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This procedure stems from the assumption that neurons average their rates. If we accept this hypothesis, we must understand that neurons compute this average relative to the time window that has a meaning for them, not for an experimenter. If we analyse an activity that repeats with strict periodicity, it is not difficult to determine its period and calculate the average value. But neurons do not exhibit monotonous spiking. So, we do not know whether the neural code is actually average rate, and we cannot confirm or refute it because we do not know the system clock of the brain. As a result, we can average infinitely using our arbitrary time windows, but it will give nothing for deciphering the code.
The spike-count rate can be determined from a single trial, but at the expense of losing all temporal resolution about variations in neural response during the course of the trial. Temporal averaging can work well in cases where the stimulus is constant or slowly varying and does not require a fast reaction of the [[organism]] — and this is the situation usually encountered in experimental protocols. Real-world input, however, is hardly stationary, but often changing on a fast time scale. For example, even when viewing a static image, humans perform [[saccades]], rapid changes of the direction of gaze. The image projected onto the retinal [[photoreceptor cell|photoreceptors]] changes therefore every few hundred milliseconds ([https://lcnwww.epfl.ch/gerstner/SPNM/node7.html Chapter 1.5] in <ref name=":0" />). More generally, whenever a rapid response of an organism is required a firing rate defined as a spike-count over a few hundred milliseconds is simply too slow.
==== Time-dependent firing rate (averaging over several trials) ====
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For sufficiently small Δt, r(t)Δt is the average number of spikes occurring between times t and t+Δt over multiple trials. If Δt is small, there will never be more than one spike within the interval between t and t+Δt on any given trial. This means that r(t)Δt is also the [[fraction (mathematics)|fraction]] of trials on which a spike occurred between those times. Equivalently, r(t)Δt is the [[probability]] that a spike occurs during this time interval.
As an experimental procedure, the time-dependent firing rate measure is a useful method to evaluate neuronal activity, in particular in the case of time-dependent stimuli. The obvious problem with this approach is that it can not be the coding scheme used by neurons in the brain. Neurons can not wait for the stimuli to repeatedly present in an exactly same manner before generating a response.<ref name=":0" /> Moreover, the dynamics of many environmental signals are measured in milliseconds, and during these milliseconds, neurons can only fire once or twice. With such a number of spikes, it is impossible to encode the signal by their average rate. But there are also faster signals. For example, a bat is capable of echolocation with a resolution of microseconds.<ref>{{Cite journal|last=McKenna|first=T.M.|last2=McMullen|first2=T.A.|last3=Shlesinger|first3=M.F.|date=1994
Can a code consisting of identical spikes provide the nervous system's observable information density, speed, and efficiency? Unfortunately for the adherents of the rate code paradigm, the answer to this question is negative. Such code is ineffective in all respects. Tempo variation does not carry enough information to represent a complex multi-parameter signal. It requires the creation of many spikes to encode simple parameters. Thus, it is too slow and energetically expensive. That is why it does not correspond to the reality of the brain. However, this model is still widely used not only in experiments but also in [[neural networks]] models. As a result, over the past decades, a vast amount of data has accumulated, but it has not brought us any closer to deciphering the meaning of the code.
