Miracle-dz/UniFAR-FTUs huggingface dataset:
Monocular Reconstruction of Neural Face Reflectance Fields

The reflectance field of a face describes the reflectance properties responsible for complex lighting effects including diffuse, specular, inter-reflection and self shadowing. Most existing methods for estimating the face reflectance from a monocular image assume faces to be diffuse with very few approaches adding a specular component. This still leaves out important perceptual aspects of reflectance such as higher-order global illumination effects and self-shadowing. We present a new neural representation for face reflectance where we can estimate all components of the reflectance responsible for the final appearance from a monocular image. Instead of modeling each component of the reflectance separately using parametric models, our neural representation allows us to generate a basis set of faces in a geometric deformation-invariant space, parameterized by the input light direction, viewpoint and face geometry. We learn to reconstruct this reflectance field of a face just from a monocular image, which can be used to render the face from any viewpoint in any light condition. Our method is trained on a light-stage dataset, which captures 300 people illuminated with 150 light conditions from 8 viewpoints. We show that our method outperforms existing monocular reflectance reconstruction methods due to better capturing of physical effects, such as sub-surface scattering, specularities, self-shadows and other higher-order effects.
Non-Lipschitz Uniform Domain Shape Optimization in Linear Acoustics

We introduce new parametrized classes of shape admissible domains in R n , n ≥ 2, and prove that they are compact with respect to the convergence in the sense of characteristic functions, the Hausdorff sense, the sense of compacts and the weak convergence of their boundary volumes. The domains in these classes are bounded (e, ∞)-domains with possibly fractal boundaries that can have parts of any non-uniform Hausdorff dimension greater or equal to n − 1 and less than n. We prove the existence of optimal shapes in such classes for maximum energy dissipation in the framework of linear acous-tics. A by-product of our proof is the result that the class of bounded (e, ∞)-domains with fixed e is stable under Hausdorff convergence. An additional and related result is the Mosco convergence of Robin-type energy functionals on converging domains.
Ultraviolet spectra of extreme nearby star-forming regions: Evidence for an overabundance of very massive stars

As deep spectroscopic campaigns extend to higher redshifts and lower stellar masses, the interpretation of galaxy spectra depends increasingly upon models for very young stellar populations. Here we present new HST/COS ultraviolet spectroscopy of seven nearby ($<120$ Mpc) star-forming regions hosting very young stellar populations ($\sim$ 4-20 Myr) with optical Wolf-Rayet stellar wind signatures, ideal laboratories in which to test these stellar models. We detect nebular C III] in all seven, but at equivalent widths uniformly $< 10$ A. This suggests that even for very young stellar populations, the highest equivalent width C III] emission at $\geq 15$ A is reserved for inefficiently-cooled gas at metallicities at or below that of the SMC. The spectra also reveal strong C IV P-Cygni profiles and broad He II emission formed in the winds of massive stars, including some of the most prominent He II stellar wind lines ever detected in integrated spectra. We find that the latest stellar population synthesis prescriptions with improved treatment of massive stars nearly reproduce the entire range of stellar He II wind strengths observed here. However, we find that these models cannot simultaneously match the strongest wind features alongside the optical nebular line constraints. This discrepancy can be naturally explained by an overabundance of very massive stars produced by a high incidence of binary mass transfer and mergers occurring on short $\lesssim 10$ Myr timescales, suggesting these processes may be crucial for understanding the highest-sSFR galaxies in the early Universe. Reproducing both the stellar and nebular light of young systems such as these will be a crucial benchmark for the next generation of stellar population synthesis models.
Hierarchical Adaptive Lasso: Learning Sparse Neural Networks with Shrinkage via Single Stage Training

