Miracle-dz/UniFAR-FTUs huggingface dataset:
A Fractional Subgrid-scale Model for Turbulent Flows: Theoretical Formulation and a Priori Study

Coherent structures/motions in turbulence inherently give rise to intermittent signals with sharp peaks, heavy-skirt, and skewed distributions of velocity increments, highlighting the non-Gaussian nature of turbulence. That suggests that the spatial nonlocal interactions cannot be ruled out of the turbulence physics. Furthermore, filtering the Navier-Stokes equations in the large eddy simulation of turbulent flows would further enhance the existing nonlocality, emerging in the corresponding subgrid scale fluid motions. That urges the development of new nonlocal closure models, which respect the corresponding non-Gaussian statistics of the subgrid stochastic motions. To this end and starting from the filtered Boltzmann equation, we model the corresponding equilibrium distribution function with a \textit{Levy}-stable distribution, leading to the proposed fractional-order modeling of subgrid-scale stresses. We approximate the filtered equilibrium distribution function with a power-law term, and derive the corresponding filtered Navier-Stokes equations. Subsequently in our functional modeling, the divergence of subgrid-scale stresses emerges as a single-parameter fractional Laplacian, $(-\Delta)^{\alpha}(\cdot)$, $\alpha \in (0,1]$, of the filtered velocity field. The only model parameter, i.e., the fractional exponent, appears to be strictly depending on the filter-width and the flow Reynolds number. We furthermore explore the main physical and mathematical properties of the proposed model under a set of mild conditions. Finally, the introduced model undergoes \textit{a priori} evaluations based on the direct numerical simulation database of forced and decaying homogeneous isotropic turbulent flows at relatively high and moderate Reynolds numbers, respectively. Such analysis provides a comparative study of predictability and performance of the proposed fractional model.
Explainable High-order Visual Question Reasoning: A New Benchmark and Knowledge-routed Network

Explanation and high-order reasoning capabilities are crucial for real-world visual question answering with diverse levels of inference complexity (e.g., what is the dog that is near the girl playing with? ) and important for users to understand and diagnose the trustworthiness of the system. Current VQA benchmarks on natural images with only an accuracy metric end up pushing the models to exploit the dataset biases and cannot provide any interpretable justification, which severally hinders advances in high-level question answering. In this work, we propose a new HVQR benchmark for evaluating explainable and high-order visual question reasoning ability with three distinguishable merits: 1) the questions often contain one or two relationship triplets, which requires the model to have the ability of multistep reasoning to predict plausible answers; 2) we provide an explicit evaluation on a multistep reasoning process that is constructed with image scene graphs and commonsense knowledge bases; and 3) each relationship triplet in a large-scale knowledge base only appears once among all questions, which poses challenges for existing networks that often attempt to overfit the knowledge base that already appears in the training set and enforces the models to handle unseen questions and knowledge fact usage. We also propose a new knowledge-routed modular network (KM-net) that incorporates the multistep reasoning process over a large knowledge base into visual question reasoning. An extensive dataset analysis and comparisons with existing models on the HVQR benchmark show that our benchmark provides explainable evaluations, comprehensive reasoning requirements and realistic challenges of VQA systems, as well as our KM-net's superiority in terms of accuracy and explanation ability.
PageRank's behavior under degree-degree correlations

The focus of this work is the asymptotic analysis of the tail distribution of Google's PageRank algorithm on large scale-free directed networks. In particular, the main theorem provides the convergence, in the Kantorovich-Rubinstein metric, of the rank of a randomly chosen vertex in graphs generated via either a directed configuration model or an inhomogeneous random digraph. The theorem fully characterizes the limiting distribution by expressing it as a random sum of i.i. d. ~copies of the attracting endogenous solution to a branching distributional fixed-point equation. In addition, we provide the asymptotic tail behavior of the limit and use it to explain the effect that in-degree/out-degree correlations in the underlying graph can have on the qualitative performance of PageRank.
COPYCAT: Practical Adversarial Attacks on Visualization-Based Malware Detection

