Miracle-dz/UniFAR-FTUs huggingface dataset:
On the dynamical system of principal curves in

Principal curves are natural generalizations of principal lines arising as first principal components in the Principal Component Analysis. They can be characterized—from a stochastic point of view—as so-called self-consistent curves based on the conditional expectation and— from the variational-calculus point of view—as saddle points of the expected difference of a random variable and its projection onto some curve, where the current curve acts as argument of the energy functional. Beyond that, Duchamp and Stützle (1993,1996) showed that planar curves can by computed as solutions of a system of ordinary differential equations. The aim of this paper is to generalize this characterization of principal curves to R with d ≥ 3. Having derived such a dynamical system, we provide several examples for principal curves related to uniform distribution on certain domains in R.
Rethinking gradient sparsification as total error minimization

Gradient compression is a widely-established remedy to tackle the communication bottleneck in distributed training of large deep neural networks (DNNs). Under the error-feedback framework, Top-$k$ sparsification, sometimes with $k$ as little as $0.1\%$ of the gradient size, enables training to the same model quality as the uncompressed case for a similar iteration count. From the optimization perspective, we find that Top-$k$ is the communication-optimal sparsifier given a per-iteration $k$ element budget. We argue that to further the benefits of gradient sparsification, especially for DNNs, a different perspective is necessary -- one that moves from per-iteration optimality to consider optimality for the entire training. We identify that the total error -- the sum of the compression errors for all iterations -- encapsulates sparsification throughout training. Then, we propose a communication complexity model that minimizes the total error under a communication budget for the entire training. We find that the hard-threshold sparsifier, a variant of the Top-$k$ sparsifier with $k$ determined by a constant hard-threshold, is the optimal sparsifier for this model. Motivated by this, we provide convex and non-convex convergence analyses for the hard-threshold sparsifier with error-feedback. Unlike with Top-$k$ sparsifier, we show that hard-threshold has the same asymptotic convergence and linear speedup property as SGD in the convex case and has no impact on the data-heterogeneity in the non-convex case. Our diverse experiments on various DNNs and a logistic regression model demonstrated that the hard-threshold sparsifier is more communication-efficient than Top-$k$.
Multiscale perspective on wetting on switchable substrates: Mapping between microscopic and mesoscopic models

To understand the non-equilibrium relaxation dynamics of a liquid droplet on a switchable substrate the interplay of different length- and time-scales needs to be understood. We present a method to map the microscopic information, resulting from a molecular dynamics simulation, to a mesoscopic scale, reflected by a thin film model. After a discussion of the mapping procedure we first analyze the relaxation of a liquid droplet upon switching the wettability of the substrate. Further, we show that a nearly identical mapping procedure can be used for the description of two coalescing droplets. With our procedure we take a first step to extend the mapping from the equilibrium case to non-equilibrium wetting dynamics, thus allowing for a quantitative multi-scale analysis.
Particle trapping by a plane gravitational wave

Bialynicki-Birula and Charzynski [1] argued that the gravitational wave emitted during the merger of a black hole binary may trap particles. In this Letter we amplify their statement by describing particle motion in the wave proposed by Lukash [2] to study anisotropic cosmological models. Bounded geodesics (found both analytically and numerically) arise when the wave is of Bianchi type VI. Their symmetries are identified. PACS numbers: 04.20. -q Classical general relativity; 04.30. -w Gravitational waves ∗ mailto: elbistan@itu.edu. tr † corresponding author. mailto:zhangpm5@mail.sysu. edu.cn ‡ mailto:horvathy@lmpt.univ-tours.fr 1 ar X iv :2 10 8. 00 83 8v 1 [ gr -q c] 2 A ug 2 02 1
Even-denominator fractional quantum Hall state in conventional triple-gated quantum point contact

The even-denominator states have attracted considerable attention owing to their possible applications in future quantum technologies. In this letter, we first report a 3/2 diagonal resistance, indicating the existence of a 3/2 state in a nanometer-sized triple-gated quantum point contact (QPC) fabricated on a high-mobility (not ultra-high-mobility) single-layer two-dimensional (2D) GaAs wafer. The center gate plays a crucial role in realizing the QPC’s 3/2 state. Our observation of the 3/2 state using a conventional QPC device, which is a suitable building block for semiconductor quantum devices, paves a new path for the development of semiconductor-based quantum technologies.
Leveraging Multiple Legacy Wi-Fi Links for Human Behavior Sensing

