Anomalous low impedance for small platinum microelectrodes

Electrical measurement of the activity of individual neurons is a primary goal for many invasive neural electrodes. Making these “single unit” measurements requires that we fabricate electrodes small enough so that only a few neurons contribute to the signal, but not so small that the impedance of the electrode creates overwhelming noise or signal attenuation. Thus, neural electrode design often must strike a balance between electrode size and electrode impedance, where the impedance is often assumed to scale linearly with electrode area. Here we test this assumption by measuring the impedance at 1 kHz for differently sized electrodes. Surprisingly, we find that for Pt electrodes (but not Au electrodes) this assumption breaks down for electrodes with diameters of less than 10 microns. For these small sizes, Pt electrodes have impedance values that are up to 3-fold lower than expected. By investigating the impedance spectrum of Pt and Au electrodes we find a transition between planar and spherical diffusion for small electrodes combined with the pseudo-capacitance of proton adsorption at the Pt surface can explain this anomalous low impedance. These results provide important intuition for designing small, single unit recording electrodes. Specifically, for materials that have a pseudo-capacitance or when diffusional capacitance dominates the total impedance, we should expect small electrodes will have lower-than-expected impedance values allowing us to scale these devices down further than previously thought before thermal noise or voltage division limits the ability to acquire high-quality single-unit recordings.

Reconciling similarity across models of continuous selections

Recently-developed models of decision making have provided accounts of the cognitive processes underlying choice on tasks where responses can fall along a continuum, such as identifying the color or orientation of a stimulus. Even though nearly all of these models seek to extend diffusion decision processes to a continuum of response options, they vary in terms of complexity, tractability, and their ability to predict patterns of data such as multimodal distributions of responses. We suggest that these differences are almost entirely due to differences in how these models account for the similarity among response options. In this theoretical note, we reconcile these differences by characterizing the existing models under a common framework, where the assumptions about psychological representations of similarity, and their implications for behavioral data (e.g., multimodal responses), are made explicit. Furthermore, we implement a simulation-based approach to computing model likelihoods that allows for greater freedom in constructing and implementing continuous response models. The resulting geometric similarity representation (GSR) can supplement approaches like the circular / spherical diffusion models by allowing them to generate multimodal distributions of responses, or simplify models like the spatially continuous diffusion model by condensing their representations of similarity and allowing them to generate simulations more efficiently. To illustrate its utility, we apply this approach to multimodal distributions responses, two-dimensional responses (such as locations on a computer screen), and continuua of response options with nontrivial, nonlinear similarity relations between response options.