Miracle-dz/UniFAR-FTUs huggingface dataset:
Numerical algorithms for solutions of Korteweg–de Vries equation

The nonlinear Korteweg–de Vries (KdVE) equation is solved numerically using both Lagrange polynomials based differential quadrature and cosine expansion‐based differential quadrature methods. The first test example is travelling single solitary wave solution of KdVE and the second test example is interaction of two solitary waves, whereas the other three examples are wave production from solitary waves. Maximum error norm and root mean square error norm are computed, and numerical comparison with some earlier works is done for the first two examples, the lowest four conserved quantities are computed for all test examples. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010
Encoder-based Domain Tuning for Fast Personalization of Text-to-Image Models

Text-to-image personalization aims to teach a pre-trained diffusion model to reason about novel, user provided concepts, embedding them into new scenes guided by natural language prompts. However, current personalization approaches struggle with lengthy training times, high storage requirements or loss of identity. To overcome these limitations, we propose an encoder-based domain-tuning approach. Our key insight is that by underfitting on a large set of concepts from a given domain, we can improve generalization and create a model that is more amenable to quickly adding novel concepts from the same domain. Specifically, we employ two components: First, an encoder that takes as an input a single image of a target concept from a given domain, e.g. a specific face, and learns to map it into a word-embedding representing the concept. Second, a set of regularized weight-offsets for the text-to-image model that learn how to effectively injest additional concepts. Together, these components are used to guide the learning of unseen concepts, allowing us to personalize a model using only a single image and as few as 5 training steps --- accelerating personalization from dozens of minutes to seconds, while preserving quality. Code and trained encoders will be available at our project page.
Models See Hallucinations: Evaluating the Factuality in Video Captioning

Video captioning aims to describe events in a video with natural language. In recent years, many works have focused on improving captioning models' performance. However, like other text generation tasks, it risks introducing factual errors not supported by the input video. These factual errors can seriously affect the quality of the generated text, sometimes making it completely unusable. Although factual consistency has received much research attention in text-to-text tasks (e.g., summarization), it is less studied in the context of vision-based text generation. In this work, we conduct a detailed human evaluation of the factuality in video captioning and collect two annotated factuality datasets. We find that 57.0% of the model-generated sentences have factual errors, indicating it is a severe problem in this field. However, existing evaluation metrics are mainly based on n-gram matching and show little correlation with human factuality annotation. We further propose a weakly-supervised, model-based factuality metric FactVC, which outperforms previous metrics on factuality evaluation of video captioning. The datasets and metrics will be released to promote future research for video captioning.
Planck constraints and gravitational wave forecasts for primordial black hole dark matter seeded by multifield inflation

We perform a Markov Chain Monte Carlo (MCMC) analysis of a simple yet generic multifield inflation model characterized by two scalar fields coupled to each other and nonminimally coupled to gravity, fit to Planck 2018 cosmic microwave background (CMB) data. In particular, model parameters are constrained by data on the amplitude of the primordial power spectrum of scalar curvature perturbations on CMB scales $A_s$, the spectral index $n_s$, and the ratio of power in tensor to scalar modes $r$, with a prior that the primordial power spectrum should also lead to primordial black hole (PBH) production sufficient to account for the observed dark matter (DM) abundance. We find that $n_s$ in particular controls the constraints on our model. Whereas previous studies of PBH formation from an ultra-slow-roll phase of inflation have highlighted the need for at least one model parameter to be highly fine-tuned, we identify a degeneracy direction in parameter space such that shifts by $\sim 10\%$ of one parameter can be compensated by comparable shifts in other parameters while preserving a close fit between model predictions and observations. Furthermore, we find this allowed parameter region produces observable gravitational wave (GW) signals in the frequency ranges to which upcoming experiments are projected to be sensitive, including Advanced LIGO and Virgo, the Einstein Telescope (ET), Cosmic Explorer (CE), DECIGO, and LISA.
: PURE, EFFECTFUL

Logical relations built on top of an operational semantics are one of the most successful proof methods in programming language semantics. In recent years, more and more expressive notions of operationally-based logical relations have been designed and applied to speciﬁc families of languages. However, a unifying abstract framework for operationally-based logical relations is still missing. We show how ﬁbrations can provide a uniform treatment of operational logical relations, using as reference example a λ -calculus with generic eﬀects endowed with a novel, abstract operational semantics deﬁned on a large class of categories. Moreover, this abstract perspective allows us to give a solid mathematical ground also to diﬀerential logical relations — a recently introduced notion of higher-order distance between programs — both pure and eﬀectful, bringing them back to a common picture with traditional ones.
A Mechanism for Destabilizing Cartels ∗

