Miracle-dz/UniFAR-FTUs huggingface dataset:
Hypergraph Clustering in the Weighted Stochastic Block Model via Convex Relaxation of Truncated MLE

We study hypergraph clustering under the weighted $d$-uniform hypergraph stochastic block model ($d$-WHSBM), where each edge consisting of $d$ nodes has higher expected weight if $d$ nodes are from the same community compared to edges consisting of nodes from different communities. We propose a new hypergraph clustering algorithm, which is a convex relaxation of truncated maximum likelihood estimator (CRTMLE), that can handle the relatively sparse, high-dimensional regime of the $d$-WHSBM with community sizes of different orders. We provide performance guarantees of this algorithm under a unified framework for different parameter regimes, and show that it achieves the order-wise optimal or the best existing results for approximately balanced community sizes. We also demonstrate the first recovery guarantees for the setting with growing number of communities of unbalanced sizes.
Eigenrays in 3D heterogeneous anisotropic media: Part IV -- Geometric spreading from traveltime Hessian

Considering 3D heterogeneous anisotropic media, in Part III of this study we obtain the finite-element solution for the stationary ray path between two fixed endpoints using the finite element approach. It involves computation of the global (all-node) traveltime gradient vector and Hessian matrix, with respect to the nodal location and direction components. The global traveltime Hessian of the resolved stationary ray also plays an important role for obtaining the dynamic characteristics along the ray. It is a band matrix that includes the spatial, directional and mixed second derivatives of the traveltime at all nodes and nodal pairs. In Parts V, VI and VII of this study we explicitly use the global traveltime Hessian for solving the dynamic ray tracing equation, to obtain the geometric spreading at each point along the ray. Moreover, the dynamic ray tracing makes it possible to identify/classify caustics along the ray. In this part (Part IV) we propose an original two-stage approach for computing the relative geometric spreading of the entire ray path without explicitly performing the dynamic ray tracing. The first stage consists of an efficient algorithm for reducing the already computed global traveltime Hessian into a endpoint spatial traveltime Hessian. The second stage involves application of a known workflow for computing the geometrical spreading using the endpoint traveltime Hessian. Note that the method proposed in this part (Part IV) does not deliver information about caustics, nor the geometric spreading at intermediate points of the stationary ray path. Throughout the examples presented in Part VII we demonstrate the accuracy of the method proposed in this part over a set of isotropic and anisotropic examples by comparing the geometric spreading computed from this method based on the traveltime Hessian reduction with the one computed from the dynamic ray tracing.
Explore Aggressively, Update Conservatively: Stochastic Extragradient Methods with Variable Stepsize Scaling

Owing to their stability and convergence speed, extragradient methods have become a staple for solving large-scale saddle-point problems in machine learning. The basic premise of these algorithms is the use of an extrapolation step before performing an update; thanks to this exploration step, extra-gradient methods overcome many of the non-convergence issues that plague gradient descent/ascent schemes. On the other hand, as we show in this paper, running vanilla extragradient with stochastic gradients may jeopardize its convergence, even in simple bilinear models. To overcome this failure, we investigate a double stepsize extragradient algorithm where the exploration step evolves at a more aggressive time-scale compared to the update step. We show that this modification allows the method to converge even with stochastic gradients, and we derive sharp convergence rates under an error bound condition.
Matter-wave interferometry using a levitated magnetic nanoparticle

The superposition principle is one of the bizarre predictions of quantum mechanics. Nevertheless, it has been experimentally verified using electrons, photons, atoms, and molecules. In this article, using a $20~$nm levitated ferromagnetic FePt nanoparticle, an exotic all optical spin polarization technique and the matter-wave interferometry, we show that a mesoscopic spatial Schrodinger cat can be created. Additionally, we argue that the maximum spatial separation between the delocalized wavepackets can be $25~\mu m$ and is significantly larger than the object itself.
Elliptic Equations with Degenerate Weights