Despite many attempts, the state-of-the-art of adversarial machine learning on malware detection systems generally yield unexecutable samples. In this work, we set out to examine the robustness of visualization-based malware detection system against adversarial examples (AEs) that not only are able to fool the model, but also maintain the executability of the original input. As such, we first investigate the application of existing off-the-shelf adversarial attack approaches on malware detection systems through which we found that those approaches do not necessarily maintain the functionality of the original inputs. Therefore, we proposed an approach to generate adversarial examples, COPYCAT, which is specifically designed for malware detection systems considering two main goals; achieving a high misclassification rate and maintaining the executability and functionality of the original input. We designed two main configurations for COPYCAT, namely AE padding and sample injection. While the first configuration results in untargeted misclassification attacks, the sample injection configuration is able to force the model to generate a targeted output, which is highly desirable in the malware attribution setting. We evaluate the performance of COPYCAT through an extensive set of experiments on two malware datasets, and report that we were able to generate adversarial samples that are misclassified at a rate of 98.9% and 96.5% with Windows and IoT binary datasets, respectively, outperforming the misclassification rates in the literature. Most importantly, we report that those AEs were executable unlike AEs generated by off-the-shelf approaches. Our transferability study demonstrates that the generated AEs through our proposed method can be generalized to other models.
Trichromatic and Tri-polarization-channel Holography with Non-interleaved Dielectric Metasurface.

Metasurfaces hold great potentials for advanced holographic display with extraordinary information capacity and pixel sizes in an ultrathin flat profile. Dual-polarization channel to encode two independent phase profiles or spatially multiplexed meta-holography by interleaved metasurfaces are captivated popular solutions to projecting multiplexed and vectorial images. However, the intrinsic limit of orthogonal polarization-channels, their crosstalk due to coupling between meta-atoms, and interleaving-induced degradation of efficiency and reconstructed image quality set great barriers for sophisticated meta-holography from being widely adopted. Here we report a non-interleaved TiO2 metasurface holography, and three distinct phase profiles are encoded into three orthogonal polarization bases with almost zero crosstalk. The corresponding three independently constructed intensity profiles are therefore assigned to trichromatic (RGB) beams, resulting in high-quality and high-efficiency vectorial meta-holography in the whole visible regime. Our strategy presents an unconventionally advanced holographic scheme by synergizing trichromatic colors and tri-polarization channels, simply realized with a minimalist non-interleaved metasurface. Our work unlocks the metasurface's potentials on massive information storage, polarization optics, polarimetric imaging, holographic data encryption, etc.
Deep Universal Graph Embedding Neural Network

Learning powerful data embeddings has become a center piece in machine learning, especially in natural language processing and computer vision domains. The crux of these embeddings is that they are pretrained on huge corpus of data in a unsupervised fashion, sometimes aided with transfer learning. However currently in the graph learning domain, embeddings learned through existing graph neural networks (GNNs) are task dependent and thus cannot be shared across different datasets. In this paper, we present a first powerful and theoretically guaranteed graph neural network that is designed to learn task-independent graph embeddings, thereafter referred to as deep universal graph embedding (DUGNN). Our DUGNN model incorporates a novel graph neural network (as a universal graph encoder) and leverages rich Graph Kernels (as a multi-task graph decoder) for both unsupervised learning and (task-specific) adaptive supervised learning. By learning task-independent graph embeddings across diverse datasets, DUGNN also reaps the benefits of transfer learning. Through extensive experiments and ablation studies, we show that the proposed DUGNN model consistently outperforms both the existing state-of-art GNN models and Graph Kernels by an increased accuracy of 3% - 8% on graph classification benchmark datasets.
Automatic Lyrics Transcription in Polyphonic Music: Does Background Music Help?

