Geometric characterization of intermittency in the parabolic Anderson model

We consider the parabolic Anderson problem $\partial_tu=\Delta u+\xi(x)u$ on $\mathbb{R}_+\times\mathbb{Z}^d$ with localized initial condition $u(0,x)=\delta_0(x)$ and random i.i.d. potential $\xi$. Under the assumption that the distribution of $\xi(0)$ has a double-exponential, or slightly heavier, tail, we prove the following geometric characterization of intermittency: with probability one, as $t\to\infty$, the overwhelming contribution to the total mass $\sum_xu(t,x)$ comes from a slowly increasing number of ``islands'' which are located far from each other. These ``islands'' are local regions of those high exceedances of the field $\xi$ in a box of side length $2t\log^2t$ for which the (local) principal Dirichlet eigenvalue of the random operator $\Delta+\xi$ is close to the top of the spectrum in the box. We also prove that the shape of $\xi$ in these regions is nonrandom and that $u(t,\cdot)$ is close to the corresponding positive eigenfunction. This is the geometric picture suggested by localization theory for the Anderson Hamiltonian.Comment: Published at http://dx.doi.org/10.1214/009117906000000764 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

A light life together: photosensing in the plant microbiota

Bacteria and fungi of the plant microbiota can be phytopathogens, parasites or symbionts that establish mutually advantageous relationships with plants. They are often rich in photoreceptors for UVA–Visible light, and in many cases, they exhibit light regulation of growth patterns, infectivity or virulence, reproductive traits, and production of pigments and of metabolites. In addition to the light-driven effects, often demonstrated via the generation of photoreceptor gene knock-outs, microbial photoreceptors can exert effects also in the dark. Interestingly, some fungi switch their attitude towards plants in dependence of illumination or dark conditions in as much as they may be symbiotic or pathogenic. This review summarizes the current knowledge about the roles of light and photoreceptors in plant-associated bacteria and fungi aiming at the identification of common traits and general working ideas. Still, reports on light-driven infection of plants are often restricted to the description of macroscopically observable phenomena, whereas detailed information on the molecular level, e.g., protein–protein interaction during signal transduction or induction mechanisms of infectivity/virulence initiation remains sparse. As it becomes apparent from still only few molecular studies, photoreceptors, often from the red- and the blue light sensitive groups interact and mutually modulate their individual effects. The topic is of great relevance, even in economic terms, referring to plant-pathogen or plant-symbionts interactions, considering the increasing usage of artificial illumination in greenhouses, the possible light-regulation of the synthesis of plant-growth stimulating substances or herbicides by certain symbionts, and the biocontrol of pests by selected fungi and bacteria in a sustainable agriculture

The Lugiato-Lefever equation with nonlinear damping caused by two photon absorption

In this paper we investigate the effect of nonlinear damping on the Lugiato-Lefever equation i∂_t a = −(i − ζ)a − da_{xx} − (1 + iκ)|a|^2 a + if on the torus or the real line. For the case of the torus it is shown that for small nonlinear damping κ > 0 stationary spatially periodic solutions exist on branches that bifurcate from constant solutions whereas all nonconstant solutions disappear when the damping parameter κ exceeds a critical value. These results apply both for normal (d 0) dispersion. For the case of the real line we show by the Implicit Function Theorem that for small nonlinear damping κ > 0 and large detuning ζ >> 1 and large forcing f >> 1 strongly localized, bright solitary stationary solutions exists in the case of anomalous dispersion d > 0. These results are achieved by using techniques from bifurcation and continuation theory and by proving a convergence result for solutions of the time-dependent Lugiato-Lefever equation

The Lugiato-Lefever equation with nonlinear damping caused by two photon absorption

