Showing papers by "Leibniz University of Hanover published in 2021"

Population Properties of Compact Objects from the Second LIGO-Virgo Gravitational-Wave Transient Catalog

Abstract: We report on the population of 47 compact binary mergers detected with a false-alarm rate of 0.01 are dynamically assembled. Third, we estimate merger rates, finding RBBH = 23.9-+8.614.3 Gpc-3 yr-1 for BBHs and RBNS = 320-+240490 Gpc-3 yr-1 for binary neutron stars. We find that the BBH rate likely increases with redshift (85% credibility) but not faster than the star formation rate (86% credibility). Additionally, we examine recent exceptional events in the context of our population models, finding that the asymmetric masses of GW190412 and the high component masses of GW190521 are consistent with our models, but the low secondary mass of GW190814 makes it an outlier.

Data-Driven Model Predictive Control With Stability and Robustness Guarantees

Abstract: We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant systems. The scheme uses an implicit model description based on behavioral systems theory and past measured trajectories. In particular, it does not require any prior identification step, but only an initially measured input–output trajectory as well as an upper bound on the order of the unknown system. First, we prove exponential stability of a nominal data-driven MPC scheme with terminal equality constraints in the case of no measurement noise. For bounded additive output measurement noise, we propose a robust modification of the scheme, including a slack variable with regularization in the cost. We prove that the application of this robust MPC scheme in a multistep fashion leads to practical exponential stability of the closed loop w.r.t. the noise level. The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme.

Observation of Gravitational Waves from Two Neutron Star–Black Hole Coalescences

Abstract: We report the observation of gravitational waves from two compact binary coalescences in LIGO’s and Virgo’s third observing run with properties consistent with neutron star–black hole (NSBH) binaries. The two events are named GW200105_162426 and GW200115_042309, abbreviated as GW200105 and GW200115; the first was observed by LIGO Livingston and Virgo and the second by all three LIGO–Virgo detectors. The source of GW200105 has component masses 8.9−1.5+1.2 and 1.9−0.2+0.3M⊙ , whereas the source of GW200115 has component masses 5.7−2.1+1.8 and 1.5−0.3+0.7M⊙ (all measurements quoted at the 90% credible level). The probability that the secondary’s mass is below the maximal mass of a neutron star is 89%–96% and 87%–98%, respectively, for GW200105 and GW200115, with the ranges arising from different astrophysical assumptions. The source luminosity distances are 280−110+110 and 300−100+150Mpc , respectively. The magnitude of the primary spin of GW200105 is less than 0.23 at the 90% credible level, and its orientation is unconstrained. For GW200115, the primary spin has a negative spin projection onto the orbital angular momentum at 88% probability. We are unable to constrain the spin or tidal deformation of the secondary component for either event. We infer an NSBH merger rate density of 45−33+75Gpc−3yr−1 when assuming that GW200105 and GW200115 are representative of the NSBH population or 130−69+112Gpc−3yr−1 under the assumption of a broader distribution of component masses.

X-ray screening identifies active site and allosteric inhibitors of SARS-CoV-2 main protease.

Abstract: The coronavirus disease (COVID-19) caused by SARS-CoV-2 is creating tremendous human suffering. To date, no effective drug is available to directly treat the disease. In a search for a drug against COVID-19, we have performed a high-throughput x-ray crystallographic screen of two repurposing drug libraries against the SARS-CoV-2 main protease (Mpro), which is essential for viral replication. In contrast to commonly applied x-ray fragment screening experiments with molecules of low complexity, our screen tested already-approved drugs and drugs in clinical trials. From the three-dimensional protein structures, we identified 37 compounds that bind to Mpro In subsequent cell-based viral reduction assays, one peptidomimetic and six nonpeptidic compounds showed antiviral activity at nontoxic concentrations. We identified two allosteric binding sites representing attractive targets for drug development against SARS-CoV-2.

