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Jürgen Müller

Publications and source records attributed to Jürgen Müller.

At least 19 recordsLinked to original sources
arXiv2026

Determination of Physical Height Differences from Time Transfer via the ACES Mission -- A Simulation Study

The determination of physical height differences using highly stable atomic clocks has emerged as a novel approach in relativistic geodesy, exploiting the gravitational redshift as a direct observable of geopotential differences. In this study, we investigate the feasibility of satellite-based clock comparisons using the Atomic Clock Ensemble in Space (ACES) onboard the International Space Station, which enables time transfer via microwave (MWL) and optical (ELT) links. Since operational optical data are not yet available, a comprehensive full-scale simulation of realistic ACES observation scenarios is performed, including detailed noise models of clocks and links. A slope-based estimation method is applied to time series of clock comparisons in order to extract the relativistic redshift signal and derive height differences between the ground stations. The performance of the approach is evaluated for quasi-common view, non-common view, and split non-common view configurations, where the latter divides the observation period into shorter intervals. The results show that optical links enable faster convergence and can achieve height accuracies at the decimeter level within a few days and at the centimeter level over longer periods, while microwave links are more strongly affected by noise and bias contributions. Non-common view processing significantly increases observation availability with only minor loss in accuracy, and the split approach provides robust solutions for larger networks. These findings demonstrate the strong potential of satellite-based clock comparisons as a remote-sensing technique for determining physical height differences on a continental scale.

physics.geo-ph↗
arXiv2026

Frequency Differences between Clocks on the Earth and the Moon

Based on general relativity, clock frequency comparisons support various geodetic applications on Earth, such as determining the gravitational potential and realizing a global height system. Future lunar clocks could extend these capabilities to the Moon, connect to terrestrial clock-comparison networks, and, in principle, serve as reference clocks. Meanwhile, especially driven by future lunar navigation plans, an independent lunar time system is becoming an urgent requirement and such a system would necessarily remain linked to terrestrial time standards. To support these future applications, we establish a comprehensive model for Earth-Moon clock frequency comparisons. This paper simulates fractional frequency differences between clocks on the Earth (E) and Moon (L) through four time transformations:proper-to-coordinate time for E-clocks and for L-clocks (both linked to the local gravity potential), the conversion between the Earth and Moon coordinate times, and the time signal propagation between E- and L-clocks. Gravity potential differences between the E- and L-clocks impact the frequency difference at the 10^-10 level. The effect of the coordinate time ratio is at 10^-11 level. Contributions from static, tidal, and non-tidal potentials, body self-rotation, and different celestial bodies are evaluated. Furthermore, we quantify the Doppler, atmospheric and Shapiro delay effects in Earth-Moon time signal propagation. For a single link, the first-order Doppler term dominates at the 10^-6 level and masks the gravity-potential and coordinate-time terms. A Doppler-cancelling multi-link strategy is needed to suppress the signal-propagation effect and extract these terms.

physics.geo-ph↗
arXiv2026

Demystifying Chains, Trees, and Graphs of Thoughts

The field of natural language processing (NLP) has witnessed significant progress in recent years, with a notable focus on improving large language models' (LLM) performance through innovative prompting techniques. Among these, prompt engineering coupled with structures has emerged as a promising paradigm, with designs such as Chain-of-Thought, Tree of Thoughts, or Graph of Thoughts, in which the overall LLM reasoning is guided by a structure such as a graph. As illustrated with numerous examples, this paradigm significantly enhances the LLM's capability to solve numerous tasks, ranging from logical or mathematical reasoning to planning or creative writing. To facilitate the understanding of this growing field and pave the way for future developments, we devise a general blueprint for effective and efficient LLM reasoning schemes. For this, we conduct an in-depth analysis of the prompt execution pipeline, clarifying and clearly defining different concepts. We then build the first taxonomy of structure-enhanced LLM reasoning schemes. We focus on identifying fundamental classes of harnessed structures, and we analyze the representations of these structures, algorithms executed with these structures, and many others. We refer to these structures as reasoning topologies, because their representation becomes to a degree spatial, as they are contained within the LLM context. Our study compares existing prompting schemes using the proposed taxonomy, discussing how certain design choices lead to different patterns in performance and cost. We also outline theoretical underpinnings, relationships between prompting and other parts of the LLM ecosystem such as knowledge bases, and the associated research challenges. Our work will help to advance future prompt engineering techniques.

