Between buildings and free factor complexes: A Cohen-Macaulay complex for Out(RAAGs)

For every finite graph $\Gamma$, we define a simplicial complex associated to the outer automorphism group of the RAAG $A_\Gamma$. These complexes are defined as coset complexes of parabolic subgroups of $Out^0(A_\Gamma)$ and interpolate between Tits buildings and free factor complexes. We show that each of these complexes is homotopy Cohen-Macaulay and in particular homotopy equivalent to a wedge of d-spheres. The dimension d can be read off from the defining graph $\Gamma$ and is determined by the rank of a certain Coxeter subgroup of $Out^0(A_\Gamma)$. In order to show this, we refine the decomposition sequence for $Out^0(A_\Gamma)$ established by Day-Wade, generalise a result of Brown concerning the behaviour of coset posets under short exact sequences and determine the homotopy type of relative free factor complexes associated to Fouxe-Rabinovitch groups.Comment: 56 pages, 5 figure

Top-degree rational cohomology in the symplectic group of a number ring

Let $K$ be a number field with ring of integers $R = \mathcal{O}_K$. We show that if $R$ is not a principal ideal domain, then the symplectic group $\operatorname{Sp}_{2n}(R)$ has non-trivial rational cohomology in its virtual cohomological dimension. This demonstrates a sharp contrast to the situation where $R$ is Euclidean. To prove our result, we study the symplectic Steinberg module, i.e. the top-dimensional homology group of the spherical building associated to $\operatorname{Sp}_{2n}(K)$. We show that this module is not generated by integral apartment classes.Comment: 19 pages, 1 figur

A central limit theorem for the two-sided descent statistic on Coxeter groups

We study the asymptotic behaviour of the statistic (des+ides) which assigns to an element w of a finite Coxeter group W the number of descents of w plus the number of descents of its inverse. Our main result is a central limit theorem for the probability distributions associated to this statistic. This answers a question of Kahle-Stump and generalises work of Chatterjee-Diaconis, \"Ozdemir and R\"ottger.Comment: 20 pages incl. appendi

Apartment classes of integral symplectic groups

In this note we present an alternative proof of a theorem of Gunnells, which states that the Steinberg module of $\operatorname{Sp_{2n}}(\mathbb{Q})$ is a cyclic $\operatorname{Sp_{2n}}(\mathbb{Z})$-module, generated by integral apartment classes.Comment: 16 pages. Comments welcome

Weight 2 cohomology of graph complexes of cyclic operads and the handlebody group

We compute the weight 2 (resp.~top$-2$) cohomology of the Feynman transforms of the cyclic (co)operads $\mathsf{BV}$, $D\mathsf{BV}$, $\mathsf{Grav}$ and $\mathsf{HyCom}$. Using a result of Giansiracusa we compute in particular the weight top$-2$-cohomology of the handlebody group. We compare the result to the weight top$-2$ cohomology of the moduli space of curves $\mathcal M_{g,n}$, recently computed by Payne and the last-named author. We also provide another proof of a recent result of Hainaut--Petersen identifying the top-weight-cohomology of the handlebody group with the Kontsevich graph cohomology

Persistent homology in cosmic shear: constraining parameters with topological data analysis

In recent years, cosmic shear has emerged as a powerful tool to study the statistical distribution of matter in our Universe. Apart from the standard two-point correlation functions, several alternative methods like peak count statistics offer competitive results. Here we show that persistent homology, a tool from topological data analysis, can extract more cosmological information than previous methods from the same dataset. For this, we use persistent Betti numbers to efficiently summarise the full topological structure of weak lensing aperture mass maps. This method can be seen as an extension of the peak count statistics, in which we additionally capture information about the environment surrounding the maxima. We first demonstrate the performance in a mock analysis of the KiDS+VIKING-450 data: we extract the Betti functions from a suite of $w$CDM $N$-body simulations and use these to train a Gaussian process emulator that provides rapid model predictions; we next run a Markov-Chain Monte Carlo analysis on independent mock data to infer the cosmological parameters and their uncertainty. When comparing our results, we recover the input cosmology and achieve a constraining power on $S_8 \equiv \sigma_8\sqrt{\Omega_\mathrm{m}/0.3}$ that is 5% tighter than that of peak count statistics. Performing the same analysis on 100 deg$^2$ of Euclid-like simulations, we are able to improve the constraints on $S_8$ and $\Omega_\mathrm{m}$ by 18% and 10%, respectively, while breaking some of the degeneracy between $S_8$ and the dark energy equation of state. To our knowledge, the methods presented here are the most powerful topological tools to constrain cosmological parameters with lensing data