A gravitational-wave measurement of the Hubble constant following the second observing run of Advanced LIGO and Virgo

Abstract: This paper presents the gravitational-wave measurement of the Hubble constant (H 0) using the detections from the first and second observing runs of the Advanced LIGO and Virgo detector network. The presence of the transient electromagnetic counterpart of the binary neutron star GW170817 led to the first standard-siren measurement of H 0. Here we additionally use binary black hole detections in conjunction with galaxy catalogs and report a joint measurement. Our updated measurement is H 0 = km s−1 Mpc−1 (68.3% of the highest density posterior interval with a flat-in-log prior) which is an improvement by a factor of 1.04 (about 4%) over the GW170817-only value of km s−1 Mpc−1. A significant additional contribution currently comes from GW170814, a loud and well-localized detection from a part of the sky thoroughly covered by the Dark Energy Survey. With numerous detections anticipated over the upcoming years, an exhaustive understanding of other systematic effects are also going to become increasingly important. These results establish the path to cosmology using gravitational-wave observations with and without transient electromagnetic counterparts.

Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning

Abstract: In this paper, we present a deep autoencoder based energy method (DAEM) for the bending, vibration and buckling analysis of Kirchhoff plates. The DAEM exploits the higher order continuity of the DAEM and integrates a deep autoencoder and the minimum total potential principle in one framework yielding an unsupervised feature learning method. The DAEM is a specific type of feedforward deep neural network (DNN) and can also serve as function approximator. With robust feature extraction capacity, the DAEM can more efficiently identify patterns behind the whole energy system, such as the field variables, natural frequency and critical buckling load factor studied in this paper. The objective function is to minimize the total potential energy. The DAEM performs unsupervised learning based on generated collocation points inside the physical domain so that the total potential energy is minimized at all points. For the vibration and buckling analysis, the loss function is constructed based on Rayleigh’s principle and the fundamental frequency and the critical buckling load is extracted. A scaled hyperbolic tangent activation function for the underlying mechanical model is presented which meets the continuity requirement and alleviates the gradient vanishing/explosive problems under bending. The DAEM is implemented using Pytorch and the LBFGS optimizer. To further improve the computational efficiency and enhance the generality of this machine learning method, we employ transfer learning. A comprehensive study of the DAEM configuration is performed for several numerical examples with various geometries, load conditions, and boundary conditions.

Upper limits on the isotropic gravitational-wave background from Advanced LIGO and Advanced Virgo’s third observing run

Abstract: We report results of a search for an isotropic gravitational-wave background (GWB) using data from Advanced LIGO’s and Advanced Virgo’s third observing run (O3) combined with upper limits from the earlier O1 and O2 runs. Unlike in previous observing runs in the advanced detector era, we include Virgo in the search for the GWB. The results of the search are consistent with uncorrelated noise, and therefore we place upper limits on the strength of the GWB. We find that the dimensionless energy density Ω GW ≤ 5.8 × 10 − 9 at the 95% credible level for a flat (frequency-independent) GWB, using a prior which is uniform in the log of the strength of the GWB, with 99% of the sensitivity coming from the band 20–76.6 Hz; Ω GW ( f ) ≤ 3.4 × 10 − 9 at 25 Hz for a power-law GWB with a spectral index of 2 / 3 (consistent with expectations for compact binary coalescences), in the band 20–90.6 Hz; and Ω GW ( f ) ≤ 3.9 × 10 − 10 at 25 Hz for a spectral index of 3, in the band 20–291.6 Hz. These upper limits improve over our previous results by a factor of 6.0 for a flat GWB, 8.8 for a spectral index of 2 / 3 , and 13.1 for a spectral index of 3. We also search for a GWB arising from scalar and vector modes, which are predicted by alternative theories of gravity; we do not find evidence of these, and place upper limits on the strength of GWBs with these polarizations. We demonstrate that there is no evidence of correlated noise of magnetic origin by performing a Bayesian analysis that allows for the presence of both a GWB and an effective magnetic background arising from geophysical Schumann resonances. We compare our upper limits to a fiducial model for the GWB from the merger of compact binaries, updating the model to use the most recent data-driven population inference from the systems detected during O3a. Finally, we combine our results with observations of individual mergers and show that, at design sensitivity, this joint approach may yield stronger constraints on the merger rate of binary black holes at z ≳ 2 than can be achieved with individually resolved mergers alone.

MOF-in-COF molecular sieving membrane for selective hydrogen separation.

