Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings

We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and Neumann boundary conditions, respectively, at a selected vertex called root. The root is either the central vertex or, in the more challenging problem, a pendant vertex of the star graph. At all other pendant vertices Dirichlet conditions are imposed; at the central vertex, at which a mass may be placed, continuity and Kirchhoff conditions are assumed. We derive conditions on two sets of real numbers to be the spectra of the above Dirichlet and Neumann problems. Our solution for the inverse problems is constructive: we establish algorithms to recover the mass distribution on the star graph (i.e. the point masses and lengths of subintervals between them) from these two spectra and from the lengths of the separate strings. If the root is a pendant vertex, the two spectra uniquely determine the parameters on the main string (i.e. the string incident to the root) if the length of the main string is known. The mass distribution on the other edges need not be unique; the reason for this is the non-uniqueness caused by the non-strict interlacing of the given data in the case when the root is the central vertex. Finally, we relate of our results to tree-patterned matrix inverse problems.

Inverse modelling of the 14C bomb pulse in stalagmites to constrain the dynamics of soil carbon cycling at selected European cave sites

The decomposition of soil organic matter (SOM) is temperature dependent, but its response to a future warmer climate remains equivocal. Enhanced rates of decomposition of SOM under increased global temperatures might cause higher CO2 emissions to the atmosphere, and could therefore constitute a strong positive feedback. The magnitude of this feedback however remains poorly understood, primarily because of the difficulty in quantifying the temperature sensitivity of stored, recalcitrant carbon that comprises the bulk (>90%) of SOM in most soils. In this study we investigated the effects of climatic conditions on soil carbon dynamics using the attenuation of the 14C ‘bomb’ pulse as recorded in selected modern European speleothems. These new data were combined with published results to further examine soil carbon dynamics, and to explore the sensitivity of labile and recalcitrant organic matter decomposition to different climatic conditions. Temporal changes in 14C activity inferred from each speleothem was modelled using a three pool soil carbon inverse model (applying a Monte Carlo method) to constrain soil carbon turnover rates at each site. Speleothems from sites that are characterised by semi-arid conditions, sparse vegetation, thin soil cover and high mean annual air temperatures (MAATs), exhibit weak attenuation of atmospheric 14C ‘bomb’ peak (a low damping effect, D in the range: 55–77%) and low modelled mean respired carbon ages (MRCA), indicating that decomposition is dominated by young, recently fixed soil carbon. By contrast, humid and high MAAT sites that are characterised by a thick soil cover and dense, well developed vegetation, display the highest damping effect (D = c. 90%), and the highest MRCA values (in the range from 350 ± 126 years to 571 ± 128 years). This suggests that carbon incorporated into these stalagmites originates predominantly from decomposition of old, recalcitrant organic matter. SOM turnover rates cannot be ascribed to a single climate variable, e.g. (MAAT) but instead reflect a complex interplay of climate (e.g. MAAT and moisture budget) and vegetation development.

Modulation of orientation-selective neurons by motion: when additive, when multiplicative?

The recurrent interaction among orientation-selective neurons in the primary visual cortex (V1) is suited to enhance contours in a noisy visual scene. Motion is known to have a strong pop-up effect in perceiving contours, but how motion-sensitive neurons in V1 support contour detection remains vastly elusive. Here we suggest how the various types of motion-sensitive neurons observed in V1 should be wired together in a micro-circuitry to optimally extract contours in the visual scene. Motion-sensitive neurons can be selective about the direction of motion occurring at some spot or respond equally to all directions (pandirectional). We show that, in the light of figure-ground segregation, direction-selective motion neurons should additively modulate the corresponding orientation-selective neurons with preferred orientation orthogonal to the motion direction. In turn, to maximally enhance contours, pandirectional motion neurons should multiplicatively modulate all orientation-selective neurons with co-localized receptive fields. This multiplicative modulation amplifies the local V1-circuitry among co-aligned orientation-selective neurons for detecting elongated contours. We suggest that the additive modulation by direction-specific motion neurons is achieved through synaptic projections to the somatic region, and the multiplicative modulation by pandirectional motion neurons through projections to the apical region of orientation-specific pyramidal neurons. For the purpose of contour detection, the V1-intrinsic integration of motion information is advantageous over a downstream integration as it exploits the recurrent V1-circuitry designed for that task.

Inverse fusion PCR cloning.

