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B-cos Networks have been shown to be effective for obtaining highly human interpretable explanations of model decisions by architecturally enforcing stronger alignment between inputs and weight. B-cos variants of convolutional networks (CNNs) and vision transformers (ViTs), which primarily replace linear layers with B-cos transformations, perform competitively to their respective standard variants while also yielding explanations that are faithful by design. However, it has so far been necessary to train these models from scratch, which is increasingly infeasible in the era of large, pre-trained foundation models. In this work, inspired by the architectural similarities in standard DNNs and B-cos networks, we propose 'B-cosification', a novel approach to transform existing pre-trained models to become inherently interpretable. We perform a thorough study of design choices to perform this conversion, both for convolutional neural networks and vision transformers. We find that B-cosification can yield models that are on par with B-cos models trained from scratch in terms of interpretability, while often outperforming them in terms of classification performance at a fraction of the training cost. Subsequently, we apply B-cosification to a pretrained CLIP model, and show that, even with limited data and compute cost, we obtain a B-cosified version that is highly interpretable and competitive on zero shot performance across a variety of datasets. We release our code and pre-trained model weights at https://github.com/shrebox/B-cosification., Comment: 31 pages, 9 figures, 12 tables, Neural Information Processing Systems (NeurIPS) 2024; added references, corrected typos

Concept Bottleneck Models (CBMs) have recently been proposed to address the 'black-box' problem of deep neural networks, by first mapping images to a human-understandable concept space and then linearly combining concepts for classification. Such models typically require first coming up with a set of concepts relevant to the task and then aligning the representations of a feature extractor to map to these concepts. However, even with powerful foundational feature extractors like CLIP, there are no guarantees that the specified concepts are detectable. In this work, we leverage recent advances in mechanistic interpretability and propose a novel CBM approach -- called Discover-then-Name-CBM (DN-CBM) -- that inverts the typical paradigm: instead of pre-selecting concepts based on the downstream classification task, we use sparse autoencoders to first discover concepts learnt by the model, and then name them and train linear probes for classification. Our concept extraction strategy is efficient, since it is agnostic to the downstream task, and uses concepts already known to the model. We perform a comprehensive evaluation across multiple datasets and CLIP architectures and show that our method yields semantically meaningful concepts, assigns appropriate names to them that make them easy to interpret, and yields performant and interpretable CBMs. Code available at https://github.com/neuroexplicit-saar/discover-then-name., Comment: 40 pages, 21 figures, 6 tables, European Conference on Computer Vision (ECCV) 2024

The validity of the subjective evaluation of steering feedback in driving simulators is crucial for modern vehicle development. Although there are established objective steering characteristics for the assessment of both stationary and dynamic feedback behaviour, factors such as steering wheel vibrations and vehicle body motion, particularly in high-frequency ranges, present challenges in simulator fidelity. This work investigates the influence of steering wheel vibration and vehicle body motion frequency content on the subjective evaluation of steering feedback during closed-loop driving in a dynamic driving simulator. A controlled subject study with 30 participants consisting of a back-to-back comparison of a reference vehicle with an electrical power steering system and three variants of its virtual representation on a dynamic driving simulator was performed. Subjective evaluation focused on the representation of road feedback in comparison to the reference vehicle. The statistical analysis of subjective results show that there is a significant influence of the frequency content of both steering wheel torque and vehicle motion on the subjective evaluation of steering feedback in a dynamic driving simulator. The results suggest an influence of frequency content on the subjective evaluation quality of steering feedback characteristics that are not associated with the dynamic feedback behaviour in the context of established performance indicators., Comment: 12 pages, 7 figures, 9 tables, submitted to the IEEE Transactions on Intelligent Vehicles

Technological advancements focus on developing comfortable and acceptable driving characteristics in autonomous vehicles. Present driving functions predominantly possess predefined parameters, and there is no universally accepted driving style for autonomous vehicles. While driving may be technically safe and the likelihood of road accidents is reduced, passengers may still feel insecure due to a mismatch in driving styles between the human and the autonomous system. Incorporating driving style preferences into automated vehicles enhances acceptance, reduces uncertainty, and poses the opportunity to expedite their adoption. Despite the increased research focus on driving styles, there remains a need for comprehensive studies investigating how variations in the driving context impact the assessment of automated driving functions. Therefore, this work evaluates lateral driving style preferences for autonomous vehicles on rural roads, considering different weather and traffic situations. A controlled study was conducted with a variety of German participants utilizing a high-fidelity driving simulator. The subjects experienced four different driving styles, including mimicking of their own driving behavior under two weather conditions. A notable preference for a more passive driving style became evident based on statistical analyses of participants' responses during and after the drives. This study could not confirm the hypothesis that subjects prefer to be driven by mimicking their own driving behavior. Furthermore, the study illustrated that weather conditions and oncoming traffic substantially influence the perceived comfort during autonomous rides. The gathered dataset is openly accessible at https://www.kaggle.com/datasets/jhaselberger/idcld-subject-study-on-driving-style-preferences., Comment: 19 pages, 5 figures; This work has been submitted to the IEEE for possible publication

Knowledge Distillation (KD) has proven effective for compressing large teacher models into smaller student models. While it is well known that student models can achieve similar accuracies as the teachers, it has also been shown that they nonetheless often do not learn the same function. It is, however, often highly desirable that the student's and teacher's functions share similar properties such as basing the prediction on the same input features, as this ensures that students learn the 'right features' from the teachers. In this work, we explore whether this can be achieved by not only optimizing the classic KD loss but also the similarity of the explanations generated by the teacher and the student. Despite the idea being simple and intuitive, we find that our proposed 'explanation-enhanced' KD (e$^2$KD) (1) consistently provides large gains in terms of accuracy and student-teacher agreement, (2) ensures that the student learns from the teacher to be right for the right reasons and to give similar explanations, and (3) is robust with respect to the model architectures, the amount of training data, and even works with 'approximate', pre-computed explanations., Comment: 32 pages, 11 figures, European Conference on Computer Vision (ECCV) 2024

Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phases wrap around the circle in a linear fashion. Here, we analyze Hopf bifurcations of twisted states in ring networks of phase oscillators with nonpairwise higher-order interactions. Hopf bifurcations give rise to quasiperiodic solutions that move along the oscillator ring at nontrivial speed. Because of the higher-order interactions, these emerging solutions may be stable. Using the Ott--Antonsen approach, we continue the emergent solution branches which approach anti-phase type solutions (where oscillators form two clusters whose phase is $\pi$ apart) as well as twisted states with a different winding number., Comment: 24 pages, 8 figures

Most detector systems used for positron emission particle tracking (PEPT) are very expensive due to the use of inorganic plastic scintillators combined with a high number of readout electronic channels. This work aims to reduce the overall cost of a PEPT-capable detector system by using large and cost-effective plastic scintillators and developing custom 2 x 2 silicon photomultiplier (SiPM) arrays, preamplifiers, and discriminators. The use of long (20 mm x 20 mm x 1000 mm) plastic scintillator bars read out with photodetectors only at their respective ends allows an overall smaller number of photodetectors and associated readout electronics, which in turn reduces the overall cost of the system. In addition, the development of a custom SiPM array and preamplifier allows a free selection of interconnection and readout, as most commercial producers only offer specific types of interconnections and therefore lack other connections such as serial or hybrid. Thus, several common circuit types for SiPMs and preamplifiers were tested and compared in this work, and it was found that a serial connection implemented in a hybrid interconnection for the SiPMs and an inverting preamplifier based on a high-frequency operational amplifier provided the best results for the proposed detector system. Measured with a Na-22 source, the combination of SiPM array and preamplifier led to a rise time of 3.7 ns and a signal amplitude of 175 mV., Comment: Published in Nuclear Instruments and Methods in Physics Research A 1057 (2023) 168767. This manuscript version is made available under the CC-BY-NC-ND 4.0 license

We present a new direction for increasing the interpretability of deep neural networks (DNNs) by promoting weight-input alignment during training. For this, we propose to replace the linear transformations in DNNs by our novel B-cos transformation. As we show, a sequence (network) of such transformations induces a single linear transformation that faithfully summarises the full model computations. Moreover, the B-cos transformation is designed such that the weights align with relevant signals during optimisation. As a result, those induced linear transformations become highly interpretable and highlight task-relevant features. Importantly, the B-cos transformation is designed to be compatible with existing architectures and we show that it can easily be integrated into virtually all of the latest state of the art models for computer vision - e.g. ResNets, DenseNets, ConvNext models, as well as Vision Transformers - by combining the B-cos-based explanations with normalisation and attention layers, all whilst maintaining similar accuracy on ImageNet. Finally, we show that the resulting explanations are of high visual quality and perform well under quantitative interpretability metrics., Comment: Extension of B-cos Networks: Alignment is All We Need for Interpretability (B\"ohle et al., CVPR 2022). Accepted for publication in IEEE Transactions on Pattern Analysis and Machine Intelligence. arXiv admin note: substantial text overlap with arXiv:2205.10268

Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical phenomena, such as synchronization. While a first-order approximation of the dynamics on the torus may be appropriate in some situations, higher-order phase reductions become necessary, for example, when the coupling strength increases. However, these are generally hard to compute and thus they have only been derived in special cases: This includes globally coupled Stuart--Landau oscillators, where the limit cycle of the uncoupled nonlinear oscillator is circular as the amplitude is independent of the phase. We go beyond this restriction and derive second-order phase reductions for coupled oscillators for arbitrary networks of coupled nonlinear oscillators with phase-dependent amplitude, a scenario more reminiscent of real-world oscillations. We analyze how the deformation of the limit cycle affects the stability of important dynamical states, such as full synchrony and splay states. By identifying higher-order phase interaction terms with hyperedges of a hypergraph, we obtain natural classes of coupled phase oscillator dynamics on hypergraphs that adequately capture the dynamics of coupled limit cycle oscillators., Comment: 30 pages, 4 figures

Most approaches for self-supervised learning (SSL) are optimised on curated balanced datasets, e.g. ImageNet, despite the fact that natural data usually exhibits long-tail distributions. In this paper, we analyse the behaviour of one of the most popular variants of SSL, i.e. contrastive methods, on long-tail data. In particular, we investigate the role of the temperature parameter $\tau$ in the contrastive loss, by analysing the loss through the lens of average distance maximisation, and find that a large $\tau$ emphasises group-wise discrimination, whereas a small $\tau$ leads to a higher degree of instance discrimination. While $\tau$ has thus far been treated exclusively as a constant hyperparameter, in this work, we propose to employ a dynamic $\tau$ and show that a simple cosine schedule can yield significant improvements in the learnt representations. Such a schedule results in a constant `task switching' between an emphasis on instance discrimination and group-wise discrimination and thereby ensures that the model learns both group-wise features, as well as instance-specific details. Since frequent classes benefit from the former, while infrequent classes require the latter, we find this method to consistently improve separation between the classes in long-tail data without any additional computational cost., Comment: ICLR 2023

Despite being highly performant, deep neural networks might base their decisions on features that spuriously correlate with the provided labels, thus hurting generalization. To mitigate this, 'model guidance' has recently gained popularity, i.e. the idea of regularizing the models' explanations to ensure that they are "right for the right reasons". While various techniques to achieve such model guidance have been proposed, experimental validation of these approaches has thus far been limited to relatively simple and / or synthetic datasets. To better understand the effectiveness of the various design choices that have been explored in the context of model guidance, in this work we conduct an in-depth evaluation across various loss functions, attribution methods, models, and 'guidance depths' on the PASCAL VOC 2007 and MS COCO 2014 datasets. As annotation costs for model guidance can limit its applicability, we also place a particular focus on efficiency. Specifically, we guide the models via bounding box annotations, which are much cheaper to obtain than the commonly used segmentation masks, and evaluate the robustness of model guidance under limited (e.g. with only 1% of annotated images) or overly coarse annotations. Further, we propose using the EPG score as an additional evaluation metric and loss function ('Energy loss'). We show that optimizing for the Energy loss leads to models that exhibit a distinct focus on object-specific features, despite only using bounding box annotations that also include background regions. Lastly, we show that such model guidance can improve generalization under distribution shifts. Code available at: https://github.com/sukrutrao/Model-Guidance., Comment: 41 pages, 38 figures, 4 tables, IEEE/CVF International Conference on Computer Vision (ICCV) 2023