Abstract: Covalent organic frameworks (COFs) are promising materials for advanced molecular-separation membranes, but their wide nanometer-sized pores prevent selective gas separation through molecular sieving. Herein, we propose a MOF-in-COF concept for the confined growth of metal-organic framework (MOFs) inside a supported COF layer to prepare MOF-in-COF membranes. These membranes feature a unique MOF-in-COF micro/nanopore network, presumably due to the formation of MOFs as a pearl string-like chain of unit cells in the 1D channel of 2D COFs. The MOF-in-COF membranes exhibit an excellent hydrogen permeance (>3000 GPU) together with a significant enhancement of separation selectivity of hydrogen over other gases. The superior separation performance for H2/CO2 and H2/CH4 surpasses the Robeson upper bounds, benefiting from the synergy combining precise size sieving and fast molecular transport through the MOF-in-COF channels. The synthesis of different combinations of MOFs and COFs in robust MOF-in-COF membranes demonstrates the versatility of our design strategy.

Food Security and the Dynamics of Wheat and Maize Value Chains in Africa and Asia

Abstract: There is an ongoing debate about how best to feed the growing world population in the long run and associated implications for research and development Some call for a new Green Revolution to secure the supply of staple foods, whereas others emphasize the importance of diversifying and improving people's diets We aim to contribute to this debate by reviewing the case of wheat and maize value chains and their contribution to food security in Africa and Asia We first identify drivers transforming food systems We then apply these to the cereal value chains and disentangle their effects on food security We thereby add to the three strands in the literature around production, consumption, and food system transformation and point to different research needs and recommendations for the future The review highlights: (1) Wheat and maize production will be increasingly impaired by ecological drivers such as land degradation, water scarcity and climate change (2) There are promising innovations to increase and maintain productivity, but constraints in adopting these innovations have to be overcome (ie, access to seeds, finance, and education/training) (3) The drivers affect all four dimensions of food security, but first and foremost they determine the availability and stability of maize and wheat This indirectly also influences the economic and physical access of people to maize and wheat (4) Research tends to focus on improving the productivity and sustainability of wheat and maize farming which is largely interlinked with the availability dimension of food security (5) The stability and utilization dimension of food security merits continued yet increased support First, to address climate change and implications for biotic and abiotic stresses Second, to promote healthier diets and enable the equitable transformation of food systems

Simulation methods for open quantum many-body systems

Abstract: This article reviews theoretical methods to deal with interacting quantum particles that are in contact with their environment and are thus described by a master equation rather than a Schr\"odinger equation. The similarities and differences are discussed between the pursuit of pure many-body ground states and mixed steady states by different methods, and an outlook is provided on the advances toward simulation of large open many-body system.

LIGO Detector Characterization in the Second and Third Observing Runs

Abstract: The characterization of the Advanced LIGO detectors in the second and third observing runs has increased the sensitivity of the instruments, allowing for a higher number of detectable gravitational-wave signals, and provided confirmation of all observed gravitational-wave events. In this work, we present the methods used to characterize the LIGO detectors and curate the publicly available datasets, including the LIGO strain data and data quality products. We describe the essential role of these datasets in LIGO–Virgo Collaboration analyses of gravitational-waves from both transient and persistent sources and include details on the provenance of these datasets in order to support analyses of LIGO data by the broader community. Finally, we explain anticipated changes in the role of detector characterization and current efforts to prepare for the high rate of gravitational-wave alerts and events in future observing runs.

An efficient optimization approach for designing machine learning models based on genetic algorithm

Abstract: Machine learning (ML) methods have shown powerful performance in different application Nonetheless, designing ML models remains a challenge and requires further research as most procedures adopt a trial and error strategy In this study, we present a methodology to optimize the architecture and the feature configurations of ML models considering a supervised learning process The proposed approach employs genetic algorithm (GA)-based integer-valued optimization for two ML models, namely deep neural networks (DNN) and adaptive neuro-fuzzy inference system (ANFIS) The selected variables in the DNN optimization problems are the number of hidden layers, their number of neurons and their activation function, while the type and the number of membership functions are the design variables in the ANFIS optimization problem The mean squared error (MSE) between the predictions and the target outputs is minimized as the optimization fitness function The proposed scheme is validated through a case study of computational material design We apply the method to predict the fracture energy of polymer/nanoparticles composites (PNCs) with a database gathered from the literature The optimized DNN model shows superior prediction accuracy compared to the classical one-hidden layer network Also, it outperforms ANFIS with significantly lower number of generations in GA The proposed method can be easily extended to optimize similar architecture properties of ML models in various complex systems