Deep neural networks achieve state-of-the-art performance in a variety of tasks, however this performance is closely tied to model size. Sparsity is one approach to limiting model size. Modern techniques for inducing sparsity in neural networks are (1) network pruning, a procedure involving iteratively training a model initialized with a previous run's weights and hard thresholding, (2) training in one-stage with a sparsity inducing penalty (usually based on the Lasso), and (3) training a binary mask jointly with the weights of the network. In this work, we study different sparsity inducing penalties from the perspective of Bayesian hierarchical models with the goal of designing penalties which perform well without retraining subnetworks in isolation. With this motivation, we present a novel penalty called Hierarchical Adaptive Lasso (HALO) which learns to adaptively sparsify weights of a given network via trainable parameters without learning a mask. When used to train over-parametrized networks, our penalty yields small subnetworks with high accuracy (winning tickets) even when the subnetworks are not trained in isolation. Empirically, on the CIFAR-100 dataset, we find that HALO is able to learn highly sparse network (only $5\%$ of the parameters) with approximately a $2\%$ and $4\%$ gain in performance over state-of-the-art magnitude pruning methods at the same level of sparsity.
M\"{o}bius cancellation on polynomial sequences and the quadratic Bateman-Horn conjecture over function fields

We establish cancellation in short sums of certain special trace functions over $\mathbb{F}_q[u]$ below the P\'{o}lya-Vinogradov range, with savings approaching square-root cancellation as $q$ grows. This is used to resolve the $\mathbb{F}_q[u]$-analog of Chowla's conjecture on cancellation in M\"{o}bius sums over polynomial sequences, and of the Bateman-Horn conjecture in degree $2$, for some values of $q$. A final application is to sums of trace functions over primes in $\mathbb{F}_q[u]$.
Fluid simulations of cosmic ray-modified shocks

Cosmic ray (CR)-modified shocks are a demanding test of numerical codes. We use them to test and validate the two-moment method for CR hydrodynamics, as well as characterize the realism of CR shock acceleration in two-fluid simulations which inevitably arises. Previously, numerical codes were unable to incorporate streaming in this demanding regime, and have never been compared against analytic solutions. First, we find a new analytic solution highly discrepant in acceleration efficiency from the standard solution. It arises from bi-directional streaming of CRs away from the subshock, similar to a Zeldovich spike in radiative shocks. Since fewer CRs diffuse back upstream, this favours a much lower acceleration efficiency, typically ${\lesssim}10{{\ \rm per\ cent}}$ (even for Mach number > 10) as opposed to ${\gtrsim}50{{\ \rm per\ cent}}$ found in previous analytic work. At Mach number ≳10, the new solution bifurcates into three branches, with efficient, intermediate, and inefficient CR acceleration. Our two-moment code accurately recovers these solutions across the entire parameter space probed, with no ad hoc closure relations. For generic initial conditions, the inefficient branch is robustly chosen by the code; the intermediate branch is unstable. The preferred branch is very weakly modified by CRs. At high Mach numbers (≳10), the gas jump conditions approach that of a purely hydrodynamic shock, and a sub-grid prescription for thermal injection is required for reasonable acceleration efficiencies ${\sim}10{{\ \rm per\ cent}}$. CR-modified shocks have very long equilibration times (∼1000 diffusion time) required to develop the precursor, which must be resolved by ≳10 cells for convergence. Non-equilibrium effects, poor resolution, and obliquity of the magnetic field all reduce CR acceleration efficiency. Shocks in galaxy-scale simulations will generally contribute little to CR acceleration without sub-grid modification.
Modeling Quasar UV/Optical Variability with the Corona-heated Accretion-disk Reprocessing (CHAR) Model

The rest-frame UV/optical variability of the quasars in the Sloan Digital Sky Survey Stripe 82 is used to test the Corona-Heated Accretion-disk Reprocessing (CHAR) model of Sun et al. We adopt our CHAR model and the observed black hole masses (MBH) and luminosities (L) to generate mock light curves that share the same measurement noise and sampling as the real observations. Without any fine-tuning, our CHAR model can satisfactorily reproduce the observed ensemble structure functions for different MBH, L, and rest-frame wavelengths. Our analyses reveal that a luminosity-dependent bolometric correction is disfavored over the constant bolometric correction for UV/optical luminosities. Our work demonstrates the possibility of extracting quasar properties (e.g., the bolometric correction or the dimensionless viscosity parameter) by comparing the physical CHAR model with quasar light curves.
A census of ultraluminous X-ray sources in the local Universe

