The Electrostatic Ion Beam Trap : a mass spectrometer of infinite mass range

We study the ions dynamics inside an Electrostatic Ion Beam Trap (EIBT) and show that the stability of the trapping is ruled by a Hill's equation. This unexpectedly demonstrates that an EIBT, in the reference frame of the ions works very similar to a quadrupole trap. The parallelism between these two kinds of traps is illustrated by comparing experimental and theoretical stability diagrams of the EIBT. The main difference with quadrupole traps is that the stability depends only on the ratio of the acceleration and trapping electrostatic potentials, not on the mass nor the charge of the ions. All kinds of ions can be trapped simultaneously and since parametric resonances are proportional to the square root of the charge/mass ratio the EIBT can be used as a mass spectrometer of infinite mass range

Curved Koszul duality theory

38 pagesInternational audienceWe extend the bar-cobar adjunction to operads and properads, not necessarily augmented. Due to the default of augmentation, the objects of the dual category are endowed with a curvature. We handle the lack of augmentation by extending the category of coproperads to include objects endowed with a curvature. As usual, the bar-cobar construction gives a (large) cofibrant resolution for any properad, such as the properad encoding unital and counital Frobenius algebras, a notion which appears in 2d-TQFT. We also define a curved Koszul duality theory for operads or properads presented with quadratic, linear and constant relations, which provides the possibility for smaller relations. We apply this new theory to study the homotopy theory and the cohomology theory of unital associative algebras

Modulated Amplitude Waves and Defect Formation in the One-Dimensional Complex Ginzburg-Landau Equation

The transition from phase chaos to defect chaos in the complex Ginzburg-Landau equation (CGLE) is related to saddle-node bifurcations of modulated amplitude waves (MAWs). First, the spatial period P of MAWs is shown to be limited by a maximum P_SN which depends on the CGLE coefficients; MAW-like structures with period larger than P_SN evolve to defects. Second, slowly evolving near-MAWs with average phase gradients $\nu \approx 0$ and various periods occur naturally in phase chaotic states of the CGLE. As a measure for these periods, we study the distributions of spacings p between neighboring peaks of the phase gradient. A systematic comparison of p and P_SN as a function of coefficients of the CGLE shows that defects are generated at locations where p becomes larger than P_SN. In other words, MAWs with period P_SN represent ``critical nuclei'' for the formation of defects in phase chaos and may trigger the transition to defect chaos. Since rare events where p becomes sufficiently large to lead to defect formation may only occur after a long transient, the coefficients where the transition to defect chaos seems to occur depend on system size and integration time. We conjecture that in the regime where the maximum period P_SN has diverged, phase chaos persists in the thermodynamic limit.Comment: 25 pages, 18 figure

Manin products, Koszul duality, Loday algebras and Deligne conjecture

In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric operads, operads, colored operads, and properads presented by generators and relations. These two products, called black and white, are dual to each other under Koszul duality functor. We study their properties and compute several examples of black and white products for operads. These products allow us to define natural operations on the chain complex defining cohomology theories. With these operations, we are able to prove that Deligne's conjecture holds for a general class of operads and is not specific to the case of associative algebras. Finally, we prove generalized versions of a few conjectures raised by M. Aguiar and J.-L. Loday related to the Koszul property of operads defined by black products. These operads provide infinitely many examples for this generalized Deligne's conjecture.Comment: Final version, a few references adde

The homotopy theory of simplicial props

The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. In this paper, the second in a series on "higher props," we show that the category of all small colored simplicial props admits a cofibrantly generated model category structure. With this model structure, the forgetful functor from props to operads is a right Quillen functor.Comment: Final version, to appear in Israel J. Mat