Deep neural networks are very successful on many vision tasks, but hard to interpret due to their black box nature. To overcome this, various post-hoc attribution methods have been proposed to identify image regions most influential to the models' decisions. Evaluating such methods is challenging since no ground truth attributions exist. We thus propose three novel evaluation schemes to more reliably measure the faithfulness of those methods, to make comparisons between them more fair, and to make visual inspection more systematic. To address faithfulness, we propose a novel evaluation setting (DiFull) in which we carefully control which parts of the input can influence the output in order to distinguish possible from impossible attributions. To address fairness, we note that different methods are applied at different layers, which skews any comparison, and so evaluate all methods on the same layers (ML-Att) and discuss how this impacts their performance on quantitative metrics. For more systematic visualizations, we propose a scheme (AggAtt) to qualitatively evaluate the methods on complete datasets. We use these evaluation schemes to study strengths and shortcomings of some widely used attribution methods over a wide range of models. Finally, we propose a post-processing smoothing step that significantly improves the performance of some attribution methods, and discuss its applicability., Comment: 35 pages, 36 figures, 2 tables, extended version of arXiv:2205.10435, IEEE Transactions on Pattern Analysis and Machine Intelligence

Transformers increasingly dominate the machine learning landscape across many tasks and domains, which increases the importance for understanding their outputs. While their attention modules provide partial insight into their inner workings, the attention scores have been shown to be insufficient for explaining the models as a whole. To address this, we propose B-cos transformers, which inherently provide holistic explanations for their decisions. Specifically, we formulate each model component - such as the multi-layer perceptrons, attention layers, and the tokenisation module - to be dynamic linear, which allows us to faithfully summarise the entire transformer via a single linear transform. We apply our proposed design to Vision Transformers (ViTs) and show that the resulting models, dubbed Bcos-ViTs, are highly interpretable and perform competitively to baseline ViTs on ImageNet. Code will be made available soon.

Context. Planets around stars in the solar neighbourhood will be prime targets for characterisation with upcoming large space- and ground-based facilities. Since large-scale exoplanet searches will not be feasible with such telescopes, it is crucial to use currently available data and instruments to find possible target planets before next generation facilities come online. Aims. We aim at detecting new extrasolar planets around stars in the solar neighbourhood by blind radial velocity (RV) search with ESPRESSO. Our target sample consist of nearby stars (d < 11 pc) with little (< 10) or no previous RV measurements. Methods. We use 31 radial velocity measurements obtained with ESPRESSO at the VLT between December 2020 and February 2022 of the nearby M dwarf star (M_star = 0.21 M_sun, d = 10.23 pc) L 363-38 to derive the orbital parameters of the newly discovered planet. In addition, we use TESS photometry and archival VLT/NaCo high contrast imaging data to put further constraints on the orbit inclination and the possible planetary system architecture around L 363-38. Results. We present the detection of a new extrasolar planet orbiting the nearby M dwarf star L 363-38. L 363-38 b is a planet with minimum mass mp sin(i) = 4.67+/-0.43 M_Earth orbiting its star with a period P = 8.781+/-0.007 d, corresponding to a semi-major axis a = 0.048+/-0.006 AU, which is well inside the inner edge of the habitable zone. We further estimate a minimum radius rp sin(i) = 1.55 - 2.75 R_Earth and an equilibrium temperature Teq = 330K., Comment: 12 pages, 11 figures

The Kuramoto model provides a prototypical framework to synchronization phenomena in interacting particle systems. Apart from full phase synchrony where all oscillators behave identically, identical Kuramoto oscillators with ring-like nonlocal coupling can exhibit more elaborate patterns such as uniformly twisted states. It was discovered by Wiley, Strogatz and Girvan in 2006 that the stability of these twisted states depends on the coupling range of each oscillator. In this paper, we analyze twisted states and their bifurcations in the infinite particle limit of ring-like nonlocal coupling. We not only consider traditional pairwise interactions as in the Kuramoto model but also demonstrate the effects of higher-order nonpairwise interactions, which arise naturally in phase reductions. We elucidate how pairwise and nonpairwise interactions affect the stability of the twisted states, compute bifurcating branches, and show that higher-order interactions can stabilize twisted states that are unstable if the coupling is only pairwise., Comment: 36 pages, 7 figures

Deep neural networks are very successful on many vision tasks, but hard to interpret due to their black box nature. To overcome this, various post-hoc attribution methods have been proposed to identify image regions most influential to the models' decisions. Evaluating such methods is challenging since no ground truth attributions exist. We thus propose three novel evaluation schemes to more reliably measure the faithfulness of those methods, to make comparisons between them more fair, and to make visual inspection more systematic. To address faithfulness, we propose a novel evaluation setting (DiFull) in which we carefully control which parts of the input can influence the output in order to distinguish possible from impossible attributions. To address fairness, we note that different methods are applied at different layers, which skews any comparison, and so evaluate all methods on the same layers (ML-Att) and discuss how this impacts their performance on quantitative metrics. For more systematic visualizations, we propose a scheme (AggAtt) to qualitatively evaluate the methods on complete datasets. We use these evaluation schemes to study strengths and shortcomings of some widely used attribution methods. Finally, we propose a post-processing smoothing step that significantly improves the performance of some attribution methods, and discuss its applicability., Comment: 30 pages, 31 figures, 2 tables, IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) 2022

We present a new direction for increasing the interpretability of deep neural networks (DNNs) by promoting weight-input alignment during training. For this, we propose to replace the linear transforms in DNNs by our B-cos transform. As we show, a sequence (network) of such transforms induces a single linear transform that faithfully summarises the full model computations. Moreover, the B-cos transform introduces alignment pressure on the weights during optimisation. As a result, those induced linear transforms become highly interpretable and align with task-relevant features. Importantly, the B-cos transform is designed to be compatible with existing architectures and we show that it can easily be integrated into common models such as VGGs, ResNets, InceptionNets, and DenseNets, whilst maintaining similar performance on ImageNet. The resulting explanations are of high visual quality and perform well under quantitative metrics for interpretability. Code available at https://www.github.com/moboehle/B-cos.