Current status of space gravitational wave antenna DECIGO and B-DECIGO

Abstract: The Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) is a future Japanese space mission with a frequency band of 0.1 Hz to 10 Hz. DECIGO aims at the detection of primordial gravitational waves, which could have been produced during the inflationary period right after the birth of the Universe. There are many other scientific objectives of DECIGO, including the direct measurement of the acceleration of the expansion of the Universe, and reliable and accurate predictions of the timing and locations of neutron star/black hole binary coalescences. DECIGO consists of four clusters of observatories placed in heliocentric orbit. Each cluster consists of three spacecraft, which form three Fabry-Perot Michelson interferometers with an arm length of 1000 km. Three DECIGO clusters will be placed far from each other, and the fourth will be placed in the same position as one of the other three to obtain correlation signals for the detection of primordial gravitational waves. We plan to launch B-DECIGO, which is a scientific pathfinder for DECIGO, before DECIGO in the 2030s to demonstrate the technologies required for DECIGO, as well as to obtain fruitful scientific results to further expand multi-messenger astronomy.

Gravitational-wave physics and astronomy in the 2020s and 2030s

Abstract: The 100 years since the publication of Albert Einstein’s theory of general relativity saw significant development of the understanding of the theory, the identification of potential astrophysical sources of sufficiently strong gravitational waves and development of key technologies for gravitational-wave detectors. In 2015, the first gravitational-wave signals were detected by the two US Advanced LIGO instruments. In 2017, Advanced LIGO and the European Advanced Virgo detectors pinpointed a binary neutron star coalescence that was also seen across the electromagnetic spectrum. The field of gravitational-wave astronomy is just starting, and this Roadmap of future developments surveys the potential for growth in bandwidth and sensitivity of future gravitational-wave detectors, and discusses the science results anticipated to come from upcoming instruments.

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Abstract: In this article, we present a nonlinear robust model predictive control (MPC) framework for general (state and input dependent) disturbances. This approach uses an online constructed tube in order to tighten the nominal (state and input) constraints. To facilitate an efficient online implementation, the shape of the tube is based on an offline computed incremental Lyapunov function with a corresponding (nonlinear) incrementally stabilizing feedback. Crucially, the online optimization only implicitly includes these nonlinear functions in terms of scalar bounds, which enables an efficient implementation. Furthermore, to account for an efficient evaluation of the worst case disturbance, a simple function is constructed offline that upper bounds the possible disturbance realizations in a neighborhood of a given point of the open-loop trajectory. The resulting MPC scheme ensures robust constraint satisfaction and practical asymptotic stability with a moderate increase in the online computational demand compared to a nominal MPC. We demonstrate the applicability of the proposed framework in comparison to state-of-the-art robust MPC approaches with a nonlinear benchmark example.

First-Principles Multiscale Modeling of Mechanical Properties in Graphene/Borophene Heterostructures Empowered by Machine-Learning Interatomic Potentials.

Abstract: Density functional theory calculations are robust tools to explore the mechanical properties of pristine structures at their ground state but become exceedingly expensive for large systems at finite temperatures. Classical molecular dynamics (CMD) simulations offer the possibility to study larger systems at elevated temperatures, but they require accurate interatomic potentials. Herein the authors propose the concept of first-principles multiscale modeling of mechanical properties, where ab initio level of accuracy is hierarchically bridged to explore the mechanical/failure response of macroscopic systems. It is demonstrated that machine-learning interatomic potentials (MLIPs) fitted to ab initio datasets play a pivotal role in achieving this goal. To practically illustrate this novel possibility, the mechanical/failure response of graphene/borophene coplanar heterostructures is examined. It is shown that MLIPs conveniently outperform popular CMD models for graphene and borophene and they can evaluate the mechanical properties of pristine and heterostructure phases at room temperature. Based on the information provided by the MLIP-based CMD, continuum models of heterostructures using the finite element method can be constructed. The study highlights that MLIPs were the missing block for conducting first-principles multiscale modeling, and their employment empowers a straightforward route to bridge ab initio level accuracy and flexibility to explore the mechanical/failure response of nanostructures at continuum scale.