Backward error analysis and the substitution law for Lie group integrators

Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector spaces. More precisely, they are formal series developments of differential operators indexed over rooted trees, and can be used to represent a large class of numerical methods. The theory of backward error analysis for differential equations has a particularly nice description when applied to methods represented by Butcher series. For the study of differential equations evolving on more general manifolds, a generalization of Butcher series has been introduced, called Lie--Butcher series. This paper presents the theory of backward error analysis for methods based on Lie--Butcher series.Comment: Minor corrections and additions. Final versio

Static and Dynamic Properties of Inhomogeneous Elastic Media on Disordered Substrate

The pinning of an inhomogeneous elastic medium by a disordered substrate is studied analytically and numerically. The static and dynamic properties of a $D$-dimensional system are shown to be equivalent to those of the well known problem of a $D$-dimensional random manifold embedded in $(D+D)$-dimensions. The analogy is found to be very robust, applicable to a wide range of elastic media, including those which are amorphous or nearly-periodic, with local or nonlocal elasticity. Also demonstrated explicitly is the equivalence between the dynamic depinning transition obtained at a constant driving force, and the self-organized, near-critical behavior obtained by a (small) constant velocity drive.Comment: 20 pages, RevTeX. Related (p)reprints also available at http://matisse.ucsd.edu/~hwa/pub.htm

Opposite role of Bax and BCL-2 in the anti-tumoral responses of the immune system

BACKGROUND: The relative role of anti apoptotic (i.e. Bcl-2) or pro-apoptotic (e.g. Bax) proteins in tumor progression is still not completely understood. METHODS: The rat glioma cell line A15A5 was stably transfected with human Bcl-2 and Bax transgenes and the viability of theses cell lines was analyzed in vitro and in vivo. RESULTS: In vitro, the transfected cell lines (huBax A15A5 and huBcl-2 A15A5) exhibited different sensitivities toward apoptotic stimuli. huBax A15A5 cells were more sensitive and huBcl-2 A15A5 cells more resistant to apoptosis than mock-transfected A15A5 cells (pCMV A15A5). However, in vivo, in syngenic rat BDIX, these cell lines behaved differently, as no tumor growth was observed with huBax A15A5 cells while huBcl-2 A15A5 cells formed large tumors. The immune system appeared to be involved in the rejection of huBax A15A5 cells since i) huBax A15A5 cells were tumorogenic in nude mice, ii) an accumulation of CD8+ T-lymphocytes was observed at the site of injection of huBax A15A5 cells and iii) BDIX rats, which had received huBax A15A5 cells developed an immune protection against pCMV A15A5 and huBcl-2 A15A5 cells. CONCLUSIONS: We show that the expression of Bax and Bcl-2 controls the sensitivity of the cancer cells toward the immune system. This sensitization is most likely to be due to an increase in immune induced cell death and/or the amplification of an anti tumour immune respons

Disruption of Dnmt1/PCNA/UHRF1 Interactions Promotes Tumorigenesis from Human and Mice Glial Cells

Global DNA hypomethylation is a hallmark of cancer cells, but its molecular mechanisms have not been elucidated. Here, we show that the disruption of Dnmt1/PCNA/UHRF1 interactions promotes a global DNA hypomethylation in human gliomas. We then demonstrate that the Dnmt1 phosphorylations by Akt and/or PKC abrogate the interactions of Dnmt1 with PCNA and UHRF1 in cellular and acelluar studies including mass spectrometric analyses and the use of primary cultured patient-derived glioma. By using methylated DNA immunoprecipitation, methylation and CGH arrays, we show that global DNA hypomethylation is associated with genes hypomethylation, hypomethylation of DNA repeat element and chromosomal instability. Our results reveal that the disruption of Dnmt1/PCNA/UHRF1 interactions acts as an oncogenic event and that one of its signatures (i.e. the low level of mMTase activity) is a molecular biomarker associated with a poor prognosis in GBM patients. We identify the genetic and epigenetic alterations which collectively promote the acquisition of tumor/glioma traits by human astrocytes and glial progenitor cells as that promoting high proliferation and apoptosis evasion