Fractal character of the neural spike train in the visual system of the cat

Malvin C. Teich; Conor Heneghan; Steven B. Lowen; Tsuyoshi Ozaki; Ehud Kaplan

doi:10.1364/JOSAA.14.000529

Journal of the Optical Society of America A
Vol. 14,
Issue 3,
pp. 529-546
(1997)
•https://doi.org/10.1364/JOSAA.14.000529

Fractal character of the neural spike train in the visual system of the cat

Malvin C. Teich, Conor Heneghan, Steven B. Lowen, Tsuyoshi Ozaki, and Ehud Kaplan

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Malvin C. Teich, Conor Heneghan, Steven B. Lowen, Tsuyoshi Ozaki, and Ehud Kaplan, "Fractal character of the neural spike train in the visual system of the cat," J. Opt. Soc. Am. A 14, 529-546 (1997)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

We used a variety of statistical measures to identify the point process that describes the maintained discharge of retinal ganglion cells (RGC’s) and neurons in the lateral geniculate nucleus (LGN) of the cat. These measures are based on both interevent intervals and event counts and include the interevent-interval histogram, rescaled range analysis, the event-number histogram, the Fano factor, the Allan factor, and the periodogram. In addition, we applied these measures to surrogate versions of the data, generated by random shuffling of the order of interevent intervals. The counting statistics reveal $1 / f$ -type fluctuations in the data (long-duration power-law correlation), which are not present in the shuffled data. Estimates of the fractal exponents measured for RGC- and their target LGN-spike trains are similar in value, indicating that the fractal behavior either is transmitted from one cell to the other or has a common origin. The gamma-r renewal process model, often used in the analysis of visual-neuron interevent intervals, describes certain short-term features of the RGC and LGN data reasonably well but fails to account for the long-duration correlation. We present a new model for visual-system nerve-spike firings: a gamma-r renewal process whose mean is modulated by fractal binomial noise. This fractal, doubly stochastic point process characterizes the statistical behavior of both RGC and LGN data sets remarkably well.

Full Article | PDF Article

More Like This

Fractal laser glints from the ocean surface

Joseph A. Shaw and James H. Churnside
J. Opt. Soc. Am. A 14(5) 1144-1150 (1997)

Refractoriness in the maintained discharge of the cat’s retinal ganglion cell*

Malvin Carl Teich, Leonard Matin, and Barry I. Cantor
J. Opt. Soc. Am. 68(3) 386-402 (1978)

Interevent-time statistics for shot-noise-driven self-exciting point processes in photon detection

Malvin Carl Teich and Bahaa E. A. Saleh
J. Opt. Soc. Am. 71(6) 771-776 (1981)

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (12)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (2)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (24)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

File Name	Cell Type	Number of Intervals	Duration of Data (s)	Luminance Level (cd/m²)	Mean Rate μ (s^-1)	Mean Interval 〈τ〉 (s)	Interval Std. Dev. σ_τ (s)	Interval CV C	FF Exponent α	AF Exponent γ	PG Exponent β
MD1-RET	X-ON	61,500	2500	33	24.6	0.0406	0.028	0.6906	0.82	0.88	1.32
MD2-RET	X-ON	140,432	6388	33	22.0	0.0455	0.028	0.6223	0.56	0.48	0.33
MD6-RET	Y-ON	126,276	3901	33	32.4	0.0309	0.016	0.5125	0.69	0.94	0.99
MDS-RET	X-ON	56,661	3226	33	17.6	0.0569	0.066	0.7715	0.82	1.13	0.93
Y0101RET	X-ON	201,496	5088	65	39.6	0.0253	0.011	0.4382	0.39	0.49	0.73
Y0102REF	X-ON	161,301	5127	6.5	31.5	0.0318	0.015	0.4823	0.32	0.68	1.00
Y0103REF	X-ON	36,502	4960	0	7.4	0.1359	0.207	1.5214	1.00	1.57	0.56
Y0202REF	X-ON	130,173	4384	65	29.7	0.0337	0.025	0.7432	0.99	1.63	1.50
Y0203REF	X-ON	38,841	4965	0	7.8	0.1279	0.349	2.7273	0.86	1.94	2.00
Y1102REF	X-OFF	47,732	5127	6.5	9.3	0.1074	0.134	1.2474	0.81	0.90	1.41
Y1103REF	X-OFF	234,096	4962	0	47.2	0.0212	0.017	0.8197	0.78	1.23	0.97
Y1202REF	X-OFF	206,627	4384	65	47.1	0.0212	0.014	0.6795	0.92	1.89	1.94
Y1203REF	X-OFF	116,470	5040	0	23.1	0.0433	0.058	1.3359	0.96	2.16	1.69
Mean		119,854	4619		26.1	0.0555	0.074	0.9686	0.76	1.22	1.18
Std. dev.					13.6	0.0406	0.101	0.6278	0.22	0.56	0.51

