Neuron model RF-PSTH (which simulates Receptive Field (RF) structure and PSTH output signal of the neuron)

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Free teaching tool for students, teachers and scientists of neuroscience, biophysics, biomedical engineering and artificial intelligence.


Currently available artificial neuron models are unable to simulate fundamentally important features of real biological neurons: 1) antagonistic receptive fields and 2) PSTH output signal of neuron to any stimulus.
Even if some neuron models try to simulate antagonistic receptive fields then they are unable to simulate PSTH output signal, and vice versa – some other models try to simulate PSTH output signal of neuron, however these models fail to explain antagonistic receptive fields of neurons. As for example, a very popular DOG (Difference Of Gaussians) model simulates antagonistic structure of the receptive field, however DOG model fails to simulate PSTH output signal of neuron. And the vast majority of artificial neural models even fail to simulate both: antagonistic receptive fields and PSTH output signal.
For the first time ever neuron model RF-PSTH is able to simulate both antagonistic receptive fields and PSTH output signal.
Neuron model RF-PSTH is based on physics of real biological neurons.

Recommended literature

Comprehensive description of the receptive field of biological neuron is available in the book “Encyclopedia of the Human Brain” written by Vilayanur S. Ramachandran MBBS PhD Hon. FRCP (Editor), published by Academic Press in July 10, 2002 (1 edition), ISBN-10: 0122272102, ISBN-13: 978-0122272103.
In this book please read Chapter “Receptive Field” written by Rajesh P. N. Rao (University of Washington), in pages 155-168.
Neuron model RF-PSTH simulates neuron’s features described in this Chapter.

The importance and advantage of new neuron model RF-PSTH

Output PSTH signal produced by neuron model RF-PSTH matches experimental measurements of real biological neurons in laboratory.
Measurements of real biological neurons show that receptive fields of sensory neurons have symmetrical concentric antagonistic circular structure, however current science does not have any convincing explanation what is the cause of this phenomenon. It is hypothesized that antagonistic concentric receptive fields are formed because neuron connects to receptors (or to other neurons) via synaptic connections and supposedly these synaptic connections are distributed in such a way that concentric antagonistic circles are formed. There is no convincing explanation why receptive fields should form concentric antagonistic circular structures.
Neuron model RF-PSTH is able to simulate concentric antagonistic circular structures of the receptive fields of sensory neurons.
Neuron model RF-PSTH claims that antagonistic circular structure of the receptive field is the internal feature of all sensory neurons, and there is no need for any external neural links (external neural networks) in order to form such antagonistic circular structures.

Neuron model RF-PSTH program

Neuron model RF-PSTH
Download “Neuron model RF-PSTH” v.1.4 native applications for the following platforms:

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Neuron model RF-PSTH program is free to use for academic and educational purposes.

Description of neuron model RF-PSTH

Neuron possesses a cell body (soma), dendrites, and an axon.

Neuron is modeled as 3D object in 3D space:
1) the soma of neuron is modeled as mathematical point;
2) the receptive field of neuron is modeled as two dimensional plane;
3) from soma of neuron the dendrites reach two dimensional plane;
4) in two dimensional plane dendrites form circular receptive field;
5) 3D shape of neuron is the right circular cone in which the apex of the cone represents neuron soma and the base of the cone represents receptive field.

A good example for such scenario is the ganglion (neural) cell which receives the input from photoreceptors in the retina. Many other neurons also fit into this scenario quite well, as for example somatosensory neurons which receive input from receptors on the skin, etc.

Neuron model RF-PSTH

Figure 1. Neuron is modeled as 3D object in 3D space

Neuron model RF-PSTH claims that if all these above mentioned conditions are fulfilled then the neuron will have symmetrical concentric antagonistic circular structure of the receptive field. However if the receptive field of neuron will have another configuration (like for example will be the part of 3D sphere or will have some other configuration) then neuron’s receptive field might be without concentric antagonistic circular structure. In other words, 3D spatial configuration of the neuron plays essential role in the formation of receptive field structure.