=== Temporal coding ===
<!-- Image with unknown copyright status removed: [[File:Firing rate.PNG|thumb|400px|'''Figure 2. Time-dependent firinig rates for different stimulus parameters.''' The rasters show multiple trias during which an MT neuron responded to the same moving, random-dot stimulus. (Adapted from Bair and Koch, 1996)]] -->Temporal code models assume that precise timing of spikes and interspike intervals carries information.<ref name=":0" /><ref name="Dayan">{{cite book |first1=Peter |last1=Dayan |first2=L. F. |last2=Abbott |title=Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems |url=https://books.google.com/books?id=5GSKQgAACAAJ |year=2001 |publisher=Massachusetts Institute of Technology Press |isbn=978-0-262-04199-7}}</ref> There is a growing body of evidence confirming this hypothesis. <ref name=":1">{{Cite journal|last1=Gollisch|first1=T.|last2=Meister|first2=M.|date=2008-02-22|title=Rapid Neural Coding in the Retina with Relative Spike Latencies|url=https://www.sciencemag.org/lookup/doi/10.1126/science.1149639|journal=Science|language=en|volume=319|issue=5866|pages=1108–1111|bibcode=2008Sci...319.1108G|doi=10.1126/science.1149639|issn=0036-8075|pmid=18292344|s2cid=1032537}}</ref><ref>{{cite journal|author=Forrest MD|year=2014|title=Intracellular Calcium Dynamics Permit a Purkinje Neuron Model to Perform Toggle and Gain Computations Upon its Inputs.|journal=Frontiers in Computational Neuroscience|volume=8|pages=86|doi=10.3389/fncom.2014.00086|pmc=4138505|pmid=25191262|doi-access=free}}</ref><ref>{{cite journal|author=Forrest MD|date=December 2014|title=The sodium-potassium pump is an information processing element in brain computation|journal=Frontiers in Physiology|volume=5|issue=472|pages=472|doi=10.3389/fphys.2014.00472|pmc=4274886|pmid=25566080|doi-access=free}}</ref> <ref>Singh & Levy, [http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0180839 "A consensus layer V pyramidal neuron can sustain interpulse-interval coding "], ''PLoS ONE'', 2017</ref> <ref name="thorpe">{{cite book|last=Thorpe|first=S.J.|url=https://books.google.com/books?id=b9gmAAAAMAAJ|title=Parallel processing in neural systems and computers|publisher=North-Holland|year=1990|isbn=978-0-444-88390-2|editor1-last=Eckmiller|editor1-first=R.|pages=91–94|chapter=Spike arrival times: A highly efficient coding scheme for neural networks|format=PDF|editor2-last=Hartmann|editor2-first=G.|editor3-last=Hauske|editor3-first=G.|editor3-link=Gert Hauske|chapter-url=https://www.researchgate.net/publication/247621744}}</ref> <ref name="Daniel">{{cite journal |vauthors=Butts DA, Weng C, Jin J, etal |title=Temporal precision in the neural code and the timescales of natural vision |journal=Nature |volume=449 |issue=7158 |pages=92–5 |date=September 2007 |pmid=17805296 |doi=10.1038/nature06105 |bibcode = 2007Natur.449...92B |s2cid=4402057 }}</ref>
Rate coding models suggest that the irregularities of neuronal firing are noise and average them. Temporal coding supplies an alternate explanation for the “noise," suggesting that it actually encodes information and affects neural processing.<ref name="van Hemmen 2006">J. Leo van Hemmen, TJ Sejnowski. 23 Problems in Systems Neuroscience. Oxford Univ. Press, 2006. p.143-158.</ref> To model this idea, binary symbols can be used to mark the spikes: 1 for a spike, 0 for no spike. Temporal coding allows the sequence 000111000111 to mean something different from 001100110011, even though the mean firing rate is the same for both sequences.<ref name="Theunissen F 1995"/> Thus, the model can be called the digital code.