We obtain new local Calderon-Zygmund estimates for elliptic equations with matrix-valued weights for linear as well as non-linear equations. We introduce a novel log-BMO condition on the weight M. In particular, we assume smallness of the logarithm of the matrix-valued weight in BMO. This allows to include degenerate, discontinuous weights. We provide examples that show the sharpness of the estimates in terms of the log-BMO-norm.
Ellipsoidal Subspace Support Vector Data Description

In this paper, we propose a novel method for transforming data into a low-dimensional space optimized for one-class classification. The proposed method iteratively transforms data into a new subspace optimized for ellipsoidal encapsulation of target class data. We provide both linear and non-linear formulations for the proposed method. The method takes into account the covariance of the data in the subspace; hence, it yields a more generalized solution as compared to the data description in the subspace by hyperspherical encapsulation of target class data. We propose different regularization terms expressing the class variance in the projected space. We compare the results with classic and recently proposed one-class classification methods and achieve competing results and show clear improvement compared to the other support vector based methods. The proposed method is also noticed to converge much faster than recently proposed Subspace Support Vector Data Description.
Observable quantum loop effects in the sky

Expanding on [1], we analyze in detail the single field chaotic inflationary models plus a cosine modulation term, augmented by a light scalar field with inflaton dependent oscillatory mass term. We work out in detail the Feynman diagrams and compute one, two and in general estimate higher loop two and three point functions in the in-in formulation. We explicitly establish how the oscillatory mass term can amplify one-loop effects to dominate over the tree as well as the higher loop contributions. The power spectrum of curvature perturbations of this model is hence enhanced compared to the simple single field chaotic model. As a consequence, one can suppress the tensor to scalar ratio r and have a different expression for scalar spectral tilt and the running of the tilt, opening the way to reconcile chaotic models with convex potential and the Planck data. As in monodromy inflation models, we also have a cosine modulation in the spectral tilt. We also analyze the bispectrum, which can be dominated by the amplified one-loop effects, yielding a new shape in non-Gaussianity. We discuss the bounds on parameter space from all available CMB observables and possible implications for reheating.
Spectral Classification of B Stars: The Empirical Sequence Using SDSS-IV/APOGEE Near-IR Data

We present a semi-empirical spectral classification scheme for normal B-type stars using near-infrared (NIR) spectra (1.5–1.7 μm) from the Sloan Digital Sky Survey Apache Point Observatory Galaxy Evolution Experiment (APOGEE2)-N data release 14 (DR14) database. The main motivation for working with B-type stars is their importance in the evolution of young stellar clusters; however, we also take advantage of having a numerous sample (316 stars) of B-type star candidates in APOGEE2-N, for which we also have optical (3600–9100 Å) counterparts from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) survey. By first obtaining an accurate spectral classification of the sources using the LAMOST DR3 spectra and the canonical spectral classification scheme, we found a linear relation between optical spectral types and the equivalent widths of the hydrogen lines of the Brackett series in the APOGEE2-N NIR spectra. This relation extends smoothly from a similar relation for O and early B stars found by Roman-Lopes et al. This way, we obtain a catalog of B-type sources with features in both the optical and NIR and a classification scheme refined down to one spectral subclass.
Adversarial Attacks on Monocular Depth Estimation

Recent advances of deep learning have brought exceptional performance on many computer vision tasks such as semantic segmentation and depth estimation. However, the vulnerability of deep neural networks towards adversarial examples have caused grave concerns for real-world deployment. In this paper, we present to the best of our knowledge the first systematic study of adversarial attacks on monocular depth estimation, an important task of 3D scene understanding in scenarios such as autonomous driving and robot navigation. In order to understand the impact of adversarial attacks on depth estimation, we first define a taxonomy of different attack scenarios for depth estimation, including non-targeted attacks, targeted attacks and universal attacks. We then adapt several state-of-the-art attack methods for classification on the field of depth estimation. Besides, multi-task attacks are introduced to further improve the attack performance for universal attacks. Experimental results show that it is possible to generate significant errors on depth estimation. In particular, we demonstrate that our methods can conduct targeted attacks on given objects (such as a car), resulting in depth estimation 3-4x away from the ground truth (e.g., from 20m to 80m).
Counting monochromatic solutions to diagonal Diophantine equations

