Stochastic Properties of Neural Coincidence Detector cells

1. Stochastic Properties of Neural Coincidence Detector cells Ram Krips and Miriam Furst

2. TOC • Neural Processing • Stochastic Analysis • Auditory Examples • Boundary Evaluation

3. Spiking information • Data within the brain travels in the form of neural spiking trains. • The information is encoded both in the rate and timing of the spiking events. • The signal is stochastic in nature

4. Neural Cells • The receivers/processors and transmitters of the spiking information within the brains are the neural cells • Common functionalities associated are: • Timing analysis • Memory • Signal generation

5. Statistical Models of Spiking Behaviour • The stochastic behavior of neural cells can be described as NHPP. • Considering the discharge history, a more general form of representation is obtained: self excitatory models such as renewal or doubly stochastic.

6. NHPP Model Definitions • Poisson process is a pure birth process: In an interval dt only one arrival with probability • Number of arrivals N(t) in a finite interval of length t obeys: non-overlapping intervals are independent. • The inter arrival times are independent and obey the Exponential distribution:

7. Neural Cells Models I&F • No mathematical • Understanding • Not suited for • Large scale • simulation CD • Simplification • Mathematical • Insight • More • assumptions • With regards to the model

8. Coincidence Detection Cells • Coincidence detection (CD) is one of the common ways to describe the functionality of a single neural cell. • Correlation • There are several type of such cells: • Excitatory Inhibitory (EI) • Excitatory Excitatory (EE) • Cumulative

9. Neural mechanisms – EE Type cells • Spikes when inputs coincide.

10. EE Formulation

11. Neural mechanisms – EI Type cells • Spikes with excitatory input unless inhibited.

12. EI Formulation

13. Complex Cells

14. Complex Cells

15. Cumulative Type Cells • Spikes if the number of excitatory events during  exceeds inhibitory by P

16. EI Cells Signal Separation • Signal separation ability is considered as most important in tasks such as cocktail party, BMLD.

17. EE Cells spontaneous rate • The spontaneous rate of cells that results from external noise reduced at higher levels

18. EE Cells Harmonic Signals Enhancement • Harmonic signals are most desirable in mammals

19. Neural Networks

20. Auditory Lateralization Cues • Interaural Time delay – The sound reaches the closest ear before the other • Interaural Level delay – The sound at the closest ear is louder

21. Auditory cues analysis - ITD

22. Auditory cues analysis - ILD

23. Auditory signals analysis Pitch

24. Before going on… • We have presented the mathematical building blocks for CD cells and networks analysis • Before going on to building networks we will develop another tool that allows us to evaluate the quality of the processor formed: Bound evaluation

25. Overall Localization Performance - MAA • Minimal Audible Angle is a common test for evaluating human localization ability .

26. Methodology • The first point of stochastic behaviour is at the auditory nerve. • An optimal neural response was considered

27. Ambiguity in Sound Lateralization • For 1 kHz, the phase difference between signals arriving at right and left ears is 180o. It is impossible to distinguish between the possibility of the sound arriving from the right or left speaker. Frequency: 1kHz Wavelength: 30cm Head size: 15cm Frequency: 2kHz Wavelength: 15cm Head size: 15cm

28. Bounds Evaluation

29. MAA evaluation using CRLB and BBLB for NHPP

30. Going into the Brain - ITD • CRLB for single neuron.

31. Summary • Analytical tools for analysis and evaluation of CD cells and networks were introduced. • Validity demonstrated comparing to biological findings