Recent experimental works have implicated astrocytes as a significant cell type underlying several neuronal processes in the mammalian brain, from encoding sensory information to neurological disorders. Despite this progress, it is still unclear how astrocytes are communicating with and driving their neuronal neighbors. While previous computational modeling works have helped propose mechanisms responsible for driving these interactions, they have primarily focused on interactions at the synaptic level, with microscale models of calcium dynamics and neurotransmitter diffusion. Since it is computationally infeasible to include the intricate microscale details in a network-scale model, little computational work has been done to understand how astrocytes may be influencing spiking patterns and synchronization of large networks. We overcome this issue by first developing an "effective" astrocyte that can be easily implemented to already established network frameworks. We do this by showing that the astrocyte proximity to a synapse makes synaptic transmission faster, weaker, and less reliable. Thus, our "effective" astrocytes can be incorporated by considering heterogeneous synaptic time constants, which are parametrized only by the degree of astrocytic proximity at that synapse. We then apply our framework to large networks of exponential integrate-and-fire neurons with various spatial structures. Depending on key parameters, such as the number of synapses ensheathed and the strength of this ensheathment, we show that astrocytes can push the network to a synchronous state and exhibit spatially correlated patterns.

Many diverse biological systems are described by randomly moving particles that can be captured by traps in their environment. Examples include neurotransmitters diffusing in the synaptic cleft before binding to receptors and prey roaming an environment before capture by predators. In most cases, the traps cannot capture particles continuously. Rather, each trap must wait a transitory "recharge" time after capturing a particle before additional captures. This recharge time is often overlooked. In the case of instant recharge, the average number of particles captured before they escape grows linearly in the total number of particles. In stark contrast, we prove that for any nonzero recharge time, the average number of captured particles grows at most logarithmically in the total particle number. This is a fundamental effect of recharge, as it holds under very general assumptions on particle motion and spatial domain. Furthermore, we characterize the parameter regime in which a given recharge time will dramatically affect a system, allowing researchers to easily verify if they need to account for recharge in their specific system. Finally, we consider a few examples, including a neural system in which recharge reduces neurotransmitter bindings by several orders of magnitude.

In many real-world classification problems, the labels of training examples are randomly corrupted. Thus, the set of training examples for each class is contaminated by examples of the other class. Previous theoretical work on this problem assumes that the two classes are separable, that the label noise is independent of the true class label, or that the noise proportions for each class are known. We introduce a general framework for classification with label noise that eliminates these assumptions. Instead, we give assumptions ensuring identifiability and the existence of a consistent estimator of the optimal risk, with associated estimation strategies. For any arbitrary pair of contaminated distributions, there is a unique pair of non-contaminated distributions satisfying the proposed assumptions, and we argue that this solution corresponds in a certain sense to maximal denoising. In particular, we find that learning in the presence of label noise is possible even when the class-conditional distributions overlap and the label noise is not symmetric. A key to our approach is a universally consistent estimator of the maximal proportion of one distribution that is present in another, a problem we refer to as“mixture proportion estimation. This work is motivated by a problem in nuclear particle classification.