Stability of Relative Equilibria of Point Vortices on a Sphere and Symplectic Integrators

This paper analyzes the dynamics of N point vortices moving on a sphere from the point of view of geometric mechanics. The formalism is developed for the general case of N vortices, and the details are provided for the (integrable) case N = 3. Stability of relative equilibria is analyzed by the energy-momentum method. Explicit criteria for stability of different configurations with generic and non-generic momenta are obtained. In each case, a group of transformations is specied, such that motion in the original (unreduced) phase space is stable modulo this group. Finally, we outline the construction of a symplectic-momentum integrator for vortex dynamics on a sphere

Relative periodic orbits in point vortex systems

We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is applied to point vortices systems on a sphere and on the plane, but works for other surfaces with isotropy (cylinder, ellipsoid, ...). The method permits also to determine some relative equilibria and heteroclinic cycles connecting these relative equilibria.Comment: 27 pages, 17 figure

The possibility of a metal insulator transition in antidot arrays induced by an external driving

It is shown that a family of models associated with the kicked Harper model is relevant for cyclotron resonance experiments in an antidot array. For this purpose a simplified model for electronic motion in a related model system in presence of a magnetic field and an AC electric field is developed. In the limit of strong magnetic field it reduces to a model similar to the kicked Harper model. This model is studied numerically and is found to be extremely sensitive to the strength of the electric field. In particular, as the strength of the electric field is varied a metal -- insulator transition may be found. The experimental conditions required for this transition are discussed.Comment: 6 files: kharp.tex, fig1.ps fig2.ps fi3.ps fig4.ps fig5.p

Strictly Toral Dynamics

This article deals with nonwandering (e.g. area-preserving) homeomorphisms of the torus $\mathbb{T}^2$ which are homotopic to the identity and strictly toral, in the sense that they exhibit dynamical properties that are not present in homeomorphisms of the annulus or the plane. This includes all homeomorphisms which have a rotation set with nonempty interior. We define two types of points: inessential and essential. The set of inessential points $ine(f)$ is shown to be a disjoint union of periodic topological disks ("elliptic islands"), while the set of essential points $ess(f)$ is an essential continuum, with typically rich dynamics (the "chaotic region"). This generalizes and improves a similar description by J\"ager. The key result is boundedness of these "elliptic islands", which allows, among other things, to obtain sharp (uniform) bounds of the diffusion rates. We also show that the dynamics in $ess(f)$ is as rich as in $\mathbb{T}^2$ from the rotational viewpoint, and we obtain results relating the existence of large invariant topological disks to the abundance of fixed points.Comment: Incorporates suggestions and corrections by the referees. To appear in Inv. Mat

Gene expression and splicing alterations analyzed by high throughput RNA sequencing of chronic lymphocytic leukemia specimens.

BackgroundTo determine differentially expressed and spliced RNA transcripts in chronic lymphocytic leukemia specimens a high throughput RNA-sequencing (HTS RNA-seq) analysis was performed.MethodsTen CLL specimens and five normal peripheral blood CD19+ B cells were analyzed by HTS RNA-seq. The library preparation was performed with Illumina TrueSeq RNA kit and analyzed by Illumina HiSeq 2000 sequencing system.ResultsAn average of 48.5 million reads for B cells, and 50.6 million reads for CLL specimens were obtained with 10396 and 10448 assembled transcripts for normal B cells and primary CLL specimens respectively. With the Cuffdiff analysis, 2091 differentially expressed genes (DEG) between B cells and CLL specimens based on FPKM (fragments per kilobase of transcript per million reads and false discovery rate, FDR q < 0.05, fold change >2) were identified. Expression of selected DEGs (n = 32) with up regulated and down regulated expression in CLL from RNA-seq data were also analyzed by qRT-PCR in a test cohort of CLL specimens. Even though there was a variation in fold expression of DEG genes between RNA-seq and qRT-PCR; more than 90 % of analyzed genes were validated by qRT-PCR analysis. Analysis of RNA-seq data for splicing alterations in CLL and B cells was performed by Multivariate Analysis of Transcript Splicing (MATS analysis). Skipped exon was the most frequent splicing alteration in CLL specimens with 128 significant events (P-value <0.05, minimum inclusion level difference >0.1).ConclusionThe RNA-seq analysis of CLL specimens identifies novel DEG and alternatively spliced genes that are potential prognostic markers and therapeutic targets. High level of validation by qRT-PCR for a number of DEG genes supports the accuracy of this analysis. Global comparison of transcriptomes of B cells, IGVH non-mutated CLL (U-CLL) and mutated CLL specimens (M-CLL) with multidimensional scaling analysis was able to segregate CLL and B cell transcriptomes but the M-CLL and U-CLL transcriptomes were indistinguishable. The analysis of HTS RNA-seq data to identify alternative splicing events and other genetic abnormalities specific to CLL is an added advantage of RNA-seq that is not feasible with other genome wide analysis

