Miracle-dz/UniFAR-FTUs huggingface dataset:
A Survey on Orthogonal Time Frequency Space: New Delay Doppler Communications Paradigm in 6G era

: In 6G era, the space-air-ground integrated networks (SAGIN) are expected to provide global coverage and thus are required to support a wide range of emerging applications in hostile environments with high-mobility. In such scenarios, conventional orthogonal frequency division multiplexing (OFDM) modulation, which has been widely deployed in the cellular and Wi-Fi communications systems, will suffer from performance degradation due to high Doppler shift. To address this challenge, a new two-dimensional (2D) modulation scheme referred to as orthogonal time frequency space (OTFS) was proposed and has been recognized as an enabling technology for future high-mobility scenarios. In particular, OTFS modulates information in the delay-Doppler (DD) domain rather than the time-frequency (TF) domain for OFDM, providing the beneﬁts of Doppler-resilience and delay-resilience, low signaling latency, low peak-to-average ratio (PAPR), and low-complexity implementation. Recent researches also show that the direct interaction of information and physical world in the DD domain makes OTFS an promising waveform for realizing integrated sensing and communications (ISAC). In this article, we will present a comprehensive survey of OTFS technology in 6G era, including the fundamentals, recent advances, and future works. Our aim is
Fairly Allocating Utility in Constrained Multiwinner Elections

Fairness in multiwinner elections is studied in varying con- texts. For instance, diversity of candidates, representation of voters, or both are separately termed as being fair. A com- mon denominator to ensure fairness across all such contexts is the use of constraints. However, across these contexts, the candidates selected to satisfy the given constraints may systematically lead to unfair outcomes for historically disadvan- taged voter populations as the cost of fairness may be borne unequally. Hence, we develop a model to select candidates that satisfy the constraints fairly across voter populations. To do so, the model maps the constrained multiwinner election problem to a problem of fairly allocating indivisible goods. We propose three variants of the model, namely, global , lo- calized , and inter-sectional . Next, we analyze the model’s computational complexity and present an empirical analysis of the utility traded-off across various settings of our model. We observe the potential impact of Simpson’s paradox on re- sults using synthetic datasets and a dataset of voting at the United Nations. Finally, we discuss the implications of our work on studies that use constraints to guarantee fairness.
Geometry-enhanced graph neural network for glassy dynamics prediction

Understanding the dynamic processes of the glassy system continues to be challenging. Recent advances have shown the power of graph neural networks (GNNs) for determining the correlation between structure and dynamics in the glassy system. These methods treat the glassy system as a topological graph. However, the inherent ”smoothness” property of the dynamics on the graph (variation of dynamics over the graph) is ignored, resulting in a deteriorated performance of GNN for dynamic predictions over various time scales. In this paper, we ﬁrst present an experimental investigation assessing the smoothness patterns of particle dynamics from the graph perspective. The results indicate that the long-time dynamics exhibit a smoother property on the graph, while the short-time dynamics reveal a distinctly non-smooth pattern. To establish the relationship between the static structure and dynamics with diﬀerent smoothness patterns, we propose a novel geometry-enhanced graph neural network (Geo-GNN) model. The Geo-GNN architecture consists of a geometry feature encoder that incorporates rotation-invariant distances and angles to enhance geometric feature learning and a geometry-enhanced aggregation block that can adaptively learn the underlying smoothness patterns during message passing. Experimental results demonstrate that our method is able to capture the inherent smoothness pattern of particles and outperforms state-of-the-art baselines in predicting the dynamics across all time scales. A subsequent study has revealed that geometric features are critical for the model to accurately capture smoothness patterns in dynamics. Our research not only reﬁnes the method for predicting glassy dynamics but also provides a new lens through which to investigate the issue of causality regarding dynamical heterogeneity in glasses.
Newly discovered Ca ii absorbers in the early Universe: statistics, element abundances, and dust