Background music affects lyrics intelligibility of singing vocals in a music piece. Automatic lyrics transcription in polyphonic music is a challenging task because the singing vocals are corrupted by the background music. In this work, we propose to learn music genre-specific characteristics to train polyphonic acoustic models. For this purpose, we firstly study and compare several automatic speech recognition pipelines for the application of lyrics transcription. Later, we present the lyrics transcription performance of these music-informed acoustic models for the best-performing pipeline, and systematically study the impact of music genre and language model on the performance. With this genre-based approach, we explicitly model the characteristics of music, instead of trying to remove the background music as noise. The proposed approach achieves a significant improvement in performance in the lyrics transcription and alignment tasks on several well-known polyphonic test datasets, outperforming all comparable existing systems.
Self-Healing Ground-and-Air Connectivity Chains

The coordination of robot swarms - large decentralized teams of robots - generally relies on robust and efficient inter-robot communication. Maintaining communication between robots is particularly challenging in field deployments. Unstructured environments, limited computational resources, low bandwidth, and robot failures all contribute to the complexity of connectivity maintenance. In this paper, we propose a novel lightweight algorithm to navigate a group of robots in complex environments while maintaining connectivity by building a chain of robots. The algorithm is robust to single robot failures and can heal broken communication links. The algorithm works in 3D environments: when a region is unreachable by wheeled robots, the chain is extended with flying robots. We test the performance of the algorithm using up to 100 robots in a physics-based simulator with three mazes and different robot failure scenarios. We then validate the algorithm with physical platforms: 7 wheeled robots and 6 flying ones, in homogeneous and heterogeneous scenarios.
Kazhdan-Lusztig Polynomials of Matroids Under Deletion

We present a formula which relates the Kazhdan–Lusztig polynomial of a matroid $M$, as defined by Elias, Proudfoot and Wakefield, to the Kazhdan–Lusztig polynomials of the matroid obtained by deleting an element, and various contractions and localizations of $M$. We give a number of applications of our formula to Kazhdan–Lusztig polynomials of graphic matroids, including a simple formula for the Kazhdan–Lusztig polynomial of a parallel connection graph.
Time-limited pseudo-optimal H2-model order reduction

A model order reduction algorithm is presented that generates a reduced-order model of the original high-order model, which ensures high fidelity within the desired time interval. The reduced model satisfies a subset of the first-order optimality conditions for the time-limited H 2 -model reduction problem. The algorithm uses a computationally efficient Krylov subspace-based framework to generate the reduced model, and it is applicable to large-scale systems. The reduced-order model is parameterised to enforce a subset of the first-order optimality conditions in an iteration-free way. The authors also propose an adaptive framework of the algorithm, which ensures a monotonic decay in the error irrespective of the choice of interpolation points and tangential directions. The efficacy of the algorithm is validated on benchmark model reduction problems.
Learning Coupled Spatial-temporal Attention for Skeleton-based Action Recognition

In this paper, we propose a coupled spatial-temporal attention (CSTA) model for skeleton-based action recognition, which aims to figure out the most discriminative joints and frames in spatial and temporal domains simultaneously. Conventional approaches usually consider all the joints or frames in a skeletal sequence equally important, which are unrobust to ambiguous and redundant information. To address this, we first learn two sets of weights for different joints and frames through two subnetworks respectively, which enable the model to have the ability of "paying attention to" the relatively informative section. Then, we calculate the cross product based on the weights of joints and frames for the coupled spatial-temporal attention. Moreover, our CSTA mechanisms can be easily plugged into existing hierarchical CNN models (CSTA-CNN) to realize their function. Extensive experimental results on the recently collected UESTC dataset and the currently largest NTU dataset have shown the effectiveness of our proposed method for skeleton-based action recognition.
Upper Body Pose Estimation Using Wearable Inertial Sensors and Multiplicative Kalman Filter