Using the Chandra Source Catalog 2.0 and a newly compiled catalogue of galaxies in the local Universe, we deliver a census of ultraluminous X-ray source (ULX) populations in nearby galaxies. We find 629 ULX candidates in 309 galaxies with distance smaller than 40\,Mpc. The foreground/background contamination is ${\sim}20\%$. The ULX populations in bona-fide star-forming galaxies scale on average with star-formation rate (SFR) and stellar mass ($M_\star$) such that the number of ULXs per galaxy is $0.45^{+0.06}_{-0.09}\times\frac{\rm SFR}{\rm M_\odot\,yr^{-1}}{+}3.3^{+3.8}_{-3.2}\times\frac{M_\star}{\rm M_\odot}$. The scaling depends strongly on the morphological type. This analysis shows that early spiral galaxies contain an additional population of ULXs that scales with $M_\star$. We also confirm the strong anti-correlation of the ULX rate with the host galaxy's metallicity. In the case of early-type galaxies we find that there is a non-linear dependence of the number of ULXs with $M_\star$, which is interpreted as the result of star-formation history differences. Taking into account age and metallicity effects, we find that the predictions from X-ray binary population synthesis models are consistent with the observed ULX rates in early-type galaxies, as well as, spiral/irregular galaxies.
Uncertainty in Bayesian Leave-One-Out Cross-Validation Based Model Comparison

Leave-one-out cross-validation (LOO-CV) is a popular method for comparing Bayesian models based on their estimated predictive performance on new, unseen, data. Estimating the uncertainty of the resulting LOO-CV estimate is a complex task and it is known that the commonly used standard error estimate is often too small. We analyse the frequency properties of the LOO-CV estimator and study the uncertainty related to it. We provide new results of the properties of the uncertainty both theoretically and empirically and discuss the challenges of estimating it. We show that problematic cases include: comparing models with similar predictions, misspecified models, and small data. In these cases, there is a weak connection in the skewness of the sampling distribution and the distribution of the error of the LOO-CV estimator. We show that it is possible that the problematic skewness of the error distribution, which occurs when the models make similar predictions, does not fade away when the data size grows to infinity in certain situations.
Spectroscopic characterization of the known O-star population in Cygnus OB2

Context. Cygnus OB2 provides a unique insight into the high-mass stellar content in one of the largest groups of young massive stars in our Galaxy. Although several studies of its massive population have been carried out over the last decades, an extensive spectroscopic study of the whole known O-star population in the association is still lacking. Aims. We aim to carry out a spectroscopic characterization of all the currently known O stars in Cygnus OB2, determining the distribution of rotational velocities and accurate stellar parameters to obtain an improved view of the evolutionary status of the region. Methods. Based on existing and new optical spectroscopy, we performed a detailed quantitative spectroscopic analysis of all the known O-type stars identified in the association. For this purpose, we used the user-friendly iacob-broad and iacob-gbat automatized tools, FASTWIND stellar models, and astrometry provided by the Gaia second data release. Results. We created the most complete spectroscopic census of O stars carried out so far in Cygnus OB2 using already existing and new spectroscopy. We present the spectra for 78 O-type stars, from which we identify new binary systems, obtain the distribution of rotational velocities, and determine the main stellar parameters for all the stars in the region that have not been detected as double-line spectroscopic binaries. We also derive radii, luminosities, and masses for those stars with reliable Gaia astrometry, in addition to creating the Hertzsprung-Russell Diagram to interpret the evolutionary status of the association. Finally, we inspect the dynamical state of the population and identify runaway candidates. Conclusions. Our spectroscopic analysis of the O-star population in Cygnus OB2 has led to the discovery of two new binary systems and the determination of the main stellar parameters, including rotational velocities, luminosities, masses, and radii for all identified stars. This work has shown the improvement reached when using accurate spectroscopic parameters and astrometry for the interpretation of the evolutionary status of a population, revealing, in the case of Cygnus OB2, at least two star-forming bursts at ~3 and ~5 Myr. We find an apparent deficit of very fast rotators in the distribution of rotational velocities. The inspection of the dynamical distribution of the sample has allowed us to identify nine O stars with peculiar proper motions and discuss a possible dynamical ejection scenario or past supernova explosions in the region.
The TASEP on Galton–Watson trees

