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<title>Neural decoding</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Neural decoding</span></span>

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<p><b>Neural decoding</b> is a <a href="Neuroscience" title="Neuroscience">neuroscience</a> field concerned with the hypothetical reconstruction of sensory and other stimuli from information that has already been encoded and represented in the <a href="Brain" title="Brain">brain</a> by <a href="Biological_neural_network" class="mw-redirect" title="Biological neural network">networks</a> of <a href="Neurons" class="mw-redirect" title="Neurons">neurons</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Reconstruction refers to the ability of the researcher to predict what sensory stimuli the subject is receiving based purely on neuron <a href="Action_potential" title="Action potential">action potentials</a>. Therefore, the main goal of neural decoding is to characterize how the <a href="Electrophysiology" title="Electrophysiology">electrical activity</a> of neurons elicit activity and responses in the brain.<sup id="cite_ref-Jacobs_2-0" class="reference"><a href="#cite_note-Jacobs-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p><p>This article specifically refers to neural decoding as it pertains to the <a href="Mammal" title="Mammal">mammalian</a> <a href="Neocortex" title="Neocortex">neocortex</a>.

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<div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2></div>

<p>When looking at a picture, people's brains are constantly making decisions about what object they are looking at, where they need to move their eyes next, and what they find to be the most salient aspects of the input stimulus. As these images hit the back of the retina, these stimuli are converted from varying wavelengths to a series of neural spikes called <a href="Action_potential" title="Action potential">action potentials</a>. These patterns of action potentials are different for different objects and different colors; we therefore say that the neurons are encoding objects and colors by varying their spike rates or temporal patterns. Now, if someone were to probe the brain by placing <a href="Electrode" title="Electrode">electrodes</a> in the <a href="Visual_cortex" title="Visual cortex">primary visual cortex</a>, they may find what appears to be random electrical activity. These neurons are actually firing in response to the lower level features of visual input, possibly the edges of a picture frame. This highlights the crux of the neural decoding hypothesis: that it is possible to reconstruct a stimulus from the response of the ensemble of neurons that represent it. In other words, it is possible to look at spike train data and say that the person or animal being recorded is looking at a red ball.

</p><p>With the recent breakthrough in large-scale neural recording and decoding technologies, researchers have begun to crack the neural code and already provided the first glimpse into the real-time neural code of memory traces as memory is formed and recalled in the hippocampus, a brain region known to be central for memory formation.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Neuroscientists have initiated a large-scale brain activity mapping or brain decoding project<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> to construct brain-wide neural codes.

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<div class="mw-heading mw-heading2"><h2 id="Encoding_to_decoding">Encoding to decoding</h2></div>

<p>Implicit about the decoding hypothesis is the assumption that neural spiking in the brain somehow represents stimuli in the external world. The decoding of neural data would be impossible if the neurons were firing randomly: nothing would be represented. This process of decoding neural data forms a loop with <a href="Neural_coding" title="Neural coding">neural encoding</a>. First, the organism must be able to perceive a set of stimuli in the world – say a picture of a hat. Seeing the stimuli must result in some internal learning: the encoding stage. After varying the range of stimuli that is presented to the observer, we expect the neurons to adapt to the statistical properties of the <a href="Signal_processing" title="Signal processing">signals</a>, encoding those that occur most frequently:<sup id="cite_ref-barlow_6-0" class="reference"><a href="#cite_note-barlow-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> the <a href="Efficient_coding_hypothesis" title="Efficient coding hypothesis">efficient-coding hypothesis</a>. Now neural decoding is the process of taking these statistical consistencies, a <a href="Statistical_model" title="Statistical model">statistical model</a> of the world, and reproducing the stimuli. This may map to the process of thinking and acting, which in turn guide what stimuli we receive, and thus, completing the loop.

</p><p>In order to build a model of neural spike data, one must both understand how information is originally stored in the brain and how this information is used at a later point in time. This <a href="Neural_coding" title="Neural coding">neural coding</a> and decoding loop is a symbiotic relationship and the crux of the brain's learning algorithm. Furthermore, the processes that underlie neural decoding and encoding are very tightly coupled and may lead to varying levels of representative ability.<sup id="cite_ref-Chacron_7-0" class="reference"><a href="#cite_note-Chacron-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Baloori_8-0" class="reference"><a href="#cite_note-Baloori-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Spatial_resolutions">Spatial resolutions</h2></div>

<p>Much of the neural decoding problem depends on the <a href="Spatial_resolution" title="Spatial resolution">spatial resolution</a> of the data being collected. The number of neurons needed to reconstruct the stimulus with reasonable accuracy depends on the means by which data is collected and the area which is being recorded. For example, <a href="Rods_and_cones" class="mw-redirect" title="Rods and cones">rods and cones</a> (which respond to colors of small visual areas) in the retina may require more recordings than <a href="Simple_cell" title="Simple cell">simple cells</a> (which respond to orientation of lines) in the primary visual cortex.

