Miracle-dz/UniFAR-FTUs huggingface dataset:
A continuous data assimilation closure for modeling statistically steady turbulence in large-eddy simulation

A closure model is presented for large-eddy simulation (LES) based on the three-dimensional variational data assimilation algorithm. The approach aims at reconstructing high-fidelity kinetic energy spectra in coarse numerical simulations by including feedback control to represent unresolved dynamics interactions in the flow as stochastic processes. The forcing uses statistics obtained from off-line high-fidelity data and requires only few parameters compared to the number of degrees of freedom of LES. This modeling strategy is applied to geostrophic turbulence on the sphere. It proves to accurately recover the energy spectra, the interscale energy transfer and the zonal velocity profiles in the coarse model, for three generic situations.
Error estimation and adaptive tuning for unregularized robust M-estimator

We consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the number of features p are both increasing such that $p/n \to \gamma\in (0,1)$. An estimator of the out-of-sample error of a robust M-estimator is analysed and proved to be consistent for a large family of loss functions that includes the Huber loss. As an application of this result, we propose an adaptive tuning procedure of the scale parameter $\lambda>0$ of a given loss function $\rho$: choosing$\hat \lambda$ in a given interval $I$ that minimizes the out-of-sample error estimate of the M-estimator constructed with loss $\rho_\lambda(\cdot) = \lambda^2 \rho(\cdot/\lambda)$ leads to the optimal out-of-sample error over $I$. The proof relies on a smoothing argument: the unregularized M-estimation objective function is perturbed, or smoothed, with a Ridge penalty that vanishes as $n\to+\infty$, and show that the unregularized M-estimator of interest inherits properties of its smoothed version.
Diffusion Models With Learned Adaptive Noise

Diffusion models have gained traction as powerful algorithms for synthesizing high-quality images. Central to these algorithms is the diffusion process, which maps data to noise according to equations inspired by thermodynamics and can significantly impact performance. A widely held assumption is that the ELBO objective of a diffusion model is invariant to the noise process (Kingma et al.,2021). In this work, we dispel this assumption -- we propose multivariate learned adaptive noise (MuLAN), a learned diffusion process that applies Gaussian noise at different rates across an image. Our method consists of three components -- a multivariate noise schedule, instance-conditional diffusion, and auxiliary variables -- which ensure that the learning objective is no longer invariant to the choice of the noise schedule as in previous works. Our work is grounded in Bayesian inference and casts the learned diffusion process as an approximate variational posterior that yields a tighter lower bound on marginal likelihood. Empirically, MuLAN sets a new state-of-the-art in density estimation on CIFAR-10 and ImageNet compared to classical diffusion. Code is available at https://github.com/s-sahoo/MuLAN
High-dimensional sparse classification using exponential weighting with empirical hinge loss

In this study, we address the problem of high-dimensional binary classification. Our proposed solution involves employing an aggregation technique founded on exponential weights and empirical hinge loss. Through the employment of a suitable sparsity-inducing prior distribution, we demonstrate that our method yields favorable theoretical results on prediction error. The efficiency of our procedure is achieved through the utilization of Langevin Monte Carlo, a gradient-based sampling approach. To illustrate the effectiveness of our approach, we conduct comparisons with the logistic Lasso on simulated data and a real dataset. Our method frequently demonstrates superior performance compared to the logistic Lasso.
A Time-Relaxation Reduced Order Model for the Turbulent Channel Flow

Reg-ROMs are stabilization strategies that leverage spatial filtering to alleviate the spurious numerical oscillations generally displayed by the classical G-ROM in under-resolved numerical simulations of turbulent flows. In this paper, we propose a new Reg-ROM, the time-relaxation ROM (TR-ROM), which filters the marginally resolved scales. We compare the new TR-ROM with the two other Reg-ROMs in current use, i.e., the L-ROM and the EFR-ROM, in the numerical simulation of the turbulent channel flow at $Re_{\tau} = 180$ and $Re_{\tau} = 395$ in both the reproduction and the predictive regimes. For each Reg-ROM, we investigate two different filters: (i) the differential filter (DF), and (ii) a new higher-order algebraic filter (HOAF). In our numerical investigation, we monitor the Reg-ROM performance for the ROM dimension, $N$, and the filter order. We also perform sensitivity studies of the three Reg-ROMs for the time interval, relaxation parameter, and filter radius. The numerical results yield the following conclusions: (i) All three Reg-ROMs are significantly more accurate than the G-ROM and (ii) more accurate than the ROM projection, representing the best theoretical approximation of the training data in the given ROM space. (iii) With the optimal parameter values, the TR-ROM is more accurate than the other two Reg-ROMs in all tests. (iv) For most $N$ values, DF yields the most accurate results for all three Reg-ROMs. (v) The optimal parameters trained in the reproduction regime are also optimal for the predictive regime for most $N$ values. (vi) All three Reg-ROMs are sensitive to the filter radius and the filter order, and the EFR-ROM and the TR-ROM are sensitive to the relaxation parameter. (vii) The optimal range for the filter radius and the effect of relaxation parameter are similar for the two $\rm Re_\tau$ values.
Can It Edit? Evaluating the Ability of Large Language Models to Follow Code Editing Instructions

