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Fabian Wagner

Publications and source records attributed to Fabian Wagner.

At least 55 records · Page 3Linked to original sources
arXiv2022

Modified uncertainty relations from classical and quantum gravity

A good hundred years after the necessity for a quantum theory of gravity was acknowledged by Albert Einstein, the search for it continues to be an ongoing endeavour. Nevertheless, the field still evolves rapidly as manifested by the recent rise of quantum gravity phenomenology supported by an enormous surge in experimental precision. In particular, the minimum length paradigm ingrained in the program of generalized uncertainty principles (GUPs) is steadily growing in importance. The present thesis is aimed at establishing a link between modified uncertainty relations, derived from deformed canonical commutators, and curved spaces - specifically, GUPs and nontrivial momentum space as well as the related extended uncertainty principles (EUPs) and curved position space. In that vein, we derive a new kind of EUP relating the radius of geodesic balls, assumed to constrain the wave functions in the underlying Hilbert space, with the standard deviation of the momentum operator. This result is gradually generalized to relativistic particles in curved spacetime in accordance with the 3+1 decomposition. In a sense pursuing the inverse route, we find an explicit correspondence between theories yielding a GUP and quantum dynamics set on non-Euclidean momentum space. Quantitatively, the coordinate noncommutativity translates to momentum space curvature in the dual description, allowing for an analogous transfer of constraints from the literature. Finally, we find a formulation of quantum mechanics which proves consistent on the arbitrarily curved cotangent bundle. Along these lines, we show that the harmonic oscillator can not be used as a means to distinguish between curvature in position and momentum space, thereby providing an explicit instantiation of Born reciprocity in the context of curved spaces.

gr-qc↗
arXiv2022

Trainable Joint Bilateral Filters for Enhanced Prediction Stability in Low-dose CT

Low-dose computed tomography (CT) denoising algorithms aim to enable reduced patient dose in routine CT acquisitions while maintaining high image quality. Recently, deep learning~(DL)-based methods were introduced, outperforming conventional denoising algorithms on this task due to their high model capacity. However, for the transition of DL-based denoising to clinical practice, these data-driven approaches must generalize robustly beyond the seen training data. We, therefore, propose a hybrid denoising approach consisting of a set of trainable joint bilateral filters (JBFs) combined with a convolutional DL-based denoising network to predict the guidance image. Our proposed denoising pipeline combines the high model capacity enabled by DL-based feature extraction with the reliability of the conventional JBF. The pipeline's ability to generalize is demonstrated by training on abdomen CT scans without metal implants and testing on abdomen scans with metal implants as well as on head CT data. When embedding two well-established DL-based denoisers (RED-CNN/QAE) in our pipeline, the denoising performance is improved by $10\,\%$/$82\,\%$ (RMSE) and $3\,\%$/$81\,\%$ (PSNR) in regions containing metal and by $6\,\%$/$78\,\%$ (RMSE) and $2\,\%$/$4\,\%$ (PSNR) on head CT data, compared to the respective vanilla model. Concluding, the proposed trainable JBFs limit the error bound of deep neural networks to facilitate the applicability of DL-based denoisers in low-dose CT pipelines.

eess.IV↗
arXiv2022

The minimal length is physical

In this paper, we clarify a foundational loose end affecting the phenomenological approach to quantum gravity centered around the generalization of Heisenberg uncertainty principle. This misconception stems from a series of recently published works in which perturbative and non-perturbative methods are confused, thereby resulting in a blurring of the distinction between changes in the deformed algebra and changes in the representation of operators. Accordingly, this reasoning would render the existence of a minimal length representation-dependent, and thus unphysical.

gr-qc↗
arXiv2022

ConFUDA: Contrastive Fewshot Unsupervised Domain Adaptation for Medical Image Segmentation

