Divided Differences & Restriction Operator on Paley-Wiener Spaces PWtaupPW_{tau}^{p} for N−N-Carleson Sequences

For a sequence of complex numbers $\Lambda$ we consider the restriction operator $R_{\Lambda}$ defined on Paley-Wiener spaces $PW_{\tau}^{p}$ ($1<p<\infty$). Lyubarskii and Seip gave necessary and sufficient conditions on $\Lambda$ for $R_{\Lambda}$ to be an isomorphism between $PW_{\tau}^{p}$ and a certain weighted $l^{p}$ space. The Carleson condition appears to be necessary. We extend their result to $N-$Carleson sequences (finite unions of $N$ disjoint Carleson sequences). More precisely, we give necessary and sufficient conditions for $R_{\Lambda}$ to be an isomorphism between $PW_{\tau}^{p}$ and an appropriate sequence space involving divided differences

Global long terminal repeat activation participates in establishing the unique gene expression programme of classical Hodgkin lymphoma

Long terminal repeat (LTR) elements are wide-spread in the human genome and have the potential to act as promoters and enhancers. Their expression is therefore under tight epigenetic control. We previously reported in classical Hodgkin Lymphoma (cHL) that a member of the THE1B class of LTR elements acted as a promoter for the proto-oncogene and growth factor receptor gene CSF1R and that expression of this gene is required for cHL tumour survival. However, to which extent and how such elements participate in globally shaping the unique cHL gene expression programme is unknown. To address this question we mapped the genome-wide activation of THE1-LTRs in cHL cells using a targeted next generation sequencing approach (RACE-Seq). Integration of these data with global gene expression data from cHL and control B cell lines showed a unique pattern of LTR activation impacting on gene expression, including genes associated with the cHL phenotype. We also show that global LTR activation is induced by strong inflammatory stimuli. Together these results demonstrate that LTR activation provides an additional layer of gene deregulation in classical Hodgkin lymphoma and highlight the potential impact of genome-wide LTR activation in other inflammatory diseases

Space as a low-temperature regime of graphs

I define a statistical model of graphs in which 2-dimensional spaces arise at low temperature. The configurations are given by graphs with a fixed number of edges and the Hamiltonian is a simple, local function of the graphs. Simulations show that there is a transition between a low-temperature regime in which the graphs form triangulations of 2-dimensional surfaces and a high-temperature regime, where the surfaces disappear. I use data for the specific heat and other observables to discuss whether this is a phase transition. The surface states are analyzed with regard to topology and defects.Comment: 22 pages, 12 figures; v3: published version; J.Stat.Phys. 201

Kinetic model of II-VI(001) semiconductor surfaces: Growth rates in atomic layer epitaxy

We present a zinc-blende lattice gas model of II-VI(001) surfaces, which is investigated by means of Kinetic Monte Carlo (KMC) simulations. Anisotropic effective interactions between surface metal atoms allow for the description of, e.g., the sublimation of CdTe(001), including the reconstruction of Cd-terminated surfaces and its dependence on the substrate temperature T. Our model also includes Te-dimerization and the potential presence of excess Te in a reservoir of weakly bound atoms at the surface. We study the self-regulation of atomic layer epitaxy (ALE) and demonstrate how the interplay of the reservoir occupation with the surface kinetics results in two different regimes: at high T the growth rate is limited to 0.5 layers per ALE cycle, whereas at low enough T each cycle adds a complete layer of CdTe. The transition between the two regimes occurs at a characteristic temperature and its dependence on external parameters is studied. Comparing the temperature dependence of the ALE growth rate in our model with experimental results for CdTe we find qualitative agreement.Comment: 9 pages (REVTeX), 8 figures (EPS). Content revised, references added, typos correcte

Hole dynamics and photoemission in a t-J model for SrCu_2(BO_3)_2

The motion of a single hole in a t-J model for the two-dimensional spin-gap compound SrCu_2(BO_3)_2 is investigated. The undoped Heisenberg model for this system has an exact dimer eigenstate and shows a phase transition between a dimerized and a Neel phase at a certain ratio of the magnetic couplings. We calculate the photoemission spectrum in the disordered phase using a generalized spin-polaron picture. By varying the inter-dimer hopping parameters we find a cross-over between a narrow quasiparticle band regime known from other strongly correlated systems and free-fermion behavior. The hole motion in the Neel-ordered phase is also briefly considered.Comment: 4 pages, 3 fig

Energetics and Possible Formation and Decay Mechanisms of Vortices in Helium Nanodroplets

The energy and angular momentum of both straight and curved vortex states of a helium nanodroplet are examined as a function of droplet size. For droplets in the size range of many experiments, it is found that during the pickup of heavy solutes, a significant fraction of events deposit sufficient energy and angular momentum to form a straight vortex line. Curved vortex lines exist down to nearly zero angular momentum and energy, and thus could in principle form in almost any collision. Further, the coalescence of smaller droplets during the cooling by expansion could also deposit sufficient angular momentum to form vortex lines. Despite their high energy, most vortices are predicted to be stable at the final temperature (0.38 K) of helium nanodroplets due to lack of decay channels that conserve both energy and angular momentum.Comment: 10 pages, 8 figures, RevTex 4, submitted to Phys. Rev.

The discontinuous nature of chromospheric activity evolution

Chromospheric activity has been thought to decay smoothly with time and, hence, to be a viable age indicator. Measurements in solar type stars in open clusters seem to point to a different conclusion: chromospheric activity undergoes a fast transition from Hyades level to that of the Sun after about 1 Gyr of main--sequence lifetime and any decaying trend before or after this transition must be much less significant than the short term variations.Comment: 6 pages, 1 figure, to be published in Astrophysics and Space Scienc

Steering of a Bosonic Mode with a Double Quantum Dot

We investigate the transport and coherence properties of a double quantum dot coupled to a single damped boson mode. Our numerically results reveal how the properties of the boson distribution can be steered by altering parameters of the electronic system such as the energy difference between the dots. Quadrature amplitude variances and the Wigner function are employed to illustrate how the state of the boson mode can be controlled by a stationary electron current through the dots.Comment: 10 pages, 6 figures, to appear in Phys. Rev.

Variance of transmitted power in multichannel dissipative ergodic structures invariant under time reversal

We use random matrix theory (RMT) to study the first two moments of the wave power transmitted in time reversal invariant systems having ergodic motion. Dissipation is modeled by a number of loss channels of variable coupling strength. To make a connection with ultrasonic experiments on ergodic elastodynamic billiards, the channels injecting and collecting the waves are assumed to be negligibly coupled to the medium, and to contribute essentially no dissipation. Within the RMT model we calculate the quantities of interest exactly, employing the supersymmetry technique. This approach is found to be more accurate than another method based on simplifying naive assumptions for the statistics of the eigenfrequencies and the eigenfunctions. The results of the supersymmetric method are confirmed by Monte Carlo numerical simulation and are used to reveal a possible source of the disagreement between the predictions of the naive theory and ultrasonic measurements.Comment: 10 pages, 2 figure