FAQ (Frequently Asked Questions) about neuron model RF-PSTH

Receptive fields of neurons can have more complicated structure than concentric antagonistic circles, as for example receptive fields of V1 neurons are lines, bars or squared shapes inclined at certain degree and so on, however neuron model RF-PSTH does not model such complicated receptive fields of the neuron thus I think that neuron model RF-PSTH is a bad/incomplete model, isn’t it?

We get this question repeatedly over and over again even from people who have high academic degrees in neuroscience so here is the answer. First of all, “receptive field of V1 neuron” (as shown in neuroscience textbooks and articles) has a misleading name – actually it is not the receptive field of the single neuron, it is the receptive field of multilayer network (from retina through LGN into V1). However multilayer network and single neuron are two different things. Neuron model RF-PSTH models the behavior of the single neuron, not the behavior of multilayer network. If you will take out truly single V1 neuron (throwing away all neighboring neurons) and if you will measure the input-output characteristics of truly single V1 neuron then you will get the same results as in neuron model RF-PSTH. In other words, the major misunderstanding comes from confusing the receptive field of the single neuron with the receptive field of multilayer network.

Which types of neurons of which part of the brain (cerebral cortex, thalamus, hypothalamus, amygdala, hippocampus, etc) does the neuron model RF-PSTH simulate?

Neuron model RF-PSTH simulates neurons which have spatial 3D shape of right circular cone (as shown in Figure 1). It does matter in which part of the brain such neuron is located, as long as it will have spatial 3D shape of right circular cone, the neuron model RF-PSTH will simulate behavior of such neuron. However in practice the neurons of right circular cone shape are most easily found in the first layer of multiple sensory modality inputs, a good example for such scenario is the ganglion (neural) cell which receives the input from photoreceptors in the retina, many other neurons also fit into this scenario quite well, as for example somatosensory neurons which receive input from receptors on the skin, etc.
Neuron model RF-PSTH supports the hypothesis of Vernon Benjamin Mountcastle (Professor Emeritus of Neuroscience at Johns Hopkins University) who noticed that different areas of neocortex (visual, auditory, etc) are remarkably uniform in appearance and structure and proposed the idea that different areas of neocortex process information performing the same basic operation.
Vernon Benjamin Mountcastle (July 15, 1918 – January 11, 2015) was Professor Emeritus of Neuroscience at Johns Hopkins University. He discovered and characterized the columnar organization of the cerebral cortex in the 1950s. This discovery was a turning point in investigations of the cerebral cortex, as nearly all cortical studies of sensory function after Mountcastle's 1957 paper, on the somatosensory cortex, used columnar organization as their basis.

Chapter: An Organizing Principle for Cerebral Function: The Unit Model and the Distributed System
By Vernon B. Mountcastle

Excerpt from pages 39-40:
Functional Properties of Distributed Systems
It is well known from classical neuroanatomy that many of the large entities of the brain are interconnected by extrinsic pathways into complex systems, including massive reentrant circuits. Three sets of recent discoveries, described above, have put the systematic organization of the brain in a new light. The first is that many of the major structures of the brain are constructed by replication of identical multicellular units. These modules are local neural circuits of hundreds or thousands of cells linked together by a complex intramodular connectivity. The modules of any one entity are more or less similar throughout, but those of different entities may differ strikingly. The modular unit of the neocortex is the vertically organized group of cells I have described earlier. These basic units are single translaminar cords of neurons, the minicolumns, which in some areas are packaged into larger processing units whose size and form appear to differ from one place to another. Nevertheless, the qualitative nature of the processing function of the neocortex is thought to be similar in different areas, though that intrinsic processing apparatus may be subject to modification as a result of past history, particularly during critical periods in ontogenetic development.
The Mindful Brain
By Gerald M. Edelman and Vernon B. Mountcastle, eds.
MIT Press. 1978. ISBN-10: 026205020X. ISBN-13: 978-0262050203.

Step-by-step instructions how to run neuron model RF-PSTH

Step #1

Set the parameters which determine the structure of receptive field of neuron. This can be accomplished in tab named “Receptive field”.
The parameters of neuron are the following:
Radius of receptive field – this parameter calculated automatically, you do not need to set this parameter;
Dendritic attenuation (exponential decay constant) – when signal travels via dendrites, the signal attenuates according to exponential decay law, this parameter sets exponential decay constant;
Distance to soma – distance from soma to the receptive field plane;
Parameter #1 – parameter related to the diameter of dendrites;
Parameter #2 – one more neuron parameter.