We report discoveries of 165 new quasar Ca ii absorbers from the Sloan Digital Sky Survey (SDSS) Data Releases 7 and 12. Our ca ii rest-frame equivalent width distribution supports the weak and strong subpopulations, split at ${W}^{\lambda 3934}_{0}=0.7$ Å. Comparison of both populations’ dust depletion shows clear consistency for weak absorber association with halo-type gas in the Milky Way (MW), while strong absorbers have environments consistent with halo and disc-type gas. We probed our high-redshift Ca ii absorbers for 2175 Å dust bumps, discovering 12 2175 Å dust absorbers (2DAs). This clearly shows that some Ca ii absorbers follow the Large Magellanic Cloud (LMC) extinction law rather than the Small Magellanic Cloud extinction law. About 33 per cent of our strong Ca ii absorbers exhibit the 2175 Å dust bump, while only 6 per cent of weak Ca ii absorbers show this bump. 2DA detection further supports the theory that strong Ca ii absorbers are associated with disc components and are dustier than the weak population. Comparing average Ca ii absorber dust depletion patterns to that of Damped Ly α absorbers (DLAs), Mg ii absorbers, and 2DAs shows that Ca ii absorbers generally have environments with more dust than DLAs and Mg ii absorbers, but less dust than 2DAs. Comparing 2175 Å dust bump strengths from different samples and also the MW and LMC, the bump strength appears to grow stronger as the redshift decreases, indicating dust growth and the global chemical enrichment of galaxies in the Universe over time.
Transfer Learning for Contextual Multi-armed Bandits

Motivated by a range of applications, we study in this paper the problem of transfer learning for nonparametric contextual multi-armed bandits under the covariate shift model, where we have data collected on source bandits before the start of the target bandit learning. The minimax rate of convergence for the cumulative regret is established and a novel transfer learning algorithm that attains the minimax regret is proposed. The results quantify the contribution of the data from the source domains for learning in the target domain in the context of nonparametric contextual multi-armed bandits. In view of the general impossibility of adaptation to unknown smoothness, we develop a data-driven algorithm that achieves near-optimal statistical guarantees (up to a logarithmic factor) while automatically adapting to the unknown parameters over a large collection of parameter spaces under an additional self-similarity assumption. A simulation study is carried out to illustrate the benefits of utilizing the data from the auxiliary source domains for learning in the target domain.
Near-optimal learning of Banach-valued, high-dimensional functions via deep neural networks

The past decade has seen increasing interest in applying Deep Learning (DL) to Computational Science and Engineering (CSE). Driven by impressive results in applications such as computer vision, Uncertainty Quantification (UQ), genetics, simulations and image processing, DL is increasingly supplanting classical algorithms, and seems poised to revolutionize scientific computing. However, DL is not yet well-understood from the standpoint of numerical analysis. Little is known about the efficiency and reliability of DL from the perspectives of stability, robustness, accuracy, and sample complexity. In particular, approximating solutions to parametric PDEs is an objective of UQ for CSE. Training data for such problems is often scarce and corrupted by errors. Moreover, the target function is a possibly infinite-dimensional smooth function taking values in the PDE solution space, generally an infinite-dimensional Banach space. This paper provides arguments for Deep Neural Network (DNN) approximation of such functions, with both known and unknown parametric dependence, that overcome the curse of dimensionality. We establish practical existence theorems that describe classes of DNNs with dimension-independent architecture size and training procedures based on minimizing the (regularized) $\ell^2$-loss which achieve near-optimal algebraic rates of convergence. These results involve key extensions of compressed sensing for Banach-valued recovery and polynomial emulation with DNNs. When approximating solutions of parametric PDEs, our results account for all sources of error, i.e., sampling, optimization, approximation and physical discretization, and allow for training high-fidelity DNN approximations from coarse-grained sample data. Our theoretical results fall into the category of non-intrusive methods, providing a theoretical alternative to classical methods for high-dimensional approximation.
Image Anomaly Detection and Localization with Position and Neighborhood Information