We study the totally asymmetric simple exclusion process (TASEP) on trees where particles are generated at the root. Particles can only jump away from the root, and they jump from $x$ to $y$ at rate $r_{x,y}$ provided $y$ is empty. Starting from the all empty initial condition, we show that the distribution of the configuration at time $t$ converges to an equilibrium. We study the current and give conditions on the transition rates such that the current is of linear order or such that there is zero current, i.e. the particles block each other. A key step, which is of independent interest, is to bound the first generation at which the particle trajectories of the first $n$ particles decouple.
Generate High Resolution Images With Generative Variational Autoencoder

In this work, we present a novel neural network to generate high resolution images. We replace the decoder of VAE with a discriminator while using the encoder as it is. The encoder uses data from a normal distribution while the generator from a gaussian distribution. The combination from both is given to a discriminator which tells whether the generated images are correct or not. We evaluate our network on 3 different datasets: MNIST, LSUN and CelebA-HQ dataset. Our network beats the previous state of the art using MMD, SSIM, log likelihood, reconstruction error, ELBO and KL divergence as the evaluation metrics while generating much sharper images. This work is potentially very exciting as we are able to combine the advantages of generative models and inference models in a principled bayesian manner.
A Multimodal Framework for Large-Scale Emotion Recognition by Fusing Music and Electrodermal Activity Signals

Considerable attention has been paid to physiological signal-based emotion recognition in the field of affective computing. For reliability and user-friendly acquisition, electrodermal activity (EDA) has a great advantage in practical applications. However, EDA-based emotion recognition with large-scale subjects is still a tough problem. The traditional well-designed classifiers with hand-crafted features produce poorer results because of their limited representation abilities. And the deep learning models with auto feature extraction suffer the overfitting drop-off because of large-scale individual differences. Since music has a strong correlation with human emotion, static music can be involved as the external benchmark to constrain various dynamic EDA signals. In this article, we make an attempt by fusing the subject’s individual EDA features and the external evoked music features. And we propose an end-to-end multimodal framework, the one-dimensional residual temporal and channel attention network (RTCAN-1D). For EDA features, the channel-temporal attention mechanism for EDA-based emotion recognition is first involved in mine the temporal and channel-wise dynamic and steady features. The comparisons with single EDA-based SOTA models on DEAP and AMIGOS datasets prove the effectiveness of RTCAN-1D to mine EDA features. For music features, we simply process the music signal with the open-source toolkit openSMILE to obtain external feature vectors. We conducted systematic and extensive evaluations. The experiments on the current largest music emotion dataset PMEmo validate that the fusion of EDA and music is a reliable and efficient solution for large-scale emotion recognition.
A Physical Interpretation of Milky Way Galaxy Dynamics from Precision Astrometrics

The dynamical and virial mass of the Milky Way galaxy is estimated using latest high precision stellar halo and dwarf galaxy satellite kinematics. The new data suggest the Galaxy is a highly compact, classically thermalized object. Kinematics exhibit significant velocity-spatial substructure, distinctive dynamic partitions, and strong Keplerian signatures that run counter to popular notions of featureless and massively extended dark matter halos. The effective local escape velocity profile of the Galaxy is quantified in terms of distribution and kinematics to reveal the physics responsible for the Mass Discrepancy-Acceleration (MDAR) and Radial Acceleration (RAR) relations.
Planck 2018 constraints on anisotropic birefringence and its cross-correlation with CMB anisotropy

