Miracle-dz/UniFAR-FTUs huggingface dataset:
For Pre-Trained Vision Models in Motor Control, Not All Policy Learning Methods are Created Equal

In recent years, increasing attention has been directed to leveraging pre-trained vision models for motor control. While existing works mainly emphasize the importance of this pre-training phase, the arguably equally important role played by downstream policy learning during control-specific fine-tuning is often neglected. It thus remains unclear if pre-trained vision models are consistent in their effectiveness under different control policies. To bridge this gap in understanding, we conduct a comprehensive study on 14 pre-trained vision models using 3 distinct classes of policy learning methods, including reinforcement learning (RL), imitation learning through behavior cloning (BC), and imitation learning with a visual reward function (VRF). Our study yields a series of intriguing results, including the discovery that the effectiveness of pre-training is highly dependent on the choice of the downstream policy learning algorithm. We show that conventionally accepted evaluation based on RL methods is highly variable and therefore unreliable, and further advocate for using more robust methods like VRF and BC. To facilitate more universal evaluations of pre-trained models and their policy learning methods in the future, we also release a benchmark of 21 tasks across 3 different environments alongside our work.
Reweighted Mixup for Subpopulation Shift

Subpopulation shift exists widely in many real-world applications, which refers to the training and test distributions that contain the same subpopulation groups but with different subpopulation proportions. Ignoring subpopulation shifts may lead to significant performance degradation and fairness concerns. Importance reweighting is a classical and effective way to handle the subpopulation shift. However, recent studies have recognized that most of these approaches fail to improve the performance especially when applied to over-parameterized neural networks which are capable of fitting any training samples. In this work, we propose a simple yet practical framework, called reweighted mixup (RMIX), to mitigate the overfitting issue in over-parameterized models by conducting importance weighting on the ''mixed'' samples. Benefiting from leveraging reweighting in mixup, RMIX allows the model to explore the vicinal space of minority samples more, thereby obtaining more robust model against subpopulation shift. When the subpopulation memberships are unknown, the training-trajectories-based uncertainty estimation is equipped in the proposed RMIX to flexibly characterize the subpopulation distribution. We also provide insightful theoretical analysis to verify that RMIX achieves better generalization bounds over prior works. Further, we conduct extensive empirical studies across a wide range of tasks to validate the effectiveness of the proposed method.
Do We Train on Test Data? The Impact of Near-Duplicates on License Plate Recognition

This work draws attention to the large fraction of near-duplicates in the training and test sets of datasets widely adopted in License Plate Recognition (LPR) research. These duplicates refer to images that, although different, show the same license plate. Our experiments, conducted on the two most popular datasets in the field, show a substantial decrease in recognition rate when six well-known models are trained and tested under fair splits, that is, in the absence of duplicates in the training and test sets. Moreover, in one of the datasets, the ranking of models changed considerably when they were trained and tested under duplicate-free splits. These findings suggest that such duplicates have significantly biased the evaluation and development of deep learning-based models for LPR. The list of near-duplicates we have found and proposals for fair splits are publicly available for further research at https://raysonlaroca.github. io/supp/lpr-train-on-test/.
Statistical mechanics for non-Hermitian quantum systems

We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in conjunction with the system's Hamiltonian, dictates the equilibrium state. By elucidating the relationship between the Hamiltonian and the supported conserved quantity, we propose criteria for discerning equilibrium states with finite relaxation times. Although our findings indicate that only non-Hermitian systems with real energy spectrum precisely possess such conserved quantities, we also demonstrate that an effective conserved quantity can manifest in certain systems with complex energy spectra. The effective conserved quantity, alongside the effective transitions within their associated subspace, collectively determines the system's equilibrium state. Our results provide valuable insights into non-Hermitian systems across more realistic contexts and hold potential for applications in a diverse range of physical systems.
Markov Games with Decoupled Dynamics: Price of Anarchy and Sample Complexity

This paper studies the finite-time horizon Markov games where the agents' dynamics are decoupled but the rewards can possibly be coupled across agents. The policy class is restricted to local policies where agents make decisions using their local state. We first introduce the notion of smooth Markov games which extends the smoothness argument for normal form games ([1], [2]) to our setting, and leverage the smoothness property to bound the price of anarchy of the Markov game. For a specific type of Markov game called the Markov potential game, we also develop a distributed learning algorithm, multi-agent soft policy iteration (MA-SPI), which provably converges to a Nash equilibrium. Sample complexity of the algorithm is also provided. Lastly, our results are validated using a dynamic covering game.
A geometric analysis of the SIRS model with secondary infections