Until recently, scientists had put the most emphasis on rate encoding as an explanation for [[post-synaptic potential]] patterns. However, functions of the brain are more temporally precise than the rate encoding allows. In addition, responses to the similar stimuli are different enough to suggest that the distinct patterns of spikes contain a higher volume of information than is possible to include in a rate code.<ref name="Zador, Stevens">{{cite web|last=Zador, Stevens|first=Charles, Anthony|title=The enigma of the brain|url=https://docs.google.com/a/stolaf.edu/viewer?a=v&pid=gmail&attid=0.1&thid=1369b5e1cdf273f9&mt=application/pdf&url=https://mail.google.com/mail/u/0/?ui%3D2%26ik%3D0a436eb2a7%26view%3Datt%26th%3D1369b5e1cdf273f9%26attid%3D0.1%26disp%3Dsafe%26realattid%3Df_h0ty13ea0%26zw&sig=AHIEtbQB4vngr9nDZaMTLUOcrk5DzePKqA|work=© Current Biology 1995, Vol 5 No 12|access-date=August 4, 2012}}</ref> The temporal structure of a spike train evoked by a stimulus is determined both by the dynamics of the stimulus and by the nature of the neural encoding process. Stimuli that change rapidly tend to generate precisely timed spikes. <ref>{{Cite journal|last1=Jolivet|first1=Renaud|last2=Rauch|first2=Alexander|last3=Lüscher|first3=Hans-Rudolf|last4=Gerstner|first4=Wulfram|date=2006-08-01|title=Predicting spike timing of neocortical pyramidal neurons by simple threshold models|url=https://doi.org/10.1007/s10827-006-7074-5|journal=Journal of Computational Neuroscience|language=en|volume=21|issue=1|pages=35–49|doi=10.1007/s10827-006-7074-5|issn=1573-6873|pmid=16633938|s2cid=8911457}}</ref> Temporal codes (also called [https://lcnwww.epfl.ch/gerstner/SPNM/node8.html spike codes] <ref name=":0" />), employ those features of the spiking activity that cannot be described by the firing rate. For example,
For very brief stimuli, a neuron's maximum firing rate may not be fast enough to produce more than a single spike. Due to the density of information
▲Temporal codes (also called [https://lcnwww.epfl.ch/gerstner/SPNM/node8.html spike codes] <ref name=":0" />), employ those features of the spiking activity that cannot be described by the firing rate. For example, '''time-to-first-spike''' after the stimulus onset, '''phase-of-firing''' with respect to background oscillations, characteristics based on the second and higher statistical [[Moment (mathematics)|moments]] of the ISI [[probability distribution]], spike randomness, or precisely timed groups of spikes ('''temporal patterns''') are candidates for temporal codes.<ref name="Kostal">{{cite journal |vauthors=Kostal L, Lansky P, Rospars JP |title=Neuronal coding and spiking randomness |journal=Eur. J. Neurosci. |volume=26 |issue=10 |pages=2693–701 |date=November 2007 |pmid=18001270 |doi=10.1111/j.1460-9568.2007.05880.x |s2cid=15367988 }}</ref> As there is no absolute time reference in the nervous system, the information is carried either in terms of the relative timing of spikes in a population of neurons (temporal patterns) or with respect to an [[neural oscillations|ongoing brain oscillation]]. (phase of firing) <ref name="thorpe" /><ref name="Stein" /> One way in which temporal codes are decoded, in presence of [[neural oscillations]], is that spikes occurring at specific phases of an oscillatory cycle are more effective in depolarizing the [[Chemical synapse|post-synaptic neuron]].<ref name = "Gupta2016">{{Cite journal|last1=Gupta|first1=Nitin|last2=Singh|first2=Swikriti Saran|last3=Stopfer|first3=Mark|date=2016-12-15|title=Oscillatory integration windows in neurons|journal=Nature Communications|volume=7|doi=10.1038/ncomms13808|issn=2041-1723|pmc=5171764|pmid=27976720|page=13808|bibcode=2016NatCo...713808G}}</ref>