cs.CL↗
arXiv2026

GraphSeek: Next-Generation Graph Analytics with LLMs

Graphs are foundational across domains but remain hard to use without deep expertise. LLMs promise accessible natural language (NL) graph analytics, yet they fail to process industry-scale property graphs effectively and efficiently: such datasets are large, highly heterogeneous, structurally complex, and evolve dynamically. To address this, we devise a novel abstraction for complex multi-query analytics over such graphs. Its key idea is to replace brittle generation of graph queries directly from NL with planning over a Semantic Catalog that describes both the graph schema and the graph operations. Concretely, this induces a clean separation between a Semantic Plane for LLM planning and broader reasoning, and an Execution Plane for deterministic, database-grade query execution over the full dataset and tool implementations. This design yields substantial gains in both token efficiency and task effectiveness even with small-context LLMs. We use this abstraction as the basis of the first LLM-enhanced graph analytics framework called GraphSeek. GraphSeek achieves substantially higher success rates (e.g., 86% over enhanced LangChain) and points toward the next generation of affordable and accessible graph analytics that unify LLM reasoning with database-grade execution over large and complex property graphs.

cs.DB↗
arXiv2026

Multi-Head RAG: Solving Multi-Aspect Problems with LLMs

Retrieval-Augmented Generation (RAG) improves Large Language Models (LLMs) by retrieving supporting documents into the prompt, but existing methods do not explicitly target queries that require fetching multiple documents with substantially different content. Such multi-aspect queries are challenging because relevant documents can be far apart in embedding space, making joint retrieval difficult. We introduce Multi-Head RAG (MRAG), which addresses this gap with a simple yet powerful idea: using Transformer multi-head attention activations rather than the standard decoder-layer embedding, as retrieval keys. It leverages the observation that different heads capture different semantic aspects. This yields multi-aspect embeddings for both documents and queries, improving retrieval accuracy on complex queries. We show MRAG's design advantages over 18 RAG baselines, up to 20% higher retrieval success ratios for real-world use cases, and improved downstream LLM generation. MRAG integrates seamlessly with existing RAG frameworks and benchmarks.

cs.CL↗
arXiv2026

NovaMoon: A Strategic Lunar Reference Station for Positioning, Timing, and Largely Enhanced Science in the Earth-Moon System

The renewed interest in lunar exploration and the development of future lunar communication and navigation services highlight the need for a precise, stable, and interoperable geodetic and timing infrastructure on the Moon. NovaMoon, proposed as a scientific and navigation payload for ESA's Argonaut lander, is designed as a lunar-based local differential, geodetic, and timing station supporting both operational needs in the Moon's south polar region and a broad range of scientific investigations. The payload integrates a lunar laser retroreflector, a Very Long Baseline Interferometry transmitter, a receiver for navigation signals compatible with LunaNet standards, high-stability atomic clocks, and direct-to-Earth radio links -- making it the first lunar station to co-locate multiple ranging, tracking, and timing techniques. NovaMoon will enable sub-metre to decimetre positioning, provide local differential corrections for lunar users, and ensure an accurate and stable realisation of position and time. Preliminary simulation studies show that this multi-technique dataset improves the lunar reference frame, orientation and ephemerides, and estimates of interior parameters like tidal response and core properties. NovaMoon will also provide the first long-duration physical realisation of a lunar time reference. Beyond its primary goals, it supports improved cartography, precise surface geolocation, and higher-resolution topography, contributing to safer landings and operations. It also enables new tests of fundamental physics, including constraints on relativity and possible deviations from classical gravity.

astro-ph.EP↗
arXiv2025

Demystifying Higher-Order Graph Neural Networks

Higher-order graph neural networks (HOGNNs) and the related architectures from Topological Deep Learning are an important class of GNN models that harness polyadic relations between vertices beyond plain edges. They have been used to eliminate issues such as over-smoothing or over-squashing, to significantly enhance the accuracy of GNN predictions, to improve the expressiveness of GNN architectures, and for numerous other goals. A plethora of HOGNN models have been introduced, and they come with diverse neural architectures, and even with different notions of what the "higher-order" means. This richness makes it very challenging to appropriately analyze and compare HOGNN models, and to decide in what scenario to use specific ones. To alleviate this, we first design an in-depth taxonomy and a blueprint for HOGNNs. This facilitates designing models that maximize performance. Then, we use our taxonomy to analyze and compare the available HOGNN models. The outcomes of our analysis are synthesized in a set of insights that help to select the most beneficial GNN model in a given scenario, and a comprehensive list of challenges and opportunities for further research into more powerful HOGNNs.

