generalized from the circuit characteristic of an inductor. It does not represent a magnetic field here. Its physical meaning is discussed below. The symbol Φ_m may be regarded as the integral of voltage over time.

In the relationship between Φ_m and q, the derivative of one with respect to the other depends on the value of one or the other, and so each memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge.

${\displaystyle M(q)=\frac{\mathrm{d}{\mathrm{\Phi }}_{\mathrm{m}}}{\mathrm{d}q}}$

Substituting the flux as the time integral of the voltage, and charge as the time integral of current, the more convenient forms are;

${\displaystyle M(q(t))=\frac{\mathrm{d}{\mathrm{\Phi }}_{}/\mathrm{d}t}{\mathrm{d}q/\mathrm{d}t}=\frac{V(t)}{I(t)}}$

To relate the memristor to the resistor, capacitor, and inductor, it is helpful to isolate the term M(q), which characterizes the device, and write it as a differential equation.

Device	Characteristic property (units)	Differential equation
Resistor (R)	Resistance (V / A, or ohm, Ω)	R = dV / dI
Capacitor (C)	Capacitance (C / V, or farad)	C = dq / dV
Inductor (L)	Inductance (Wb / A, or henry)	L = dΦm / dI
Memristor (M)	Memristance (Wb / C, or ohm)	M = dΦm / dq

The above table covers all meaningful ratios of differentials of I, q, Φ_m, and V. No device can relate dI to dq, or dΦ_m to dV, because I is the derivative of q and Φ_m is the integral of V.

It can be inferred from this that memristance is charge-dependent resistance. If M(q(t)) is a constant, then we obtain Ohm's law R(t) = V(t)/I(t). If M(q(t)) is nontrivial, however, the equation is not equivalent because q(t) and M(q(t)) can vary with time. Solving for voltage as a function of time produces

${\displaystyle V(t)=M(q(t))I(t)}$

This equation reveals that memristance defines a linear relationship between current and voltage, as long as M does not vary with charge. Nonzero current implies time varying charge. Alternating current, however, may reveal the linear dependence in circuit operation by inducing a measurable voltage without net charge movement—as long as the maximum change in q does not cause much change in M.

Furthermore, the memristor is static if no current is applied. If I(t) = 0, we find V(t) = 0 and M(t) is constant. This is the essence of the memory effect.

Analogously, we can define a ${\displaystyle W(\varphi (t))}$ as menductance.

${\displaystyle i(t)=W(\varphi (t))v(t)}$

The power consumption characteristic recalls that of a resistor, I²R.

${\displaystyle P(t)=I(t)V(t)=I^2(t)M(q(t))}$

As long as M(q(t)) varies little, such as under alternating current, the memristor will appear as a constant resistor. If M(q(t)) increases rapidly, however, current and power consumption will quickly stop.

M(q) is physically restricted to be positive for all values of q (assuming the device is passive and does not become superconductive at some q). A negative value would mean that it would perpetually supply energy when operated with alternating current.

Modelling and validation

In order to understand the nature of memristor function, some knowledge of fundamental circuit theoretic concepts is useful, starting with the concept of device modeling.

Engineers and scientists seldom analyze a physical system in its original form. Instead, they construct a model which approximates the behaviour of the system. By analyzing the behaviour of the model, they hope to predict the behaviour of the actual system. The primary reason for constructing models is that physical systems are usually too complex to be amenable to a practical analysis.

In the 20th century, work was done on devices where researchers did not recognize the memristive characteristics. This has raised the suggestion that such devices should be recognised as memristors. Pershin and Di Ventra have proposed a test that can help to resolve some of the long-standing controversies about whether an ideal memristor does actually exist or is a purely mathematical concept.

The rest of this article primarily addresses memristors as related to ReRAM devices, since the majority of work since 2008 has been concentrated in this area.

Superconducting memristor component

Dr. Paul Penfield, in a 1974 MIT technical report mentions the memristor in connection with Josephson junctions. This was an early use of the word "memristor" in the context of a circuit device.

One of the terms in the current through a Josephson junction is of the form:

${\displaystyle \begin{array}{rl}{i}_M(v)& =ϵ\cos ({\varphi }_0)v\\ & =W({\varphi }_0)v\end{array}}$

where ${\displaystyle ϵ}$ is a constant based on the physical superconducting materials, ${\displaystyle v}$ is the voltage across the junction and ${\displaystyle i_M}$ is the current through the junction.

Through the late 20th century, research regarding this phase-dependent conductance in Josephson junctions was carried out. A more comprehensive approach to extracting this phase-dependent conductance appeared with Peotta and DiVentra's seminal paper in 2014.

Memristor circuits

Due to the practical difficulty of studying the ideal memristor, we will discuss other electrical devices which can be modelled using memristors. For a mathematical description of a memristive device (systems), see Theory.

A discharge tube can be modelled as a memristive device, with resistance being a function of the number of conduction electrons ${\displaystyle n_e}$.

${\displaystyle \begin{array}{rl}{v}_M& =R(n_e)i_M\\ \frac{d{n}_e}{dt}& =\beta n+\alpha R(n_e)i_M^2\end{array}}$

${\displaystyle v_M}$ is the voltage across the discharge tube, ${\displaystyle i_M}$ is the current flowing through it and ${\displaystyle n_e}$ is the number of conduction electrons. A simple memristance function is ${\displaystyle R(n_e)=\frac{F}{n_e}}$. ${\displaystyle \alpha ,\beta }$ and ${\displaystyle F}$ are parameters depending on the dimensions of the tube and the gas fillings. An experimental identification of memristive behaviour is the "pinched hysteresis loop" in the ${\displaystyle v-i}$ plane. For an experiment that shows such a characteristic for a common discharge tube, see "A physical memristor Lissajous figure" (YouTube). The video also illustrates how to understand deviations in the pinched hysteresis characteristics of physical memristors.

Thermistors can be modelled as memristive devices.

${\displaystyle \begin{array}{rl}v& =R_0(T_0)\exp \left[\beta \left(\frac{1}{T}-\frac{1}{T_0}\right)\right]i\\ & \equiv R(T)i\\ \frac{dT}{dt}& =\frac{1}{C}\left[-\delta \cdot (T-T_0)+R(T)i^2\right]\end{array}}$

${\displaystyle \beta }$ is a material constant, ${\displaystyle T}$ is the absolute body temperature of the thermistor, ${\displaystyle T_0}$ is the ambient temperature (both temperatures in Kelvin), ${\displaystyle R_0(T_0)}$ denotes the cold temperature resistance at ${\displaystyle T=T_0}$, ${\displaystyle C}$ is the heat capacitance and ${\displaystyle \delta }$ is the dissipation constant for the thermistor.

A fundamental phenomenon that has hardly been studied is memristive behaviour in pn-junctions. The memristor plays a crucial role in mimicking the charge storage effect in the diode base, and is also responsible for the conductivity modulation phenomenon (that is so important during forward transients).

Criticisms

In 2008, a team at HP Labs found experimental evidence for the Chua's memristor based on an analysis of a thin film of titanium dioxide, thus connecting the operation of ReRAM devices to the memristor concept. According to HP Labs, the memristor would operate in the following way: the memristor's electrical resistance is not constant but depends on the current that had previously flowed through the device, i.e., its present resistance depends on how much electric charge has previously flowed through it and in what direction; the device remembers its history—the so-called non-volatility property. When the electric power supply is turned off, the memristor remembers its most recent resistance until it is turned on again.

The HP Labs result was published in the scientific journal Nature. Following this claim, Leon Chua has argued that the memristor definition could be generalized to cover all forms of two-terminal non-volatile memory devices based on resistance switching effects. Chua also argued that the memristor is the oldest known circuit element, with its effects predating the resistor, capacitor, and inductor. There are, however, some serious doubts as to whether a genuine memristor can actually exist in physical reality. Additionally, some experimental evidence contradicts Chua's generalization since a non-passive nanobattery effect is observable in resistance switching memory. A simple test has been proposed by Pershin and Di Ventra to analyze whether such an ideal or generic memristor does actually exist or is a purely mathematical concept. Up to now, there seems to be no experimental resistance switching device (ReRAM) which can pass the test.

These devices are intended for applications in nanoelectronic memory devices, computer logic, and neuromorphic/neuromemristive computer architectures. In 2013, Hewlett-Packard CTO Martin Fink suggested that memristor memory may become commercially available as early as 2018. In March 2012, a team of researchers from HRL Laboratories and the University of Michigan announced the first functioning memristor array built on a CMOS chip.

An array of 17 purpose-built oxygen-depleted titanium dioxide memristors built at HP Labs, imaged by an atomic force microscope. The wires are about 50 nm, or 150 atoms, wide. Electric current through the memristors shifts the oxygen vacancies, causing a gradual and persistent change in electrical resistance.

