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Comparing the mean vectors across different groups is a cornerstone in the realm of multivariate statistics, with quadratic forms commonly serving as test statistics. However, when the overall hypothesis is rejected, identifying specific vector components or determining the groups among which differences exist requires additional investigations. Conversely, employing multiple contrast tests (MCT) allows conclusions about which components or groups contribute to these differences. However, they come with a trade-off, as MCT lose some benefits inherent to quadratic forms. In this paper, we combine both approaches to get a quadratic form based multiple contrast test that leverages the advantages of both. To understand its theoretical properties, we investigate its asymptotic distribution in a semiparametric model. We thereby focus on two common quadratic forms - the Wald-type statistic and the Anova-type statistic - although our findings are applicable to any quadratic form. Furthermore, we employ Monte-Carlo and resampling techniques to enhance the test's performance in small sample scenarios. Through an extensive simulation study, we assess the performance of our proposed tests against existing alternatives, highlighting their advantages.

A machine learning-based methodology for blending data-driven turbulent closures for the Reynolds-Averaged Navier-Stokes (RANS) equations is proposed to improve the generalizability across different flow scenarios. Data-driven models based on sparse Bayesian learning and symbolic regression are pre-trained for specific flow classes, including turbulent channel flows, separated flows, and axisymmetric jets. The specialized models (called "\textit{experts}") are then blended using a set of weighting functions that reflect the local likelihood of a model to capture the reference data. The weighting functions are expressed as functions of a set of local flow features, and Random Forest regressors (RFR) are trained alongside the expert models to learn the mapping between the features and the weights. The training dataset includes additional data for flows ranging from shear flows at equilibrium to separated flows. The resulting blended model is then used to predict unseen flows, including a turbulent zero-pressure-gradient flat plate and a wall-mounted hump involving attached and separated boundary layer regions. The results show that the blending strategy adapts to the local flow conditions and effectively leverages the strengths of individual models, promoting the best-performing models locally, in a manner consistent with the training scenarios. The blended model provides a robust approximation for unseen flows that exhibit similar underlying physical characteristics to the training cases, while also successfully extrapolating to flows with different geometries and physical configurations.

We present a hybrid approach combining isogeometric analysis with deep operator networks to solve electromagnetic scattering problems. The neural network takes a computer-aided design representation as input and predicts the electromagnetic field in a de Rham conforming B-spline basis such that for example the tangential continuity of the electric field is respected. The physical problem is included in the loss function during training. Our numerical results demonstrate that a trained network accurately predicts the electric field, showing convergence to the analytical solution with optimal rate. Additionally, training on a variety of geometries highlights the network's generalization capabilities, achieving small error increases when applied to new geometries not included in the training set.

In medical, ecological and psychological research, there is a need for methods to handle multiple testing, for example to consider group comparisons with more than two groups. Typical approaches that deal with multiple testing are mean or variance based which can be less effective in the context of heavy-tailed and skewed data. Here, the median is the preferred measure of location and the interquartile range (IQR) is an adequate alternative to the variance. Therefore, it may be fruitful to formulate research questions of interest in terms of the median or the IQR. For this reason, we compare different inference approaches for two-sided and non-inferiority hypotheses formulated in terms of medians or IQRs in an extensive simulation study. We consider multiple contrast testing procedures combined with a bootstrap method as well as testing procedures with Bonferroni correction. As an example of a multiple testing problem based on heavy-tailed data we analyse an ecological trait variation in early and late breeding in a medium-sized bird of prey.

