Search

For decades the external globus pallidus (GPe) has been viewed as a passive way-station in the indirect pathway of the cortico-basal ganglia-thalamic (CBGT) circuit, sandwiched between striatal inputs and basal ganglia outputs. According to this model, one-way descending striatal signals in the indirect pathway amplify the suppression of downstream thalamic nuclei by inhibiting GPe activity. Here we revisit this assumption, in light of new and emerging work on the cellular complexity, connectivity, and functional role of the GPe in behavior. We show how, according to this new circuit-level logic, the GPe is ideally positioned for relaying ascending and descending control signals within the basal ganglia. Focusing on the problem of inhibitory control, we illustrate how this bidirectional flow of information allows for the integration of reactive and proactive control mechanisms during action selection. Taken together, this new evidence points to the GPe as being a central hub in the CBGT circuit, participating in bidirectional information flow and linking multifaceted control signals to regulate behavior.

Similar activity patterns may arise from model neural networks with distinct coupling properties and individual unit dynamics. These similar patterns may, however, respond differently to parameter variations and, specifically, to tuning of inputs that represent control signals. In this work, we analyze the responses resulting from modulation of a localized input in each of three classes of model neural networks that have been recognized in the literature for their capacity to produce robust three-phase rhythms: coupled fast-slow oscillators, near-heteroclinic oscillators, and threshold-linear networks. Triphasic rhythms, in which each phase consists of a prolonged activation of a corresponding subgroup of neurons followed by a fast transition to another phase, represent a fundamental activity pattern observed across a range of central pattern generators underlying behaviors critical to survival, including respiration, locomotion, and feeding. To perform our analysis, we extend the recently developed local timing response curve (lTRC), which allows us to characterize the timing effects due to perturbations, and we complement our lTRC approach with model-specific dynamical systems analysis. Interestingly, we observe disparate effects of similar perturbations across distinct model classes. Thus, this work provides an analytical framework for studying control of oscillations in nonlinear dynamical systems, and may help guide model selection in future efforts to study systems exhibiting triphasic rhythmic activity., Comment: 49 pages, 21 figures, 8 tables

Our recent work lays out a general framework for inferring information about the parameters and associated dynamics of a differential equation model from a discrete set of data points collected from the system being modeled. Rigorous mathematical results have justified this approach and have identified some common features that arise for certain classes of integrable models. In this work we present a thorough numerical investigation that shows that several of these core features extend to a paradigmatic linear-in-parameters model, the Lotka-Volterra (LV) system, which we consider in the conservative case as well as under the addition of terms that perturb the system away from this regime. A central construct for this analysis is a concise representation of parameter features in the data space that we call the $P_n$-diagram, which is particularly useful for visualization of results for low-dimensional (small $n$) systems. Our work also exposes some new properties related to non-uniqueness that arise for these LV systems, with non-uniqueness manifesting as a multi-layered structure in the associated $P_2$-diagrams., Comment: Main text(32 pages, 13 figures) and one supplementary material(7 pages, 3 figures)

The development of face recognition algorithms by academic and commercial organizations is growing rapidly due to the onset of deep learning and the widespread availability of training data. Though tests of face recognition algorithm performance indicate yearly performance gains, error rates for many of these systems differ based on the demographic composition of the test set. These "demographic differentials" in algorithm performance can contribute to unequal or unfair outcomes for certain groups of people, raising concerns with increased worldwide adoption of face recognition systems. Consequently, regulatory bodies in both the United States and Europe have proposed new rules requiring audits of biometric systems for "discriminatory impacts" (European Union Artificial Intelligence Act) and "fairness" (U.S. Federal Trade Commission). However, no standard for measuring fairness in biometric systems yet exists. This paper characterizes two proposed measures of face recognition algorithm fairness (fairness measures) from scientists in the U.S. and Europe. We find that both proposed methods are challenging to interpret when applied to disaggregated face recognition error rates as they are commonly experienced in practice. To address this, we propose a set of interpretability criteria, termed the Functional Fairness Measure Criteria (FFMC), that outlines a set of properties desirable in a face recognition algorithm fairness measure. We further develop a new fairness measure, the Gini Aggregation Rate for Biometric Equitability (GARBE), and show how, in conjunction with the Pareto optimization, this measure can be used to select among alternative algorithms based on the accuracy/fairness trade-space. Finally, we have open-sourced our dataset of machine-readable, demographically disaggregated error rates. We believe this is currently the largest open-source dataset of its kind.

Intensive computational and theoretical work has led to the development of mutliple mathematical models for bursting in respiratory neurons in the pre-B\"otzinger Complex (pre-B\"otC) of the mammalian brainstem. Nonetheless, these previous models have not captured the pre-inspiratory ramping aspects of these neurons' activity patterns, in which relatively slow tonic spiking gradually progresses to faster spiking and a full blown burst, with a corresponding gradual development of an underlying plateau potential. In this work, we show that the incorporation of the dynamics of the extracellular potassium ion concentration into an existing model for pre-B\"otC neuron bursting, along with some parameter updates, suffices to induce this ramping behavior. Using fast-slow decomposition, we show that this activity can be considered as a form of parabolic bursting, but with burst termination at a homoclinic bifurcation rather than as a SNIC bifurcation. We also investigate the parameter-dependence of these solutions and show that the proposed model yields a greater dynamic range of burst frequencies, durations, and duty cycles than those produced by other models in the literature., Comment: 23 pages, 10 figures, submitted to Journal of Computational Neuroscience