Taking advantage of the rich information provided by Wi-Fi measurement setups, Wi-Fi-based human behavior sensing leveraging Channel State Information (CSI) measurements has received a lot of research attention in recent years. The CSI-based human sensing algorithms typically either rely on an explicit channel propagation model or, more recently, adopt machine learning so as to robustify feature extraction. In most related work, the considered CSI is extracted from a single dedicated Access Point (AP) communication setup. In this paper, we consider a more realistic setting where a legacy network of multiple APs is already deployed for communications purposes and leveraged for sensing benefits using machine learning. The use of legacy network presents challenges and opportunities as many Wi-Fi links can present with richer yet unequally useful data sets. In order to break the curse of dimensionality associated with training over a too large dimensional CSI, we propose a link selection mechanism based on Reinforcement Learning (RL) which allows for dimension reduction while preserving the data that is most relevant for human behavior sensing. The method is based on a sequential state decision-making process in which the CSI is modeled as a part of the state. From actual experiment results, our method is shown to perform better than state-of-the-art approaches in a scenario with multiple available Wi-Fi links.
Cross-Modal Knowledge Transfer via Inter-Modal Translation and Alignment for Affect Recognition

Multi-modal affect recognition models leverage complementary information in different modalities to outperform their uni-modal counterparts. However, due to the unavailability of modality-specific sensors or data, multi-modal models may not be always employable. For this reason, we aim to improve the performance of uni-modal affect recognition models by transferring knowledge from a better-performing (or stronger) modality to a weaker modality during training. Our proposed multi-modal training framework for cross-modal knowledge transfer relies on two main steps. First, an encoder-classifier model creates task-specific representations for the stronger modality. Then, cross-modal translation generates multi-modal intermediate representations, which are also aligned in the latent space with the stronger modality representations. To exploit the contextual information in temporal sequential affect data, we use Bi-GRU and transformer encoder. We validate our approach on two multi-modal affect datasets, namely CMU-MOSI for binary sentiment classification and RECOLA for dimensional emotion regression. The results show that the proposed approach consistently improves the uni-modal test-time performance of the weaker modalities.
Simple, fast, and flexible framework for matrix completion with infinite width neural networks

Significance Matrix completion is a fundamental problem in machine learning that arises in various applications. We envision that our infinite width neural network framework for matrix completion will be easily deployable and produce strong baselines for a wide range of applications at limited computational costs. We demonstrate the flexibility of our framework through competitive results on virtual drug screening and image inpainting/reconstruction. Simplicity and speed are showcased by the fact that most results in this work require only a central processing unit and commodity hardware. Through its connection to semisupervised learning, our framework provides a principled approach for matrix completion that can be easily applied to problems well beyond those of image completion and virtual drug screening considered in this paper.
Supercritical Accretion of Stellar-mass Compact Objects in Active Galactic Nuclei

Accretion disks of active galactic nuclei (AGNs) have been proposed as promising sites for producing both (stellar-mass) compact object mergers and extreme mass ratio inspirals. Along with disk-assisted migration, ambient gas inevitably accretes onto compact objects. In previous studies, it was commonly assumed that either an Eddington rate or a Bondi rate takes place, although they can differ by several orders of magnitude. As a result, the mass and spin evolution of compact objects within AGN disks are essentially unknown. In this work, we construct a relativistic supercritical inflow–outflow model for black hole (BH) accretion. We show that the radiation efficiency of the supercritical accretion of a stellar-mass BH (sBH) is generally too low to explain the proposed electromagnetic counterpart of GW 190521. Applying this model to sBHs embedded in AGN disks, we find that, although the gas inflow rates at Bondi radii of these sBHs are commonly highly super-Eddington, a large fraction of inflowing gas eventually escapes as outflows so that only a small fraction accretes onto the sBH, resulting in mildly super-Eddington BH absorption in most cases. We also apply this model to neutron stars (NSs) and white dwarfs (WDs) in AGN disks. It turns out to be difficult for WDs to grow to the Chandrasekhar limit via accretion because WDs are spun up more efficiently to reach the shedding limit before the Chandrasekhar limit. For NSs accretion-induced collapse is possible if NS magnetic fields are sufficiently strong to keep the NS slowly rotating during accretion.
A Training-Based Mutual Information Lower Bound for Large-Scale Systems

We provide a mutual information lower bound that can be used to analyze the effect of training in models with unknown parameters. For large-scale systems, we show that this bound can be calculated using the difference between two derivatives of a conditional entropy function. We provide a step-by-step process for computing the bound, and apply the steps to a quantized large-scale multiple-antenna wireless communication system with an unknown channel. Numerical results demonstrate the interplay between quantization and training.
What do Firms Gain from Patenting? The Case of the Global ICT Industry.