Given a finite colouring of the positive integers, we count monochromatic solutions to a variety of Diophantine equations, each of which can be written by setting a diagonal quadratic form equal to a linear form. As a consequence, we determine an algebraic criterion for when such equations are partition regular. Our methods involve discrete harmonic analysis and require a number of `mixed' restriction estimates, which may be of independent interest.
Markovian Score Climbing: Variational Inference with KL(p||q)

Modern variational inference (VI) uses stochastic gradients to avoid intractable expectations, enabling large-scale probabilistic inference in complex models. VI posits a family of approximating distributions $q$ and then finds the member of that family that is closest to the exact posterior $p$. Traditionally, VI algorithms minimize the "exclusive KL" KL$(q\|p)$, often for computational convenience. Recent research, however, has also focused on the "inclusive KL" KL$(p\|q)$, which has good statistical properties that makes it more appropriate for certain inference problems. This paper develops a simple algorithm for reliably minimizing the inclusive KL. Consider a valid MCMC method, a Markov chain whose stationary distribution is $p$. The algorithm we develop iteratively samples the chain $z[k]$, and then uses those samples to follow the score function of the variational approximation, $\nabla \log q(z[k])$ with a Robbins-Monro step-size schedule. This method, which we call Markovian score climbing (MSC), converges to a local optimum of the inclusive KL. It does not suffer from the systematic errors inherent in existing methods, such as Reweighted Wake-Sleep and Neural Adaptive Sequential Monte Carlo, which lead to bias in their final estimates. In a variant that ties the variational approximation directly to the Markov chain, MSC further provides a new algorithm that melds VI and MCMC. We illustrate convergence on a toy model and demonstrate the utility of MSC on Bayesian probit regression for classification as well as a stochastic volatility model for financial data.
Spectral Clustering Revisited: Information Hidden in the Fiedler Vector

We are interested in the clustering problem on graphs: it is known that if there are two underlying clusters, then the signs of the eigenvector corresponding to the second largest eigenvalue of the adjacency matrix can reliably reconstruct the two clusters. We argue that the vertices for which the eigenvector has the largest and the smallest entries, respectively, are unusually strongly connected to their own cluster and more reliably classified than the rest. This can be regarded as a discrete version of the Hot Spots conjecture and should be useful in applications. We give a rigorous proof for the stochastic block model and several examples.
A numerical approach for fluid deformable surfaces

Abstract Fluid deformable surfaces show a solid–fluid duality which establishes a tight interplay between tangential flow and surface deformation. We derive the governing equations as a thin film limit and provide a general numerical approach for their solution. The simulation results demonstrate the rich dynamics resulting from this interplay, where, in the presence of curvature, any shape change is accompanied by a tangential flow and, vice versa, the surface deforms due to tangential flow. However, they also show that the only possible stable stationary state in the considered setting is a sphere with zero velocity.
Probabilistic Dual Network Architecture Search on Graphs

We present the first differentiable Network Architecture Search (NAS) for Graph Neural Networks (GNNs). GNNs show promising performance on a wide range of tasks, but require a large amount of architecture engineering. First, graphs are inherently a non-Euclidean and sophisticated data structure, leading to poor adaptivity of GNN architectures across different datasets. Second, a typical graph block contains numerous different components, such as aggregation and attention, generating a large combinatorial search space. To counter these problems, we propose a Probabilistic Dual Network Architecture Search (PDNAS) framework for GNNs. PDNAS not only optimises the operations within a single graph block (micro-architecture), but also considers how these blocks should be connected to each other (macro-architecture). The dual architecture (micro- and marco-architectures) optimisation allows PDNAS to find deeper GNNs on diverse datasets with better performance compared to other graph NAS methods. Moreover, we use a fully gradient-based search approach to update architectural parameters, making it the first differentiable graph NAS method. PDNAS outperforms existing hand-designed GNNs and NAS results, for example, on the PPI dataset, PDNAS beats its best competitors by 1.67 and 0.17 in F1 scores.
On the diameter of the polytope of the stable marriage with ties

