@phdthesis{18104, abstract = {We introduce a new all-electric platform, that strong couples light to mechanical motion by ensuring that the external environmental coupling dominates over internal mechanical dissipation. The system only has three everyday components: AC, DC, and a fip-chip, in which a metallized silicon nitride membrane is fipped on top of the device under test. This everyday electromechanical device can be operated at low or room temperature and has 10000× lower insertion loss than a comparable commercial quartz crystal, achieves a position imprecision matching state-of-the-art optical interferometer, and enables remote cooling of mechanical motion. The spatial properties of higher order mechanical modes are a promising feature for reconstructing unknown charge distributions. }, author = {Puglia, Denise}, issn = {2663-337X}, pages = {63}, publisher = {Institute of Science and Technology Austria}, title = {{Everyday electromechanics: Capacitive strong coupling to mechanical motion}}, doi = {10.15479/at:ista:18104}, year = {2024}, } @unpublished{18143, abstract = {Strong optomechanical coupling -- a regime where mechanical motion is damped by environmental radiation -- has traditionally required demanding experimental ingredients such as superconducting resonators, high-quality optical cavities, or large magnetic fields. Here we demonstrate a room temperature, cavity-free, all-electric device reaching this regime at radio frequencies, enabled by a mechanically compliant parallel-plate capacitor with a nanoscale plate separation and an aspect ratio exceeding 1,000. The device has four orders of magnitude lower insertion loss than a comparable commercial quartz crystal, and achieves a position imprecision rivaling an optical interferometer. With the help of a back-action isolation scheme, we observe radiative cooling of mechanical motion by a remote cryogenic load. This work provides a technologically accessible route to high-precision sensing, transduction, and signal processing.}, author = {Puglia, Denise and Odessey, Rachel H and Burns, Peter S. and Luhmann, Niklas and Schmid, Silvan and Higginbotham, Andrew P}, booktitle = {arXiv}, title = {{Room temperature, cavity-free capacitive strong coupling to mechanical motion}}, doi = {10.48550/arXiv.2407.15314}, year = {2024}, } @phdthesis{18642, abstract = {This thesis consists of two pieces of work in the broader feld of computational biology, both of which are methods for the analysis of large scale biological data, implemented in efcient software. Chapter 2 introduces a statistical software for causal discovery and inference from observed genetic marker and phenotypic trait data. We explore in simulation how well the method can fne-map genetic efects, fnd the correct causal structure among tens of traits and millions of genetic markers, and infer the causal efect size for the discovered causal relations. We then apply the method to 8 million markers and 17 traits from the UK Biobank and show that many relationships found with other methods are likely due to the efects of hidden confounders. Chapter 3 describes how this method can be applied to longitudinal data. I show how one can incorporate the background knowledge present in the known order of measurements to improve the accuracy of the causal discovery process, and explore the method’s ability to identify age specifc genetic efects, and how the error rates of this recovery are infuenced by missing data due to diferent censoring mechanisms. Chapter 4 introduces a statistical software for the comparison of chromatin contact maps based on the structural similarity index. We explore the robustness of the method to noise and size diferences of the compared maps, show how it can measure evolutionary conservation of topological features by providing a similarity ranking of syntenic regions, and fnally how it can detect alterations in 3D genome structure due to genetic mutations in samples of medical relevance. }, author = {Machnik, Nick N}, issn = {2663-337X}, pages = {138}, publisher = {Institute of Science and Technology Austria}, title = {{Algorithms for causal learning and comparative analysis for genomic data}}, doi = {10.15479/at:ista:18642}, year = {2024}, } @unpublished{18648, abstract = {Statistical causal learning in genomics relies on the instrumental variable method of Mendelian Randomization (MR). Currently, an overwhelming number of MR studies purport to show causal relationships among a wide range of risk factors and outcomes. Here, we show that selecting instrument variables from genome-wide association study estimates leads to high false discovery