cs.LG↗
arXiv2025

The projective cover of the trivial module in characteristic $11$ for the sporadic simple Janko group $J_4$ revisited

This is a sequel to arXiv:2509.05805 [math.RT], where we have determined the $11$-modular projective indecomposable summands of the permutation character of $J_4$ on the cosets of an $11'$-subgroup of maximal order, amongst them the projective cover of the trivial module, up to a certain parameter. Here, we fix this parameter, by applying a new condensation method for induced modules which uses enumeration techniques for long orbits.

math.RT↗
arXiv2025

Psychologically Enhanced AI Agents

We introduce MBTI-in-Thoughts, a framework for enhancing the effectiveness of Large Language Model (LLM) agents through psychologically grounded personality conditioning. Drawing on the Myers-Briggs Type Indicator (MBTI), our method primes agents with distinct personality archetypes via prompt engineering, enabling control over behavior along two foundational axes of human psychology, cognition and affect. We show that such personality priming yields consistent, interpretable behavioral biases across diverse tasks: emotionally expressive agents excel in narrative generation, while analytically primed agents adopt more stable strategies in game-theoretic settings. Our framework supports experimenting with structured multi-agent communication protocols and reveals that self-reflection prior to interaction improves cooperation and reasoning quality. To ensure trait persistence, we integrate the official 16Personalities test for automated verification. While our focus is on MBTI, we show that our approach generalizes seamlessly to other psychological frameworks such as Big Five, HEXACO, or Enneagram. By bridging psychological theory and LLM behavior design, we establish a foundation for psychologically enhanced AI agents without any fine-tuning.

cs.AI↗
arXiv2025

Machine Learning Algorithms for Transplanting Accelerometer Observations in Future Satellite Gravimetry Missions

Accurate and continuous monitoring of Earth's gravity field is essential for tracking mass redistribution processes linked to climate variability, hydrological cycles, and geodynamic phenomena. While the GRACE and GRACE Follow-On (GRACE-FO) missions have set the benchmark for satellite gravimetry using low-low satellite to satellite tracking (LL-SST), the precision of gravity field recovery still strongly depends on the quality of accelerometer (ACC) performance and the continuity of ACC data. Traditional electrostatic accelerometers (EA) face limitations that can hinder mission outcomes, prompting exploration of advanced sensor technologies and data recovery techniques. This study presents a systematic evaluation of accelerometer data transplantation using novel accelerometer configurations, including Cold Atom Interferometry (CAI) accelerometers and hybrid EA-CAI setups, and applying both analytical and machine learning-based methods. Using comprehensive closed-loop LL-SST simulations, we compare four scenarios ranging from the conventional EA-only setup to ideal dual hybrid configurations, with a particular focus on the performance of transplant-based approaches using different neural network approaches. Our results show that the dual hybrid configuration provides the most accurate gravity field retrieval. However, the transplant-based hybrid setup, especially when supported by machine learning, emerges as a robust and cost-effective alternative, achieving comparable performance with minimal extra hardware. These findings highlight the promise of combining quantum sensor technology and data-driven transplantation for future satellite gravimetry missions, paving the way for improved global monitoring of Earth's dynamic gravity field.

physics.geo-ph↗
arXiv2025

Higher-Order Graph Databases

Recent advances in graph databases (GDBs) have been driving interest in large-scale analytics, yet current systems fail to support higher-order (HO) interactions beyond first-order (one-hop) relations, which are crucial for tasks such as subgraph counting, polyadic modeling, and HO graph learning. We address this by introducing a new class of systems, higher-order graph databases (HO-GDBs) that use lifting and lowering paradigms to seamlessly extend traditional GDBs with HO. We provide a theoretical analysis of OLTP and OLAP queries, ensuring correctness, scalability, and ACID compliance. We implement a lightweight, modular, and parallelizable HO-GDB prototype that offers native support for hypergraphs, node-tuples, subgraphs, and other HO structures under a unified API. The prototype scales to large HO OLTP & OLAP workloads and shows how HO improves analytical tasks, for example enhancing accuracy of graph neural networks within a GDB by 44%. Our work ensures low latency and high query throughput, and generalizes both ACID-compliant and eventually consistent systems.

cs.DB↗
arXiv2025

Realization of a clock-based global height system: A simulation study for Europe and Brazil