According to the original 1971 definition, the memristor is the fourth fundamental circuit element, forming a non-linear relationship between electric charge and magnetic flux linkage. In 2011, Chua argued for a broader definition that includes all two-terminal non-volatile memory devices based on resistance switching. Williams argued that MRAM, phase-change memory and ReRAM are memristor technologies. Some researchers argued that biological structures such as blood and skin fit the definition. Others argued that the memory device under development by HP Labs and other forms of ReRAM are not memristors, but rather part of a broader class of variable-resistance systems, and that a broader definition of memristor is a scientifically unjustifiable land grab that favored HP's memristor patents.

In 2011, Meuffels and Schroeder noted that one of the early memristor papers included a mistaken assumption regarding ionic conduction. In 2012, Meuffels and Soni discussed some fundamental issues and problems in the realization of memristors. They indicated inadequacies in the electrochemical modeling presented in the Nature article "The missing memristor found" because the impact of concentration polarization effects on the behavior of metal−TiO_2−x−metal structures under voltage or current stress was not considered. This critique was referred to by Valov et al. in 2013.

In a kind of thought experiment, Meuffels and Soni furthermore revealed a severe inconsistency: If a current-controlled memristor with the so-called non-volatility property exists in physical reality, its behavior would violate Landauer's principle, which places a limit on the minimum amount of energy required to change "information" states of a system. This critique was finally adopted by Di Ventra and Pershin in 2013.

Within this context, Meuffels and Soni pointed to a fundamental thermodynamic principle: Non-volatile information storage requires the existence of free-energy barriers that separate the distinct internal memory states of a system from each other; otherwise, one would be faced with an "indifferent" situation, and the system would arbitrarily fluctuate from one memory state to another just under the influence of thermal fluctuations. When unprotected against thermal fluctuations, the internal memory states exhibit some diffusive dynamics, which causes state degradation. The free-energy barriers must therefore be high enough to ensure a low bit-error probability of bit operation. Consequently, there is always a lower limit of energy requirement – depending on the required bit-error probability – for intentionally changing a bit value in any memory device.

In the general concept of memristive system the defining equations are (see Theory):

${\displaystyle \begin{array}{rl}y(t)& =g(\mathbf{x},u,t)u(t),\\ \dot{\mathbf{x}}& =f(\mathbf{x},u,t),\end{array}}$

where u(t) is an input signal, and y(t) is an output signal. The vector x represents a set of n state variables describing the different internal memory states of the device. ẋ is the time-dependent rate of change of the state vector x with time.

When one wants to go beyond mere curve fitting and aims at a real physical modeling of non-volatile memory elements, e.g., resistive random-access memory devices, one has to keep an eye on the aforementioned physical correlations. To check the adequacy of the proposed model and its resulting state equations, the input signal u(t) can be superposed with a stochastic term ξ(t), which takes into account the existence of inevitable thermal fluctuations. The dynamic state equation in its general form then finally reads:

${\displaystyle \dot{\mathbf{x}}=f(\mathbf{x},u(t)+\xi (t),t),}$

where ξ(t) is, e.g., white Gaussian current or voltage noise. On base of an analytical or numerical analysis of the time-dependent response of the system towards noise, a decision on the physical validity of the modeling approach can be made, e.g., would the system be able to retain its memory states in power-off mode?

Such an analysis was performed by Di Ventra and Pershin with regard to the genuine current-controlled memristor. As the proposed dynamic state equation provides no physical mechanism enabling such a memristor to cope with inevitable thermal fluctuations, a current-controlled memristor would erratically change its state in course of time just under the influence of current noise. Di Ventra and Pershin thus concluded that memristors whose resistance (memory) states depend solely on the current or voltage history would be unable to protect their memory states against unavoidable Johnson–Nyquist noise and permanently suffer from information loss, a so-called "stochastic catastrophe". A current-controlled memristor can thus not exist as a solid-state device in physical reality.

The above-mentioned thermodynamic principle furthermore implies that the operation of two-terminal non-volatile memory devices (e.g. "resistance-switching" memory devices (ReRAM)) cannot be associated with the memristor concept, i.e., such devices cannot by itself remember their current or voltage history. Transitions between distinct internal memory or resistance states are of probabilistic nature. The probability for a transition from state {i} to state {j} depends on the height of the free-energy barrier between both states. The transition probability can thus be influenced by suitably driving the memory device, i.e., by "lowering" the free-energy barrier for the transition {i} → {j} by means of, for example, an externally applied bias.

A "resistance switching" event can simply be enforced by setting the external bias to a value above a certain threshold value. This is the trivial case, i.e., the free-energy barrier for the transition {i} → {j} is reduced to zero. In case one applies biases below the threshold value, there is still a finite probability that the device will switch in course of time (triggered by a random thermal fluctuation), but – as one is dealing with probabilistic processes – it is impossible to predict when the switching event will occur. That is the basic reason for the stochastic nature of all observed resistance-switching (ReRAM) processes. If the free-energy barriers are not high enough, the memory device can even switch without having to do anything.

When a two-terminal non-volatile memory device is found to be in a distinct resistance state {j}, there exists therefore no physical one-to-one relationship between its present state and its foregoing voltage history. The switching behavior of individual non-volatile memory devices thus cannot be described within the mathematical framework proposed for memristor/memristive systems.

An extra thermodynamic curiosity arises from the definition that memristors/memristive devices should energetically act like resistors. The instantaneous electrical power entering such a device is completely dissipated as Joule heat to the surrounding, so no extra energy remains in the system after it has been brought from one resistance state x_i to another one x_j. Thus, the internal energy of the memristor device in state x_i, U(V, T, x_i), would be the same as in state x_j, U(V, T, x_j), even though these different states would give rise to different device's resistances, which itself must be caused by physical alterations of the device's material.

Other researchers noted that memristor models based on the assumption of linear ionic drift do not account for asymmetry between set time (high-to-low resistance switching) and reset time (low-to-high resistance switching) and do not provide ionic mobility values consistent with experimental data. Non-linear ionic-drift models have been proposed to compensate for this deficiency.

A 2014 article from researchers of ReRAM concluded that Strukov's (HP's) initial/basic memristor modeling equations do not reflect the actual device physics well, whereas subsequent (physics-based) models such as Pickett's model or Menzel's ECM model (Menzel is a co-author of that article) have adequate predictability, but are computationally prohibitive. As of 2014, the search continues for a model that balances these issues; the article identifies Chang's and Yakopcic's models as potentially good compromises.

Martin Reynolds, an electrical engineering analyst with research outfit Gartner, commented that while HP was being sloppy in calling their device a memristor, critics were being pedantic in saying that it was not a memristor.

Experimental tests

Chua suggested experimental tests to determine if a device may properly be categorized as a memristor:

• The Lissajous curve in the voltage–current plane is a pinched hysteresis loop when driven by any bipolar periodic voltage or current without respect to initial conditions.
• The area of each lobe of the pinched hysteresis loop shrinks as the frequency of the forcing signal increases.
• As the frequency tends to infinity, the hysteresis loop degenerates to a straight line through the origin, whose slope depends on the amplitude and shape of the forcing signal.

According to Chua all resistive switching memories including ReRAM, MRAM and phase-change memory meet these criteria and are memristors. However, the lack of data for the Lissajous curves over a range of initial conditions or over a range of frequencies complicates assessments of this claim.

Experimental evidence shows that redox-based resistance memory (ReRAM) includes a nanobattery effect that is contrary to Chua's memristor model. This indicates that the memristor theory needs to be extended or corrected to enable accurate ReRAM modeling.

Theory

In 2008, researchers from HP Labs introduced a model for a memristance function based on thin films of titanium dioxide. For R_ON ≪ R_OFF the memristance function was determined to be

${\displaystyle M(q(t))=R_{\mathrm{O}\mathrm{F}\mathrm{F}}\cdot \left(1-\frac{{\mu }_v{R}_{\mathrm{O}\mathrm{N}}}{D^2}q(t)\right)}$

where R_OFF represents the high resistance state, R_ON represents the low resistance state, μ_v represents the mobility of dopants in the thin film, and D represents the film thickness. The HP Labs group noted that "window functions" were necessary to compensate for differences between experimental measurements and their memristor model due to non-linear ionic drift and boundary effects.

Operation as a switch

For some memristors, applied current or voltage causes substantial change in resistance. Such devices may be characterized as switches by investigating the time and energy that must be spent to achieve a desired change in resistance. This assumes that the applied voltage remains constant. Solving for energy dissipation during a single switching event reveals that for a memristor to switch from R_on to R_off in time T_on to T_off, the charge must change by ΔQ = Q_on−Q_off.

${\displaystyle E_{\mathrm{s}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{c}\mathrm{h}}=V^2{\int }_{T_{\mathrm{o}\mathrm{f}\mathrm{f}}}^{T_{\mathrm{o}\mathrm{n}}}\frac{\mathrm{d}t}{M(q(t))}=V^2{\int }_{Q_{\mathrm{o}\mathrm{f}\mathrm{f}}}^{Q_{\mathrm{o}\mathrm{n}}}\frac{\mathrm{d}q}{I(q)M(q)}=V^2{\int }_{Q_{\mathrm{o}\mathrm{f}\mathrm{f}}}^{Q_{\mathrm{o}\mathrm{n}}}\frac{\mathrm{d}q}{V(q)}=V\mathrm{\Delta }Q}$

Substituting V = I(q)M(q), and then ∫dq/V = ∆Q/V for constant VTo produces the final expression. This power characteristic differs fundamentally from that of a metal oxide semiconductor transistor, which is capacitor-based. Unlike the transistor, the final state of the memristor in terms of charge does not depend on bias voltage.