Attention has recently been focused on the possibility of artiﬁcially intelligent sellers on platforms colluding to form cartels to limit output and raise prices. Such cartels, however, feature an incentive for individual sellers to deviate from the prescribed quantities and prices (cheating) to increase their own proﬁts. Stabilizing such cartels therefore requires credible threats of punishments such as price wars. In this paper, I propose a mechanism to destabilize cartels by protecting any cheaters from a price war by guaranteeing a stream of proﬁts which is unaﬀected by arbitrary punishments. This method applies to the sale of diﬀerentiated goods on (multiple) platforms or homogeneous goods through direct sales. This method for destabilizing cartels operates purely oﬀ-equilibrium, induces no welfare losses, features very low informational requirements (sale price and quantity data suﬃces) and does not depend on the choice of discount factors.
Multi-Symmetry Ensembles: Improving Diversity and Generalization via Opposing Symmetries

Deep ensembles (DE) have been successful in improving model performance by learning diverse members via the stochasticity of random initialization. While recent works have attempted to promote further diversity in DE via hyperparameters or regularizing loss functions, these methods primarily still rely on a stochastic approach to explore the hypothesis space. In this work, we present Multi-Symmetry Ensembles (MSE), a framework for constructing diverse ensembles by capturing the multiplicity of hypotheses along symmetry axes, which explore the hypothesis space beyond stochastic perturbations of model weights and hyperparameters. We leverage recent advances in contrastive representation learning to create models that separately capture opposing hypotheses of invariant and equivariant functional classes and present a simple ensembling approach to efficiently combine appropriate hypotheses for a given task. We show that MSE effectively captures the multiplicity of conflicting hypotheses that is often required in large, diverse datasets like ImageNet. As a result of their inherent diversity, MSE improves classification performance, uncertainty quantification, and generalization across a series of transfer tasks.
A Multi-GPU Aggregation-Based AMG Preconditioner for Iterative Linear Solvers

We present and release in open source format a sparse linear solver which efficiently exploits heterogeneous parallel computers. The solver can be easily integrated into scientific applications that need to solve large and sparse linear systems on modern parallel computers made of hybrid nodes hosting Nvidia Graphics Processing Unit (GPU) accelerators. The work extends previous efforts of some of the authors in the exploitation of a single GPU accelerator and proposes an implementation, based on the hybrid MPI-CUDA software environment, of a Krylov-type linear solver relying on an efficient Algebraic MultiGrid (AMG) preconditioner already available in the BootCMatchG library. Our design for the hybrid implementation has been driven by the best practices for minimizing data communication overhead when multiple GPUs are employed, yet preserving the efficiency of the GPU kernels. Strong and weak scalability results of the new version of the library on well-known benchmark test cases are discussed. Comparisons with the Nvidia AmgX solution show a speedup, in the solve phase, up to 2.0x.
Examining the decline in the C iv content of the Universe over 4.3 ≲ z  ≲ 6.3 using the E-XQR-30 sample

Intervening C iv absorbers are key tracers of metal-enriched gas in galaxy haloes over cosmic time. Previous studies suggest that the C iv cosmic mass density ($\Omega _{\rm C \, \small {IV}}$) decreases slowly over 1.5 $\lesssim \, z\lesssim$ 5 before declining rapidly at z ≳ 5, but the cause of this downturn is poorly understood. We characterize the $\Omega _{\rm C \, \small {IV}}$ evolution over 4.3 ≲ z ≲ 6.3 using 260 absorbers found in 42 XSHOOTER spectra of z ∼ 6 quasars, of which 30 come from the ESO Large Program XQR-30. The large sample enables us to robustly constrain the rate and timing of the downturn. We find that $\Omega _{\rm C \, \small {IV}}$ decreases by a factor of 4.8 ± 2.0 over the ∼300 Myr interval between z ∼ 4.7 and ∼5.8. The slope of the column density (log N) distribution function does not change, suggesting that C iv absorption is suppressed approximately uniformly across 13.2 ≤ log N/cm−2 < 15.0. Assuming that the carbon content of galaxy haloes evolves as the integral of the cosmic star formation rate density (with some delay due to stellar lifetimes and outflow travel times), we show that chemical evolution alone could plausibly explain the fast decline in $\Omega _{\rm C \, \small {IV}}$ over 4.3 ≲ z ≲ 6.3. However, the C iv/C ii ratio decreases at the highest redshifts, so the accelerated decline in $\Omega _{\rm C \, \small {IV}}$ at z ≳ 5 may be more naturally explained by rapid changes in the gas ionization state driven by evolution of the UV background towards the end of hydrogen reionization.
Interpretable reduced-order modeling with time-scale separation

