Miracle-dz/UniFAR-FTUs huggingface dataset:
Improved bilinear Strichartz estimates with application to the well-posedness of periodic generalized KdV type equations

We improve our previous result [L. Molinet and T. Tanaka, Unconditional well-posedness for some nonlinear periodic one-dimensional dispersive equations, J. Funct. Anal. 283 (2022), 109490] on the Cauchy problem for one dimensional dispersive equations with a quite general nonlinearity in the periodic setting. Under the same hypotheses that the dispersive operator behaves for high frequencies as a Fourier multiplier by $ i |\xi|^\alpha \xi $, with $ 1 \le \alpha\le 2 $, and that the nonlinear term is of the form $ \partial_x f(u) $ where $f $ is a real analytic function whose Taylor series around the origin has an infinite radius of convergence, we prove the unconditional LWP of the Cauchy problem in $H^s(\mathbb{T}) $ for $ s\ge 1-\frac{\alpha}{4} $ with $ s>1/2 $. It is worth noticing that this result is optimal in the case $\alpha=2$ (generalized KdV equation) in view of the restriction $ s>1/2 $ for the continuous injection of $ H^s(\mathbb{T}) $ into $ L^\infty(\mathbb{T}) $. Our main new ingredient is the remplacement of improved Strichartz estimates by improved bilinear estimates in the treatment of the worst resonant interactions. Such improved bilinear estimates already appeared in the work of Hani in the context of Schr\"odinger equations on a compact manifold. Finally note that this enables us to derive global existence results for $ \alpha \in [4/3,2] $.
An Information-Theoretic Analysis of Bayesian Reinforcement Learning

Building on the framework introduced by Xu and Raginsky [1] for supervised learning problems, we study the best achievable performance for model-based Bayesian reinforcement learning problems. With this purpose, we define the minimum Bayesian regret (MBR) as the difference between the maximum expected cumulative reward obtainable either by learning from the collected data or by knowing the environment and its dynamics. We specialize this definition to reinforcement learning problems modeled as Markov decision processes (MDPs) whose kernel parameters are unknown to the agent and whose uncertainty is expressed by a prior distribution. One method for deriving upper bounds on the MBR is presented and specific bounds based on the relative entropy and the Wasserstein distance are given. We then focus on two particular cases of MDPs, the multi-armed bandit problem (MAB) and the online optimization with partial feedback problem. For the latter problem, we show that our bounds can recover from below the current information-theoretic bounds by Russo and Van Roy [2].
Far-from-equilibrium kinetic dynamics of $\lambda \phi^4$ theory in an expanding universe

We investigate the far-from-equilibrium behavior of the Boltzmann equation for a gas of massless scalar ﬁeld particles with quartic (tree level) self-interactions ( λφ 4 ) in Friedmann-Lemaitre-Robertson-Walker spacetime. Using a new covariant generating function for the moments of the Boltzmann distribution function, we analytically determine a subset of the spectrum and the corresponding eigenfunctions of the linearized Boltzmann collision operator. We show how the covariant generating function can be also used to ﬁnd the exact equations for the moments in the full nonlinear regime. Diﬀerent than the case of a ultrarelativistic gas of hard spheres (where the total cross section is constant), for λφ 4 the fact that the cross section decreases with energy implies that moments of arbitrarily high order directly couple to low order moments. Numerical solutions for the scalar ﬁeld case are presented and compared to those found for a gas of hard spheres.
A first look at the SMACS0723 JWST ERO: spectroscopic redshifts, stellar masses and star-formation histories