Estimating the limbs pose in a wearable way may benefit multiple areas such as rehabilitation, teleoperation, human-robot interaction, gaming, and many more. Several solutions are commercially available, but they are usually expensive or not wearable/portable. We present a wearable pose estimation system (WePosE), based on inertial measurements units (IMUs), for motion analysis and body tracking. Differently from camera-based approaches, the proposed system does not suffer from occlusion problems and lighting conditions, it is cost effective and it can be used in indoor and outdoor environments. Moreover, since only accelerometers and gyroscopes are used to estimate the orientation, the system can be used also in the presence of iron and magnetic disturbances. An experimental validation using a high precision optical tracker has been performed. Results confirmed the effectiveness of the proposed approach.
Explicit and Efficient Constructions of Coding Schemes for the Binary Deletion Channel and the Poisson Repeat Channel

This work gives an explicit construction of a family of error correcting codes for the binary deletion channel and for the Poisson repeat channel. In the binary deletion channel with parameter $p$ (BDC$_p$) every bit is deleted independently with probability $p$. A lower bound of $(1-p)/9$ is known on the capacity of the BDC$_p$ \cite{mitzenmacher2006simple}, yet no explicit construction is known to achieve this rate. We give an explicit family of codes of rate $(1-p)/16$, for every $p$. This improves upon the work of Guruswami and Li \cite{guruswami2017efficiently} that gave a construction of rate $(1-p)/120$. The codes in our family have polynomial time encoding and decoding algorithms. Another channel considered in this work is the Poisson repeat channel with parameter $\lambda$ (PRC$_{\lambda}$) in which every bit is replaced with a discrete Poisson number of copies of that bit, where the number of copies has mean $\lambda$. We show that our construction works for this channel as well. As far as we know, this is the first explicit construction of an error correcting code for PRC$_{\lambda}$.
Presentations of groups with even length relations

Abstract We study the properties of groups that have presentations in which the generating set is a fixed set of involutions and all additional relations are of even length. We consider the parabolic subgroups of such a group and show that every element has a factorization with respect to a given parabolic subgroup. Furthermore, we give a counterexample, using a cluster group presentation, which demonstrates that this factorization is not necessarily unique.
Online DCM Trajectory Generation for Push Recovery of Torque-Controlled Humanoid Robots

We present a computationally efficient method for online planning of bipedal walking trajectories with push recovery. In particular, the proposed methodology fits control architectures where the Divergent-Component-of-Motion (DCM) is planned beforehand, and adds a step adapter to adjust the planned trajectories and achieve push recovery. Assuming that the robot is in a single support state, the step adapter generates new positions and timings for the next step. The step adapter is active in single support phases only, but the proposed torque-control architecture considers double support phases too. The key idea for the design of the step adapter is to impose both initial and final DCM step values using an exponential interpolation of the time varying ZMP trajectory. This allows us to cast the push recovery problem as a Quadratic Programming (QP) one, and to solve it online with state-of-the-art optimisers. The overall approach is validated with simulations of the torque-controlled 33 kg humanoid robot iCub. Results show that the proposed strategy prevents the humanoid robot from falling while walking at 0.28 m/s and pushed with external forces up to 150 Newton for 0.05 seconds.
Distributed and Localized Model Predictive Control via System Level Synthesis

We present the Distributed and Localized Model Predictive Control (DLMPC) algorithm for large-scale structured linear systems, wherein only local state and model information needs to be exchanged between subsystems for the computation and implementation of control actions. We use the System Level Synthesis (SLS) framework to reformulate the MPC problem as an optimization problem over closed loop system responses, and show that this allows us to naturally impose localized communication constraints between sub-controllers, such that only local state and system model information needs to be exchanged for both computation and implementation of closed loop MPC control policies. In particular, we show that the structure of the resulting optimization problem can be exploited to develop an Alternating Direction Method of Multipliers (ADMM) based algorithm that allows for distributed and localized computation of control decisions. Moreover, our approach can accommodate constraints and objective functions that couple the behavior of different subsystems, so long as the coupled systems are able to communicate directly with each other, allowing for a broader class of MPC problems to be solved via distributed optimization. We conclude with numerical simulations to demonstrate the usefulness of our method, and in particular, we demonstrate that the computational complexity of the subproblems solved by each subsystem in DLMPC is independent of the size of the global system.
Super poly-harmonic properties, Liouville theorems and classification of nonnegative solutions to equations involving higher-order fractional Laplacians