</p><p>Previous recording methods relied on <a href="Neurostimulation" title="Neurostimulation">stimulating single neurons</a> over a repeated series of tests in order to generalize this neuron's behavior.<sup id="cite_ref-Hubel_9-0" class="reference"><a href="#cite_note-Hubel-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> New techniques such as high-density <a href="Multielectrode_array" class="mw-redirect" title="Multielectrode array">multi-electrode array recordings</a> and <a href="Two-photon_excitation_microscopy" title="Two-photon excitation microscopy">multi-photon calcium imaging techniques</a> now make it possible to record from upwards of a few hundred neurons. Even with better recording techniques, the focus of these recordings must be on an area of the brain that is both manageable and qualitatively understood. Many studies look at spike train data gathered from the <a href="Retinal_ganglion_cell" title="Retinal ganglion cell">ganglion cells</a> in the retina, since this area has the benefits of being strictly <a href="Feedforward_neural_network" title="Feedforward neural network">feedforward</a>, <a href="Retinotopy" title="Retinotopy">retinotopic</a>, and amenable to current recording granularities. The duration, intensity, and location of the stimulus can be controlled to sample, for example, a particular subset of ganglion cells within a structure of the visual system.<sup id="cite_ref-Warland_10-0" class="reference"><a href="#cite_note-Warland-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Other studies use spike trains to evaluate the discriminatory ability of non-visual senses such as rat facial whiskers<sup id="cite_ref-Arabzadeh_11-0" class="reference"><a href="#cite_note-Arabzadeh-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> and the olfactory coding of moth pheromone receptor neurons.<sup id="cite_ref-kostal_12-0" class="reference"><a href="#cite_note-kostal-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>

</p><p>Even with ever-improving recording techniques, one will always run into the limited sampling problem: given a limited number of recording trials, it is impossible to completely account for the error associated with noisy data obtained from stochastically functioning neurons. (For example, a neuron's <a href="Electric_potential" title="Electric potential">electric potential</a> fluctuates around its <a href="Resting_potential" title="Resting potential">resting potential</a> due to a constant influx and efflux of <a href="Voltage-gated_sodium_channel" title="Voltage-gated sodium channel">sodium</a> and <a href="Voltage-gated_potassium_channel" title="Voltage-gated potassium channel">potassium</a> ions.) Therefore, it is not possible to perfectly reconstruct a stimulus from spike data. Luckily, even with noisy data, the stimulus can still be reconstructed within acceptable error bounds.<sup id="cite_ref-Rolls_13-0" class="reference"><a href="#cite_note-Rolls-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Temporal_resolutions">Temporal resolutions</h2></div>

<p>Timescales and frequencies of stimuli being presented to the observer are also of importance to decoding the neural code. Quicker timescales and higher frequencies demand faster and more precise responses in neural spike data. In humans, millisecond precision has been observed throughout the <a href="Visual_cortex" title="Visual cortex">visual cortex</a>, the <a href="Retina" title="Retina">retina</a>,<sup id="cite_ref-berry_14-0" class="reference"><a href="#cite_note-berry-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> and the <a href="Lateral_geniculate_nucleus" title="Lateral geniculate nucleus">lateral geniculate nucleus</a>. So one would suspect this to be the appropriate measuring frequency. This has been confirmed in studies that quantify the responses of neurons in the lateral geniculate nucleus to white-noise and naturalistic movie stimuli.<sup id="cite_ref-Butts_15-0" class="reference"><a href="#cite_note-Butts-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> At the cellular level, <a href="Spike-timing-dependent_plasticity" title="Spike-timing-dependent plasticity">spike-timing-dependent plasticity</a> operates at millisecond timescales.<sup id="cite_ref-Song_16-0" class="reference"><a href="#cite_note-Song-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Therefore models seeking biological relevance should be able to perform at these temporal scales.

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<div class="mw-heading mw-heading2"><h2 id="Probabilistic_decoding">Probabilistic decoding</h2></div>

<p>When decoding neural data, arrival times of each spike <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{1},{\text{ }}t_{2},{\text{ }}...,{\text{ }}t_{n}{\text{ }}={\text{ }}\{t_{i}\}}">

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<annotation encoding="application/x-tex">{\displaystyle t_{1},{\text{ }}t_{2},{\text{ }}...,{\text{ }}t_{n}{\text{ }}={\text{ }}\{t_{i}\}}</annotation>

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</math></span><img src="./d7f55f83b5d73d17f6a8ade4eb60b4103fa83bd8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.015ex; height:2.843ex;" alt="{\displaystyle t_{1},{\text{ }}t_{2},{\text{ }}...,{\text{ }}t_{n}{\text{ }}={\text{ }}\{t_{i}\}}" loading="lazy"></span>, and the <a href="Probability" title="Probability">probability</a> of seeing a certain stimulus, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P[s(t)]}">

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<annotation encoding="application/x-tex">{\displaystyle P[s(t)]}</annotation>

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</math></span><img src="./fb6efde3985a474b225faf6610573e053f1a8ea0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.778ex; height:2.843ex;" alt="{\displaystyle P[s(t)]}" loading="lazy"></span> may be the extent of the available data. The <a href="Prior_probability" title="Prior probability">prior distribution</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P[s(t)]}">