In this paper we investigate the effect of nonlinear damping on the Lugiato-Lefever equation \i \partial_t a = -(\i-\zeta) a - da_{xx} -(1+\i\kappa)|a|^2a +\i f on the torus or the real line. For the case of the torus it is shown that for small nonlinear damping $\kappa>0$ stationary spatially periodic solutions exist on branches that bifurcate from constant solutions whereas all nonconstant solutions disappear when the damping parameter $\kappa$ exceeds a critical value. These results apply both for normal ($d0$) dispersion. For the case of the real line we show by the Implicit Function Theorem that for small nonlinear damping $\kappa>0$ and large detuning $\zeta\gg 1$ and large forcing $f\gg 1$ strongly localized, bright solitary stationary solutions exists in the case of anomalous dispersion $d>0$. These results are achieved by using techniques from bifurcation and continuation theory and by proving a convergence result for solutions of the time-dependent Lugiato-Lefever equation.Comment: 28 pages, 5 figures, 1 tabl

Permafrost biases climate signals in δ18Otree-ring series from a sub-alpine tree stand in Val Bever/Switzerland

During recent decades, stable oxygen isotopes derived from tree-ring cellulose (δ18OTRC) have been frequently utilised as the baseline for palaeoclimatic reconstructions. In this context, numerous studies take advantage of the high sensitivity of trees close to their ecological distribution limit (high elevation or high latitudes). However, this increases the chance that indirect climatic forces such as cold ground induced by permafrost can distort the climate-proxy relationship. In this study, a tree stand of sub-alpine larch trees (Larix decidua Mill.) located in an inner alpine dry valley (Val Bever), Switzerland, was analysed for its δ18OTRC variations during the last 180 years. A total of eight L. decidua trees were analysed on an individual base, half of which are located on verified sporadic permafrost lenses approximately 500 m below the expected lower limit of discontinuous permafrost. The derived isotope time series are strongly dependent on variations in summer temperature, precipitation and large-scale circulation patterns (geopotential height fields). The results demonstrate that trees growing outside of the permafrost distribution provide a significantly stronger and more consistent climate-proxy relationship over time than permafrost-affected tree stands. The climate sensitivity of permafrost-affected trees is analogical to the permafrost-free tree stands (positive and negative correlations with temperature and precipitation, respectively) but attenuated partly leading to a complete loss of significance. In particular, decadal summer temperature variations are well reflected in δ18OTRC from permafrost-free sites (r = 0.62, p 0.05). Since both tree stands are located just a few meters away from one another and are subject to the same climatic influences, discrepancies in the isotope time series can only be attributed to variations in the trees’ source water that constraints the climatic fingerprints on δ18OTRC. If the two individual time series are merged to one local mean chronology, the climatic sensitivity reflects an intermediate between the permafrost-free and –affected δ18OTRC time series. It can be deduced, that a significant loss of information on past climate variations arises by simply averaging both tree stands without prior knowledge of differing subsurface conditions

FRET in a Synthetic Flavin- and Bilin-binding Protein

The last decade has seen development and application of a large number of novel fluorescence-based techniques that have revolutionized fluorescence microscopy in life sciences. Preferred tags for such applications are genetically encoded fluorescent proteins (FP), mostly derivatives of the green fluorescent protein (GFP). Combinations of FPs with wavelength-separated absorption/fluorescence properties serve as excellent tools for molecular interaction studies, for example, protein-protein complexes or enzyme-substrate interactions, based on the FRET phenomenon (Förster resonance energy transfer). However, alternatives are requested for experimental conditions where FP proteins or FP couples are not or less efficiently applicable. We here report as a "proof of principle" a specially designed, non-naturally occurring protein (LG1) carrying a combination of a flavin-binding LOV- and a photochromic bilin-binding GAF domain and demonstrate a FRET process between both chromophores

Bandwidth and conversion efficiency analysis of dissipative Kerr soliton frequency combs based on bifurcation theory

Dissipative Kerr soliton frequency combs generated in high-Q microresonators may unlock novel perspectives in a variety of applications and crucially rely on quantitative models for systematic device design. Here, we present a global bifurcation study of the Lugiato-Lefever equation which describes Kerr comb formation. Our study allows systematic investigation of stationary comb states over a wide range of technically relevant parameters. Quantifying key performance parameters of bright and dark-soliton combs, our findings may serve as a design guideline for Kerr comb generators

Qualitätssicherungsverfahren, Prozess- und Ergebnisqualität an Schulen in Berlin und Brandenburg

