arXiv subjects

Fabian Fuchs

Publications and source records attributed to Fabian Fuchs.

12 recordsLinked to original sources

arXiv2026

Risk-sensitive exit-time control for stochastic differential equations with path-dependent coefficients

In this work, we study small-noise asymptotics of risk-sensitive exit-time control problems governed by stochastic differential equations with path-dependent coefficients. Our main result establishes the convergence of the $\log$-transformed exit-time problem to a deterministic control problem with path-dependent coefficients. For its proof, we first derive a novel variational representation for general $\log$-transformed stochastic control problems with path-dependent coefficients, combining tools from the theory of path-dependent partial differential equations and convex expectations on path spaces. In a second step, we use probabilistic methods to analyze the convergence of the resulting variational formulas. To illustrate the scope of our analysis, we consider a computable example for a stochastic differential equation with memory and characterize the limiting problem and associated control strategies.

math.OC↗

arXiv2026

Projected Evolutionary Lifting and Well-Posedness of Stationary Hamilton-Jacobi-Bellman Equations in Infinite Dimensions

This paper establishes the existence and uniqueness of mild solutions to stationary Hamilton-Jacobi-Bellman (HJB) equations associated with infinite-horizon stochastic optimal control problems in separable Hilbert spaces. Our framework includes settings with a lack of global smoothing properties of the transition semigroup, singular dynamics involving unbounded control operators, and state-dependent running costs. We overcome these challenges by lifting the state space using the Projected Evolutionary Lifting technique. This work is an extension of G. Bolli and F. Gozzi, Lifting and partial smoothing for stationary HJB equations and related control problems in infinite dimensions, 2025, in which existence and uniqueness is proved via a contraction mapping argument and is consequently restricted to sufficiently large discount factors. We remove this restriction, proving existence and uniqueness for any discount rate $\lambda > 0$ using tools from the theory of maximally monotone operators.

math.OC↗

arXiv2025

In-Context Learning for Seismic Data Processing

Seismic processing transforms raw data into subsurface images essential for geophysical applications. Traditional methods face challenges, such as noisy data, and manual parameter tuning, among others. Recently deep learning approaches have proposed alternative solutions to some of these problems. However, important challenges of existing deep learning approaches are spatially inconsistent results across neighboring seismic gathers and lack of user-control. We address these limitations by introducing ContextSeisNet, an in-context learning model, to seismic demultiple processing. Our approach conditions predictions on a support set of spatially related example pairs: neighboring common-depth point gathers from the same seismic line and their corresponding labels. This allows the model to learn task-specific processing behavior at inference time by observing how similar gathers should be processed, without any retraining. This method provides both flexibility through user-defined examples and improved lateral consistency across seismic lines. On synthetic data, ContextSeisNet outperforms a U-Net baseline quantitatively and demonstrates enhanced spatial coherence between neighboring gathers. On field data, our model achieves superior lateral consistency compared to both traditional Radon demultiple and the U-Net baseline. Relative to the U-Net, ContextSeisNet also delivers improved near-offset performance and more complete multiple removal. Notably, ContextSeisNet achieves comparable field data performance despite being trained on 90% less data, demonstrating substantial data efficiency. These results establish ContextSeisNet as a practical approach for spatially consistent seismic demultiple with potential applicability to other seismic processing tasks.

cs.CV↗

arXiv2025

A Strict Comparison Principle for Integro-Differential Hamilton-Jacobi-Bellman Equations on Domains with Boundary

This work provides a comparison principle for viscosity solutions to boundary value problems on (partially) bounded, cylindrical spaces. The comparison principle is based on a test function framework, that allows for the simultaneous treatment of diffusive as well as jump terms. Estimates in the proof of the comparison principle incorporate the use of Lyapunov functions that act as growth bounds for the solutions, effectively yielding a theory for unbounded viscosity solutions. We apply the results to a wide class of parabolic equations and elliptic problems on a space with corners.