Chronometric levelling is a novel technique for the realisation of the International Height Reference System (IHRS). A detailed study of this technique is carried out through closed-loop simulations, aiming to unify regional/local height systems (LHS) in Europe and Brazil. Focusing on a unification accuracy of 1 cm, realistic scenarios with various error parameters/vertical datum parameters in LHS and clock observation uncertainties were analysed. The errors associated with local heights raised from datum offsets, local vertical datum alignment discrepancies in latitude and longitude, accumulated tilts depending on the distance from the reference tide gauge and levelling point elevation-dependent offsets were introduced. Clocks achieving a fractional uncertainty of 10^-18 and 10^-17 were assumed in the simulations, considering temporal correlations of clock intrinsic uncertainties, external effects on clock observations such as tidal effects, propagation delay in terms of link uncertainties and presence of outliers. We determine the preferred distributions of clocks in a network for the best estimation of error parameters. The estimation of the error parameters is related to the spatial distribution of the clocks, hence, an optimal setup of placing clocks at the most distant levelling points, reference tide gauges and elevated points is implemented. Further, a configuration of clock distribution is proposed with master clocks and local clocks with reduced links. Taking into consideration all these realistic constraints, a unification accuracy of 1 cm can be obtained. The unified European and Brazilian height systems are further related to the global geoid such that all geoid-related heights achieve an accuracy of 3 cm.

physics.geo-ph↗
arXiv2025

Reasoning Language Models: A Blueprint

Reasoning language models (RLMs), also known as Large Reasoning Models (LRMs), such as OpenAI's o1 and o3, DeepSeek-R1, and Alibaba's QwQ, have redefined AI's problem-solving capabilities by extending LLMs with advanced reasoning mechanisms. Yet, their high costs, proprietary nature, and complex architectures - uniquely combining reinforcement learning (RL), search heuristics, and LLMs - present accessibility and scalability challenges. To address these, we propose a comprehensive blueprint that organizes RLM components into a modular framework, based on a survey and analysis of all RLM works. This blueprint incorporates diverse reasoning structures (chains, trees, graphs, and nested forms), reasoning strategies (e.g., Monte Carlo Tree Search, Beam Search), RL concepts (policy, value models and others), supervision schemes (Outcome-Based and Process-Based Supervision), and other related concepts (e.g., Test-Time Compute, Retrieval-Augmented Generation, agent tools). We also provide detailed mathematical formulations and algorithmic specifications to simplify RLM implementation. By showing how schemes like LLaMA-Berry, QwQ, Journey Learning, and Graph of Thoughts fit as special cases, we demonstrate the blueprint's versatility and unifying potential. To illustrate its utility, we introduce x1, a modular implementation for rapid RLM prototyping and experimentation. Using x1 and a literature review, we provide key insights, such as multi-phase training for policy and value models, and the importance of familiar training distributions. Finally, we discuss scalable RLM cloud deployments and we outline how RLMs can integrate with a broader LLM ecosystem. Our work demystifies RLM construction, democratizes advanced reasoning capabilities, and fosters innovation, aiming to mitigate the gap between "rich AI" and "poor AI" by lowering barriers to RLM design and experimentation.

cs.AI↗
arXiv2025

Evaluation of Deployable Solar Panels on GRACE-like Satellites by Closed-Loop Simulations

Future satellite gravimetry missions seek to surpass the performance of CHAMP, GOCE, GRACE, and GRACE-FO to meet increasing scientific and operational demands. These missions will integrate advanced technologies, including optical and quantum accelerometers, high-precision inter-satellite laser ranging, and micro-Newton electric thrusters. However, increased power demands for sensors and propulsion systems require larger solar panels, constrained by payload mass and launcher limitations. This study assesses the impact of modified satellite shapes on gravity field recovery (GFR) using closed-loop simulation. Five satellite configurations were analyzed: a standard shape and variations with single and double solar panels mounted on the top and bottom of the satellite body, each modeled with distinct finite element models and moments of inertia. Orbit simulations accounted for non-spherical static gravity and time-variable non-gravitational forces. Performance of a simplified gravitational reference sensor (SGRS) with optical interferometer test mass displacement readout was evaluated. The air drag coefficient, a complex parameter influenced by multiple factors, was varied from 2.25 (standard) to 4.5 (double-panel). Time-variable gravity background models were excluded to isolate instrument performance effects. Gravity models were evaluated in the spectral domain using Degree RMS of spherical harmonic coefficient differences. Discrepancies between configurations stemmed primarily from variations in SGRS actuation noise due to satellite cross-sectional area. Convergence of residuals in the spectral domain for the double-panel configuration under different drag coefficients confirmed the dominant role of SGRS performance in GFR accuracy.

