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Utilizing nonlinear interferometers for sensing with undetected light enables new sensing and imaging techniques in spectral ranges that are difficult to detect. To enhance this method for future applications, it is advantageous to extract both amplitude and phase information of an object. This study introduces two approaches for synthetic quantum holography with undetected light, which allows for obtaining an object's amplitude and phase information in a nonlinear interferometer by capturing only a single image. One method is based on quasi-phase-shifting holography using superpixel structures displayed on a spatial light modulator. The other method relies on synthetic off-axis holography implemented through a linear phase gradient on a spatial light modulator. Both approaches are experimentally analyzed for applicability and compared against available multi-acquisition methods., Comment: 13 pages, 9 figures

Identifying conservation laws is central to every subfield of physics, as they illuminate the underlying symmetries and fundamental principles. These laws have far-reaching implications, not only enhancing our theoretical understanding but also enabling practical applications. A prime example can be found in quantum optics: The conservation of orbital angular momentum (OAM) during spontaneous parametric down-conversion (SPDC) enables the generation of a photon pair with entangled OAM. This quantum correlation is commonly attributed to the conservation of the topological charge of a strong coherent pump field driving the process. However, the topological charge of such a classical field only determines the average OAM per photon, so that the total OAM carried by the field has fluctuations as a direct consequence of its photon statistics. In this article, we report on the first realisation of SPDC pumped by a single twisted photon. Our results confirm OAM conservation at the single-photon level and directly transfer to SPDC induced by classical pump fields by averaging over their photon statistics. In addition to verifying a central property of SPDC, our results present the first implementation of cascaded down-conversion in bulk media, setting the stage for experiments on the direct generation of multi-photon high-dimensional entanglement using all degrees of freedom of light.

Planar scanning probe microscopy is a recently emerging alternative approach to tip-based scanning probe imaging. It can scan an extended planar sensor, such as a polished bulk diamond doped with magnetic-field-sensitive nitrogen-vacancy (NV) centers, in nanometer-scale proximity of a planar sample. So far, this technique has been limited to optical near-field microscopy, and has required nanofabrication of the sample of interest. Here we extend this technique to magnetometry using NV centers, and present a modification that removes the need for sample-side nanofabrication. We harness this new ability to perform a hitherto infeasible measurement - direct imaging of the three-dimensional vector magnetic field of magnetic vortices in a thin film magnetic heterostructure, based on repeated scanning with NV centers with different orientations within the same scanning probe. Our result opens the door to quantum sensing using multiple qubits within the same scanning probe, a prerequisite for the use of entanglement-enhanced and massively parallel schemes.

The INTENTAS project aims to develop an atomic sensor utilizing entangled Bose-Einstein condensates (BECs) in a microgravity environment. This key achievement is necessary to advance the capability for measurements that benefit from both entanglement-enhanced sensitivities and extended interrogation times. The project addresses significant challenges related to size, weight, and power management (SWaP) specific to the experimental platform at the Einstein-Elevator in Hannover. The design ensures a low-noise environment essential for the creation and detection of entanglement. Additionally, the apparatus features an innovative approach to the all-optical creation of BECs, providing a flexible system for various configurations and meeting the requirements for rapid turnaround times. Successful demonstration of this technology in the Einstein-Elevator will pave the way for a future deployment in space, where its potential applications will unlock high-precision quantum sensing.

Increasing the sensitivity of light-pulse atom interferometers progressively relies on large-momentum transfer techniques. Precise control of such methods is imperative to exploit the full capabilities of these quantum sensors. One key element is the mitigation of deleterious effects such as parasitic paths deteriorating the interferometric signal. In this work, we present the experimental realization of dichroic mirror pulses for atom interferometry specifically designed for higher-order Bragg diffraction. Our approach selectively reflects resonant atom paths into the detected interferometer output, ensuring that these contribute to the signal with intent. Simultaneously, parasitic paths are efficiently transmitted by the mirror and not directed to the relevant interferometer outputs. This method effectively isolates the desired interferometric signal from noise induced by unwanted paths. It not only demonstrates enhanced control over the atomic trajectories but also represents a significant step forward in optimizing the performance of light-pulse atom interferometers for high-precision applications.