A significant amount of research is focused on developing and evaluating large language models for a variety of code synthesis tasks. These include synthesizing code from natural language, synthesizing tests from code, and synthesizing explanations of code. In contrast, the behavior of instructional code editing with LLMs is understudied. These are tasks in which the model is provided a block of code and an instruction to modify the code. The editing instruction may ask for a feature to be added or removed, describe a bug and ask for a fix, or ask for a different kind of solution. We introduce a carefully crafted benchmark of code editing tasks and use it to evaluate several cutting edge LLMs. Our evaluation exposes a significant gap between the capabilities of state-of-the-art open and closed models. For example, even GPT-3.5-Turbo is better than the best open model at code editing tasks. We also introduce a new, carefully curated, permissively licensed training dataset of code editing tasks coupled with natural language instructions. Using this training dataset, we show that we can fine-tune open Code LLMs to significantly improve their code editing capabilities, closing the gap between open and closed models. All code, data, and models are available at https://github.com/nuprl/CanItEdit.
Model-Based Control with Sparse Neural Dynamics

Learning predictive models from observations using deep neural networks (DNNs) is a promising new approach to many real-world planning and control problems. However, common DNNs are too unstructured for effective planning, and current control methods typically rely on extensive sampling or local gradient descent. In this paper, we propose a new framework for integrated model learning and predictive control that is amenable to efficient optimization algorithms. Specifically, we start with a ReLU neural model of the system dynamics and, with minimal losses in prediction accuracy, we gradually sparsify it by removing redundant neurons. This discrete sparsification process is approximated as a continuous problem, enabling an end-to-end optimization of both the model architecture and the weight parameters. The sparsified model is subsequently used by a mixed-integer predictive controller, which represents the neuron activations as binary variables and employs efficient branch-and-bound algorithms. Our framework is applicable to a wide variety of DNNs, from simple multilayer perceptrons to complex graph neural dynamics. It can efficiently handle tasks involving complicated contact dynamics, such as object pushing, compositional object sorting, and manipulation of deformable objects. Numerical and hardware experiments show that, despite the aggressive sparsification, our framework can deliver better closed-loop performance than existing state-of-the-art methods.
Fibrations by Lagrangian tori for maximal Calabi-Yau degenerations and beyond

We introduce a general technique to construct Lagrangian torus fibrations in degenerations of K\"ahler manifolds. We show that such torus fibrations naturally occur at the boundary of the A'Campo space. This space extends a degeneration over a punctured disc to a hybrid space involving its real oriented blowup and the dual complex of the special fiber; equipped with an exact modification of a given K\"ahler form which becomes fiberwise symplectic at the boundary. Therefore, it allows to move Lagrangian tori from the boundary using the symplectic connection. In the setting of maximal Calabi-Yau degenerations, we prove that our tori have some asymptotic properties expected from the (conjectural) Strominger-Yau-Zaslow fibration.
Interpolating Bremsstrahlung function in ABJM

In ABJM theory, enriched RG flows between circular 1/6 BPS bosonic and 1/2 BPS fermionic Wilson loops have been introduced in arXiv:2211.16501. These flows are triggered by deformations corresponding to parametric 1/6 BPS fermionic loops. In this paper we revisit the study of these operators, but instead of circular contours we consider an interpolating cusped line and a latitude and study their RG flow in perturbation theory. This allows for the definition of a Bremsstrahlung function away from fixed points. We generalize to this case the known cusp/latitude correspondence that relates the Bremsstrahlung function to a latitude Wilson loop. We find that away from the conformal fixed points the ordinary identity is broken by the conformal anomaly in a controlled way. From a defect perspective, the breaking of the correspondence can be traced back to the appearance of an anomalous dimension for fermionic operators localized on the defect. As a by-product, we provide a brand new result for the two-loop cusp anomalous dimension of the 1/6 BPS fermionic and the 1/6 BPS bosonic Wilson lines.
Unravelling T-Duality: Magnetic Quivers in Rank-zero Little String Theories