The stable marriage problem with ties is a well-studied and interesting problem in game theory. We are given a set of men and a set of women. Each individual has a preference ordering on the opposite group, which can possibly contain ties. A stable marriage is given by a matching between men and women for which there is no blocking pair, i.e., a men and a women who strictly prefer each other to their current partner in the matching. In this paper, we study the diameter of the polytope given by the convex hull of characteristic vectors of stable marriages, in the setting with ties. We prove an upper bound of $\lfloor \frac{n}{3}\rfloor$ on the diameter, where $n$ is the total number of men and women, and give a family of instances for which the bound holds tight. Our result generalizes the bound on the diameter of the standard stable marriage polytope (i.e., the well-known polytope that describes the setting without ties), developed previously in the literature.
Comparing VVC, HEVC and AV1 using Objective and Subjective Assessments

In this paper, the performance of three state-of-the-art video codecs: High Efficiency Video Coding (HEVC) Test Model (HM), AOMedia Video 1 (AV1) and Versatile Video Coding Test Model (VTM), are evaluated using both objective and subjective quality assessments. Nine source sequences were carefully selected to offer both diversity and representativeness, and different resolution versions were encoded by all three codecs at pre-defined target bitrates. The compression efficiency of the three codecs are evaluated using two commonly used objective quality metrics, PSNR and VMAF. The subjective quality of their reconstructed content is also evaluated through psychophysical experiments. Furthermore, HEVC and AV1 are compared within a dynamic optimization framework (convex hull rate-distortion optimization) across resolutions with a wider bitrate, using both objective and subjective evaluations. Finally the computational complexities of three tested codecs are compared. The subjective assessments indicate that, for the tested versions there is no significant difference between AV1 and HM, while the tested VTM version shows significant enhancements. The selected source sequences, compressed video content and associated subjective data are available online, offering a resource for compression performance evaluation and objective video quality assessment.
First Embedded Cluster Formation in California Molecular Cloud

We performed a multi-wavelength observation toward the LkHα 101 embedded cluster and its adjacent 85′×60′ region. The LkHα 101 embedded cluster is the first and only significant cluster in the California molecular cloud (CMC). These observations have revealed that the LkHα 101 embedded cluster is located just at the projected intersectional region of two filaments. One filament is the highest-density section of the CMC, the other is a new identified filament with a low-density gas emission. Toward the projected intersection, we find the bridging features connecting the two filaments in velocity, and identify a V-shaped gas structure. These agree with the scenario that the two filaments are colliding with each other. Using the Five-hundred-meter Aperture Spherical radio Telescope, we measured the radio recombination line velocity of the LkHα 101 H ii region to be 0.5 km s−1, which is related to the velocity component of the CMC filament. Moreover, there are some young stellar objects (YSOs) distributed outside the intersectional region. We suggest that the cloud–cloud collision, together with the fragmentation of the main filament, may play an important role in the YSOs’ formation of the cluster.
Search for non-thermal X-ray emission in the colliding wind binary Cygnus OB2 #8A