Dynamics of large-scale network processes underlies crucial phenomena ranging across all sciences. Forward simulation of large network models is often computationally prohibitive. Yet, most networks have intrinsic community structure. We exploit these communities and propose a fast simulation algorithm for network dynamics. In particular, aggregating the inputs a node receives constitutes the limiting factor in numerically simulating large-scale network dynamics. We develop community integration algorithms (CIAs) significantly reducing function-evaluations. We obtain a substantial reduction from polynomial to linear computational complexity. We illustrate our results in multiple applications including classical and higher-order Kuramoto-type systems for synchronisation and Cucker--Smale systems exhibiting flocking behaviour on synthetic as well as real-world networks. Numerical comparison and theoretical analysis confirm the robustness and efficiency of CIAs., Comment: 12 pages, 6 figures

We introduce a new family of neural network models called Convolutional Dynamic Alignment Networks (CoDA Nets), which are performant classifiers with a high degree of inherent interpretability. Their core building blocks are Dynamic Alignment Units (DAUs), which are optimised to transform their inputs with dynamically computed weight vectors that align with task-relevant patterns. As a result, CoDA Nets model the classification prediction through a series of input-dependent linear transformations, allowing for linear decomposition of the output into individual input contributions. Given the alignment of the DAUs, the resulting contribution maps align with discriminative input patterns. These model-inherent decompositions are of high visual quality and outperform existing attribution methods under quantitative metrics. Further, CoDA Nets constitute performant classifiers, achieving on par results to ResNet and VGG models on e.g. CIFAR-10 and TinyImagenet. Lastly, CoDA Nets can be combined with conventional neural network models to yield powerful classifiers that more easily scale to complex datasets such as Imagenet whilst exhibiting an increased interpretable depth, i.e., the output can be explained well in terms of contributions from intermediate layers within the network., Comment: Extension of "Convolutional Dynamic Alignment Networks for Interpretable Classifications" (B\"ohle et al., CVPR 2021). arXiv admin note: substantial text overlap with arXiv:2104.00032

We develop a general theory of random walks on hypergraphs which includes, as special cases, the different models that are found in literature. In particular, we introduce and analyze general random walk Laplacians for hypergraphs, and we compare them to hypergraph normalized Laplacians that are not necessarily related to random walks, but which are motivated by biological and chemical networks. We show that, although these two classes of Laplacians coincide in the case of graphs, they appear to have important conceptual differences in the general case. We study the spectral properties of both classes, as well as their applications to Coupled Hypergraph Maps: discrete-time dynamical systems that generalize the well-known Coupled Map Lattices on graphs. Our results also show why for some hypergraph Laplacian variants one expects more classical results from (weighted) graphs to generalize directly, while these results must fail for other hypergraph Laplacians.

We present observations of ionized gas outflows in eleven z$ =1.39-2.59$ radio-loud quasar host galaxies. Data was taken with the integral field spectrograph (IFS) OSIRIS and the adaptive optics system at the W.M. Keck Observatory targeting nebular emission lines (H$\beta$, [OIII], H$\alpha$, [NII] and [SII]) redshifted into the near-infrared (1-2.4 \micron). Outflows with velocities of 500 - 1700 km\,s$^{-1}$ are detected in 10 systems on scales ranging from $<1$ kpc to 10 kpc with outflow rates from 8-2400 M$_\odot$yr$^{-1}$. For five sources, the outflow momentum rates are 4-80 times $L_{AGN}$/c, consistent with outflows being driven by an energy conserving shock. The five other outflows are either driven by radiation pressure or an isothermal shock. The outflows are the dominant source of gas depletion, and we find no evidence for star formation along the outflow paths. For eight objects, the outflow paths are consistent with the orientation of the jets. Yet, given the calculated pressures, we find no evidence of the jets currently doing work on these galactic-scale ionized outflows. We find that galactic-scale feedback occurs well before galaxies establish a substantial fraction of their stellar mass, as expected from local scaling relationships., Comment: 39 pages, 18 figures, 7 tables, accepted for publication in ApJ

Aims. We aim to detect molecules in the atmosphere of the young forming companion PDS70 b by searching for atmospheric absorption features typical of substellar objects. Methods. We obtained medium-resolution (R$\approx$5075) spectra of the PDS70 planetary system with the SINFONI integral field spectrograph at the Very Large Telescope. We applied molecular mapping, based on cross-correlation with synthetic spectra, to identify signatures of molecular species in the atmosphere of the planet. Results. Although the planet emission is clearly detected when resampling the data to lower resolution, no molecular species could be identified with the cross-correlation technique. We estimated upper limits on the abundances of H$_2$O, CO and CH$_4$ ($\log(X_\mathrm{mol}) < -4.0$, $-4.1$ and $-4.9$, respectively) assuming a clear atmosphere, and we explored the impact of clouds, which increase the upper limits by a factor up to 0.7 dex. Assuming that the observations directly probe the planet's atmosphere, we found a lack of molecular species compared to other directly imaged companions or field objects. Under the assumption that the planet atmosphere presents similar characteristics to other directly imaged planets, we conclude that a dusty environment surrounds the planet, effectively obscuring any feature generated in its atmosphere. We quantify the extinction necessary to impede the detection ($A_V\approx16-17$ mag), pointing to the possibility of higher optical thickness than previously estimated from other studies. Finally, the non-detection of molecular species conflicts with atmospheric models previously proposed to describe the forming planet. Conclusions. To unveil how giant planets form, a comprehensive approach that includes constraints from multiple techniques needs to be undertaken. Molecular mapping emerges as an alternative to more classical techniques like SED fitting., Comment: Accepted for publication in A&A (16 pages, 10 figures)