Receptive field
Figure 2. Tab “Receptive field” in neuron model RF-PSTH.
The receptive field of a sensory neuron is a region of space in which the presence of a stimulus will alter the firing of that neuron. Receptive fields have been identified for neurons of the auditory system, the somatosensory system, and the visual system.
The concept of receptive fields can be extended to further up the neural system; if many sensory receptors all form synapses with a single cell further up, they collectively form the receptive field of that cell. For example, the receptive field of a ganglion cell in the retina of the eye is composed of input from all of the photoreceptors which synapse with it, and a group of ganglion cells in turn forms the receptive field for a cell in the brain. This process is called convergence.
On center and off center retinal ganglion cells respond oppositely to light in the center and surround of their receptive fields. A strong response means high frequency firing, a weak response is firing at a low frequency, and no response means no action potential is fired.

Step #2

Create the stimulus with the parameters needed. This can be accomplished in tab named “Stimulus”.
Stimulus is painted with white color over the receptive field of the neuron.

Stimulus can be of several types:
1) circular stimulus – you can change the radius of the circle and coordinates (x, y);
2) grating stimulus – you can change the width of the grating, translation coordinates (x, y), and rotation angle (in degrees);
3) inverted stimulus – inverts stimulated and non-stimulated areas.

Circular stimulus can be manipulated directly with mouse (resized and moved) by clicking with mouse on stimulus image.
Grating stimulus can be manipulated only by sliding trackbars.
Neuron model RF-PSTH also allows to simulate reaction of neuron to the moving stimulus, however this program provides the ability to simulate only static non-moving stimulus.

Figure 3. Tab “Stimulus” in neuron model RF-PSTH.
In physiology, a stimulus (plural stimuli) is a detectable change in the internal or external environment. The ability of an organism or organ to respond to external stimuli is called sensitivity. When a stimulus is applied to a sensory receptor, it normally elicits or influences a reflex via stimulus transduction. These sensory receptors can receive information from outside the body, as in touch receptors found in the skin or light receptors in the eye, as well as from inside the body, as in chemoreceptors and mechanorceptors.

Step #3

Simulate neuron output signal as the reaction to input stimulus. This can be accomplished in tab named “Peri-stimulus-time-histogram (PSTH)”.
Stimulus is turned on when time is zero. Stimulus is turned off automatically, when neuron output signal stabilizes and becomes almost stationary. Neuron output is painted yellow when stimulus is on, and painted gray when stimulus is off.

Figure 4. Tab “Peri-stimulus-time-histogram (PSTH)” in neuron model RF-PSTH.
In neurophysiology, peristimulus time histogram and poststimulus time histogram, both abbreviated PSTH or PST histogram, are histograms of the times at which neurons fire. These histograms are used to visualize the rate and timing of neuronal spike discharges in relation to an external stimulus or event. The peristimulus time histogram is sometimes called perievent time histogram, and post-stimulus and peri-stimulus are often hyphenated.
The prefix peri, for through, is typically used in the case of periodic stimuli, in which case the PSTH show neuron firing times wrapped to one cycle of the stimulus. The prefix post is used when the PSTH shows the timing of neuron firings in response to a stimulus event or onset.
To make a PSTH, a spike train recorded from a single neuron is aligned with the onset, or a fixed phase point, of an identical stimulus repeatedly presented to an animal. The aligned sequences are superimposed in time, and then used to construct a histogram.

Additional notes about PSTH output

Real biological neurons cannot produce negative frequency of spikes in the output. However this negative output signal can be measured as reduced presynaptic potential inside neuron soma in place where axon connects to soma. The simulation program shows and reveals internal processes in the neuron.