State-of-the-Art and Comparative Review of Adaptive Sampling Methods for Kriging

Abstract: Metamodels aim to approximate characteristics of functions or systems from the knowledge extracted on only a finite number of samples. In recent years kriging has emerged as a widely applied metamodeling technique for resource-intensive computational experiments. However its prediction quality is highly dependent on the size and distribution of the given training points. Hence, in order to build proficient kriging models with as few samples as possible adaptive sampling strategies have gained considerable attention. These techniques aim to find pertinent points in an iterative manner based on information extracted from the current metamodel. A review of adaptive schemes for kriging proposed in the literature is presented in this article. The objective is to provide the reader with an overview of the main principles of adaptive techniques, and insightful details to pertinently employ available tools depending on the application at hand. In this context commonly applied strategies are compared with regards to their characteristics and approximation capabilities. In light of these experiments, it is found that the success of a scheme depends on the features of a specific problem and the goal of the analysis. In order to facilitate the entry into adaptive sampling a guide is provided. All experiments described herein are replicable using a provided open source toolbox.

Contrasting pathways of carbon sequestration in paddy and upland soils

Abstract: Paddy soils make up the largest anthropogenic wetlands on earth, and are characterized by a prominent potential for organic carbon (C) sequestration. By quantifying the plant- and microbial-derived C in soils across four climate zones, we identified that organic C accrual is achieved via contrasting pathways in paddy and upland soils. Paddies are 39%-127% more efficient in soil organic C (SOC) sequestration than their adjacent upland counterparts, with greater differences in warmer than cooler climates. Upland soils are more replenished by microbial-derived C, whereas paddy soils are enriched with a greater proportion of plant-derived C, because of the retarded microbial decomposition under anaerobic conditions induced by the flooding of paddies. Under both land-use types, the maximal contribution of plant residues to SOC is at intermediate mean annual temperature (15-20°C), neutral soil (pH~7.3), and low clay/sand ratio. By contrast, high temperature (~24°C), low soil pH (~5), and large clay/sand ratio are favorable for strengthening the contribution of microbial necromass. The greater contribution of microbial necromass to SOC in waterlogged paddies in warmer climates is likely due to the fast anabolism from bacteria, whereas fungi are unlikely to be involved as they are aerobic. In the scenario of land-use conversion from paddy to upland, a total of 504 Tg C may be lost as CO2 from paddy soils (0-15 cm) solely in eastern China, with 90% released from the less protected plant-derived C. Hence, preserving paddy systems and other anthropogenic wetlands and increasing their C storage through sustainable management are critical for maintaining global soil C stock and mitigating climate change.

Auto-Pytorch: Multi-Fidelity MetaLearning for Efficient and Robust AutoDL

Abstract: While early AutoML frameworks focused on optimizing traditional ML pipelines and their hyperparameters, a recent trend in AutoML is to focus on neural architecture search. In this paper, we introduce Auto-PyTorch, which brings together the best of these two worlds by jointly and robustly optimizing the network architecture and the training hyperparameters to enable fully automated deep learning (AutoDL). Auto-PyTorch achieves state-of-the-art performance on several tabular benchmarks by combining multi-fidelity optimization with portfolio construction for warmstarting and ensembling of deep neural networks (DNNs) and common baselines for tabular data. To thoroughly study our assumptions on how to design such an AutoDL system, we additionally introduce a new benchmark on learning curves for DNNs, dubbed LCBench, and run extensive ablation studies of the full Auto-PyTorch on typical AutoML benchmarks, eventually showing that Auto-PyTorch performs better than several state-of-the-art competitors.