The type of memristor described by Williams ceases to be ideal after switching over its entire resistance range, creating hysteresis, also called the "hard-switching regime". Another kind of switch would have a cyclic M(q) so that each off-on event would be followed by an on-off event under constant bias. Such a device would act as a memristor under all conditions, but would be less practical.

Memristive systems

In the more general concept of an n-th order memristive system the defining equations are

${\displaystyle \begin{array}{rl}y(t)& =g(\mathbf{\text{x}},u,t)u(t),\\ \dot{\mathbf{\text{x}}}& =f(\mathbf{\text{x}},u,t)\end{array}}$

where u(t) is an input signal, y(t) is an output signal, the vector x represents a set of n state variables describing the device, and g and f are continuous functions. For a current-controlled memristive system the signal u(t) represents the current signal i(t) and the signal y(t) represents the voltage signal v(t). For a voltage-controlled memristive system the signal u(t) represents the voltage signal v(t) and the signal y(t) represents the current signal i(t).

The pure memristor is a particular case of these equations, namely when x depends only on charge (x = q) and since the charge is related to the current via the time derivative dq/dt = i(t). Thus for pure memristors f (i.e. the rate of change of the state) must be equal or proportional to the current i(t) .

Pinched hysteresis

Example of pinched hysteresis curve, V versus I

One of the resulting properties of memristors and memristive systems is the existence of a pinched hysteresis effect. For a current-controlled memristive system, the input u(t) is the current i(t), the output y(t) is the voltage v(t), and the slope of the curve represents the electrical resistance. The change in slope of the pinched hysteresis curves demonstrates switching between different resistance states which is a phenomenon central to ReRAM and other forms of two-terminal resistance memory. At high frequencies, memristive theory predicts the pinched hysteresis effect will degenerate, resulting in a straight line representative of a linear resistor. It has been proven that some types of non-crossing pinched hysteresis curves (denoted Type-II) cannot be described by memristors.

Memristive networks and mathematical models of circuit interactions

The concept of memristive networks was first introduced by Leon Chua in his 1965 paper "Memristive Devices and Systems." Chua proposed the use of memristive devices as a means of building artificial neural networks that could simulate the behavior of the human brain. In fact, memristive devices in circuits have complex interactions due to Kirchhoff's laws. A memristive network is a type of artificial neural network that is based on memristive devices, which are electronic components that exhibit the property of memristance. In a memristive network, the memristive devices are used to simulate the behavior of neurons and synapses in the human brain. The network consists of layers of memristive devices, each of which is connected to other layers through a set of weights. These weights are adjusted during the training process, allowing the network to learn and adapt to new input data. One advantage of memristive networks is that they can be implemented using relatively simple and inexpensive hardware, making them an attractive option for developing low-cost artificial intelligence systems. They also have the potential to be more energy efficient than traditional artificial neural networks, as they can store and process information using less power. However, the field of memristive networks is still in the early stages of development, and more research is needed to fully understand their capabilities and limitations. For the simplest model with only memristive devices with voltage generators in series, there is an exact and in closed form equation (Caravelli-Traversa-Di Ventra equation, CTD) which describes the evolution of the internal memory of the network for each device. For a simple memristor model (but not realistic) of a switch between two resistance values, given by the Williams-Strukov model ${\displaystyle R(x)=R_{off}(1-x)+R_{on}x}$, with ${\displaystyle dx/dt=I/\beta -\alpha x}$, there is a set of nonlinearly coupled differential equations that takes the form:

${\displaystyle \frac{d\overrightarrow{x}}{dt}=-\alpha \overrightarrow{x}+\frac{1}{\beta }(I-\chi \mathrm{\Omega }X{)}^{-1}\mathrm{\Omega }\overrightarrow{S}}$

where ${\displaystyle X}$ is the diagonal matrix with elements ${\displaystyle x_i}$ on the diagonal, ${\displaystyle \alpha ,\beta ,\chi }$ are based on the memristors physical parameters. The vector ${\displaystyle \overrightarrow{S}}$ is the vector of voltage generators in series to the memristors. The circuit topology enters only in the projector operator ${\displaystyle {\mathrm{\Omega }}^2=\mathrm{\Omega }}$, defined in terms of the cycle matrix of the graph. The equation provides a concise mathematical description of the interactions due to Kirchhoff 's laws. Interestingly, the equation shares many properties in common with a Hopfield network, such as the existence of Lyapunov functions and classical tunnelling phenomena. In the context of memristive networks, the CTD equation may be used to predict the behavior of memristive devices under different operating conditions, or to design and optimize memristive circuits for specific applications.

Extended systems

Some researchers have raised the question of the scientific legitimacy of HP's memristor models in explaining the behavior of ReRAM. and have suggested extended memristive models to remedy perceived deficiencies.

One example attempts to extend the memristive systems framework by including dynamic systems incorporating higher-order derivatives of the input signal u(t) as a series expansion

${\displaystyle \begin{array}{rl}y(t)& =g_0(\mathbf{\text{x}},u)u(t)+g_1(\mathbf{\text{x}},u)\frac{{\mathrm{d}}^{2}u}{\mathrm{d}{t}^2}+g_2(\mathbf{\text{x}},u)\frac{{\mathrm{d}}^{4}u}{\mathrm{d}{t}^4}+\dots +g_m(\mathbf{\text{x}},u)\frac{{\mathrm{d}}^{2m}u}{\mathrm{d}{t}^{2m}},\\ \dot{\mathbf{\text{x}}}& =f(\mathbf{\text{x}},u)\end{array}}$

where m is a positive integer, u(t) is an input signal, y(t) is an output signal, the vector x represents a set of n state variables describing the device, and the functions g and f are continuous functions. This equation produces the same zero-crossing hysteresis curves as memristive systems but with a different frequency response than that predicted by memristive systems.

Another example suggests including an offset value ${\displaystyle a}$ to account for an observed nanobattery effect which violates the predicted zero-crossing pinched hysteresis effect.

${\displaystyle \begin{array}{rl}y(t)& =g_0(\mathbf{\text{x}},u)(u(t)-a),\\ \dot{\mathbf{\text{x}}}& =f(\mathbf{\text{x}},u)\end{array}}$

Implementations

Titanium dioxide memristor

Interest in the memristor revived when an experimental solid-state version was reported by R. Stanley Williams of Hewlett Packard in 2007. The article was the first to demonstrate that a solid-state device could have the characteristics of a memristor based on the behavior of nanoscale thin films. The device neither uses magnetic flux as the theoretical memristor suggested, nor stores charge as a capacitor does, but instead achieves a resistance dependent on the history of current.

Although not cited in HP's initial reports on their TiO₂ memristor, the resistance switching characteristics of titanium dioxide were originally described in the 1960s.

The HP device is composed of a thin (50 nm) titanium dioxide film between two 5 nm thick electrodes, one titanium, the other platinum. Initially, there are two layers to the titanium dioxide film, one of which has a slight depletion of oxygen atoms. The oxygen vacancies act as charge carriers, meaning that the depleted layer has a much lower resistance than the non-depleted layer. When an electric field is applied, the oxygen vacancies drift (see Fast ion conductor), changing the boundary between the high-resistance and low-resistance layers. Thus the resistance of the film as a whole is dependent on how much charge has been passed through it in a particular direction, which is reversible by changing the direction of current. Since the HP device displays fast ion conduction at nanoscale, it is considered a nanoionic device.

Memristance is displayed only when both the doped layer and depleted layer contribute to resistance. When enough charge has passed through the memristor that the ions can no longer move, the device enters hysteresis. It ceases to integrate q=∫I dt, but rather keeps q at an upper bound and M fixed, thus acting as a constant resistor until current is reversed.

Memory applications of thin-film oxides had been an area of active investigation for some time. IBM published an article in 2000 regarding structures similar to that described by Williams. Samsung has a U.S. patent for oxide-vacancy based switches similar to that described by Williams.

In April 2010, HP labs announced that they had practical memristors working at 1 ns (~1 GHz) switching times and 3 nm by 3 nm sizes, which bodes well for the future of the technology. At these densities it could easily rival the current sub-25 nm flash memory technology.

Silicon dioxide memristor

It seems that memristance has been reported in nanoscale thin films of silicon dioxide as early as the 1960s .

However, hysteretic conductance in silicon was associated to memristive effects only in 2009.  More recently, beginning in 2012, Tony Kenyon, Adnan Mehonic and their group clearly demonstrated that the resistive switching in silicon oxide thin films is due to the formation of oxygen vacancy filaments in defect-engineered silicon dioxide, having probed directly the movement of oxygen under electrical bias, and imaged the resultant conductive filaments using conductive atomic force microscopy. 

