arXiv subjects

Martin Reuter

Publications and source records attributed to Martin Reuter.

At least 37 records · Page 2Linked to original sources

arXiv2020

Background Independent Field Quantization with Sequences of Gravity-Coupled Approximants

We outline, test, and apply a new scheme for nonpertubative analyses of quantized field systems in contact with dynamical gravity. While gravity is treated classically in the present paper, the approach lends itself for a generalization to full Quantum Gravity. We advocate the point of view that quantum field theories should be regularized by sequences of quasi-physical systems comprising a well defined number of the field's degrees of freedom. In dependence on this number, each system backreacts autonomously and self-consistently on the gravitational field. In this approach, the limit which removes the regularization automatically generates the physically correct spacetime geometry, i.e., the metric the quantum states of the field prefer to "live" in. We apply the scheme to a Gaussian scalar field on maximally symmetric spacetimes, thereby confronting it with the standard approaches. As an application, the results are used to elucidate the cosmological constant problem allegedly arising from the vacuum fluctuations of quantum matter fields. An explicit calculation shows that the problem disappears if the pertinent continuum limit is performed in the improved way advocated here. A further application concerns the thermodynamics of de Sitter space where the approach offers a natural interpretation of the micro-states that are counted by the Bekenstein-Hawking entropy.

gr-qc↗

arXiv2020

Learning Anatomical Segmentations for Tractography from Diffusion MRI

Deep learning approaches for diffusion MRI have so far focused primarily on voxel-based segmentation of lesions or white-matter fiber tracts. A drawback of representing tracts as volumetric labels, rather than sets of streamlines, is that it precludes point-wise analyses of microstructural or geometric features along a tract. Traditional tractography pipelines, which do allow such analyses, can benefit from detailed whole-brain segmentations to guide tract reconstruction. Here, we introduce fast, deep learning-based segmentation of 170 anatomical regions directly on diffusion-weighted MR images, removing the dependency of conventional segmentation methods on T 1-weighted images and slow pre-processing pipelines. Working natively in diffusion space avoids non-linear distortions and registration errors across modalities, as well as interpolation artifacts. We demonstrate consistent segmentation results between 0 .70 and 0 .87 Dice depending on the tissue type. We investigate various combinations of diffusion-derived inputs and show generalization across different numbers of gradient directions. Finally, integrating our approach to provide anatomical priors for tractography pipelines, such as TRACULA, removes hours of pre-processing time and permits processing even in the absence of high-quality T 1-weighted scans, without degrading the quality of the resulting tract estimates.

eess.IV↗

arXiv2020

FastSurfer -- A fast and accurate deep learning based neuroimaging pipeline

Traditional neuroimage analysis pipelines involve computationally intensive, time-consuming optimization steps, and thus, do not scale well to large cohort studies with thousands or tens of thousands of individuals. In this work we propose a fast and accurate deep learning based neuroimaging pipeline for the automated processing of structural human brain MRI scans, replicating FreeSurfer's anatomical segmentation including surface reconstruction and cortical parcellation. To this end, we introduce an advanced deep learning architecture capable of whole brain segmentation into 95 classes. The network architecture incorporates local and global competition via competitive dense blocks and competitive skip pathways, as well as multi-slice information aggregation that specifically tailor network performance towards accurate segmentation of both cortical and sub-cortical structures. Further, we perform fast cortical surface reconstruction and thickness analysis by introducing a spectral spherical embedding and by directly mapping the cortical labels from the image to the surface. This approach provides a full FreeSurfer alternative for volumetric analysis (in under 1 minute) and surface-based thickness analysis (within only around 1h runtime). For sustainability of this approach we perform extensive validation: we assert high segmentation accuracy on several unseen datasets, measure generalizability and demonstrate increased test-retest reliability, and high sensitivity to group differences in dementia.

eess.IV↗

arXiv2020

Critical reflections on asymptotically safe gravity

Asymptotic safety is a theoretical proposal for the ultraviolet completion of quantum field theories, in particular for quantum gravity. Significant progress on this program has led to a first characterization of the Reuter fixed point. Further advancement in our understanding of the nature of quantum spacetime requires addressing a number of open questions and challenges. Here, we aim at providing a critical reflection on the state of the art in the asymptotic safety program, specifying and elaborating on open questions of both technical and conceptual nature. We also point out systematic pathways, in various stages of practical implementation, towards answering them. Finally, we also take the opportunity to clarify some common misunderstandings regarding the program.

gr-qc↗

arXiv2019

FatSegNet : A Fully Automated Deep Learning Pipeline for Adipose Tissue Segmentation on Abdominal Dixon MRI