Anomaly detection and localization are essential in many areas, where collecting enough anomalous samples for training is almost impossible. To overcome this difﬁculty, many existing methods use a pre-trained network to encode input images and non-parametric modeling to estimate the encoded feature distribution. In the modeling process, however, they overlook that position and neighborhood information affect the distribution of normal features. To use the information, in this paper, the normal distribution is estimated with conditional probability given neighborhood features, which is modeled with a multi-layer perceptron network. At the same time, positional information can be used by building a histogram of representative features at each position. While existing methods simply resize the anomaly map into the resolution of an input image, the proposed method uses an additional reﬁne network that is trained from synthetic anomaly images to perform better interpolation considering the shape and edge of the input image. For the popular industrial dataset, MVTec AD benchmark, the experimental results show 99.52% and 98.91% AUROC scores in anomaly detection and localization, which is state-of-the-art performance.
Subgroup Robustness Grows On Trees: An Empirical Baseline Investigation

Researchers have proposed many methods for fair and robust machine learning, but comprehensive empirical evaluation of their subgroup robustness is lacking. In this work, we address this gap in the context of tabular data, where sensitive subgroups are clearly-defined, real-world fairness problems abound, and prior works often do not compare to state-of-the-art tree-based models as baselines. We conduct an empirical comparison of several previously-proposed methods for fair and robust learning alongside state-of-the-art tree-based methods and other baselines. Via experiments with more than $340{,}000$ model configurations on eight datasets, we show that tree-based methods have strong subgroup robustness, even when compared to robustness- and fairness-enhancing methods. Moreover, the best tree-based models tend to show good performance over a range of metrics, while robust or group-fair models can show brittleness, with significant performance differences across different metrics for a fixed model. We also demonstrate that tree-based models show less sensitivity to hyperparameter configurations, and are less costly to train. Our work suggests that tree-based ensemble models make an effective baseline for tabular data, and are a sensible default when subgroup robustness is desired. For associated code and detailed results, see https://github.com/jpgard/subgroup-robustness-grows-on-trees .
Nonlinear evolution of high-latitude ionospheric interchange instabilities with scale-size-dependent magnetospheric coupling

The Naval Research Laboratory high-latitude ionosphere-magnetosphere mesoscale coupling model has been generalized to include scale-size-dependent magnetospheric coupling. With this model, the nonlinear evolution of plasma interchangelike instabilities and processes in the high-latitude ionosphere has been studied using computer simulation techniques. We find that the principal effect in the high-latitude ionosphere of magnetospheric coupling, i.e., increased inertial effects, is most pronounced for long-wavelength interchange-driven ionospheric fluctuations of several tens of kilometers and greater. For scale sizes of a few kilometers to tens of kilometers the phenomenology and time scales of the nonlinear evolution of ionospheric interchange modes can be characterized as neither purely inertial (magnetospheric control) nor purely collisional (ionospheric control). For scale sizes less than a few kilometers the nonlinear interchange evolution can be described as a purely collisional process. Density and electric field fluctuation power spectra have been computed from the simulations and found to be in agreement with experimental observations. With scale-size-dependent magnetospheric coupling, spectral breaks at scale sizes of the order of a few kilometers are observed in the density and electric field spectra. Applications to mesoscale dynamics, structure, and the stability of convecting inhomogeneities and large-scale plasma density structures in the high-latitude ionosphere have been made.
A Swing of the Pendulum: The Chemodynamics of the Local Stellar Halo Indicate Contributions from Several Radial Merger Events