The past decade has seen increasing efforts in detecting and characterising exoplanets by high contrast imaging in the near/mid-infrared, which is the optimal wavelength domain for studying old, cold planets. In this work, we present deep AO imaging observations of the nearby Sun-like star $\epsilon$ Ind A with NaCo ($L^{\prime}$) and NEAR (10-12.5 microns) instruments at VLT, in an attempt to directly detect its planetary companion whose presence has been indicated from radial velocity (RV) and astrometric trends. We derive brightness limits from the non-detection of the companion with both instruments, and interpret the corresponding sensitivity in mass based on both cloudy and cloud-free atmospheric and evolutionary models. For an assumed age of 5 Gyr for the system, we get detectable mass limits as low as 4.4 $M_{\rm J}$ in NaCo $L^{\prime}$ and 8.2 $M_{\rm J}$ in NEAR bands at 1.5$\arcsec$ from the central star. If the age assumed is 1 Gyr, we reach even lower mass limits of 1.7 $M_{\rm J}$ in NaCo $L^{\prime}$ and 3.5 $M_{\rm J}$ in NEAR bands, at the same separation. However, based on the dynamical mass estimate (3.25 $M_{\rm J}$) and ephemerides from astrometry and RV, we find that the non-detection of the planet in these observations puts a constraint of 2 Gyr on the lower age limit of the system. NaCo offers the highest sensitivity to the planetary companion in these observations, but the combination with the NEAR wavelength range adds a considerable degree of robustness against uncertainties in the atmospheric models. This underlines the benefits of including a broad set of wavelengths for detection and characterisation of exoplanets in direct imaging studies., Comment: 13 pages, 9 figures, 2 tables Accepted for publication in section 10. Planets and planetary systems of Astronomy and Astrophysics

The direct imaging of rocky exoplanets is one of the major science goals for upcoming large telescopes. The contrast requirement for imaging such planets is challenging. However, the mid-IR (InfraRed) regime provides the optimum contrast to directly detect the thermal signatures of exoplanets in our solar neighbourhood. We aim to exploit novel fast chopping techniques newly developed for astronomy with the aid of adaptive optics to look for thermal signatures of exoplanets around bright stars in the solar neighbourhood. We use the upgraded VISIR (Very Large Telescope Imager and Spectrometer for the mid-InfraRed) instrument with high contrast imaging (HCI) capability optimized for observations at 10~$\mu$m to look for exoplanets around five nearby ($d$ < 4 pc) stars. The instrument provides an improved signal-to-noise (S/N) by a factor of $\sim$4 in the N-band compared to standard VISIR for a given S/N and time. In this work we achieve a detection sensitivity of sub-mJy, which is sufficient to detect few Jupiter mass planets in nearby systems. Although no detections are made we achieve most sensitive limits within $<2''$ for all the observed targets compared to previous campaigns. For $\epsilon$ Indi A and $\epsilon$ Eri we achieve detection limits very close to the giant planets discovered by RV, with the limits on $\epsilon$ Indi A being the most sensitive to date. Our non-detection therefore supports an older age for $\epsilon$ Indi A. The results presented here show the promise for high contrast imaging and exoplanet detections in the mid-IR regime., Comment: Accepted for publication in A&A

Over the last decade, the vector-apodizing phase plate (vAPP) coronagraph has been developed from concept to on-sky application in many high-contrast imaging systems on 8-m class telescopes. The vAPP is an geometric-phase patterned coronagraph that is inherently broadband, and its manufacturing is enabled only by direct-write technology for liquid-crystal patterns. The vAPP generates two coronagraphic PSFs that cancel starlight on opposite sides of the point spread function (PSF) and have opposite circular polarization states. The efficiency, that is the amount of light in these PSFs, depends on the retardance offset from half-wave of the liquid-crystal retarder. Using different liquid-crystal recipes to tune the retardance, different vAPPs operate with high efficiencies ($>96\%$) in the visible and thermal infrared (0.55 $\mu$m to 5 $\mu$m). Since 2015, seven vAPPs have been installed in a total of six different instruments, including Magellan/MagAO, Magellan/MagAO-X, Subaru/SCExAO, and LBT/LMIRcam. Using two integral field spectrographs installed on the latter two instruments, these vAPPs can provide low-resolution spectra (R$\sim$30) between 1 $\mu$m and 5 $\mu$m. We review the design process, development, commissioning, on-sky performance, and first scientific results of all commissioned vAPPs. We report on the lessons learned and conclude with perspectives for future developments and applications., Comment: 38 pages, 17 figures, accepted for publication in Applied Optics, added NSF grant acknowledgement

We introduce a new family of neural network models called Convolutional Dynamic Alignment Networks (CoDA-Nets), which are performant classifiers with a high degree of inherent interpretability. Their core building blocks are Dynamic Alignment Units (DAUs), which linearly transform their input with weight vectors that dynamically align with task-relevant patterns. As a result, CoDA-Nets model the classification prediction through a series of input-dependent linear transformations, allowing for linear decomposition of the output into individual input contributions. Given the alignment of the DAUs, the resulting contribution maps align with discriminative input patterns. These model-inherent decompositions are of high visual quality and outperform existing attribution methods under quantitative metrics. Further, CoDA-Nets constitute performant classifiers, achieving on par results to ResNet and VGG models on e.g. CIFAR-10 and TinyImagenet., Comment: Published at CVRP 2021 (oral)