rates for many MR approaches, which can be greatly reduced by employing a graphical inference approach which: (i) explicitly tests instrumental variable assumptions; (ii) distinguishes direct from indirect factors in very high-dimensional data; (iii) discriminates pleiotropic from trait-specific markers, controlling for LD genome-wide; (iv) accommodates rare variants and binary outcomes in a principled way; and (v) identifies potential unobserved latent confounding. For 17 traits and 8.4M variants recorded for 458,747 individuals in the UK Biobank, we show that standard MR analysis gives an abundance of findings that disappear under stringent assumption checks, with many relationships reflecting potential unmeasured confounding. This implies that mixtures of temporal precedence and potential for reverse-causality prohibit understanding the underlying nature of phenotypic and genetic correlations in biobank data. We propose that well-curated longitudinal records are likely needed and that our approach provides a first-step toward robust principled screening for potential causal links. }, author = {Machnik, Nick N and Mahmoudi, Seyed Mahdi and Borczyk, Malgorzata and Krätschmer, Ilse and Bauer, Markus J. and Robinson, Matthew Richard}, booktitle = {bioRxiv}, title = {{Causal inference for multiple risk factors and diseases from genomics data}}, doi = {10.1101/2023.12.06.570392}, year = {2024}, } @phdthesis{18574, abstract = {Biological vision is unlike a camera; rather than transmitting light information faithfully, early visual circuits process the visual scene to convey only the relevant information in an efficient manner. Consequentially, the nature of this visual processing then depends on what is the relevant information in a scene and on the notion of efficiency. In this work, I study how visual processing is modulated by two different variations in the visual scene. First, I discovered that in the mouse (Mus musculus) retina, Retinal Ganglion Cells in the upper and lower visual field have differences in the center surround structure of their receptive fields. Comparison with models of efficient coding show that this adaptation likely evolved to cope with the brightness gradient from the sky to the ground that is pervasive in natural scenes. In the second project, I study how the downstream neurons in the Superior Colliculus dynamically change their temporal selectivity depending on the ambient luminance and behavioral state. As the scene gets darker or when the animal is is less aroused, the neuronal responses get laggier, while still maintaining their relative timing with respect to the population. Overall, this work emphasises the need to understand visual processing in the context of specific demands of the animal in its the environment. The adaptive changes in the visual system, from the retinal ganglion cells to the superior colliculus, highlight the intricate ways in which biological vision optimizes the processing of visual information. }, author = {Gupta, Divyansh}, isbn = {978-3-99078-050-3}, issn = {2663-337X}, pages = {86}, publisher = {Institute of Science and Technology Austria}, title = {{Visual adaptations to natural statistics}}, doi = {10.15479/at:ista:18574}, year = {2024}, } @phdthesis{18471, abstract = {Spatial omics technologies are enriching our understanding of complex biological samples, by allowing us to study their molecular composition while preserving the spatial relationships between molecules in their native context. As the field continues to advance, there are technical challenges that need to be addressed in order to take full advantage of the spatial capabilities of these methods. In this work, I present two technical developments that I established for multiplexed error robust FISH (MERFISH) throughout my PhD: (1) pushing the spatial resolution limits to the nanoscale, and (2) adding rich tissue context to the mouse brain transcriptome. To achieve nanoscale resolution with MERFISH in cultured cells, I combined it with stimulated emission depletion (STED) and expansion microscopy (ExM) to achieve a spatial resolution as low as ~20 nm, and explored the compatibility of MERFISH with singlemolecule localization microscopy (SMLM) techniques. To visualize targeted mRNAs in mouse brain tissue, I applied the comprehensive analysis of tissues across scales (CATS) toolbox, which provides an unbiased morphological readout by labeling the extracellular domain. I successfully established this method, which we call CATS-MERFISH-ExM, to work with thick mouse brain slices, being able to extract transcriptomics information with 3D tissue