We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria of the system and analyze their stability. We find conditions for the existence of two endemic equilibria, for some cases in which $\mathcal{R}_0<1$. Then, we unravel the interplay of the three time scales, providing conditions to foresee whether the system evolves in all three scales, or only in the fast and the intermediate ones. We conclude with numerical simulations and bifurcation analysis, to complement our analytical results.
Magnetic field driven micro-convection in the Hele-Shaw cell: the Brinkman model and its comparison with experiment

The micro-convection caused by the ponderomotive forces of the self-magnetic field in a magnetic fluid is studied here both numerically and experimentally. The theoretical approach based on the general Brinkman model substantially improves the description with respect to the previously proposed Darcy model. The predictions of both models are here compared to finely controlled experiments. The Brinkman model, in contrast to the Darcy model, allows us to describe the formation of mushrooms on the plumes of the micro-convective flow and the width of the fingers. In the Brinkman approach, excellent quantitative agreement is also obtained for the finger velocity dynamics and the velocity maximal values as a function of the magnetic Rayleigh number. The diffusion coefficient of particles of the water-based magnetic colloid determined by the threshold field strength value of the micro-convection is significantly larger than the diffusion coefficient of individual particles. This result is confirmed by independent measurements of the diffusion coefficient at the smearing of the diffusion front.
On the state-space model of unawareness

We show that the knowledge of an agent carrying non-trivial unawareness violates the standard property of 'necessitation', therefore necessitation cannot be used to refute the standard state-space model. A revised version of necessitation preserves non-trivial unawareness and solves the classical Dekel-Lipman-Rustichini result. We propose a generalised knowledge operator consistent with the standard state-space model of unawareness, including the model of infinite state-space.
Stability for the Surface Diffusion Flow

We study the global existence and stability of surface diffusion flow (the normal velocity is given by the Laplacian of the mean curvature) of smooth boundaries of subsets of the $n$--dimensional flat torus. More precisely, we show that if a smooth set is ``close enough'' to a strictly stable critical set for the Area functional under a volume constraint, then the surface diffusion flow of its boundary hypersurface exists for all time and asymptotically converges to the boundary of a ``translated'' of the critical set. This result was obtained in dimension $n=3$ by Acerbi, Fusco, Julin and Morini (extending previous results for spheres of Escher, Mayer and Simonett and Elliott and Garcke in dimension $n=2$). Our work generalizes such conclusion to any dimension $n\in\mathbb N$. For sake of clarity, we show all the details in dimension $n=4$ and we list the necessary modifications to the quantities involved in the proof in the general $n$--dimensional case, in the last section.
Prophet Inequalities: Separating Random Order from Order Selection

Prophet inequalities are a central object of study in optimal stopping theory. A gambler is sent values online, sampled from an instance of independent distributions, in an adversarial, random or selected order, depending on the model. When observing each value, the gambler either accepts it as a reward or irrevocably rejects it and proceeds to observe the next value. The goal of the gambler, who cannot see the future, is maximising the expected value of the reward while competing against the expectation of a prophet (the offline maximum). In other words, one seeks to maximise the gambler-to-prophet ratio of the expectations. The model, in which the gambler selects the arrival order first, and then observes the values, is known as Order Selection. In this model a ratio of $0.7251$ has been proved to be attainable for any instance. In very recent work, this has been improved up to $0.7258$. If the gambler chooses the arrival order (uniformly) at random, we obtain the Random Order model. The worst case ratio over all possible instances has been extensively studied for at least $40$ years. In the recent work aforementioned, through simulations, this ratio has been shown to be at most $0.7254$ for the Random Order model, thus establishing for the first time that carefully choosing the order, instead of simply taking it at random, benefits the gambler. We give an alternative, more rigorous proof of this fact, by showing mathematically that in the Random Order model, no algorithm can achieve a ratio larger than $0.7235$. This sets a new state-of-the-art hardness for this model, and establishes more formally that there is a real benefit in choosing the order.
MJO Moisture Budget during DYNAMO in a Cloud-Resolving Model