Polymeric memristor

In 2004, Krieger and Spitzer described dynamic doping of polymer and inorganic dielectric-like materials that improved the switching characteristics and retention required to create functioning nonvolatile memory cells. They used a passive layer between electrode and active thin films, which enhanced the extraction of ions from the electrode. It is possible to use fast ion conductor as this passive layer, which allows a significant reduction of the ionic extraction field.

In July 2008, Erokhin and Fontana claimed to have developed a polymeric memristor before the more recently announced titanium dioxide memristor.

In 2010, Alibart, Gamrat, Vuillaume et al. introduced a new hybrid organic/nanoparticle device (the NOMFET : Nanoparticle Organic Memory Field Effect Transistor), which behaves as a memristor and which exhibits the main behavior of a biological spiking synapse. This device, also called a synapstor (synapse transistor), was used to demonstrate a neuro-inspired circuit (associative memory showing a pavlovian learning).

In 2012, Crupi, Pradhan and Tozer described a proof of concept design to create neural synaptic memory circuits using organic ion-based memristors. The synapse circuit demonstrated long-term potentiation for learning as well as inactivity based forgetting. Using a grid of circuits, a pattern of light was stored and later recalled. This mimics the behavior of the V1 neurons in the primary visual cortex that act as spatiotemporal filters that process visual signals such as edges and moving lines.

In 2012, Erokhin and co-authors have demonstrated a stochastic three-dimensional matrix with capabilities for learning and adapting based on polymeric memristor.

Layered memristor

In 2014, Bessonov et al. reported a flexible memristive device comprising a MoO_x/MoS₂ heterostructure sandwiched between silver electrodes on a plastic foil. The fabrication method is entirely based on printing and solution-processing technologies using two-dimensional layered transition metal dichalcogenides (TMDs). The memristors are mechanically flexible, optically transparent and produced at low cost. The memristive behaviour of switches was found to be accompanied by a prominent memcapacitive effect. High switching performance, demonstrated synaptic plasticity and sustainability to mechanical deformations promise to emulate the appealing characteristics of biological neural systems in novel computing technologies.

Atomristor

Atomristor is defined as the electrical devices showing memristive behavior in atomically thin nanomaterials or atomic sheets. In 2018, Ge and Wu et al. in the Akinwande group at the University of Texas, first reported a universal memristive effect in single-layer TMD (MX₂, M = Mo, W; and X = S, Se) atomic sheets based on vertical metal-insulator-metal (MIM) device structure. The work was later extended to monolayer hexagonal boron nitride, which is the thinnest memory material of around 0.33 nm. These atomristors offer forming-free switching and both unipolar and bipolar operation. The switching behavior is found in single-crystalline and poly-crystalline films, with various conducting electrodes (gold, silver and graphene). Atomically thin TMD sheets are prepared via CVD/MOCVD, enabling low-cost fabrication. Afterwards, taking advantage of the low "on" resistance and large on/off ratio, a high-performance zero-power RF switch is proved based on MoS₂ or h-BN atomristors, indicating a new application of memristors for 5G, 6G and THz communication and connectivity systems. In 2020, atomistic understanding of the conductive virtual point mechanism was elucidated in an article in nature nanotechnology.

Ferroelectric memristor

The ferroelectric memristor is based on a thin ferroelectric barrier sandwiched between two metallic electrodes. Switching the polarization of the ferroelectric material by applying a positive or negative voltage across the junction can lead to a two order of magnitude resistance variation: R_OFF ≫ R_ON (an effect called Tunnel Electro-Resistance). In general, the polarization does not switch abruptly. The reversal occurs gradually through the nucleation and growth of ferroelectric domains with opposite polarization. During this process, the resistance is neither R_ON or R_OFF, but in between. When the voltage is cycled, the ferroelectric domain configuration evolves, allowing a fine tuning of the resistance value. The ferroelectric memristor's main advantages are that ferroelectric domain dynamics can be tuned, offering a way to engineer the memristor response, and that the resistance variations are due to purely electronic phenomena, aiding device reliability, as no deep change to the material structure is involved.

Carbon nanotube memristor

In 2013, Ageev, Blinov et al. reported observing memristor effect in structure based on vertically aligned carbon nanotubes studying bundles of CNT by scanning tunneling microscope.

Later it was found that CNT memristive switching is observed when a nanotube has a non-uniform elastic strain ΔL0. It was shown that the memristive switching mechanism of strained СNT is based on the formation and subsequent redistribution of non-uniform elastic strain and piezoelectric field Edef in the nanotube under the influence of an external electric field E(x,t).

Biomolecular memristor

Biomaterials have been evaluated for use in artificial synapses and have shown potential for application in neuromorphic systems. In particular, the feasibility of using a collagen‐based biomemristor as an artificial synaptic device has been investigated, whereas a synaptic device based on lignin demonstrated rising or lowering current with consecutive voltage sweeps depending on the sign of the voltage furthermore a natural silk fibroin demonstrated memristive properties; spin-memristive systems based on biomolecules are also being studied.

In 2012, Sandro Carrara and co-authors have proposed the first biomolecular memristor with aims to realize highly sensitive biosensors. Since then, several memristive sensors have been demonstrated.

Spin memristive systems

Spintronic memristor

Chen and Wang, researchers at disk-drive manufacturer Seagate Technology described three examples of possible magnetic memristors. In one device resistance occurs when the spin of electrons in one section of the device points in a different direction from those in another section, creating a "domain wall", a boundary between the two sections. Electrons flowing into the device have a certain spin, which alters the device's magnetization state. Changing the magnetization, in turn, moves the domain wall and changes the resistance. The work's significance led to an interview by IEEE Spectrum. A first experimental proof of the spintronic memristor based on domain wall motion by spin currents in a magnetic tunnel junction was given in 2011.

Memristance in a magnetic tunnel junction

The magnetic tunnel junction has been proposed to act as a memristor through several potentially complementary mechanisms, both extrinsic (redox reactions, charge trapping/detrapping and electromigration within the barrier) and intrinsic (spin-transfer torque).

Extrinsic mechanism

Based on research performed between 1999 and 2003, Bowen et al. published experiments in 2006 on a magnetic tunnel junction (MTJ) endowed with bi-stable spin-dependent states (resistive switching). The MTJ consists in a SrTiO3 (STO) tunnel barrier that separates half-metallic oxide LSMO and ferromagnetic metal CoCr electrodes. The MTJ's usual two device resistance states, characterized by a parallel or antiparallel alignment of electrode magnetization, are altered by applying an electric field. When the electric field is applied from the CoCr to the LSMO electrode, the tunnel magnetoresistance (TMR) ratio is positive. When the direction of electric field is reversed, the TMR is negative. In both cases, large amplitudes of TMR on the order of 30% are found. Since a fully spin-polarized current flows from the half-metallic LSMO electrode, within the Julliere model, this sign change suggests a sign change in the effective spin polarization of the STO/CoCr interface. The origin to this multistate effect lies with the observed migration of Cr into the barrier and its state of oxidation. The sign change of TMR can originate from modifications to the STO/CoCr interface density of states, as well as from changes to the tunneling landscape at the STO/CoCr interface induced by CrOx redox reactions.

Reports on MgO-based memristive switching within MgO-based MTJs appeared starting in 2008 and 2009. While the drift of oxygen vacancies within the insulating MgO layer has been proposed to describe the observed memristive effects, another explanation could be charge trapping/detrapping on the localized states of oxygen vacancies and its impact on spintronics. This highlights the importance of understanding what role oxygen vacancies play in the memristive operation of devices that deploy complex oxides with an intrinsic property such as ferroelectricity or multiferroicity.

Intrinsic mechanism

The magnetization state of a MTJ can be controlled by Spin-transfer torque, and can thus, through this intrinsic physical mechanism, exhibit memristive behavior. This spin torque is induced by current flowing through the junction, and leads to an efficient means of achieving a MRAM. However, the length of time the current flows through the junction determines the amount of current needed, i.e., charge is the key variable.

The combination of intrinsic (spin-transfer torque) and extrinsic (resistive switching) mechanisms naturally leads to a second-order memristive system described by the state vector x = (x₁,x₂), where x₁ describes the magnetic state of the electrodes and x₂ denotes the resistive state of the MgO barrier. In this case the change of x₁ is current-controlled (spin torque is due to a high current density) whereas the change of x₂ is voltage-controlled (the drift of oxygen vacancies is due to high electric fields). The presence of both effects in a memristive magnetic tunnel junction led to the idea of a nanoscopic synapse-neuron system.

Spin memristive system

A fundamentally different mechanism for memristive behavior has been proposed by Pershin and Di Ventra. The authors show that certain types of semiconductor spintronic structures belong to a broad class of memristive systems as defined by Chua and Kang. The mechanism of memristive behavior in such structures is based entirely on the electron spin degree of freedom which allows for a more convenient control than the ionic transport in nanostructures. When an external control parameter (such as voltage) is changed, the adjustment of electron spin polarization is delayed because of the diffusion and relaxation processes causing hysteresis. This result was anticipated in the study of spin extraction at semiconductor/ferromagnet interfaces, but was not described in terms of memristive behavior. On a short time scale, these structures behave almost as an ideal memristor. This result broadens the possible range of applications of semiconductor spintronics and makes a step forward in future practical applications.