context. CATS-MERFISH-ExM enabled us to identify cell types and further visualize the subcellular distribution of transcripts in mouse brain tissue, shedding light on the neuropil-specific transcriptome. This method provides integrated information on cellular structure and transcriptomes in situ, and could potentially be applied with other modalities, opening new avenues for scientific discovery. }, author = {Agudelo Duenas, Nathalie}, isbn = {978-3-99078-044-2}, issn = {2663-337X}, pages = {97}, publisher = {Institute of Science and Technology Austria}, title = {{Visualizing the neuronal transcriptional landscape with tissue context}}, doi = {10.15479/at:ista:18471}, year = {2024}, } @article{17148, abstract = {During neural tube (NT) development, the notochord induces an organizer, the floorplate, which secretes Sonic Hedgehog (SHH) to pattern neural progenitors. Conversely, NT organoids (NTOs) from embryonic stem cells (ESCs) spontaneously form floorplates without the notochord, demonstrating that stem cells can self-organize without embryonic inducers. Here, we investigated floorplate self-organization in clonal mouse NTOs. Expression of the floorplate marker FOXA2 was initially spatially scattered before resolving into multiple clusters, which underwent competition and sorting, resulting in a stable “winning” floorplate. We identified that BMP signaling governed long-range cluster competition. FOXA2+ clusters expressed BMP4, suppressing FOXA2 in receiving cells while simultaneously expressing the BMP-inhibitor NOGGIN, promoting cluster persistence. Noggin mutation perturbed floorplate formation in NTOs and in the NT in vivo at mid/hindbrain regions, demonstrating how the floorplate can form autonomously without the notochord. Identifying the pathways governing organizer self-organization is critical for harnessing the developmental plasticity of stem cells in tissue engineering.}, author = {Krammer, Teresa and Stuart, Hannah T. and Gromberg, Elena and Ishihara, Keisuke and Cislo, Dillon and Melchionda, Manuela and Becerril Perez, Fernando and Wang, Jingkui and Costantini, Elena and Rus, Stefanie and Arbanas, Laura and Hörmann, Alexandra and Neumüller, Ralph A. and Elvassore, Nicola and Siggia, Eric and Briscoe, James and Kicheva, Anna and Tanaka, Elly M.}, issn = {1878-1551}, journal = {Developmental Cell}, number = {15}, pages = {1940--1953.e10}, publisher = {Elsevier}, title = {{Mouse neural tube organoids self-organize floorplate through BMP-mediated cluster competition}}, doi = {10.1016/j.devcel.2024.04.021}, volume = {59}, year = {2024}, } @article{18601, abstract = {Geometrically controlled stem cell differentiation promotes reproducible pattern formation. Here, we present a protocol to fabricate elastomeric stencils for patterned stem cell differentiation. We describe procedures for using photolithography to produce molds, followed by molding polydimethylsiloxane (PDMS) to obtain stencils with through holes. We then provide instructions for culturing cells on stencils and, finally, removing stencils to allow colony growth and cell migration. This approach yields reproducible two-dimensional organoids tailored for quantitative studies of growth and pattern formation. For complete details on the use and execution of this protocol, please refer to Lehr et al.1}, author = {Rus, Stefanie and Merrin, Jack and Kulig, Monika Aleksandra and Minchington, Thomas and Kicheva, Anna}, issn = {2666-1667}, journal = {STAR Protocols}, number = {4}, publisher = {Elsevier}, title = {{Protocol for fabricating elastomeric stencils for patterned stem cell differentiation}}, doi = {10.1016/j.xpro.2024.103187}, volume = {5}, year = {2024}, } @article{17890, abstract = {Our understanding of the molecular pathways that regulate oogenesis and define cellular identity in the Arthropod female reproductive system and the extent of their conservation is currently very limited. This is due to the focus on model systems, including Drosophila and Daphnia, which do not reflect the observed diversity of morphologies, reproductive modes, and sex chromosome systems. We use single-nucleus RNA and ATAC sequencing to produce a comprehensive single nucleus atlas of the adult Artemia franciscana female reproductive system. We map our data to the Fly Cell Atlas single-nucleus dataset of the Drosophila melanogaster ovary, shedding light on the conserved regulatory programs between the two distantly related Arthropod species. We identify the major cell types known to be present in the Artemia ovary, including germ cells, follicle cells, and ovarian muscle cells. Additionally, we use the germ cells to explore gene regulation and expression of the Z chromosome during meiosis, highlighting its unique regulatory dynamics and allowing us to explore the presence of meiotic sex chromosome silencing in this group.