PSTH output is calculated without short-term depression (STD) and short-term facilitation (STF).
Short-term plasticity (STP), also called dynamical synapses, refers to a phenomenon in which synaptic efficacy changes over time in a way that reflects the history of presynaptic activity. Two types of STP, with opposite effects on synaptic efficacy, have been observed in experiments. They are known as short-term depression (STD) and short-term facilitation (STF). STD is caused by depletion of neurotransmitters consumed during the synaptic signaling process at the axon terminal of a pre-synaptic neuron, whereas STF is caused by influx of calcium into the axon terminal after spike generation, which increases the release probability of neurotransmitters. STP has been found in various cortical regions and exhibits great diversity in properties. Synapses in different cortical areas can have varied forms of plasticity, being either STD-dominated, STF-dominated, or showing a mixture of both forms.
Compared with long-term plasticity, which is hypothesized as the neural substrate for experience-dependent modification of neural circuit, STP has a shorter time scale, typically on the order of hundreds to thousands of milliseconds. The modification it induces to synaptic efficacy is temporary. Without continued presynaptic activity, the synaptic efficacy will quickly return to its baseline level.

Step #4

Simulate circular stimulus of variable radius experiment. This can be accomplished in tab named “Circular stimulus of variable radius experiment”.

The description of experiment is following. Circular stimulus is placed in the center of the receptive field. The size of stimulus is increased in steps of one, starting from zero till the size of the receptive field. In each step PSTH output signal is calculated. In each step a range of output values from PSTH graph are taken and the average spike frequency for that defined range is calculated. The final produced graph of the experiment is the average spike frequency dependency from the stimulus size. The form of final produced graph is sensitive on the selected range from PSTH output signal from which average spike frequency is calculated. The changing of the selected range (of PSTH output signal) changes the graph of final experiment graph. There are no rules in neuroscience which define which exactly range of PSTH signal should be taken for average spike frequency calculation, thus you need to experiment with the range values yourself in order to find out which range better suits your needs.

Circular stimulus of variable radius experiment
Figure 5. Tab “Circular stimulus of variable radius experiment” in neuron model RF-PSTH.

The flaws of currently available artificial neuron models and the superiority of neuron model RF-PSTH

Mathematical modeling of any physical phenomenon requires simplifications (reductions) of the phenomenon in order to decrease the number of parameters and to reduce the number of calculations.
The technical question is how much the phenomenon can be simplified (reduced) in order not to loose essential information which is needed for solving of the particular problem.
As for example, when we need to analyze a car driving on the road, we can simplify the car into mathematical point (without dimension and without mass) which moves across two dimensional space with some speed. Such simplified car model is perfectly good when we want to calculate, for example, how much time it will take to drive a car from point A to point B. However, if we want to find out what force is applied to brake plates of the car when the driver pushes the brake pedal in order to stop the car, then a model in which the car is represented as mathematical point will be insufficient to solve such problem. If you want to find out what force is applied to brake plates of the car when the driver pushes the brake pedal then you need to know the mass of the car, the diameter of the wheels, etc – however all these parameters were eliminated in the car model described above. In other words, when mathematical model is created, some essential features (parameters) can be eliminated, without which it will be impossible to solve some special practical problems.

Let’s look more closely what artificial neuron models are used today.

The first artificial neuron was the Threshold Logic Unit (TLU) first proposed by Warren McCulloch and Walter Pitts in 1943. As a transfer function, it employed a threshold, equivalent to using the Heaviside step function. Initially, only a simple model was considered, with binary inputs and outputs, some restrictions on the possible weights, and a more flexible threshold value. Since the beginning it was already noticed that any boolean function could be implemented by networks of such devices, what is easily seen from the fact that one can implement the AND and OR functions, and use them in the disjunctive or the conjunctive normal form.
Researchers also soon realized that cyclic networks, with feedbacks through neurons, could define dynamical systems with memory, but most of the research concentrated (and still does) on strictly feed-forward networks because of the smaller difficulty they present.
One important and pioneering artificial neural network that used the linear threshold function was the perceptron, developed by Frank Rosenblatt. This model already considered more flexible weight values in the neurons, and was used in machines with adaptive capabilities. The representation of the threshold values as a bias term was introduced by Bernard Widrow in 1960.
In the late 1980s, when research on neural networks regained strength, neurons with more continuous shapes started to be considered. The possibility of differentiating the activation function allows the direct use of the gradient descent and other optimization algorithms for the adjustment of the weights. Neural networks also started to be used as a general function approximation model.
Basic structure