If the quantum mechanical recoil of the electron due to its scattering from the undulator and laser fields dominates the dynamics, a regime of the free-electron laser emerges where quantum effects lead to a drastic change in the radiation properties. However, the large interaction length required for a single-pass quantum free-electron laser impedes the experimental realization. The quantum free-electron laser oscillator, proposed in the present article, is a possible scheme to resolve this issue. Here we show that this device features a photon statistics that is closer to a coherent state in comparison to existing classical free-electron lasers. The device can be even operated in such a way that a sub-Poissonian statistics is obtained. Beside the benefit of demonstrating this pure quantum effect, the narrowing of the photon distribution implies reduced intensity fluctuations of the emitted radiation, which in turn lead to decreased noise in imaging experiments or to an enhanced sensitivity in interferometric applications.

When silica-filled rubber compounds are deformed, structural modifications in the material's bulk lead to irreversible damage, the most significant of which is cavitation appearing within the interfaces of interconnected polymer and filler networks. This work introduces a new method to analyze cavitation in industrial-grade rubbers based on Ultra Small-Angle X-ray Scattering. This method employs a specially designed multi-sample stretching device for high-throughput measurements with statistical relevance. The proposed data reduction approach allows for early detection and quantification of cavitation while providing at the same time information on the hierarchical filler structures at length scales ranging from the primary particle size to large silica agglomerates over four orders of magnitude. To validate the method, the scattering of SSBR rubber compounds filled with highly dispersible silica at different ratios was measured under quasi-static strain. The strain was applied in incremental steps up to a maximum achievable elongation or breakage of the sample. From the measurements performed in multiple repetitions, it was found that the minimum strain necessary for cavity formation and the size evolution of the cavities with increasing strain are comparable between these samples. The sample with the highest polymer content showed the lowest rate of cavity formation and higher durability of silica structures. The structural stability of the compounds was determined by the evolution of the filler hierarchical structures, obtained by fitting data across the available strain range., Comment: 17 pages with 2 tables and 13 figures

High-level visual brain regions contain subareas in which neurons appear to respond more strongly to examples of a particular semantic category, like faces or bodies, rather than objects. However, recent work has shown that while this finding holds on average, some out-of-category stimuli also activate neurons in these regions. This may be due to visual features common among the preferred class also being present in other images. Here, we propose a deep-learning-based approach for visualizing these features. For each neuron, we identify relevant visual features driving its selectivity by modelling responses to images based on latent activations of a deep neural network. Given an out-of-category image which strongly activates the neuron, our method first identifies a reference image from the preferred category yielding a similar feature activation pattern. We then backpropagate latent activations of both images to the pixel level, while enhancing the identified shared dimensions and attenuating non-shared features. The procedure highlights image regions containing shared features driving responses of the model neuron. We apply the algorithm to novel recordings from body-selective regions in macaque IT cortex in order to understand why some images of objects excite these neurons. Visualizations reveal object parts which resemble parts of a macaque body, shedding light on neural preference of these objects., Comment: Replaced by camera-ready version for NeurIPS 2024. Fixed some typos and a small inaccuracy in the method decription

Generative foundation models like Stable Diffusion comprise a diverse spectrum of knowledge in computer vision with the potential for transfer learning, e.g., via generating data to train student models for downstream tasks. This could circumvent the necessity of collecting labeled real-world data, thereby presenting a form of data-free knowledge distillation. However, the resultant student models show a significant drop in accuracy compared to models trained on real data. We investigate possible causes for this drop and focus on the role of the different layers of the student model. By training these layers using either real or synthetic data, we reveal that the drop mainly stems from the model's final layers. Further, we briefly investigate other factors, such as differences in data-normalization between synthetic and real, the impact of data augmentations, texture vs.\ shape learning, and assuming oracle prompts. While we find that some of those factors can have an impact, they are not sufficient to close the gap towards real data. Building upon our insights that mainly later layers are responsible for the drop, we investigate the data-efficiency of fine-tuning a synthetically trained model with real data applied to only those last layers. Our results suggest an improved trade-off between the amount of real training data used and the model's accuracy. Our findings contribute to the understanding of the gap between synthetic and real data and indicate solutions to mitigate the scarcity of labeled real data.