Unsupervised domain adaptation (UDA) aims to transfer knowledge learned from a labeled source domain to an unlabeled target domain. Contrastive learning (CL) in the context of UDA can help to better separate classes in feature space. However, in image segmentation, the large memory footprint due to the computation of the pixel-wise contrastive loss makes it prohibitive to use. Furthermore, labeled target data is not easily available in medical imaging, and obtaining new samples is not economical. As a result, in this work, we tackle a more challenging UDA task when there are only a few (fewshot) or a single (oneshot) image available from the target domain. We apply a style transfer module to mitigate the scarcity of target samples. Then, to align the source and target features and tackle the memory issue of the traditional contrastive loss, we propose the centroid-based contrastive learning (CCL) and a centroid norm regularizer (CNR) to optimize the contrastive pairs in both direction and magnitude. In addition, we propose multi-partition centroid contrastive learning (MPCCL) to further reduce the variance in the target features. Fewshot evaluation on MS-CMRSeg dataset demonstrates that ConFUDA improves the segmentation performance by 0.34 of the Dice score on the target domain compared with the baseline, and 0.31 Dice score improvement in a more rigorous oneshot setting.

cs.CV↗
arXiv2022

A New Guest in the Third Quantized Multiverse

In the present article we point out a conceptual issue of the Third Quantization formalism for Canonical Quantum Gravity. Based on earlier results on interuniversal entanglement, the picture of noninteracting universe-antiuniverse pairs is incomplete. In particular, the variation of the entanglement entropy with the scale factor, understood as a measure of time, implies either an interaction between pairs of universes or universes with a heat bath, i.e. an external field. We propose a simple solution to the problem by adding a new quantum field to the formalism. Correspondingly, particles of this field mediate interactions between universes -- depending on the model at tree level or one loop -- and may further provide a heat bath in the background.

gr-qc↗
arXiv2022

Ultra Low-Parameter Denoising: Trainable Bilateral Filter Layers in Computed Tomography

Computed tomography is widely used as an imaging tool to visualize three-dimensional structures with expressive bone-soft tissue contrast. However, CT resolution and radiation dose are tightly entangled, highlighting the importance of low-dose CT combined with sophisticated denoising algorithms. Most data-driven denoising techniques are based on deep neural networks and, therefore, contain hundreds of thousands of trainable parameters, making them incomprehensible and prone to prediction failures. Developing understandable and robust denoising algorithms achieving state-of-the-art performance helps to minimize radiation dose while maintaining data integrity. This work presents an open-source CT denoising framework based on the idea of bilateral filtering. We propose a bilateral filter that can be incorporated into a deep learning pipeline and optimized in a purely data-driven way by calculating the gradient flow toward its hyperparameters and its input. Denoising in pure image-to-image pipelines and across different domains such as raw detector data and reconstructed volume, using a differentiable backprojection layer, is demonstrated. Although only using three spatial parameters and one range parameter per filter layer, the proposed denoising pipelines can compete with deep state-of-the-art denoising architectures with several hundred thousand parameters. Competitive denoising performance is achieved on x-ray microscope bone data (0.7053 and 33.10) and the 2016 Low Dose CT Grand Challenge dataset (0.9674 and 43.07) in terms of SSIM and PSNR. Due to the extremely low number of trainable parameters with well-defined effect, prediction reliance and data integrity is guaranteed at any time in the proposed pipelines, in contrast to most other deep learning-based denoising architectures.

eess.IV↗
arXiv2022

Learned Cone-Beam CT Reconstruction Using Neural Ordinary Differential Equations

Learned iterative reconstruction algorithms for inverse problems offer the flexibility to combine analytical knowledge about the problem with modules learned from data. This way, they achieve high reconstruction performance while ensuring consistency with the measured data. In computed tomography, extending such approaches from 2D fan-beam to 3D cone-beam data is challenging due to the prohibitively high GPU memory that would be needed to train such models. This paper proposes to use neural ordinary differential equations to solve the reconstruction problem in a residual formulation via numerical integration. For training, there is no need to backpropagate through several unrolled network blocks nor through the internals of the solver. Instead, the gradients are obtained very memory-efficiently in the neural ODE setting allowing for training on a single consumer graphics card. The method is able to reduce the root mean squared error by over 30% compared to the best performing classical iterative reconstruction algorithm and produces high quality cone-beam reconstructions even in a sparse view scenario.

eess.IV↗
arXiv2021

The ensemble Kalman filter for rare event estimation

We present a novel sampling-based method for estimating probabilities of rare or failure events. Our approach is founded on the Ensemble Kalman filter (EnKF) for inverse problems. Therefore, we reformulate the rare event problem as an inverse problem and apply the EnKF to generate failure samples. To estimate the probability of failure, we use the final EnKF samples to fit a distribution model and apply Importance Sampling with respect to the fitted distribution. This leads to an unbiased estimator if the density of the fitted distribution admits positive values within the whole failure domain. To handle multi-modal failure domains, we localise the covariance matrices in the EnKF update step around each particle and fit a mixture distribution model in the Importance Sampling step. For affine linear limit-state functions, we investigate the continuous-time limit and large time properties of the EnKF update. We prove that the mean of the particles converges to a convex combination of the most likely failure point and the mean of the optimal Importance Sampling density if the EnKF is applied without noise. We provide numerical experiments to compare the performance of the EnKF with Sequential Importance Sampling.

math.NA↗
arXiv2021

Generalized uncertainty principle or curved momentum space?