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<annotation encoding="application/x-tex">{\displaystyle P[s(t)]}</annotation>

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</math></span><img src="./fb6efde3985a474b225faf6610573e053f1a8ea0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.778ex; height:2.843ex;" alt="{\displaystyle P[s(t)]}" loading="lazy"></span> defines an ensemble of signals, and represents the <a href="Likelihood_function" title="Likelihood function">likelihood</a> of seeing a stimulus in the world based on previous experience. The spike times may also be drawn from a <a href="Probability_distribution" title="Probability distribution">distribution</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P[\{t_{i}\}]}">

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<annotation encoding="application/x-tex">{\displaystyle P[\{t_{i}\}]}</annotation>

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</math></span><img src="./9cd4d8ff52f32afdc6446c709f183a1936951237.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.003ex; height:2.843ex;" alt="{\displaystyle P[\{t_{i}\}]}" loading="lazy"></span>; however, what we want to know is the <a href="Probability_distribution" title="Probability distribution">probability distribution</a> over a set of stimuli given a series of spike trains <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P[s(t)|\{t_{i}\}]}">

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<annotation encoding="application/x-tex">{\displaystyle P[s(t)|\{t_{i}\}]}</annotation>

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</math></span><img src="./8e8be99c9d3ff1d201a79876542204cc4cab83be.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.39ex; height:2.843ex;" alt="{\displaystyle P[s(t)|\{t_{i}\}]}" loading="lazy"></span>, which is called the <a href="Conditional_probability" title="Conditional probability">response-conditional</a> ensemble. What remains is the characterization of the neural code by translating stimuli into spikes, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P[\{t_{i}\}|s(t)]}">

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<annotation encoding="application/x-tex">{\displaystyle P[\{t_{i}\}|s(t)]}</annotation>

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</math></span><img src="./37ddc31853e6fd42b2c744f16fe600fca8f123ef.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.39ex; height:2.843ex;" alt="{\displaystyle P[\{t_{i}\}|s(t)]}" loading="lazy"></span>; the traditional approach to calculating this probability distribution has been to fix the stimulus and examine the responses of the neuron. Combining everything using <a href="Bayes'_Rule" class="mw-redirect" title="Bayes' Rule">Bayes' Rule</a> results in the simplified probabilistic characterization of neural decoding: <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P[s(t)|\{t_{i}\}]=P[\{t_{i}\}|s(t)]*(P[s(t)]/P[\{t_{i}\}])}">

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</math></span><img src="./d4bd74b54a96cbc0b6ef79fff2af7684aab6700f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:44.826ex; height:2.843ex;" alt="{\displaystyle P[s(t)|\{t_{i}\}]=P[\{t_{i}\}|s(t)]*(P[s(t)]/P[\{t_{i}\}])}" loading="lazy"></span>. An area of active research consists of finding better ways of representing and determining <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P[\{t_{i}\}|s(t)]}">

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<div class="mw-heading mw-heading3"><h3 id="Spike_train_number">Spike train number</h3></div>

<p>The simplest coding strategy is the <a href="Neural_coding#Spike-count_rate" title="Neural coding">spike train number coding</a>. This method assumes that the spike number is the most important quantification of spike train data. In spike train number coding, each stimulus is represented by a unique firing rate across the sampled neurons. The color red may be signified by 5 total spikes across the entire set of neurons, while the color green may be 10 spikes; each spike is pooled together into an overall count. This is represented by:

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<annotation encoding="application/x-tex">{\displaystyle P(r|s)=\prod _{}P(n_{ij}|s)}</annotation>

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</math></span><img src="./10d42871ddb42480035efa05ea3d0eab30e044bd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:20.96ex; height:5.509ex;" alt="{\displaystyle P(r|s)=\prod _{}P(n_{ij}|s)}" loading="lazy"></span>

</p><p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r=n=}">

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</math></span><img src="./a694958a44fcdb22d282639ec1559475814bdbc6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.995ex; height:1.676ex;" alt="{\displaystyle r=n=}" loading="lazy"></span> the number of spikes, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{ij}}">

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</math></span><img src="./1fe0c890f9b1fa32445c5fabf93574fee42b30f7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.872ex; height:2.343ex;" alt="{\displaystyle n_{ij}}" loading="lazy"></span> is the number of spikes of neuron <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}">

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</math></span><img src="./add78d8608ad86e54951b8c8bd6c8d8416533d20.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}" loading="lazy"></span> at stimulus presentation time <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle j}">

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<div class="mw-heading mw-heading3"><h3 id="Instantaneous_rate_code">Instantaneous rate code</h3></div>

<p>Adding a small temporal component results in the <a href="Neural_coding#Time-dependent_firing_rate" title="Neural coding">spike timing coding</a> strategy. Here, the main quantity measured is the number of spikes that occur within a predefined <a href="Window_function" title="Window function">window</a> of time T. This method adds another dimension to the previous. This timing code is given by:

</p><p><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P(r|s)=\prod _{l}\left[\prod _{i,j}v_{i}(t_{ijl}|s)dt\right]exp\left[-\sum _{i}\int _{0}^{T}dtv_{i}(t|s)\right]}">

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<annotation encoding="application/x-tex">{\displaystyle P(r|s)=\prod _{l}\left[\prod _{i,j}v_{i}(t_{ijl}|s)dt\right]exp\left[-\sum _{i}\int _{0}^{T}dtv_{i}(t|s)\right]}</annotation>

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</math></span><img src="./c8710813f9eb534043fd5cc0ebca909c68e5c15c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:54.813ex; height:7.676ex;" alt="{\displaystyle P(r|s)=\prod _{l}\left[\prod _{i,j}v_{i}(t_{ijl}|s)dt\right]exp\left[-\sum _{i}\int _{0}^{T}dtv_{i}(t|s)\right]}" loading="lazy"></span>

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</math></span><img src="./83e54c1e0dfb66ca2631c1b13a07245029d528c0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.807ex; height:2.676ex;" alt="{\displaystyle t_{ijl}}" loading="lazy"></span> is the jth spike on the lth presentation of neuron i, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{i}(t|s)}">

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<annotation encoding="application/x-tex">{\displaystyle v_{i}(t|s)}</annotation>

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</math></span><img src="./37ea616b45ac066d637ad958d4bdfd3197f7e89f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.314ex; height:2.843ex;" alt="{\displaystyle v_{i}(t|s)}" loading="lazy"></span> is the firing rate of neuron i at time t, and 0 to T is the start to stop times of each trial.

</p>

<div class="mw-heading mw-heading3"><h3 id="Temporal_correlation">Temporal correlation</h3></div>

<p><a href="Neural_coding#Temporal_coding" title="Neural coding">Temporal correlation code</a>, as the name states, adds <a href="Correlations" class="mw-redirect" title="Correlations">correlations</a> between individual spikes. This means that the time between a spike <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{i}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle t_{i}}</annotation>

</semantics>

</math></span><img src="./8b61e3d4d909be4a19c9a554a301684232f59e5a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.639ex; height:2.343ex;" alt="{\displaystyle t_{i}}" loading="lazy"></span> and its preceding spike <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{i-1}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle t_{i-1}}</annotation>

</semantics>

</math></span><img src="./ee5aa084171a4d706db1844d2abf40370248c5dc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.74ex; height:2.343ex;" alt="{\displaystyle t_{i-1}}" loading="lazy"></span> is included. This is given by:

</p><p><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P(r|s)=\prod _{l}\left[\prod _{i,j}v_{i}(t_{ijl},\tau (t_{ijl})|s)dt\right]exp\left[-\sum _{i}\int _{0}^{T}dtv_{i}(t,\tau (t)|s)\right]}">

</mrow>

</mrow>

</munder>

<mrow>

<mrow>

</mrow>

</munder>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</mrow>

<mrow>

<mrow>

</mrow>

</munder>

</mrow>

</mrow>

</msubsup>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P(r|s)=\prod _{l}\left[\prod _{i,j}v_{i}(t_{ijl},\tau (t_{ijl})|s)dt\right]exp\left[-\sum _{i}\int _{0}^{T}dtv_{i}(t,\tau (t)|s)\right]}</annotation>

</semantics>

</math></span><img src="./32a14358caba9836f1b12f352d3b6d3dc40fab8c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:66.55ex; height:7.676ex;" alt="{\displaystyle P(r|s)=\prod _{l}\left[\prod _{i,j}v_{i}(t_{ijl},\tau (t_{ijl})|s)dt\right]exp\left[-\sum _{i}\int _{0}^{T}dtv_{i}(t,\tau (t)|s)\right]}" loading="lazy"></span>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \tau (t)}</annotation>

</semantics>

</math></span><img src="./e3492908614e5c2bae068384e9b19dc28557a73b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.851ex; height:2.843ex;" alt="{\displaystyle \tau (t)}" loading="lazy"></span> is the time interval between a neurons spike and the one preceding it.

</p>

<div class="mw-heading mw-heading3"><h3 id="Ising_decoder">Ising decoder</h3></div>

<p>Another description of neural spike train data uses the <a href="Ising_model" title="Ising model">Ising model</a> borrowed from the physics of magnetic spins. Because neural spike trains are effectively binarized (either on or off) at small time scales (10 to 20 ms), the <a href="Ising_model" title="Ising model">Ising model</a> is able to effectively capture the present pairwise correlations,<sup id="cite_ref-Ising_18-0" class="reference"><a href="#cite_note-Ising-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> and is given by:

</p><p><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P(r|s)={\frac {1}{\mathrm {Z} (s)}}exp\left(\sum _{i}h_{i}(s)r_{i}+{\frac {1}{2}}\sum _{i\neq j}J_{ij}(s)r_{i}r_{j}\right)}">