AbstractContributions by different physical processes and cloud types to the sum of the large-scale vertical moisture advection and apparent moisture sink observed by the DYNAMO field campaign northern sounding array during the passage of a Madden–Julian oscillation (MJO) event are estimated using a cloud-resolving model. The sum of these two moisture budget terms is referred to as the column-confined moisture tendency MC. Assuming diabatic balance, the contribution of different physical processes and cloud types to the large-scale vertical velocity and MC can be estimated using simulated diabatic tendencies and the domain-averaged static stability and vertical moisture gradient. Low-level moistening preceding MJO passage is captured by MC and dominated by the effects of shallow clouds. Because of the large vertical moisture gradient at this level, condensational heating in these clouds generates ascent and vertical moisture advection overwhelming the removal of water vapor by condensation. Shallow convec.
Deep Learning of Systematic Sea Ice Model Errors From Data Assimilation Increments

Data assimilation is often viewed as a framework for correcting short‐term error growth in dynamical climate model forecasts. When viewed on the time scales of climate however, these short‐term corrections, or analysis increments, can closely mirror the systematic bias patterns of the dynamical model. In this study, we use convolutional neural networks (CNNs) to learn a mapping from model state variables to analysis increments, in order to showcase the feasibility of a data‐driven model parameterization which can predict state‐dependent model errors. We undertake this problem using an ice‐ocean data assimilation system within the Seamless system for Prediction and EArth system Research (SPEAR) model, developed at the Geophysical Fluid Dynamics Laboratory, which assimilates satellite observations of sea ice concentration every 5 days between 1982 and 2017. The CNN then takes inputs of data assimilation forecast states and tendencies, and makes predictions of the corresponding sea ice concentration increments. Specifically, the inputs are states and tendencies of sea ice concentration, sea‐surface temperature, ice velocities, ice thickness, net shortwave radiation, ice‐surface skin temperature, sea‐surface salinity, as well as a land‐sea mask. We find the CNN is able to make skillful predictions of the increments in both the Arctic and Antarctic and across all seasons, with skill that consistently exceeds that of a climatological increment prediction. This suggests that the CNN could be used to reduce sea ice biases in free‐running SPEAR simulations, either as a sea ice parameterization or an online bias correction tool for numerical sea ice forecasts.
Computing equivalence classes of finite group actions on orientable surfaces: A dynamic survey

This paper focuses on the classification of classes of topological equivalence of finite group actions on Riemann surfaces. By the Riemann-Hurwitz bound, there are just finitely many groups that act conformally on a closed orientable surface $\mathcal{S}_g$ of genus $g\geq 2$. With each such action of a group $\mathrm{G}$ on $\mathcal{S}_g$ one can associate the fundamental group $\Gamma=\pi(\mathcal{O})$ of the quotient orbifold $\mathcal{O}=\mathcal{S}_g/\mathrm{G}$, isomorphic to a Fuchsian group determined completely by orbifold's signature. The Riemann existence theorem reduces the problem of the existence of an action of $\mathrm{G}$ on $\mathcal{S}_g$ to a purely group-theoretical problem of deciding whether there is an smooth epimorphism mapping the Fuchsian group $\Gamma$ onto the group $\mathrm{G}$. Using computer algebra systems such as \textsc{Magma} or GAP, together with the library of small groups, the generation of all finite group actions on a surface of fixed small genus $g\geq 2$ becomes almost a routine procedure. The difficult part is to determine the classes of these actions with respect to topological equivalence. To achieve this, one needs to investigate the action of the automorphism group of a Fuchsian group on the set of finite group actions on $\mathcal{S}_g$ with the corresponding signature. In this paper we derive several results on the topological equivalence of finite group actions on Riemann surfaces. As an application, we derive complete lists of finite group actions of genus $g\leq 9$ distinguished up to the topological equivalence. A summary of the actions can be found in Appendix, the reader interested in more details is referred to the web page [22]. It is expected that we will be able to extend the list to higher genera, refreshed partial results are available on the web page. The following text is an extended version of the paper [23].
Extractive Summarization via ChatGPT for Faithful Summary Generation

Extractive summarization is a crucial task in natural language processing that aims to condense long documents into shorter versions by directly extracting sentences. The recent introduction of large language models has attracted significant interest in the NLP community due to its remarkable performance on a wide range of downstream tasks. This paper first presents a thorough evaluation of ChatGPT's performance on extractive summarization and compares it with traditional fine-tuning methods on various benchmark datasets. Our experimental analysis reveals that ChatGPT exhibits inferior extractive summarization performance in terms of ROUGE scores compared to existing supervised systems, while achieving higher performance based on LLM-based evaluation metrics. In addition, we explore the effectiveness of in-context learning and chain-of-thought reasoning for enhancing its performance. Furthermore, we find that applying an extract-then-generate pipeline with ChatGPT yields significant performance improvements over abstractive baselines in terms of summary faithfulness. These observations highlight potential directions for enhancing ChatGPT's capabilities in faithful summarization using two-stage approaches.
Quasi‐linear simulations of inner radiation belt electron pitch angle and energy distributions