The concept of minimum length, widely accepted as a low-energy effect of quantum gravity, manifests itself in quantum mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at the heart of similar applications such as doubly special relativity. We introduce a duality between theories yielding generalized uncertainty principles and quantum mechanics on nontrivial momentum space. In particular, we find canonically conjugate variables which map the former into the latter. In that vein, we explicitly derive the vielbein corresponding to a generic generalized uncertainty principle in $d$ dimensions. Assuming the predominantly used quadratic form of the modification, the curvature tensor in momentum space is proportional to the noncommutativity of the coordinates in the modified Heisenberg algebra. Yet, the metric is non-Euclidean even in the flat case corresponding to commutative space, because the resulting momentum basis is noncanonical. These insides are used to constrain the curvature and the deviation from the canonical basis.

gr-qc↗
arXiv2021

Relativistic Extended Uncertainty Principle from Spacetime Curvature

The investigations presented in this study are directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. These findings generalize previous work which is recovered in the nonrelativistic limit. Applying the 3+1-splitting in accordance with the ADM-formalism, we find the relativistic physical momentum operator and compute its standard deviation for wave functions confined to a geodesic ball on a spacelike hypersurface. Its radius can then be understood as a measure of position uncertainty. Under the assumtion of small position uncertainties in comparison to background curvature length scales, we obtain the corresponding corrections to the uncertainty relation in flat space. Those depend on the Ricci scalar of the effective spatial metric, the particle is moving on, and, if there are nonvanishing time-space components of the spacetime metric, gradients of the shift vector and the lapse function. Interestingly, this result is applicable not only to massive but also to massless particles. Over all, this is not a covariant, yet a consistently general relativistic approach. We further speculate on a possible covariant extension.

gr-qc↗
arXiv2021

Error analysis for probabilities of rare events with approximate models

The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit-state function, which depends on the solution of a partial differential equation (PDE). In many applications, the PDE cannot be solved analytically. We can only evaluate an approximation of the exact PDE solution. Therefore, the probability of rare events is estimated with respect to an approximation of the limit-state function. This leads to an approximation error in the estimate of the probability of rare events. Indeed, we prove an error bound for the approximation error of the probability of failure, which behaves like the discretization accuracy of the PDE multiplied by an approximation of the probability of failure, the first order reliability method (FORM) estimate. This bound requires convexity of the failure domain. For non-convex failure domains, we prove an error bound for the relative error of the FORM estimate. Hence, we derive a relationship between the required accuracy of the probability of rare events estimate and the PDE discretization level. This relationship can be used to guide practicable reliability analyses and, for instance, multilevel methods.

math.NA↗
arXiv2021

Gravitationally induced uncertainty relations in curved backgrounds

This paper aims at investigating the influence of space-time curvature on the uncertainty relation. In particular, relying on previous findings, we assume the quantum wave function to be confined to a geodesic ball on a given space-like hypersurface whose radius is a measure of the position uncertainty. On the other hand, we concurrently work out a viable physical definition of the momentum operator and its standard deviation in the non-relativistic limit of the 3+1 formalism. Finally, we evaluate the uncertainty relation which to second order depends on the Ricci scalar of the effective 3-metric and the corresponding covariant derivative of the shift vector. For the sake of illustration, we apply our general result to a number of examples arising in the context of both general relativity and extended theories of gravity.

gr-qc↗
arXiv2020

Intensity interferometry-based 3D imaging

The development of single-photon counting detectors and arrays has made tremendous steps in recent years, not the least because of various new applications in, e.g., LIDAR devices. In this work, a 3D imaging device based on real thermal light intensity interferometry is presented. By using gated SPAD technology, a basic 3D scene is imaged in reasonable measurement time. Compared to conventional approaches, the proposed synchronized photon counting allows using more light modes to enhance 3D ranging performance. Advantages like robustness to atmospheric scattering or autonomy by exploiting external light sources can make this ranging approach interesting for future applications.

