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Exploratory Landscape Analysis is a powerful technique for numerically characterizing landscapes of single-objective continuous optimization problems. Landscape insights are crucial both for problem understanding as well as for assessing benchmark set diversity and composition. Despite the irrefutable usefulness of these features, they suffer from their own ailments and downsides. Hence, in this work we provide a collection of different approaches to characterize optimization landscapes. Similar to conventional landscape features, we require a small initial sample. However, instead of computing features based on that sample, we develop alternative representations of the original sample. These range from point clouds to 2D images and, therefore, are entirely feature-free. We demonstrate and validate our devised methods on the BBOB testbed and predict, with the help of Deep Learning, the high-level, expert-based landscape properties such as the degree of multimodality and the existence of funnel structures. The quality of our approaches is on par with methods relying on the traditional landscape features. Thereby, we provide an exciting new perspective on every research area which utilizes problem information such as problem understanding and algorithm design as well as automated algorithm configuration and selection.

Multi-view image acquisition systems with two or more cameras can be rather costly due to the number of high resolution image sensors that are required. Recently, it has been shown that by covering a low resolution sensor with a non-regular sampling mask and by using an efficient algorithm for image reconstruction, a high resolution image can be obtained. In this paper, a stereo image reconstruction setup for multi-view scenarios is proposed. A scene is captured by a pair of non-regular sampling sensors and by incorporating information from the adjacent view, the reconstruction quality can be increased. Compared to a state-of-the-art single-view reconstruction algorithm, this leads to a visually noticeable average gain in PSNR of 0.74 dB., Comment: 4 pages, 5 figures, 1 table, International Conference on Image Processing (ICIP)

The reconstruction of clipped speech signals is an important task in audio signal processing to achieve an enhanced audio quality for further processing. In this paper, Frequency Selective Extrapolation (FSE), which is commonly used for error concealment or the reconstruction of incomplete image data, is adapted to be able to restore audio signals which are distorted from clipping. For this, FSE generates a model of the signal as an iterative superposition of Fourier basis functions. Clipped samples can then be replaced by estimated samples from the model. The performance of the proposed algorithm is evaluated by using different speech test data sets. Compared to other state-of-the-art declipping algorithms, this leads to a maximum gain in SNR of up to 3:5 dB and an average gain of 1 dB., Comment: 4 pages, 5 figures, 2 tables, Speech Communication 11. ITG Symposium

Recently, it has been shown that a high resolution image can be obtained without the usage of a high resolution sensor. The main idea has been that a low resolution sensor is covered with a non-regular sampling mask followed by a reconstruction of the incomplete high resolution image captured this way. In this paper, a multi-frame reconstruction approach is proposed where a video is taken by a non-regular sampling sensor and fully reconstructed afterwards. By utilizing the temporal correlation between neighboring frames, the reconstruction quality can be further enhanced. Compared to a state-of-the-art single-frame reconstruction approach, this leads to a visually noticeable gain in PSNR of up to 1.19 dB on average., Comment: 4 pages, 9 figures, 1 table, Visual Communications and Image Processing (VCIP)

Increasing spatial image resolution is an often required, yet challenging task in image acquisition. Recently, it has been shown that it is possible to obtain a high resolution image by covering a low resolution sensor with a non-regular sampling mask. Due to the masking, however, some pixel information in the resulting high resolution image is not available and has to be reconstructed by an efficient image reconstruction algorithm in order to get a fully reconstructed high resolution image. In this paper, the influence of different sampling masks with a reduced randomness of the non-regularity on the image reconstruction process is evaluated. Simulation results show that it is sufficient to use sampling masks that are non-regular only on a smaller scale. These sampling masks lead to a visually noticeable gain in PSNR compared to arbitrary chosen sampling masks which are non-regular over the whole image sensor size. At the same time, they simplify the manufacturing process and allow for efficient storage., Comment: 4 pages, 5 figures, 1 table, Visual Communications and Image Processing (VCIP)

Data-driven algorithm design is a promising, learning-based approach for beyond worst-case analysis of algorithms with tunable parameters. An important open problem is the design of computationally efficient data-driven algorithms for combinatorial algorithm families with multiple parameters. As one fixes the problem instance and varies the parameters, the "dual" loss function typically has a piecewise-decomposable structure, i.e. is well-behaved except at certain sharp transition boundaries. In this work we initiate the study of techniques to develop efficient ERM learning algorithms for data-driven algorithm design by enumerating the pieces of the sum dual loss functions for a collection of problem instances. The running time of our approach scales with the actual number of pieces that appear as opposed to worst case upper bounds on the number of pieces. Our approach involves two novel ingredients -- an output-sensitive algorithm for enumerating polytopes induced by a set of hyperplanes using tools from computational geometry, and an execution graph which compactly represents all the states the algorithm could attain for all possible parameter values. We illustrate our techniques by giving algorithms for pricing problems, linkage-based clustering and dynamic-programming based sequence alignment., Comment: 41 pages, 3 figures, accepted at NeurIPS 2024

