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In cancer progression, tumor microenvironments (TME) progressively become denser and hypoxic, and cell migrate toward higher oxygen levels as they invade across the tumor-stromal boundary. Although cell invasion dependence on optimal collagen density is well appreciated, it remains unclear whether past oxygen conditions alter future invasion phenotype of cells. Here, we show that normal human mammary epithelial cells (MCF10A) and leader-like human breast tumor cells (BT549) undergo higher rates of invasion and collagen deformation after past exposure to hypoxia, compared with normoxia controls. Upon increasing collagen density by ∼50%, cell invasion under normoxia reduced, as expected due to the increased matrix crowding. However, surprisingly, past hypoxia increased cell invasion in future normoxic dense collagen, with more pronounced invasion of cancer cells. This culmination of cancer-related conditions of hypoxia history, tumor cell, and denser collagen led to more aggressive invasion phenotypes. We found that hypoxia-primed cancer cells produce laminin332, a basement membrane protein required for cell–matrix adhesions, which could explain the additional adhesion feedback from the matrix that led to invasion after hypoxia priming. Depletion of Cdh3 disrupts the hypoxia-dependent laminin production and thus disables the rise in rates of cancer cell invasion and collagen deformation caused by hypoxia memory. These findings highlight the importance of considering past oxygen conditions in combination with current mechanical composition of tissues to better understand tumor invasion in physically evolving TME. 

We present a high-assurance and high-speed implementation of the SHA-3 hash function. Our implementation is written in the Jasmin programming language, and is formally verified for functional correctness, provable security and timing attack resistance in the EasyCrypt proof assistant. Our implementation is the first to achieve simultaneously the four desirable properties (efficiency, correctness, provable security, and side-channel protection) for a non-trivial cryptographic primitive. Concretely, our mechanized proofs show that: 1) the SHA-3 hash function is indifferentiable from a random oracle, and thus is resistant against collision, first and second preimage attacks; 2) the SHA-3 hash function is correctly implemented by a vectorized x86 implementation. Furthermore, the implementation is provably protected against timing attacks in an idealized model of timing leaks. The proofs include new EasyCrypt libraries of independent interest for programmable random oracles and modular indifferentiability proofs.