Toward the realization of a primary low-pressure standard using a superconducting microwave resonator.

We describe a primary gas pressure standard based on the measurement of the refractive index of helium gas using a microwave resonant cavity in the range between 500 Pa and 20 kPa. To operate in this range, the sensitivity of the microwave refractive gas manometer (MRGM) to low-pressure variations is substantially enhanced by a niobium coating of the resonator surface, which becomes superconducting at temperatures below 9 K, allowing one to achieve a frequency resolution of about 0.3 Hz at 5.

Counting phylogenetic networks of level 1 and 2.

Phylogenetic networks generalize phylogenetic trees, and have been introduced in order to describe evolution in the case of transfer of genetic material between coexisting species. There are many classes of phylogenetic networks, which can all be modeled as families of graphs with labeled leaves. In this paper, we focus on rooted and unrooted level-k networks and provide enumeration formulas (exact and asymptotic) for rooted and unrooted level-1 and level-2 phylogenetic networks with a given number of leaves.

Rearrangement moves on rooted phylogenetic networks.

Phylogenetic tree reconstruction is usually done by local search heuristics that explore the space of the possible tree topologies via simple rearrangements of their structure. Tree rearrangement heuristics have been used in combination with practically all optimization criteria in use, from maximum likelihood and parsimony to distance-based principles, and in a Bayesian context. Their basic components are rearrangement moves that specify all possible ways of generating alternative phylogenies from a given one, and whose fundamental property is to be able to transform, by repeated application, any phylogeny into any other phylogeny.

Uprooted Phylogenetic Networks.

The need for structures capable of accommodating complex evolutionary signals such as those found in, for example, wheat has fueled research into phylogenetic networks. Such structures generalize the standard model of a phylogenetic tree by also allowing for cycles and have been introduced in rooted and unrooted form. In contrast to phylogenetic trees or their unrooted versions, rooted phylogenetic networks are notoriously difficult to understand.