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This paper is concerned with the online bandit nonlinear control, which aims to learn the best stabilizing controller from a pool of stabilizing and destabilizing controllers of unknown types for a given nonlinear dynamical system. We develop an algorithm, named Dynamic Batch length and Adaptive learning Rate (DBAR), and study its stability and regret. Unlike the existing Exp3 algorithm requiring an exponentially stabilizing controller, DBAR only needs a significantly weaker notion of controller stability, in which case substantial time may be required to certify the system stability. Dynamic batch length in DBAR effectively addresses this issue and enables the system to attain asymptotic stability, where the algorithm behaves as if there were no destabilizing controllers. Moreover, adaptive learning rate in DBAR only uses the state norm information to achieve a tight regret bound even when none of the stabilizing controllers in the pool are exponentially stabilizing., Comment: 38 pages, 7 figures

This paper studies the linear system identification problem in the general case where the disturbance is sub-Gaussian, correlated, and possibly adversarial. First, we consider the case with noncentral (nonzero-mean) disturbances for which the ordinary least-squares (OLS) method fails to correctly identify the system. We prove that the $l_1$-norm estimator accurately identifies the system under the condition that each disturbance has equal probabilities of being positive or negative. This condition restricts the sign of each disturbance but allows its magnitude to be arbitrary. Second, we consider the case where each disturbance is adversarial with the model that the attack times happen occasionally but the distributions of the attack values are completely arbitrary. We show that when the probability of having an attack at a given time is less than 0.5, the $l_1$-norm estimator prevails against any adversarial noncentral disturbances and the exact recovery is achieved within a finite time. These results pave the way to effectively defend against arbitrarily large noncentral attacks in safety-critical systems., Comment: 8 pages, 2 figures

A Riemannian manifold $(M,g)$ is called \emph{weakly Einstein} if the tensor $R_{iabc}R_{j}^{~~abc}$ is a scalar multiple of the metric tensor $g_{ij}$. We give a complete classification of weakly Einstein hypersurfaces in the spaces of nonzero constant curvature (the classification in a Euclidean space has been previously known). The main result states that such a hypersurface can only be the product of two spaces of constant curvature or a rotation hypersurface., Comment: 19 pages

Optimal control problems can be solved via a one-shot (single) optimization or a sequence of optimization using dynamic programming (DP). However, the computation of their global optima often faces NP-hardness, and thus only locally optimal solutions may be obtained at best. In this work, we consider the discrete-time finite-horizon optimal control problem in both deterministic and stochastic cases and study the optimization landscapes associated with two different approaches: one-shot and DP. In the deterministic case, we prove that each local minimizer of the one-shot optimization corresponds to some control input induced by a locally minimum control policy of DP, and vice versa. However, with a parameterized policy approach, we prove that deterministic and stochastic cases both exhibit the desirable property that each local minimizer of DP corresponds to some local minimizer of the one-shot optimization, but the converse does not necessarily hold. Nonetheless, under different technical assumptions for deterministic and stochastic cases, if there exists only a single locally minimum control policy, one-shot and DP turn out to capture the same local solution. These results pave the way to understand the performance and stability of local search methods in optimal control., Comment: 16 pages, 4 figures

We develop new techniques in order to deal with Riccati-type equations, subject to a further algebraic constraint, on Riemannian manifolds $(M^3,g)$. We find that the obstruction to solve the aforementioned equation has order $4$ in the metric coefficients and is fully described by an homogeneous polynomial in $\mathrm{Sym}^{16}TM$. Techniques from real algebraic geometry, reminiscent of those used for the "PositiveStellen-Satz " problem, allow determining the geometry in terms of explicit exterior differential systems. Analysis of the latter shows flatness for the metric $g$; in particular we complete the classification of asymptotically harmonic manifolds of dimension $3$, establishing those are either flat or real hyperbolic spaces., Comment: minor changes, a few typos caught

Deploying deep models in real-world scenarios entails a number of challenges, including computational efficiency and real-world (e.g., long-tailed) data distributions. We address the combined challenge of learning long-tailed distributions using highly resource-efficient binary neural networks as backbones. Specifically, we propose a calibrate-and-distill framework that uses off-the-shelf pretrained full-precision models trained on balanced datasets to use as teachers for distillation when learning binary networks on long-tailed datasets. To better generalize to various datasets, we further propose a novel adversarial balancing among the terms in the objective function and an efficient multiresolution learning scheme. We conducted the largest empirical study in the literature using 15 datasets, including newly derived long-tailed datasets from existing balanced datasets, and show that our proposed method outperforms prior art by large margins (>14.33% on average).

