We give a new analysis of Petrov-Galerkin finite element methods for solving linear singularly perturbed two-point boundary value problems without turning points. No use is made of finite difference methodology such as discrete maximum principles, nor of asymptotic expansions. On meshes which are either arbitrary or slightly restricted, we derive energy norm and L norm error bounds. These bound...

Daniel Burgarth,1,2 Koji Maruyama,2 Michael Murphy,3 Simone Montangero,3 Tommaso Calarco,3,4 Franco Nori,2,5 and Martin B. Plenio1,6 1IMS and QOLS, Imperial College, London SW7 2PG, United Kingdom 2Advanced Science Institute, The Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama 351-0198, Japan 3Institut für Quanteninformationsverarbeitung, Universität Ulm, D-89069 Ulm, Ger...

We present a new autoencoder-type architecture that is trainable in an unsupervised mode, sustains both generation and inference, and has the quality of conditional and unconditional samples boosted by adversarial learning. Unlike previous hybrids of autoencoders and adversarial networks, the adversarial game in our approach is set up directly between the encoder and the generator, and no exter...

Permutation pattern classes that are defined by avoiding two permutations only and which contain only finitely many simple permutations are characterized and their growth rates are determined.

ParaHox genes (Gsx, Pdx, and Cdx) are an ancient family of developmental genes closely related to the Hox genes. They play critical roles in the patterning of brain and gut. The basal chordate, amphioxus, contains a single ParaHox cluster comprising one member of each family, whereas nonteleost jawed vertebrates contain four ParaHox genomic loci with six or seven ParaHox genes. Teleosts, which ...

The potato is a versatile vegetable. You can boil it, broil it, fry it, roast it, bake it and grill it. You can dice it and have it with eggs for breakfast, slice it and have it with a burger for lunch, and mash it and have it with a steak for dinner. And if you are Chris Voigt, you have it all these ways and more — every meal, every day for two months. On Oct. 1, Voigt, the executive director ...

We evaluated the proposal that there exist detectors of the following four cardinal phases in human vision: +cosine, -cosine, +sine, and -sine. First, we assessed whether there was evidence that these cardinal phases were processed by independent 'labeled lines,' using a discrimination at detection threshold paradigm. Second, we assessed whether suprathreshold phase discrimination was best at p...