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction crucial. We propose such a data-driven scheme that automates the identification of the time-scales involved and can produce stable predictions forward in time as well as under different initial conditions not included in the training data. To this end, we combine a non-linear autoencoder architecture with a time-continuous model for the latent dynamics in the complex space. It readily allows for the inclusion of sparse and irregularly sampled training data. The learned, latent dynamics are interpretable and reveal the different temporal scales involved. We show that this data-driven scheme can automatically learn the independent processes that decompose a system of linear ODEs along the eigenvectors of the system's matrix. Apart from this, we demonstrate the applicability of the proposed framework in a hidden Markov Model and the (discretized) Kuramoto-Shivashinsky (KS) equation. Additionally, we propose a probabilistic version, which captures predictive uncertainties and further improves upon the results of the deterministic framework.
Accurate and Efficient Trajectory-based Contact Tracing with Secure Computation and Geo-Indistinguishability

Contact tracing has been considered as an effective measure to limit the transmission of infectious disease such as COVID-19. Trajectory-based contact tracing compares the trajectories of users with the patients, and allows the tracing of both direct contacts and indirect contacts. Although trajectory data is widely considered as sensitive and personal data, there is limited research on how to securely compare trajectories of users and patients to conduct contact tracing with excellent accuracy, high efficiency, and strong privacy guarantee. Traditional Secure Multiparty Computation (MPC) techniques suffer from prohibitive running time, which prevents their adoption in large cities with millions of users. In this work, we propose a technical framework called ContactGuard to achieve accurate, efficient, and privacy-preserving trajectory-based contact tracing. It improves the efficiency of the MPC-based baseline by selecting only a small subset of locations of users to compare against the locations of the patients, with the assist of Geo-Indistinguishability, a differential privacy notion for Location-based services (LBS) systems. Extensive experiments demonstrate that ContactGuard runs up to 2.6$\times$ faster than the MPC baseline, with no sacrifice in terms of the accuracy of contact tracing.
A Unified Algebraic Perspective on Lipschitz Neural Networks

Important research efforts have focused on the design and training of neural networks with a controlled Lipschitz constant. The goal is to increase and sometimes guarantee the robustness against adversarial attacks. Recent promising techniques draw inspirations from different backgrounds to design 1-Lipschitz neural networks, just to name a few: convex potential layers derive from the discretization of continuous dynamical systems, Almost-Orthogonal-Layer proposes a tailored method for matrix rescaling. However, it is today important to consider the recent and promising contributions in the field under a common theoretical lens to better design new and improved layers. This paper introduces a novel algebraic perspective unifying various types of 1-Lipschitz neural networks, including the ones previously mentioned, along with methods based on orthogonality and spectral methods. Interestingly, we show that many existing techniques can be derived and generalized via finding analytical solutions of a common semidefinite programming (SDP) condition. We also prove that AOL biases the scaled weight to the ones which are close to the set of orthogonal matrices in a certain mathematical manner. Moreover, our algebraic condition, combined with the Gershgorin circle theorem, readily leads to new and diverse parameterizations for 1-Lipschitz network layers. Our approach, called SDP-based Lipschitz Layers (SLL), allows us to design non-trivial yet efficient generalization of convex potential layers. Finally, the comprehensive set of experiments on image classification shows that SLLs outperform previous approaches on certified robust accuracy. Code is available at https://github.com/araujoalexandre/Lipschitz-SLL-Networks.
Ultrafast Plasmon-mediated Superradiance from Vertically Standing Molecules in Metallic Nanocavities

Plasmon-mediated superradiance for molecules around metallic nanospheres was proposed ten years ago. However, its demonstration has not been achieved yet due to the experimental difficulty of positioning molecules, and the theoretical limitation to the enhanced collective rate of low excited molecules. In this Letter, we propose that the ultrafast plasmon-mediated superradiant pulses can be observed with strongly excited methylene blue molecules standing vertically inside gold nanoparticle-on-mirror nanocavities. Our simulations indicate that in this system the molecules could interact with each other via plasmon- and free-space mediated coherent and dissipative coupling. More importantly, the coherent coupling mediated by short-ranged propagating surface plasmons cancel largely the direct dipole-dipole coupling mediated by the free-space field, and the dominated dissipative coupling mediated by relatively long-ranged gap plasmons enables the ultrafast superradiant pulses within picosecond scale. Our study opens up the possibility of studying the rich superradiant effects from the quantum emitters in a sub-wavelength volumn by engineering the plasmonic environments.
Learning to reason over visual objects