Im Mittelpunkt des Berichts des Instituts für Schulqualität der Länder Berlin und Brandenburg (ISQ) stehen die Eckpunkte der Bildungssysteme, wichtige Faktoren der Qualitätssicherung von schulischen Prozessen sowie zentrale Bildungsergebnisse im Verlauf der Schülerkarriere in Berlin und Brandenburg. Dabei präsentiert der Schulqualitätsbericht für Berlin und Brandenburg eine problemorientierte Analyse der Bildungssituation in der Region. Problemorientierung heißt, zentrale Entwicklungen im Bildungswesen für Politik und Öffentlichkeit erkennbar zu machen und möglichen Handlungsbedarf aufzuzeigen, ohne jedoch Wertungen vorzunehmen oder politische Empfehlungen abzugeben. Der vorliegende Bericht verfolgt dasselbe Ziel wie seine Vorgänger (wenn auch in thematisch engerem Rahmen): In der Zusammenstellung relevanter und empirisch gesicherter Daten und Informationen soll ein Beitrag geleistet werden, Diskussionen und Entscheidungen im Bildungsbereich durch die Bereitstellung von (zusätzlichen) Fakten anzureichern

Photocycle of a cyanobacteriochrome: a charge defect on ring C impairs conjugation in chromophore

A large number of novel phytochromes named cyanobacteriochromes (CBCRs) have been recently identified. CBCRs appear to be attractive for further in-depth studies as paradigms for phytochromes because of their related photochemistry, but simpler domain architecture. Elucidating the mechanisms of spectral tuning for the bilin chromophore down to the molecular/atomic level is a prerequisite to design fine-tuned photoswitches for optogenetics. Several explanations for the blue shift during photoproduct formation associated with the red/green CBCRs represented by Slr1393g3 have been developed. There are, however, only sparse mechanistic data concerning the factors controlling stepwise absorbance changes along the reaction pathways from the dark state to the photoproduct and vice versa in this subfamily. Conventional cryotrapping of photocycle intermediates of phytochromes has proven experimentally intractable for solid-state NMR spectroscopy within the probe. Here, we have developed a simple method to circumvent this hindrance by incorporating proteins into trehalose glasses which allows four photocycle intermediates of Slr1393g3 to be isolated for NMR use. In addition to identifying the chemical shifts and chemical shift anisotropy principal values of selective chromophore carbons in various photocycle states, we generated QM/MM models of the dark state and photoproduct as well as of the primary intermediate of the backward-reaction. We find the motion of all three methine bridges in both reaction directions but in different orders. These molecular events channel light excitation to drive distinguishable transformation processes. Our work also suggests that polaronic self-trapping of a conjugation defect by displacement of the counterion during the photocycle would play a role in tuning the spectral properties of both the dark state and photoproduct

Structural elements regulating the photochromicity in a cyanobacteriochrome

The three-dimensional (3D) crystal structures of the GAF3 domain of cyanobacteriochrome Slr1393 (Synechocystis PCC6803) carrying a phycocyanobilin chromophore could be solved in both 15-Z dark-adapted state, Pr, λmax = 649 nm, and 15-E photoproduct, Pg, λmax = 536 nm (resolution, 1.6 and 1.86 Å, respectively). The structural data allowed identifying the large spectral shift of the Pr-to-Pg conversion as resulting from an out-of-plane rotation of the chromophore’s peripheral rings and an outward movement of a short helix formed from a formerly unstructured loop. In addition, a third structure (2.1-Å resolution) starting from the photoproduct crystals allowed identification of elements that regulate the absorption maxima. In this peculiar form, generated during X-ray exposition, protein and chromophore conformation still resemble the photoproduct state, except for the D-ring already in 15-Z configuration and tilted out of plane akin the dark state. Due to its formation from the photoproduct, it might be considered an early conformational change initiating the parental state-recovering photocycle. The high quality and the distinct features of the three forms allowed for applying quantum-chemical calculations in the framework of multiscale modeling to rationalize the absorption maxima changes. A systematic analysis of the PCB chromophore in the presence and absence of the protein environment showed that the direct electrostatic effect is negligible on the spectral tuning. However, the protein forces the outer pyrrole rings of the chromophore to deviate from coplanarity, which is identified as the dominating factor for the color regulation