For a given artificial neuron, let there be m + 1 inputs with signals x0 through xm and weights w0 through wm. Usually, the x0 input is assigned the value +1, which makes it a bias input with wk0 = bk. This leaves only m actual inputs to the neuron: from x1 to xm.
The output of kth neuron is:
Neuron basic formula
Where φ is the transfer function.
artificial neuron model
The output is analogous to the axon of a biological neuron, and its value propagates to input of the next layer, through a synapse. It may also exit the system, possibly as part of an output vector.
It has no learning process as such. Its transfer function weights are calculated and threshold value are predetermined.
Types of transfer functions

The transfer function of a neuron is chosen to have a number of properties which either enhance or simplify the network containing the neuron. Crucially, for instance, any multilayer perceptron using a linear transfer function has an equivalent single-layer network; a non-linear function is therefore necessary to gain the advantages of a multi-layer network.
Below, u refers in all cases to the weighted sum of all the inputs to the neuron, i.e. for n inputs,
weighted sum of all the inputs to the neuron
where w is a vector of synaptic weights and x is a vector of inputs.

Step function

The output y of this transfer function is binary, depending on whether the input meets a specified threshold, θ. The "signal" is sent, i.e. the output is set to one, if the activation meets the threshold.
Step function
This function is used in perceptrons and often shows up in many other models. It performs a division of the space of inputs by a hyperplane. It is specially useful in the last layer of a network intended to perform binary classification of the inputs. It can be approximated from other sigmoidal functions by assigning large values to the weights.

Linear combination

In this case, the output unit is simply the weighted sum of its inputs plus a bias term. A number of such linear neurons perform a linear transformation of the input vector. This is usually more useful in the first layers of a network. A number of analysis tools exist based on linear models, such as harmonic analysis, and they can all be used in neural networks with this linear neuron. The bias term allows us to make affine transformations to the data.


A fairly simple non-linear function, a Sigmoid function such as the logistic function also has an easily calculated derivative, which can be important when calculating the weight updates in the network. It thus makes the network more easily manipulable mathematically, and was attractive to early computer scientists who needed to minimize the computational load of their simulations. It is commonly seen in multilayer perceptrons using a backpropagation algorithm.
Comparison to biological neurons

Artificial neurons bear a striking similarity to their biological counterparts.
Dendrites - In a biological neuron, the dendrites act as the input vector. These dendrites allow the cell to receive signals from a large (>1000) number of neighboring neurons. As in the above mathematical treatment, each dendrite is able to perform "multiplication" by that dendrite's "weight value." The multiplication is accomplished by increasing or decreasing the ratio of synaptic neurotransmitters to signal chemicals introduced into the dendrite in response to the synaptic neurotransmitter. A negative multiplication effect can be achieved by transmitting signal inhibitors (i.e. oppositely charged ions) along the dendrite in response to the reception of synaptic neurotransmitters.
Soma - In a biological neuron, the soma acts as the summation function, seen in the above mathematical description. As positive and negative signals (exciting and inhibiting, respectively) arrive in the soma from the dendrites, the positive and negative ions are effectively added in summation, by simple virtue of being mixed together in the solution inside the cell's body.
Axon - The axon gets its signal from the summation behavior which occurs inside the soma. The opening to the axon essentially samples the electrical potential of the solution inside the soma. Once the soma reaches a certain potential, the axon will transmit an all-in signal pulse down its length. In this regard, the axon behaves as the ability for us to connect our artificial neuron to other artificial neurons.
Unlike most artificial neurons, however, biological neurons fire in discrete pulses. Each time the electrical potential inside the soma reaches a certain threshold, a pulse is transmitted down the axon. This pulsing can be translated into continuous values. The rate (activations per second, etc.) at which an axon fires converts directly into the rate at which neighboring cells get signal ions introduced into them. The faster a biological neuron fires, the faster nearby neurons accumulate electrical potential (or lose electrical potential, depending on the "weighting" of the dendrite that connects to the neuron that fired). It is this conversion that allows computer scientists and mathematicians to simulate biological neural networks using artificial neurons which can output distinct values (often from -1 to 1).