Purpose: Development of a fast and fully automated deep learning pipeline (FatSegNet) to accurately identify, segment, and quantify abdominal adipose tissue on Dixon MRI from the Rhineland Study - a large prospective population-based study. Method: FatSegNet is composed of three stages: (i) consistent localization of the abdominal region using two 2D-Competitive Dense Fully Convolutional Networks (CDFNet), (ii) segmentation of adipose tissue on three views by independent CDFNets, and (iii) view aggregation. FatSegNet is trained with 33 manually annotated subjects, and validated by: 1) comparison of segmentation accuracy against a testingset covering a wide range of body mass index (BMI), 2) test-retest reliability, and 3) robustness in a large cohort study. Results: The CDFNet demonstrates increased robustness compared to traditional deep learning networks. FatSegNet dice score outperforms manual raters on the abdominal visceral adipose tissue (VAT, 0.828 vs. 0.788), and produces comparable results on subcutaneous adipose tissue (SAT, 0.973 vs. 0.982). The pipeline has very small test-retest absolute percentage difference and excellent agreement between scan sessions (VAT: APD = 2.957%, ICC=0.998 and SAT: APD= 3.254%, ICC=0.996). Conclusion: FatSegNet can reliably analyze a 3D Dixon MRI in1 min. It generalizes well to different body shapes, sensitively replicates known VAT and SAT volume effects in a large cohort study, and permits localized analysis of fat compartments.

cs.CV↗

arXiv2019

Background Independent Quantum Field Theory and Gravitating Vacuum Fluctuations

The scale dependent effective average action for quantum gravity complies with the fundamental principle of Background Independence. Ultimately the background metric it formally depends on is selected self-consistently by means of a suitable generalization of Einstein's equation. Self-consistent backround spacetimes are scale dependent, and therefore "going on-shell" at the points along a given renormalization group (RG) trajectory requires understanding two types of scale dependencies: the (familiar) direct one carried by the off-shell action functional, and an indirect one related to the self-consistent background geometry. This paper is devoted to a careful delineation and analysis of certain general questions concerning the indirect scale dependence, as well as a detailed explicit investigation of the case where the self-consistent metrics are determined predominantly by the RG running of the cosmological constant. Mathematically, the object of interest is the spectral flow induced by the background Laplacian which, on-shell, acquires an explicit scale dependence. It encodes the information about the specific set of field modes which, at any given scale, are the degrees of freedom constituting the respective effective field theory. For a large class of RG trajectories we discover a seemingly paradoxical behavior: the theory looses rather than gains degrees of freedom at increasing energies. As an application, we investigate to what extent it is possible to reformulate the exact theory in terms of matter and gravity fluctuations on a rigid flat space. It turns out that, in vacuo, this "rigid picture" breaks down after a very short RG time. Furthermore, we reanalyze, and refute the claim that the huge energy densities one obtains in standard quantum field theory by summing up to zero-point energies imply a naturalness problem for the observed small value of the cosmological constant.

gr-qc↗

arXiv2018

Competition vs. Concatenation in Skip Connections of Fully Convolutional Networks

Increased information sharing through short and long-range skip connections between layers in fully convolutional networks have demonstrated significant improvement in performance for semantic segmentation. In this paper, we propose Competitive Dense Fully Convolutional Networks (CDFNet) by introducing competitive maxout activations in place of naive feature concatenation for inducing competition amongst layers. Within CDFNet, we propose two architectural contributions, namely competitive dense block (CDB) and competitive unpooling block (CUB) to induce competition at local and global scales for short and long-range skip connections respectively. This extension is demonstrated to boost learning of specialized sub-networks targeted at segmenting specific anatomies, which in turn eases the training of complex tasks. We present the proof-of-concept on the challenging task of whole body segmentation in the publicly available VISCERAL benchmark and demonstrate improved performance over multiple learning and registration based state-of-the-art methods.

cs.CV↗

arXiv2018

Complex Fully Convolutional Neural Networks for MR Image Reconstruction

Undersampling the k-space data is widely adopted for acceleration of Magnetic Resonance Imaging (MRI). Current deep learning based approaches for supervised learning of MRI image reconstruction employ real-valued operations and representations by treating complex valued k-space/spatial-space as real values. In this paper, we propose complex dense fully convolutional neural network ($\mathbb{C}$DFNet) for learning to de-alias the reconstruction artifacts within undersampled MRI images. We fashioned a densely-connected fully convolutional block tailored for complex-valued inputs by introducing dedicated layers such as complex convolution, batch normalization, non-linearities etc. $\mathbb{C}$DFNet leverages the inherently complex-valued nature of input k-space and learns richer representations. We demonstrate improved perceptual quality and recovery of anatomical structures through $\mathbb{C}$DFNet in contrast to its real-valued counterparts.