To account for the fast encoding of visual stimuli, it has been suggested that neurons of the retina encode visual information in the latency time between stimulus onset and first action potential, also called latency to first spike or time-to-first-spike.<ref>{{cite journal|last=Gollisch|first=T.|author2=Meister, M.|title=Rapid Neural Coding in the Retina with Relative Spike Latencies|journal=Science|date=22 February 2008|volume=319|issue=5866|pages=1108–1111|doi=10.1126/science.1149639|pmid=18292344|bibcode=2008Sci...319.1108G|s2cid=1032537|url=https://semanticscholar.org/paper/3a06deb42293b278fbfcb6be2507ad2003df7ddd}}</ref> This type of temporal coding has been shown also in the auditory and somato-sensory system. The main drawback of such a coding scheme is its sensitivity to intrinsic neuronal fluctuations.<ref>{{cite journal|last=Wainrib|first=Gilles|author2=Michèle, Thieullen |author3=Khashayar, Pakdaman |title=Intrinsic variability of latency to first-spike|journal=Biological Cybernetics|date=7 April 2010|volume=103|issue=1|pages=43–56|doi=10.1007/s00422-010-0384-8|pmid=20372920|s2cid=7121609}}</ref> In the [[Visual cortex#Primary visual cortex (V1)|primary visual cortex]] of macaques, the timing of the first spike relative to the start of the stimulus was found to provide more information than the interval between spikes. However, the interspike interval could be used to encode additional information, which is especially important when the spike rate reaches its limit, as in high-contrast situations. For this reason, temporal coding may play a part in coding defined edges rather than gradual transitions.<ref>{{cite journal | last1 = Victor | first1 = Johnathan D | year = 2005 | title = Spike train metrics | doi = 10.1016/j.conb.2005.08.002 | pmid = 16140522 | journal = Current Opinion in Neurobiology | volume = 15 | issue = 5| pages = 585–592 | pmc = 2713191 }}</ref> ▼
As with the visual system, in [[mitral cell|mitral/tufted cells]] in the [[olfactory bulb]] of mice, first-spike latency relative to the start of a sniffing action seemed to encode much of the information about an odor. This strategy of using spike latency allows for rapid identification of and reaction to an odorant. In addition, some mitral/tufted cells have specific firing patterns for given odorants.
The mammalian [[gustatory system]] is useful for studying temporal coding because of its fairly distinct stimuli and the easily discernible responses of the organism.<ref>{{cite journal | last1 = Hallock | first1 = Robert M. | last2 = Di Lorenzo | first2 = Patricia M. | year = 2006 | title = Temporal coding in the gustatory system | doi = 10.1016/j.neubiorev.2006.07.005 | pmid = 16979239 | journal = Neuroscience & Biobehavioral Reviews | volume = 30 | issue = 8| pages = 1145–1160 | s2cid = 14739301 }}</ref> Temporally encoded information may help an organism discriminate between different tastants of the same category (sweet, bitter, sour, salty, umami) that elicit very similar responses in terms of spike count. The temporal component of the pattern elicited by each tastant may be used to determine its identity (e.g., the difference between two bitter tastants, such as quinine and denatonium). In this way, both rate coding and temporal coding may be used in the gustatory system – rate for basic tastant type, temporal for more specific differentiation.<ref name="Carleton A 2010">{{cite journal | last1 = Carleton | first1 = Alan | last2 = Accolla | first2 = Riccardo | last3 = Simon | first3 = Sidney A. | year = 2010 | title = Coding in the mammalian gustatory system | doi = 10.1016/j.tins.2010.04.002 | pmid = 20493563 | journal = Trends in Neurosciences | volume = 33 | issue = 7| pages = 326–334 | pmc = 2902637 }}</ref> Research on mammalian gustatory system has shown that there is an abundance of information present in temporal patterns across populations of neurons, and this information is different from that which is determined by rate coding schemes
The assumption that the neural code is binary (spikes and interspike intervals as 1 and 0) significantly increases the capacity of the code and makes the model more plausible. But the same question arises of correlating the information capacity of the code and the real speed of the brain, which manages to encode a complex multi-parameter signal within one or two spikes. The brain does not have time to build a long binary chain that could contain all the information. In this it is fundamentally different from artificial digital systems. For all the tremendous speed of their processors, which are orders of magnitude higher than the frequencies of the brain, they cannot match it in performance, speed and energy efficiency. The problem is they need to handle long binary code chains. The brain must be using some additional capacity in its code.