In this work, a novel approach for the reliable and efficient numerical integration of the Kuramoto model on graphs is studied. For this purpose, the notion of order parameters is revisited for the classical Kuramoto model describing all-to-all interactions of a set of oscillators. First numerical experiments confirm that the precomputation of certain sums significantly reduces the computational cost for the evaluation of the right-hand side and hence enables the simulation of high-dimensional systems. In order to design numerical integration methods that are favourable in the context of related dynamical systems on network graphs, the concept of localised order parameters is proposed. In addition, the detection of communities for a complex graph and the transformation of the underlying adjacency matrix to block structure is an essential component for further improvement. It is demonstrated that for a submatrix comprising relatively few coefficients equal to zero, the precomputation of sums is advantageous, whereas straightforward summation is appropriate in the complementary case. Concluding theoretical considerations and numerical comparisons show that the strategy of combining effective community detection algorithms with the localisation of order parameters potentially reduces the computation time by several orders of magnitude., Comment: 33 pages, 19 figures

Giant exoplanets on wide orbits have been directly imaged around young stars. If the thermal background in the mid-infrared can be mitigated, then exoplanets with lower masses can also be imaged. Here we present a ground-based mid-infrared observing approach that enables imaging low-mass temperate exoplanets around nearby stars, and in particular within the closest stellar system, Alpha Centauri. Based on 75-80% of the best quality images from 100 hours of cumulative observations, we demonstrate sensitivity to warm sub-Neptune-sized planets throughout much of the habitable zone of Alpha Centauri A. This is an order of magnitude more sensitive than state-of-the-art exoplanet imaging mass detection limits. We also discuss a possible exoplanet or exozodiacal disk detection around Alpha Centauri A. However, an instrumental artifact of unknown origin cannot be ruled out. These results demonstrate the feasibility of imaging rocky habitable-zone exoplanets with current and upcoming telescopes., Comment: 29 pages, 11 figures, published in Nature Communications

Coupled map lattices (CMLs) are prototypical dynamical systems on networks/graphs. They exhibit complex patterns generated via the interplay of diffusive/Laplacian coupling and nonlinear reactions modelled by a single iterated map at each node; the maps are often taken as unimodal, e.g., logistic or tent maps. In this letter, we propose a class of higher-order coupled dynamical systems involving the hypergraph Laplacian, which we call coupled hypergraph maps (CHMs). By combining linearized (in-)stability analysis of synchronized states, hypergraph spectral theory, and numerical methods, we detect robust regions of chaotic cluster synchronization occurring in parameter space upon varying coupling strength and the main bifurcation parameter of the unimodal map. Furthermore, we find key differences between Laplacian and hypergraph Laplacian coupling and detect various other classes of periodic and quasi-periodic patterns. The results show the high complexity of coupled graph maps and indicate that they might be an excellent universal model class to understand the similarities and differences between dynamics on classical graphs and dynamics on hypergraphs., Comment: 6 pages, 5 figures

We present detailed observations of photoionization conditions and galaxy kinematics in eleven z$=1.39-2.59$ radio-loud quasar host galaxies. Data was taken with OSIRIS integral field spectrograph (IFS) and the adaptive optics system at the W.M. Keck Observatory that targeted nebular emission lines (H$\beta$,[OIII],H$\alpha$,[NII]) redshifted into the near-infrared (1-2.4 \micron). We detect extended ionized emission on scales ranging from 1-30 kpc photoionized by stars, shocks, and active galactic nuclei (AGN). Spatially resolved emission-line ratios indicate that our systems reside off the star formation and AGN-mixing sequence on the Baldwin, Phillips $\&$ Terlevich (BPT) diagram at low redshift. The dominant cause of the difference between line ratios of low redshift galaxies and our sample is due to lower gas-phase metallicities, which are 2-5$\times$ less compared to galaxies with AGN in the nearby Universe. Using gas velocity dispersion as a proxy to stellar velocity dispersion and dynamical mass measurement through inclined disk modeling we find that the quasar host galaxies are under-massive relative to their central supermassive black hole (SMBH) mass, with all systems residing off the local scaling ($M_{\bullet}-\sigma~$,$M_{\bullet}-M_{*}~$) relationship. These quasar host galaxies require substantial growth, up to an order of magnitude in stellar mass, to grow into present-day massive elliptical galaxies. Combining these results with part I of our sample paper (Vayner et al. 2021) we find evidence for winds capable of causing feedback before the AGN host galaxies land on the local scaling relation between black hole and galaxy stellar mass, and before the enrichment of the ISM to a level observed in local galaxies with AGN., Comment: 31 pages, 18 figures, 7 tables. Accepted for publication in ApJ

The classical Kuramoto model consists of finitely many pairwise coupled oscillators on the circle. In many applications a simple pairwise coupling is not sufficient to describe real-world phenomena as higher-order (or group) interactions take place. Hence, we replace the classical coupling law with a very general coupling function involving higher-order terms. Furthermore, we allow for multiple populations of oscillators interacting with each other through a very general law. In our analysis, we focus on the characteristic system and the mean-field limit of this generalized class of Kuramoto models. While there are several works studying particular aspects of our program, we propose a general framework to work with all three aspects (higher-order, multi-population, and mean-field) simultaneously. Assuming identical oscillators in each population, we derive equations for the evolution of oscillator populations in the mean-field limit. First, we clarify existence and uniqueness of our set of characteristic equations, which are formulated in the space of probability measures together with the bounded-Lipschitz metric. Then, we investigate dynamical properties within the framework of the characteristic system. We identify invariant subspaces and stability of the state, in which all oscillators are synchronized within each population. Even though it turns out that this so called all-synchronized state is never asymptotically stable, under some conditions and with a suitable definition of stability, the all-synchronized state can be proven to be at least locally stable. In summary, our work provides a rigorous mathematical framework upon which the further study of multi-population higher-order coupled particle systems can be based., Comment: 35 pages, 0 figures

We report evidence for the first generation of XUV spectra from relativistic surface high-harmonic generation (SHHG) on plasma mirrors at a kilohertz repetition rate, emitted simultaneously with energetic electrons. SHHG spectra and electron angular distributions are measured as a function of the experimentally controlled plasma density gradient scale length $L_\mathrm{g}$ for three increasingly short and intense driving pulses: 24~fs and $a_0=1.1$, 8~fs and $a_0=1.6$, and finally 4~fs and $a_0\approx2.1$, where $a_0$ is the peak vector potential normalized by $m_\mathrm{e} c/e$ with the elementary charge $e$, the electron rest mass $m_\mathrm{e}$, and the vacuum light velocity $c$. For all driver pulses, we observe correlated relativistic SHHG and electron emission in the range $L_\mathrm{g}\in[\lambda/25,\lambda/5]$, with an optimum gradient scale length of $L_\mathrm{g}\approx\lambda/10$.