}, author = {Elkrewi, Marwan N and Vicoso, Beatriz}, issn = {1553-7404}, journal = {PLoS Genetics}, number = {8}, publisher = {Public Library of Science}, title = {{Single-nucleus atlas of the Artemia female reproductive system suggests germline repression of the Z chromosome}}, doi = {10.1371/journal.pgen.1011376}, volume = {20}, year = {2024}, } @article{15009, abstract = {Since the commercialization of brine shrimp (genus Artemia) in the 1950s, this lineage, and in particular the model species Artemia franciscana, has been the subject of extensive research. However, our understanding of the genetic mechanisms underlying various aspects of their reproductive biology, including sex determination, is still lacking. This is partly due to the scarcity of genomic resources for Artemia species and crustaceans in general. Here, we present a chromosome-level genome assembly of A. franciscana (Kellogg 1906), from the Great Salt Lake, United States. The genome is 1 GB, and the majority of the genome (81%) is scaffolded into 21 linkage groups using a previously published high-density linkage map. We performed coverage and FST analyses using male and female genomic and transcriptomic reads to quantify the extent of differentiation between the Z and W chromosomes. Additionally, we quantified the expression levels in male and female heads and gonads and found further evidence for dosage compensation in this species.}, author = {Bett, Vincent K and Macon, Ariana and Vicoso, Beatriz and Elkrewi, Marwan N}, issn = {1759-6653}, journal = {Genome Biology and Evolution}, number = {1}, publisher = {Oxford University Press}, title = {{Chromosome-level assembly of Artemia franciscana sheds light on sex chromosome differentiation}}, doi = {10.1093/gbe/evae006}, volume = {16}, year = {2024}, } @article{17183, abstract = {The photon blockade breakdown in a continuously driven cavity QED system has been proposed as a prime example for a first-order driven-dissipative quantum phase transition. However, the predicted scaling from a microscopic behavior—dominated by quantum fluctuations—to a macroscopic one—characterized by stable phases—and the associated exponents and phase diagram have not been observed so far. In this work we couple a single transmon qubit with a fixed coupling strength 𝑔 to a superconducting cavity that is in situ bandwidth 𝜅 tunable to controllably approach this thermodynamic limit. Even though the system remains microscopic, we observe its behavior becoming increasingly macroscopic as a function of 𝑔/𝜅. For the highest realized 𝑔/𝜅 of approximately 287, the system switches with a characteristic timescale as long as 6 s between a bright coherent state with approximately 8×103 intracavity photons and the vacuum state. This exceeds the microscopic timescales by 6 orders of magnitude and approaches the perfect hysteresis expected between two macroscopic attractors in the thermodynamic limit. These findings and interpretation are qualitatively supported by neoclassical theory and large-scale quantum-jump Monte Carlo simulations. Besides shedding more light on driven-dissipative physics in the limit of strong light-matter coupling, this system might also find applications in quantum sensing and metrology.}, author = {Sett, Riya and Hassani, Farid and Phan, Duc T and Barzanjeh, Shabir and Vukics, Andras and Fink, Johannes M}, issn = {2691-3399}, journal = {PRX Quantum}, number = {1}, publisher = {American Physical Society}, title = {{Emergent macroscopic bistability induced by a single superconducting qubit}}, doi = {10.1103/prxquantum.5.010327}, volume = {5}, year = {2024}, } @article{14796, abstract = {Key innovations are fundamental to biological diversification, but their genetic basis is poorly understood. A recent transition from egg-laying to live-bearing in marine snails (Littorina spp.) provides the opportunity to study the genetic architecture of an innovation that has evolved repeatedly across animals. Individuals do not cluster by reproductive mode in a genome-wide phylogeny, but local genealogical analysis revealed numerous small genomic regions where all live-bearers carry the same core haplotype. Candidate regions show evidence for live-bearer–specific positive selection and are enriched for genes that are differentially expressed between egg-laying and live-bearing reproductive systems. Ages of selective sweeps suggest that live-bearer–specific alleles accumulated over more than 200,000 generations. Our results suggest that new functions evolve through the recruitment of many alleles rather than in a single evolutionary step.