Homomorphic encryption (HE) enables privacy-preserving deep learning by allowing computations on encrypted data without decryption. However, deploying convolutional neural networks (CNNs) with HE is challenging due to the need to convert input data into a two-dimensional matrix for convolution using the im2col technique, which rearranges the input for efficient computation. This restricts the types of CNN models that can be used since the encrypted data structure must be compatible with the specific model. UniHENN is a novel HE-based CNN architecture that eliminates the need for im2col, enhancing its versatility and compatibility with a broader range of CNN models. UniHENN flattens input data to one dimension without using im2col. The kernel performs convolutions by traversing the image, using incremental rotations and structured multiplication on the flattened input, with results spaced by the stride interval. Experimental results show that UniHENN significantly outperforms the state-of-the-art 2D CNN inference architecture named PyCrCNN in terms of inference time. For example, on the LeNet-1 model, UniHENN achieves an average inference time of 30.089 seconds, about 26.6 times faster than PyCrCNN's 800.591 seconds. Furthermore, UniHENN outperforms TenSEAL, an im2col-optimized CNN model, in concurrent image processing. For ten samples, UniHENN (16.247 seconds) was about 3.9 times faster than TenSEAL (63.706 seconds), owing to its support for batch processing of up to 10 samples. We demonstrate UniHENN's adaptability to various CNN architectures, including a 1D CNN and six 2D CNNs, highlighting its flexibility and efficiency for privacy-preserving cloud-based CNN services., Comment: 20 pages, 15 figures, Accepted by IEEE ACCESS

Single image super-resolution (SISR) has experienced significant advancements, primarily driven by deep convolutional networks. Traditional networks, however, are limited to upscaling images to a fixed scale, leading to the utilization of implicit neural functions for generating arbitrarily scaled images. Nevertheless, these methodologies have imposed substantial computational demands as they involve querying every target pixel to a single resource-intensive decoder. In this paper, we introduce a novel and efficient framework, the Mixture of Experts Implicit Super-Resolution (MoEISR), which enables super-resolution at arbitrary scales with significantly increased computational efficiency without sacrificing reconstruction quality. MoEISR dynamically allocates the most suitable decoding expert to each pixel using a lightweight mapper module, allowing experts with varying capacities to reconstruct pixels across regions with diverse complexities. Our experiments demonstrate that MoEISR successfully reduces up to 73% in floating point operations (FLOPs) while delivering comparable or superior peak signal-to-noise ratio (PSNR).

Endoscopic ultrasound (EUS) imaging has a trade-off between resolution and penetration depth. By considering the in-vivo characteristics of human organs, it is necessary to provide clinicians with appropriate hardware specifications for precise diagnosis. Recently, super-resolution (SR) ultrasound imaging studies, including the SR task in deep learning fields, have been reported for enhancing ultrasound images. However, most of those studies did not consider ultrasound imaging natures, but rather they were conventional SR techniques based on downsampling of ultrasound images. In this study, we propose a novel deep learning-based high-resolution in-depth imaging probe capable of offering low- and high-frequency ultrasound image pairs. We developed an attachable dual-element EUS probe with customized low- and high-frequency ultrasound transducers under small hardware constraints. We also designed a special geared structure to enable the same image plane. The proposed system was evaluated with a wire phantom and a tissue-mimicking phantom. After the evaluation, 442 ultrasound image pairs from the tissue-mimicking phantom were acquired. We then applied several deep learning models to obtain synthetic high-resolution in-depth images, thus demonstrating the feasibility of our approach for clinical unmet needs. Furthermore, we quantitatively and qualitatively analyzed the results to find a suitable deep-learning model for our task. The obtained results demonstrate that our proposed dual-element EUS probe with an image-to-image translation network has the potential to provide synthetic high-frequency ultrasound images deep inside tissues., Comment: 10 pages, 9 figures

In [14], it was shown that, if M is a 3-dimensional asymptotically harmonic with minimal horospheres, then M is flat. However, there is a gap in the proof of this paper. In this paper, we provide the correct proof of the result. Thus we complete the classification of asymptotically harmonic manifolds of dimension 3: An asymptotically harmonic manifold of dimension 3 is either a flat or real hyperbolic space., Comment: 7 pages

The efficient optical second-harmonic generation (SHG) of two-dimensional (2D) crystals, coupled with their atomic thickness that circumvents the phase-match problem, has garnered considerable attention. While various 2D heterostructures have shown promising applications in photodetectors, switching electronics, and photovoltaics, the modulation of nonlinear optical properties in such hetero-systems remains unexplored. In this study, we investigate exciton sensitized SHG in heterobilayers of transition metal dichalcogenides (TMDs), where photoexcitation of one donor layer enhances the SHG response of the other as an acceptor. We utilize polarization-resolved interferometry to detect the SHG intensity and phase of each individual layer, revealing the energetic match between the excitonic resonances of donors and the SHG enhancement of acceptors for four TMD combinations. Our results also uncover the dynamic nature of interlayer coupling, as evidenced by the dependence of sensitization on interlayer gap spacing and the average power of the fundamental beam. This work provides insights into how interlayer coupling of two different layers can modify nonlinear optical phenomena in 2D heterostructures., Comment: 24 pages, 5 figures

