Are Chinese loess deposits essentially continuous?

On Essentially Absolutely Continuous Plane Transformations

How does Chinese loess become magnetized?

Intersecting Families are Essentially Contained in Juntas

A family J of subsets of {1, . . . , n} is called a j-junta if there exists J ⊆ {1, . . . , n}, with |J | = j, such that the membership of a set S in J depends only on S ∩ J . In this paper we provide a simple description of intersecting families of sets. Let n and k be positive integers with k < n/2, and let A be a family of pairwise intersecting subsets of {1, . . . , n}, all of size k. We sh...

Completely Integrable Differential Systems Are Essentially Linear

Let ẋ = f(x) be a C autonomous differential system with k ∈ N ∪ {∞, ω} defined in an open subset Ω of R. Assume that the system ẋ = f(x) is C completely integrable, i.e. there exist n−1 functionally independent first integrals of class C with 2 ≤ r ≤ k. If the divergence of system ẋ = f(x) is non–identically zero, then any Jacobian multiplier is functionally independent of the n − 1 first integ...

Essentially all models are wrong, but some are useful.

Recent advances in high-throughput technologies, such as genome-wide SNP analysis and microarray gene expression profiling, have led to a multitude of ranked lists, where the features (SNPs, genes) are sorted based on their individual correlation with a phenotype. Multiple reviews have shown that most such rankings vary considerably across different studies, even in the case of subsampling from...