Mode signature and stability for a Hamiltonian model of electron temperature gradient turbulence

Stability properties and mode signature for equilibria of a model of electron temperature gradient (ETG) driven turbulence are investigated by Hamiltonian techniques. After deriving the infinite families of Casimir invariants, associated with the noncanonical Poisson bracket of the model, a sufficient condition for stability is obtained by means of the Energy-Casimir method. Mode signature is then investigated for linear motions about homogeneous equilibria. Depending on the sign of the equilibrium "translated" pressure gradient, stable equilibria can either be energy stable, i.e.\ possess definite linearized perturbation energy (Hamiltonian), or spectrally stable with the existence of negative energy modes (NEMs). The ETG instability is then shown to arise through a Kre\u{\i}n-type bifurcation, due to the merging of a positive and a negative energy mode, corresponding to two modified drift waves admitted by the system. The Hamiltonian of the linearized system is then explicitly transformed into normal form, which unambiguously defines mode signature. In particular, the fast mode turns out to always be a positive energy mode (PEM), whereas the energy of the slow mode can have either positive or negative sign

On Krein-like theorems for noncanonical Hamiltonian systems with continuous spectra: application to Vlasov-Poisson

The notions of spectral stability and the spectrum for the Vlasov-Poisson system linearized about homogeneous equilibria, f_0(v), are reviewed. Structural stability is reviewed and applied to perturbations of the linearized Vlasov operator through perturbations of f_0. We prove that for each f_0 there is an arbitrarily small delta f_0' in W^{1,1}(R) such that f_0+delta f_0$is unstable. When$f_0$ is perturbed by an area preserving rearrangement, f_0 will always be stable if the continuous spectrum is only of positive signature, where the signature of the continuous spectrum is defined as in previous work. If there is a signature change, then there is a rearrangement of f_0 that is unstable and arbitrarily close to f_0 with f_0' in W^{1,1}. This result is analogous to Krein's theorem for the continuous spectrum. We prove that if a discrete mode embedded in the continuous spectrum is surrounded by the opposite signature there is an infinitesimal perturbation in C^n norm that makes f_0 unstable. If f_0 is stable we prove that the signature of every discrete mode is the opposite of the continuum surrounding it.Comment: Submitted to the journal Transport Theory and Statistical Physics. 36 pages, 12 figure

Absorbing boundary conditions for the Westervelt equation

The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is pseudo-differential calculus. This approach enables to develop high order boundary conditions in a consistent way which are typically more accurate than their low order analogs. Under the hypothesis of small initial data, we establish local well-posedness for the Westervelt equation with the absorbing boundary conditions. The performed numerical experiments illustrate the efficiency of the proposed boundary conditions for different regimes of wave propagation

Criticality Analysis of Activity Networks under Interval Uncertainty

Dedicated to the memory of Professor Stefan Chanas - The extended abstract version of this paper has appeared in Proceedings of 11th International Conference on Principles and Practice of Constraint Programming (CP2005) ("Interval Analysis in Scheduling", Fortin et al. 2005)International audienceThis paper reconsiders the Project Evaluation and Review Technique (PERT) scheduling problem when information about task duration is incomplete. We model uncertainty on task durations by intervals. With this problem formulation, our goal is to assert possible and necessary criticality of the different tasks and to compute their possible earliest starting dates, latest starting dates, and floats. This paper combines various results and provides a complete solution to the problem. We present the complexity results of all considered subproblems and efficient algorithms to solve them

Initiator Elements Function to Determine the Activity State of BX-C Enhancers

A >300 kb cis-regulatory region is required for the proper expression of the three bithorax complex (BX-C) homeotic genes. Based on genetic and transgenic analysis, a model has been proposed in which the numerous BX-C cis-regulatory elements are spatially restricted through the activation or repression of parasegment-specific chromatin domains. Particular early embryonic enhancers, called initiators, have been proposed to control this complex process. Here, in order to better understand the process of domain activation, we have undertaken a systematic in situ dissection of the iab-6 cis-regulatory domain using a new method, called InSIRT. Using this method, we create and genetically characterize mutations affecting iab-6 function, including mutations specifically modifying the iab-6 initiator. Through our mutagenesis of the iab-6 initiator, we provide strong evidence that initiators function not to directly control homeotic gene expression but rather as domain control centers to determine the activity state of the enhancers and silencers within a cis-regulatory domain