cs.CV↗

arXiv2018

Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity

Entanglement entropies calculated in the framework of quantum field theory on classical, flat or curved, spacetimes are known to show an intriguing area law in four dimensions, but they are also notorious for their quadratic ultraviolet divergences. In this paper we demonstrate that the analogous entanglement entropies when computed within the Asymptotic Safety approach to background independent quantum gravity are perfectly free from such divergences. We argue that the divergences are an artifact due to the over-idealization of a rigid, classical spacetime geometry which is insensitive to the quantum dynamics.

gr-qc↗

arXiv2017

Composite Operators in Asymptotic Safety

We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert truncation, and two dimensional quantum gravity. Finally, we briefly argue that our construction paves the way to approach observables in the Asymptotic Safety program.

gr-qc↗

arXiv2017

DeepNAT: Deep Convolutional Neural Network for Segmenting Neuroanatomy

We introduce DeepNAT, a 3D Deep convolutional neural network for the automatic segmentation of NeuroAnaTomy in T1-weighted magnetic resonance images. DeepNAT is an end-to-end learning-based approach to brain segmentation that jointly learns an abstract feature representation and a multi-class classification. We propose a 3D patch-based approach, where we do not only predict the center voxel of the patch but also neighbors, which is formulated as multi-task learning. To address a class imbalance problem, we arrange two networks hierarchically, where the first one separates foreground from background, and the second one identifies 25 brain structures on the foreground. Since patches lack spatial context, we augment them with coordinates. To this end, we introduce a novel intrinsic parameterization of the brain volume, formed by eigenfunctions of the Laplace-Beltrami operator. As network architecture, we use three convolutional layers with pooling, batch normalization, and non-linearities, followed by fully connected layers with dropout. The final segmentation is inferred from the probabilistic output of the network with a 3D fully connected conditional random field, which ensures label agreement between close voxels. The roughly 2.7 million parameters in the network are learned with stochastic gradient descent. Our results show that DeepNAT compares favorably to state-of-the-art methods. Finally, the purely learning-based method may have a high potential for the adaptation to young, old, or diseased brains by fine-tuning the pre-trained network with a small training sample on the target application, where the availability of larger datasets with manual annotations may boost the overall segmentation accuracy in the future.

cs.CV↗

arXiv2015

The unitary conformal field theory behind 2D Asymptotic Safety

Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in $d>2$ dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge $c=25$. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety program. In particular, we discuss its field parametrization dependence and argue that there might exist more than one universality class of metric gravity theories in two dimensions. Furthermore, studying the gravitational dressing in 2D asymptotically safe gravity coupled to conformal matter we uncover a mechanism which leads to a complete quenching of the a priori expected Knizhnik-Polyakov-Zamolodchikov (KPZ) scaling. A possible connection of this prediction to Monte Carlo results obtained in the discrete approach to 2D quantum gravity based upon causal dynamical triangulations is mentioned. Similarities of the fixed point theory to, and differences from, non-critical string theory are also described. On the technical side, we provide a detailed analysis of an intriguing connection between the Einstein-Hilbert action in $d>2$ dimensions and Polyakov's induced gravity action in two dimensions.

hep-th↗

arXiv2015

On selfdual spin-connections and Asymptotic Safety

We explore Euclidean quantum gravity using the tetrad field together with a selfdual or anti-selfdual spin-connection as the basic field variables. Setting up a functional renormalization group (RG) equation of a new type which is particularly suitable for the corresponding theory space we determine the non-perturbative RG flow within a two-parameter truncation suggested by the Holst action. We find that the (anti-)selfdual theory is likely to be asymptotically safe. The existing evidence for its non-perturbative renormalizability is comparable to that of Einstein-Cartan gravity without the selfduality condition.

hep-th↗

arXiv2015

The metric on field space, functional renormalization, and metric-torsion quantum gravity

Searching for new non-perturbatively renormalizable quantum gravity theories, functional renormalization group (RG) flows are studied on a theory space of action functionals depending on the metric and the torsion tensor, the latter parameterized by three irreducible component fields. A detailed comparison with Quantum Einstein-Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and "tetrad-only" gravity, all based on different theory spaces, is performed. It is demonstrated that, over a generic theory space, the construction of a functional RG equation (FRGE) for the effective average action requires the specification of a metric on the infinite-dimensional field manifold as an additional input. A modified FRGE is obtained if this metric is scale-dependent, as it happens in the metric-torsion system considered.

