Optimality program in segment and string graphs

Planar graphs are known to allow subexponential algorithms running in time $2^{O(\sqrt n)}$ or $2^{O(\sqrt n \log n)}$ for most of the paradigmatic problems, while the brute-force time $2^{\Theta(n)}$ is very likely to be asymptotically best on general graphs. Intrigued by an algorithm packing curves in $2^{O(n^{2/3}\log n)}$ by Fox and Pach [SODA'11], we investigate which problems have subexponential algorithms on the intersection graphs of curves (string graphs) or segments (segment intersection graphs) and which problems have no such algorithms under the ETH (Exponential Time Hypothesis). Among our results, we show that, quite surprisingly, 3-Coloring can also be solved in time $2^{O(n^{2/3}\log^{O(1)}n)}$ on string graphs while an algorithm running in time $2^{o(n)}$ for 4-Coloring even on axis-parallel segments (of unbounded length) would disprove the ETH. For 4-Coloring of unit segments, we show a weaker ETH lower bound of $2^{o(n^{2/3})}$ which exploits the celebrated Erd\H{o}s-Szekeres theorem. The subexponential running time also carries over to Min Feedback Vertex Set but not to Min Dominating Set and Min Independent Dominating Set.Comment: 19 pages, 15 figure

Localized instabilities of the Wigner equation as a model for the emergence of Rogue Waves

In this paper, we model Rogue Waves as localized instabilities emerging from homogeneous and stationary background wavefields, under NLS dynamics. This is achieved in two steps: given any background Fourier spectrum P(k), we use the Wigner transform and Penrose’s method to recover spatially periodic unstable modes, which we call unstable Penrose modes. These can be seen as generalized Benjamin–Feir modes, and their parameters are obtained by resolving the Penrose condition, a system of nonlinear equations involving P(k). Moreover, we show how the superposition of unstable Penrose modes can result in the appearance of localized unstable modes. By interpreting the appearance of an unstable mode localized in an area not larger than a reference wavelength λ0 as the emergence of a Rogue Wave, a criterion for the emergence of Rogue Waves is formulated. Our methodology is applied to δ spectra, where the standard Benjamin–Feir instability is recovered, and to more general spectra. In that context, we present a scheme for the numerical resolution of the Penrose condition and estimate the sharpest possible localization of unstable modes. Keywords: Rogue Waves; Wigner equation; Nonlinear Schrodinger equation; Penrose modes; Penrose conditio

Nonlinear wave interaction in coastal and open seas -- deterministic and stochastic theory

We review the theory of wave interaction in finite and infinite depth. Both of these strands of water-wave research begin with the deterministic governing equations for water waves, from which simplified equations can be derived to model situations of interest, such as the mild slope and modified mild slope equations, the Zakharov equation, or the nonlinear Schr\"odinger equation. These deterministic equations yield accompanying stochastic equations for averaged quantities of the sea-state, like the spectrum or bispectrum. We discuss several of these in depth, touching on recent results about the stability of open ocean spectra to inhomogeneous disturbances, as well as new stochastic equations for the nearshore

FcγRIa–γ-chain complexes trigger antibody-dependent cell-mediated cytotoxicity (ADCC) in CD5+ B cell/macrophage IIA1.6 cells

Most receptors for immunoglobulins exist as multi-subunit complexes, with unique ligand binding α-chains, combined with accessory signalling (γ-, β-, or ζ-) chains. The myeloid class I receptor for IgG (FcγRIa) has been shown to be dependent on the FcR γ-chain for surface expression in vivo. In this study we assess the capacity of FcγRIa–γ-chain complexes expressed in IIA1.6 cells to trigger phagocytosis and ADCC. An intact immunoreceptor tyrosine-based activation motif (ITAM) signalling motif proved essential for triggering of biological function via the FcγRIa receptor complex. Both the FcR γ-chain and the FcγRIIa–ITAM proved active in directing phagocytosis of Staphylococcus aureus and ADCC of erythrocytes, triggered by the FcγRIa complex. The capacity of FcγRIa to trigger phagocytic and cytolytic activity by IIA1.6 cells, both considered ‘professional phagocyte’ functions, motivated us to re-evaluate the cell lineage and developmental stage of IIA1.6 cells. Although originally described as mouse B lymphocytes, the IIA1.6 cells proved positive for non-specific esterase activity and expressed the CD5 antigen. These combined characteristics place the IIA1.6 cells within a unique CD5+ B cell/macrophage lineage, optimally suited for cell biological analyses of phagocyte receptors

Immunoproteasome dysfunction augments alternative polarization of alveolar macrophages.

The proteasome is a central regulatory hub for intracellular signaling by degrading numerous signaling mediators. Immunoproteasomes are specialized types of proteasomes involved in shaping adaptive immune responses, but their role in innate immune signaling is still elusive. Here, we analyzed immunoproteasome function for polarization of alveolar macrophages, highly specialized tissue macrophages of the alveolar lung surface. Classical activation (M1 polarization) of primary alveolar macrophages by LPS/IFNγ transcriptionally induced all three immunoproteasome subunits, low molecular mass protein 2 (LMP2), LMP7 and multicatalytic endopeptidase complex-like 1, which was accompanied by increased immunoproteasome activity in M1 cells. Deficiency of LMP7 had no effect on the LPS/IFNγ-triggered M1 profile indicating that immunoproteasome function is dispensable for classical alveolar macrophage activation. In contrast, IL-4 triggered alternative (M2) activation of primary alveolar macrophages was accompanied by a transcriptionally independent amplified expression of LMP2 and LMP7 and an increase in immunoproteasome activity. Alveolar macrophages from LMP7 knockout mice disclosed a distorted M2 profile upon IL-4 stimulation as characterized by increased M2 marker gene expression and CCL17 cytokine release. Comparative transcriptome analysis revealed enrichment of IL-4-responsive genes and of genes involved in cellular response to defense, wounding and inflammation in LMP7-deficient alveolar macrophages indicating a distinct M2 inflammation resolving phenotype. Moreover, augmented M2 polarization was accompanied by amplified AKT/STAT6 activation and increased RNA and protein expression of the M2 master transcription factor interferon regulatory factor 4 in LMP7(-/-) alveolar macrophages. IL-13 stimulation of LMP7-deficient macrophages induced a similar M2-skewed profile indicative for augmented signaling via the IL-4 receptor α (IL4Rα). IL4Rα expression was generally elevated only on protein but not RNA level in LMP7(-/-) alveolar macrophages. Importantly, specific catalytic inhibition with an LMP7-specific proteasome inhibitor confirmed augmented IL-4-mediated M2 polarization of alveolar macrophages. Our results thus suggest a novel role of immunoproteasome function for regulating alternative activation of macrophages by limiting IL4Rα expression and signaling