High resolution images can be acquired using a non-regular sampling sensor which consists of an underlying low resolution sensor that is covered with a non-regular sampling mask. The reconstructed high resolution image is then obtained during post-processing. Recently, it has been shown that the temporal correlation between neighboring frames can be exploited in order to enhance the reconstruction quality of non-regularly sampled video data. In this paper, a new recursive multi-frame reconstruction approach is proposed in order to further increase the reconstruction quality. By using a new reference order, previously reconstructed frames can be used for the subsequent motion estimation and a new weighting function allows for the incorporation of multiple pixels projected onto the same position. With the new recursive multi-frame approach, a visually noticeable average gain in PSNR of up to 1.13 dB with respect to a state-of-the-art single-frame reconstruction approach can be achieved. Compared to the existing multi-frame approach, a gain of 0.31 dB is possible. SSIM results show the same behavior as PSNR results. Additionally, the pre-reconstruction step of the existing multi-frame approach can be avoided and the new algorithm is, in general, capable of real-time processing., Comment: 5 pages, 7 figures, 3 tables, Picture Coding Symposium (PCS)

Both a high spatial and a high temporal resolution of images and videos are desirable in many applications such as entertainment systems, monitoring manufacturing processes, or video surveillance. Due to the limited throughput of pixels per second, however, there is always a trade-off between acquiring sequences with a high spatial resolution at a low temporal resolution or vice versa. In this paper, a modified sensor concept is proposed which is able to acquire both a high spatial and a high temporal resolution. This is achieved by dynamically reading out only a subset of pixels in a non-regular order to obtain a high temporal resolution. A full high spatial resolution is then obtained by performing a subsequent three-dimensional reconstruction of the partially acquired frames. The main benefit of the proposed dynamic readout is that for each frame, different sampling points are available which is advantageous since this information can significantly enhance the reconstruction quality of the proposed reconstruction algorithm. Using the proposed dynamic readout strategy, gains in PSNR of up to 8.55 dB are achieved compared to a static readout strategy. Compared to other state-of-the-art techniques like frame rate up-conversion or super-resolution which are also able to reconstruct sequences with both a high spatial and a high temporal resolution, average gains in PSNR of up to 6.58 dB are possible., Comment: 14 pages, 12 figures, 3 tables, IEEE Transactions on Circuits and Systems for Video Technology (TCSVT)

There exist many scenarios where pixel information is available only on a non-regular subset of pixel positions. For further processing, however, it is required to reconstruct such images on a regular grid. Besides many other algorithms, frequency selective reconstruction can be applied for this task. It performs a block-wise generation of a sparse signal model as an iterative superposition of Fourier basis functions and uses this model to replace missing or corrupted pixels in an image. In this paper, it is shown that it is not required to spend the same amount of iterations on both homogeneous and heterogeneous regions. Hence, a new texture-dependent approach for frequency selective reconstruction is introduced that distributes the number of iterations depending on the texture of the regions to be reconstructed. Compared to the original frequency selective reconstruction and depending on the number of iterations, visually noticeable gains in PSNR of up to 1.47 dB can be achieved., Comment: 5 pages, 6 figures, 2 tables, Picture Coding Symposium (PCS)

We propose a parameterization of a nonlinear dynamic controller based on the recurrent equilibrium network, a generalization of the recurrent neural network. We derive constraints on the parameterization under which the controller guarantees exponential stability of a partially observed dynamical system with sector bounded nonlinearities. Finally, we present a method to synthesize this controller using projected policy gradient methods to maximize a reward function with arbitrary structure. The projection step involves the solution of convex optimization problems. We demonstrate the proposed method with simulated examples of controlling nonlinear plants, including plants modeled with neural networks., Comment: Submitted to IEEE CDC 2022. arXiv admin note: text overlap with arXiv:2109.03861

