Miracle-dz/UniFAR-FTUs huggingface dataset:
On BIBO Stability of Infinite-Dimensional Linear State-Space Systems

In this paper we consider BIBO stability of systems described by infinite-dimensional linear state-space representations, filling the so far unattended gap of a formal definition and characterization of BIBO stability in this general case. Furthermore, we provide several sufficient conditions guaranteeing BIBO stability of a particular system and discuss to which extent this property is preserved under additive and multiplicative perturbations of the system.
Self-organization of jets in electrospinning from free liquid surface: A generalized approach

Electrospinning has enabled creation of excellent materials for a great number of applications. Previously, it was based on less productive capillary spinners. The present study is based on recent efforts to elevate electrospinning technology to an industrial level by simultaneously provoking innumerable polymeric jets from a sufficiently large liquid surface to increase productivity. Particularly, it deals with electrospinning from free surface of conductive liquids and validates a formulated hypothesis that explains self-organization of jets on one-dimensional free liquid surfaces in terms of electrohydrodynamic instability of surface waves. Here, it is shown how the hypothesis, based on a profound analysis of a dispersion law, explains that above a certain critical value of applied electric field intensity∕field strength the system starts to be self-organized in mesocopic scale due to the mechanism of the “fastest forming instability. ” The mechanism plays a key role in selecting a particular wave with .
Numerical Simulation of Aerodynamic Characteristics of Two Rectangular Cylinders in Side-by-side Arrangement

We present numerical results of flows around two rectangular cylinders in side-by-side arrangement by three-dimensional computations. The two rectangular cylinders are arranged with various distances between the cylinders. The three-dimensional flow structures around two rectangular cylinders denote significant features depending on the distance between the cylinders. In our computations, the Reynolds number Re is set as 10,000, and both the aspect ratio of section of two rectangular cylinders and the distance between the cylinders are considered as parameters to calculate the flow around two rectangular cylinders. The obtained numerical results are also compared with experimental data.
Age of Incorrect Information With Hybrid ARQ Under a Resource Constraint for N-ary Symmetric Markov Sources

The Age of Incorrect Information (AoII) is a recently proposed metric for real-time remote monitoring systems. In particular, AoII measures the time the information at the monitor is incorrect, weighted by the magnitude of this incorrectness, thereby combining the notions of freshness and distortion. This paper addresses the definition of an AoII-optimal transmission policy in a discrete-time communication scheme with a resource constraint and a hybrid automatic repeat request (HARQ) protocol. Considering an $N$-ary symmetric Markov source, the problem is formulated as an infinite-horizon average-cost constrained Markov decision process (CMDP). The source model is characterized by the cardinality of the state space and the probability of staying at the same state. Interestingly, it is proved that under some conditions, the optimal transmission policy is to never transmit. This reveals that there exists a region of the source dynamics where communication is inadequate in reducing the AoII. Elsewhere, there exists an optimal transmission policy, which is a randomized mixture of two discrete threshold-based policies that randomize at one state. The optimal threshold and the randomization component are derived analytically. Numerical results illustrate the impact of source dynamics, channel conditions, and resource constraints on the average AoII.
A Survey on Automated Program Repair Techniques

With the rapid development and large-scale popularity of program software, modern society increasingly relies on software systems. However, the problems exposed by software have also come to the fore. Software defect has become an important factor troubling developers. In this context, Automated Program Repair (APR) techniques have emerged, aiming to automatically fix software defect problems and reduce manual debugging work. In particular, benefiting from the advances in deep learning, numerous learning-based APR techniques have emerged in recent years, which also bring new opportunities for APR research. To give researchers a quick overview of APR techniques' complete development and future opportunities, we revisit the evolution of APR techniques and discuss in depth the latest advances in APR research. In this paper, the development of APR techniques is introduced in terms of four different patch generation schemes: search-based, constraint-based, template-based, and learning-based. Moreover, we propose a uniform set of criteria to review and compare each APR tool, summarize the advantages and disadvantages of APR techniques, and discuss the current state of APR development. Furthermore, we introduce the research on the related technical areas of APR that have also provided a strong motivation to advance APR development. Finally, we analyze current challenges and future directions, especially highlighting the critical opportunities that large language models bring to APR research.
IC-FPS: Instance-Centroid Faster Point Sampling Module for 3D Point-base Object Detection