Self-directed channel memristor

In 2017, Kris Campbell formally introduced the self-directed channel (SDC) memristor. The SDC device is the first memristive device available commercially to researchers, students and electronics enthusiast worldwide. The SDC device is operational immediately after fabrication. In the Ge₂Se₃ active layer, Ge-Ge homopolar bonds are found and switching occurs. The three layers consisting of Ge₂Se₃/Ag/Ge₂Se₃, directly below the top tungsten electrode, mix together during deposition and jointly form the silver-source layer. A layer of SnSe is between these two layers ensuring that the silver-source layer is not in direct contact with the active layer. Since silver does not migrate into the active layer at high temperatures, and the active layer maintains a high glass transition temperature of about 350 °C (662 °F), the device has significantly higher processing and operating temperatures at 250 °C (482 °F) and at least 150 °C (302 °F), respectively. These processing and operating temperatures are higher than most ion-conducting chalcogenide device types, including the S-based glasses (e.g. GeS) that need to be photodoped or thermally annealed. These factors allow the SDC device to operate over a wide range of temperatures, including long-term continuous operation at 150 °C (302 °F).

Potential applications

Memristors remain a laboratory curiosity, as yet made in insufficient numbers to gain any commercial applications. Despite this lack of mass availability, according to Allied Market Research the memristor market was worth $3.2 million in 2015 and was at the time projected to be worth $79.0 million by 2022. In fact, it was worth $190.0 million in 2022.

A potential application of memristors is in analog memories for superconducting quantum computers.

Memristors can potentially be fashioned into non-volatile solid-state memory, which could allow greater data density than hard drives with access times similar to DRAM, replacing both components. HP prototyped a crossbar latch memory that can fit 100 gigabits in a square centimeter, and proposed a scalable 3D design (consisting of up to 1000 layers or 1 petabit per cm³). In May 2008 HP reported that its device reaches currently about one-tenth the speed of DRAM. The devices' resistance would be read with alternating current so that the stored value would not be affected. In May 2012, it was reported that the access time had been improved to 90 nanoseconds, which is nearly one hundred times faster than the contemporaneous Flash memory. At the same time, the energy consumption was just one percent of that consumed by Flash memory.

Memristors have applications in programmable logic signal processing, super-resolution imaging physical neural networks, control systems, reconfigurable computing, in-memory computing, brain–computer interfaces and RFID. Memristive devices are potentially used for stateful logic implication, allowing a replacement for CMOS-based logic computation Several early works have been reported in this direction.

In 2009, a simple electronic circuit consisting of an LC network and a memristor was used to model experiments on adaptive behavior of unicellular organisms. It was shown that subjected to a train of periodic pulses, the circuit learns and anticipates the next pulse similar to the behavior of slime molds Physarum polycephalum where the viscosity of channels in the cytoplasm responds to periodic environment changes. Applications of such circuits may include, e.g., pattern recognition. The DARPA SyNAPSE project funded HP Labs, in collaboration with the Boston University Neuromorphics Lab, has been developing neuromorphic architectures which may be based on memristive systems. In 2010, Versace and Chandler described the MoNETA (Modular Neural Exploring Traveling Agent) model. MoNETA is the first large-scale neural network model to implement whole-brain circuits to power a virtual and robotic agent using memristive hardware. Application of the memristor crossbar structure in the construction of an analog soft computing system was demonstrated by Merrikh-Bayat and Shouraki. In 2011, they showed how memristor crossbars can be combined with fuzzy logic to create an analog memristive neuro-fuzzy computing system with fuzzy input and output terminals. Learning is based on the creation of fuzzy relations inspired from Hebbian learning rule.

In 2013 Leon Chua published a tutorial underlining the broad span of complex phenomena and applications that memristors span and how they can be used as non-volatile analog memories and can mimic classic habituation and learning phenomena.

Derivative devices

Memistor and memtransistor

The memistor and memtransistor are transistor-based devices which include memristor function.

Memcapacitors and meminductors

In 2009, Di Ventra, Pershin, and Chua extended the notion of memristive systems to capacitive and inductive elements in the form of memcapacitors and meminductors, whose properties depend on the state and history of the system, further extended in 2013 by Di Ventra and Pershin.

Memfractance and memfractor, 2nd- and 3rd-order memristor, memcapacitor and meminductor

In September 2014, Mohamed-Salah Abdelouahab, Rene Lozi, and Leon Chua published a general theory of 1st-, 2nd-, 3rd-, and nth-order memristive elements using fractional derivatives.

History

Precursors

Sir Humphry Davy is said by some to have performed the first experiments which can be explained by memristor effects as long ago as 1808. However the first device of a related nature to be constructed was the memistor (i.e. memory resistor), a term coined in 1960 by Bernard Widrow to describe a circuit element of an early artificial neural network called ADALINE. A few years later, in 1968, Argall published an article showing the resistance switching effects of TiO₂ which was later claimed by researchers from Hewlett Packard to be evidence of a memristor.

Theoretical description

Leon Chua postulated his new two-terminal circuit element in 1971. It was characterized by a relationship between charge and flux linkage as a fourth fundamental circuit element. Five years later he and his student Sung Mo Kang generalized the theory of memristors and memristive systems including a property of zero crossing in the Lissajous curve characterizing current vs. voltage behavior.

Twenty-first century

On May 1, 2008, Strukov, Snider, Stewart, and Williams published an article in Nature identifying a link between the two-terminal resistance switching behavior found in nanoscale systems and memristors.

On 23 January 2009, Di Ventra, Pershin, and Chua extended the notion of memristive systems to capacitive and inductive elements, namely capacitors and inductors, whose properties depend on the state and history of the system.

In July 2014, the MeMOSat/LabOSat group (composed of researchers from Universidad Nacional de General San Martín (Argentina), INTI, CNEA, and CONICET) put memory devices into a Low Earth orbit. Since then, seven missions with different devices are performing experiments in low orbits, onboard Satellogic's Ñu-Sat satellites.

On 7 July 2015, Knowm Inc announced Self Directed Channel (SDC) memristors commercially. These devices remain available in small numbers.

On 13 July 2018, MemSat (Memristor Satellite) was launched to fly a memristor evaluation payload.

In 2021, Jennifer Rupp and Martin Bazant of MIT started a "Lithionics" research programme to investigate applications of lithium beyond their use in battery electrodes, including lithium oxide-based memristors in neuromorphic computing.

In the September 2023 issue of Science Magazine, Chinese scientists Wenbin Zhang et al. described the development and testing of a memristor-based integrated circuit, designed to dramatically increase the speed and efficiency of Machine Learning and Artificial Intelligence tasks, optimized for Edge Computing applications.

Computational neurogenetic modeling

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Computational_neurogenetic_modeling 

Computational neurogenetic modeling (CNGM) is concerned with the study and development of dynamic neuronal models for modeling brain functions with respect to genes and dynamic interactions between genes. These include neural network models and their integration with gene network models. This area brings together knowledge from various scientific disciplines, such as computer and information science, neuroscience and cognitive science, genetics and molecular biology, as well as engineering.

Levels of processing

Molecular kinetics

Models of the kinetics of proteins and ion channels associated with neuron activity represent the lowest level of modeling in a computational neurogenetic model. The altered activity of proteins in some diseases, such as the amyloid beta protein in Alzheimer's disease, must be modeled at the molecular level to accurately predict the effect on cognition. Ion channels, which are vital to the propagation of action potentials, are another molecule that may be modeled to more accurately reflect biological processes. For instance, to accurately model synaptic plasticity (the strengthening or weakening of synapses) and memory, it is necessary to model the activity of the NMDA receptor (NMDAR). The speed at which the NMDA receptor lets Calcium ions into the cell in response to Glutamate is an important determinant of Long-term potentiation via the insertion of AMPA receptors (AMPAR) into the plasma membrane at the synapse of the postsynaptic cell (the cell that receives the neurotransmitters from the presynaptic cell).

Genetic regulatory network

An example of a model of a gene network. The genes, G₁ through G₄, are modified by either inhibitory signals, represented by bars and negative coefficients, or excitatory signals, represented by arrows and positive coefficients. The interactions are represented numerically by the matrix on the right, R.

In most models of neural systems neurons are the most basic unit modeled. In computational neurogenetic modeling, to better simulate processes that are responsible for synaptic activity and connectivity, the genes responsible are modeled for each neuron.

A gene regulatory network, protein regulatory network, or gene/protein regulatory network, is the level of processing in a computational neurogenetic model that models the interactions of genes and proteins relevant to synaptic activity and general cell functions. Genes and proteins are modeled as individual nodes, and the interactions that influence a gene are modeled as excitatory (increases gene/protein expression) or inhibitory (decreases gene/protein expression) inputs that are weighted to reflect the effect a gene or protein is having on another gene or protein. Gene regulatory networks are typically designed using data from microarrays.