Context: The growing size of graph-based modeling artifacts in model-driven engineering calls for techniques that enable efficient execution of graph queries. Incremental approaches based on the RETE algorithm provide an adequate solution in many scenarios, but are generally designed to search for query results over the entire graph. However, in certain situations, a user may only be interested in query results for a subgraph, for instance when a developer is working on a large model of which only a part is loaded into their workspace. In this case, the global execution semantics can result in significant computational overhead. Contribution: To mitigate the outlined shortcoming, in this paper we propose an extension of the RETE approach that enables local, yet fully incremental execution of graph queries, while still guaranteeing completeness of results with respect to the relevant subgraph. Results: We empirically evaluate the presented approach via experiments inspired by a scenario from software development and an independent social network benchmark. The experimental results indicate that the proposed technique can significantly improve performance regarding memory consumption and execution time in favorable cases, but may incur a noticeable linear overhead in unfavorable cases., Comment: This preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this contribution is published in Graph Transformation, and is available online at https://doi.org/10.1007/978-3-031-64285-2_7

What time does a clock tell after quantum tunneling? Predictions and indirect measurements range from superluminal or instantaneous tunneling to finite durations, depending on the specific experiment and the precise definition of the elapsed time. Proposals and implementations utilize the atomic motion to define this delay, even though the inherent quantum nature of atoms implies a delocalization and is in sharp contrast to classical trajectories. Here, we rely on an operational approach: we prepare atoms in a coherent superposition of internal states and study the time read off via a Ramsey sequence after the tunneling process without the notion of classical trajectories or velocities. Our operational framework (a) unifies definitions of tunneling delay within one approach; (b) connects the time to a frequency standard given by a conventional atomic clock which can be boosted by differential light shifts; and (c) highlights that there exists no superluminal or instantaneous tunneling., Comment: 9 pages, 5 figures

Ultracold atomic gases hold unique promise for space science by capitalizing on quantum advantages and extended freefall, afforded in a microgravity environment, to enable next-generation precision sensors. Atom interferometers are a class of quantum sensors which can use freely falling gases of atoms cooled to sub-photon-recoil temperatures to provide unprecedented sensitivities to accelerations, rotations, and gravitational forces, and are currently being developed for space-based applications in gravitational, earth, and planetary sciences, as well as to search for subtle forces that could signify physics beyond General Relativity and the Standard Model. NASA's Cold Atom Lab (CAL) operates onboard the International Space Station as a multi-user facility for studies of ultracold atoms and to mature quantum technologies, including atom interferometry, in persistent microgravity. In this paper, we report on path-finding experiments utilizing ultracold $^{87}$Rb atoms in the CAL atom interferometer, which was enabled by an on-orbit upgrade of the CAL science module: A three-pulse Mach-Zehnder interferometer was studied to understand limitations from the influence of ISS vibrations. Additionally, Ramsey shear-wave interferometry was used to manifest interference patterns in a single run that were observable for over 150 ms free-expansion time. Finally, the CAL atom interferometer was used to remotely measure the photon recoil from the atom interferometer laser as a demonstration of the first quantum sensor using matter-wave interferometry in space., Comment: 14 pages, 5 figures

The mimicking of human-like arm movement characteristics involves the consideration of three factors during control policy synthesis: (a) chosen task requirements, (b) inclusion of noise during movement execution and (c) chosen optimality principles. Previous studies showed that when considering these factors (a-c) individually, it is possible to synthesize arm movements that either kinematically match the experimental data or reproduce the stereotypical triphasic muscle activation pattern. However, to date no quantitative comparison has been made on how realistic the arm movement generated by each factor is; as well as whether a partial or total combination of all factors results in arm movements with human-like kinematic characteristics and a triphasic muscle pattern. To investigate this, we used reinforcement learning to learn a control policy for a musculoskeletal arm model, aiming to discern which combination of factors (a-c) results in realistic arm movements according to four frequently reported stereotypical characteristics. Our findings indicate that incorporating velocity and acceleration requirements into the reaching task, employing reward terms that encourage minimization of mechanical work, hand jerk, and control effort, along with the inclusion of noise during movement, leads to the emergence of realistic human arm movements in reinforcement learning. We expect that the gained insights will help in the future to better predict desired arm movements and corrective forces in wearable assistive devices.

