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The EBFS is built of three components: an input ensemble forecaster (IEF), which simulates the uncertainty associated with random inputs; a deterministic hydrologic model (of any complexity), which simulates physical processes within a river basin; and a hydrologic uncertainty processor (HUP), which simulates the hydrologic uncertainty (an aggregate of all uncertainties except input).

ChIP-seq data were deposited to Gene Expression Omnibus (GEO) under accession number [GSE69946] except input DNA of GS and PS (separately deposited to [GSE55060]).

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The number of nodes in each layer is set to be 2048 except for input and output layers2.

Each layers except the input layer shown in the figure, are pre-trained with an auto-encoder.

Except two input variables (P and m), all others are kept constant as defined in this section.

In general, all nodes (except the input layer) are by default unconstrained.

The same binomial regression models were set up except the input of prevalence of diabetes mellitus (Table  8).

Each vertex has an in-degree two except for the input vertex which has in-degree zero.

Except for the input nodes, each node is a neuron (or processing element) with a nonlinear activation function.

Each vertex has an in-degree n, except for the input vertex which has in-degree zero.

The RRTs are similar to the CRTs, except for the input model that is constructed from the obtained (Q^{ - 1}) structure (Additional file 1: Figure S4).

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