}, author = {Stankowski, Sean and Zagrodzka, Zuzanna B. and Garlovsky, Martin D. and Pal, Arka and Shipilina, Daria and Garcia Castillo, Diego Fernando and Lifchitz, Hila and Le Moan, Alan and Leder, Erica and Reeve, James and Johannesson, Kerstin and Westram, Anja M and Butlin, Roger K.}, issn = {1095-9203}, journal = {Science}, number = {6678}, pages = {114--119}, publisher = {American Association for the Advancement of Science}, title = {{The genetic basis of a recent transition to live-bearing in marine snails}}, doi = {10.1126/science.adi2982}, volume = {383}, year = {2024}, } @misc{18978, abstract = {Data analysis files for the manuscript "Emergent Macroscopic Bistability Induced by a Single Superconducting Qubit". This contains the raw data and the data analysis files for generating the figures in the manuscript. Figure1 file - The raw data of cavity transmission spectra for 6 different kappas are there. They are fitted with input-output theory in the python file. Figure2 file - The raw data at 8 MHz kappa are included. all hte figures in figure 2 are generated in the python file Figure3 file - The raw data of PBB single shot measurements at all kappas are included. The detailed analysis and the Figure3 generated for the paper are all in the python analysis file. Also, thefiles containing the time-evolution of the intensity from Master Equation solution are included. Figure4 file - The raw data at 2.6 MHz for different drive detunings and the corresponding analyses are included. And the python file includes the analysis of the experimental data as well as approximate neoclassical equations solutions for 2-level and 3-level transmons are included. }, author = {Sett, Riya and Hassani, Farid and Phan, Duc T and Barzanjeh, Shabir and Vukics, Andras and Fink, Johannes M}, publisher = {Zenodo}, title = {{Data Analysis files for "Emergent Macroscopic Bistability Induced by a Single Superconducting Qubit"}}, doi = {10.5281/ZENODO.10518320}, year = {2024}, } @article{11479, abstract = {Understanding population divergence that eventually leads to speciation is essential for evolutionary biology. High species diversity in the sea was regarded as a paradox when strict allopatry was considered necessary for most speciation events because geographical barriers seemed largely absent in the sea, and many marine species have high dispersal capacities. Combining genome-wide data with demographic modelling to infer the demographic history of divergence has introduced new ways to address this classical issue. These models assume an ancestral population that splits into two subpopulations diverging according to different scenarios that allow tests for periods of gene flow. Models can also test for heterogeneities in population sizes and migration rates along the genome to account, respectively, for background selection and selection against introgressed ancestry. To investigate how barriers to gene flow arise in the sea, we compiled studies modelling the demographic history of divergence in marine organisms and extracted preferred demographic scenarios together with estimates of demographic parameters. These studies show that geographical barriers to gene flow do exist in the sea but that divergence can also occur without strict isolation. Heterogeneity of gene flow was detected in most population pairs suggesting the predominance of semipermeable barriers during divergence. We found a weak positive relationship between the fraction of the genome experiencing reduced gene flow and levels of genome-wide differentiation. Furthermore, we found that the upper bound of the ‘grey zone of speciation’ for our dataset extended beyond that found before, implying that gene flow between diverging taxa is possible at higher levels of divergence than previously thought. Finally, we list recommendations for further strengthening the use of demographic modelling in speciation research. These include a more balanced representation of taxa, more consistent and comprehensive modelling, clear reporting of results and simulation studies to rule out nonbiological explanations for general results.