Inverse fusion PCR cloning (IFPC) is an easy, PCR based three-step cloning method that allows the seamless and directional insertion of PCR products into virtually all plasmids, this with a free choice of the insertion site. The PCR-derived inserts contain a vector-complementary 5'-end that allows a fusion with the vector by an overlap extension PCR, and the resulting amplified insert-vector fusions are then circularized by ligation prior transformation. A minimal amount of starting material is needed and experimental steps are reduced. Untreated circular plasmid, or alternatively bacteria containing the plasmid, can be used as templates for the insertion, and clean-up of the insert fragment is not urgently required. The whole cloning procedure can be performed within a minimal hands-on time and results in the generation of hundreds to ten-thousands of positive colonies, with a minimal background.

The inverse problem for Schwinger pair production

The production of electron–positron pairs in time-dependent electric fields (Schwinger mechanism) depends non-linearly on the applied field profile. Accordingly, the resulting momentum spectrum is extremely sensitive to small variations of the field parameters. Owing to this non-linear dependence it is so far unpredictable how to choose a field configuration such that a predetermined momentum distribution is generated. We show that quantum kinetic theory along with optimal control theory can be used to approximately solve this inverse problem for Schwinger pair production. We exemplify this by studying the superposition of a small number of harmonic components resulting in predetermined signatures in the asymptotic momentum spectrum. In the long run, our results could facilitate the observation of this yet unobserved pair production mechanism in quantum electrodynamics by providing suggestions for tailored field configurations.

Validation of the Swiss methane emission inventory by atmospheric observations and inverse modelling

Atmospheric inverse modelling has the potential to provide observation-based estimates of greenhouse gas emissions at the country scale, thereby allowing for an independent validation of national emission inventories. Here, we present a regional-scale inverse modelling study to quantify the emissions of methane (CH₄) from Switzerland, making use of the newly established CarboCount-CH measurement network and a high-resolution Lagrangian transport model. In our reference inversion, prior emissions were taken from the "bottom-up" Swiss Greenhouse Gas Inventory (SGHGI) as published by the Swiss Federal Office for the Environment in 2014 for the year 2012. Overall we estimate national CH₄ emissions to be 196 ± 18 Gg yr⁻¹ for the year 2013 (1σ uncertainty). This result is in close agreement with the recently revised SGHGI estimate of 206 ± 33 Gg yr⁻¹ as reported in 2015 for the year 2012. Results from sensitivity inversions using alternative prior emissions, uncertainty covariance settings, large-scale background mole fractions, two different inverse algorithms (Bayesian and extended Kalman filter), and two different transport models confirm the robustness and independent character of our estimate. According to the latest SGHGI estimate the main CH₄ source categories in Switzerland are agriculture (78 %), waste handling (15 %) and natural gas distribution and combustion (6 %). The spatial distribution and seasonal variability of our posterior emissions suggest an overestimation of agricultural CH₄ emissions by 10 to 20 % in the most recent SGHGI, which is likely due to an overestimation of emissions from manure handling. Urban areas do not appear as emission hotspots in our posterior results, suggesting that leakages from natural gas distribution are only a minor source of CH₄ in Switzerland. This is consistent with rather low emissions of 8.4 Gg yr⁻¹ reported by the SGHGI but inconsistent with the much higher value of 32 Gg yr⁻¹ implied by the EDGARv4.2 inventory for this sector. Increased CH₄ emissions (up to 30 % compared to the prior) were deduced for the north-eastern parts of Switzerland. This feature was common to most sensitivity inversions, which is a strong indicator that it is a real feature and not an artefact of the transport model and the inversion system. However, it was not possible to assign an unambiguous source process to the region. The observations of the CarboCount-CH network provided invaluable and independent information for the validation of the national bottom-up inventory. Similar systems need to be sustained to provide independent monitoring of future climate agreements.

Inverse and symmetrical voice: On languages with two transitive constructions

In voice and alignment typology, a categorical distinction is generally made between inverse systems on the one hand and symmetrical voice systems on the other. A major reason for distinguishing between these two types is the assumption that inverse systems are governed by a hierarchy involving grammatical, semantic, and ontological criteria, while symmetrical voice systems are based on discourse-pragmatic factors. However, the two types also have several important properties in common, in particular the fact that they have more than one nonderived transitive construction. Based on data from three native languages of South America, we show that the line between the two types is not always easy to draw, and that features of the inverse type can coexist with those of the symmetrical-voice type in the same language.