In this paper we introduce a contact process in an evolving random environment (CPERE) on a connected and transitive graph with bounded degree, where we assume that this environment is described through an ergodic spin systems with finite range. We show that under a certain growth condition the phase transition of survival is independent of the initial configuration of the process. We study the invariant laws of the CPERE and show that under aforementioned growth condition the phase transition for survival coincides with the phase transition of non-triviality of the upper invariant law. Furthermore, we prove continuity properties for the survival probability and derive equivalent conditions for complete convergence, in an analogous way as for the classical contact process. We then focus on the special case, where the evolving random environment is described through a dynamical percolation. We show that the contact process on a dynamical percolation on the $d$-dimensional integer dies out a.s. at criticality and complete convergence holds for all parameter choices. In the end we derive some comparison results between a dynamical percolation and ergodic spin systems with finite range such that we get bounds on the survival probability of a contact process in an evolving random environment and we determine in this case that complete convergence holds in a certain parameter regime., Comment: 53 pages, 19 figures, (revised version) Some gaps in the proof of Proposition 2.6 were filled, which resulted in a stronger statement. Manuskript was accepted in EJP

We introduce the notion of a relative marked basis over quasi-stable ideals, together with constructive methods and a functorial interpretation, developing computational methods for the study of Hilbert schemes over quotients of polynomial rings. Then we focus on two applications. The first has a theoretical flavour and produces an explicit open cover of the Hilbert scheme when the quotient ring is Cohen-Macaulay on quasi-stable ideals. Together with relative marked bases, we use suitable general changes of variables which preserve the structure of the quasi-stable ideal, against the expectations. The second application has a computational flavour. When the quotient rings are Macaulay-Lex on quasi-stable ideals, we investigate the lex-point of the Hilbert schemes and find examples of both smooth and singular lex-points., Comment: 27 pages, comments are welcome

Quarter sampling is a novel sensor design that allows for an acquisition of higher resolution images without increasing the number of pixels. When being used for video data, one out of four pixels is measured in each frame. Effectively, this leads to a non-regular spatio-temporal sub-sampling. Compared to purely spatial or temporal sub-sampling, this allows for an increased reconstruction quality, as aliasing artifacts can be reduced. For the fast reconstruction of such sensor data with a fixed mask, recursive variant of frequency selective reconstruction (FSR) was proposed. Here, pixels measured in previous frames are projected into the current frame to support its reconstruction. In doing so, the motion between the frames is computed using template matching. Since some of the motion vectors may be erroneous, it is important to perform a proper consistency checking. In this paper, we propose faster consistency checking methods as well as a novel recursive FSR that uses the projected pixels different than in literature and can handle dynamic masks. Altogether, we are able to significantly increase the reconstruction quality by + 1.01 dB compared to the state-of-the-art recursive reconstruction method using a fixed mask. Compared to a single frame reconstruction, an average gain of about + 1.52 dB is achieved for dynamic masks. At the same time, the computational complexity of the consistency checks is reduced by a factor of 13 compared to the literature algorithm., Comment: 5 pages, 5 figures, 3 tables, IEEE International Conference on Image Processing (ICIP)

We present a new data structure for representation of polynomial variables in the parsing of sum-of-squares (SOS) programs. In SOS programs, the variables $s(x;Q)$ are polynomial in the independent variables $x$, but linear in the decision variables $Q$. Current SOS parsers, however, fail to exploit the semi-linear structure of the polynomial variables, treating the decision variables as independent variables in their representation. This results in unnecessary overhead in storage and manipulation of the polynomial variables, prohibiting the parser from addressing larger-scale optimization problems. To eliminate this computational overhead, we introduce a new representation of polynomial variables, the "dpvar" structure, that is affine in the decision variables. We show that the complexity of operations on variables in the dpvar representation scales favorably with the number of decision variables. We further show that the required memory for storing polynomial variables is relatively small using the dpvar structure, particularly when exploiting the MATLAB sparse storage structure. Finally, we incorporate the dpvar data structure into SOSTOOLS 4.00, and test the performance of the parser for several polynomial optimization problems.

