What Does The False Response Text Field Signify?

The Stochastic Resonance simulation is based on the properties of a receptor that is basically a mechanoreceptor of the type you usually associate with an animal’s ‘ear’. That is, it’s a receptor that transduces the energy content of the oscillating pressure waves we refer to as “sound”. Such a receptor is responsible for providing information about (i) whether a signal is present, (ii) the amplitude of the signal, and (iii) the frequency of the signal. This information would be transmitted to the appropriate part(s) of the animal’s central nervous system, where it would be used to make decisions about what sort of response might be required.

The initial response of the receptor to any vibration, whether signal or noise, is a change in V_m that is referred to as a generator or receptor potential. If this change in V_m is large enough to reach the membrane’s threshold, the receptor will generate an action potential. As discussed earlier, it doesn’t matter to the receptor whether the change in V_m is signal-induced or noise-induced, since the receptor responds to vibration from any source. This means that the receptor can generate action potentials even when no true signal is present (i.e., there’s no swimming fish in the area and the Signal amplitude = 0). All that’s required is that the noise-induced change ( = the product of the noise function and the Noise slider's numerical value) in the receptor’s V_m exceed the receptor’s threshold. In other words, any noise that’s loud enough will stimulate the receptor to generate action potentials, whether or not a signal is present. These action potentials, because they’re being generated in response to noise rather than signal, convey no useful information.

In fact, spurious action potentials can actually confuse the sensory system and cause problems for the organism. Consequently, it’s important to ‘keep track’ of these spurious action potentials. The simulation does this by estimating how many action potentials would be generated by the noise alone, given the settings for the Noise and Threshold sliders, and ignoring the Signal amplitude (in essence setting the Signal strength to 0). The number of action potentials thus generated by the receptor would then be reported in the “False” text field.

What about when a signal is present along with the noise? Well, given a strong-enough noise, a certain proportion of the Total action potential count must be attributed to the noise. Since these 'false' signals can serve to confuse the sensory system, knowledge of what proportion of the Total action potential count is due to these false signals is necessary. Thus, the simulation automatically counts the spurious signals that would have been expected to occur by chance in the absence of any signal at all. It reports this count in the “False” response text field, while the Total text field reports the number of action potentials that were actually generated by the receptor.

Suggested Exercises

1. Set the Signal amplitude to zero and the Noise amplitude set to a value large enough that it exceeds threshold some of the time. Do a series of 10 or so runs at these settings. How do the Total and False Response values compare for each run? Are the values constant across runs? What is your interpretation of your results?

2. Add some signal to the simulation (settings as in Exercise #1) and do a number of repeat runs, clearing the display in between each run. How do the values for Total and False Responses compare? Can you account for any unexpected results?

3. Do the results of #1 and #2 depend on the type of noise – uniform or Gaussian – you’ve selected?