3D object detection is one of the most important tasks in autonomous driving and robotics. Our research focuses on tackling low efficiency issue of point-based methods on large-scale point clouds. Existing point-based methods adopt farthest point sampling (FPS) strategy for downsampling, which is computationally expensive in terms of inference time and memory consumption when the number of point cloud increases. In order to improve efficiency, we propose a novel Instance-Centroid Faster Point Sampling Module (IC-FPS) , which effectively replaces the first Set Abstraction (SA) layer that is extremely tedious. IC-FPS module is comprised of two methods, local feature diffusion based background point filter (LFDBF) and Centroid-Instance Sampling Strategy (CISS). LFDBF is constructed to exclude most invalid background points, while CISS substitutes FPS strategy by fast sampling centroids and instance points. IC-FPS module can be inserted to almost every point-based models. Extensive experiments on multiple public benchmarks have demonstrated the superiority of IC-FPS. On Waymo dataset, the proposed module significantly improves performance of baseline model and accelerates inference speed by 3.8 times. For the first time, real-time detection of point-based models in large-scale point cloud scenario is realized.
Inferring networks from time series: A neural approach

Abstract Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media. Yet, as they often cannot be observed directly, their connectivities must be inferred from observations of the dynamics to which they give rise. In this work, we present a powerful computational method to infer large network adjacency matrices from time series data using a neural network, in order to provide uncertainty quantification on the prediction in a manner that reflects both the degree to which the inference problem is underdetermined as well as the noise on the data. This is a feature that other approaches have hitherto been lacking. We demonstrate our method’s capabilities by inferring line failure locations in the British power grid from its response to a power cut, providing probability densities on each edge and allowing the use of hypothesis testing to make meaningful probabilistic statements about the location of the cut. Our method is significantly more accurate than both Markov-chain Monte Carlo sampling and least squares regression on noisy data and when the problem is underdetermined, while naturally extending to the case of nonlinear dynamics, which we demonstrate by learning an entire cost matrix for a nonlinear model of economic activity in Greater London. Not having been specifically engineered for network inference, this method in fact represents a general parameter estimation scheme that is applicable to any high-dimensional parameter space.
Convex Hulls of Reachable Sets

We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing over-approximation tools tend to be conservative or computationally expensive. In this work, we characterize the convex hulls of reachable sets as the convex hulls of solutions of an ordinary differential equation with initial conditions on the sphere. This finite-dimensional characterization unlocks an efficient sampling-based estimation algorithm to accurately over-approximate reachable sets. We also study the structure of the boundary of the reachable convex hulls and derive error bounds for the estimation algorithm. We give applications to neural feedback loop analysis and robust MPC.
Adaptive Model Prediction Control-Based Multi-Terrain Trajectory Tracking Framework for Mobile Spherical Robots

Owing to uncertainties in both kinematics and dynamics, the current trajectory tracking framework for mobile robots like spherical robots cannot function effectively on multiple terrains, especially uneven and unknown ones. Since this is a prerequisite for robots to execute tasks in the wild, we enhance our previous hierarchical trajectory tracking framework to handle this issue. First, a modified adaptive RBF neural network (RBFNN) is proposed to represent all uncertainties in kinodynamics. Then the Lyapunov function is utilized to design its adaptive law, and a variable step-size algorithm is employed in the weights update procedure to accelerate convergence and improve stability. Hence, a new adaptive model prediction control-based instruction planner (VAN-MPC) is proposed. Without modifying the bottom controllers, we finally develop the multi-terrain trajectory tracking framework by employing the new instruction planner VAN-MPC. The practical experiments demonstrate its effectiveness and robustness.
The Interaction of Numerically Simulated Supercells Initiated along Lines