All these artificial neuron models are unable to explain and to simulate antagonistic receptive fields and PSTH output signal of real biological neurons.
Artificial Neural Networks are built using such incapable artificial neurons.
If Artificial Neural Network (ANN) is built from neurons with linear transfer function then such multilayer network can be simplified into single-layer network which will be equivalent to original multilayer network. A nonlinear transfer function is therefore necessary in order to gain advantages of a multilayer network.
The Need For Non-Linearity

We have noted before that if we have a regression problem with non-binary network outputs, then it is appropriate to have a linear output activation function. So why not simply use linear activation functions on the hidden layers as well?
With activation functions f(n)(x) at layer n, the outputs of a two-layer MLP are
so if the hidden layer activations are linear, i.e. f(1)(x) = x, this simplifies to
But this is equivalent to a single layer network with weights
and we know that such a network cannot deal with non-linearly separable problems.
Learning in Multi-Layer Perceptrons - Back-Propagation
Neural Computation : Lecture 7
John A. Bullinaria, 2013

If artificial neuron will be built using linear transfer function and if the number of neuron inputs will be reduced to one(1) input then information processing capabilities of such neuron will drop almost to zero. This example clearly shows that oversimplification of real physical object will render mathematical model incapable of solving practical problems.

Computer scientists who work with artificial neural networks prefer to use:
1) neurons with nonlinear transfer function believing that nonlinear perceptron is superior to linear perceptron;
2) multilayer networks with nonlinear transfer function because it was proved that single-layer network could not be trained to recognize many classes of patterns.
The perceptron algorithm was invented in 1957 at the Cornell Aeronautical Laboratory by Frank Rosenblatt.
Although the perceptron initially seemed promising, it was eventually proved that perceptrons could not be trained to recognize many classes of patterns. This led to the field of neural network research stagnating for many years, before it was recognised that a feedforward neural network with two or more layers (also called a multilayer perceptron) had far greater processing power than perceptrons with one layer (also called a single layer perceptron). Single layer perceptrons are only capable of learning linearly separable patterns; in 1969 a famous book entitled Perceptrons by Marvin Minsky and Seymour Papert showed that it was impossible for these classes of network to learn an XOR function. It is often believed that they also conjectured (incorrectly) that a similar result would hold for a multi-layer perceptron network. However, this is not true, as both Minsky and Papert already knew that multi-layer perceptrons were capable of producing an XOR Function. <...> Three years later Stephen Grossberg published a series of papers introducing networks capable of modelling differential, contrast-enhancing and XOR functions. (The papers were published in 1972 and 1973, see e.g.: Grossberg, Contour enhancement, short-term memory, and constancies in reverberating neural networks. Studies in Applied Mathematics, 52 (1973), 213-257, online). Nevertheless the often-miscited Minsky/Papert text caused a significant decline in interest and funding of neural network research. It took ten more years until neural network research experienced a resurgence in the 1980s. This text was reprinted in 1987 as "Perceptrons - Expanded Edition" where some errors in the original text are shown and corrected.
The kernel perceptron algorithm was already introduced in 1964 by Aizerman et al. Margin bounds guarantees were given for the Perceptron algorithm in the general non-separable case first by Freund and Schapire (1998), and more recently by Mohri and Rostamizadeh (2013) who extend previous results and give new L1 bounds.

Computer scientists fail to notice one key fundamental feature of the perceptron – when perceptron is used for pattern recognition tasks the perceptron acts as a simple template matching technique and it does not matter if the transfer function of the perceptron is linear or nonlinear, nonlinearity does not help at all – the perceptron acts as simple template matching technique. And it is well known fact that template matching technique fails to recognize object when object is resized, rotated or moved. In other words, computer scientists fail to notice the obvious fact that perceptron is fundamentally unable to recognize object which is transformed (resized, rotated or moved).
When backpropagation training technique is used to train nonlinear perceptron to filter out audio signal then experimental results show that when the number of training iterations approach to the infinity then the weights of perceptron approach the coefficients of DSP filter which is optimal to filter out that particular signal. In other words, it does not matter if the transfer function of the perceptron is linear or nonlinear – the perceptron acts as a simple linear DSP filter. The nonlinearity of the perceptron’s transfer function does not provide any advantage over linear DSP filter.