Easy-to-interpret effect estimands are highly desirable in survival analysis. In the competing risks framework, one good candidate is the restricted mean time lost (RMTL). It is defined as the area under the cumulative incidence function up to a prespecified time point and, thus, it summarizes the cumulative incidence function into a meaningful estimand. While existing RMTL-based tests are limited to two-sample comparisons and mostly to two event types, we aim to develop general contrast tests for factorial designs and an arbitrary number of event types based on a Wald-type test statistic. Furthermore, we avoid the often-made, rather restrictive continuity assumption on the event time distribution. This allows for ties in the data, which often occur in practical applications, e.g., when event times are measured in whole days. In addition, we develop more reliable tests for RMTL comparisons that are based on a permutation approach to improve the small sample performance. In a second step, multiple tests for RMTL comparisons are developed to test several null hypotheses simultaneously. Here, we incorporate the asymptotically exact dependence structure between the local test statistics to gain more power. The small sample performance of the proposed testing procedures is analyzed in simulations and finally illustrated by analyzing a real data example about leukemia patients who underwent bone marrow transplantation.

The motility of living things and synthetic self-propelled objects is often described using Active Brownian particles. To capture the interaction of these particles with their often complex environment, this model can be augmented with empirical forces or torques, for example, to describe their alignment with an obstacle or wall after a collision. Here, we assess the quality of these empirical models by comparing their output predictions with trajectories of rod-shaped active particles that scatter sterically at a flat wall. We employ a classical least-squares method to evaluate the instantaneous torque. In addition, we lay out a Bayesian inference procedure to construct the posterior distribution of plausible model parameters. In contrast to the least squares fit, the Bayesian approach does not require orientational data of the active particle and can readily be applied to experimental tracking data.

The functional delta-method has a wide range of applications in statistics. Applications on functionals of empirical processes yield various limit results for classical statistics. To improve the finite sample properties of statistical inference procedures that are based on the limit results, resampling procedures such as random permutation and bootstrap methods are a popular solution. In order to analyze the behaviour of the functionals of the resampling empirical processes, corresponding conditional functional delta-methods are desirable. While conditional functional delta-methods for some special cases already exist, there is a lack of more general conditional functional delta-methods for resampling procedures for empirical processes, such as the permutation and pooled bootstrap method. This gap is addressed in the present paper. Thereby, a general multiple sample problem is considered. The flexible application of the developed conditional delta-method is shown in various relevant examples.

Medical doctors rely on images of the human anatomy, such as magnetic resonance imaging (MRI), to localize regions of interest in the patient during diagnosis and treatment. Despite advances in medical imaging technology, the information conveyance remains unimodal. This visual representation fails to capture the complexity of the real, multisensory interaction with human tissue. However, perceiving multimodal information about the patient's anatomy and disease in real-time is critical for the success of medical procedures and patient outcome. We introduce a Multimodal Medical Image Interaction (MMII) framework to allow medical experts a dynamic, audiovisual interaction with human tissue in three-dimensional space. In a virtual reality environment, the user receives physically informed audiovisual feedback to improve the spatial perception of anatomical structures. MMII uses a model-based sonification approach to generate sounds derived from the geometry and physical properties of tissue, thereby eliminating the need for hand-crafted sound design. Two user studies involving 34 general and nine clinical experts were conducted to evaluate the proposed interaction framework's learnability, usability, and accuracy. Our results showed excellent learnability of audiovisual correspondence as the rate of correct associations significantly improved (p < 0.001) over the course of the study. MMII resulted in superior brain tumor localization accuracy (p < 0.05) compared to conventional medical image interaction. Our findings substantiate the potential of this novel framework to enhance interaction with medical images, for example, during surgical procedures where immediate and precise feedback is needed., Comment: Accepted for publication in IEEE TVCG; presentation at IEEE ISMAR 2024