This study investigates the relationship between patenting activity, productivity, and market competition at the firm level. We focus on the Information and Communication Technology (ICT) industry as a particular case of an innovative sector whose contribution to modern economies is pivotal. For our purpose, we exploit financial accounts and patenting activity in 2009-2017 by 179,660 companies operating in 39 countries. Our identification strategy relies on the most recent approaches for a difference-in-difference setup in the presence of multiple periods and with variation in treatment time. We find that companies being granted patents increase on average market shares by 11%, firm size by 12%, and capital intensity by 10%. Notably, we do not register a significant impact of patenting on firms' productivity after challenging results for reverse causality and robustness checks. Findings are robust after we consider ownership structures separating patents owned by parent companies and their subsidiaries. We complement our investigation with an analysis of market allocation dynamics. Eventually, we argue that policymakers should reconsider the trade-off between IPR protection and market competition, especially when the benefits to firms' competitiveness are not immediately evident.
Self-supervised Learning with Local Attention-Aware Feature

In this work, we propose a novel methodology for self-supervised learning for generating global and local attention-aware visual features. Our approach is based on training a model to differentiate between specific image transformations of an input sample and the patched images. Utilizing this approach, the proposed method is able to outperform the previous best competitor by 1.03% on the Tiny-ImageNet dataset and by 2.32% on the STL-10 dataset. Furthermore, our approach outperforms the fully-supervised learning method on the STL-10 dataset. Experimental results and visualizations show the capability of successfully learning global and local attention-aware visual representations.
Empirical Constraints on Core-collapse Supernova Yields Using Very Metal-poor Damped Lyα Absorbers

We place empirical constraints on the yields from zero- and low-metallicity core-collapse supernovae (CCSNe) using abundances measured in very metal-poor (VMP; [Fe/H] ≤ −2) damped Lyα absorbers (DLAs). For some abundance ratios ([N,Al,S/Fe]), VMP DLAs constrain the metal yields of the first SNe more reliably than VMP stars. We compile a large sample of high-S/N VMP DLAs from over 30 yr of literature, most with high-resolution spectral measurements. We infer the initial-mass-function-averaged CCSNe yield from the median values from the DLA abundance ratios of C, N, O, Al, Si, S, and Fe (over Fe and O). We assume that the DLAs are metal-poor enough that they represent galaxies in their earliest stages of evolution, when CCSNe are the only nucleosynthetic sources of the metals we analyze. We compare five sets of zero- and low-metallicity theoretical yields to the empirical yields derived in this work. We find that the five models agree with the DLA yields for ratios containing Si and S. Only one model (Heger & Woosley 2010, hereafter HW10) reproduced the DLA values for N, and one other model (Limongi & Chieffi 2018, hereafter LC18) reproduced [N/O]. We found little change in the theoretical yields with the adoption of an SN explosion landscape (where certain progenitor masses collapse into black holes, contributing no yields) onto HW10, but fixing explosion energy to progenitor mass results in wide disagreements between the predictions and DLA abundances. We investigate the adoption of a simple, observationally motivated initial distribution of rotational velocities for LC18 and find a slight improvement.
Online Spatio-temporal Calibration of Tightly-coupled Ultrawideband-aided Inertial Localization

The combination of ultrawideband (UWB) radios and inertial measurement units (IMU) can provide accurate positioning in environments where the Global Positioning System (GPS) service is either unavailable or has unsatisfactory performance. The two sensors, IMU and UWB radio, are often not co-located on a moving system. The UWB radio is typically located at the extremities of the system to ensure reliable communication, whereas the IMUs are located closer to its center of gravity. Furthermore, without hardware or software synchronization, data from heterogeneous sensors can arrive at different time instants resulting in temporal offsets. If uncalibrated, these spatial and temporal offsets can degrade the positioning performance. In this paper, using observability and identifiability criteria, we derive the conditions required for successfully calibrating the spatial and the temporal offset parameters of a tightly-coupled UWB-IMU system. We also present an online method for jointly calibrating these offsets. The results show that our calibration approach results in improved positioning accuracy while simultaneously estimating (i) the spatial offset parameters to millimeter precision and (ii) the temporal offset parameter to millisecond precision.
The Substructures in Disks Undergoing Vertical Shear Instability. II. Observational Predictions for the Dust Continuum

High-angular resolution observations at submillimeter/millimeter wavelengths of disks surrounding young stars have shown that their morphology is made of azimuthally symmetric or point-symmetric substructures, in some cases with spiral arms or localized spur- or crescent-shaped features. The majority of theoretical studies with the aim of interpreting the observational results have focused on disk models with planets under the assumption that the disk substructures are due to disk–planet interaction. However, so far, only in very few cases have exoplanets been detected in these systems. Furthermore, some substructures are expected to appear before planets form, as they are necessary to drive the concentration of small solids which can lead to the formation of planetesimals. In this work we present observational predictions from high-resolution 3D radiative hydrodynamical models that follow the evolution of gas and solids in a prototoplanetary disk. We focus on substructures in the distribution of millimeter-sized and smaller solid particles produced by the vertical shear instability. We show that their characteristics are compatible with some of the shallow gaps detected in recent observations at sub-mm/mm wavelengths and present predictions for future observations with better sensitivity and angular resolution with ALMA and a Next Generation Very Large Array.
SDEdit: Image Synthesis and Editing with Stochastic Differential Equations