math.AP↗

arXiv2025

Automated Charge Transition Detection in Quantum Dot Charge Stability Diagrams

Gate-defined semiconductor quantum dots require an appropriate number of electrons to function as qubits. The number of electrons is usually tuned by analyzing charge stability diagrams, in which charge transitions manifest as edges. Therefore, to fully automate qubit tuning, it is necessary to recognize these edges automatically and reliably. This paper investigates possible detection methods, describes their training with simulated data from the SimCATS framework, and performs a quantitative comparison with a future hardware implementation in mind. Furthermore, we investigated the quality of the optimized approaches on experimentally measured data from a GaAs and a SiGe qubit sample.

cond-mat.mes-hall↗

arXiv2025

Foundation Models For Seismic Data Processing: An Extensive Review

Seismic processing plays a crucial role in transforming raw data into high-quality subsurface images, pivotal for various geoscience applications. Despite its importance, traditional seismic processing techniques face challenges such as noisy and damaged data and the reliance on manual, time-consuming workflows. The emergence of deep learning approaches has introduced effective and user-friendly alternatives, yet many of these deep learning approaches rely on synthetic datasets and specialized neural networks. Recently, foundation models have gained traction in the seismic domain, due to their success in the natural image domain. Therefore, we investigate the application of natural image foundation models on the three seismic processing tasks: demultiple, interpolation, and denoising. We evaluate the impact of different model characteristics, such as pre-training technique and neural network architecture, on performance and efficiency. Rather than proposing a single seismic foundation model, we critically examine various natural image foundation models and suggest some promising candidates for future exploration.

cs.CV↗

arXiv2025

Existence of Viscosity Solutions to Abstract Cauchy Problems via Nonlinear Semigroups

In this work, we provide conditions for nonlinear monotone semigroups on locally convex vector lattices to give rise to a generalized notion of viscosity solutions to a related nonlinear partial differential equation. The semigroup needs to satisfy a convexity estimate, so called $K$-convexity, w.r.t. another family of operators, defined on a potentially larger locally convex vector lattice. We then show that, under mild continuity requirements on the bounding family of operators, the semigroup yields viscosity solutions to the abstract Cauchy problem given in terms of its generator in the larger locally convex vector lattice. We apply our results to drift control problems for infinite-dimensional L\'evy processes and robust optimal control problems for infinite-dimensional Ornstein-Uhlenbeck processes.

math.AP↗

arXiv2024

A comparison principle based on couplings of partial integro-differential operators

This paper is concerned with a comparison principle for viscosity solutions to Hamilton-Jacobi (HJ), -Bellman (HJB), and -Isaacs (HJI) equations for general classes of partial integro-differential operators. Our approach innovates in three ways: (1) We reinterpret the classical doubling-of-variables method in the context of second-order equations by casting the Ishii-Crandall Lemma into a test function framework. This adaptation allows us to effectively handle non-local integral operators, such as those associated with L\'evy processes. (2) We translate the key estimate on the difference of Hamiltonians in terms of an adaptation of the probabilistic notion of couplings, providing a unified approach that applies to differential, difference, and integral operators. (3) We strengthen the sup-norm contractivity resulting from the comparison principle to one that encodes continuity in the strict topology. We apply our theory to a variety of examples, in particular, to second-order differential operators and, more generally, generators of spatially inhomogeneous L\'evy processes.

math.AP↗

arXiv2015

Experimental Evaluation of Distributed Node Coloring Algorithms for Wireless Networks