We find that the chemical abundances and dynamics of APOGEE and GALAH stars in the local stellar halo are inconsistent with a scenario in which the inner halo is primarily composed of debris from a single massive, ancient merger event, as has been proposed to explain the Gaia-Enceladus/Gaia Sausage (GSE) structure. The data contain trends of chemical composition with energy that are opposite to expectations for a single massive, ancient merger event, and multiple chemical evolution paths with distinct dynamics are present. We use a Bayesian Gaussian mixture model regression algorithm to characterize the local stellar halo, and find that the data are fit best by a model with four components. We interpret these components as the Virgo Radial Merger (VRM), Cronus, Nereus, and Thamnos; however, Nereus and Thamnos likely represent more than one accretion event because the chemical abundance distributions of their member stars contain many peaks. Although the Cronus and Thamnos components have different dynamics, their chemical abundances suggest they may be related. We show that the distinct low- and high-α halo populations from Nissen & Schuster are explained by VRM and Cronus stars, as well as some in situ stars. Because the local stellar halo contains multiple substructures, different popular methods of selecting GSE stars will actually select different mixtures of these substructures, which may change the apparent chemodynamic properties of the selected stars. We also find that the Splash stars in the Solar region are shifted to higher v ϕ and slightly lower [Fe/H] than previously reported.
Analytical solutions of the Dirac equation using the Tridiagonal Representation Approach: General study, limitations, and possible applications

This paper aims at extending our previous work on the solution of the one-dimensional Dirac equation using the Tridiagonal Representation Approach (TRA). In the approach, we expand the spinor wavefunction in terms of suitable square integrable basis functions that support a tridiagonal matrix representation of the wave operator. This will transform the problem from solving a system of coupled first order differential equations to solving an algebraic three-term recursion relation for the expansion coefficients of the wavefunction. In some cases, solutions to this recursion relation can be related to well-known classes of orthogonal polynomials whereas in other situations solutions represent new class of polynomials. In this work, we will discuss various solvable potentials that obey the tridiagonal representation requirement with special emphasis on simple cases with spin-symmetric and pseudospin-symmetric potential couplings. We conclude by mentioning some potential applications in graphene.
CLUSTER ALGEBRAS ARISING FROM INFINITY-GON

We introduce a handy construction of cluster algebras of type A∞, we give a complete classification of the cluster algebras arising from the infinitygon, and finally we construct the category of the diagonals of the infinity-gon and show that it is triangle-equivalent to the infinite cluster category of type A∞ described by Holm and Jorgensen.
Latent Video Diffusion Models for High-Fidelity Video Generation with Arbitrary Lengths

AI-generated content has attracted lots of attention recently, but photo-realistic video synthesis is still challenging. Although many attempts using GANs and autoregressive models have been made in this area, the visual quality and length of generated videos are far from satisfactory. Diffusion models (DMs) are another class of deep generative models and have recently achieved remarkable performance on various image synthesis tasks. However, training image diffusion models usually requires substantial computational resources to achieve a high performance, which makes expanding diffusion models to high-dimensional video synthesis tasks more computationally expensive. To ease this problem while leveraging its advantages, we introduce lightweight video diffusion models that synthesize high-ﬁdelity and arbitrary-long videos from pure noise. Speciﬁcally, we propose to perform diffusion and de-noising in a low-dimensional 3D latent space, which sig-niﬁcantly outperforms previous methods on 3D pixel space when under a limited computational budget. In addition, though trained on tens of frames, our models is generate videos with arbitrary lengths, i.e., thousands of frames, in an autoregressive way. Finally, we further introduce conditional latent perturbation to reduce performance degradation during generating long-duration videos. Extensive experiments on various datasets and generated lengths suggest that our framework is able to sample much more realistic and longer videos than previous approaches, including GAN-based, autoregressive-based, and diffusion-based methods.
Stochastic Approach to Turbulence: A Comprehensive Review