▲For very brief stimuli, a neuron's maximum firing rate may not be fast enough to produce more than a single spike. Due to the density of information about the abbreviated stimulus contained in this single spike, it would seem that the timing of the spike itself would have to convey more information than simply the average frequency of action potentials over a given period of time. This model is especially important for [[sound localization]], which occurs within the brain on the order of milliseconds. The brain must obtain a large quantity of information based on a relatively short neural response. Additionally, if low firing rates on the order of ten spikes per second must be distinguished from arbitrarily close rate coding for different stimuli, then a neuron trying to discriminate these two stimuli may need to wait for a second or more to accumulate enough information. This is not consistent with numerous organisms which are able to discriminate between stimuli in the time frame of milliseconds, suggesting that a rate code is not the only model at work.<ref name="Theunissen F 1995">{{cite journal | last1 = Theunissen | first1 = F | last2 = Miller | first2 = JP | year = 1995 | title = Temporal Encoding in Nervous Systems: A Rigorous Definition | journal = Journal of Computational Neuroscience | volume = 2 | issue = 2| pages = 149–162 | doi=10.1007/bf00961885| pmid = 8521284 | s2cid = 206786736 }}</ref>
In addition, the question of the system clock arises again. Two zeros of the code is a pause twice as long as one zero. But how can we determine that the interspike pause means two zeros or one if we do not know the time scale of the system under study? Measuring the pause by an external clock gives a lot of data, but says nothing about how many zeros are in that particular pause and how they relate to the spike units. In other words, we cannot determine if neuron activity means 0001 or 001. For a real qualitative analysis, it is necessary to normalize the system data by its own time. Then we can express our analysis in any unit of measurement. Finding this fundamental frequency as a basis for normalisation is probably of paramount importance when trying to decipher the brain code no matter which code model we are testing, since the time parameter remains anyway.
▲To account for the fast encoding of visual stimuli, it has been suggested that neurons of the retina encode visual information in the latency time between stimulus onset and first action potential, also called latency to first spike or time-to-first-spike.<ref>{{cite journal|last=Gollisch|first=T.|author2=Meister, M.|title=Rapid Neural Coding in the Retina with Relative Spike Latencies|journal=Science|date=22 February 2008|volume=319|issue=5866|pages=1108–1111|doi=10.1126/science.1149639|pmid=18292344|bibcode=2008Sci...319.1108G|s2cid=1032537|url=https://semanticscholar.org/paper/3a06deb42293b278fbfcb6be2507ad2003df7ddd}}</ref> This type of temporal coding has been shown also in the auditory and somato-sensory system. The main drawback of such a coding scheme is its sensitivity to intrinsic neuronal fluctuations.<ref>{{cite journal|last=Wainrib|first=Gilles|author2=Michèle, Thieullen |author3=Khashayar, Pakdaman |title=Intrinsic variability of latency to first-spike|journal=Biological Cybernetics|date=7 April 2010|volume=103|issue=1|pages=43–56|doi=10.1007/s00422-010-0384-8|pmid=20372920|s2cid=7121609}}</ref> In the [[Visual cortex#Primary visual cortex (V1)|primary visual cortex]] of macaques, the timing of the first spike relative to the start of the stimulus was found to provide more information than the interval between spikes. However, the interspike interval could be used to encode additional information, which is especially important when the spike rate reaches its limit, as in high-contrast situations. For this reason, temporal coding may play a part in coding defined edges rather than gradual transitions.<ref>{{cite journal | last1 = Victor | first1 = Johnathan D | year = 2005 | title = Spike train metrics | doi = 10.1016/j.conb.2005.08.002 | pmid = 16140522 | journal = Current Opinion in Neurobiology | volume = 15 | issue = 5| pages = 585–592 | pmc = 2713191 }}</ref>