CBCT-guided small animal irradiators encounter challenges in localizing soft-tissue targets due to low imaging contrast. Bioluminescence tomography (BLT) offers a promising solution, but they have largely remained in laboratorial development, limiting accessibility for researchers. In this work, we develop a universal, commercial-graded BLT-guided system (MuriGlo) designed to seamlessly integrate with commercial irradiators and empower researchers for translational studies. We demonstrate its capabilities in supporting in vitro and in vivo studies. The MuriGlo comprises detachable mouse bed, thermostatic control, mirrors, filters, and CCD, enabling multi-projection and multi-spectral imaging. We evaluate that the thermostatic control effectively sustains animal temperature at 37{\deg}C throughout imaging, and quantify that the system can detect as few as 61 GL261-AkaLuc cells in vitro. To illustrate how the MuriGlo can be utilized for in vivo image-guided research, we present 3 strategies, BLT-guided 5-arc, 2-field box, and BLI-guided single-beam, ranging from complicated high-conformal to simplest high-throughput plans. The high conformal BLT-guided 5-arc plan fully covers the gross tumor volume (GTV) at prescribed dose with minimal normal tissue exposure (3.9%), while the simplified, high-throughput BLT-guided 2-field box achieves 100% GTV coverage but results in higher normal tissue exposure (13.1%). Moreover, we demonstrate that the localization accuracy of MuriGlo for both widely-used SARRP and SmART irradiators is within1 mm, and the tumor coverage reaches over 97% with 0.75mm margin. The universal BLT-guided system offers seamless integration with commercial irradiators, achieving comparable localization accuracy, expected to supporting high-precision radiation research.

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs to compare different groups or to infer factor effects. We propose a new class of testing procedures for arbitrary linear hypotheses in general factorial designs with functional data. Our methods allow global as well as multiple inference of both, univariate and multivariate mean functions without assuming particular error distributions nor homoscedasticity. That is, we allow for different structures of the covariance functions between groups. To this end, we use point-wise quadratic-form-type test functions that take potential heteroscedasticity into account. Taking the supremum over each test function, we define a class of local test statistics. We analyse their (joint) asymptotic behaviour and propose a resampling approach to approximate the limit distributions. The resulting global and multiple testing procedures are asymptotic valid under weak conditions and applicable in general functional MANOVA settings. We evaluate their small-sample performance in extensive simulations and finally illustrate their applicability by analysing a multivariate functional air pollution data set.

We consider the global dynamics of finite energy solutions to energy-critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the maximal time of existence. Our main result for (HMHF) gives a complete classification of their dynamics for equivariance indices $D\geq3$; (i) they exist globally in time, (ii) the number of bubbles and signs are determined by the energy class of the initial data, and (iii) the scales of bubbles are asymptotically given by a universal sequence of rates up to scaling symmetry. In parallel, we also obtain a complete classification of $\dot{H}^{1}$-bounded radial solutions to (NLH) in dimensions $N\geq7$, building upon soliton resolution for such solutions. To our knowledge, this provides the first rigorous classification of bubble tree dynamics within symmetry. We introduce a new approach based on the energy method that does not rely on maximum principle. The key ingredient of the proof is a monotonicity estimate near any bubble tree configurations, which in turn requires a delicate construction of modified multi-bubble profiles also., Comment: 44 pages

In computational chemistry, accurately predicting molecular configurations that exhibit specific properties remains a critical challenge. Its intricacies become especially evident in the study of molecular aggregates, where the light-induced functionality is tied to highly structure-dependent electronic couplings between molecules. Here, we present an efficient strategy for the targeted screening of the structural space employing a "functionality optimization" technique, in which a chosen descriptor, constrained by the ground state energy expression, is optimized. The chosen algorithmic differentiation (AD) framework allows to automatically obtain gradients without its tedious implementation. We demonstrate the effectiveness of the approach by identifying Perylene Bisiimide (PBI) dimer motifs with enhanced SF rate. Our findings reveal that certain structural modifications of the PBI monomer, such as helical twisting and bending, as well as slipped-rotated packing arrangements, can significantly increase the SF rate.