</mrow>

<mfrac>

<mrow>

</mrow>

</mrow>

</mfrac>

</mrow>

<mrow>

<mrow>

</mrow>

</munder>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<mfrac>

</mfrac>

</mrow>

</mrow>

</munder>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P(r|s)={\frac {1}{\mathrm {Z} (s)}}exp\left(\sum _{i}h_{i}(s)r_{i}+{\frac {1}{2}}\sum _{i\neq j}J_{ij}(s)r_{i}r_{j}\right)}</annotation>

</semantics>

</math></span><img src="./e868aeed74dd1616ea3009a73f886ab6111c8eaa.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:51.317ex; height:7.843ex;" alt="{\displaystyle P(r|s)={\frac {1}{\mathrm {Z} (s)}}exp\left(\sum _{i}h_{i}(s)r_{i}+{\frac {1}{2}}\sum _{i\neq j}J_{ij}(s)r_{i}r_{j}\right)}" loading="lazy"></span>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle r=(r_{1},r_{2},...,r_{n})^{T}}</annotation>

</semantics>

</math></span><img src="./486fd71d3b5281f6a932bb59ed0a633a9a97aa5e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.022ex; height:3.176ex;" alt="{\displaystyle r=(r_{1},r_{2},...,r_{n})^{T}}" loading="lazy"></span> is the set of binary responses of neuron i, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{i}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle h_{i}}</annotation>

</semantics>

</math></span><img src="./d535f210cbd9b9fe6689e61427b3e213e5b2d547.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.139ex; height:2.509ex;" alt="{\displaystyle h_{i}}" loading="lazy"></span> is the <a href="Mean_field_theory" class="mw-redirect" title="Mean field theory">external fields function</a>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J_{ij}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle J_{ij}}</annotation>

</semantics>

</math></span><img src="./1a5daff3ca4e673277d8780ceb49b6922bbf6fac.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.767ex; height:2.843ex;" alt="{\displaystyle J_{ij}}" loading="lazy"></span> is the <a href="Ising_model#Neuroscience" title="Ising model">pairwise couplings function</a>, and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Z} (s)}">

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \mathrm {Z} (s)}</annotation>

</semantics>

</math></span><img src="./4ba2ad90a2f832999a7b77ff043c2c9ec036d8f3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.32ex; height:2.843ex;" alt="{\displaystyle \mathrm {Z} (s)}" loading="lazy"></span> is the <a href="Partition_function_(mathematics)" title="Partition function (mathematics)">partition function</a>

</p>

<div class="mw-heading mw-heading2"><h2 id="Agent-based_decoding">Agent-based decoding</h2></div>

<p>In addition to the probabilistic approach, <a href="Agent-based_model" title="Agent-based model">agent-based models</a> exist that capture the spatial dynamics of the neural system under scrutiny. One such model is <a href="Hierarchical_temporal_memory" title="Hierarchical temporal memory">hierarchical temporal memory</a>, which is a <a href="Machine_learning" title="Machine learning">machine learning</a> framework that organizes the visual perception problem into a <a href="Hierarchy" title="Hierarchy">hierarchy</a> of interacting nodes (neurons). The connections between nodes on the same level and lower levels are termed <a href="Chemical_synapse" title="Chemical synapse">synapses</a>, and their interactions are subsequently learning. Synapse strengths modulate learning and are altered based on the temporal and spatial firing of nodes in response to input patterns.<sup id="cite_ref-Hawkins_19-0" class="reference"><a href="#cite_note-Hawkins-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Hawkins2_20-0" class="reference"><a href="#cite_note-Hawkins2-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup>

</p><p>While it is possible to transform the firing rates of these modeled neurons into the probabilistic and mathematical frameworks described above, agent-based models provide the ability to observe the behavior of the entire population of modeled neurons. Researchers can circumvent the limitations implicit with lab-based recording techniques. Because this approach does rely on modeling biological systems, error arises in the assumptions made by the researcher and in the data used in <a href="Parameter_estimation" class="mw-redirect" title="Parameter estimation">parameter estimation</a>.

</p>

<div class="mw-heading mw-heading2"><h2 id="Applicability">Applicability</h2></div>

<p>The advancement in our understanding of neural decoding benefits the development of <a href="Brain-machine_interfaces" class="mw-redirect" title="Brain-machine interfaces">brain-machine interfaces</a>, <a href="Prosthetics" class="mw-redirect" title="Prosthetics">prosthetics</a><sup id="cite_ref-Donoghue_21-0" class="reference"><a href="#cite_note-Donoghue-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> and the understanding of neurological disorders such as <a href="Epilepsy" title="Epilepsy">epilepsy</a>.<sup id="cite_ref-Gross_22-0" class="reference"><a href="#cite_note-Gross-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup>

</p>

<ul><li><a href="Brain-reading" title="Brain-reading">Brain-reading</a></li>

<li><a href="Bursting" title="Bursting">Bursting</a></li>

<li><a href="Correlation_coding" class="mw-redirect" title="Correlation coding">Correlation coding</a></li>

<li><a href="Grandmother_cell" title="Grandmother cell">Grandmother cell</a></li>

<li><a href="Independent-spike_coding" class="mw-redirect" title="Independent-spike coding">Independent-spike coding</a></li>