}, author = {De Jode, Aurélien and Le Moan, Alan and Johannesson, Kerstin and Faria, Rui and Stankowski, Sean and Westram, Anja M and Butlin, Roger K. and Rafajlović, Marina and Fraisse, Christelle}, issn = {1752-4571}, journal = {Evolutionary Applications}, number = {2}, pages = {542--559}, publisher = {Wiley}, title = {{Ten years of demographic modelling of divergence and speciation in the sea}}, doi = {10.1111/eva.13428}, volume = {16}, year = {2023}, } @article{11706, abstract = {We say that (Formula presented.) if, in every edge coloring (Formula presented.), we can find either a 1-colored copy of (Formula presented.) or a 2-colored copy of (Formula presented.). The well-known states that the threshold for the property (Formula presented.) is equal to (Formula presented.), where (Formula presented.) is given by (Formula presented.) for any pair of graphs (Formula presented.) and (Formula presented.) with (Formula presented.). In this article, we show the 0-statement of the Kohayakawa–Kreuter conjecture for every pair of cycles and cliques. }, author = {Liebenau, Anita and Mattos, Letícia and Mendonca Dos Santos, Walner and Skokan, Jozef}, issn = {1098-2418}, journal = {Random Structures and Algorithms}, number = {4}, pages = {1035--1055}, publisher = {Wiley}, title = {{Asymmetric Ramsey properties of random graphs involving cliques and cycles}}, doi = {10.1002/rsa.21106}, volume = {62}, year = {2023}, } @article{11741, abstract = {Following E. Wigner’s original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices H+xA with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just using the randomness of a single scalar real random variable x. Both results constitute quenched versions of bulk universality that has so far only been proven in annealed sense with respect to the probability space of the matrix ensemble.}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {1432-2064}, journal = {Probability Theory and Related Fields}, pages = {1183–1218}, publisher = {Springer Nature}, title = {{Quenched universality for deformed Wigner matrices}}, doi = {10.1007/s00440-022-01156-7}, volume = {185}, year = {2023}, } @article{11999, abstract = {A simple drawing D(G) of a graph G is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge e in the complement of G can be inserted into D(G) if there exists a simple drawing of G+e extending D(G). As a result of Levi’s Enlargement Lemma, if a drawing is rectilinear (pseudolinear), that is, the edges can be extended into an arrangement of lines (pseudolines), then any edge in the complement of G can be inserted. In contrast, we show that it is NP-complete to decide whether one edge can be inserted into a simple drawing. This remains true even if we assume that the drawing is pseudocircular, that is, the edges can be extended to an arrangement of pseudocircles. On the positive side, we show that, given an arrangement of pseudocircles A and a pseudosegment σ, it can be decided in polynomial time whether there exists a pseudocircle Φσ extending σ for which A∪{Φσ} is again an arrangement of pseudocircles.}, author = {Arroyo Guevara, Alan M and Klute, Fabian and Parada, Irene and Vogtenhuber, Birgit and Seidel, Raimund and Wiedera, Tilo}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {745–770}, publisher = {Springer Nature}, title = {{Inserting one edge into a simple drawing is hard}}, doi = {10.1007/s00454-022-00394-9}, volume = {69}, year = {2023}, } @article{12086, abstract = {We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-k mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order-k mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation. We extend this algorithm to compute higher-order α-shapes and provide open-source implementations. We present experimental results for properties of higher-order Delaunay mosaics of random point sets.}, author = {Edelsbrunner, Herbert and Osang, Georg F}, issn = {1432-0541}, journal = {Algorithmica}, pages = {277--295}, publisher = {Springer Nature}, title = {{A simple algorithm for higher-order Delaunay mosaics and alpha shapes}}, doi = {10.1007/s00453-022-01027-6}, volume = {85}, year = {2023}, } @article{12087, abstract = {Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers over group algebras and generalized depolarizing semigroups.}, author = {Wirth, Melchior and Zhang, Haonan}, issn = {1424-0637}, journal = {Annales Henri Poincare}, pages = {717--750}, publisher = {Springer Nature}, title = {{Curvature-dimension conditions for symmetric quantum Markov semigroups}}, doi = {10.1007/s00023-022-01220-x}, volume = {24}, year = {2023}, } @article{12104, abstract = {We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces.}, author = {Dello Schiavo, Lorenzo and Wirth, Melchior}, issn = {1424-3202}, journal = {Journal of Evolution Equations}, number = {1}, publisher = {Springer Nature}, title = {{Ergodic decompositions of Dirichlet forms under order isomorphisms}}, doi = {10.1007/s00028-022-00859-7}, volume = {23}, year = {2023}, }