We present a ﬁrst-look analysis of the JWST ERO data in the SMACS J0723.3-7327 cluster ﬁeld. We begin by reporting 10 new spectroscopic redshifts from 𝜆 obs = 1 . 8 − 5 . 2 𝜇 m NIRSpec medium-resolution ( 𝑅 = 𝜆 / Δ 𝜆 = 1000) data. These are all determined via multiple high-SNR emission line detections, with 5 objects at 1 < 𝑧 < 3 displaying multiple rest-frame near-infrared Hydrogen Paschen lines, and 5 objects at 5 < 𝑧 < 9 displaying rest-frame optical Oxygen and Hydrogen Balmer lines. For the 5 higher-redshift galaxies we extract ﬂuxes in 6 NIRCam bands spanning 𝜆 obs = 0 . 8 − 5 𝜇 m and perform spectral energy distribution ﬁtting using these data in combination with existing HST photometry. The 7 < 𝑧 < 9 objects exhibit a U-shaped pattern across the F277W, F356W and F444W bands, indicating the presence of a Balmer break seen in emission (Balmer jump) and high-equivalent-width [O iii] emission. This is indicative of an extremely young stellar population, with the bulk of the current mass having formed within the past 10 Myr. We report robust stellar masses and mean stellar ages from our spectral ﬁtting, with the four 𝑧 > 6 galaxies exhibiting low stellar masses from log 10 ( 𝑀 ∗ / M (cid:12) ) = 7 . 4 − 8 . 6 and correspondingly young mean stellar ages of only a few Myr. This work highlights the critical importance of combining large upcoming NIRCam surveys with NIRSpec follow-up to measure the spectroscopic redshifts necessary to robustly constrain physical parameters.
Factorization of Toeplitz operators

In this article, by considering $T=(T_1,\dots, T_d)$, an $d$-tuple of commuting contractions on a Hilbert space $\mathcal{H}$, we study $T$-Toeplitz operators which consists of bounded operators $X$ on $\mathcal{H}$ such that \[ T_i^*XT_i=X \] for all $i=1,\dots,d$. We show that any positive $T$-Toeplitz operator can be factorized in terms of an isometric pseudo-extension of $T$. A similar factorization result is also obtained for positive pure lower $T$-Toeplitz operators. However, the latter factorization is obtained in terms of a special type of isometric pseudo-extension of $T$, and a certain difference has been observed between the case $d=2$ and $d>2$. In a more general context, by considering $d$-tuples of commuting contractions $S$ and $T$, we also study $(S, T)$-Toeplitz operators.
Multi-block-Single-probe Variance Reduced Estimator for Coupled Compositional Optimization

Variance reduction techniques such as SPIDER/SARAH/STORM have been extensively studied to improve the convergence rates of stochastic non-convex optimization, which usually maintain and update a sequence of estimators for a single function across iterations. What if we need to track multiple functional mappings across iterations but only with access to stochastic samples of $\mathcal{O}(1)$ functional mappings at each iteration? There is an important application in solving an emerging family of coupled compositional optimization problems in the form of $\sum_{i=1}^m f_i(g_i(\mathbf{w}))$, where $g_i$ is accessible through a stochastic oracle. The key issue is to track and estimate a sequence of $\mathbf g(\mathbf{w})=(g_1(\mathbf{w}), \ldots, g_m(\mathbf{w}))$ across iterations, where $\mathbf g(\mathbf{w})$ has $m$ blocks and it is only allowed to probe $\mathcal{O}(1)$ blocks to attain their stochastic values and Jacobians. To improve the complexity for solving these problems, we propose a novel stochastic method named Multi-block-Single-probe Variance Reduced (MSVR) estimator to track the sequence of $\mathbf g(\mathbf{w})$. It is inspired by STORM but introduces a customized error correction term to alleviate the noise not only in stochastic samples for the selected blocks but also in those blocks that are not sampled. With the help of the MSVR estimator, we develop several algorithms for solving the aforementioned compositional problems with improved complexities across a spectrum of settings with non-convex/convex/strongly convex/Polyak-{\L}ojasiewicz (PL) objectives. Our results improve upon prior ones in several aspects, including the order of sample complexities and dependence on the strong convexity parameter. Empirical studies on multi-task deep AUC maximization demonstrate the better performance of using the new estimator.
A Comprehensive Empirical Investigation on Failure Clustering in Parallel Debugging