Accelerated carbonation of waste incinerator bottom ash for trace metal immobilisation

Bottom ash (BA) constitutes the dominant solid residue of municipal solid waste incineration and millions of tonnes are annually produced, worldwide. Fresh BA contains highly reactive constituents which are metastable under environmental conditions. Their transformation has been referred to as the ageing of BA. It has long since been recognized that ageing reduces the reactivity of BA and therewith the leachability of critical trace metals. Carbonation is a key process in the aging and is initiated by the access of CO2. Passive ageing is commonly applied in many European countries prior to geotechnical utilization or landfilling of BA. However, it requires a large quantity of space, time, and lacks any process control. Carbonation of BA may be accelerated by contacting the material with CO2-rich exhaust gas. Although this has long since been recognized, practical applications have remained beyond reach since reactor sys-tems did not allow for the necessary throughput. Recent studies demonstrated that the material dynamics in rotating drum reactors favour the accelerated carbonation and that rotating drums may be suited for a process implementation at the industrial scale. Yet, knowledge regarding optimum drum operation for accelerated carbonation of BA is still scarce. This thesis aimed at delineating both the technical set-up and the operation parameters suited for process integration of accelerated carbonation at incinerator sites. This included the devel-opment of a screening technique to evaluate the progress of carbonation as well as a stepwise transfer of the reactor system from a jar test into a continuously fed rotating drum reactor sys-tem. Effects of rotation speed and reactor fill level on the solid’s motion were cinematograph-ically analysed. Carbonation performance was assessed by thermogravimetric analyses and the leaching behaviour of the treated BA. The BA used in this study was sampled from a grate-type refuse derived fuel incinerator located in central Germany. Leachate values and particu-larly the high leachate concentrations of Pb characterized fresh BA as a hazardous waste. Laboratory results demonstrated the serviceability and reproducibility of the developed method for the monitoring and quantification of the CO2 uptake by BA in both static and dynamic reac-tor systems. The method is based on following the pressure drop in the gas phase induced by the CO2 uptake of BA close to atmospheric pressure conditions. The monitoring method was next applied to evaluate carbonation kinetics and the influence of fundamental parameters (CO2 concentration, fill level, BA moisture) on accelerated carbona-tion of BA in a rotating drum batch reactor. Both the CO2 uptake rate and the final level of car-bonation increased as the CO2 concentration was raised from 15 to 75 vol.-%. The optimum moisture content for the tested BA was found to be 21 wt.-%, which is roughly in the range of the typical moisture content of BA after temporary storage in a roofed pile. The fill level was not a limiting factor for BA carbonation within the tested range (7 - 45 vol.-%). The latter could be explained by findings obtained by the study of the solids’ motion. The bed behaviour of BA strongly differed from that of standard materials and was more affected by fill level than by ro-tation speed. With increasing fill level, the bed motion changed from slipping to slumping thereby favouring the mixing process. Complementary logging of relative humidity and temper-ature showed constant moisture conditions and self-heating, induced by the exothermal car-bonation reaction. A close relationship between CO2 uptake and reactor temperature was con-firmed by benchmarking a heat balance model against the carbonation enthalpy. Excellent agreement demonstrated that temperature monitoring may be an alternative way of evaluating the progress of carbonation. As a next step carbonation of BA was studied with a continuous feed of the reactant gas and the effects of specific CO2 supply, mixing tools, and reactor loadings on process performance were assessed. The reaction could be accelerated to around 100 minutes and was further en-hanced by the use of mixing tools. Of the configurations tested, a perforated mixing cage per-formed best, even at fill levels of up to 50 %. This set-up was also least prone to the formation of BA incrustations. Finally, a rotating drum reactor continuously fed with both, the reactant gas (60 L/min; 10 vol.-% CO2) and the BA (9 - 18 kg/h), was developed and tested at varied BA residence times. Pro-jected and experimental residence times were compared by mass balancing and by analysing the breakthrough curves of a tracer. Good agreement indicated adequate control of reactor loading and the BA feed rate. In one test, the gas was heated and humidified. Leachates and solid phase properties of the treated BA served to evaluate the carbonation performance. Overall, carbonation improved the leachate quality of BA as the leachate concentrations of critical trace metals (Pb, Zn, Cu) decreased by at least one order of magnitude. A residence time of 80 min was sufficient to reduce the BA leachability such as to characterize the car-bonated material as a non-hazardous waste. This would allow for a disposal on a class 1 land-fill or alternatively for a geotechnical reuse in accordance with the draft of the German Ordi-nance on Secondary Construction Materials. Other than the amphoteric metals, oxyanions like Cr, Mo and V became more mobile upon carbonation. This side effect did not outweigh the benefits since oxyanion concentrations remained below the specific limit values. Therefore, the accelerated carbonation of BA provides a material that is both suited for the cost-effective dis-posal on a lower landfill class and for geotechnical applications. In view of relatively short resi-dence times and stable process performance, the rotating drum reactor seems promising for a full-scale implementation of BA carbonation

