The probabilistic finite element method (PFEM) is formulated for linear and non-linear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in non-linear continua.The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elasticlplastic wave propagation problem and a two-dimensional plane-stress beam bending problem. The moments calculated compare favourably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

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SUMMARY Center-surround antagonism has been used as the canonical model to describe receptive fields of retinal ganglion cells (RGCs) for decades. We describe a newly identified RGC type in mouse, called the ON delayed (OND) RGC, with receptive field properties that deviate from center-surround organization. Responding with an unusually long latency to light stimulation, OND RGCs respond earlier as the visual stimulus increases in size. Furthermore, OND RGCs are excited by light falling far beyond their dendrites. We unravel details of the circuit mechanisms behind these phenomena, revealing new roles for inhibition in controlling both temporal and spatial receptive field properties. The non-canonical receptive field properties of the OND RGC – integration of long temporal and large spatial scales – suggest that unlike typical RGCs, it may encode a slowly varying, global property of the visual scene.

Classification and characterization of neuronal types is critical for understanding their function and dysfunction. Neuronal classification schemes typically rely on measurements of electrophysiological, morphological and molecular features, but aligning these data sets has been challenging. Here, we present a unified classification of retinal ganglion cells (RGCs), the sole retinal output neurons. We used visually-evoked responses to classify 1777 mouse RGCs into 42 types. We also obtained morphological or transcriptomic data from subsets and used these measurements to align the functional classification to publicly available morphological and transcriptomic data sets. We created an online database that allows users to browse or download the data and to classify RGCs from their light responses using a machine-learning algorithm. This work provides a resource for studies of RGCs, their upstream circuits in the retina, and their projections in the brain, and establishes a framework for future efforts in neuronal classification and open data distribution.