The clustering technique has attracted a lot of attention as a promising strategy for parallel debugging in multi-fault scenarios, this heuristic approach (i.e., failure indexing or fault isolation) enables developers to perform multiple debugging tasks simultaneously through dividing failed test cases into several disjoint groups. When using statement ranking representation to model failures for better clustering, several factors influence clustering effectiveness, including the risk evaluation formula (REF), the number of faults (NOF), the fault type (FT), and the number of successful test cases paired with one individual failed test case (NSP1F). In this paper, we present the first comprehensive empirical study of how these four factors influence clustering effectiveness. We conduct extensive controlled experiments on 1060 faulty versions of 228 simulated faults and 141 real faults, and the results reveal that: 1) GP19 is highly competitive across all REFs, 2) clustering effectiveness decreases as NOF increases, 3) higher clustering effectiveness is easier to achieve when a program contains only predicate faults, and 4) clustering effectiveness remains when the scale of NSP1F is reduced to 20%.
Adversarial Pixel Restoration as a Pretext Task for Transferable Perturbations

Transferable adversarial attacks optimize adversaries from a pretrained surrogate model and known label space to fool the unknown black-box models. Therefore, these attacks are restricted by the availability of an effective surrogate model. In this work, we relax this assumption and propose Adversarial Pixel Restoration as a self-supervised alternative to train an effective surrogate model from scratch under the condition of no labels and few data samples. Our training approach is based on a min-max scheme which reduces overfitting via an adversarial objective and thus optimizes for a more generalizable surrogate model. Our proposed attack is complimentary to the adversarial pixel restoration and is independent of any task specific objective as it can be launched in a self-supervised manner. We successfully demonstrate the adversarial transferability of our approach to Vision Transformers as well as Convolutional Neural Networks for the tasks of classification, object detection, and video segmentation. Our training approach improves the transferability of the baseline unsupervised training method by 16.4% on ImageNet val. set. Our codes&pre-trained surrogate models are available at: https://github.com/HashmatShadab/APR
Spatial and temporal correlations in neural networks with structured connectivity

Correlated fluctuations in the activity of neural populations reflect the network's dynamics and connectivity. The temporal and spatial dimensions of neural correlations are interdependent. However, prior theoretical work mainly analyzed correlations in either spatial or temporal domains, oblivious to their interplay. We show that the network dynamics and connectivity jointly define the spatiotemporal profile of neural correlations. We derive analytical expressions for pairwise correlations in networks of binary units with spatially arranged connectivity in one and two dimensions. We find that spatial interactions among units generate multiple timescales in auto- and cross-correlations. Each timescale is associated with fluctuations at a particular spatial frequency, making a hierarchical contribution to the correlations. External inputs can modulate the correlation timescales when spatial interactions are nonlinear, and the modulation effect depends on the operating regime of network dynamics. These theoretical results open new ways to relate connectivity and dynamics in cortical networks via measurements of spatiotemporal neural correlations.
Josephson Diode Effect in High-Mobility InSb Nanoflags

We report nonreciprocal dissipation-less transport in single ballistic InSb nanoflag Josephson junctions. Applying an in-plane magnetic field, we observe an inequality in supercurrent for the two opposite current propagation directions. Thus, these devices can work as Josephson diodes, with dissipation-less current flowing in only one direction. For small fields, the supercurrent asymmetry increases linearly with external field, and then it saturates as the Zeeman energy becomes relevant, before it finally decreases to zero at higher fields. The effect is maximum when the in-plane field is perpendicular to the current vector, which identifies Rashba spin–orbit coupling as the main symmetry-breaking mechanism. While a variation in carrier concentration in these high-quality InSb nanoflags does not significantly influence the supercurrent asymmetry, it is instead strongly suppressed by an increase in temperature. Our experimental findings are consistent with a model for ballistic short junctions and show that the diode effect is intrinsic to this material.
Shrinking target for $C^1$ weakly conformal IFS with overlaps

In this article, we study the Hausdor dimension of weakly conformal IFS's shrinking targets with possible overlaps, provided the conformality dimension of the systems and the dimension of the attractor are equal. Those results extends the works of Hill-Velani as well as the results obtained in [6] for self-similar IFS's.
MixTailor: Mixed Gradient Aggregation for Robust Learning Against Tailored Attacks

