418 research outputs found
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
The Maslov index and nondegenerate singularities of integrable systems
We consider integrable Hamiltonian systems in R^{2n} with integrals of motion
F = (F_1,...,F_n) in involution. Nondegenerate singularities are critical
points of F where rank dF = n-1 and which have definite linear stability. The
set of nondegenerate singularities is a codimension-two symplectic submanifold
invariant under the flow. We show that the Maslov index of a closed curve is a
sum of contributions +/- 2 from the nondegenerate singularities it is encloses,
the sign depending on the local orientation and stability at the singularities.
For one-freedom systems this corresponds to the well-known formula for the
Poincar\'e index of a closed curve as the oriented difference between the
number of elliptic and hyperbolic fixed points enclosed. We also obtain a
formula for the Liapunov exponent of invariant (n-1)-dimensional tori in the
nondegenerate singular set. Examples include rotationally symmetric n-freedom
Hamiltonians, while an application to the periodic Toda chain is described in a
companion paper.Comment: 27 pages, 1 figure; published versio
Mutations and deletions of the SUZ12 polycomb gene in myeloproliferative neoplasms
International audienceNo abstract availabl
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
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