An intriguing class of 6d supersymmetric theories are known as little strings theories, which exhibit a rich network of T-dualities. A robust feature of these theories are their Higgs branches. Focusing on the little string theories that are realised on a single curve of zero self-intersection, we utilise brane systems to derive the magnetic quivers. Using a variety of techniques (including branching rules, brane dynamics, F-theory geometry, quiver subtraction, and the decay and fission algorithm), we detail the Higgs branch Hasse diagram and determine the transverse slices for every elementary Higgs branch RG-flow. Building on these insights, we pursue two directions: firstly, we used the established connection between the change of the 2-Group structure constants along Higgs branch RG-flows and the transition-type in the Hasse diagram to infer putative T-dual models. Secondly, we conjecture an algorithm that predicts the non-Abelian flavour symmetry of the compactified little string theory by inspecting the magnetic quivers of all T-dual frames.
A new method to partition climate and catchment effect on the mean annual runoff based on the Budyko complementary relationship

Effect of climate change and catchment change on the long‐term water balance is of considerable interest at a range of spatial scales. The total differential of runoff within the Budyko framework, which has been widely used to attribute the change in runoff to the effect of climate and catchment changes, is not precise in which there is always some residual between the observed and estimated change in runoff. The objective of this study is to propose and evaluate a new partition method based on the Budyko complementary relationship for runoff. Algebraic identities have ensured that the change in runoff can be decomposed into two components precisely without any residuals using this complementary method. In addition, the complementary method allows estimation of the upper and lower bounds of the climate effect and catchment effect. The new method was compared with the total differential method and an extrapolation method for 15 catchments in Australia. Results show that the average range of the catchment effect using the complementary method was 6.7 mm for 14 of the 15 catchments, which is much smaller than that estimated with the total differential method (51.5 mm). The average of the upper and lower bounds was shown to be in good agreement with the effect of climate and catchment changes estimated using the extrapolation method (R2 = 0.98 for both). Correlation analysis indicates that the average of these bounds is the best estimate of the magnitude of the climate and catchment effect for the 15 catchments examined.
Combinatorial Gaussian Process Bandits in Bayesian Settings: Theory and Application for Energy-Efficient Navigation

We consider a combinatorial Gaussian process semi-bandit problem with time-varying arm availability. Each round, an agent is provided a set of available base arms and must select a subset of them to maximize the long-term cumulative reward. Assuming the expected rewards are sampled from a Gaussian process (GP) over the arm space, the agent can efficiently learn. We study the Bayesian setting and provide novel Bayesian regret bounds for three GP-based algorithms: GP-UCB, Bayes-GP-UCB and GP-TS. Our bounds extend previous results for GP-UCB and GP-TS to a combinatorial setting with varying arm availability and to the best of our knowledge, we provide the first Bayesian regret bound for Bayes-GP-UCB. Time-varying arm availability encompasses other widely considered bandit problems such as contextual bandits. We formulate the online energy-efficient navigation problem as a combinatorial and contextual bandit and provide a comprehensive experimental study on synthetic and real-world road networks with detailed simulations. The contextual GP model obtains lower regret and is less dependent on the informativeness of the prior compared to the non-contextual Bayesian inference model. In addition, Thompson sampling obtains lower regret than Bayes-UCB for both the contextual and non-contextual model.
A Case Study on Test Case Construction with Large Language Models: Unveiling Practical Insights and Challenges

This paper presents a detailed case study examining the application of Large Language Models (LLMs) in the construction of test cases within the context of software engineering. LLMs, characterized by their advanced natural language processing capabilities, are increasingly garnering attention as tools to automate and enhance various aspects of the software development life cycle. Leveraging a case study methodology, we systematically explore the integration of LLMs in the test case construction process, aiming to shed light on their practical efficacy, challenges encountered, and implications for software quality assurance. The study encompasses the selection of a representative software application, the formulation of test case construction methodologies employing LLMs, and the subsequent evaluation of outcomes. Through a blend of qualitative and quantitative analyses, this study assesses the impact of LLMs on test case comprehensiveness, accuracy, and efficiency. Additionally, delves into challenges such as model interpretability and adaptation to diverse software contexts. The findings from this case study contributes with nuanced insights into the practical utility of LLMs in the domain of test case construction, elucidating their potential benefits and limitations. By addressing real-world scenarios and complexities, this research aims to inform software practitioners and researchers alike about the tangible implications of incorporating LLMs into the software testing landscape, fostering a more comprehensive understanding of their role in optimizing the software development process.
Benchmarks for Retrospective Automated Driving System Crash Rate Analysis Using Police-Reported Crash Data