Since Kolmogorov's theory, turbulence has been studied using various methods, many of which could be now be understood in a probabilistic framework. Herein, a comprehensive review of the advances made on stochastic theory of turbulence since Kolmogorov has been provided. It has been suggested that stochastic theory would be able to provide a natural foundation for a unified theory of turbulence as a wide range of problems related to turbulence could be treated using stochastic methods. At first, the mathematical theory of stochastic hydrodynamics has been studied and the results such as well-Posedness and ergodicity have been discussed for stochastic Burgers and Naiver-Stokes equations. The theory of turbulence was then assessed where a special attention was paid to stochastic methods. Concepts including Burgers turbulence, scalar advection, incompressible turbulence, field theoretic methods, and stochastic variational principle have been studied to provide detailed discussion on the stochastic theory of turbulence. Moreover, an introduction to some stochastic numerical methods has also been provided. None of the covered methods have a counterpart in deterministic theories due to their derivation or inherent limitations of deterministic theories.
Optimistic Gradient Descent Ascent in Zero-Sum and General-Sum Bilinear Games

We study the convergence of Optimistic Gradient Descent Ascent in unconstrained bilinear games. In a first part, we consider the zerosum case and extend previous results by Daskalakis et al. [5], Liang and Stokes [15] and others: we prove, for any payoff matrix, the exponential convergence of OGDA to a saddle point and also provide a new, optimal, geometric ratio for the convergence. We also characterize the step sizes inducing convergence, and are able to deduce the optimal step size for the speed of convergence. In a second part, we introduce OGDA for general-sum bilinear games: we show that in an interesting class of games, either OGDA converges exponentially fast to a Nash equilibrium, or the payoffs for both players converge exponentially fast to +∞ (which might be interpreted as endogenous emergence of coordination, or cooperation, among players). We also give sufficient conditions for convergence of OGDA to a Nash equilibrium. These conditions are used to increase the speed of convergence of a min-max problem involving a matrix A, by introducing a generalsum game using the Moore-Penrose inverse matrix of A. This shows for the first time, at our knowledge, that general-sum games can be used to optimally improve algorithms designed for min-max problems. We finally illustrate our results on simple examples of Generative Adversarial Networks.
Frequency Measurement with Superradiant Pulses of Incoherently Pumped Calcium Atoms: Role of Quantum Measurement Backaction

A recent experiment demonstrated heterodyne detection-based frequency measurements with superradiant pulses from coherently pumped strontium atoms in an optical lattice clock system, while another experiment has analyzed the statistics of superradiant pulses from incoherently pumped calcium atoms in a similar system. In this article, we propose to perform heterodyne detection of the superradiant pulses from the calcium atoms, and analyze theoretically the corresponding atomic ensemble dynamics in terms of the rotation of a collective spin vector and the incoherent quantum jumps among superradiant Dicke states. We examine the eﬀect of quantum measurement backaction on the emitted ﬁeld and the collective spin vector dynamics, and we demonstrate that it plays an essential role in the modelling of the frequency measurements. We develop a stochastic mean ﬁeld theory, which is also applicable to model frequency measurements with steady-state superradiance signals, and to explore quantum measurement eﬀects in the dynamics of atomic ensembles.
Retrieval-Augmented Multimodal Language Modeling

Recent multimodal models such as DALL-E and CM3 have achieved remarkable progress in textto-image and image-to-text generation. However, these models store all learned knowledge (e.g., the appearance of the Eiffel Tower) in the model parameters, requiring increasingly larger models and training data to capture more knowledge. To integrate knowledge in a more scalable and modular way, we propose a retrievalaugmented multimodal model, which enables a base multimodal model (generator) to refer to relevant knowledge fetched by a retriever from external memory (e.g., multimodal documents on the web). Specifically, we implement a retriever using the pretrained CLIP model and a generator using the CM3 Transformer architecture, and train this model using the LAION dataset. Our resulting model, named Retrieval-Augmented CM3 (RA-CM3), is the first multimodal model that can retrieve and generate mixtures of text and images. We show that RA-CM3 significantly outperforms baseline multimodal models such as DALL-E and CM3 on both image and caption generation tasks (12 FID and 17 CIDEr improvements on MSCOCO), while requiring much less compute for training (<30% of DALL-E). Moreover, we show that RA-CM3 exhibits novel capabilities such as knowledge-intensive image generation and multimodal in-context learning