Ultrafast ultrasound imaging is essential for advanced ultrasound imaging techniques such as ultrasound localization microscopy (ULM) and functional ultrasound (fUS). Current ultrafast ultrasound imaging is challenged by the ultrahigh data bandwidth associated with the radio frequency (RF) signal, and by the latency of the computationally expensive beamforming process. As such, continuous ultrafast data acquisition and beamforming remain elusive with existing software beamformers based on CPUs or GPUs. To address these challenges, the proposed work introduces a novel method of implementing an ultrafast ultrasound beamformer specifically for ultrafast plane wave imaging (PWI) on a field programmable gate array (FPGA) by using high-level synthesis. A parallelized implementation of the beamformer on a single FPGA was proposed by 1) utilizing a delay compression technique to reduce the delay profile size, which enables both run-time pre-calculated delay profile loading from external memory and delay reuse 2) vectorizing channel data fetching which is enabled by delay reuse, and 3) using fixed summing networks to reduce consumption of logic resources. Our proposed method presents two unique advantages over current FPGA beamformers: 1) high scalability that allows fast adaptation to different FPGA resources and beamforming speed demands by using Xilinx High-Level Synthesis as the development tool, and 2) allow a compact form factor design by using a single FPGA to complete the beamforming instead of multiple FPGAs. With the proposed method, a sustainable average beamforming rate of 4.83 G samples/second in terms of input raw RF sample was achieved. The resulting image quality of the proposed beamformer was compared with the software beamformer on the Verasonics Vantage system for both phantom imaging and in vivo imaging of a mouse brain.

Patterson discussed the curvature identities on Riemannian manifolds in [14], and a curvature identity for any 6-dimensional Riemannian manifold was independently derived from the Chern-Gauss-Bonnet Theorem [8]. In this paper, we provide the explicit formulae of Patterson's curvature identity that holds on 5-dimensional and 6-dimensional Einstein manifolds. We confirm that the curvature identities on the Einstein manifold from the previous work [8] are the same as the curvature identities deduced from Patterson's result. We also provide examples that support the theorems., Comment: 15 pages

We prove that a 2-stein submanifold in a space form whose normal connection is flat or whose codimension is at most 2, has constant curvature., Comment: 5 pages

Although the values of individual soccer players have become astronomical, subjective judgments still play a big part in the player analysis. Recently, there have been new attempts to quantitatively grasp players' styles using video-based event stream data. However, they have some limitations in scalability due to high annotation costs and sparsity of event stream data. In this paper, we build a triplet network named 6MapNet that can effectively capture the movement styles of players using in-game GPS data. Without any annotation of soccer-specific actions, we use players' locations and velocities to generate two types of heatmaps. Our subnetworks then map these heatmap pairs into feature vectors whose similarity corresponds to the actual similarity of playing styles. The experimental results show that players can be accurately identified with only a small number of matches by our method., Comment: 12 pages, 4 figures, In 8th Workshop on Machine Learning and Data Mining for Sports Analytics (MLSA21)

We document the activities performed during the second MadAnalysis 5 workshop on LHC recasting, that was organised in KIAS (Seoul, Korea) on February 12-20, 2020. We detail the implementation of 12 new ATLAS and CMS searches in the MadAnalysis 5 Public Analysis Database, and the associated validation procedures. Those searches probe the production of extra gauge and scalar/pseudoscalar bosons, supersymmetry, seesaw models and deviations from the Standard Model in four-top production., Comment: 119 pages, 37 figures, 48 tables and 12 new analyses added to the MadAnalysis 5 Public Analysis Database. More information available from https://indico.cern.ch/event/873524/ and http://madanalysis.irmp.ucl.ac.be/wiki/PublicAnalysisDatabase

Document image enhancement and binarization methods are often used to improve the accuracy and efficiency of document image analysis tasks such as text recognition. Traditional non-machine-learning methods are constructed on low-level features in an unsupervised manner but have difficulty with binarization on documents with severely degraded backgrounds. Convolutional neural network-based methods focus only on grayscale images and on local textual features. In this paper, we propose a two-stage color document image enhancement and binarization method using generative adversarial neural networks. In the first stage, four color-independent adversarial networks are trained to extract color foreground information from an input image for document image enhancement. In the second stage, two independent adversarial networks with global and local features are trained for image binarization of documents of variable size. For the adversarial neural networks, we formulate loss functions between a discriminator and generators having an encoder-decoder structure. Experimental results show that the proposed method achieves better performance than many classical and state-of-the-art algorithms over the Document Image Binarization Contest (DIBCO) datasets, the LRDE Document Binarization Dataset (LRDE DBD), and our shipping label image dataset. We plan to release the shipping label dataset as well as our implementation code at github.com/opensuh/DocumentBinarization/., Comment: Submitted to Pattern Recognition, Elsevier

Highly asymmetric optical properties of b-Ga2O3 are investigated by polarization-dependent photoluminescence (PL) excitation spectroscopy for assessing its potential use for a novel ultraviolet emitter and nonlinear optical material. Based on power-dependent excitation and two-photon depth scan, it is demonstrated that the underlying mechanism for the PL occurring far below the bandgap is not caused by intrinsic polaron effects, but by excitonic recombination at extrinsic defect sites., Comment: 23 pages, 6 figures