Simulations play a crucial role in the modern scientific process. Yet despite (or due to) their ubiquity, the Data Science community shares neither a comprehensive definition for a "high-quality" study nor a consolidated guide to designing one. Inspired by the Predictability-Computability-Stability (PCS) framework for 'veridical' Data Science, we propose six MERITS that a Data Science simulation should satisfy. Modularity and Efficiency support the Computability of a study, encouraging clean and flexible implementation. Realism and Stability address the conceptualization of the research problem: How well does a study Predict reality, such that its conclusions generalize to new data/contexts? Finally, Intuitiveness and Transparency encourage good communication and trustworthiness of study design and results. Drawing an analogy between simulation and cooking, we moreover offer (a) a conceptual framework for thinking about the anatomy of a simulation 'recipe'; (b) a baker's dozen in guidelines to aid the Data Science practitioner in designing one; and (c) a case study deconstructing a simulation through the lens of our framework to demonstrate its practical utility. By contributing this "PCS primer" for high-quality Data Science simulation, we seek to distill and enrich the best practices of simulation across disciplines into a cohesive recipe for trustworthy, veridical Data Science., Comment: 26 pages (main text); 1 figure; 2 tables; *Authors contributed equally to this manuscript; **Authors contributed equally to this manuscript

The Wide-field Spectroscopic Telescope (WST) is proposed as a new facility dedicated to the efficient delivery of spectroscopic surveys. This white paper summarises the initial concept as well as the corresponding science cases. WST will feature simultaneous operation of a large field-of-view (3 sq. degree), a high multiplex (20,000) multi-object spectrograph (MOS) and a giant 3x3 sq. arcmin integral field spectrograph (IFS). In scientific capability these requirements place WST far ahead of existing and planned facilities. Given the current investment in deep imaging surveys and noting the diagnostic power of spectroscopy, WST will fill a crucial gap in astronomical capability and work synergistically with future ground and space-based facilities. This white paper shows that WST can address outstanding scientific questions in the areas of cosmology; galaxy assembly, evolution, and enrichment, including our own Milky Way; origin of stars and planets; time domain and multi-messenger astrophysics. WST's uniquely rich dataset will deliver unforeseen discoveries in many of these areas. The WST Science Team (already including more than 500 scientists worldwide) is open to the all astronomical community. To register in the WST Science Team please visit https://www.wstelescope.com/for-scientists/participate, Comment: 194 pages, 66 figures. Comments are welcome (wstelescope@gmail.com)

The Gaia-ESO Survey is an European Southern Observatory (ESO) public spectroscopic survey that targeted $10^5$ stars in the Milky Way covering the major populations of the disk, bulge and halo. The observations were made using FLAMES on the VLT obtaining both UVES high ($R\sim47,000$) and GIRAFFE medium ($R\sim20,000$) resolution spectra. The analysis of the Gaia-ESO spectra was the work of multiple analysis teams (nodes) within five working groups (WG). The homogenisation of the stellar parameters within WG11 (high resolution observations of FGK stars) and the homogenisation of the stellar parameters within WG10 (medium resolution observations of FGK stars) is described here. In both cases, the homogenisation was carried out using a bayesian Inference method developed specifically for the Gaia-ESO Survey by WG11. The WG10 homogenisation primarily used the cross-match of stars with WG11 as the reference set in both the stellar parameter and chemical abundance homogenisation. In this way the WG10 homogenised results have been placed directly onto the WG11 stellar parameter and chemical abundance scales. The reference set for the metal-poor end was sparse which limited the effectiveness of the homogenisation in that regime. For WG11, the total number of stars for which stellar parameters were derived was 6,231 with typical uncertainties for Teff, log g and [Fe/H] of 32~K, 0.05 and 0.05 respectively. One or more chemical abundances out of a possible 39 elements were derived for 6,188 of the stars. For WG10, the total number of stars for which stellar parameters were derived was 76,675 with typical uncertainties for Teff, log g and [Fe/H] of 64~K, 0.15 and 0.07 respectively. One or more chemical abundances out of a possible 30 elements were derived for 64,177 of the stars., Comment: 31 pages, 19 figures