<li><a href="Multielectrode_array" class="mw-redirect" title="Multielectrode array">Multielectrode array</a></li>

<li><a href="Nervous_system_network_models" title="Nervous system network models">Nervous system network models</a></li>

<li><a href="Neural_coding" title="Neural coding">Neural coding</a></li>

<li><a href="Neural_synchronization" class="mw-redirect" title="Neural synchronization">Neural synchronization</a></li>

<li><a href="NeuroElectroDynamics" class="mw-redirect" title="NeuroElectroDynamics">NeuroElectroDynamics</a></li>

<li><a href="Patch_clamp" title="Patch clamp">Patch clamp</a></li>

<li><a href="Phase-of-firing_code" class="mw-redirect" title="Phase-of-firing code">Phase-of-firing code</a></li>

<li><a href="Population_coding" class="mw-redirect" title="Population coding">Population coding</a></li>

<li><a href="Rate_coding" class="mw-redirect" title="Rate coding">Rate coding</a></li>

<li><a href="Sparse_coding" class="mw-redirect" title="Sparse coding">Sparse coding</a></li>

<li><a href="Temporal_coding" class="mw-redirect" title="Temporal coding">Temporal coding</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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/* end https://en.wikipedia.org/ */

</style><cite id="CITEREFJohnson2000" class="citation journal cs1">Johnson, K. O. (June 2000). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0896-6273%2800%2981193-9">"Neural coding"</a>. <i>Neuron</i>. <b>26</b> (3): <span class="nowrap">563–</span>566. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0896-6273%2800%2981193-9">10.1016/S0896-6273(00)81193-9</a></span>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0896-6273">0896-6273</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/10896153">10896153</a>.</cite></span>

</li>

<li id="cite_note-Jacobs-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Jacobs_2-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFJacobsFridmanDouglas2009" class="citation journal cs1">Jacobs AL, Fridman G, Douglas RM, et al. (April 2009). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2657589">"Ruling out and ruling in neural codes"</a>. <i>Proc. Natl. Acad. Sci. U.S.A</i>. <b>106</b> (14): <span class="nowrap">5936–</span>41. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009PNAS..106.5936J">2009PNAS..106.5936J</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.0900573106">10.1073/pnas.0900573106</a></span>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2657589">2657589</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/19297621">19297621</a>.</cite></span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFChenWangTsien2009" class="citation journal cs1">Chen G, Wang LP, Tsien JZ (Dec 2009). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2788416">"Neural population-level memory traces in the mouse hippocampus"</a>. <i>PLOS ONE</i>. <b>4</b> (12): e8256. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009PLoSO...4.8256C">2009PLoSO...4.8256C</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1371%2Fjournal.pone.0008256">10.1371/journal.pone.0008256</a></span>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2788416">2788416</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/20016843">20016843</a>.</cite><span style="position:relative; top: -2px;"><span typeof="mw:File"><a href="Open_access" title="open access publication – free to read"></a></span></span></span>

</li>

<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFZhangChenKuangTsien2013" class="citation journal cs1">Zhang H, Chen G, Kuang H, Tsien JZ (Nov 2013). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3841182">"Mapping and deciphering neural codes of NMDA receptor-dependent fear memory engrams in the hippocampus"</a>. <i>PLOS ONE</i>. <b>8</b> (11): e79454. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013PLoSO...879454Z">2013PLoSO...879454Z</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1371%2Fjournal.pone.0079454">10.1371/journal.pone.0079454</a></span>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3841182">3841182</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/24302990">24302990</a>.</cite><span style="position:relative; top: -2px;"><span typeof="mw:File"><a href="Open_access" title="open access publication – free to read"></a></span></span></span>

</li>

<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">The Brain Decoding Project. <a rel="nofollow" class="external free" href="http://braindecodingproject.org/">http://braindecodingproject.org/</a></span>

</li>

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<li id="cite_note-Rieke-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-Rieke_17-0">^</a></b></span> <span class="reference-text">Rieke, F. (1999). Spikes: exploring the neural code. exploring the neural code (p. 395). The MIT Press.</span>

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<li id="cite_note-Hawkins-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hawkins_19-0">^</a></b></span> <span class="reference-text">Hawkins, J., Ahmad, S., & Dubinsky, D. (2006). Hierarchical temporal memory: Concepts, theory and terminology. Whitepaper.</span>

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</style><div id="Neuroscience515" style="font-size:114%;margin:0 4em"><a href="Neuroscience" title="Neuroscience">Neuroscience</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="3"><div>

<ul><li><a href="Outline_of_neuroscience" title="Outline of neuroscience">Outline</a></li>

<li><a href="History_of_neuroscience" title="History of neuroscience">History</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Basic_research" title="Basic research">Basic<br>science</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Behavioral_epigenetics" title="Behavioral epigenetics">Behavioral epigenetics</a></li>

<li><a href="Behavioural_genetics" title="Behavioural genetics">Behavioral genetics</a></li>

<li><a href="Brain_mapping" title="Brain mapping">Brain mapping</a></li>

<li><a href="Brain-reading" title="Brain-reading">Brain-reading</a></li>

<li><a href="Cellular_neuroscience" title="Cellular neuroscience">Cellular neuroscience</a></li>