Computer scientists who work with artificial neural networks use oversimplified mathematical models of the neuron which are incapable to solve practical pattern recognition problems. When artificial neuron was invented it was claimed that soon mankind will have the machines which are able to solve the same pattern recognition tasks as the biological brain is able to solve. However, despite the decades of research and tedious work, the nonlinear multilayer perceptrons are still incapable to solve even most primitive pattern recognition tasks. The reason of such failure is obvious – the models of artificial neuron are oversimplified and lack some essential features of real biological neuron. As for example these neuron models lack antagonistic receptive field structure, etc.
As a rule, computer scientists don’t even know what the thing “receptive field” is and their knowledge about features and parameters of real biological neurons is almost zero - they do not know that receptive fields of sensory neurons have symmetrical concentric antagonistic circular structure and so on.
Neuron model RF-PSTH overcomes the flaws and limitations of current artificial neuron models.

Receptive field structure of real biological neurons

Receptive fields of sensory neurons have symmetrical concentric antagonistic circular structure. Several examples from neuroscience textbooks are provided below.
The receptive fields of bipolar cells are circular. But the centre and the surrounding area of each circle work in opposite ways: a ray of light that strikes the centre of the field has the opposite effect from one that strikes the area surrounding it (known as the "surround").
In fact, there are two types of bipolar cells, distinguished by the way they respond to light on the centers of their receptive fields. They are called ON-centre cells and OFF-centre cells.
If a light stimulus applied to the centre of a bipolar cell's receptive field has an excitatory effect on that cell, causing it to become depolarized, it is an ON-centre cell. A ray of light that falls only on the surround, however, will have the opposite effect on such a cell, inhibiting (hyperpolarizing) it.
on off receptive fields

The other kind of bipolar cells, OFF-centre cells, display exactly the reverse behavior: light on the field's centre has an inhibitory (hyperpolarizing) effect, while light on the surround has an excitatory (depolarizing ) effect.
on off receptive fields

Just like bipolar cells, ganglion cells have concentric receptive fields with a centre-surround antagonism. But contrary to the two types of bipolar cells, ON-centre ganglion cells and OFF-centre ganglion cells do not respond by depolarizing or hyperpolarizing, but rather by increasing or decreasing the frequency with which they discharge action potentials.
That said, the response to the stimulation of the centre of the receptive field is always inhibited by the stimulation of the surround.
on off receptive fields

The Brain from Top to Bottom
on off receptive fields
Notes: Vision (Part 1)
PSYC 2: Biological Foundations - Fall 2012 - Professor Claffey
on off receptive fields
Quizlet. (7) Somatosensory System
on off receptive fields
Quizlet. (7) Neuro ~ Block3
Olfactory and Gustatory Receptive Fields
olfactory receptive fields are analogous to retinal center-surround receptive fields: Mitral cells in the olfactory bulb exhibit excitatory responses to certain chemical compounds in a homologous series of compounds and inhibitory responses to neighboring compounds that flank the excitatory compounds in the series. The presence of antagonistic center-surround receptive fields in the olfactory system suggests that higher level receptive fields, such as those of neurons in the olfactory cortex, may possess an oriented structure analogous to visual and auditory cortical receptive fields. However, the orientation would be in the space of chemical concentration and time, implying a sensitivity toward increasing or decreasing amounts of particular chemical compounds at a particular rate.
Encyclopedia of The Human Brain - Vol. I, II, III and IV (2002). Editor-in-Chief: V. S. Ramachandran. ISBN: 978-0-12-227210-3.
Volume IV, Page 165
On-center and Off-center receptive fields. The receptive fields of retinal ganglion cells and thalamic neurons are organized as two concentric circles with different contrast polarities. On-center neurons respond to the presentation of a light spot on a dark background and off-center neurons to the presentation of a dark spot on a light background.

