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=== Population coding ===
Population coding is a method to represent stimuli by using the joint activities of a number of neurons. In population coding, each neuron has a distribution of responses over some set of inputs, and the responses of many neurons may be combined to determine some value about the inputs. From the theoretical point of view, population coding is one of a few mathematically well-formulated problems in neuroscience. It grasps the essential features of neural coding and yet is simple enough for theoretic analysis.<ref name="Wu">{{cite journal |vauthors=Wu S, Amari S, Nakahara H |title=Population coding and decoding in a neural field: a computational study |journal=Neural Comput |volume=14 |issue=5 |pages=999–1026 |date=May 2002 |pmid=11972905 |doi=10.1162/089976602753633367 |s2cid=1122223 }}</ref> Experimental studies have revealed that this coding paradigm is widely used to decode neural representations in the sensor and motor areas of the brain.
For example, in the visual area [[Medial temporal lobe|medial temporal]] (MT), neurons are tuned to the moving direction.<ref name="Maunsell">{{cite journal |vauthors=Maunsell JH, Van Essen DC |title=Functional properties of neurons in middle temporal visual area of the macaque monkey. I. Selectivity for stimulus direction, speed, and orientation |journal=J. Neurophysiol. |volume=49 |issue=5 |pages=1127–47 |date=May 1983 |pmid=6864242 |doi=10.1152/jn.1983.49.5.1127 |s2cid=8708245 }}</ref> In response to an object moving in a particular direction, many neurons in MT fire with a noise-corrupted and [[Normal distribution|bell-shaped]] activity pattern across the population. The moving direction of the object is retrieved from the population activity, to be immune from the fluctuation existing in a single neuron's signal. When monkeys are trained to move a joystick towards a lit target, a single neuron will fire for multiple target directions. However it fires the fastest for one direction and more slowly depending on how close the target was to the neuron's "preferred" direction.<ref>{{Cite web|url=http://homepage.psy.utexas.edu/homepage/class/psy394U/hayhoe/IntroSensoryMotorSystems/week6/Ch38.pdf|title=Intro to Sensory Motor Systems Ch. 38 page 766|access-date=2014-02-03|archive-date=2012-05-11|archive-url=https://web.archive.org/web/20120511112450/http://homepage.psy.utexas.edu/homepage/class/psy394U/hayhoe/IntroSensoryMotorSystems/week6/Ch38.pdf|url-status=dead}}</ref><ref>Science. 1986 Sep 26;233(4771):1416-9</ref> If each neuron represents movement in its preferred direction, and the vector sum of all neurons is calculated (each neuron has a firing rate and a preferred direction), the sum points in the direction of motion. In this manner, the population of neurons codes the signal for the motion.{{citation needed|date=November 2013}} This particular population code is referred to as [[population vector]] coding.
Moreover, with the development of large-scale neural recording arrays, Researchers have studied how memories of fearful events (earthquakes, roller-coast ride, etc.) are encoded in the CA1 region of the mouse hippocampus on a moment-to-moment time scale. By applying dimensionaility-reduction methods such as multiple-discriminant analysis (MDA), Researchers showed that real-time encoding of fearful experiences can be nicely classified and visualized <ref>{{Journal|last1=Lin|first1=LN|last2=Osan|first2=R|last3=Shoham|first3=S|last4=Tsien|first4=JZ|title=Identification of network-level coding units for real-time representation of episodic experiences in the hippocampus|journal=Proc Natl Acad Sci U S A|date=Apr 2005|volume=102|issue=17|pages=6125-30|doi=10.1073/pnas.0408233102|}}</ref> <ref>{{cite journal|last1=Chen|first1=G|last2=Wang|first2=L|last3=Tsien|first3=JZ|title=Neural population-level memory traces in the mouse hippocampus|journal=PLoS One|date=Dec 2009|volume=4|issue=12:e8256|doi=10.1371/journal.pone.0008256|}}</ref>
Place-time population codes, termed the averaged-localized-synchronized-response (ALSR) code, have been derived for neural representation of auditory acoustic stimuli. This exploits both the place or tuning within the auditory nerve, as well as the phase-locking within each nerve fiber auditory nerve. The first ALSR representation was for steady-state vowels;<ref>{{cite journal|last1=Sachs|first1=Murray B.|last2=Young|first2=Eric D.|title=Representation of steady-state vowels in the temporal aspects of the discharge patterns of populations of auditory-nerve fibers|journal= The Journal of the Acoustical Society of America|date=November 1979|volume=66|issue=5|pages=1381–1403|doi=10.1121/1.383532|pmid=500976|bibcode=1979ASAJ...66.1381Y}}</ref> ALSR representations of pitch and formant frequencies in complex, non-steady state stimuli were later demonstrated for voiced-pitch,<ref>{{cite journal|last1=Miller|first1=M.I.|last2=Sachs|first2=M.B.|title=Representation of voice pitch in discharge patterns of auditory-nerve fibers|journal=Hearing Research|date=June 1984|volume=14|issue=3|pages=257–279|pmid=6480513|doi=10.1016/0378-5955(84)90054-6|s2cid=4704044}}</ref> and formant representations in consonant-vowel syllables.<ref>{{cite journal|last1=Miller|first1=M.I.|last2=Sachs|first2=M.B.|title=Representation of stop consonants in the discharge patterns of auditory-nerve fibrers|journal= The Journal of the Acoustical Society of America|date=1983|volume=74|issue=2|pages=502–517|doi=10.1121/1.389816|pmid=6619427|bibcode=1983ASAJ...74..502M}}</ref>
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Sparse coding may be a general strategy of neural systems to augment memory capacity. To adapt to their environments, animals must learn which stimuli are associated with rewards or punishments and distinguish these reinforced stimuli from similar but irrelevant ones. Such tasks require implementing stimulus-specific [[associative memory (psychology)|associative memories]] in which only a few neurons out of a [[Neural ensemble|population]] respond to any given stimulus and each neuron responds to only a few stimuli out of all possible stimuli.
