Kolmogorov condition near hyperbolic singularities of integrable Hamiltonian systems

In this paper we show that, if an integrable Hamiltonian system admits a nondegenerate hyperbolic singularity then it will satisfy the Kolmogorov condegeneracy condition near that singularity (under a mild additional condition, which is trivial if the singularity contains a fixed point)Comment: revised version, 11p, accepted for publication in a sepecial volume in Regular and Chaotic Dynamics in honor of Richard Cushma

Mutations and deletions of the SUZ12 polycomb gene in myeloproliferative neoplasms

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Targeted molecular characterization shows differences between primary and secondary myelofibrosis

INTRODUCTION: In BCR-ABL1-negative myeloproliferative neoplasms, myelofibrosis (MF) is either primary (PMF) or secondary (SMF) to polycythemia vera or essential thrombocythemia. MF is characterized by an increased risk of transformation to acute myeloid leukemia (AML) and a shortened life expectancy. METHODS: Because natural histories of PMF and SMF are different, we studied by targeted next generation sequencing the differences in the molecular landscape of 86 PMF and 59 SMF and compared their prognosis impact. RESULTS: PMF had more ASXL1 (47.7%) and SRSF2 (14%) gene mutations than SMF (respectively 27.1% and 3.4%, P = .04). Poorer survival was associated with RNA splicing mutations (especially SRSF2) and TP53 in PMF (P = .0003), and with ASXL1 and TP53 mutations in SMF (P < .0001). These mutations of poor prognosis were associated with biological features of scoring systems (DIPSS and MYSEC-PM score). Mutations in TP53/SRSF2 in PMF or TP53/ASXL1 in SMF were more frequent as the risk of these scores increased. This allowed for a better stratification of MF patients, especially within the DIPSS intermediate-1 risk group (DIPSS) or the MYSEC-PM high risk group. AML transformation occurred faster in SMF than in PMF and patients who transformed to AML were more SRSF2-mutated and less CALR-mutated at MF sampling. CONCLUSIONS: PMF and SMF have different but not specific molecular profiles and different prognosis depending on the molecular profile. This may be due to differences in disease history. Combining mutations and existing scores should improve prognosis assessment

Singularities, Lax degeneracies and Maslov indices of the periodic Toda chain

The n-particle periodic Toda chain is a well known example of an integrable but nonseparable Hamiltonian system in R^{2n}. We show that Sigma_k, the k-fold singularities of the Toda chain, ie points where there exist k independent linear relations amongst the gradients of the integrals of motion, coincide with points where there are k (doubly) degenerate eigenvalues of representatives L and Lbar of the two inequivalent classes of Lax matrices (corresponding to degenerate periodic or antiperiodic solutions of the associated second-order difference equation). The singularities are shown to be nondegenerate, so that Sigma_k is a codimension-2k symplectic submanifold. Sigma_k is shown to be of elliptic type, and the frequencies of transverse oscillations under Hamiltonians which fix Sigma_k are computed in terms of spectral data of the Lax matrices. If mu(C) is the (even) Maslov index of a closed curve C in the regular component of R^{2n}, then (-1)^{\mu(C)/2} is given by the product of the holonomies (equal to +/- 1) of the even- (or odd-) indexed eigenvector bundles of L and Lmat.Comment: 25 pages; published versio

Extracting quantitative data from tuft flow visualizations on utility scale wind turbines

First results of a novel measurement technique that allows to extract quantitative data from tuft flow visualizations on real-world wind turbine blades are presented. The instantaneous flow structure is analyzed by tracking individual flow indicators in each of the snapshot images. The obtained per-tuft statistics are correlated with logged turbine data to provide an insight into the surface flow structure under the influence of wind speed. A histogram filter is used to identify two flow states: a separated flow state that occurs at higher wind speeds and a maximal attached flow state that mainly occurs in the lower wind speed range

Features of Time-independent Wigner Functions

The Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantizations. General features of time-independent Wigner functions are explored here, including the functional ("star") eigenvalue equations they satisfy; their projective orthogonality spectral properties; their Darboux ("supersymmetric") isospectral potential recursions; and their canonical transformations. These features are illustrated explicitly through simple solvable potentials: the harmonic oscillator, the linear potential, the Poeschl-Teller potential, and the Liouville potential.Comment: 18 pages, plain LaTex, References supplemente

Noncommutative cosmological models coupled to a perfect fluid and a cosmological constant

In this work we carry out a noncommutative analysis of several Friedmann-Robert-Walker models, coupled to different types of perfect fluids and in the presence of a cosmological constant. The classical field equations are modified, by the introduction of a shift operator, in order to introduce noncommutativity in these models. We notice that the noncommutative versions of these models show several relevant differences with respect to the correspondent commutative ones.Comment: 27 pages. 7 figures. JHEP style.arXiv admin note: substantial text overlap with arXiv:1104.481