Alzheimer's disease (AD) is a progressive neurodegenerative disorder leading to cognitive decline. [$^{18}$F]-Fluorodeoxyglucose positron emission tomography ([$^{18}$F]-FDG PET) is used to monitor brain metabolism, aiding in the diagnosis and assessment of AD over time. However, the feasibility of multi-time point [$^{18}$F]-FDG PET scans for diagnosis is limited due to radiation exposure, cost, and patient burden. To address this, we have developed a predictive image-to-image translation (I2I) model to forecast future [$^{18}$F]-FDG PET scans using baseline and year-one data. The proposed model employs a convolutional neural network architecture with long-short term memory and was trained on [$^{18}$F]-FDG PET data from 161 individuals from the Alzheimer's Disease Neuroimaging Initiative. Our I2I network showed high accuracy in predicting year-two [18F]-FDG PET scans, with a mean absolute error of 0.031 and a structural similarity index of 0.961. Furthermore, the model successfully predicted PET scans up to seven years post-baseline. Notably, the predicted [$^{18}$F]-FDG PET signal in an AD-susceptible meta-region was highly accurate for individuals with mild cognitive impairment across years. In contrast, a linear model was sufficient for predicting brain metabolism in cognitively normal and dementia subjects. In conclusion, both the I2I network and the linear model could offer valuable prognostic insights, guiding early intervention strategies to preemptively address anticipated declines in brain metabolism and potentially to monitor treatment effects., Comment: Accepted to SPIE Medical Imaging 2024

We present a new strategy to approximate the global solution of the Fokker-Planck equation efficiently in higher dimensions and show its convergence. The main ingredients are the Euler scheme to solve the associated stochastic differential equation and a histogram method for tree-structured density estimation on a data-dependent partitioning of the state space R^d.

This paper explores the use of open generative Large Language Models (LLMs) for annotation tasks in the social sciences. The study highlights the challenges associated with proprietary models, such as limited reproducibility and privacy concerns, and advocates for the adoption of open (source) models that can be operated on independent devices. Two examples of annotation tasks, sentiment analysis in tweets and identification of leisure activities in childhood aspirational essays are provided. The study evaluates the performance of different prompting strategies and models (neural-chat-7b-v3-2, Starling-LM-7B-alpha, openchat_3.5, zephyr-7b-alpha and zephyr-7b-beta). The results indicate the need for careful validation and tailored prompt engineering. The study highlights the advantages of open models for data privacy and reproducibility.

For the theoretical screening of Singlet Fission (SF) rates in molecular aggregates, commonly dimer model systems are employed. However, there is experimental evidence, that the SF process proceeds from the $^{1}$(TT) state via an triplet-triplet energy transfer process to a further intermediate: a $^{1}$(T...T) state with two non-adjacent, spin-correlated triplets, which cannot be captured by the dimer models. In this work, we extend Michl's diabatic frontier orbital model to trimer systems, for which we automatically generate the diabatic two and three-center couplings using symbolic algebra. We apply this method to study the packing dependence of the $^{1}$(T...T) formation in the perylene diimide (PDI) trimer stack. We find that efficient triplet-triplet energy transfer is facilitated by structural motifs for which also significant excimer character can be observed. Furthermore, the coupling shows a local maximum for the structural motif that has been assigned to efficient $^{1}$(TT) population. Employing second order perturbation theory, we study the interference of the individual electronic pathways that arise in the PDI trimer system, allowing us to reproduce the packing dependence of the SF rates derived from the Redfield simulations in the work by Mirjani et. al. (Phys. Chem. C 2014, 118, 26, 14192-14199).

The Gaia mission is delivering a large number of astrometric orbits for binary stars. By combining these with spectroscopic orbits for systems with two observable spectra (SB2), it is possible to derive the masses of both components. However, to get masses with a good accuracy requires accurate spectroscopic orbits, which is the major aim of the present paper. A subsidiary aim is to discover SB2 systems hiding among known SB1, and even though this search may often prove unsuccessful, the acquired radial velocities may be used anyway to improve the existing spectroscopic orbits. New radial velocities for 58 binary systems from the Ninth Catalogue of Spectroscopic Binary Orbits (SB9), obtained using the high-resolution HERMES spectrograph installed on the 1.2 m Mercator telescope, were used to possibly identify hitherto undetected SB2 systems. For SB1 systems with inaccurate orbits, these new radial-velocity measurements were used to improve the orbital accuracy. This paper provides 51 orbits (41 SB1 and 10 SB2) that have been improved with respect to the solution listed in the SB9 catalogue, out of the 58 SB9 orbits studied, which belong to 56 stellar systems. Among them, there are five triple and four quadruple systems. Despite the high resolution of HERMES, HIP 115142 A is the only system which we detected as a new SB2 system. The B component of the visual binary HIP 92726 has now been found to be a spectroscopic system as well, which makes HIP 92726 a newly discovered quadruple system (SB1+SB1). The high HERMES resolution allowed us moreover to better isolate the signature of the secondary component of HIP 12390, HIP 73182 and HIP 111170. More accurate masses have thus been derived for them. Among the 30 SB also present in Gaia Data Release 3 (DR3) and with periods shorter than the Gaia DR3 time span (1000 d), only 5 were flagged as binaries by DR3., Comment: 27 pages, many figures, 6 tables. Accepted for publication in Astronomy and Astrophysics