Output response of real biological neurons to the stimulus

Below are several examples of experimental measurement data of real biological neurons.
Typical LGN cell responses

Figure 6. Typical LGN cell responses. The peri-stimulus-time histogram (PSTH) on top shows a typical temporal waveform of a geniculate (thick line) and retinal (broken line) visual response to a light spot flashed on and off within the center of the receptive field. The response to a sudden increment and decrement of RF illumination can show up to 8 components: 1) initial transient response (overshoot, peak), 2) post-peak inhibition, 3) early rebound response, 4) tonic response, 5) stimulus off inhibition (off-response), 6) first post-inhibitory rebound, 7) late inhibitory response, and 8) second post-inhibitory rebound. The response profile of the retinal input is less complex.
F Wörgötter, K Suder, N Pugeault, and K Funke (2003)
Response characteristics in the lateral geniculate nucleus and their primary afferent influences on the visual cortex of cat
Modulation of Neuronal Responses: Implications for Active Vision. (G T Buracas, O Ruksenas, G M Boyton and T D Albright, eds.) NATO Science Series 1: Life and Behavioral Sciences 334:165–188.
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Linear, X-type (A) and nonlinear, Y-type (B) spatial contrast integration
Figure 7. Linear, X-type (A) and nonlinear, Y-type (B) spatial contrast integration. A) The strongest visual responses of the linear type are elicited in LGN X-cells by a contrast pattern of a spatial frequency that fits well to the diameter of the center of the RF. The strength of the visual response depends on the spatial phase of the pattern (e.g. a grating). A balanced stimulation of the RF center (and surround) by bright and dark bars results in the null-response (middle) which is characterized by only small, if any, change in activity. B) Y-cell activity is more phasic and is also characterized by the lack of a null-response. Non-linear (second order) response peaks are observed irrespective of the spatial frequency of the stimulus.
F Wörgötter, K Suder, N Pugeault, and K Funke (2003)
Response characteristics in the lateral geniculate nucleus and their primary afferent influences on the visual cortex of cat
Modulation of Neuronal Responses: Implications for Active Vision. (G T Buracas, O Ruksenas, G M Boyton and T D Albright, eds.) NATO Science Series 1: Life and Behavioral Sciences 334:165–188.
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Effect of electrical PBR-stimulation on the spatial receptive field profile for an on-centre nonlagged Y-cell
Figure 8. Effect of electrical PBR-stimulation on the spatial receptive field profile for an on-centre nonlagged Y-cell. A. Responses to a light slit presented in different position across the receptive field. The width of the slit was about 1/3 of the width of the handplotted receptive field centre, the slit length about 3 times the diameter of the hand-plotted receptive field centre. Each data point is the average of 5 stimulus presentations. Open circles, response of the dLGN cell in the control condition, open squares, retinal input measured by S-potentials. Filled spots, response of dLGN cell to electrical stimulation of PBR (140 Hz for 70 ms). B-D: Example of response patterns for the dLGN cell response in the control condition, with PBR-stimulation, and for the retinal input. The long horizontal line below the abcissa marks the period when the stimulus was on, the short bar marks the period with electrical PBR stimulation.
Paul Heggelund (2003)
Signal Processing in the Dorsal Lateral Geniculate Nucleus
Modulation of Neuronal Responses: Implications for Active Vision. (G T Buracas, O Ruksenas, G M Boyton and T D Albright, eds.) NATO Science Series 1: Life and Behavioral Sciences 334:109–134.
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Comparison of the response of an on-centre X-cell and the response in its retinal input
Figure 9. Comparison of the response of an on-centre X-cell and the response in its retinal input. The stimulus was a circular light spot of variable diameter but fixed contrast, centered on the receptive field. A. Open squares, retinal input, open circles, dLGN cell response. The response was measured as the average firing rate during a 500 ms period of spot presentation. Each point is the average from 20 stimulus presentations. Retinal input was measured as average frequency of S-potentials. The filled symbols mark spontaneous activity. B. The difference between retinal input and dLGN cell response. The data show the reduction in the average response to the various spot diameters. C. Transfer ratio calculated as output /input firing rate.
Paul Heggelund (2003)
Signal Processing in the Dorsal Lateral Geniculate Nucleus
Modulation of Neuronal Responses: Implications for Active Vision. (G T Buracas, O Ruksenas, G M Boyton and T D Albright, eds.) NATO Science Series 1: Life and Behavioral Sciences 334:109–134.
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Additional reading

Neurocluster Brain Model

“Neuron model RF-PSTH” and “Neurocluster Brain Model” – are two different, unrelated models.
The correctness or falseness of “Neuron model RF-PSTH” is completely unrelated to the correctness or falseness of “Neurocluster Brain Model”.

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