▲The mammalian [[gustatory system]] is useful for studying temporal coding because of its fairly distinct stimuli and the easily discernible responses of the organism.<ref>{{cite journal | last1 = Hallock | first1 = Robert M. | last2 = Di Lorenzo | first2 = Patricia M. | year = 2006 | title = Temporal coding in the gustatory system | doi = 10.1016/j.neubiorev.2006.07.005 | pmid = 16979239 | journal = Neuroscience & Biobehavioral Reviews | volume = 30 | issue = 8| pages = 1145–1160 | s2cid = 14739301 }}</ref> Temporally encoded information may help an organism discriminate between different tastants of the same category (sweet, bitter, sour, salty, umami) that elicit very similar responses in terms of spike count. The temporal component of the pattern elicited by each tastant may be used to determine its identity (e.g., the difference between two bitter tastants, such as quinine and denatonium). In this way, both rate coding and temporal coding may be used in the gustatory system – rate for basic tastant type, temporal for more specific differentiation.<ref name="Carleton A 2010">{{cite journal | last1 = Carleton | first1 = Alan | last2 = Accolla | first2 = Riccardo | last3 = Simon | first3 = Sidney A. | year = 2010 | title = Coding in the mammalian gustatory system | doi = 10.1016/j.tins.2010.04.002 | pmid = 20493563 | journal = Trends in Neurosciences | volume = 33 | issue = 7| pages = 326–334 | pmc = 2902637 }}</ref> Research on mammalian gustatory system has shown that there is an abundance of information present in temporal patterns across populations of neurons, and this information is different from that which is determined by rate coding schemes. Groups of neurons may synchronize in response to a stimulus. In studies dealing with the front cortical portion of the brain in primates, precise patterns with short time scales only a few milliseconds in length were found across small populations of neurons which correlated with certain information processing behaviors. However, little information could be determined from the patterns; one possible theory is they represented the higher-order processing taking place in the brain.<ref name="Zador, Stevens"/>
▲As with the visual system, in [[mitral cell|mitral/tufted cells]] in the [[olfactory bulb]] of mice, first-spike latency relative to the start of a sniffing action seemed to encode much of the information about an odor. This strategy of using spike latency allows for rapid identification of and reaction to an odorant. In addition, some mitral/tufted cells have specific firing patterns for given odorants. This type of extra information could help in recognizing a certain odor, but is not completely necessary, as average spike count over the course of the animal's sniffing was also a good identifier.<ref>{{cite journal | last1 = Wilson | first1 = Rachel I | year = 2008 | title = Neural and behavioral mechanisms of olfactory perception | journal = Current Opinion in Neurobiology | volume = 18 | issue = 4| pages = 408–412 | doi=10.1016/j.conb.2008.08.015| pmid = 18809492 | pmc = 2596880 }}</ref> Along the same lines, experiments done with the olfactory system of rabbits showed distinct patterns which correlated with different subsets of odorants, and a similar result was obtained in experiments with the locust olfactory system.<ref name="Theunissen F 1995"/>
==== Temporal coding applications ====
The specificity of temporal coding requires highly refined technology to measure informative, reliable, experimental data. Advances made in [[optogenetics]] allow neurologists to control spikes in individual neurons, offering electrical and spatial single-cell resolution. For example, blue light causes the light-gated ion channel [[channelrhodopsin]] to open, depolarizing the cell and producing a spike. When blue light is not sensed by the cell, the channel closes, and the neuron ceases to spike. The pattern of the spikes matches the pattern of the blue light stimuli. By inserting channelrhodopsin gene sequences into mouse DNA, researchers can control spikes and therefore certain behaviors of the mouse (e.g., making the mouse turn left).<ref name="youtube.com">Karl Diesseroth, Lecture. "Personal Growth Series: Karl Diesseroth on Cracking the Neural Code." Google Tech Talks. November 21, 2008. https://www.youtube.com/watch?v=5SLdSbp6VjM</ref> Researchers, through optogenetics, have the tools to effect different temporal codes in a neuron while maintaining the same mean firing rate, and thereby can test whether or not temporal coding occurs in specific neural circuits.<ref name="Han X 2009">Han X, Qian X, Stern P, Chuong AS, Boyden ES. "Informational lesions: optical perturbations of spike timing and neural synchrony via microbial opsin gene fusions." Cambridge, Massachusetts: MIT Media Lad, 2009.</ref> Understanding any temporally encoded aspects of the neural code and replicating these sequences in neurons could allow for greater control and treatment of neurological and mental disorders such as [[depression (mood)|depression]], [[schizophrenia]], and [[Parkinson's disease]].
