The task of decoupling, i.e., removing unwanted internal couplings of a quantum system and its couplings to an environment, plays an important role in quantum control theory. There are many efficient decoupling schemes based on combinatorial concepts such as orthogonal arrays, difference schemes, and Hadamard matrices. So far these combinatorial decoupling schemes have relied on the ability to ...

A graph (digraph) G = (V,E) with a set T ⊆ V of terminals is called inner Eulerian if each nonterminal node v has even degree (resp. the numbers of edges entering and leaving v are equal). Cherkassky [1] and Lovász [15] showed that the maximum number of pairwise edge-disjoint T -paths in an inner Eulerian graph G is equal to 1 2 ∑ s∈T λ(s), where λ(s) is the minimum number of edges whose remova...

Designing a protocol to exchange a secret key is one of the most fundamental subjects in cryptography. Using a random deal of cards, pairs of card players (agents) can share information-theoretically secure keys that are secret from an eavesdropper. In this paper we first introduce the notion of an Eulerian secret key exchange, in which the pairs of players sharing secret keys form an Eulerian ...

Eulerian hydrodynamical simulations are a powerful and popular tool for modelling fluids in astrophysical systems. In this work, we critically examine recent claims that these methods violate Galilean invariance of the Euler equations. We demonstrate that Eulerian hydrodynamics methods do converge to a Galilean-invariant solution, provided a well-defined convergent solution exists. Specifically...

Further work of Brylawski and Heron (see [4, p. 315]) explores other characterizations of Eulerian binary matroids. They showed, independently, that a binary matroid M is Eulerian if and only if its dual, M∗, is a binary affine matroid. More recently, Shikare and Raghunathan [5] have shown that a binary matroid M is Eulerian if and only if the number of independent sets of M is odd. This chapte...

Graphs are among the most frequently used structures in Computer Science. Some of the properties that must be checked in many applications are connectivity, acyclicity and the Eulerian and Hamiltonian properties. In this work, we analyze how we can express these four properties with modal logics. This involves two issues: whether each of the modal languages under consideration has enough expres...

In this article we define an Eulerian level set method for a partial differential equation on an evolving hypersurface Γ (t) contained in a domain Ω ⊂ R. The key idea is based on formulating the partial differential equations on all level set surfaces of a prescribed time dependent function Φ whose zero level set is Γ (t). The resulting equation is then solved in one dimension higher but can be...

We consider the problem of sampling from the uniform distribution on the set of Eulerian orientations of subgraphs of the triangular lattice. Although it is known that this can be achieved in polynomial time for any graph, the algorithm studied here is more natural in the context of planar Eulerian graphs. We analyse the mixing time of a Markov chain on the Eulerian orientations of a planar gra...

In this research announcement we present a new q-analog of a classical formula for the exponential generating function of the Eulerian polynomials. The Eulerian polynomials enumerate permutations according to their number of descents or their number of excedances. Our q-Eulerian polynomials are the enumerators for the joint distribution of the excedance statistic and the major index. There is a...

A 2-cell embedding of an Eulerian digraph in a closed surface is said to be directed if the boundary of each face is a directed closed walk in G. We prove Kuratowski-type theorems about obstructions to directed embeddings of Eulerian digraphs in the plane.