Modeling of genes and proteins allows individual responses of neurons in an artificial neural network that mimic responses in biological nervous systems, such as division (adding new neurons to the artificial neural network), creation of proteins to expand their cell membrane and foster neurite outgrowth (and thus stronger connections with other neurons), up-regulate or down-regulate receptors at synapses (increasing or decreasing the weight (strength) of synaptic inputs), uptake more neurotransmitters, change into different types of neurons, or die due to necrosis or apoptosis. The creation and analysis of these networks can be divided into two sub-areas of research: the gene up-regulation that is involved in the normal functions of a neuron, such as growth, metabolism, and synapsing; and the effects of mutated genes on neurons and cognitive functions.

A model of an individual neuron. The inputs, x₀ to x_m, are modified by the input weights, w₀ to w_m, and then combined into one input, v_k. The transfer function, ${\displaystyle \phi }$, then uses this input to determine the output, y_k.

An artificial neural network generally refers to any computational model that mimics the central nervous system, with capabilities such as learning and pattern recognition. With regards to computational neurogenetic modeling, however, it is often used to refer to those specifically designed for biological accuracy rather than computational efficiency. Individual neurons are the basic unit of an artificial neural network, with each neuron acting as a node. Each node receives weighted signals from other nodes that are either excitatory or inhibitory. To determine the output, a transfer function (or activation function) evaluates the sum of the weighted signals and, in some artificial neural networks, their input rate. Signal weights are strengthened (long-term potentiation) or weakened (long-term depression) depending on how synchronous the presynaptic and postsynaptic activation rates are (Hebbian theory).

The synaptic activity of individual neurons is modeled using equations to determine the temporal (and in some cases, spatial) summation of synaptic signals, membrane potential, threshold for action potential generation, the absolute and relative refractory period, and optionally ion receptor channel kinetics and Gaussian noise (to increase biological accuracy by incorporation of random elements). In addition to connectivity, some types of artificial neural networks, such as spiking neural networks, also model the distance between neurons, and its effect on the synaptic weight (the strength of a synaptic transmission).

Combining gene regulatory networks and artificial neural networks

For the parameters in the gene regulatory network to affect the neurons in the artificial neural network as intended there must be some connection between them. In an organizational context, each node (neuron) in the artificial neural network has its own gene regulatory network associated with it. The weights (and in some networks, frequencies of synaptic transmission to the node), and the resulting membrane potential of the node (including whether an action potential is produced or not), affect the expression of different genes in the gene regulatory network. Factors affecting connections between neurons, such as synaptic plasticity, can be modeled by inputting the values of synaptic activity-associated genes and proteins to a function that re-evaluates the weight of an input from a particular neuron in the artificial neural network.

Incorporation of other cell types

Other cell types besides neurons can be modeled as well. Glial cells, such as astroglia and microglia, as well as endothelial cells, could be included in an artificial neural network. This would enable modeling of diseases where pathological effects may occur from sources other than neurons, such as Alzheimer's disease.

Factors affecting choice of artificial neural network

While the term artificial neural network is usually used in computational neurogenetic modeling to refer to models of the central nervous system meant to possess biological accuracy, the general use of the term can be applied to many gene regulatory networks as well.

Time variance

Artificial neural networks, depending on type, may or may not take into account the timing of inputs. Those that do, such as spiking neural networks, fire only when the pooled inputs reach a membrane potential is reached. Because this mimics the firing of biological neurons, spiking neural networks are viewed as a more biologically accurate model of synaptic activity.

Growth and shrinkage

To accurately model the central nervous system, creation and death of neurons should be modeled as well. To accomplish this, constructive artificial neural networks that are able to grow or shrink to adapt to inputs are often used. Evolving connectionist systems are a subtype of constructive artificial neural networks (evolving in this case referring to changing the structure of its neural network rather than by mutation and natural selection).

Randomness

Both synaptic transmission and gene-protein interactions are stochastic in nature. To model biological nervous systems with greater fidelity some form of randomness is often introduced into the network. Artificial neural networks modified in this manner are often labeled as probabilistic versions of their neural network sub-type (e.g., pSNN).

Incorporation of fuzzy logic

Fuzzy logic is a system of reasoning that enables an artificial neural network to deal in non-binary and linguistic variables. Biological data is often unable to be processed using Boolean logic, and moreover accurate modeling of the capabilities of biological nervous systems requires fuzzy logic. Therefore, artificial neural networks that incorporate it, such as evolving fuzzy neural networks (EFuNN) or Dynamic Evolving Neural-Fuzzy Inference Systems (DENFIS), are often used in computational neurogenetic modeling. The use of fuzzy logic is especially relevant in gene regulatory networks, as the modeling of protein binding strength often requires non-binary variables.

Types of learning

Artificial Neural Networks designed to simulate of the human brain require an ability to learn a variety of tasks that is not required by those designed to accomplish a specific task. Supervised learning is a mechanism by which an artificial neural network can learn by receiving a number of inputs with a correct output already known. An example of an artificial neural network that uses supervised learning is a multilayer perceptron (MLP). In unsupervised learning, an artificial neural network is trained using only inputs. Unsupervised learning is the learning mechanism by which a type of artificial neural network known as a self-organizing map (SOM) learns. Some types of artificial neural network, such as evolving connectionist systems, can learn in both a supervised and unsupervised manner.

Improvement

Both gene regulatory networks and artificial neural networks have two main strategies for improving their accuracy. In both cases the output of the network is measured against known biological data using some function, and subsequent improvements are made by altering the structure of the network. A common test of accuracy for artificial neural networks is to compare some parameter of the model to data acquired from biological neural systems, such as from an EEG. In the case of EEG recordings, the local field potential (LFP) of the artificial neural network is taken and compared to EEG data acquired from human patients. The relative intensity ratio (RIRs) and fast Fourier transform (FFT) of the EEG are compared with those generated by the artificial neural networks to determine the accuracy of the model.

Genetic algorithm

Because the amount of data on the interplay of genes and neurons and their effects is not enough to construct a rigorous model, evolutionary computation is used to optimize artificial neural networks and gene regulatory networks, a common technique being the genetic algorithm. A genetic algorithm is a process that can be used to refine models by mimicking the process of natural selection observed in biological ecosystems. The primary advantages are that, due to not requiring derivative information, it can be applied to black box problems and multimodal optimization. The typical process for using genetic algorithms to refine a gene regulatory network is: first, create a population; next, to create offspring via a crossover operation and evaluate their fitness; then, on a group chosen for high fitness, simulate mutation via a mutation operator; finally, taking the now mutated group, repeat this process until a desired level of fitness is demonstrated. 

Evolving systems

Methods by which artificial neural networks may alter their structure without simulated mutation and fitness selection have been developed. A dynamically evolving neural network is one approach, as the creation of new connections and new neurons can be modeled as the system adapts to new data. This enables the network to evolve in modeling accuracy without simulated natural selection. One method by which dynamically evolving networks may be optimized, called evolving layer neuron aggregation, combines neurons with sufficiently similar input weights into one neuron. This can take place during the training of the network, referred to as online aggregation, or between periods of training, referred to as offline aggregation. Experiments have suggested that offline aggregation is more efficient.

Potential applications

A variety of potential applications have been suggested for accurate computational neurogenetic models, such as simulating genetic diseases, examining the impact of potential treatments, better understanding of learning and cognition, and development of hardware able to interface with neurons.

The simulation of disease states is of particular interest, as modeling both the neurons and their genes and proteins allows linking genetic mutations and protein abnormalities to pathological effects in the central nervous system. Among those diseases suggested as being possible targets of computational neurogenetic modeling based analysis are epilepsy, schizophrenia, mental retardation, brain aging and Alzheimer's disease, and Parkinson's disease.

Personal construct theory

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Personal_construct_theory

Within personality psychology, personal construct theory (PCT) or personal construct psychology (PCP) is a theory of personality and cognition developed by the American psychologist George Kelly in the 1950s. The theory addresses the psychological reasons for actions. Kelly proposed that individuals can be psychologically evaluated according to similarity–dissimilarity poles, which he called personal constructs (schemas, or ways of seeing the world). The theory is considered by some psychologists as forerunner to theories of cognitive therapy.

From the theory, Kelly derived a psychotherapy approach, as well as a technique called the repertory grid interview, that helped his patients to analyze their own personal constructs with minimal intervention or interpretation by the therapist. The repertory grid was later adapted for various uses within organizations, including decision-making and interpretation of other people's world-views. The UK Council for Psychotherapy, a regulatory body, classifies PCP therapy within the experiential subset of the constructivist school.

Principles

A main tenet of PCP theory is that a person's unique psychological processes are channeled by the way they anticipate events. Kelly believed that anticipation and prediction are the main drivers of our mind. "Every man is, in his own particular way, a scientist", said Kelly: people are constantly building up and refining theories and models about how the world works so that they can anticipate future events. People start doing this at birth (for example, a child discovers that if they start to cry, their mother will come to them) and continue refining their theories as they grow up.

Kelly proposed that every construct is bipolar, specifying how two things are similar to each other (lying on the same pole) and different from a third thing, and they can be expanded with new ideas. (More recent researchers have suggested that constructs need not be bipolar.) People build theories—often stereotypes—about other people and also try to control them or impose on others their own theories so as to be better able to predict others' actions. All these theories are built up from a system of constructs. A construct has two extreme points, such as "happy–sad," and people tend to place items at either extreme or at some point in between. People's minds, said Kelly, are filled up with these constructs at a low level of awareness.