<li><a href="Computational_neuroscience" title="Computational neuroscience">Computational neuroscience</a></li>

<li><a href="Connectomics" title="Connectomics">Connectomics</a></li>

<li><a href="Imaging_genetics" title="Imaging genetics">Imaging genetics</a></li>

<li><a href="Integrative_neuroscience" title="Integrative neuroscience">Integrative neuroscience</a></li>

<li><a href="Molecular_neuroscience" title="Molecular neuroscience">Molecular neuroscience</a></li>

<li><a href="Neural_engineering" title="Neural engineering">Neural engineering</a></li>

<li><a href="Neuroanatomy" title="Neuroanatomy">Neuroanatomy</a></li>

<li><a href="Neurobiology" class="mw-redirect" title="Neurobiology">Neurobiology</a></li>

<li><a href="Neurochemistry" title="Neurochemistry">Neurochemistry</a></li>

<li><a href="Neuroendocrinology" title="Neuroendocrinology">Neuroendocrinology</a></li>

<li><a href="Neurogenetics" title="Neurogenetics">Neurogenetics</a></li>

<li><a href="Neuroinformatics" title="Neuroinformatics">Neuroinformatics</a></li>

<li><a href="Neurometrics" title="Neurometrics">Neurometrics</a></li>

<li><a href="Neuromorphology" title="Neuromorphology">Neuromorphology</a></li>

<li><a href="Neurophysics" title="Neurophysics">Neurophysics</a></li>

<li><a href="Neurophysiology" title="Neurophysiology">Neurophysiology</a></li>

<li><a href="Systems_neuroscience" title="Systems neuroscience">Systems neuroscience</a></li></ul>

</div></td><td class="noviewer navbox-image" rowspan="5" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Clinical_neuroscience" title="Clinical neuroscience">Clinical<br>neuroscience</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Behavioral_neurology" title="Behavioral neurology">Behavioral neurology</a></li>

<li><a href="Clinical_neurophysiology" title="Clinical neurophysiology">Clinical neurophysiology</a></li>

<li><a href="Epileptology" class="mw-redirect" title="Epileptology">Epileptology</a></li>

<li><a href="Neurocardiology" title="Neurocardiology">Neurocardiology</a></li>

<li><a href="Neuroepidemiology" title="Neuroepidemiology">Neuroepidemiology</a></li>

<li><a href="Enteric_nervous_system#Function" title="Enteric nervous system">Neurogastroenterology</a></li>

<li><a href="Neuroimmunology" title="Neuroimmunology">Neuroimmunology</a></li>

<li><a href="Neurointensive_care" title="Neurointensive care">Neurointensive care</a></li>

<li><a href="Neurology" title="Neurology">Neurology</a></li>

<li><a href="Neuro-oncology" title="Neuro-oncology">Neuro-oncology</a></li>

<li><a href="Neuro-ophthalmology" title="Neuro-ophthalmology">Neuro-ophthalmology</a></li>

<li><a href="Neuropathology" title="Neuropathology">Neuropathology</a></li>

<li><a href="Neuropharmacology" title="Neuropharmacology">Neuropharmacology</a></li>

<li><a href="Neuroprosthetics" title="Neuroprosthetics">Neuroprosthetics</a></li>

<li><a href="Neuropsychiatry" title="Neuropsychiatry">Neuropsychiatry</a></li>

<li><a href="Neuroradiology" title="Neuroradiology">Neuroradiology</a></li>

<li>Neurorehabilitation</li>

<li><a href="Neurosurgery" title="Neurosurgery">Neurosurgery</a></li>

<li><a href="Neurotology" title="Neurotology">Neurotology</a></li>

<li><a href="Neurovirology" title="Neurovirology">Neurovirology</a></li>

<li><a href="Nutritional_neuroscience" title="Nutritional neuroscience">Nutritional neuroscience</a></li>

<li><a href="Psychiatry" title="Psychiatry">Psychiatry</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Cognitive_neuroscience" title="Cognitive neuroscience">Cognitive<br>neuroscience</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Affective_neuroscience" title="Affective neuroscience">Affective neuroscience</a></li>

<li><a href="Behavioral_neuroscience" title="Behavioral neuroscience">Behavioral neuroscience</a></li>

<li><a href="Chronobiology" title="Chronobiology">Chronobiology</a></li>

<li><a href="Molecular_cellular_cognition" title="Molecular cellular cognition">Molecular cellular cognition</a></li>

<li><a href="Motor_control" title="Motor control">Motor control</a></li>

<li><a href="Neurolinguistics" title="Neurolinguistics">Neurolinguistics</a></li>

<li><a href="Neuropsychology" title="Neuropsychology">Neuropsychology</a></li>

<li><a href="Sensory_neuroscience" title="Sensory neuroscience">Sensory neuroscience</a></li>