Parity-violating extensions of standard electromagnetism produce cosmic birefringence, the in vacuo rotation of the linear polarisation direction of a photon during propagation. We employ Planck 2018 CMB polarised data to constrain anisotropic birefringence, modeled by its angular power spectrum Cℓα α, and the cross-correlation with CMB temperature maps, Cℓα T, at scales larger than ∼15 degrees. We present joint limits on the scale invariant quantity, Aα α ≡ ℓ (ℓ +1) Cℓα α / 2 π, and on the analogous amplitude for the cross-correlation, Aα T ≡ ℓ (ℓ +1) Cℓα T / 2 π. We find no evidence of birefringence within the error budget and obtain Aα α < 0.104 [deg^2] and Aα T=1.50+2.41−4.10 [\muK\cdotdeg] both at 95 % C.L. The latter bound appears competitive in constraining a few early dark energy models recently proposed to alleviate the H0 tension. Slicing the joint likelihood at 0Aα T=, the bound on Aα α becomes tighter at Aα α < 0.085 [deg^2] at 95% C.L. In addition we recast the constraints on Aα α as a bound on the amplitude of primordial magnetic fields responsible for Faraday rotation, finding B1 Mpc < 26.9 nG and B1 Mpc < 24.3 nG at 95% C.L. for the marginalised and sliced case respectively.
Fast Transit Computation Using Tabulated Stellar Intensities

Limb-darkening laws are convenient parameterizations of the stellar intensity center-to-limb variation, and their use is ubiquitous in eclipse and transit modeling. But they are not “laws” in any sense—they are simple approximations of the real intensity variations, and their limitations are becoming more and more apparent as stellar atmosphere models improve and higher precision data become available. When fitting eclipses and transit light curves, one would ideally like to use model intensities that are based on fundamental stellar parameters such as the mass, radius, and effective temperature of the star, rather than a limb-darkening law representation and its coefficients. This is especially true when attempting to detect higher-order effects such as planetary oblateness, rings, satellites, or atmospheres. However, using model intensities requires numerically integrating many small-area “tiles” on the model stellar surface(s), and this has traditionally been too computationally expensive for general use. Here we present a fast technique to compute light curves and the Rossiter–McLaughlin effect that uses tabulated stellar models intensities. This is a step in the development of tools that obviate the need for limb-darkening laws.
Sampling-based Reachability Analysis: A Random Set Theory Approach with Adversarial Sampling

Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too restrictive, too slow, too conservative, or approximate and therefore lack guarantees. In this paper, we propose a simple yet effective sampling-based approach to perform reachability analysis for arbitrary dynamical systems. Our key novel idea consists of using random set theory to give a rigorous interpretation of our method, and prove that it returns sets which are guaranteed to converge to the convex hull of the true reachable sets. Additionally, we leverage recent work on robust deep learning and propose a new adversarial sampling approach to robustify our algorithm and accelerate its convergence. We show that our method is faster and less conservative than other approaches, present results for approximate reachability analysis of neural networks and robust trajectory optimization of high-dimensional uncertain nonlinear systems, and discuss future applications.
On the Bogomolov-Gieseker inequality in positive characteristic

We prove a version of the Bogomolov-Gieseker inequality on smooth projective surfaces of general type in positive characteristic, which is stronger than the result by Langer when the ranks of vector bundles are sufficiently large. Our inequality enables us to construct Bridgeland stability conditions with full support property on all smooth projective surfaces in positive characteristic.
When Inverse Propensity Scoring does not Work: Affine Corrections for Unbiased Learning to Rank

Besides position bias, which has been well-studied, trust bias is another type of bias prevalent in user interactions with rankings: users are more likely to click incorrectly w.r. t. their preferences on highly ranked items because they trust the ranking system. While previous work has observed this behavior in users, we prove that existing Counterfactual Learning to Rank (CLTR) methods do not remove this bias, including methods specifically designed to mitigate this type of bias. Moreover, we prove that Inverse Propensity Scoring (IPS) is principally unable to correct for trust bias under non-trivial circumstances. Our main contribution is a new estimator based on affine corrections: it both reweights clicks and penalizes items displayed on ranks with high trust bias. Our estimator is the first estimator that is proven to remove the effect of both trust bias and position bias. Furthermore, we show that our estimator is a generalization of the existing (CLTR) framework: if no trust bias is present, it reduces to the original (IPS) estimator. Our semi-synthetic experiments indicate that by removing the effect of trust bias in addition to position bias, (CLTR) can approximate the optimal ranking system even closer than previously possible.