To control the current outbreak of the Coronavirus Disease 2019, constant monitoring of the epidemic is required since, as of today, no vaccines or antiviral drugs against it are known. We provide daily updated estimates of the reproduction number over time at https://stochastik-tu-ilmenau.github.io/COVID-19/. In this document, we describe the estimator we are using which was developed in (Fraser 2007), derive its asymptotic properties, and we give details on its implementation. Furthermore, we validate the estimator on simulated data, demonstrate that estimates on real data lead to plausible results, and perform a sensitivity analysis. Finally, we discuss why the estimates obtained need to be interpreted with care.

function of the CEP, we observe a transition from a modulated to a continuous SHHG spectrum, indicating the transition from double to high-contrast isolated attosecond pulse emission. Single shot-acquisitions of XUV spectral continua support isolated attosecond pulses with isolation degrees between 10 and 50 for the majority of the driving pulse CEPs, which represents a significant improvement in terms of isolation degree as well as repetition rate over previous results obtained with 2-cycle drivers at 10-Hz. 2D Particle-in-cell simulations corroborate this interpretation and predict percent-level efficiencies for the generation of an isolated attosecond pulse even without any spectral filtering.

In this paper, we study a certain class of nonlocal partial differential equations (PDEs). The equations arise from a key problem in network science, i.e., network generation from local interaction rules, which result in a change of the degree distribution as time progresses. The evolution of the generating function of this degree distribution can be described by a nonlocal PDE. To address this equation we will rigorously convert it into a local first order PDE. Then, we use theory of characteristics to prove solvability and regularity of the solution. Next, we investigate the existence of steady states of the PDE. We show that this problem reduces to an implicit ODE, which we subsequently analyze. Finally, we perform numerical simulations, which show stability of the steady states., Comment: 20 pages, 6 figures

Nearby stars are prime targets for exoplanet searches and characterization using a variety of detection techniques. Combining constraints from the complementary detection methods of high contrast imaging (HCI) and radial velocity (RV) can further constrain the planetary architectures of these systems because these methods place limits at different regions of the companion mass and semi-major axis parameter space. We aim to constrain the planetary architectures from the combination of HCI and RV data for 6 nearby stars within 6 pc: $\tau$ Ceti, Kapteyn's star, AX Mic, 40 Eri, HD 36395, and HD 42581. We compiled the sample from stars with available archival VLT/NACO HCI data at L$^{\prime}$ band (3.8 $\mu$m). The NACO data were fully reanalyzed using the state-of-the-art direct imaging pipeline PynPoint and combined with RV data from HARPS, Keck/HIRES, and CORALIE. A Monte Carlo approach was used to assess the completeness in the companion mass/semi-major axis parameter space from the combination of the HCI and RV data sets. We find that the HCI data add significant information to the RV constraints, increasing the completeness for certain companions masses/semi-major axes by up to 68 - 99% for 4 of the 6 stars in our sample, and by up to 1 - 13% for the remaining stars. The improvements are strongest for intermediate semi-major axes (15 - 40 AU), corresponding to the semi-major axes of the ice giants in our own solar system. The HCI mass limits reach 5 - 20 $M_{\textrm{Jup}}$ in the background-limited regime, depending on the age of the star. Through the combination of HCI and RV data, we find that stringent constraints can be placed on the possible substellar companions in these systems. Applying these methods systematically to nearby stars will quantify our current knowledge of the planet population in the solar neighborhood and inform future observations., Comment: 17 pages, 12 figures, accepted for publication in A&A

We present a laser source delivering waveform-controlled 1.5-cycle pulses that can be focused to relativistic intensity at 1 kHz repetition rate. These pulses are generated by nonlinear compression of high-temporal-contrast sub-25\,fs pulses from a kHz Ti:Sapphire double-chirped pulse amplifier in a stretched flexible hollow fiber compressor scaled for high peak power. The unique capabilities of this source are demonstrated by observing carrier-envelope phase effects in laser-wakefield acceleration of relativistic electrons for the first time.

Deep neural networks have led to state-of-the-art results in many medical imaging tasks including Alzheimer's disease (AD) detection based on structural magnetic resonance imaging (MRI) data. However, the network decisions are often perceived as being highly non-transparent, making it difficult to apply these algorithms in clinical routine. In this study, we propose using layer-wise relevance propagation (LRP) to visualize convolutional neural network decisions for AD based on MRI data. Similarly to other visualization methods, LRP produces a heatmap in the input space indicating the importance/relevance of each voxel contributing to the final classification outcome. In contrast to susceptibility maps produced by guided backpropagation ("Which change in voxels would change the outcome most?"), the LRP method is able to directly highlight positive contributions to the network classification in the input space. In particular, we show that (1) the LRP method is very specific for individuals ("Why does this person have AD?") with high inter-patient variability, (2) there is very little relevance for AD in healthy controls and (3) areas that exhibit a lot of relevance correlate well with what is known from literature. To quantify the latter, we compute size-corrected metrics of the summed relevance per brain area, e.g., relevance density or relevance gain. Although these metrics produce very individual "fingerprints" of relevance patterns for AD patients, a lot of importance is put on areas in the temporal lobe including the hippocampus. After discussing several limitations such as sensitivity toward the underlying model and computation parameters, we conclude that LRP might have a high potential to assist clinicians in explaining neural network decisions for diagnosing AD (and potentially other diseases) based on structural MRI data.