Implementations of SGD on distributed systems create new vulnerabilities, which can be identified and misused by one or more adversarial agents. Recently, it has been shown that well-known Byzantine-resilient gradient aggregation schemes are indeed vulnerable to informed attackers that can tailor the attacks (Fang et al., 2020; Xie et al., 2020b). We introduce MixTailor, a scheme based on randomization of the aggregation strategies that makes it impossible for the attacker to be fully informed. Deterministic schemes can be integrated into MixTailor on the fly without introducing any additional hyperparameters. Randomization decreases the capability of a powerful adversary to tailor its attacks, while the resulting randomized aggregation scheme is still competitive in terms of performance. For both iid and non-iid settings, we establish almost sure convergence guarantees that are both stronger and more general than those available in the literature. Our empirical studies across various datasets, attacks, and settings, validate our hypothesis and show that MixTailor successfully defends when well-known Byzantine-tolerant schemes fail.
MWS and FWS Codes for Coordinate-Wise Weight Functions

A combinatorial problem concerning the maximum size of the (hamming) weight set of an $[n,k]_q$ linear code was recently introduced. Codes attaining the established upper bound are the Maximum Weight Spectrum (MWS) codes. Those $[n,k]_q $ codes with the same weight set as $ \mathbb{F}_q^n $ are called Full Weight Spectrum (FWS) codes. FWS codes are necessarily ``short", whereas MWS codes are necessarily ``long". For fixed $ k,q $ the values of $ n $ for which an $ [n,k]_q $-FWS code exists are completely determined, but the determination of the minimum length $ M(H,k,q) $ of an $ [n,k]_q $-MWS code remains an open problem. The current work broadens discussion first to general coordinate-wise weight functions, and then specifically to the Lee weight and a Manhattan like weight. In the general case we provide bounds on $ n $ for which an FWS code exists, and bounds on $ n $ for which an MWS code exists. When specializing to the Lee or to the Manhattan setting we are able to completely determine the parameters of FWS codes. As with the Hamming case, we are able to provide an upper bound on $ M(\mathcal{L},k,q) $ (the minimum length of Lee MWS codes), and pose the determination of $ M(\mathcal{L},k,q) $ as an open problem. On the other hand, with respect to the Manhattan weight we completely determine the parameters of MWS codes.
Massively Parallel Algorithms for Small Subgraph Counting

Over the last two decades, frameworks for distributed-memory parallel computation, such as MapReduce, Hadoop, Spark and Dryad, have gained significant popularity with the growing prevalence of large network datasets. The Massively Parallel Computation (MPC) model is the de-facto standard for studying graph algorithms in these frameworks theoretically. Subgraph counting is one such fundamental problem in analyzing massive graphs, with the main algorithmic challenges centering on designing methods which are both scalable and accurate. Given a graph $G=(V, E)$ with $n$ vertices, $m$ edges and $T$ triangles, our first result is an algorithm that outputs a $(1+\varepsilon)$-approximation to $T$, with asymptotically \emph{optimal round and total space complexity} provided any $S \geq \max{(\sqrt m, n^2/m)}$ space per machine and assuming $T=\Omega(\sqrt{m/n})$. Our result gives a quadratic improvement on the bound on $T$ over previous works. We also provide a simple extension of our result to counting \emph{any} subgraph of $k$ size for constant $k \geq 1$. Our second result is an $O_{\varepsilon}(\log \log n)$-round algorithm for exactly counting the number of triangles, whose total space usage is parametrized by the \emph{arboricity} $\alpha$ of the input graph. We extend this result to exactly counting $k$-cliques for any constant $k$. Finally, we prove that a recent result of Bera, Pashanasangi and Seshadhri (ITCS 2020) for exactly counting all subgraphs of size at most $5$ can be implemented in the MPC model in total space.
Limits of Dense Simplicial Complexes

We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0,1]-valued functions on unit cubes of increasing dimension, each corresponding to a dimension of the abstract simplicial complex. We show that convergence in homomorphism density implies convergence in a cut-metric, and vice versa, as well as showing that simplicial complexes sampled from the limit objects closely resemble its structure. Applying this framework, we also partially characterize the convergence of nonuniform hypergraphs.
The Lottery Ticket Hypothesis for Self-attention in Convolutional Neural Network