The High-Resolution Multi-Object Spectrograph (HRMOS) is a facility instrument that we plan to propose for the Very Large Telescope (VLT) of the European Southern Observatory (ESO), following the initial presentation at the VLT 2030 workshop held at ESO in June 2019. HRMOS provides a combination of capabilities that are essential to carry out breakthrough science across a broad range of active research areas from stellar astrophysics and exoplanet studies to Galactic and Local Group archaeology. HRMOS fills a gap in capabilities amongst the landscape of future instrumentation planned for the next decade. The key characteristics of HRMOS will be high spectral resolution (R = 60000 - 80000) combined with multi-object (20-100) capabilities and long term stability that will provide excellent radial velocity precision and accuracy (10m/s). Initial designs predict that a SNR~100 will be achievable in about one hour for a star with mag(AB) = 15, while with the same exposure time a SNR~ 30 will be reached for a star with mag(AB) = 17. The combination of high resolution and multiplexing with wavelength coverage extending to relatively blue wavelengths (down to 380\,nm), makes HRMOS a spectrograph that will push the boundaries of our knowledge and that is envisioned as a workhorse instrument in the future. The science cases presented in this White Paper include topics and ideas developed by the Core Science Team with the contributions from the astronomical community, also through the wide participation in the first HRMOS Workshop (https://indico.ict.inaf.it/event/1547/) that took place in Firenze (Italy) in October 2021., Comment: 88 pages, 39 figures. Comments and expressions of interest are welcome by contacting members of the Core Science Team

The Gaia-ESO Survey (GES) is a large public spectroscopic survey which acquired spectra for more than 100000 stars across all major components of the Milky Way. In addition to atmospheric parameters and stellar abundances that have been derived in previous papers of this series, the GES spectra allow us to detect spectroscopic binaries with one (SB1), two (SB2) or more (SBn $\ge$ 3) components. Cross-correlation functions (CCFs) have been re-computed thanks to a dozen spectral masks probing a range of effective temperatures, surface gravities and metallicities. By optimising the mask choice for a given spectrum, the new computed so-called Nacre (Narrow cross-correlation experiment) CCFs are narrower and allow to unblend more stellar components than standard masks. The Doe (Detection of Extrema) extremum-finding code then selects the individual components and provides their radial velocities. From the sample of HR10 and HR21 spectra corresponding to 37565 objects, the present study leads to the detection of 322 SB2, ten (three of them being tentative) SB3, and two tentative SB4. In particular, compared to our previous study, the Nacre CCFs allow us to multiply the number of SB2 candidates by $\approx$ 1.5. The colour-magnitude diagram reveals, as expected, the shifted location of the SB2 main sequence. A comparison between the SB identified in Gaia DR3 and the ones detected in the present work is performed and the complementarity of the two censuses is discussed. An application to mass-ratio determination is presented, and the mass-ratio distribution of the GES SB2 is discussed. When accounting for the SB2 detection rate, an SB2 frequency of $\approx$ 1.4% is derived within the present stellar sample of mainly FGK-type stars. As primary outliers identified within the GES data, SBn spectra produce a wealth of information and useful constraints for the binary population synthesis studies.