The way the media presents events can significantly affect public perception, which in turn can alter people's beliefs and views. Media bias describes a one-sided or polarizing perspective on a topic. This article summarizes the research on computational methods to detect media bias by systematically reviewing 3140 research papers published between 2019 and 2022. To structure our review and support a mutual understanding of bias across research domains, we introduce the Media Bias Taxonomy, which provides a coherent overview of the current state of research on media bias from different perspectives. We show that media bias detection is a highly active research field, in which transformer-based classification approaches have led to significant improvements in recent years. These improvements include higher classification accuracy and the ability to detect more fine-granular types of bias. However, we have identified a lack of interdisciplinarity in existing projects, and a need for more awareness of the various types of media bias to support methodologically thorough performance evaluations of media bias detection systems. Concluding from our analysis, we see the integration of recent machine learning advancements with reliable and diverse bias assessment strategies from other research areas as the most promising area for future research contributions in the field.

Quantum sensing using non-linear interferometers offers the possibility of bicolour imaging, using light that never interacted with the object of interest, and provides a way to achieve phase supersensitivity, i.e. a Heisenberg-type scaling of the phase uncertainty. Such a scaling behaviour is extremely susceptible to noise and only arises at specific phases that define the optimal working point of the device. While phase-shifting algorithms are to some degree robust against the deleterious effects induced by noise they extract an image by tuning the interferometer phase over a broad range, implying an operation beyond the working point. In our theoretical study, we investigate both the spontaneous and the high-gain regime of operation of a non-linear interferometer. In fact, in the spontaneous regime using a distillation technique and operating at the working point leads to a qualitatively similar behaviour. In the high-gain regime, however, typical distillation techniques inherently forbid a scaling better than the standard-quantum limit, as a consequence of the photon statistics of squeezed vacuum. In contrast, an operation at the working point still may lead to a sensitivity below shot noise, even in the presence of noise. Therefore, this procedure opens the perspective of bicolour imaging with a better than shot-noise phase uncertainty by working in the vicinity of the working point. Our results transfer quantum imaging distillation in a noisy environment to the high-gain regime with the ultimate goal of harnessing its full potential by combining bicolour imaging and phase supersensitivity.

The Search for Extraterrestrial Intelligence aims to find evidence of technosignatures, which can point toward the possible existence of technologically advanced extraterrestrial life. Radio signals similar to those engineered on Earth may be transmitted by other civilizations, motivating technosignature searches across the entire radio spectrum. In this endeavor, the low-frequency radio band has remained largely unexplored; with prior radio searches primarily above 1 GHz. In this survey at 110-190 MHz, observations of 1,631,198 targets from TESS and Gaia are reported. Observations took place simultaneously with two international stations (noninterferometric) of the Low Frequency Array in Ireland and Sweden. We can reject the presence of any Doppler drifting narrowband transmissions in the barycentric frame of reference, with equivalent isotropic radiated power of 10 17 W, for 0.4 million (or 1.3 million) stellar systems at 110 (or 190) MHz. This work demonstrates the effectiveness of using multisite simultaneous observations for rejecting anthropogenic signals in the search for technosignatures., Comment: 15 Pages, 16 Figures, 2 Machine Readable Tables

The complex chemistry that occurs in star-forming regions can provide insight into the formation of prebiotic molecules at various evolutionary stages of star formation. To study this process, we present millimeter-wave interferometric observations of the neighboring hot cores W3(H$_2$O) and W3(OH) carried out using the NOEMA interferometer. We have analyzed distributions of six molecules that account for most observed lines across both cores and have constructed physical parameter maps for rotational temperature, column density, and velocity field with corresponding uncertainties. We discuss the derived spatial distributions of these parameters in the context of the physical structure of the source. We propose the use of HCOOCH$_3$ as a new temperature tracer in W3(H$_2$O) and W3(OH) in addition to the more commonly used CH$_3$CN. By analyzing the physically-derived parameters for each molecule across both W3(H$_2$O) and W3(OH), the work presented herein further demonstrates the impact of physical environment on hot cores at different evolutionary stages., Comment: Accepted to The Astrophysical Journal

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions., Comment: Summary of the Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at CERN: https://indico.cern.ch/event/1208783/