Recently many plug-and-play self-attention modules (SAMs) are proposed to enhance the model generalization by exploiting the internal information of deep convolutional neural networks (CNNs). In general, previous works ignore where to plug in the SAMs since they connect the SAMs individually with each block of the entire CNN backbone for granted, leading to incremental computational cost and the number of parameters with the growth of network depth. However, we empirically find and verify some counterintuitive phenomena that: (a) Connecting the SAMs to all the blocks may not always bring the largest performance boost, and connecting to partial blocks would be even better; (b) Adding the SAMs to a CNN may not always bring a performance boost, and instead it may even harm the performance of the original CNN backbone. Therefore, we articulate and demonstrate the Lottery Ticket Hypothesis for Self-attention Networks: a full self-attention network contains a subnetwork with sparse self-attention connections that can (1) accelerate inference, (2) reduce extra parameter increment, and (3) maintain accuracy. In addition to the empirical evidence, this hypothesis is also supported by our theoretical evidence. Furthermore, we propose a simple yet effective reinforcement-learning-based method to search the ticket, i.e., the connection scheme that satisfies the three above-mentioned conditions. Extensive experiments on widely-used benchmark datasets and popular self-attention networks show the effectiveness of our method. Besides, our experiments illustrate that our searched ticket has the capacity of transferring to some vision tasks, e.g., crowd counting and segmentation.
Examining the Properties of Low-luminosity Hosts of Type Ia Supernovae from ASAS-SN

We present a spectroscopic analysis of 44 low-luminosity host galaxies of Type Ia supernovae (SNe Ia) detected by the All-Sky Automated Survey for Supernovae (ASAS-SN), using hydrogen, oxygen, and sulfur emission lines to measure metallicities and star formation rates. We find no statistically significant evidence that the star formation activity and metallicities of the galaxies in our sample are inconsistent with galaxies of similar luminosities and masses. We identify two 3σ outlier galaxies that have high metallicities for their stellar masses, but find that their other properties are consistent with general galaxies. The overall consistency between our sample and general galaxy samples further strengthens the evidence from more luminous SN Ia host galaxy samples that SN Ia host galaxies are typical.
Explosion Mechanism of Core-collapse Supernovae: Role of the Si/Si–O Interface

We present a simple criterion to predict the explodability of massive stars based on the density and entropy profiles before collapse. If a pronounced density jump is present near the Si/Si–O interface, the star will likely explode. We develop a quantitative criterion by using ∼1300 1D simulations where ν-driven turbulence is included via time-dependent mixing-length theory. This criterion correctly identifies the outcome of the supernova more than 90% of the time. We also find no difference in how this criterion performs on two different sets of progenitors, evolved using two different stellar evolution codes: FRANEC and KEPLER. The explodability as a function of mass of the two sets of progenitors is very different, showing: (i) that uncertainties in the stellar evolution prescriptions influence the predictions of supernova explosions; (ii) the most important properties of the pre-collapse progenitor that influence the explodability are its density and entropy profiles. We highlight the importance that ν-driven turbulence plays in the explosion by comparing our results to previous works.
Learning correspondence in Frequency Domain by a Latent-Space Similarity Loss for Multispectral Pansharpening

The process of fusing a high spatial resolution (HR) panchromatic (PAN) image and a low spatial resolution (LR) multispectral (MS) image to obtain an HRMS image is known as pansharpening. With the development of convolutional neural networks, the performance of pansharpening methods has been improved, however, the blurry eﬀects and the spectral distortion still exist in their fusion results due to the insuﬃciency in details learning and the mismatch between the high-frequency (HF) and low-frequency (LF) components. Therefore, the improvements of spatial details at the premise of reducing spectral distortion is still a challenge. In this paper, we propose a frequency-aware network (FAN) together with a novel latent-space similarity loss to address above mentioned problems. FAN is composed of three modules, where the frequency feature extraction module aims to extract features in the frequency domain with the help of discrete wavelet transform (DWT) layers, and the inverse DWT (IDWT) layers are then utilized in the frequency feature fusion module to reconstruct the features. Finally, the fusion results are obtained through the reconstruction module. In order to learn the correspondence, we also propose a latent-∗