File Name	Cell Type	Number of Intervals	Duration of Data (s)	Luminance Level (cd/m²)	Mean Rate μ (s^-1)	Mean Interval 〈τ〉 (s)	Interval Std. Dev. σ_τ (s)	Interval CV C	FF Exponent α	AF Exponent γ	PG Exponent β
MD1-LGN	X-ON	1688	2500	33	6.8	0.1481	0.167	1.1271	0.37	0.33	0.70
MD2-LGN	X-ON	70,320	6388	33	11.0	0.0908	0.305	1.0268	0.34	0.38	0.46
MD6-LGN	Y-ON	33,890	3901	33	8.7	0.1150	0.147	1.2821	0.84	1.26	1.66
MDS-LGN	X-ON	24,285	3226	33	7.5	0.1328	0.197	1.4824	0.56	0.63	0.80
Y0101LGN	X-ON	22,852	5088	65	4.5	0.2227	0.255	1.1469	0.37	0.43	0.56
Y0102LGN	X-ON	31,878	5127	6.5	6.2	0.1608	0.189	1.1750	0.78	0.53	0.48
Y0103LGN	X-ON	25,234	4960	0	5.1	0.1966	0.533	1.4425	1.00	1.27	0.19
Y0202LGN	X-ON	18,376	4384	65	4.2	0.2385	0.401	1.6808	0.49	0.67	1.21
Y0203LGN	X-ON	29,265	4965	0	5.9	0.1696	0.471	2.7800	0.92	1.86	1.62
Y1102LGN	X-OFF	27,734	5127	6.5	5.4	0.1848	0.220	1.1855	0.39	0.63	1.06
Y1103LGN	X-OFF	79,453	4962	0	16.0	0.0624	0.064	1.0190	0.70	0.38	0.29
Y1202LGN	X-OFF	5338	4384	65	1.2	0.8200	1.29	1.5728	0.83	1.10	1.22
Y1203LGN	X-OFF	18,297	5040	0	3.6	0.2754	0.439	1.5953	0.68	1.76	1.85
Mean		29893	4619		6.6	0.2167	0.360	1.4243	0.64	0.86	0.93
Std. dev.					3.7	0.1907	0.312	0.4642	0.23	0.53	0.55