OSIRIS is a near-infrared (1.0--2.4 $\mu$m) integral field spectrograph operating behind the adaptive optics system at Keck Observatory, and is one of the first lenslet-based integral field spectrographs. Since its commissioning in 2005, it has been a productive instrument, producing nearly half the laser guide star adaptive optics (LGS AO) papers on Keck. The complexity of its raw data format necessitated a custom data reduction pipeline (DRP) delivered with the instrument in order to iteratively assign flux in overlapping spectra to the proper spatial and spectral locations in a data cube. Other than bug fixes and updates required for hardware upgrades, the bulk of the DRP has not been updated since initial instrument commissioning. We report on the first major comprehensive characterization of the DRP using on-sky and calibration data. We also detail improvements to the DRP including characterization of the flux assignment algorithm; exploration of spatial rippling in the reduced data cubes; and improvements to several calibration files, including the rectification matrix, the bad pixel mask, and the wavelength solution. We present lessons learned from over a decade of OSIRIS data reduction that are relevant to the next generation of integral field spectrograph hardware and data reduction software design., Comment: 18 pages, 16 figures; accepted for publication in AJ

The direct detection and characterization of planetary and substellar companions at small angular separations is a rapidly advancing field. Dedicated high-contrast imaging instruments deliver unprecedented sensitivity, enabling detailed insights into the atmospheres of young low-mass companions. In addition, improvements in data reduction and PSF subtraction algorithms are equally relevant for maximizing the scientific yield, both from new and archival data sets. We aim at developing a generic and modular data reduction pipeline for processing and analysis of high-contrast imaging data obtained with pupil-stabilized observations. The package should be scalable and robust for future implementations and in particular well suitable for the 3-5 micron wavelength range where typically (ten) thousands of frames have to be processed and an accurate subtraction of the thermal background emission is critical. PynPoint is written in Python 2.7 and applies various image processing techniques, as well as statistical tools for analyzing the data, building on open-source Python packages. The current version of PynPoint has evolved from an earlier version that was developed as a PSF subtraction tool based on PCA. The architecture of PynPoint has been redesigned with the core functionalities decoupled from the pipeline modules. Modules have been implemented for dedicated processing and analysis steps, including background subtraction, frame registration, PSF subtraction, photometric and astrometric measurements, and estimation of detection limits. The pipeline package enables end-to-end data reduction of pupil-stabilized data and supports classical dithering and coronagraphic data sets. As an example, we processed archival VLT/NACO L' and M' data of beta Pic b and reassessed the planet's brightness and position with an MCMC analysis, and we provide a derivation of the photometric error budget., Comment: 16 pages, 9 figures, accepted for publication in A&A, PynPoint is available at https://github.com/PynPoint/PynPoint

We present high spatial resolution, integral field spectrograph (IFS) observations of the nearby LINER (low ionization nuclear emission line region) galaxy NGC 404 at 1.25 $\mu$m (J band) and 2.2 $\mu$m (K band) near-infrared wavelengths. Although NGC 404 is thought to host an intermediate mass black hole at its center, it has been unclear whether accretion onto the black hole or another mechanism such as shock excitation drives its LINER emission at optical/near-infrared wavelengths. We use the OSIRIS IFS at Keck Observatory behind laser guide star adaptive optics to map the strength and kinematics of [FeII], H$_2$, and hydrogen recombination lines at spatial resolutions of 1 pc across the central 30 pc of the galaxy. The H$_2$ gas is in a central rotating disk and ratios of multiple H$_2$ lines indicate that the molecular gas is thermally excited, with some contribution from UV fluorescence. The [FeII] emission is more extended and diffuse than the molecular gas and has a different kinematic structure that reaches higher velocities/dispersions. We also map the strength of the CO stellar absorption feature and constrain the dominant age of the nuclear stellar population to $\sim$1 Gyr. Finally, we find regions across the nucleus of NGC 404 with [FeII]/Pa$\beta$ line ratios up to 6.5, $\sim$2.5 times higher than the ratio measured from spatially-integrated spectra. From these high line ratios, we conclude that shocks are the dominate physical mechanism exciting NGC 404's LINER emission and argue that a possible source of this shock excitation is a supernova remnant., Comment: 34 pages, 14 figures, accepted to ApJ

ERIS is an instrument that will both extend and enhance the fundamental diffraction limited imaging and spectroscopy capability for the VLT. It will replace two instruments that are now being maintained beyond their operational lifetimes, combine their functionality on a single focus, provide a new wavefront sensing module that makes use of the facility Adaptive Optics System, and considerably improve their performance. The instrument will be competitive with respect to JWST in several regimes, and has outstanding potential for studies of the Galactic Center, exoplanets, and high redshift galaxies. ERIS had its final design review in 2017, and is expected to be on sky in 2020. This contribution describes the instrument concept, outlines its expected performance, and highlights where it will most excel., Comment: 12 pages, Proc SPIE 10702 "Ground-Based and Airborne Instrumentation for Astronomy VII"

We measure the emission of energetic electrons from the interaction between ultrashort laser pulses and a solid density plasma in the relativistic regime. We detect an electron beam that only appears with few-cycle pulses (< 10 fs) and large plasma scale lengths ($L > \lambda_0$). Numerical simulations, in agreement with the experiments, reveal that these electrons are accelerated by a laser wakefield. Plasma waves are indeed resonantly excited by the few-cycle laser pulses in the near-critical-density region of the plasma. Electrons are then injected by ionization into the plasma waves and accelerated to relativistic energies. This study provides an unprecedented insight into the physics happening in the few-cycle regime.

We report for the first time on the anticorrelated emission of high-order harmonics and energetic electron beams from a solid-density plasma with a sharp vacuum interface$-$plasma mirror$-$driven by an intense ultrashort laser pulse. We highlight the key role played by the nanoscale structure of the plasma surface during the interaction by measuring the spatial and spectral properties of harmonics and electron beams emitted by a plasma mirror. We show that the nanoscale behavior of the plasma mirror can be controlled by tuning the scale length of the electronic density gradient, which is measured in-situ using spatial-domain interferometry.