In this paper, we are concerned with equations \eqref{PDE} involving higher-order fractional Laplacians. By introducing a new approach, we prove the super poly-harmonic properties for nonnegative solutions to \eqref{PDE} (Theorem \ref{Thm0}). Our theorem seems to be the first result on this problem. As a consequence, we derive many important applications of the super poly-harmonic properties. For instance, we establish Liouville theorems, integral representation formula and classification results for nonnegative solutions to fractional higher-order equations \eqref{PDE} with general nonlinearities $f(x,u,Du,\cdots)$ including conformally invariant and odd order cases. In particular, our results completely improve the classification results for third order equations in Dai and Qin \cite{DQ1} by removing the assumptions on integrability. We also derive a characterization for $\alpha$-harmonic functions via averages in the appendix.
Recurrent Neural Network-based Model for Accelerated Trajectory Analysis in AIMD Simulations

The presented work demonstrates the training of recurrent neural networks (RNNs) from distributions of atom coordinates in solid state structures that were obtained using ab initio molecular dynamics (AIMD) simulations. AIMD simulations on solid state structures are treated as a multi-variate time-series problem. By referring interactions between atoms over the simulation time to temporary correlations among them, RNNs find patterns in the multi-variate time-dependent data, which enable forecasting trajectory paths and potential energy profiles. Two types of RNNs, namely gated recurrent unit and long short-term memory networks, are considered. The model is described and compared against a baseline AIMD simulation on an iridium oxide slab. Findings demonstrate that both networks can potentially be harnessed for accelerated statistical sampling in computational materials research.
Distributed Conjugate Gradient Tracking for Resource Allocation in Unbalanced Networks

This paper proposes a distributed conjugate gradient tracking algorithm (DCGT) to solve resource allocation problems in a possibly unbalanced network, where each node of the network computes its optimal resource via interacting only with its neighboring nodes. Our key idea is the novel use of the celebrated $\mathcal{A}\mathcal{B}$ algorithm to the dual of the resource allocation problem. To study the convergence of DCGT, we first establish the sublinear convergence of $\mathcal{A}\mathcal{B}$ for non-convex objective functions, which advances the existing results on $\mathcal{A}\mathcal{B}$ as they require the strong-convexity of objective functions. Then we show that DCGT converges linearly for strongly convex and Lipschitz smooth objective functions, and sublinearly without the Lipschitz smoothness. Finally, simulation results validate that DCGT outperforms state-of-the-art algorithms in distributed resource allocation problems.
Shape and interaction decoupling for colloidal preassembly

Creating materials with structure that is independently controllable at a range of scales requires breaking naturally occurring hierarchies. Breaking these hierarchies can be achieved via the decoupling of building block attributes from structure during assembly. Here, we demonstrate, through computer simulations and experiments, that shape and interaction decoupling occur in colloidal cuboids suspended in evaporating emulsion droplets. The resulting colloidal clusters serve as “preassembled” mesoscale building blocks for larger-scale structures. We show that clusters of up to nine particles form mesoscale building blocks with geometries that are independent of the particles’ degree of faceting and dipolar magnetic interactions. To highlight the potential of these superball clusters for hierarchical assembly, we demonstrate, using computer simulations, that clusters of six to nine particles can assemble into high-order structures that differ from bulk self-assembly of individual particles. Our results suggest that preassembled building blocks present a viable route to hierarchical materials design.