We introduce a new image editing and synthesis framework, Stochastic Differential Editing (SDEdit), based on a recent generative model using stochastic differential equations (SDEs). Given an input image with user edits ( e.g ., hand-drawn color strokes), we ﬁrst add noise to the input according to an SDE, and subsequently denoise it by simulating the reverse SDE to gradually increase its likelihood under the prior. Our method does not require task-speciﬁc loss function designs, which are critical components for recent image editing methods based on GAN inversion. Compared to conditional GANs, we do not need to collect new datasets of original and edited images for new applications. Therefore, our method can quickly adapt to various editing tasks at test time without re-training models. Our approach achieves strong performance on a wide range of applications, including image synthesis and editing guided by stroke paintings and image compositing.
Dynamical phase transition in the activity-biased fully-connected random field Ising model: connection with glass-forming systems

We analyse biased ensembles of trajectories for the random-field Ising model on a fully-connected lattice, which is described exactly by mean-field theory. By coupling the activity of the system to a dynamical biasing field, we find a range of dynamical phase transitions, including spontaneous symmetry breaking into ordered states. For weak bias, the phase behaviour is controlled by extrema of the free energy, which may be local minima or saddle points. For large bias, the system tends to states of extremal activity, which may differ strongly from free energy minima. We discuss connections of these results to random first-order transition theory of glasses, which motivates an extension of the analysis to random-field Ising models where the dynamical activity is not symmetric under magnetisation reversal.
Convergent evolution in a large cross-cultural database of musical scales

Scales, sets of discrete pitches that form the basis of melodies, are thought to be one of the most universal hallmarks of music. But we know relatively little about cross-cultural diversity of scales or how they evolved. To remedy this, we assemble a cross-cultural database (Database of Musical Scales: DaMuSc) of scale data, collected over the past century by various ethnomusicologists. Statistical analyses of the data highlight that certain intervals (e.g., the octave, fifth, second) are used frequently across cultures. Despite some diversity among scales, it is the similarities across societies which are most striking: step intervals are restricted to 100-400 cents; most scales are found close to equidistant 5- and 7-note scales. We discuss potential mechanisms of variation and selection in the evolution of scales, and how the assembled data may be used to examine the root causes of convergent evolution.
To adjust or not to adjust? Estimating the average treatment effect in randomized experiments with missing covariates

: Complete randomization allows for consistent estimation of the average treatment effect based on the difference in means of the outcomes without strong modeling assumptions on the outcome-generating process. Appropriate use of the pretreatment covariates can further improve the estimation efficiency. However, missingness in covariates is common in experiments and raises an im-portant question: should we adjust for covariates subject to missingness, and if so, how? The unadjusted difference in means is always unbiased. The complete-covariate analysis adjusts for all completely observed covariates and improves the efficiency of the difference in means if at least one completely observed covariate is predictive of the outcome. Then what is the additional gain of adjusting for covariates subject to missingness? A key insight is that the missingness indica-tors act as fully observed pretreatment covariates as long as missingness is not affected by the treatment, and can thus be used in covariate adjustment to bring additional estimation efficiency. This motivates adding the missingness indica-tors to the regression adjustment, yielding the missingness-indicator method as a well-known but not so popular strategy in the literature of missing data. We recommend it due to its many advantages. We also propose modifications to the missingness-indicator method based on asymptotic and finite-sample con-siderations. To reconcile the conflicting recommendations in the missing data literature, we analyze and compare various strategies for analyzing randomized experiments with missing covariates under the design-based framework. This framework treats randomization as the basis for inference and does not impose any modeling assumptions on the outcome-generating process and missing-data mechanism.
ELLIPSDF: Joint Object Pose and Shape Optimization with a Bi-level Ellipsoid and Signed Distance Function Description

Autonomous systems need to understand the semantics and geometry of their surroundings in order to comprehend and safely execute object-level task specifications. This paper proposes an expressive yet compact model for joint object pose and shape optimization, and an associated optimization algorithm to infer an object-level map from multi-view RGB-D camera observations. The model is expressive because it captures the identities, positions, orientations, and shapes of objects in the environment. It is compact because it relies on a low-dimensional latent representation of implicit object shape, allowing onboard storage of large multi-category object maps. Different from other works that rely on a single object representation format, our approach has a bi-level object model that captures both the coarse level scale as well as the fine level shape details. Our approach is evaluated on the large-scale real-world ScanNet dataset and compared against state-of-the-art methods.