RAD21 Cooperates with Pluripotency Transcription Factors in the Maintenance of Embryonic Stem Cell Identity

For self-renewal, embryonic stem cells (ESCs) require the expression of specific transcription factors accompanied by a particular chromosome organization to maintain a balance between pluripotency and the capacity for rapid differentiation. However, how transcriptional regulation is linked to chromosome organization in ESCs is not well understood. Here we show that the cohesin component RAD21 exhibits a functional role in maintaining ESC identity through association with the pluripotency transcriptional network. ChIP-seq analyses of RAD21 reveal an ESC specific cohesin binding pattern that is characterized by CTCF independent co-localization of cohesin with pluripotency related transcription factors Oct4, Nanog, Sox2, Esrrb and Klf4. Upon ESC differentiation, most of these binding sites disappear and instead new CTCF independent RAD21 binding sites emerge, which are enriched for binding sites of transcription factors implicated in early differentiation. Furthermore, knock-down of RAD21 causes expression changes that are similar to expression changes after Nanog depletion, demonstrating the functional relevance of the RAD21 - pluripotency transcriptional network association. Finally, we show that Nanog physically interacts with the cohesin or cohesin interacting proteins STAG1 and WAPL further substantiating this association. Based on these findings we propose that a dynamic placement of cohesin by pluripotency transcription factors contributes to a chromosome organization supporting the ESC expression program

The Caravan Rolls On

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68409/2/10.1177_107554707900100103.pd

Chromosomal organization at the level of gene complexes

Metazoan genomes primarily consist of non-coding DNA in comparison to coding regions. Non-coding fraction of the genome contains cis-regulatory elements, which ensure that the genetic code is read properly at the right time and space during development. Regulatory elements and their target genes define functional landscapes within the genome, and some developmentally important genes evolve by keeping the genes involved in specification of common organs/tissues in clusters and are termed gene complex. The clustering of genes involved in a common function may help in robust spatio-temporal gene expression. Gene complexes are often found to be evolutionarily conserved, and the classic example is the hox complex. The evolutionary constraints seen among gene complexes provide an ideal model system to understand cis and trans-regulation of gene function. This review will discuss the various characteristics of gene regulatory modules found within gene complexes and how they can be characterized

Association between Acquired Uniparental Disomy and Homozygous Mutations and HER2/ER/PR Status in Breast Cancer

Background: Genetic alterations in cellular signaling networks are a hallmark of cancer, however, effective methods to discover them are lacking. A novel form of abnormality called acquired uniparental disomy (aUPD) was recently found to pinpoint the region of mutated genes in various cancers, thereby identifying the region for next-generation sequencing. Methods/Principal Findings: We retrieved large genomic data sets from the Gene Expression Omnibus database to perform genome-wide analysis of aUPD in breast tumor samples and cell lines using approaches that can reliably detect aUPD. Aupd was identified in 52.29% of the tumor samples. The most frequent aUPD regions were located at chromosomes 2q, 3p, 5q, 9p, 9q, 10q, 11q, 13q, 14q and 17q. We evaluated the data for any correlation between the most frequent aUPD regions and HER2/neu, ER, and PR status, and found a statistically significant correlation between the recurrent regions of aUPD and triple negative (TN) breast cancers. aUPD at chromosome 17q (VEZF1, WNT3), 3p (SUMF1, GRM7), 9p (MTAP, NFIB) and 11q (CASP1, CASP4, CASP5) are predictors for TN. The frequency of aUPD was found to be significantly higher in TN breast cancer cases compared to HER2/neu-positive and/or ER or PR-positive cases. Furthermore, using previously published mutation data, we found TP53 homozygously mutated in cell lines having aUPD in that locus. Conclusions/Significance: We conclude that aUPD is a common and non-random molecular feature of breast cancer that is most prominent in triple negative cases. As aUPD regions are different among the main pathological subtypes, specific aUPD regions may aid the sub-classification of breast cancer. In addition, we provide statistical support using TP53 as an example that identifying aUPD regions can be an effective approach in finding aberrant genes. We thus conclu