physics.geo-ph↗
arXiv2024

Combined Classical and Quantum Accelerometers For the Next Generation of Satellite Gravity Missions

Cold atom interferometry (CAI)-based quantum accelerometers are very promising for future satellite gravity missions thanks to their strength in providing long-term stable and precise measurements of non-gravitational accelerations. However, their limitations due to the low measurement rate and the existence of ambiguities in the raw sensor measurements call for hybridization of the quantum accelerometer (Q-ACC) with a classical one (e.g., electrostatic) with higher bandwidth. While previous hybridization studies have so far considered simple noise models for the Q-ACC and neglected the impact of satellite rotation on the phase shift of the accelerometer, we perform here a more advanced hybridization simulation by implementing a comprehensive noise model for the satellite-based quantum accelerometers and considering the full impact of rotation, gravity gradient, and self-gravity on the instrument. We perform simulation studies for scenarios with different assumptions about quantum and classical sensors and satellite missions. The performance benefits of the hybrid solutions, taking the synergy of both classical and quantum accelerometers into account, will be quantified. We found that implementing a hybrid accelerometer onboard a future gravity mission improves the gravity solution by one to two orders in lower and higher degrees. In particular, the produced global gravity field maps show a drastic reduction in the instrumental contribution to the striping effect after introducing measurements from the hybrid accelerometers.

physics.ins-det↗
arXiv2024

Advances in Atom Interferometry and their Impacts on the Performance of Quantum Accelerometers On-board Future Satellite Gravity Missions

Recent advances in cold atom interferometry have cleared the path for space applications of quantum inertial sensors, whose level of stability is expected to increase dramatically with the longer interrogation times accessible in space. In this study, a comprehensive in-orbit model is developed for a Mach-Zehnder-type cold-atom accelerometer. Performance tests are realized under different assumptions, and the impact of various sources of errors on instrument stability is evaluated. Current and future advances for space-based atom interferometry are discussed, and their impact on the performance of quantum sensors on-board satellite gravity missions is investigated in three different scenarios: state-of-the-art scenario, near-future (between the next 5 and 10 years) and far-future scenarios (between the next 10 to 20 years). We show that one can achieve a sensitivity level close to 5E-10 with the current state-of-the-art technology. We also estimate that in the near and far-future, atom interferometry in space is expected to achieve sensitivity levels of 1E-11 and 1E-12, respectively. A roadmap for improvements in atom interferometry is provided that would maximize the performance of future CAI accelerometers, considering their technical capabilities. Finally, the possibility and challenges of having ultra-sensitive atom interferometry in space for future space missions are discussed.

physics.ins-det↗
arXiv2024

Benefit of enhanced electrostatic and optical accelerometry for future gravimetry missions

Twenty years of gravity observations from various satellite missions have provided unique data about mass redistribution processes in the Earth system. This paper studies the benefit of enhanced electrostatic and novel optical accelerometers and gradiometers for the future gravimetry missions. One of the limiting factors in the current space gravimetry missions is the drift of the Electrostatic Accelerometers (EA). This study focuses on the modeling of enhanced EAs with laser-interferometric readout, so called 'optical accelerometers', and on evaluating their performance for gravity field recovery in future satellite missions. In this paper, we simulate gravimetry missions in multiple scopes, applying the various software modules for satellite dynamics integration, accelerometer (ACC) and gradiometer simulation and gravity field recovery. The total noise budget of the modeled enhanced Electrostatic and optical ACCs show a similar sensitivity as the ACC concepts from other research groups. Parametrization w.r.t. ACCs test mass (TM) weight and the gap between the test mass and surrounding electrode housing confirmed previously known results that an ACC with a heavier TM and larger gap will have better performance. Our results suggest that the anticipated gain of novel ACCs might at some point be potentially limited by noise from the inter-satellite laser ranging interferometry. In order to present the advantage of the novel sensors, time-variable background models and associated aliasing errors were not considered in our simulations. Utilization of enhanced EA and optical ACC show a significant improvement of accuracy w.r.t. current GRACE-like EA. Also, their benefit in double satellite pairs in a so called 'Bender' constellations as well as in the combination of low-low satellite-to-satellite tracking with cross-track gradiometry has been investigated.

physics.geo-ph↗