<li><a href="Social_cognitive_neuroscience" title="Social cognitive neuroscience">Social cognitive neuroscience</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Interdisciplinary<br>fields</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Consumer_neuroscience" title="Consumer neuroscience">Consumer neuroscience</a></li>

<li><a href="Cultural_neuroscience" title="Cultural neuroscience">Cultural neuroscience</a></li>

<li><a href="Educational_neuroscience" title="Educational neuroscience">Educational neuroscience</a></li>

<li><a href="Evolutionary_neuroscience" title="Evolutionary neuroscience">Evolutionary neuroscience</a></li>

<li><a href="Global_neurosurgery" title="Global neurosurgery">Global neurosurgery</a></li>

<li><a href="Neuroanthropology" title="Neuroanthropology">Neuroanthropology</a></li>

<li><a href="Neural_engineering" title="Neural engineering">Neural engineering</a></li>

<li><a href="Neurotechnology" title="Neurotechnology">Neurobiotics</a></li>

<li><a href="Neurocinema" title="Neurocinema">Neurocinema</a></li>

<li><a href="Neurocriminology" title="Neurocriminology">Neurocriminology</a></li>

<li><a href="Neuroeconomics" title="Neuroeconomics">Neuroeconomics</a></li>

<li><a href="Neuroepistemology" title="Neuroepistemology">Neuroepistemology</a></li>

<li><a href="Neuroesthetics" title="Neuroesthetics">Neuroesthetics</a></li>

<li><a href="Neuroethics" title="Neuroethics">Neuroethics</a></li>

<li><a href="Neuroethology" title="Neuroethology">Neuroethology</a></li>

<li><a href="Neurohistory" title="Neurohistory">Neurohistory</a></li>

<li><a href="Neurolaw" title="Neurolaw">Neurolaw</a></li>

<li><a href="Neuromarketing" title="Neuromarketing">Neuromarketing</a></li>

<li><a href="Neuromorphic_engineering" class="mw-redirect" title="Neuromorphic engineering">Neuromorphic engineering</a></li>

<li><a href="Neuroscience_of_music" title="Neuroscience of music">Neuroscience of music</a></li>

<li><a href="Neurophenomenology" title="Neurophenomenology">Neurophenomenology</a></li>

<li><a href="Neurophilosophy" title="Neurophilosophy">Neurophilosophy</a></li>

<li><a href="Neuropolitics" title="Neuropolitics">Neuropolitics</a></li>

<li><a href="Neurorobotics" title="Neurorobotics">Neurorobotics</a></li>

<li><a href="Neuroscience_of_religion" title="Neuroscience of religion">Neurotheology</a></li>

<li><a href="Paleoneurobiology" title="Paleoneurobiology">Paleoneurobiology</a></li>

<li><a href="Social_neuroscience" title="Social neuroscience">Social neuroscience</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Brain%E2%80%93computer_interface" title="Brain–computer interface">Brain–computer interface</a></li>

<li><a href="Development_of_the_nervous_system" title="Development of the nervous system">Development of the nervous system</a></li>

<li><a href="Artificial_neural_network" class="mw-redirect" title="Artificial neural network">Neural network (artificial)</a></li>

<li><a href="Neural_circuit" title="Neural circuit">Neural network (biological)</a></li>

<li><a href="Detection_theory" title="Detection theory">Detection theory</a></li>

<li><a href="Intraoperative_neurophysiological_monitoring" title="Intraoperative neurophysiological monitoring">Intraoperative neurophysiological monitoring</a></li>

<li><a href="Neurochip" title="Neurochip">Neurochip</a></li>

<li><a href="Neurodegenerative_disease" title="Neurodegenerative disease">Neurodegenerative disease</a></li>

<li><a href="Neurodevelopmental_disorder" title="Neurodevelopmental disorder">Neurodevelopmental disorder</a></li>

<li><a href="Neurodiversity" title="Neurodiversity">Neurodiversity</a></li>

<li><a href="Neurogenesis" title="Neurogenesis">Neurogenesis</a></li>

<li><a href="Neuroimaging" title="Neuroimaging">Neuroimaging</a></li>

<li><a href="Neuroimmune_system" title="Neuroimmune system">Neuroimmune system</a></li>

<li><a href="Neuromanagement" title="Neuromanagement">Neuromanagement</a></li>

<li><a href="Neuromodulation" title="Neuromodulation">Neuromodulation</a></li>

<li><a href="Neuroplasticity" title="Neuroplasticity">Neuroplasticity</a></li>

<li><a href="Neurotechnology" title="Neurotechnology">Neurotechnology</a></li>

<li><a href="Neurotoxin" title="Neurotoxin">Neurotoxin</a></li>

<li><a href="Neural_basis_of_self" title="Neural basis of self">Self-awareness</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="3"><div>

<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> <b>Category</b></li>

<li><span class="noviewer" typeof="mw:File"><span title="Commons page"></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Neuroscience" class="extiw external" title="commons:Category:Neuroscience">Commons</a></b></li></ul>

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This article is issued from <a class="external text" title="Last edited on 2024-09-13" href="https://en.wikipedia.org/wiki/?title=Neural_decoding&oldid=1245510063">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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