In recent years, due to a higher demand for portable devices, which provide restricted amounts of processing capacity and battery power, the need for energy and time efficient hard- and software solutions has increased. Preliminary estimations of time and energy consumption can thus be valuable to improve implementations and design decisions. To this end, this paper presents a method to estimate the time and energy consumption of a given software solution, without having to rely on the use of a traditional Cycle Accurate Simulator (CAS). Instead, we propose to utilize a combination of high-level functional simulation with a mechanistic extension to include non-functional properties: Instruction counts from virtual execution are multiplied with corresponding specific energies and times. By evaluating two common image processing algorithms on an FPGA-based CPU, where a mean relative estimation error of 3% is achieved for cacheless systems, we show that this estimation tool can be a valuable aid in the development of embedded processor architectures. The tool allows the developer to reach well-suited design decisions regarding the optimal processor hardware configuration for a given algorithm at an early stage in the design process., Comment: 6 pages, 4 figures, 2015 IEEE International Parallel and Distributed Processing Symposium Workshop (IPDPS)

Quarter sampling is a novel sensor concept that enables the acquisition of higher resolution images without increasing the number of pixels. This is achieved by covering three quarters of each pixel of a low-resolution sensor such that only one quadrant of the sensor area of each pixel is sensitive to light. By randomly masking different parts, effectively a non-regular sampling of a higher resolution image is performed. Combining a properly designed mask and a high-quality reconstruction algorithm, a higher image quality can be achieved than using a low-resolution sensor and subsequent upsampling. For the latter case, the image quality can be enhanced using super resolution algorithms. Recently, algorithms based on machine learning such as the Very Deep Super Resolution network (VDSR) proofed to be successful for this task. In this work, we transfer the concepts of VDSR to the special case of quarter sampling. Besides adapting the network layout to take advantage of the case of quarter sampling, we introduce a novel data augmentation technique enabled by quarter sampling. Altogether, using the quarter sampling sensor, the image quality in terms of PSNR can be increased by +0.67 dB for the Urban 100 dataset compared to using a low-resolution sensor with VDSR., Comment: 5 pages, 5 figures, 2020 IEEE International Conference on Image Processing (ICIP)

Even though image signals are typically acquired on a regular two dimensional grid, there exist many scenarios where non-regular sampling is possible. Non-regular sampling can remove aliasing. In terms of the non-regular sampling patterns, there is a high degree of freedom in how to actually arrange the sampling positions. In literature, random patterns show higher reconstruction quality compared to regular patterns due to reduced aliasing effects. On the downside, random patterns feature large void areas which is also disadvantageous. In the scope of this work, we present two techniques to design optimized non-regular image sampling patterns for arbitrary sampling densities. Both techniques create incremental sampling patterns, i.e., one pixel position is added in each step until the desired sampling density is reached. Our proposed patterns increase the reconstruction quality by more than +0.5 dB in PSNR for a broad density range. Visual comparisons are provided., Comment: 6 pages, 7 figures, 2018 IEEE International Conference on Imaging Systems and Techniques (IST)

Non-regular sampling can reduce aliasing at the expense of noise. Recently, it has been shown that non-regular sampling can be carried out using a conventional regular imaging sensor when the surface of its individual pixels is partially covered. This technique is called quarter sampling (also 1/4 sampling), since only one quarter of each pixel is sensitive to light. For this purpose, the choice of a proper sampling mask is crucial to achieve a high reconstruction quality. In the scope of this work, we present an iterative algorithm to improve an arbitrary quarter sampling mask which results in a continuous increase of the reconstruction quality. In terms of the reconstruction algorithms, we test two simple algorithms, namely, linear interpolation and nearest neighbor interpolation, as well as two more sophisticated algorithms, namely, steering kernel regression and frequency selective extrapolation. Besides PSNR gains of +0.31 dB to +0.68 dB relative to a random quarter sampling mask resulting from our optimized mask, visually noticeable enhancements are perceptible., Comment: 5 pages, 8 figures, 25th IEEE International Conference on Image Processing (ICIP)

Frequency Selective Reconstruction (FSR) is a state-of-the-art algorithm for solving diverse image reconstruction tasks, where a subset of pixel values in the image is missing. However, it entails a high computational complexity due to its iterative, blockwise procedure to reconstruct the missing pixel values. Although the complexity of FSR can be considerably decreased by performing its computations in the frequency domain, the reconstruction procedure still takes multiple seconds up to multiple minutes depending on the parameterization. However, FSR has the potential for a massive parallelization greatly improving its reconstruction time. In this paper, we introduce a novel highly parallelized formulation of FSR adapted to the capabilities of modern GPUs and propose a considerably accelerated calculation of the inherent argmax calculation. Altogether, we achieve a 100-fold speed-up, which enables the usage of FSR for real-time applications., Comment: 6 pages, 5 figures, Source code available at https://gitlab.lms.tf.fau.de/LMS/gpu-fsr