“Peculiar” or “butterfly” electron pitch angle distributions (PADs), with minima near 90°, have recently been observed in the inner radiation belt. These electrons are traditionally treated by pure pitch angle diffusion, driven by plasmaspheric hiss, lightning‐generated whistlers, and VLF transmitter signals. Since this leads to monotonic PADs, energy diffusion by magnetosonic waves has been proposed to account for the observations. We show that the observed PADs arise readily from two‐dimensional diffusion at L = 2, with or without magnetosonic waves. It is necessary to include cross diffusion, which accounts for the relationship between pitch angle and energy changes. The distribution of flux with energy is also in good agreement with observations between 200 keV and 1 MeV, dropping to very low levels at higher energy. Thus, at this location radial diffusion may be negligible at subrelativistic as well as ultrarelativistic energy.
A Hybrid Domain Decomposition Method and its Applications to Contact Problems TR2009-924

Our goal is to solve nonlinear contact problems. We consider bodies in contact with each other divided into subdomains, which in turn are unions of elements. The contact surface between the bodies is unknown a priori, and we have a nonpenetration condition between the bodies, which is essentially an inequality constraint. We choose to use an active set method to solve such problems, which has both outer iterations in which the active set is updated, and inner iterations in which a (linear) minimization problem is solved on the current active face. In the first part of this dissertation, we review the basics of domain decomposition methods. In the second part, we consider how to solve the inner minimization problems. Using an approach based purely on FETI algorithms with only Lagrange multi- pliers as unknowns, as has been developed by the engineering community, does not lead to a scalable algorithm with respect to the number of subdomains in each body. We prove that such an algorithm has a condition number estimate which depends linearly on the number of subdomains across a body; numerical experiments suggest that this is the best possible bound. We also consider a new method based on the saddle point formulation of the FETI methods with both displacement vectors and Lagrange multipliers as unknowns. The resulting system is solved with a block-diagonal preconditioner which combines the one-level FETI and the BDDC methods. This approach allows the use of inexact solvers. We show that this new method is scalable with respect to the number of subdomains, and that its convergence rate depends only logarithmically on the number of degrees of freedom of the subdomains and bodies. In the last part of this dissertation, a model contact problem is solved by two approaches. The first one is a nonlinear algorithm which combines an active set method and the new method of Chapter 4. We also present a novel way of finding an initial active set. The second one uses the SMALBE algorithm, developed by Dostal et al. We show that the former approach has advantages over the latter.
Rotation in Event Horizon Telescope Movies

The Event Horizon Telescope (EHT) has produced images of M87* and Sagittarius A*, and will soon produce time sequences of images, or movies. In anticipation of this, we describe a technique to measure the rotation rate, or pattern speed Ω p , from movies using an autocorrelation technique. We validate the technique on Gaussian random field models with a known rotation rate and apply it to a library of synthetic images of Sgr A* based on general relativistic magnetohydrodynamics simulations. We predict that EHT movies will have Ω p ≈ 1° per GMc −3, which is of order 15% of the Keplerian orbital frequency in the emitting region. We can plausibly attribute the slow rotation seen in our models to the pattern speed of inward-propagating spiral shocks. We also find that Ω p depends strongly on inclination. Application of this technique will enable us to compare future EHT movies with the clockwise rotation of Sgr A* seen in near-infrared flares by GRAVITY. Pattern speed analysis of future EHT observations of M87* and Sgr A* may also provide novel constraints on black hole inclination and spin, as well as an independent measurement of black hole mass.
Twelve-crystal prototype of Li2MoO4 scintillating bolometers for CUPID and CROSS experiments

An array of twelve 0.28 kg lithium molybdate (LMO) low-temperature bolometers equipped with 16 bolometric Ge light detectors, aiming at optimization of detector structure for CROSS and CUPID double-beta decay experiments, was constructed and tested in a low-background pulse-tube-based cryostat at the Canfranc underground laboratory in Spain. Performance of the scintillating bolometers was studied depending on the size of phonon NTD-Ge sensors glued to both LMO and Ge absorbers, shape of the Ge light detectors (circular vs. square, from two suppliers), in different light collection conditions (with and without reflector, with aluminum coated LMO crystal surface). The scintillating bolometer array was operated over 8 months in the low-background conditions that allowed to probe a very low, μBq/kg, level of the LMO crystals radioactive contamination by 228Th and 226Ra.