Sensory quality of turnip greens and turnip tops grown in northwestern Spain

In Galicia (northwestern Spain), Brassica rapa var. rapa L. includes turnip greens and turnip tops as vegetable products. They are characterized by a particular sulfurous aroma, pungent flavor, and a bitter taste. In this work twelve local varieties grown as turnip greens and turnip tops were evaluated to define the sensory attributes, to relate them with secondary metabolites, and to select those sensorial traits that better describe these crops. Results showed differences in the sensory profiles of B. rapa varieties. Turnip greens were significantly differed for aroma intensity, leaf color, and salty taste, while turnip tops were for color and firmness of leaves, moistness and fibrosity in mouth, sharpness, and bitter taste. Secondary metabolites as glucosinolates in turnip greens and phenolic compounds in turnip tops were highly correlated with texture and flavor. Glucosinolates especially progoitrin (in turnip greens) and gluconapin (in turnip tops) showed correlation with bitter taste and aftertaste persistence. Correlation between sensory traits showed highest values between leaf firmness and stalk firmness (0.94**), leaf firmness and fibrosity (R=0.92**), aftertaste persistence and bitterness (R=0.91**) and between bitterness and moistness (R=-0.89**).Research supported by the Xunta de Galicia (PGIDIT06RAG40302PR) and Excma. Diputación Provincial de Pontevedra.Peer reviewe

The Neural Correlates of Face-Voice-Integration in Social Anxiety Disorder

Faces and voices are very important sources of threat in social anxiety disorder (SAD), a common psychiatric disorder where core elements are fears of social exclusion and negative evaluation. Previous research in social anxiety evidenced increased cerebral responses to negative facial or vocal expressions and also generally increased hemodynamic responses to voices and faces. But it is unclear if also the cerebral process of face-voice-integration is altered in SAD. Applying functional magnetic resonance imaging, we investigated the correlates of the audiovisual integration of dynamic faces and voices in SAD as compared to healthy individuals. In the bilateral midsections of the superior temporal sulcus (STS) increased integration effects in SAD were observed driven by greater activation increases during audiovisual stimulation as compared to auditory stimulation. This effect was accompanied by increased functional connectivity with the visual association cortex and a more anterior position of the individual integration maxima along the STS in SAD. These findings demonstrate that the audiovisual integration of facial and vocal cues in SAD is not only systematically altered with regard to intensity and connectivity but also the individual location of the integration areas within the STS. These combined findings offer a novel perspective on the neuronal representation of social signal processing in individuals suffering from SAD

Ab initio modeling and experimental investigation of Fe2_2P by DFT and spin spectroscopies

Fe$_2$P alloys have been identified as promising candidates for magnetic refrigeration at room-temperature and for custom magnetostatic applications. The intent of this study is to accurately characterize the magnetic ground state of the parent compound, Fe$_2$P, with two spectroscopic techniques, $\mu$SR and NMR, in order to provide solid bases for further experimental analysis of Fe$_2$P-type transition metal based alloys. We perform zero applied field measurements using both techniques below the ferromagnetic transition $T_C=220~\mathrm K$. The experimental results are reproduced and interpreted using first principles simulations validating this approach for quantitative estimates in alloys of interest for technological applications.Comment: 10 pages, 2 figure