We report on polarization combining 2D grating couplers (2D GCs) on amorphous Si:H, fabricated in the backend of line of a photonic BiCMOS platform. The 2D GCs can be used as an interface of a hybrid silicon photonic coherent transmitter, which can be implemented on bulk Si wafers. The fabricated 2D GCs operate in the telecom C-band and show an experimental coupling efficiency of -5 dB with a wafer variation of +/-1.2 dB. Possibilities for efficiency enhancement and improved performance stability in future design generations are outlined and extension towards O-band devices is investigated as well., Comment: This is an accepted version of a peer-reviewed manuscript, considered for publication by the Springer's journal Frontiers of Optoelectronics

Many existing region-of-attraction (ROA) analysis tools find difficulty in addressing feedback systems with large-scale neural network (NN) policies and/or high-dimensional sensing modalities such as cameras. In this paper, we tailor the projected gradient descent (PGD) attack method developed in the adversarial learning community as a general-purpose ROA analysis tool for large-scale nonlinear systems and end-to-end perception-based control. We show that the ROA analysis can be approximated as a constrained maximization problem whose goal is to find the worst-case initial condition which shifts the terminal state the most. Then we present two PGD-based iterative methods which can be used to solve the resultant constrained maximization problem. Our analysis is not based on Lyapunov theory, and hence requires minimum information of the problem structures. In the model-based setting, we show that the PGD updates can be efficiently performed using back-propagation. In the model-free setting (which is more relevant to ROA analysis of perception-based control), we propose a finite-difference PGD estimate which is general and only requires a black-box simulator for generating the trajectories of the closed-loop system given any initial state. We demonstrate the scalability and generality of our analysis tool on several numerical examples with large-scale NN policies and high-dimensional image observations. We believe that our proposed analysis serves as a meaningful initial step toward further understanding of closed-loop stability of large-scale nonlinear systems and perception-based control., Comment: Submitted to L4DC 2022

Motion compensated inter prediction is a common component of all video coders. The concept was established in traditional hybrid coding and successfully transferred to learning-based video compression. To compress the residual signal after prediction, usually the difference of the two signals is compressed using a standard autoencoder. However, information theory tells us that a general conditional coder is more efficient. In this paper, we provide a solid foundation based on information theory and Shannon entropy to show the potentials but also the limits of conditional coding. Building on those results, we then propose the generalized difference coder, a special case of a conditional coder designed to avoid limiting bottlenecks. With this coder, we are able to achieve average rate savings of 27.8% compared to a standard autoencoder, by only adding a moderate complexity overhead of less than 7%.

This paper considers the robust stability of a discrete-time Lurye system consisting of the feedback interconnection between a linear system and a bounded and monotone nonlinearity. It has been conjectured that the existence of a suitable linear time-invariant (LTI) O'Shea-Zames-Falb multiplier is not only sufficient but also necessary. Roughly speaking, a successful proof of the conjecture would require: (a) a conic parameterization of a set of multipliers that describes exactly the set of nonlinearities, (b) a lossless S-procedure to show that the non-existence of a multiplier implies that the Lurye system is not uniformly robustly stable over the set of nonlinearities, and (c) the existence of a multiplier in the set of multipliers used in (a) implies the existence of an LTI multiplier. We investigate these three steps, showing the current bottlenecks for proving this conjecture. In addition, we provide an extension of the class of multipliers which may be used to disprove the conjecture., Comment: 25 Pages

In complex Langevin simulations, the insufficient decay of the probability density near infinity leads to boundary terms that spoil the formal argument for correctness. We present a formulation of this term that is cheaply measurable in lattice models, and in principle allows also the direct estimation of the systematic error of the CL method. Results for a toy model, 3d XY model and HDQCD are presented., Comment: 7 pages, 5 figures, contribution to the 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather@MIT, USA

Motivated by the recent empirical success of policy-based reinforcement learning (RL), there has been a research trend studying the performance of policy-based RL methods on standard control benchmark problems. In this paper, we examine the effectiveness of policy-based RL methods on an important robust control problem, namely $\mu$ synthesis. We build a connection between robust adversarial RL and $\mu$ synthesis, and develop a model-free version of the well-known $DK$-iteration for solving state-feedback $\mu$ synthesis with static $D$-scaling. In the proposed algorithm, the $K$ step mimics the classical central path algorithm via incorporating a recently-developed double-loop adversarial RL method as a subroutine, and the $D$ step is based on model-free finite difference approximation. Extensive numerical study is also presented to demonstrate the utility of our proposed model-free algorithm. Our study sheds new light on the connections between adversarial RL and robust control., Comment: Accepted to ACC 2022

Adversarial examples can easily degrade the classification performance in neural networks. Empirical methods for promoting robustness to such examples have been proposed, but often lack both analytical insights and formal guarantees. Recently, some robustness certificates have appeared in the literature based on system theoretic notions. This work proposes an incremental dissipativity-based robustness certificate for neural networks in the form of a linear matrix inequality for each layer. We also propose an equivalent spectral norm bound for this certificate which is scalable to neural networks with multiple layers. We demonstrate the improved performance against adversarial attacks on a feed-forward neural network trained on MNIST and an Alexnet trained using CIFAR-10.