A given person, set of persons, any event, or circumstance can be characterized fairly precisely by the set of constructs applied to it and by the position of the thing within the range of each construct. For example, Fred may feel as though he is not happy or sad (an example of a construct); he feels as though he is between the two. However, he feels he is more clever than he is stupid (another example of a construct).  A baby may have a preverbal construct of what behaviors may cause their mother to come to them. Constructs can be applied to anything people put their attention to, and constructs also strongly influence what people fix their attention on. People can construe reality by constructing different constructs. Hence, determining a person's system of constructs would go a long way towards understanding them, especially the person's essential constructs that represent their very strong and unchangeable beliefs and their self-construal.

Kelly did not use the concept of the unconscious; instead, he proposed the notion of "levels of awareness" to explain why people did what they did. He identified "construing" as the highest level and "preverbal" as the lowest level of awareness.

Some psychologists have suggested that PCT is not a psychological theory but a metatheory because it is a theory about theories.

Therapy approach

Kelly believed in a non-invasive or non-directive approach to psychotherapy. Rather than having the therapist interpret the person's psyche, which would amount to imposing the doctor's constructs on the patient, the therapist should just act as a facilitator of the patient finding his or her own constructs. The patient's behavior is then mainly explained as ways to selectively observe the world, act upon it and update the construct system in such a way as to increase predictability. To help the patient find his or her constructs, Kelly developed the repertory grid interview technique.

Kelly explicitly stated that each individual's task in understanding their personal psychology is to put in order the facts of his or her own experience. Then the individual, like the scientist, is to test the accuracy of that constructed knowledge by performing those actions the constructs suggest. If the results of their actions are in line with what the knowledge predicted, then they have done a good job of finding the order in their personal experience. If not, then they can modify the construct: their interpretations or their predictions or both. This method of discovering and correcting constructs is roughly analogous to the general scientific method that is applied in various ways by modern sciences to discover truths about the universe.

The repertory grid

Main article: Repertory grid

The repertory grid serves as part of various assessment methods to elicit and examine an individual's repertoire of personal constructs. There are different formats such as card sorts, verbally administered group format, and the repertory grid technique.

The repertory grid itself is a matrix where the rows represent constructs found, the columns represent the elements, and cells indicate with a number the position of each element within each construct. There is software available to produce several reports and graphs from these grids.

To build a repertory grid for a patient, Kelly might first ask the patient to select about seven elements (although there are no fixed rules for the number of elements) whose nature might depend on whatever the patient or therapist are trying to discover. For instance, "Two specific friends, two work-mates, two people you dislike, your mother and yourself", or something of that sort. Then, three of the elements would be selected at random, and then the therapist would ask: "In relation to ... (whatever is of interest), in which way are two of these people alike but different from the third?" The answer is sure to indicate one of the extreme points of one of the patient's constructs. He might say for instance that Fred and Sarah are very communicative whereas John isn't. Further questioning would reveal the other end of the construct (say, introvert) and the positions of the three characters between extremes. Repeating the procedure with different sets of three elements ends up revealing several constructs the patient might not have been fully aware of.

In the book Personal Construct Methodology, researchers Brian R. Gaines and Mildred L.G. Shaw noted that they "have also found concept mapping and semantic network tools to be complementary to repertory grid tools and generally use both in most studies" but that they "see less use of network representations in PCP studies than is appropriate". They encouraged practitioners to use semantic network techniques in addition to the repertory grid.

Organizational applications

PCP has always been a minority interest among psychologists. During the last 30 years, it has gradually gained adherents in the US, Canada, the UK, Germany, Australia, Ireland, Italy and Spain. While its chief fields of application remain clinical and educational psychology, there is an increasing interest in its applications to organizational development, employee training and development, job analysis, job description and evaluation. The repertory grid is often used in the qualitative phase of market research, to identify the ways in which consumers construe products and services.

Self-reference effect

From Wikipedia, the free encyclopedia

The self-reference effect is a tendency for people to encode information differently depending on whether they are implicated in the information. When people are asked to remember information when it is related in some way to themselves, the recall rate can be improved.

Research

In 1955, George Kelly published his theory about how humans create personal constructs. This was a more general cognitive theory based on the idea that each individual's psychological processes are influenced by the way they anticipate events. This lays the groundwork for the ideas of personal constructs. Attribution theory is an explanation of the way people attribute the causes of behavior and events, which also involved creating a construct of self, since people can explain things related to themselves differently from the same thing happening to someone else. Related to the attribution theory, the fundamental attribution error is an explanation of when an individual explains someone's given behavior in a situation through emphasis on internal characteristics (personality) rather than considering the situation's external factors. Studies such as one by Jones, Sensenig, and Haley corroborated the idea that the self has a special construct, by simply asking experiment subjects to describe their "most significant characteristics". The results showed that the majority of responses were based on positive characteristics such as "sensitive", "intelligent", and "friendly". This ties in very well with other cognitive phenomena such as illusory superiority, in that it is a well observed fact that people rate themselves differently from how they rate others. In 2012, Stanley B. Klein published an article on the self and memory and how it relates to the self-reference effect. In recent years, studies on the self-reference effect have shifted from identifying mechanisms to using the self-reference as a research tool in understanding the nature of memory. Klein discusses words encoded with respect to oneself (the self-relevance effect) are recalled more often than words that are unrelated to the self.

In Japan, regarding memory, people who showed higher altruism tend not to exhibit self-reference effect.

Associated brain regions

Cortical mid-line structures

In the past 20 years plus there has been an increase in cognitive neuroscience studies that focus on the concept of the self. These studies were developed in hopes of determining if there are certain brain regions that can account for the encoding advantages involved in the self-reference effect. A great deal of research has been focused on several regions of the brain collectively identified as the cortical midline region. Brain imaging studies have raised the question of whether neural activity in cortical midline regions is self-specific. A quantitative meta-analysis that included 87 studies, representing 1433 participants, was conducted to discuss these questions. The analysis uncovered activity within several cortical midline structures in activities in which participants performed tasks involving the concept of self. Most studies that report such midline activations use tasks that are geared towards uncovering neural processes that are related to social or psychological aspects of the self, such as self-referential judgments, self-appraisal, and judgments of personality traits. Also, in addition to their perceived role in several forms of self-representation, cortical midline structures are also involved in the processing of social relationships and recognizing personally familiar others. Studies that show midline activations during understanding of social interactions between others or ascribing social traits to others (impression formation) typically require subjects to reference the mental state of others.

Prefrontal cortex

There are several areas within the cortical midline structure that are believed to be associated with the self-reference effect. One of the more active regions involved in the self-reference effect appears to be the medial prefrontal cortex (mPFC). The prefrontal cortex (PFC) is the area of the brain that is believed to be involved in the planning of complex behavior and the expression and regulation of personality characteristics in social situations. The implication that the prefrontal cortex is involved in the regulation of unique internal personality characteristics illustrates how it may be an important component of the self-reference effect. The medial prefrontal cortex in both hemispheres has been proposed as a site of the "self model" which is a theoretical construct made of essential features such as feelings of continuity and unity as well as experience of agency.

The idea of the self-reference effect being linked to the medial prefrontal cortex stems from several experiments attempting to locate the mechanisms involved in the self-referencing process. Experiments in which participants were assigned tasks that required them to reflect on, or introspect about their own mental states showed activity in the medial prefrontal cortex. For example, activity in the ventromedial prefrontal cortex has been observed in tasks in which participants report on their own personalities or preferences, adopt a first person perspective, or reflect on their current affective state. Similar activity in the ventromedial prefrontal cortex is displayed in cases where participants show the memory advantage that emerges when items are encoded in a self-relevant manner. During various functional magnetic resonance imaging (fMRI) tests conducted while participants were performing self-referential tasks, there was a consistent showing of increases in blood-oxygen-level dependent (BOLD) signals in the ventral medial and dorsal medial prefrontal cortex. Measuring BOLD signals is necessary for a sound interpretation of fMRI signals, as BOLD fMRI reflects a complex monitoring of changes in cerebral blood flow, cerebral blood volume and blood oxygenation.

Parietal lobe

In addition to areas of the prefrontal cortex, research has suggested that there are areas within the parietal lobe that also play a role in activating the self-reference effect. During fMRI given during self-referential tasks there also appeared to be increases in BOLD signals within the medial and lateral parietal cortex To further determine whether or not the medial parietal lobe plays a role in self-referencing, participants were subjected to transcranial magnetic stimulation over the region. Stimulation over this region produced a decrease in the ability of participants to retrieve previous judgments of mental self when compared to the retrieval of judgment of others.