Theoretical work on [[sparse distributed memory]] has suggested that sparse coding increases the capacity of associative memory by reducing overlap between representations.<ref>Kanerva, Pentti. Sparse distributed memory. MIT press, 1988</ref> Experimentally, sparse representations of sensory information have been observed in many systems, including vision,<ref>{{cite journal | last1 = Vinje | first1 = WE | last2 = Gallant | first2 = JL | year = 2000 | title = Sparse coding and decorrelation in primary visual cortex during natural vision | journal = Science | volume = 287 | issue = 5456| pages = 1273–1276 | pmid = 10678835 | doi=10.1126/science.287.5456.1273| bibcode = 2000Sci...287.1273V | citeseerx = 10.1.1.456.2467 }}</ref> audition,<ref>{{cite journal | last1 = Hromádka | first1 = T | last2 = Deweese | first2 = MR | last3 = Zador | first3 = AM | year = 2008 | title = Sparse representation of sounds in the unanesthetized auditory cortex | journal = PLOS Biol | volume = 6 | issue = 1| page = e16 | pmid = 18232737 | doi=10.1371/journal.pbio.0060016 | pmc=2214813 | doi-access = free }}</ref> touch,<ref>{{cite journal | last1 = Crochet | first1 = S | last2 = Poulet | first2 = JFA | last3 = Kremer | first3 = Y | last4 = Petersen | first4 = CCH | year = 2011 | title = Synaptic mechanisms underlying sparse coding of active touch | journal = Neuron | volume = 69 | issue = 6| pages = 1160–1175 | pmid = 21435560 | doi=10.1016/j.neuron.2011.02.022| doi-access = free }}</ref> and olfaction.<ref>{{cite journal | last1 = Ito | first1 = I | last2 = Ong | first2 = RCY | last3 = Raman | first3 = B | last4 = Stopfer | first4 = M | year = 2008 | title = Sparse odor representation and olfactory learning | journal = Nat Neurosci | volume = 11 | issue = 10| pages = 1177–1184 | pmid = 18794840 | doi=10.1038/nn.2192 | pmc=3124899}}</ref> However, despite the accumulating evidence for widespread sparse coding and theoretical arguments for its importance, a demonstration that sparse coding improves the stimulus-specificity of associative memory has been difficult to obtain.
Interestingly, there is a report that the abstract concept of nest or home is encoded by a small number of neurons in the mouse hippocampus<ref>{{cite journal|last1=Lin|first1=LN|last2=Chen|first2=GF|last3=Kuang|first3=H|last4=Wang|first4=D|last5=Tsien|first5=JZ|title=Neural encoding of the concept of nest in the mouse brain|title=Proc Natl Acad Sci U S A|date=Apr 2007|volume=104|issue=14|pages=6066-71|doi=10.1073/pnas.0701106104}}</ref>. This is the very first experimental demonstration that the sparse coding is used in the memory region to represent categorical concepts of objects or tools, that is, the neural coding is achieved based on the perceptual determination of the fuctionality of a given class of objects rather than by its shapes, forms, colors, odors or constructing materials.
In the ''[[Drosophila]]'' [[olfactory system]], sparse odor coding by the [[Kenyon cell]]s of the [[Mushroom bodies|mushroom body]] is thought to generate a large number of precisely addressable locations for the storage of odor-specific memories.<ref>A sparse memory is a precise memory. Oxford Science blog. 28 Feb 2014. http://www.ox.ac.uk/news/science-blog/sparse-memory-precise-memory</ref> Sparseness is controlled by a negative feedback circuit between Kenyon cells and [[GABAergic]] anterior paired lateral (APL) neurons. Systematic activation and blockade of each leg of this feedback circuit shows that Kenyon cells activate APL neurons and APL neurons inhibit Kenyon cells. Disrupting the Kenyon cell–APL feedback loop decreases the sparseness of Kenyon cell odor responses, increases inter-odor correlations, and prevents flies from learning to discriminate similar, but not dissimilar, odors. These results suggest that feedback inhibition suppresses Kenyon cell activity to maintain sparse, decorrelated odor coding and thus the odor-specificity of memories.<ref>Lin, Andrew C., et al. "[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4000970/ Sparse, decorrelated odor coding in the mushroom body enhances learned odor discrimination]." Nature Neuroscience 17.4 (2014): 559-568.</ref>
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