For modern high-resolution imaging sensors, pixel binning is performed in low-lighting conditions and in case high frame rates are required. To recover the original spatial resolution, single-image super-resolution techniques can be applied for upscaling. To achieve a higher image quality after upscaling, we propose a novel binning concept using tetromino-shaped pixels. It is embedded into the field of compressed sensing and the coherence is calculated to motivate the sensor layouts used. Next, we investigate the reconstruction quality using tetromino pixels for the first time in literature. Instead of using different types of tetrominoes as proposed elsewhere, we show that using a small repeating cell consisting of only four T-tetrominoes is sufficient. For reconstruction, we use a locally fully connected reconstruction (LFCR) network as well as two classical reconstruction methods from the field of compressed sensing. Using the LFCR network in combination with the proposed tetromino layout, we achieve superior image quality in terms of PSNR, SSIM, and visually compared to conventional single-image super-resolution using the very deep super-resolution (VDSR) network. For PSNR, a gain of up to \SI[retain-explicit-plus]{+1.92}{dB} is achieved., Comment: 10 pages, 9 figures, 4 tables. This work has been submitted to the IEEE for possible publication

Divergent density of states offers the unique opportunity to explore a wide variety of correlated electron physics. In the thinnest limit, this has been predicted and verified in the ultra-flat bands of magic-angle twisted bilayer graphene, the band touching points of few-layer rhombohedral graphite, and the lightly doped rhombohedral trilayer graphene. The simpler and seemingly better understood Bernal bilayer graphene is also susceptible to orbital magnetism-driven phases at charge neutrality, such as layer antiferromagnet and quantum anomalous Hall octet. Here we report the discovery of a cascade of novel correlated phases in the vicinity of electric-field-controlled Lifshitz transitions and van Hove singularities in trigonally warped bilayer graphene. We provide compelling evidence for the observation of Stoner ferromagnets - half and quarter metals. More prominently, we identify signatures consistent with a topologically nontrivial Wigner-Hall crystal at zero magnetic field and its transition to a trivial Wigner crystal, as well as two correlated metals whose behavior deviates from standard Fermi liquids. Our results in this reproducible, tunable, simple system opens a new chapter for studying strongly correlated electrons.

An established way of realizing topologically protected states in a two-dimensional electron gas is by applying a perpendicular magnetic field thus creating quantum Hall edge channels. In electrostatically gapped bilayer graphene intriguingly, even in the absence of a magnetic field topologically protected electronic states can emerge at naturally occurring stacking domain walls. While individually both types of topologically protected states have been investigated, their intriguing interplay remains poorly understood. Here, we focus on the interplay between topological domain wall states and quantum Hall edge transport within the eight-fold degenerate zeroth Landau level of high-quality suspended bilayer graphene. We find that the two-terminal conductance remains approximately constant for low magnetic fields throughout the distinct quantum Hall states since the conduction channels are traded between domain wall and device edges. For high magnetic fields, however, we observe evidence of transport suppression at the domain wall, which can be attributed to the emergence of spectral minigaps. This indicates that stacking domain walls do potentially do not correspond to a topological domain wall in the order parameter.

The complex Langevin method is a general method to treat systems with complex action, such as QCD at nonzero density. The formal justification relies on the absence of certain boundary terms, both at infinity and at the unavoidable poles of the drift force. Here I focus on the boundary terms at these poles for simple models, which so far have not been discussed in detail. The main result is that those boundary terms (for the "un-evolved" observables) arise after running the Langevin process for a finite time and vanish again as the Langevin time goes to infinity. This is in contrast to the boundary terms at infinity, which can be found to occur in the long time limit (cf. the contribution by D\'enes Sexty)., Comment: 7 pages, 2 figures. Contribution to Lattice 21