With fully automated driving systems (ADS; SAE level 4) ride-hailing services expanding in the US, we are now approaching an inflection point, where the process of retrospectively evaluating ADS safety impact can start to yield statistically credible conclusions. An ADS safety impact measurement requires a comparison to a"benchmark"crash rate. This study aims to address, update, and extend the existing literature by leveraging police-reported crashes to generate human crash rates for multiple geographic areas with current ADS deployments. All of the data leveraged is publicly accessible, and the benchmark determination methodology is intended to be repeatable and transparent. Generating a benchmark that is comparable to ADS crash data is associated with certain challenges, including data selection, handling underreporting and reporting thresholds, identifying the population of drivers and vehicles to compare against, choosing an appropriate severity level to assess, and matching crash and mileage exposure data. Consequently, we identify essential steps when generating benchmarks, and present our analyses amongst a backdrop of existing ADS benchmark literature. One analysis presented is the usage of established underreporting correction methodology to publicly available human driver police-reported data to improve comparability to publicly available ADS crash data. We also identify important dependencies in controlling for geographic region, road type, and vehicle type, and show how failing to control for these features can bias results. This body of work aims to contribute to the ability of the community - researchers, regulators, industry, and experts - to reach consensus on how to estimate accurate benchmarks.
Is post-editing really faster than human translation?

Time efficiency is paramount for the localisation industry, which demands ever-faster turnaround times. However, translation speed is largely underresearched, and there is a lack of clarity about how language service providers (LSPs) can evaluate the performance of their post-editing (PE) and human translation (HT) services. This study constitutes the first large-scale investigation of translation and revision speed in HT and in the PE of neural machine translation, based on real-world data from an LSP. It uses an exploratory data analysis approach to investigate data for 90 million words translated by 879 linguists across 11 language pairs, over 2.5 years. The results of this research indicate that (a) PE is usually but not always faster than HT; (b) average speed values may be misleading; (c) translation speed is highly variable; and (d) edit distance cannot be used as a proxy for post-editing productivity, because it does not correlate strongly with speed.
Tuning the activation function to optimize the forecast horizon of a reservoir computer

Reservoir computing is a machine learning framework where the readouts from a nonlinear system (the reservoir) are trained so that the output from the reservoir, when forced with an input signal, reproduces a desired output signal. A common implementation of reservoir computers is to use a recurrent neural network as the reservoir. The design of this network can have significant effects on the performance of the reservoir computer. In this paper we study the effect of the node activation function on the ability of reservoir computers to learn and predict chaotic time series. We find that the Forecast Horizon (FH), the time during which the reservoir's predictions remain accurate, can vary by an order of magnitude across a set of 16 activation functions used in machine learning. By using different functions from this set, and by modifying their parameters, we explore whether the entropy of node activation levels or the curvature of the activation functions determine the predictive ability of the reservoirs. We find that the FH is low when the activation function is used in a region where it has low curvature, and a positive correlation between curvature and FH. For the activation functions studied we find that the largest FH generally occurs at intermediate levels of the entropy of node activation levels. Our results show that the performance of reservoir computers is very sensitive to the activation function shape. Therefore, modifying this shape in hyperparameter optimization algorithms can lead to improvements in reservoir computer performance.
Frieze patterns and Farey complexes

Frieze patterns have attracted significant attention recently, motivated by their relationship with cluster algebras. A longstanding open problem has been to provide a combinatorial model for frieze patterns over the ring of integers modulo $n$ akin to Conway and Coxeter's celebrated model for positive integer frieze patterns. Here we solve this problem using the Farey complex of the ring of integers modulo $n$; in fact, using more general Farey complexes we provide combinatorial models for frieze patterns over any rings whatsoever. Our strategy generalises that of the first author and of Morier-Genoud et al. for integers and that of Felikson et al. for Eisenstein integers. We also generalise results of Singerman and Strudwick on diameters of Farey graphs, we recover a theorem of Morier-Genoud on enumerating friezes over finite fields, and we classify those frieze patterns modulo $n$ that lift to frieze patterns over the integers in terms of the topology of the corresponding Farey complexes.
Twist-3 contribution to deeply virtual electroproduction of pions

The twist-3 contribution, consisting of twist-2 transversity generalized parton distributions (GPDs) and a twist-3 meson wave function, to deeply virtual pion electroproduction is discussed. The twist-3 meson wave function includes both the $q\bar{q}$ and the $q\bar{q}g$ Fock components. Two methods to regularize the end-point singularities are introduced - quark transverse momenta and a gluon mass. Using existing GPD parameterizations the transverse and the transverse-transverse interference cross sections for $\pi^0$ production are calculated and compared to experimental data.