hep-th↗

arXiv2015

Towards a $C$-function in 4D quantum gravity

We develop a generally applicable method for constructing functions, $C$, which have properties similar to Zamolodchikov's $C$-function, and are geometrically natural objects related to the theory space explored by non-perturbative functional renormalization group (RG) equations. Employing the Euclidean framework of the Effective Average Action (EAA), we propose a $C$-function which can be defined for arbitrary systems of gravitational, Yang-Mills, ghost, and bosonic matter fields, and in any number of spacetime dimensions. It becomes stationary both at critical points and in classical regimes, and decreases monotonically along RG trajectories provided the breaking of the split-symmetry which relates background and quantum fields is sufficiently weak. Within the Asymptotic Safety approach we test the proposal for Quantum Einstein Gravity in $d>2$ dimensions, performing detailed numerical investigations in $d=4$. We find that the bi-metric Einstein-Hilbert truncation of theory space introduced recently is general enough to yield perfect monotonicity along the RG trajectories, while its more familiar single-metric analog fails to achieve this behavior which we expect on general grounds. Investigating generalized crossover trajectories connecting a fixed point in the ultraviolet to a classical regime with positive cosmological constant in the infrared, the $C$-function is shown to depend on the choice of the gravitational instanton which constitutes the background spacetime. For de Sitter space in 4 dimensions, the Bekenstein-Hawking entropy is found to play a role analogous to the central charge in conformal field theory. We also comment on the idea of a `$Λ$-$N$ connection' and the `$N$-bound' discussed earlier.

hep-th↗

arXiv2015

Is there a $C$-function in 4D Quantum Einstein Gravity?

We describe a functional renormalization group-based method to search for `$C$-like' functions with properties similar to that in 2D conformal field theory. It exploits the mode counting properties of the effective average action and is particularly suited for theories including quantized gravity. The viability of the approach is demonstrated explicitly in a truncation of 4 dimensional Quantum Einstein Gravity, i.e. asymptotically safe metric gravity.

hep-th↗

arXiv2014

A new functional flow equation for Einstein-Cartan quantum gravity

We construct a special-purpose functional flow equation which facilitates non-perturbative renormalization group (RG) studies on theory spaces involving a large number of independent field components that are prohibitively complicated using standard methods. Its main motivation are quantum gravity theories in which the gravitational degrees of freedom are carried by a complex system of tensor fields, a prime example being Einstein-Cartan theory, possibly coupled to matter. We describe a sequence of approximation steps leading from the functional RG equation of the Effective Average Action to the new flow equation which, as a consequence, is no longer fully exact on the untruncated theory space. However, it is by far more "user friendly" when it comes to projecting the abstract equation on a concrete (truncated) theory space and computing explicit beta-functions. The necessary amount of (tensor) algebra reduces drastically, and the usually very hard problem of diagonalizing the pertinent Hessian operator is sidestepped completely. In this paper we demonstrate the reliability of the simplified equation by applying it to a truncation of the Einstein-Cartan theory space. It is parametrized by a scale dependent Holst action, depending on a O(4) spin-connection and the tetrad as the independent field variables. We compute the resulting RG flow, focusing in particular on the running of the Immirzi parameter, and compare it to the results of an earlier computation where the exact equation had been applied to the same truncation. We find consistency between the two approaches and provide further evidence for the conjectured non-perturbative renormalizability (asymptotic safety) of quantum Einstein-Cartan gravity. We also investigate a duality symmetry relating small and large values of the Immirzi parameter which is displayed by the beta-functions in absence of a cosmological constant.

hep-th↗

arXiv2014

Propagating gravitons vs. dark matter in asymptotically safe quantum gravity

Within the Asymptotic Safety scenario, we discuss whether Quantum Einstein Gravity (QEG) can give rise to a semi-classical regime of propagating physical gravitons (gravitational waves) governed by an effective theory which complies with the standard rules of local quantum field theory. According to earlier investigations based on single-metric truncations there is a tension between this requirement and the condition of Asymptotic Safety since the former (latter) requires a positive (negative) anomalous dimension of Newton's constant. We show that the problem disappears using the bi-metric renormalization group flows that became available recently: They admit an asymptotically safe UV limit and, at the same time, a genuine semi-classical regime with a positive anomalous dimension. This brings the gravitons of QEG on a par with arbitrary (standard model, etc.) particles which exist as asymptotic states. We also argue that metric perturbations on almost Planckian scales might not be propagating, and we propose an interpretation as a form of `dark matter'.

hep-th↗