Abstract Supercells in the southern plains are often localized, forming as cells along a convective line, even though the environment may support supercell formation over a much broader, mesoscale region. A set of numerical experiments is devised in which it is demonstrated that the evolution of supercells in a homogeneous environment depends upon the orientation of the vertical-shear profile with respect to the orientation of the line along which convection is initiated (the “line of forcing”). This work is motivated by the observations that the nature and consequences of the interaction of neighboring cells depend upon differential cell motion, which in turn is a function of the characteristics and orientation of the vertical-shear profile and its impact on the behavior of outflow boundaries. Results for various orientations of the vertical-shear vector with respect to the line along which cells are initiated are described and interpreted physically. It is found that in idealized numerical simulations, .
Neural Microfacet Fields for Inverse Rendering

We present Neural Microfacet Fields, a method for recovering materials, geometry, and environment illumination from images of a scene. Our method uses a microfacet reflectance model within a volumetric setting by treating each sample along the ray as a (potentially non-opaque) surface. Using surface-based Monte Carlo rendering in a volumetric setting enables our method to perform inverse rendering efficiently by combining decades of research in surface-based light transport with recent advances in volume rendering for view synthesis. Our approach outperforms prior work in inverse rendering, capturing high fidelity geometry and high frequency illumination details; its novel view synthesis results are on par with state-of-the-art methods that do not recover illumination or materials.
Statistically steady measurements of Rayleigh-Taylor mixing in a gas channel

A novel gas channel experiment is described to study the development of high Atwood number Rayleigh-Taylor mixing. Two gas streams, one containing air and the other containing a helium-air mixture, flow parallel to each other separated by a thin splitter plate. The streams meet at the end of a splitter plate leading to the formation of an unstable interface and of buoyancy driven mixing. This buoyancy driven mixing experiment allows for long data collection times, has short transients, and is statistically steady. The facility was designed to be capable of large Atwood number studies (At∼0.75). We describe initial validation work to measure the self similar evolution of mixing at density differences (0.035<At<0.1). The purpose of this paper is to describe the new high Atwood number gas channel facility and present validation results for experimental runs at Atwood numbers up to 0.1. Diagnostics include a constant temperature hot wire anemometer, and high resolution digital image analysis. The hot-wire pro.
Asking Better Questions - The Art and Science of Forecasting: A mechanism for truer answers to high-stakes questions

Without the ability to estimate and benchmark AI capability advancements, organizations are left to respond to each change reactively, impeding their ability to build viable mid and long-term strategies. This paper explores the recent growth of forecasting, a political science tool that uses explicit assumptions and quantitative estimation that leads to improved prediction accuracy. Done at the collective level, forecasting can identify and verify talent, enable leaders to build better models of AI advancements and improve inputs into design policy. Successful approaches to forecasting and case studies are examined, revealing a subclass of"superforecasters"who outperform 98% of the population and whose insights will be most reliable. Finally, techniques behind successful forecasting are outlined, including Phillip Tetlock's"Ten Commandments. "To adapt to a quickly changing technology landscape, designers and policymakers should consider forecasting as a first line of defense.
The Chemical Composition of Halo Stars on Extreme Orbits