physics.optics↗
arXiv2020

Asymptotic Generalized Extended Uncertainty Principle

We present a formalism which allows for the perturbative derivation of the Extended Uncertainty Principle (EUP) for arbitrary spatial curvature models and observers. Entering the realm of small position uncertainties, we derive a general asymptotic EUP. The leading 2nd order curvature induced correction is proportional to the Ricci scalar, while the 4th order correction features the 0th order Cartan invariant Psi^2 (a scalar quadratic in curvature tensors) and the curved space Laplacian of the Ricci scalar all of which are evaluated at the expectation value of the position operator, i.e. the expected position when performing a measurement. This result is first verified for previously derived homogeneous space models and then applied to other non-trivial curvature related effects such as inhomogeneities, rotation and an anisotropic stress fluid leading to black hole "hair". Our main achievement combines the method we introduce with the Generalized Uncertainty Principle (GUP) by virtue of deformed commutators to formulate a generic form of what we call the Asymptotic Generalized Extended Uncertainty Principle (AGEUP).

gr-qc↗
arXiv2020

Multilevel Sequential Importance Sampling for Rare Event Estimation

The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit state function, which depends on the solution of a partial differential equation (PDE). Since numerical evaluations of PDEs are computationally expensive, estimating such probabilities of failure by Monte Carlo sampling is intractable. More efficient sampling methods from reliability analysis, such as Subset Simulation, are popular, but can still be impracticable if the PDE evaluations are very costly. In this article, we develop a novel, highly efficient estimator for probabilities of rare events. Our method is based on a Sequential Importance sampler using discretizations of PDE-based limit state functions with different accuracies. A twofold adaptive algorithm ensures that we obtain an estimate based on the desired discretization accuracy. In contrast to the Multilevel Subset Simulation estimator of [Ullmann, Papaioannou 2015; SIAM/ASA J. Uncertain. Quantif. 3(1):922-953], our estimator overcomes the nestedness problem. Of particular importance in Sequential Importance sampling algorithms is the correct choice of the MCMC kernel. Instead of the popular adaptive conditional sampling method, we propose a new algorithm that uses independent proposals from an adaptively constructed von Mises-Fischer-Nakagami distribution. The proposed algorithm is applied to test problems in 1D and 2D space, respectively, and is compared to the Multilevel Subset Simulation estimator and to single-level versions of Sequential Importance Sampling and Subset Simulation.

math.NA↗
arXiv2019

Extended Uncertainty Principle for Rindler and cosmological horizons

We find exact formulas for the Extended Uncertainty Principle (EUP) for the Rindler and Friedmann horizons and show that they can be expanded to obtain asymptotic forms known from the previous literature. We calculate the corrections to Hawking temperature and Bekenstein entropy of a black hole in the universe due to Rindler and Friedmann horizons. The effect of the EUP is similar to the canonical corrections of thermal fluctuations and so it rises the entropy signalling further loss of information.

gr-qc↗
arXiv2013

Beating the Generator-Enumeration Bound for $p$-Group Isomorphism

We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G cong H. For several decades, the n^(log_p n + O(1)) generator-enumeration bound (where p is the smallest prime dividing the order of the group) has been the best worst-case result for general groups. In this work, we show the first improvement over the generator-enumeration bound for p-groups, which are believed to be the hard case of the group isomorphism problem. We start by giving a Turing reduction from group isomorphism to n^((1 / 2) log_p n + O(1)) instances of p-group composition-series isomorphism. By showing a Karp reduction from p-group composition-series isomorphism to testing isomorphism of graphs of degree at most p + O(1) and applying algorithms for testing isomorphism of graphs of bounded degree, we obtain an n^(O(p)) time algorithm for p-group composition-series isomorphism. Combining these two results yields an algorithm for p-group isomorphism that takes at most n^((1 / 2) log_p n + O(p)) time. This algorithm is faster than generator-enumeration when p is small and slower when p is large. Choosing the faster algorithm based on p and n yields an upper bound of n^((1 / 2 + o(1)) log n) for p-group isomorphism.

cs.DS↗