Hamiltonian flows on null curves

The local motion of a null curve in Minkowski 3-space induces an evolution equation for its Lorentz invariant curvature. Special motions are constructed whose induced evolution equations are the members of the KdV hierarchy. The null curves which move under the KdV flow without changing shape are proven to be the trajectories of a certain particle model on null curves described by a Lagrangian linear in the curvature. In addition, it is shown that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlev\'e equation.Comment: 14 pages, v2: final version; minor changes in the expositio

Binary trees, coproducts, and integrable systems

We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.Comment: 15 pages, 6 figures, v2: minor correction in theorem 1, two new appendices adde

Classical Dynamical Systems from q-algebras:"cluster" variables and explicit solutions

A general procedure to get the explicit solution of the equations of motion for N-body classical Hamiltonian systems equipped with coalgebra symmetry is introduced by defining a set of appropriate collective variables which are based on the iterations of the coproduct map on the generators of the algebra. In this way several examples of N-body dynamical systems obtained from q-Poisson algebras are explicitly solved: the q-deformed version of the sl(2) Calogero-Gaudin system (q-CG), a q-Poincare' Gaudin system and a system of Ruijsenaars type arising from the same (non co-boundary) q-deformation of the (1+1) Poincare' algebra. Also, a unified interpretation of all these systems as different Poisson-Lie dynamics on the same three dimensional solvable Lie group is given.Comment: 19 Latex pages, No figure

Bubble concentration on spheres for supercritical elliptic problems

We consider the supercritical Lane-Emden problem (P_\eps)\qquad -\Delta v= |v|^{p_\eps-1} v \ \hbox{in}\ \mathcal{A} ,\quad u=0\ \hbox{on}\ \partial\mathcal{A} where $\mathcal A$ is an annulus in \rr^{2m}, $m\ge2$ and p_\eps={(m+1)+2\over(m+1)-2}-\eps, \eps>0. We prove the existence of positive and sign changing solutions of (P_\eps) concentrating and blowing-up, as \eps\to0, on $(m-1)-$dimensional spheres. Using a reduction method (see Ruf-Srikanth (2010) J. Eur. Math. Soc. and Pacella-Srikanth (2012) arXiv:1210.0782)we transform problem (P_\eps) into a nonhomogeneous problem in an annulus \mathcal D\subset \rr^{m+1} which can be solved by a Ljapunov-Schmidt finite dimensional reduction

Excursion Sets and Non-Gaussian Void Statistics

Primordial non-Gaussianity (NG) affects the large scale structure (LSS) of the universe by leaving an imprint on the distribution of matter at late times. Much attention has been focused on using the distribution of collapsed objects (i.e. dark matter halos and the galaxies and galaxy clusters that reside in them) to probe primordial NG. An equally interesting and complementary probe however is the abundance of extended underdense regions or voids in the LSS. The calculation of the abundance of voids using the excursion set formalism in the presence of primordial NG is subject to the same technical issues as the one for halos, which were discussed e.g. in arXiv:1005.1203. However, unlike the excursion set problem for halos which involved random walks in the presence of one barrier $\delta_c$, the void excursion set problem involves two barriers $\delta_v$ and $\delta_c$. This leads to a new complication introduced by what is called the "void-in-cloud" effect discussed in the literature, which is unique to the case of voids. We explore a path integral approach which allows us to carefully account for all these issues, leading to a rigorous derivation of the effects of primordial NG on void abundances. The void-in-cloud issue in particular makes the calculation conceptually rather different from the one for halos. However, we show that its final effect can be described by a simple yet accurate approximation. Our final void abundance function is valid on larger scales than the expressions of other authors, while being broadly in agreement with those expressions on smaller scales.Comment: 28 pages (18+appendices), 7 figures; v2 -- minor changes in sec 3.2, version published in PR

Gaudin Models and Bending Flows: a Geometrical Point of View

In this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals associated with the 'standard' Lax representation of the Gaudin model. These integrals, in the case of su(2), coincide wih the Hamiltonians of the 'bending flows' in the moduli space of polygons in Euclidean space introduced by Kapovich and Millson. We finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the r=2 case.Comment: 27 pages, LaTeX with amsmath and amssym

The Interconnections of the LHC Cryomagnets at CERN: Strategy Applied and First Results of the Industrialization Process

The final interconnections of the LHC superconducting magnets in the underground tunnel are performed by a contractor on a result-oriented basis. A consortium of firms was awarded the contract after competitive tendering based on a technical and commercial specification. The implementation of the specific technologies and tooling developed and qualified by CERN has required an important effort to transfer the know-how and implement the follow-up of the contractor. This paper summarizes the start-up phase and the difficulties encountered. The organization and management tools put in place during the ramping-up phase are presented. In addition to contractual adaptations of the workforce, several configuration changes to the workflows were necessary to reach production rates compatible with the overall schedule and with the different constraints: availability of magnets, co-activities with magnets transport and alignment, handling of non-conformities, etc. Also the QA procedures underwent many changes to reach the high level of quality mandatory to ensure the LHC performance. The specificities of this worksite are underlined and first figures of merit of the learning process are presented

Exact Solution of the Quantum Calogero-Gaudin System and of its q-Deformation

A complete set of commuting observables for the Calogero-Gaudin system is diagonalized, and the explicit form of the corresponding eigenvalues and eigenfunctions is derived. We use a purely algebraic procedure exploiting the co-algebra invariance of the model; with the proper technical modifications this procedure can be applied to the $q-$deformed version of the model, which is then also exactly solved.Comment: 20 pages Late

Clinical implications of discordant early molecular responses in CML patients treated with imatinib

A reduction in BCR-ABL1/ABL1IS transcript levels to <10% after 3 months or <1% after 6 months of tyrosine kinase inhibitor therapy are associated with superior clinical outcomes in chronic myeloid leukemia (CML) patients. In this study, we investigated the reliability of multiple BCR-ABL1 thresholds in predicting treatment outcomes for 184 subjects diagnosed with CML and treated with standard-dose imatinib mesylate (IM). With a median follow-up of 61 months, patients with concordant BCR-ABL1/ABL1IS transcripts below the defined thresholds (10% at 3 months and 1% at 6 months) displayed significantly superior rates of event-free survival (86.1% vs. 26.6%) and deep molecular response (≥ MR4; 71.5% vs. 16.1%) compared to individuals with BCR-ABL1/ABL1IS levels above these defined thresholds. We then analyzed the outcomes of subjects displaying discordant molecular transcripts at 3-and 6-month time points. Among these patients, those with BCR-ABL1/ABL1IS values >10% at 3 months but <1% at 6 months fared significantly better than individuals with BCR-ABL1/ABL1IS <10% at 3 months but >1% at 6 months (event-free survival 68.2% vs. 32.7%; p < 0.001). Likewise, subjects with BCR-ABL1/ABL1IS at 3 months >10% but <1% at 6 months showed a higher cumulative incidence of MR4 compared to patients with BCR-ABL1/ABL1IS <10% at 3 months but >1% at 6 months (75% vs. 18.2%; p < 0.001). Finally, lower BCR-ABL1/GUSIS transcripts at diagnosis were associated with BCR-ABL1/ABL1IS values <1% at 6 months (p < 0.001). Our data suggest that when assessing early molecular responses to therapy, the 6-month BCR-ABL1/ABL1IS level displays a superior prognostic value compared to the 3-month measurement in patients with discordant oncogenic transcripts at these two pivotal time points