Presented within is a fine spectroscopic analysis of 11 metal-poor (-2.15 < [Fe/H] < -1.00) dwarf stars on orbits that penetrate the outermost regions of the Galactic halo. Abundances for a select group of light metals (Na, Mg, Si, Ca, and Ti), Fe-peak nuclides (Cr, Fe, and Ni), and neutron-capture elements (Y and Ba) were calculated using line strengths measured from high-resolution (R ≈ 48,000), high signal-to-noise ratio (S/N ≈ 110 pixel-1) echelle spectra acquired with the Keck I 10 m telescope and HIRES spectrograph. Ten of the stars have apogalactica, a proxy for stellar birthplace, which stretch between 25 and 90 kpc; however, these "outer halo" stars exhibit strikingly uniform abundances. The average, Fe-normalized abundances—⟨[Mg/Fe]⟩ = +0.23 ± 0.09, ⟨[Si/Fe]⟩ = +0.24 ± 0.10, ⟨[Ca/Fe]⟩ = +0.22 ± 0.07, ⟨[Ti/Fe]⟩ = +0.20 ± 0.08, ⟨[Cr/Fe]⟩ = 0.02 ± 0.07, ⟨[Ni/Fe]⟩ = -0.09 ± 0.07, and ⟨[Ba/Fe]⟩ = +0.01 ± 0.12—exhibit little intrinsic scatter; moreover, the evolution of individual ratios (as a function of [Fe/H]) is generally consistent with the predictions of galactic chemical evolution models dominated by the ejecta of core-collapse supernovae. Only ⟨[Y/Fe]⟩ = -0.13 ± 0.21 exhibits a dispersion larger than observational uncertainties, which suggests a different nucleosynthesis site for this element. It has been conjectured that stars on high-energy orbits—either those that penetrate the remote halo or ones with extreme retrograde velocities—were once associated with a cannibalized satellite galaxy. Such stars, as shown here, are indistinguishable from metal-poor dwarfs of the inner Galactic halo. The uniformity of the abundances, regardless of kinematic properties, suggests that physically, spatially, and temporally distinct star-forming regions within (or near) the growing Milky Way experienced grossly similar chemical evolution histories. Implications for galaxy formation scenarios are discussed.
High Frobenius pushforwards generate the bounded derived category

This work concerns generators for the bounded derived category of coherent sheaves over a noetherian scheme $X$ of prime characteristic. The main result is that when the Frobenius map on $X$ is finite, for any compact generator $G$ of $\mathsf{D}(X)$ the Frobenius pushforward $F ^e_*G$ generates the bounded derived category whenever $p^e$ is larger than the codepth of $X$, an invariant that is a measure of the singularity of $X$. The conclusion holds for all positive integers $e$ when $X$ is locally complete intersection. The question of when one can take $G=\mathcal{O}_X$ is also investigated. For smooth projective complete intersections it reduces to a question of generation of the Kuznetsov component.
Exact Bending Solutions of Axisymmetric Reissner Plates in Terms of Classical Thin Plate Solutions

This paper presents exact bending solutions of circular and annular plates under rotationally symmetric loads based on the Reissner plate theory. The exact Reissner plate solutions are cast in the form of a general set of relationships linking the Reissner plate quantities to their corresponding Kirchhoff (classical thin) plate counterparts. The Reissner plate solutions may be readily deduced upon supplying the classical thin plate solutions that are well documented in the open literature. This form of displaying exact solutions is very compact and does away with the conventional need for numerous tables and charts in presenting the results of axisymmetric thick plates. Some illustrative examples in determining the Reissner plate solutions using the relationships are given. These example problems involve circular and annular plates under different loading and support conditions. In order to verify the correctness of the relationships, the results are compared with numerically obtained Reissner plate results and also with Mindlin plate results.
The curvature operator of the second kind in dimension three

This article aims to understand the behavior of the curvature operator of the second kind under the Ricci flow in dimension three. First, we express the eigenvalues of the curvature operator of the second kind explicitly in terms of that of the curvature operator (of the first kind). Second, we prove that $\a$-positive/$\a$-nonnegative curvature operator of the second kind is preserved by the Ricci flow in dimension three for all $\a \in [1,5]$.
Single Image Depth Prediction Made Better: A Multivariate Gaussian Take