A core component of human intelligence is the ability to identify abstract patterns inherent in complex, high-dimensional perceptual data, as exemplified by visual reasoning tasks such as Raven's Progressive Matrices (RPM). Motivated by the goal of designing AI systems with this capacity, recent work has focused on evaluating whether neural networks can learn to solve RPM-like problems. Previous work has generally found that strong performance on these problems requires the incorporation of inductive biases that are specific to the RPM problem format, raising the question of whether such models might be more broadly useful. Here, we investigated the extent to which a general-purpose mechanism for processing visual scenes in terms of objects might help promote abstract visual reasoning. We found that a simple model, consisting only of an object-centric encoder and a transformer reasoning module, achieved state-of-the-art results on both of two challenging RPM-like benchmarks (PGM and I-RAVEN), as well as a novel benchmark with greater visual complexity (CLEVR-Matrices). These results suggest that an inductive bias for object-centric processing may be a key component of abstract visual reasoning, obviating the need for problem-specific inductive biases.
Social Media COVID-19 Contact Tracing Using Mobile Social Payments and Facebook Data

Many in the US were reluctant to report their COVID-19 cases at the height of the pandemic (e.g., for fear of missing work or other obligations due to quarantine mandates). Other methods such as using public social media data can therefore help augment current approaches to surveilling pandemics. This study evaluated the effectiveness of using social media data as a data source for tracking public health pandemics. There have been several attempts at using social media data from platforms like Twitter for analyzing the COVID-19 pandemic. While these provide a multitude of useful insights, new platforms like Venmo, a popular U.S. mobile social payment app often used during in-person activities, remain understudied. We developed unique computational methods (combining Venmo- and Facebook- derived data) to classify post content, including the location where the content was likely posted. This approach enabled geotemporal COVID-19-related infoveillance. By examining 135M publicly available Venmo transactions from 22.1M unique users, we found significant spikes in the use of COVID-19 related keywords in March 2020. Using Facebook-based geotags for 9K users along with transaction geo-parsing (i.e., parsing text to detect place names), we identified 38K location-based clusters. Within these groups, we found a strong correlation (0.81) between the use of COVID-19 keywords in a region and the number of reported COVID-19 cases as well as an aggregate decrease in transactions during lockdowns and an increase when lockdowns are lifted. Surprisingly, we saw a weak negative correlation between the number of transactions and reported cases over time (-0.49). Our results indicate that using non-Twitter social media trace data can aid pandemic- and other health-related infoveillance.
Boundary approximation for sticky jump-reflected processes on the half-line

The Skorokhod reflection was used in 1961 to create a reflected diffusion on the half-line. Later, it was used for processes with jumps such as reflected L\'evy processes. Like a Brownian motion, which is a weak limit of random walks, reflected processes on the half-line serve as weak limits of random walks with switching regimes at zero: one regime away from zero, the other around zero. In this article, we develop a general theory of this regime change and prove convergence to a function with generalized reflection. Our results are deterministic and can be applied to a wide class of stochastic processes. Applications include storage processes, heavy traffic limits, diffusion on a half-line with a combination of continuous reflection, jump exit, and a delay at 0.
A study of the ultraviolet evolution of U Geminorum between outbursts

This paper examines the ultraviolet evolution of the dwarf nova U Gem from one outburst to the next. A series of seven sets of IUE observations that monitor the quiescent period of 22-103 days after outbursts is presented. An eighth set of observations obtained 75 days after the second outburst is included for comparison. In agreement with earlier studies, analyses of Ly-alpha profiles and 1200-2000-A continuum spectra during 103 days of quiescence are consistent with the presence of a 30,000 K white dwarf. Direct evidence is provided that the UV flux levels continue to decrease throughout optical quiescence. These changes in flux appear consistent with the added presence of a hot component (perhaps the inner part of the disk or boundary layer) in addition to the white dwarf. Analyses of the absorption line spectra are also inconsistent with a single photospheric origin. 17 refs.
Learning High-Dimensional Single-Neuron ReLU Networks with Finite Samples

This paper considers the problem of learning a single ReLU neuron with squared loss (a.k.a., ReLU regression) in the overparameterized regime, where the input dimension can exceed the number of samples. We analyze a Perceptron-type algorithm called GLM-tron (Kakade et al., 2011), and provide its dimension-free risk upper bounds for high-dimensional ReLU regression in both well-speciﬁed and misspeciﬁed settings. Our risk bounds recover several existing results as special cases. Moreover, in the well-speciﬁed setting, we also provide an instance-wise matching risk lower bound for GLM-tron. Our upper and lower risk bounds provide a sharp characterization of the high-dimensional ReLU regression problems that can be learned via GLM-tron. On the other hand, we provide some negative results for stochastic gradient descent (SGD) for ReLU regression with symmetric Bernoulli data: if the model is well-speciﬁed, the excess risk of SGD is provably no better than that of GLM-tron ignoring constant factors, for each problem instance; and in the noiseless case, GLM-tron can achieve a small risk while SGD unavoidably suﬀers from a constant risk in expectation. These results together suggest that GLM-tron might be preferable than SGD for high-dimensional ReLU regression.