Coupled Ito equations of continuous quantum state measurement, and estimation

We discuss a non-linear stochastic master equation that governs the time-evolution of the estimated quantum state. Its differential evolution corresponds to the infinitesimal updates that depend on the time-continuous measurement of the true quantum state. The new stochastic master equation couples to the two standard stochastic differential equations of time-continuous quantum measurement. For the first time, we can prove that the calculated estimate almost always converges to the true state, also at low-efficiency measurements. We show that our single-state theory can be adapted to weak continuous ensemble measurements as well.Comment: 5 pages, RevTeX4. In version v2 some minor revisions and clarifications have been incorporated. Moreover, a new reference has been included. Accepted for publication in Journal of Physics A: Mathematical and Genera

Combined Molecular Phylogenetic Analysis of the Orthoptera (Arthropoda, Insecta) and Implications for Their Higher Systematics

A phylogenetic analysis of mitochondrial and nuclear rDNA sequences from species of all the superfamilies of the insect order Orthoptera (grasshoppers, crickets, and relatives) confirmed that although mitochondrial sequences provided good resolution of the youngest superfamilies, nuclear rDNA sequences were necessary to separate the basal groups. To try to reconcile these data sets into a single, fully resolved orthopteran phylogeny, we adopted consensus and combined data strategies. The consensus analysis produced a partially resolved tree that lacked several well-supported features of the individual analyses. However, this lack of resolution was explained by an examination of resampled data sets, which identified the likely source of error as the relatively short length of the individual mitochondrial data partitions. In a subsequent comparison in which the mitochondrial sequences were initially combined, we observed less conflict. We then used two approaches to examine the validity of combining all of the data in a single analysis: comparative analysis of trees recovered from resampled data sets, and the application of a randomization test. Because the results did not point to significant levels of heterogeneity in phylogenetic signal between the mitochondrial and nuclear data sets, we therefore proceeded with a combined analysis. Reconstructing phylogenies under the minimum evolution and maximum likelihood optimality criteria, we examined monophyly of the major orthopteran groups, using nonparametric and parametric bootstrap analysis and Kishino-Hasegawa tests. Our analysis suggests that phylogeny reconstruction under the maximum likelihood criteria is the most discriminating approach for the combined sequences. The results indicate, moreover, that the caeliferan Pneumoroidea and Pamphagoidea, as previously suggested, are polyphyletic. The Acridoidea is redefined to include all pamphagoid families other than the Pyrgomorphidae, which we propose should be accorded superfamily statu

Applying formal verification to microkernel IPC at meta

We use Iris, an implementation of concurrent separation logic in the Coq proof assistant, to verify two queue data structures used for inter-process communication in an operating system under development. Our motivations are twofold. First, we wish to leverage formal verification to boost confidence in a delicate piece of industrial code that was subject to numerous revisions. Second, we aim to gain information on the cost-benefit tradeoff of applying a state-of-the-art formal verification tool in our industrial setting. On both fronts, our endeavor has been a success. The verification effort proved that the queue algorithms are correct and uncovered four algorithmic simplifications as well as bugs in client code. The simplifications involve the removal of two memory barriers, one atomic load, and one boolean check, all in a performance-sensitive part of the OS. Removing the redundant boolean check revealed unintended uses of uninitialized memory in multiple device drivers, which were fixed. The proof work was completed in person months, not years, by engineers with no prior familiarity with Iris. These findings are spurring further use of verification at Meta

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

Reflexive Cones

Reflexive cones in Banach spaces are cones with weakly compact intersection with the unit ball. In this paper we study the structure of this class of cones. We investigate the relations between the notion of reflexive cones and the properties of their bases. This allows us to prove a characterization of reflexive cones in term of the absence of a subcone isomorphic to the positive cone of \ell_{1}. Moreover, the properties of some specific classes of reflexive cones are investigated. Namely, we consider the reflexive cones such that the intersection with the unit ball is norm compact, those generated by a Schauder basis and the reflexive cones regarded as ordering cones in a Banach spaces. Finally, it is worth to point out that a characterization of reflexive spaces and also of the Schur spaces by the properties of reflexive cones is given.Comment: 23 page