File Name	Cell Type	Number of Intervals	Duration of Data (s)	Luminance Level (cd/m²)	Mean Rate μ (s^-1)	Mean Interval 〈τ〉 (s)	Interval Std. Dev. σ_τ (s)	Interval CV C	FF Exponent α	AF Exponent γ	PG Exponent β
MD1-RET	X-ON	61,500	2500	33	24.6	0.0406	0.028	0.6906	0.82	0.88	1.32
MD2-RET	X-ON	140,432	6388	33	22.0	0.0455	0.028	0.6223	0.56	0.48	0.33
MD6-RET	Y-ON	126,276	3901	33	32.4	0.0309	0.016	0.5125	0.69	0.94	0.99
MDS-RET	X-ON	56,661	3226	33	17.6	0.0569	0.066	0.7715	0.82	1.13	0.93
Y0101RET	X-ON	201,496	5088	65	39.6	0.0253	0.011	0.4382	0.39	0.49	0.73
Y0102REF	X-ON	161,301	5127	6.5	31.5	0.0318	0.015	0.4823	0.32	0.68	1.00
Y0103REF	X-ON	36,502	4960	0	7.4	0.1359	0.207	1.5214	1.00	1.57	0.56
Y0202REF	X-ON	130,173	4384	65	29.7	0.0337	0.025	0.7432	0.99	1.63	1.50
Y0203REF	X-ON	38,841	4965	0	7.8	0.1279	0.349	2.7273	0.86	1.94	2.00
Y1102REF	X-OFF	47,732	5127	6.5	9.3	0.1074	0.134	1.2474	0.81	0.90	1.41
Y1103REF	X-OFF	234,096	4962	0	47.2	0.0212	0.017	0.8197	0.78	1.23	0.97
Y1202REF	X-OFF	206,627	4384	65	47.1	0.0212	0.014	0.6795	0.92	1.89	1.94
Y1203REF	X-OFF	116,470	5040	0	23.1	0.0433	0.058	1.3359	0.96	2.16	1.69
Mean		119,854	4619		26.1	0.0555	0.074	0.9686	0.76	1.22	1.18
Std. dev.					13.6	0.0406	0.101	0.6278	0.22	0.56	0.51

File Name	Cell Type	Number of Intervals	Duration of Data (s)	Luminance Level (cd/m²)	Mean Rate μ (s^-1)	Mean Interval 〈τ〉 (s)	Interval Std. Dev. σ_τ (s)	Interval CV C	FF Exponent α	AF Exponent γ	PG Exponent β
MD1-LGN	X-ON	1688	2500	33	6.8	0.1481	0.167	1.1271	0.37	0.33	0.70
MD2-LGN	X-ON	70,320	6388	33	11.0	0.0908	0.305	1.0268	0.34	0.38	0.46
MD6-LGN	Y-ON	33,890	3901	33	8.7	0.1150	0.147	1.2821	0.84	1.26	1.66
MDS-LGN	X-ON	24,285	3226	33	7.5	0.1328	0.197	1.4824	0.56	0.63	0.80
Y0101LGN	X-ON	22,852	5088	65	4.5	0.2227	0.255	1.1469	0.37	0.43	0.56
Y0102LGN	X-ON	31,878	5127	6.5	6.2	0.1608	0.189	1.1750	0.78	0.53	0.48
Y0103LGN	X-ON	25,234	4960	0	5.1	0.1966	0.533	1.4425	1.00	1.27	0.19
Y0202LGN	X-ON	18,376	4384	65	4.2	0.2385	0.401	1.6808	0.49	0.67	1.21
Y0203LGN	X-ON	29,265	4965	0	5.9	0.1696	0.471	2.7800	0.92	1.86	1.62
Y1102LGN	X-OFF	27,734	5127	6.5	5.4	0.1848	0.220	1.1855	0.39	0.63	1.06
Y1103LGN	X-OFF	79,453	4962	0	16.0	0.0624	0.064	1.0190	0.70	0.38	0.29
Y1202LGN	X-OFF	5338	4384	65	1.2	0.8200	1.29	1.5728	0.83	1.10	1.22
Y1203LGN	X-OFF	18,297	5040	0	3.6	0.2754	0.439	1.5953	0.68	1.76	1.85
Mean		29893	4619		6.6	0.2167	0.360	1.4243	0.64	0.86	0.93
Std. dev.					3.7	0.1907	0.312	0.4642	0.23	0.53	0.55

Abstract

Cited By

Figures (12)

Tables (2)

Equations (24)

Journal of the Optical Society of America A