In this paper we evaluate distributed node coloring algorithms for wireless networks using the network simulator Sinalgo [by DCG@ETHZ]. All considered algorithms operate in the realistic signal-to-interference-and-noise-ratio (SINR) model of interference. We evaluate two recent coloring algorithms, Rand4DColor and ColorReduction (in the following ColorRed), proposed by Fuchs and Prutkin in [SIROCCO'15], the MW-Coloring algorithm introduced by Moscibroda and Wattenhofer [DC'08] and transferred to the SINR model by Derbel and Talbi [ICDCS'10], and a variant of the coloring algorithm of Yu et al. [TCS'14]. We additionally consider several practical improvements to the algorithms and evaluate their performance in both static and dynamic scenarios. Our experiments show that Rand4DColor is very fast, computing a valid (4Degree)-coloring in less than one third of the time slots required for local broadcasting, where Degree is the maximum node degree in the network. Regarding other O(Degree)-coloring algorithms Rand4DColor is at least 4 to 5 times faster. Additionally, the algorithm is robust even in networks with mobile nodes and an additional listening phase at the start of the algorithm makes Rand4DColor robust against the late wake-up of large parts of the network. Regarding (Degree+1)-coloring algorithms, we observe that ColorRed it is significantly faster than the considered variant of the Yu et al. coloring algorithm, which is the only other (Degree+1)-coloring algorithm for the SINR model. Further improvement can be made with an error-correcting variant that increases the runtime by allowing some uncertainty in the communication and afterwards correcting the introduced conflicts.

cs.DS↗

arXiv2015

On the Distributed Computation of Fractional Connected Dominating Set Packings

One of the most fundamental problems in wireless networks is to achieve high throughput. Fractional Connected Dominating Set (FCDS) Packings can achieve a throughput of ${\Theta}(k/\log n)$ messages for networks with node connectivity $k$, which is optimal regarding routing-based message transmission. FCDS were proposed by Censor-Hillel \emph{et al.} [SODA'14,PODC'14] and are a natural generalization to Connected Dominating Sets (CDS), allowing each node to participate with a fraction of its weight in multiple FCDS. Thus, $\Omega(k)$ co-existing transmission backbones are established, taking full advantage of the networks connectivity. We propose a modified distributed algorithm that improves upon previous algorithms for $k\Delta \in o(\min\{\frac{n \log n}{k} ,D,\sqrt{n \log n} \log^* n\}\log n)$, where $\Delta$ is the maximum node degree, $D$ the diameter and $n$ the number of nodes in the network. We achieve this by explicitly computing connections between tentative dominating sets.

cs.DC↗

arXiv2015

Simple Distributed Delta + 1 Coloring in the SINR Model

In wireless ad hoc or sensor networks, distributed node coloring is a fundamental problem closely related to establishing efficient communication through TDMA schedules. For networks with maximum degree Delta, a Delta + 1 coloring is the ultimate goal in the distributed setting as this is always possible. In this work we propose Delta + 1 coloring algorithms for the synchronous and asynchronous setting. All algorithms have a runtime of O(Delta log n) time slots. This improves on the previous algorithms for the SINR model either in terms of the number of required colors or the runtime and matches the runtime of local broadcasting in the SINR model (which can be seen as a lower bound).

cs.DS↗

arXiv2014

Arbitrary Transmission Power in the SINR Model: Local Broadcasting, Coloring and MIS

In the light of energy conservation and the expansion of existing networks, wireless networks face the challenge of nodes with heterogeneous transmission power. However, for more realistic models of wireless communication only few algorithmic results are known. In this paper we consider nodes with arbitrary, possibly variable, transmission power in the so-called physical or SINR model. Our first result is a bound on the probabilistic interference from all simultaneously transmitting nodes on receivers. This result implies that current local broadcasting algorithms can be generalized to the case of non-uniform transmission power with minor changes. The algorithms run in $Ø(Γ^{2} Δ\log n)$ time slots if the maximal degree $Δ$ is known, and $Ø((Δ+ \log n)Γ^{2} \log n)$ otherwise, where $Γ$ is the ratio between the maximal and the minimal transmission range. The broad applicability of our result on bounding the interference is further highlighted, by generalizing a distributed coloring algorithm to this setting.

cs.DS↗