Recently, Bravyi and König have shown that there is a trade-off between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a constant-depth geometrically-local circuit and are thus fault-tolerant by construction. In particular, they shown that, for local stabilizer codes in D spatial dime...

Motivated by applications to proving regularity of solutions to degenerate parabolic equations arising in population genetics, we study existence, uniqueness and the strong Markov property of weak solutions to a class of degenerate stochastic differential equations. The stochastic differential equations considered in our article admit solutions supported in the set [0,∞)×R, and they are degener...

In response to the Ebola virus disease (EVD) outbreak in West Africa, the World Health Organization has advised all nations to prepare for the detection, investigation and management of confirmed and suspected EVD cases in order to prevent further spread through international travel. To gain insights into the state of preparedness of European hospitals, an electronic survey was circulated in Au...

Logical Forms are an exceptionally important linguistic representation for highly demanding semantically related tasks like Question/ Answering and Text Understanding, but their automatic production at runtime is higly error-prone. The use of a tool like XWNet and other similar resources would be beneficial for all the NLP community, but not only. The problem is: Logical Forms are useful as lon...

We consider a class of fourth-order nonlinear difference equations. The classification of nonoscillatory solutions is given. Next, we divide the set of solutions of these equations into two types: F+and F−-solutions. Relations between these types of solutions and their nonoscillatory behavior are obtained. Necessary and sufficient conditions are obtained for the difference equation to admit the...

In a certain class of differential-difference equations for dissipative systems, we show that hyperbolic tangent model is the only the nonlinear system of equations which can admit some particular solutions of the Toda lattice. We give one parameter family of exact solutions, which include as special cases the Toda lattice solutions as well as the Whitham’s solutions in the Newell’s model. Our ...

We study some nonlinear elliptic equations on compact Riemannian manifolds. Our main concern is to find conditions which imply that such equations admit only constant solutions.