Neural-network-based single image depth prediction (SIDP) is a challenging task where the goal is to predict the scene's per-pixel depth at test time. Since the problem, by definition, is illposed, the fundamental goal is to come up with an approach that can reliably model the scene depth from a set of training examples. In the pursuit of perfect depth estimation, most existing state-of-the-art learning techniques predict a single scalar depth value per-pixel. Yet, it is well-known that the trained model has accuracy limits and can predict imprecise depth. Therefore, an SIDP approach must be mindful of the expected depth variations in the model's prediction at test time. Accordingly, we introduce an approach that performs continuous modeling of per-pixel depth, where we can predict and reason about the per-pixel depth and its distribution. To this end, we model per-pixel scene depth using a multivariate Gaussian distribution. Moreover, contrary to the existing uncertainty modeling methods—in the same spirit, where per-pixel depth is assumed to be independent, we introduce per-pixel covariance modeling that encodes its depth dependency w.r. t. all the scene points. Unfortunately, per-pixel depth covariance modeling leads to a computationally expensive continuous loss function, which we solve efficiently using the learned low-rank approximation of the overall covariance matrix. Notably, when tested on benchmark datasets such as KITTI, NYU, and SUN-RGB-D, the SIDP model obtained by optimizing our loss function shows state-of-the-art results. Our method's accuracy (named MG) is among the top on the KITTI depth-prediction benchmark leaderboard11http://www.cvlibs. net/datasets/kitti/eval–depth.php? benchmark=depth–prediction.
Acousto-optic fiber interferometer based on concatenated flexural wave modulation

Abstract. An acousto-optic fiber interferometer has been proposed and experimentally demonstrated by employing two MgF2 sandwiches to implement concatenated flexural acoustic wave modulation onto single-mode optical fibers. The transmission spectrum of the acoustic grating pair has been experimentally investigated. Experimental results indicate that interferometric spectral fringes possess a frequency sensitivity as large as −499.0 nm/MHz due to the Mach–Zehnder interference. Moreover, the applied radio frequency signal voltage for flexural wave generation has a great impact on the transmission spectral properties. The work presented would be of importance for the understanding of the acousto-optic interaction mechanism in concatenated acoustic fiber gratings and is helpful for the design of related acousto-optic fiber devices.
Lattice-based kernel approximation and serendipitous weights for parametric PDEs in very high dimensions

We describe a fast method for solving elliptic partial differential equations (PDEs) with uncertain coefficients using kernel interpolation at a lattice point set. By representing the input random field of the system using the model proposed by Kaarnioja, Kuo, and Sloan (SIAM J.~Numer.~Anal.~2020), in which a countable number of independent random variables enter the random field as periodic functions, it was shown by Kaarnioja, Kazashi, Kuo, Nobile, and Sloan (Numer.~Math.~2022) that the lattice-based kernel interpolant can be constructed for the PDE solution as a function of the stochastic variables in a highly efficient manner using fast Fourier transform (FFT). In this work, we discuss the connection between our model and the popular ``affine and uniform model'' studied widely in the literature of uncertainty quantification for PDEs with uncertain coefficients. We also propose a new class of weights entering the construction of the kernel interpolant -- \emph{serendipitous weights} -- which dramatically improve the computational performance of the kernel interpolant for PDE problems with uncertain coefficients, and allow us to tackle function approximation problems up to very high dimensionalities. Numerical experiments are presented to showcase the performance of the serendipitous weights.
New estimation of Sobol' indices using kernels

In this work, we develop an approach mentioned by da Veiga and Gamboa in 2013. It consists in extending the very interestingpoint of view introduced in \cite{gine2008simple} to estimate general nonlinear integral functionals of a density on the real line, by using empirically a kernel estimator erasing the diagonal terms. Relaxing the positiveness assumption on the kernel and choosing a kernel of order large enough, we are able to prove a central limit theorem for estimating Sobol' indices of any order (the bias is killed thanks to this signed kernel).