Ultrafast magnetization dynamics are governed by energy flow between electronic, magnetic, and lattice degrees of freedom. A quantitative understanding of these dynamics must be based on a model that agrees with experimental results for all three subsystems. However, ultrafast dynamics of the lattice remain largely unexplored experimentally. Here, we combine femtosecond electron diffraction experiments of the lattice dynamics with energy-conserving atomistic spin dynamics (ASD) simulations and ab-initio calculations to study the intrinsic energy flow in the 3d ferromagnets cobalt (Co) and iron (Fe). The simulations yield a good description of experimental data, in particular an excellent description of our experimental results for the lattice dynamics. We find that the lattice dynamics are influenced significantly by the magnetization dynamics due to the energy cost of demagnetization. Our results highlight the role of the spin system as the dominant heat sink in the first hundreds of femtoseconds. Together with previous findings for nickel [Zahn et al., Phys. Rev. Research 3, 023032 (2021)], our work demonstrates that energy-conserving ASD simulations provide a general and consistent description of the laser-induced dynamics in all three elemental 3d ferromagnets.

Revealing the bonding and time-evolving atomic dynamics in functional materials with complex lattice structures can update the fundamental knowledge on rich physics therein, and also help to manipulate the material properties as desired. As the most prototypical chalcogenide phase change material, Ge2Sb2Te5 has been widely used in optical data storage and non-volatile electric memory due to the fast switching speed and the low energy consumption. However, the basic understanding of the structural dynamics on the atomic scale is still not clear. Using femtosecond electron diffraction, structure factor calculation and TDDFT-MD simulation, we reveal the photoinduced ultrafast transition of the local correlated structure in the averaged rock-salt phase of Ge2Sb2Te5. The randomly oriented Peierls distortion among unit cells in the averaged rock-salt phase of Ge2Sb2Te5 is termed as local correlated structures. The ultrafast suppression of the local Peierls distortions in individual unit cell gives rise to a local structure change from the rhombohedral to the cubic geometry within ~ 0.3 ps. In addition, the impact of the carrier relaxation and the large amount of vacancies to the ultrafast structural response is quantified and discussed. Our work provides new microscopic insights into contributions of the local correlated structure to the transient structural and optical responses in phase change materials. Moreover, we stress the significance of femtosecond electron diffraction in revealing the local correlated structure in the subunit cell and the link between the local correlated structure and physical properties in functional materials with complex microstructures.

Neural network controllers have become popular in control tasks thanks to their flexibility and expressivity. Stability is a crucial property for safety-critical dynamical systems, while stabilization of partially observed systems, in many cases, requires controllers to retain and process long-term memories of the past. We consider the important class of recurrent neural networks (RNN) as dynamic controllers for nonlinear uncertain partially-observed systems, and derive convex stability conditions based on integral quadratic constraints, S-lemma and sequential convexification. To ensure stability during the learning and control process, we propose a projected policy gradient method that iteratively enforces the stability conditions in the reparametrized space taking advantage of mild additional information on system dynamics. Numerical experiments show that our method learns stabilizing controllers while using fewer samples and achieving higher final performance compared with policy gradient.

This paper focuses on safety critical control with sector-bounded uncertainties at the plant input. The uncertainties can represent nonlinear and/or time-varying components. We propose a new robust control barrier function (RCBF) approach to enforce safety requirements in the presence of these uncertainties. The primary objective is to minimally alter the given baseline control command to guarantee safety in the presence of modeled uncertainty. The resulting min-norm optimization problem can be recast as a Second-Order Cone Program (SOCP) to enable online implementation. Properties of this controller are studied and a numerical example is provided to illustrate the effectiveness of this approach., Comment: 7 Pages, 4 Figures, Submitted to LCSS/ACC 2022

Bernal-stacked multilayer graphene is a versatile platform to explore quantum transport phenomena and interaction physics due to its exceptional tunability via electrostatic gating. For instance, upon applying a perpendicular electric field, its band structure exhibits several off-center Dirac points (so-called Dirac gullies) in each valley. Here, the formation of Dirac gullies and the interaction-induced breakdown of gully coherence is explored via magnetotransport measurements in high-quality Bernal-stacked (ABA) trilayer graphene. In the absence of a magnetic field, multiple Lifshitz transitions as function of electric field and charge carrier density indicating the formation of Dirac gullies are identified. In the quantum Hall regime and high electric fields, the emergence of Dirac gullies is evident as an increase in Landau level degeneracy. When tuning both electric and magnetic fields, electron-electron interactions can be controllably enhanced until the gully degeneracy is eventually lifted. The arising correlated ground state is consistent with a previously predicted nematic phase that spontaneously breaks the rotational gully symmetry.