The Space Time Explorer and QUantum Equivalence principle Space Test (STE-QUEST) recently proposed, aims at performing a precision test of the weak equivalence principle (WEP), a fundamental cornerstone of General Relativity. Taking advantage of the ideal operation conditions for high-precision quantum sensing on board of a satellite, it aims to detect possible violations of WEP down to the $10^{-17}$ level. This level of performance leads to stringent environmental requirements on the control of the spacecraft. We assume an operation of a dual-species atom interferometer of rubidium and potassium isotopes in a double-diffraction configuration and derive the constraints to achieve an E\"otv\"os parameter $\eta=10^{-17}$ in statistical and systematic uncertainties. We show that technical heritage of previous satellite missions, such as MICROSCOPE, satisfies the platform requirements to achieve the proposed objectives underlying the technical readiness of the STE-QUEST mission proposal., Comment: 18 pages, 6 figures

Atom interferometers with long baselines are envisioned to complement the ongoing search for dark matter. They rely on atomic manipulation based on internal (clock) transitions or state-preserving atomic diffraction. Principally, dark matter can act on the internal as well as the external degrees of freedom to both of which atom interferometers are susceptible. We therefore study in this contribution the effects of dark matter on the internal atomic structure and the atoms' motion. In particular, we show that the atomic transition frequency depends on the mean coupling and the differential coupling of the involved states to dark matter, scaling with the unperturbed atomic transition frequency and the Compton frequency, respectively. The differential coupling is only of relevance when internal states change, which makes detectors, e.g., based on single-photon transitions sensitive to both coupling parameters. For sensors generated by state-preserving diffraction mechanisms like Bragg diffraction, the mean coupling modifies only the motion of the atom as the dominant contribution. Finally, we compare both effects observed in terrestrial dark-matter detectors.

Several terrestrial detectors for gravitational waves and dark matter based on long-baseline atom interferometry are currently in the final planning stages or already under construction. These upcoming vertical sensors are inherently subject to gravity and thus feature gradiometer or multi-gradiometer configurations using single-photon transitions for large momentum transfer. While there has been significant progress on optimizing these experiments against detrimental noise sources and for deployment at their projected sites, finding optimal configurations that make the best use of the available resources are still an open issue. Even more, the fundamental limit of the device's sensitivity is still missing. Here we fill this gap and show that (a) resonant-mode detectors based on multi-diamond fountain gradiometers achieve the optimal, shot-noise limited, sensitivity if their height constitutes 20% of the available baseline; (b) this limit is independent of the dark-matter oscillation frequency; and (c) doubling the baseline decreases the ultimate measurement uncertainty by approximately 65%. Moreover, we propose a multi-diamond scheme with less mirror pulses where the leading-order gravitational phase contribution is suppressed, compare it to established geometries, and demonstrate that both configurations saturate the same fundamental limit., Comment: 9 pages, 2 figures

Single-photon transitions are one of the key technologies for designing and operating very-long-baseline atom interferometers tailored for terrestrial gravitational-wave and dark-matter detection. Since such setups aim at the detection of relativistic and beyond-Standard-Model physics, the analysis of interferometric phases as well as of atomic diffraction must be performed to this precision and including these effects. In contrast, most treatments focused on idealized diffraction so far. Here, we study single-photon transitions, both magnetically-induced and direct ones, in gravity and Standard-Model extensions modeling dark matter as well as Einstein-equivalence-principle violations. We take into account relativistic effects like the coupling of internal to center-of-mass degrees of freedom, induced by the mass defect, as well as the gravitational redshift of the diffracting light pulse. To this end, we also include chirping of the light pulse required by terrestrial setups, as well as its associated modified momentum transfer for single-photon transitions., Comment: 12 pages, 3 figures, 2 tables