Aims. Cyg OB2 #8A is a massive O-type binary displaying strong non-thermal radio emission. Owing to the compactness of this binary, emission of non-thermal X-ray photons via inverse Compton scattering is expected. Methods. We first revised the orbital solution for Cyg OB2 #8A using new optical spectra. We then reduced and analysed X-ray spectra obtained with XMM-Newton, Swift, INTEGRAL, and NuSTAR. Results. The analysis of the XMM-Newton and Swift data allows us to better characterise the X-ray emission from the stellar winds and colliding winds region at energies below 10 keV. We confirm the variation of the broad-band light curve of Cyg OB2 #8A along the orbit with, for the first time, the observation of the maximum emission around phase 0.8. The minimum ratio of the X-ray to bolometric flux of Cyg OB2 #8A remains well above the level expected for single O-type stars, indicating that the colliding wind region is not disrupted during the periastron passage. The analysis of the full set of publicly available INTEGRAL observations allows us to refine the upper limit on the non-thermal X-ray flux of the Cyg OB2 region between 20 and 200 keV. Two NuSTAR observations (phases 0.028 and 0.085) allow us to study the Cyg OB2 #8A spectrum up to 30 keV. These data do not provide evidence of the presence of non-thermal X-rays, but bring more stringent constraints on the flux of a putative non-thermal component. Finally, we computed, thanks to a new dedicated model, the anisotropic inverse Compton emission generated in the wind shock region. The theoretical non-thermal emission appears to be compatible with observational limits and the kinetic luminosity computed from these models is in good agreement with the unabsorbed flux observed below 10 keV.
Quantum Conference Key Agreement: A Review

Conference key agreement (CKA), or multipartite key distribution, is a cryptographic task where more than two parties wish to establish a common secret key. A composition of bipartite quantum key distribution protocols can accomplish this task. However, the existence of multipartite quantum correlations allows for new and potentially more efficient protocols, to be applied in future quantum networks. Here, the existing quantum CKA protocols based on multipartite entanglement are reviewed, both in the device‐dependent and the device‐independent scenario.
Cosmic ray feedback from supernovae in dwarf galaxies

The regulation of the baryonic content in dwarf galaxies is a long-standing problem. Supernovae (SNe) are supposed to play a key role in forming large-scale galactic winds by removing important amounts of gas from galaxies. SNe are efficient accelerators of non-thermal particles, so-called cosmic rays (CRs), which can substantially modify the dynamics of the gas and conditions to form large-scale galactic winds. We investigate how CR injection by SNe impacts the star formation and the formation of large-scale winds in dwarf galaxies, and whether it can produce galaxy star-formation rates (SFR) and wind properties closer to observations. We ran CR magneto-hydrodynamical simulations of dwarf galaxies at high resolution (9 pc) with the adaptive mesh refinement code RAMSES. Those disc galaxies are embedded in isolated halos of mass of 1010 and 1011 M⊙, and CRs are injected by SNe. We included CR isotropic and anisotropic diffusion with various diffusion coefficients, CR radiative losses, and CR streaming. The injection of CR energy into the interstellar medium smooths out the highest gas densities, which reduces the SFR by a factor of 2–3. Mass outflow rates are significantly greater with CR diffusion, by 2 orders of magnitudes for the higher diffusion coefficients. Without diffusion and streaming, CRs are inefficient at generating winds. CR streaming alone allows for the formation of winds but which are too weak to match observations. The formation of galactic winds strongly depends on the diffusion coefficient: for low coefficients, CR energy stays confined in high density regions where CR energy losses are highest, and higher coefficients, which allow for a more efficient leaking of CRs out of dense gas, produce stronger winds. CR diffusion leads to colder and denser winds than without CRs, and brings outflow rates and mass loading factors much closer to observations.
Kinetic energy of the Langevin particle

We compute the kinetic energy of the Langevin particle using different approaches. We build stochastic differential equations that describe this physical quantity based on both the Itô and Stratonovich stochastic integrals. It is shown that the Itô equation possesses a unique solution, whereas the Stratonovich one possesses infinitely many, all but one absent of physical meaning. We discuss how this fact matches with the existent discussion on the Itô vs Stratonovich dilemma and the apparent preference toward the Stratonovich interpretation in the physical literature.