Development over the lifespan

Childhood

The development of a sense of self and the understanding that one is separate and uniquely different from others is vital in the development of the self-reference effect advantage. As young children grow, their sense of self and understanding of the world around them is continuously increasing. Although this occurs at different stages for each child, research has shown rather early development of the self-reference advantage. Research focusing on the recall abilities of children have shown the self-referencing advantage in children as young as five years old. Language development appears to play a significant role in the development and use of the self-reference effect. Verbal labeling is among the first strategic behaviors shown by young children in order to enhance memory, and as children progress in age and language development, their performance on memory tasks involving self-referencing increases. A study done in 2011 on preschoolers found that observations on children as young as three years old suggests that the self-reference effect is apparent in event memory, by their ability to self-recognize.

Adulthood

Like children, the continuous development of a self-concept is related to the development of self-referencing in individuals. The relationships formed with intimate others over the lifespan appear to have an effect on self-referencing in relation to memory. The extent to which we include others in our self-concept has been a topic of particular interest for social psychologists. Theories of intimacy and personal relationships might suggest that the self-reference effect is affected by the closeness of a relationship with the other used as a target. Some researchers define closeness as an extension of self into other and suggest that one's cognitive processes about a close other develop in a way so as to include that person as part of the self. Consistent with this idea, it has been demonstrated that the memorial advantage afforded to self-referenced material can be diminished or eliminated when the comparison target is an intimate other such as a parent, friend, or spouse The capacity for utilizing the self-reference effect remains relatively high throughout the lifespan, even well into old age. Normally functioning older adults can benefit from self-referencing. Ageing is marked by cognitive impairments in a number of domains including long-term memory, but older adults' memory performance is malleable. Memory strategies and orientations that engage "deep" encoding processes benefit older adults. For example, older adults exhibit increased recall when using self-generated strategies that rely on personally relevant information (e.g., important birthdates) relative to other mnemonic strategies. However, research has shown that there are some differences between older adults and younger adults use of the self-reference advantage. Like young adults, older adults exhibit superior recognition for self-referenced items. But the amount of cognitive resources an individual has influence on how much older adults benefit from self referencing. Self-referencing improves older adult's memory, but its benefits are restricted regardless of the social and personally relevant nature of the task. A reason for this change in self referencing may be the change in brain activation that has been observed in older adults when studying self-referencing. Older adults showed more activity in the medial prefrontal cortex and along the cingulate gyrus than young adults. Because these regions often are associated with self-referential processing, these results suggest that older adults' mnemonic boost for positive information may stem from an increased tendency to process this information in relation to themselves. It has been proposed that this "positivity shift" may occur because older adults put more emphasis on emotion regulation goals than do young adults, with older adults having a greater motivation to derive emotional meaning from life and to maintain positive affect.

Effect on students

Students are often challenged when faced with the attempt to recall memories. It is therefore important to understand the effects of self-reference encoding for students and beneficial ways it can increase their recall of information. The purpose of the current study was to examine the effects of, self-referent encoding.

Rogers, Kuiper, and Kirker (1977) performed one of the first studies examining the self-reference effect making it a foundational article. The focus of the study was to identify the importance of the self and how it is implicated when processing personal information. The self-reference effect has been considered a robust encoding strategy and has been effective over the past 30 years (Gutches et al., 2007). The process behind this study was to gather students and divide them into four different task groups and they would be asked to give a yes or no answer to a trait adjective being presented to them. The four tasks that were used were: structural, phonemic, semantic, and self-reference. There were some different theories that support the study. The personality theory stressed that the observer's network when looking at the trait adjectives is an essential part of how they process personal information Hastorf et al. (1970). Another theory that supports this study is the attribution theory. It is another example where a person's organization traits fit with the self-reference effect Jones et al. (1971). The self is visualized as a schema that is involved with processing personal information, interpretation, and memories which is considered a powerful and effective process (Rogers et al., 1977).

Gutchess, Kensinger, and Schacter (2007) performed a study where they used age as a factor when looking at the self-reference effect. The first and second experiment looks at the young and older adults and they are presented with encoded adjectives and they must decide if it describes them. The third experiment is deciding if they found these traits desirable towards themselves. The age difference was shown effective with the self-reference effect leaving the older adults showing superiority of recognition for self-referenced items that were relative. Although, self-referencing the older adults did not have the same restoring level as the younger adults. A major factor that played in this study was the availability of cognitive resources. When there was a greater availability of cognitive resources, the ability to enhance memory similarly for both young and older adults diverged from socioemotional processing (Gutches et al., 2007).

Hartlep and Forsyth (2001) performed a study using two different approaches when studying for an exam. The first approach was the survey, question, read, reflect, recite, and review method which is called the SQR4. The other method was the self-reference method. The third group was a controlled group and received no special instructions on their studying process (Hartlep & Forsyth, 2001). This study is considered an applied study. People who have a more elaborative cognitive framework, the better they will be able to retrieve a memory. The most elaborative cognitive framework someone can have is knowledge of themselves (Hartlep & Forsyth, 2001). The self-reference effect is viable when having strict lab conditions. When students are studying, if they can see the material as an elaboration of what they already remember or can relate to personal experiences, their recall would be enhanced (Hartlep & Forsyth, 2001). Although, the self-reference method can enhance recall of memory in certain instances, unfortunately for this study, there were no significant differences between the two study methods.

Serbun, Shih and Gutchess (2011) performed a study involving the effects of general and specific memory when using the self-reference effect. The study created a gap in research due to the experiments being tested. The first experiment uses visuals details of objects where the second and third experiment use verbal memory to assess the self-reference effect. The self-reference effect enhances both general and specific memory and can improve the accuracy and richness of a memory (Serbun et al., 2011). We know how the self-reference effect works, but instead of using trait adjectives to assess recall, we are looking at trait adjectives. The results from the experiments show that self-referencing does not function only through the increase in familiarity or general memory for the object, but enhances memory for details of an event. This likely draws on more recollected processes. This information supports that self-referencing is effective of encoding a rich, detailed memory towards not only general memory, but specific memories.

(Nakao et al., 2012) performed a study to show the relation between the self-reference effect and people that are highly in altruism and low in altruism. This all starts with the medical prefrontal cortex (MPFC). People who are high in altruism did not show the self-reference effect compared to the participants low in altruism. The participants who frequently chose the altruistic behavior refer to the social desirability as a backboard (Nakoa et al., 2012). The relation the self-reference effect and altruism is the MPFC. When using the self-reference effect, people who are low in altruism, the same part of the brain is being used. Whereas the same is for people who are high in altruism when using social desirability. Social desirability ties into the different types of memory enhancement can vary for individual differences of past experiences. People's individual differences can show similar effects as the self-reference effect (Nakoa et al., 2012).

The self-reference effect is a rich and powerful encoding process that can be used multiple ways. The self-reference effect shows better results over the semantic method when processing personal information. Processing personal information can be distinguished and recalled differently with age. The older the subject, the more rich and vivid the memory can be due to the amount of information the brain has processed. The self-reference just as effective as the SQR4 method when study for exams, but the self-reference method is preferred. Defining general and specific memories using objects, verbal cues, etc. can be effective when using the self-reference effect. When using these different method, the same part of the brain is being active resulting in relation and better recall. It was expected that participants would recall the most number of words from the self-referent list rather than from the semantic or structural lists and more words from the semantic list than from the structural list. It was also expected that for the words encoded in the self-referent condition, fewer words would be recalled by participants in the high altruism group than in the low altruism group.

Evolutional Mechanism

Research suggests that the self-reference effect is connected to personal survival among the human race. There is this survival effect which is defined as the enhancement of memory when encoding material meant for survival, which has shown to have a significant correlation with the self-reference effect. The interesting thing is research has found that this memory enhancement does not work when given by another person, in order for it to work, it must come from the person themselves. As this advancement of encoding incoming memories is an evolutional mechanism that we the human race has inherited from the challenges faced by our ancestors. Nairne et al. (2007) noted that our advanced ability to recall past events may be to help us as a species to solve issues, which would relate to survival. Weinstein et al. (2008) concluded in their study that people are able to encode and retrieve information that is related to survival more than information that doesn't relate to survival. However, it is important to note that researchers theorize that there is not just one kind of self-reference effect that people pose, rather a group of them for different purposes other than survival.

Examples

• The tendency to attribute someone else's behavior to their disposition, and to attribute one's own behavior to the situation. (The Fundamental attribution error)
• When asked to remember words relating to themselves, subjects had greater recall than those receiving other instructions.
• In connection with the levels-of-processing effect, more processing and more connections are made within the mind in relation to a topic connected to the self.
• In the field of marketing, Asian consumers self-referenced Asian models in advertising more than White consumers. Also Asian models advertising products that were not typically endorsed by Asian models resulted in more self-referencing from consumers.
• People are more likely to remember birthdays that are closer to their own birthday than birthdays that are more distant.
• Research shows that long term memory is improved when learning occurs under self-reference conditions
• Research shows that female consumers engage in self-referencing when viewing female models of different body shapes in advertising. For example, Martin, Veer and Pervan (2007) examined how the weight locus of control of women (i.e., beliefs about the control of body weight) influence how they react to female models in advertising of different body shapes. They found that women who believe they can control their weight ("internals"), respond most favorably to slim models in advertising, and this favorable response is mediated by self-referencing.