The 2021 outburst of the symbiotic recurrent nova RS Oph was monitored with the Neutron Star Interior Composition Explorer Mission (NICER) in the 0.2-12 keV range from day one after the optical maximum, until day 88, producing an unprecedented, detailed view of the outburst development. The X-ray flux preceding the supersoft X-ray phase peaked almost 5 days after optical maximum and originated only in shocked ejecta for 21 to 25 days. The emission was thermal; in the first 5 days only a non-collisional-ionization equilibrium model fits the spectrum, and a transition to equilibrium occurred between days 6 and 12. The ratio of peak X-rays flux measured in the NICER range to that measured with Fermi in the 60 MeV-500 GeV range was about 0.1, and the ratio to the peak flux measured with H.E.S.S. in the 250 GeV-2.5 TeV range was about 100. The central supersoft X-ray source (SSS), namely the shell hydrogen burning white dwarf (WD), became visible in the fourth week, initially with short flares. A huge increase in flux occurred on day 41, but the SSS flux remained variable. A quasi-periodic oscillation every ~35 s was always observed during the SSS phase, with variations in amplitude and a period drift that appeared to decrease in the end. The SSS has characteristics of a WD of mass >1 M(solar). Thermonuclear burning switched off shortly after day 75, earlier than in 2006 outburst. We discuss implications for the nova physics., Comment: Accepted for publication in the Astrophysical Journal

Presented here are NOEMA interferometric observations of the neighboring hot cores W3(H$_{2}$O) and W3(OH). The presence of two star-forming cores at different evolutionary stages within the same parent cloud presents a unique opportunity to study how the physics of the source and its evolutionary stage impact the chemistry. Through spectral analysis and imaging, we identify over twenty molecules in these cores. Most notably, we have detected HDO and CH$_{3}$CH$_{2}$CN in W3(OH), which were previously not detected in this core. We have imaged the molecular emission, revealing new structural features within these sources. W3(OH) shows absorption in a "dusty cocoon" surrounded by molecular emission. These observations also reveal extended emission that is potentially indicative of a low-velocity shock. From the information obtained herein, we have constructed column density and temperature maps for methanol and compared this information to the molecular images. By comparing the spatial distribution of molecules which may be destroyed at later stages of star formation, this work demonstrates the impact of physical environment on chemistry in star-forming regions at different evolutionary stages., Comment: Published in The Astrophysical Journal

Atomic high-precision measurements have become a competitive and essential technique for tests of fundamental physics, the Standard Model, and our theory of gravity. It is therefore self-evident that such measurements call for a consistent relativistic description of atoms that eventually originates from quantum field theories like quantum electrodynamics. Most quantum-metrological approaches even postulate effective field-theoretical treatments to describe a precision enhancement through techniques like squeezing. However, a consistent derivation of interacting atomic quantum gases from an elementary quantum field theory that includes both the internal structure as well as the center of mass of atoms, has not yet been addressed. We present such a subspace effective field theory for interacting, spin carrying, and possibly charged ensembles of atoms composed of nucleus and electron that form composite bosons called cobosons, where the interaction with light is included in a multipolar description. Relativistic corrections to the energy of a single coboson, light-matter interaction, and the scattering potential between cobosons arise in a consistent and natural manner. In particular, we obtain a relativistic coupling between the coboson's center-of-mass motion and internal structure encoded by the mass defect. We use these results to derive modified bound-state energies, including the motion of ions, modified scattering potentials, a relativistic extension of the Gross-Pitaevskii equation, and the mass defect applicable to atomic clocks or quantum clock interferometry., Comment: 35 pages, 8 figures, 6 tables

Like conventional software projects, projects in model-driven software engineering require adequate management of multiple versions of development artifacts, importantly allowing living with temporary inconsistencies. In previous work, multi-version models for model-driven software engineering have been introduced, which allow checking well-formedness and finding merge conflicts for multiple versions of a model at once. However, also for multi-version models, situations where different artifacts, that is, different models, are linked via automatic model transformations have to be handled. In this paper, we propose a technique for jointly handling the transformation of multiple versions of a source model into corresponding versions of a target model, which enables the use of a more compact representation that may afford improved execution time of both the transformation and further analysis operations. Our approach is based on the well-known formalism of triple graph grammars and the aforementioned encoding of model version histories called multi-version models. In addition to batch transformation of an entire model version history, the technique also covers incremental synchronization of changes in the framework of multi-version models. We show the correctness of our approach with respect to the standard semantics of triple graph grammars and conduct an empirical evaluation to investigate the performance of our technique regarding execution time and memory consumption. Our results indicate that the proposed technique affords lower memory consumption and may improve execution time for batch transformation of large version histories, but can also come with computational overhead in unfavorable cases., Comment: arXiv admin note: substantial text overlap with arXiv:2301.00623