Novel Ag decorated, BiOCl surface doped AgVO3 nanobelt ternary composite with Z-scheme homojunction-heterojunction interface for high prolific photo switching, quantum efficiency and hole mediated photocatalysis

Abstract: A ternary composite Ag@AgVO3/BiOCl possessing homojunction-heterojunction interface with varied BiOCl concentration was obtained through a facile hydrothermal route. Ag deposition in Ag@AgVO3 nano-belt was achieved through in-situ generation and deposition of Ag forming a homojunction. Whereas Ag@AgVO3/BiOCl heterojunction was constructed through the surface doping. This unique two-way interaction and the interface formation were revealed through the electron microscope and crystallographic analysis. The localized surface plasmon resonance of Ag and the efficient orbital mixing with BiOCl of 1:1 B/Ag@A compound has imparted a remarkable light harvesting and photo switching ability in the ternary composite material. Conductive nature of the Ag nanoparticle has promoted light absorption in the visible region and reduced the charge transfer resistance. Reduction of width in space charge region along with the increase in the amount of surface charge carrier has resulted in an outstanding increment in photocurrent. The solar photocatalysis evaluated against the aqueous phase removal of methyl orange and Bisphenol A showed 100 % and 51 % removal in 50 and 240 min, respectively. Studies were extended to understand the sensitization effect of dye. Theoretical modelling of band structure drawn from charge trapping experiments showed the prevalence of Z-scheme mechanism with holes mediated catalytic degradation. Improved charge harvest, separation and transmission has inserted a higher quantum efficiency in the material. BPA removal was enhanced to 82 % after the peroxide activation.

Inositol pyrophosphates promote the interaction of SPX domains with the coiled-coil motif of PHR transcription factors to regulate plant phosphate homeostasis

Abstract: Phosphorus is an essential nutrient taken up by organisms in the form of inorganic phosphate (Pi). Eukaryotes have evolved sophisticated Pi sensing and signaling cascades, enabling them to stably maintain cellular Pi concentrations. Pi homeostasis is regulated by inositol pyrophosphate signaling molecules (PP-InsPs), which are sensed by SPX domain-containing proteins. In plants, PP-InsP-bound SPX receptors inactivate Myb coiled-coil (MYB-CC) Pi starvation response transcription factors (PHRs) by an unknown mechanism. Here we report that a InsP8-SPX complex targets the plant-unique CC domain of PHRs. Crystal structures of the CC domain reveal an unusual four-stranded anti-parallel arrangement. Interface mutations in the CC domain yield monomeric PHR1, which is no longer able to bind DNA with high affinity. Mutation of conserved basic residues located at the surface of the CC domain disrupt interaction with the SPX receptor in vitro and in planta, resulting in constitutive Pi starvation responses. Together, our findings suggest that InsP8 regulates plant Pi homeostasis by controlling the oligomeric state and hence the promoter binding capability of PHRs via their SPX receptors.

Quantum Droplets of Dipolar Mixtures

Abstract: Recently achieved two-component dipolar Bose-Einstein condensates open exciting possibilities for the study of mixtures of ultradilute quantum liquids. While nondipolar self-bound (without external confinement) mixtures are necessarily miscible with an approximately fixed ratio between the two densities, the density ratio for the dipolar case is free. Therefore, self-bound dipolar mixtures present qualitatively novel and much richer physics, characterized by three possible ground-state phases: miscible, symmetric immiscible, and asymmetric immiscible, which may in principle occur at any population imbalance. Self-bound immiscible droplets are possible due to mutual nonlocal intercomponent attraction, which results in the formation of a droplet molecule. Moreover, our analysis of the impurity regime shows that quantum fluctuations in the majority component crucially modify the miscibility of impurities. Our work opens intriguing perspectives for the exploration of spinor physics in ultradilute liquids, which should resemble to some extent that of ^{4}He-^{3}He droplets and impurity-doped helium droplets.

Planning nature-based solutions: Principles, steps, and insights.

Abstract: Nature-based solutions (NBS) find increasing attention as actions to address societal challenges through harnessing ecological processes, yet knowledge gaps exist regarding approaches to landscape planning with NBS. This paper aims to provide suggestions of how planning NBS can be conceptualized and applied in practice. We develop a framework for planning NBS by merging insights from literature and a case study in the Lahn river landscape, Germany. Our framework relates to three key criteria that define NBS, and consists of six steps of planning: Co-define setting, Understand challenges, Create visions and scenarios, Assess potential impacts, Develop solution strategies, and Realize and monitor. Its implementation is guided by five principles, namely Place-specificity, Evidence base, Integration, Equity, and Transdisciplinarity. Drawing on the empirical insights from the case study, we suggest suitable methods and a checklist of supportive procedures for applying the framework in practice. Taken together, our framework can facilitate planning NBS and provides further steps towards mainstreaming.