# Using a Linear Non-linear Cascade with a Non-Random (deterministic) Stimulus

I'm attempting to use a computational model, in particular a linear non-linear cascade (LNP) to encode the spiking of a neuron responding to a thermal stimulus. In a LNP, it assumes that the stimulus is 'radially symmetric' , for example having a Gaussian probability distribution. However, is it possible to use a LNP model (or another well known encoding model) when the stimulus is deterministic? The stimulus I'm using is a ramping thermal stimulus.

 Chichilnisky EJ (2001) A simple white noise analysis of neuronal light responses. Network (Bristol, England) 12: 199–213.

• Yes. The stimulus generation model is totally separable from the neural response model. – honi Jul 8 '16 at 19:23
• @honi so how do I find the linear filter if the spike triggered average may not be proportional for a deterministic stimulus? I've read a paper indicating that it's possible by calculating the auto-covariance matrix and cross correlation vector (Theunisson, David, Singh et al 2001). Is this a valid approach? – kw3rti Jul 9 '16 at 8:01
• what do you mean by "may not be proportional"? – honi Jul 10 '16 at 16:44
• assuming this researchgate.net/publication/… is the paper you are referring to, their method seems pretty reasonable, and has been used in (cited by) high-profile publications. – honi Jul 10 '16 at 16:45
• In the Chichilinsky paper, the 'radially symmetric' property of the stimulus distribution allows you to derive that the spike triggered average is proportional to the linear component of the model. I will look further into the method in the Theunisson paper, thanks :) – kw3rti Jul 10 '16 at 22:20

The short answer is yes. The longer answer involves a more precise meaning of deterministic and a number of research considerations.

In the strict sense of deterministic, which means that given the same input, the same output will always occur, any probability distribution modeled on a computer is deterministic, since most digital computers have a deterministic instruction set. However, this isn't quite relevant for your task, since the samples from the distribution that your model sees are largely uncorrelated with the model properties, making them appear random to the model.

Researchers often use probabilistic or stochastic stimuli because they are the simplest option and because they do not want to introduce a number of potential biases that occur when the model interacts with or entrains to specific patterns in deterministic stimuli. Such patterns would produce effects that are not representative of the general properties of the model, which may be misleading. Introducing a probability distribution therefore becomes a simple way to explore more of the state space of the model. Additional reasons why people introduce noise (through a stochastic stimulus) include the fact that real neurons tend to exist in noisy environments (modeling considerations), and the fact that some kinds of proofs about model performance are easier to perform for probabilistic stimuli.

Your choice as to whether you want to use a deterministic stimulus depends largely on your goals in this research project. Do you want to know what happens when the model sees a specific pattern? Do you care if this pattern has noise in it? Do you want to perform mathematical proofs? Do you care about perturbation stability (some deterministic models may falsely appear stable because they are not moved off of their tiny equilibrium point by noise)? What process are you modeling?

Given these considerations, you should be able to choose what kind of stimulus to use. Your model will accept many kinds of stimuli as input, but the choice of stimulus affects what you will learn from the specific simulation.

• In my project the stimulus has already been chosen as a ramping thermal stimulus, and then the neural responses to both a fast ramp and slow ramp have been recorded. My concern is that because the stimulus is fixed (only with slight variation between trials) I can't use the spike triggered average. – kw3rti Jul 10 '16 at 22:15
• unless i'm misunderstanding your paradigm, you can't properly describe the receptive field properties of your neuron if you only use two stimuli... – honi Jul 10 '16 at 23:10
• To fully describe the set up: a metal plate is placed on the hind paw of a rat, where the temperature is raised from 25° to 60° at two different rates. The neural responses to each ramp have been recorded over multiple trials. Although the stimulus is either a fixed fast or slow ramp, can I not describe the receptive field properties from the fact that all temperatures (within a reasonable range) are covered? Having said that, reading the answer above reasonably suggests that the fixed ramps may introduce bias... – kw3rti Jul 11 '16 at 8:37
• The two different rates are used to stimulate two different nociceptors. I'm then looking to analyse the difference in encoding between these different nociceptors. – kw3rti Jul 11 '16 at 8:51
• So perhaps I'm not too concerned about a possible bias being introduced because I'm actively trying to trigger the specific nociceptors using the fixed ramps. The question is then whether I can still use the LNP model using the techniques mentioned above to model the encoding. I apologise for my inexperience in this field! – kw3rti Jul 11 '16 at 9:10