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The accommodation index is a statistic used in the neurosciences for describing spike train data. Many methods of experimental neuroscience, such as voltage clamp recordings, give their output in the form of measured voltages of individual neurons. Generally, the only important element of these voltage traces is the occurrence of spikes in the voltage, representing action potentials. It is often useful to be able to describe the data in terms of the spike timings; for instance, when optimizing a compartmental model towards observed behaviour, statistics such as this can be used to gauge error. Various statistics are used to do this, such as spike rate, average interspike interval, and the accommodation index.

It is similar to other measures of accommodation such as the local variance introduced by Shinomoto et al. in 2003. It is defined by the average of the difference in length of two consecutive interspike intervals (ISIs) normalized by the summed duration of these two ISIs. The equation for the accommodation index is

$A={\frac {1}{N-k-1}}\displaystyle \sum _{i=k}^{N}{\frac {(\operatorname {isi} _{i}-\operatorname {isi} _{i-1})}{(\operatorname {isi} _{i}+\operatorname {isi} _{i-1})}}$

Where N is the number of APs and k determines the number of ISIs that will be disregarded in order not to take into account possible transient behavior as observed in Markram et al., 2004. A reasonable value for k is either four ISIs or one-fifth of the total number of ISIs, whichever is the smaller of the two.

References

Druckmann, Shaul; Banitt, Yoav; Gidon, Albert; Schürmann, Felix; Markram, Henry; Segev, Idan (15 October 2007). "A novel multiple objective optimization framework for constraining conductance-based neuron models by experimental data". Frontiers in Neuroscience. 1 (1): 7–18. doi:10.3389/neuro.01.1.1.001.2007.
Shinomoto, Shigeru; Shima, Keisetsu; Tanji, Jun (1 December 2003). "Differences in spiking patterns among cortical neurons". Neural Computation. 15 (12): 2823–2842. doi:10.1162/089976603322518759.
Markram, Henry; Toledo-Rodriguez, Maria; Wang, Yun; Gupta, Anirudh; Silberberg, Gilad; Wu, Caizhi (October 2004). "Interneurons of the neocortical inhibitory system". Nature Reviews Neuroscience. 5 (10): 793–807. doi:10.1038/nrn1519.

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-The '''accommodation index''' is a [[Metric (mathematics)|metric]] used in the [[neuroscience]]s for describing [[spike train]] data. Many methods of experimental neuroscience, such as voltage clamp recordings, give their output in the form of measured voltages of individual neurons. Generally, the only important element of these voltage traces is the occurrence of spikes in the voltage, representing [[action potentials]]. It is often useful to be able to describe the data in terms of the spike timings, for instance we wish to optimize a compartmental model towards observed behaviour, then metrics such as this would be used as error functions. Various metrics are used to do this, such as [[spike rate]], average [[interspike interval]] and, the accommodation index.
+The '''accommodation index''' is a [[statistic]] used in the [[neuroscience]]s for describing [[spike train]] data. Many methods of experimental neuroscience, such as voltage clamp recordings, give their output in the form of measured voltages of individual neurons. Generally, the only important element of these voltage traces is the occurrence of spikes in the voltage, representing [[action potentials]]. It is often useful to be able to describe the data in terms of the spike timings; for instance, when optimizing a compartmental model towards observed behaviour, statistics such as this can be used to gauge error. Various statistics are used to do this, such as [[spike rate]], average [[interspike interval]], and the accommodation index.
 It is similar to other measures of accommodation such as the local variance introduced by Shinomoto et al. in 2003. It is defined by the average of the difference in length of two consecutive interspike intervals (ISIs) normalized by the summed duration of these two ISIs.  The equation for the accommodation index is
-<math>A=\frac{1}{N-k-1}\displaystyle\sum_{i=k}^{N}\frac{(isi_i-isi_{i-1})}{(isi_i+isi_{i-1})}</math>
+<math>A=\frac{1}{N-k-1}\displaystyle\sum_{i=k}^{N}\frac{(\operatorname{isi}_i-\operatorname{isi}_{i-1})}{(\operatorname{isi}_i+\operatorname{isi}_{i-1})}</math>
 Where N is the number of APs and k determines the number of ISIs that will be disregarded in order not to take into account possible transient behavior as observed in Markram et al., 2004. A reasonable value for k is either four ISIs or one-fifth of the total number of ISIs, whichever is the smaller of the two.
 ==References==
-*Shaul Druckmann, Yoah Banitt, 'A novel multiple objective optimization framework for constraining conductance-based neuron models by experimental data', Frontiers in Neuroscience, 2007
+*{{cite journal |last1=Druckmann |first1=Shaul |last2=Banitt |first2=Yoav |last3=Gidon |first3=Albert |last4=Schürmann |first4=Felix |last5=Markram |first5=Henry |last6=Segev |first6=Idan |title=A novel multiple objective optimization framework for constraining conductance-based neuron models by experimental data |journal=Frontiers in Neuroscience |date=15 October 2007 |volume=1 |issue=1 |pages=7–18 |doi=10.3389/neuro.01.1.1.001.2007 |doi-access=free}}
-*Shinomoto, S., Shima, K., and Tanji, J. (2003). Differences in spiking patterns among cortical neurons. Neural Comput. 15, 2823–2842.
+*{{cite journal |last1=Shinomoto |first1=Shigeru |last2=Shima |first2=Keisetsu |last3=Tanji |first3=Jun |title=Differences in spiking patterns among cortical neurons |journal=Neural Computation |date=1 December 2003 |volume=15 |issue=12 |pages=2823–2842 |doi=10.1162/089976603322518759}}
-*Markram, H., Toledo-Rodriguez, M., Wang, Y., Gupta, A., Silberberg, G., and Wu, C. (2004). Interneurons of the neocortical inhibitory system. Nat. Rev. Neurosci. 5, 793–807.
+*{{cite journal |last1=Markram |first1=Henry |last2=Toledo-Rodriguez |first2=Maria |last3=Wang |first3=Yun |last4=Gupta |first4=Anirudh |last5=Silberberg |first5=Gilad |last6=Wu |first6=Caizhi |title=Interneurons of the neocortical inhibitory system |journal=Nature Reviews Neuroscience |date=October 2004 |volume=5 |issue=10 |pages=793–807 |doi=10.1038/nrn1519}}
 [[Category:Metrics]]