Telomerase activity, apoptosis and cell cycle progression in ataxia telangiectasia lymphocytes expressing TCL1

Individuals affected by ataxia telangiectasia (AT) have a marked susceptibility to cancer. Ataxia telangiectasia cells, in addition to defects in cell cycle checkpoints, show dysfunction of apoptosis and of telomeres, which are both thought to have a role in the progression of malignancy. In 1-5% of patients with AT, clonal expansion of T lymphocytes carrying t(14;14) chromosomal translocation, deregulating TCL1 gene(s), has been described. While it is known that these cells can progress with time to a frank leukaemia, the molecular pathway leading to tumorigenesis has not yet been fully investigated. In this study, we compared AT clonal cells, representing 88% of the entire T lymphocytes (AT94-1) and expressing TCL1 oncogene (ATM- TCL1 +), cell cycle progression to T lymphocytes of AT patients without TCL1 expression (ATM- TCL1-) by analysing their spontaneous apoptosis rate, spontaneous telomerase activity and telomere instability. We show that in ATM- TCL1+ lymphocytes, apoptosis rate and cell cycle progression are restored back to a rate comparable with that observed in normal lymphocytes while telomere dysfunction is maintained. © 2003 Cancer Research UK

The nuclear orphan receptor Nr4a2 induces Foxp3 and regulates differentiation of CD4+ T cells

Regulatory T cells (Tregs) have a central role in maintaining immune homoeostasis through various mechanisms. Although the Forkhead transcription factor Foxp3 defines the Treg cell lineage and functions, the molecular mechanisms of Foxp3 induction and maintenance remain elusive. Here we show that Foxp3 is one of the direct targets of Nr4a2. Nr4a2 binds to regulatory regions of Foxp3, where it mediates permissive histone modifications. Ectopic expression of Nr4a2 imparts Treg-like suppressive activity to naïve CD4+ T cells by inducing Foxp3 and by repressing cytokine production, including interferon-γ and interleukin-2. Deletion of Nr4a2 in T cells attenuates induction of Tregs and causes aberrant induction of Th1, leading to the exacerbation of colitis. Nr4a2-deficeint Tregs are prone to lose Foxp3 expression and have attenuated suppressive ability both in vitro and in vivo. Thus, Nr4a2 has the ability to maintain T-cell homoeostasis by regulating induction, maintenance and suppressor functions of Tregs, and by repression of aberrant Th1 induction

Coordinated Silencing of MYC-Mediated miR-29 by HDAC3 and EZH2 as a Therapeutic Target of Histone Modification in Aggressive B-Cell Lymphomas

We investigated the transcriptional and epigenetic repression of miR-29 by MYC, HDAC3, and EZH2 in mantle cell lymphoma and other MYC-associated lymphomas. We demonstrate that miR-29 is repressed by MYC through a corepressor complex with HDAC3 and EZH2. MYC contributes to EZH2 upregulation via repression of the EZH2 targeting miR-26a, and EZH2 induces MYC via inhibition of the MYC targeting miR-494 to create positive feedback. Combined inhibition of HDAC3 and EZH2 cooperatively disrupted the MYC-EZH2-miR-29 axis, resulting in restoration of miR-29 expression, downregulation of miR-29-targeted genes, and lymphoma growth suppression in vitro and in vivo. These findings define a MYC-mediated miRNA repression mechanism, shed light on MYC lymphomagenesis mechanisms, and reveal promising therapeutic targets for aggressive B-cell malignancies