==== Phase-of-firing code ====
{{main|Phase precession}}
{{further|Phase resetting in neurons}}
Phase-of-firing code is a neural coding scheme that combines the [[action potential|spike]] count code with a time reference based on [[Neural oscillations|oscillations]]. This type of code takes into account a time label for each spike according to a time reference based on phase of local ongoing oscillations at low<ref name="Montemurro" /> or high frequencies.<ref name="Gamma cycle">{{cite journal |vauthors=Fries P, Nikolić D, Singer W |title=The gamma cycle |journal=Trends Neurosci. |volume=30 |issue=7 |pages=309–16 |date=July 2007 |pmid=17555828 |doi=10.1016/j.tins.2007.05.005 |s2cid=3070167 }}</ref> It has been shown that neurons in some cortical sensory areas encode
▲It has been shown that neurons in some cortical sensory areas encode rich naturalistic stimuli in terms of their spike times relative to the phase of ongoing network oscillatory fluctuations, rather than only in terms of their spike count.<ref name="Montemurro">{{cite journal|doi=10.1016/j.cub.2008.02.023|pmid=18328702|title=Phase-of-Firing Coding of Natural Visual Stimuli in Primary Visual Cortex|journal=Current Biology|volume=18|issue=5|pages=375–380|year=2008|last1=Montemurro|first1=Marcelo A.|last2=Rasch|first2=Malte J.|last3=Murayama|first3=Yusuke|last4=Logothetis|first4=Nikos K.|last5=Panzeri|first5=Stefano|doi-access=free}}</ref><ref>[http://pop.cerco.ups-tlse.fr/fr_vers/documents/thorpe_sj_90_91.pdf Spike arrival times: A highly efficient coding scheme for neural networks] {{webarchive|url=https://web.archive.org/web/20120215151304/http://pop.cerco.ups-tlse.fr/fr_vers/documents/thorpe_sj_90_91.pdf |date=2012-02-15 }}, SJ Thorpe - Parallel processing in neural systems, 1990</ref> The [[local field potential]] signals reflect population (network) oscillations. The phase-of-firing code is often categorized as a temporal code although the time label used for spikes (i.e. the network oscillation phase) is a low-resolution (coarse-grained) reference for time. As a result, often only four discrete values for the phase are enough to represent all the information content in this kind of code with respect to the phase of oscillations in low frequencies. Phase-of-firing code is loosely based on the [[Place cell#Phase precession|phase precession]] phenomena observed in place cells of the [[hippocampus]]. Another feature of this code is that neurons adhere to a preferred order of spiking between a group of sensory neurons, resulting in firing sequence.<ref name="Firing sequences">{{cite journal |vauthors=Havenith MN, Yu S, Biederlack J, Chen NH, Singer W, Nikolić D |title=Synchrony makes neurons fire in sequence, and stimulus properties determine who is ahead |journal=J. Neurosci. |volume=31 |issue=23 |pages=8570–84 |date=June 2011 |pmid=21653861 |pmc=6623348 |doi=10.1523/JNEUROSCI.2817-10.2011 |doi-access=free }}</ref>
This version of the code aims to overcome the limitations of the previous models. It shows that spike counting requires a frame of reference and suggests searching for it in the frequencies of the brain. But this model continues to consider actions potentials to be similar impulses and looks for information only in the rhythmic structure of neuronal activation. Thus, it faces the same question: how can neurons encode signals that change within the time frame of a single spike? Placing a discrete event on the exact timescale is an essential part of the encoding process. Still, it is not enough to represent all the parameters of a signal within tight temporal limits that the natural environment sets for the brain.
=== Population coding ===
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