This paper presents a control design method that achieves safety for systems with unmodeled dynamics at the plant input. The proposed method combines control barrier functions (CBFs) and integral quadratic constraints (IQCs). Simplified, low-order models are often used in the design of the controller. Parasitic, unmodeled dynamics (e.g. actuator dynamics, time delays, etc) can lead to safety violations. The proposed method bounds the input-output behavior of these unmodeled dynamics in the time-domain using an alpha-IQC. The alpha-IQC is then incorporated into the CBF constraint to ensure safety. The approach is demonstrated with a simple example.

The quantum anomalous Hall (QAH) effect - a macroscopic manifestation of chiral band topology at zero magnetic field - has only been experimentally realized by magnetic doping of topological insulators (1 - 3) and delicate design of Moire heterostructures (4 - 8). However, the seemingly simple bilayer graphene without magnetic doping or Moire engineering has long been predicted to host competing ordered states with QAH effects (9 - 11). Here, we explore states in bilayer graphene with conductance of 2 e2/h that not only survive down to anomalously small magnetic fields and up to temperatures of 5 K, but also exhibit magnetic hysteresis. Together, the experimental signatures provide compelling evidence for orbital magnetism driven QAH behavior with a Chern number tunable via electric and magnetic fields as well as carrier sign. The observed octet of QAH phases is distinct from previous observations due to its peculiar ferrimagnetic and ferrielectric order that is characterized by quantized anomalous charge, spin, valley, and spin-valley Hall behavior.

We discuss a class of models for particulate gels in which the particle contacts are described by an effective interaction combining a two-body attraction and a three-body angular repulsion. Using molecular dynamics, we show how varying the model parameters allows us to sample, for a given gelation protocol, a variety of gel morphologies. For a specific set of the model parameters, we identify the local elastic structures that get interlocked in the gel network. Using the analytical expression of their elastic energy from the microscopic interactions, we can estimate their contribution to the emergent elasticity of the gel and gain new insight into its origin.

Manipulating crystal structure and the corresponding electronic properties in quantum materials provides opportunities for the exploration of exotic physics and practical applications. Here, by ultrafast electron diffraction, structure factor calculation and TDDFT-MD simulations, we report the photoinduced concurrent intralayer and interlayer structural transitions in the Td and 1T' phase of XTe2 (X=Mo, W). Concomitant with the interlayer structural transition by shear displacement, the ultrafast suppression of the intralayer Peierls distortion within 0.3 ps is demonstrated and attributed to Mo-Mo (W-W) bond stretching. We discuss the modification of multiple quantum electronic states associated with the intralayer and interlayer structural transitions, such as the topological band inversion and the higher-order topological state. The twin structure and the stacking fault in XTe2 are identified by the ultrafast structural response. Our work elucidates the pathway of the photoinduced intralayer and interlayer structural transitions in atomic and femtosecond spatiotemporal scale. Moreover, the concurrent intralayer and interlayer structural transitions reveals the traversal of all double-well potential energy surfaces (DWPES) by laser excitation in material system, which may be an intrinsic mechanism in the field of photoexcitation-driven symmetry engineering, beyond the single DWPES transition model and the order-disorder transition model.

This paper proposes a uniqueness Shapley measure to compare the extent to which different variables are able to identify a subject. Revealing the value of a variable on subject $t$ shrinks the set of possible subjects that $t$ could be. The extent of the shrinkage depends on which other variables have also been revealed. We use Shapley value to combine all of the reductions in log cardinality due to revealing a variable after some subset of the other variables has been revealed. This uniqueness Shapley measure can be aggregated over subjects where it becomes a weighted sum of conditional entropies. Aggregation over subsets of subjects can address questions like how identifying is age for people of a given zip code. Such aggregates have a corresponding expression in terms of cross entropies. We use uniqueness Shapley to investigate the differential effects of revealing variables from the North Carolina voter registration rolls and in identifying anomalous solar flares. An enormous speedup (approaching 2000 fold in one example) is obtained by using the all dimension trees of Moore and Lee (1998) to store the cardinalities we need.

Cohort Shapley value is a model-free method of variable importance grounded in game theory that does not use any unobserved and potentially impossible feature combinations. We use it to evaluate algorithmic fairness, using the well known COMPAS recidivism data as our example. This approach allows one to identify for each individual in a data set the extent to which they were adversely or beneficially affected by their value of a protected attribute such as their race. The method can do this even if race was not one of the original predictors and even if it does not have access to a proprietary algorithm that has made the predictions. The grounding in game theory lets us define aggregate variable importance for a data set consistently with its per subject definitions. We can investigate variable importance for multiple quantities of interest in the fairness literature including false positive predictions.