Miracle-dz/UniFAR-FTUs huggingface dataset:
Towards a sharp, structure preserving two-velocity model for two-phase flow: transport of mass and momentum

The numerical modelling of convection dominated high density ratio two-phase flow poses several challenges, amongst which is resolving the relatively thin shear layer at the interface. To this end we propose a sharp discretisation of the two-velocity model of the two-phase Navier-Stokes (NS) equations. This results in the ability to model the shear layer, rather than resolving it, by allowing for a velocity discontinuity in the direction(s) tangential to the interface. In this paper we focus our attention on the transport of mass and momentum in the presence of such a velocity discontinuity. We propose a generalisation of the dimensionally unsplit geometric volume of fluid (VOF) method for the advection of the interface in the two-velocity formulation. Sufficient conditions on the construction of donating regions are derived that ensure boundedness of the volume fraction for dimensionally unsplit advection methods. We propose to interpolate the mass fluxes resulting from the dimensionally unsplit geometric VOF method for the advection of the staggered momentum field, resulting in semi-discrete energy conservation. Division of the momentum by the respective mass, to obtain the velocity, is not always well-defined for nearly empty control volumes and therefore care is taken in the construction of the momentum flux interpolant: our proposed flux interpolant guarantees that this division is always well-defined without being unnecessarily dissipative. Besides the newly proposed two-velocity model we also detail our exactly conservative (mass per phase and total linear momentum) implementation of the one-velocity formulation of the two-phase NS equations, which will be used for comparison. The discretisation methods are validated using classical time-reversible flow fields, where in this paper the advection is uncoupled from the NS solver, which will be developed in a later paper.
Towards an explanation of certain that-t phenomena : The COMP-node in Bavarian

In this paper an attempt is made to trace back to some minimal parametrical variations some major syntactic differences between Standard German (SG) and Bavarian (B), the variety of German spoken in the south-east of West-Germany. My main concern is to arrive at an explanation for the violations of the *that-t filter which occur frequently in B. The Government and Binding framework, as developed in Chomsky (1981) offers a theory which allows us to derive the Bavarian da/3-t phenomena and certain cases of pro-drop without stipulations.
Hyper-Representations as Generative Models: Sampling Unseen Neural Network Weights

Learning representations of neural network weights given a model zoo is an emerging and challenging area with many potential applications from model inspection, to neural architecture search or knowledge distillation. Recently, an autoencoder trained on a model zoo was able to learn a hyper-representation, which captures intrinsic and extrinsic properties of the models in the zoo. In this work, we extend hyper-representations for generative use to sample new model weights. We propose layer-wise loss normalization which we demonstrate is key to generate high-performing models and several sampling methods based on the topology of hyper-representations. The models generated using our methods are diverse, performant and capable to outperform strong baselines as evaluated on several downstream tasks: initialization, ensemble sampling and transfer learning. Our results indicate the potential of knowledge aggregation from model zoos to new models via hyper-representations thereby paving the avenue for novel research directions.
Du Bois property of log centers

The analytic aspects of multiplier ideals, log canonical thresholds and log canonical centers played an important role in several papers of Demailly, including [DEL00, Dem01, DK01, Dem12, DP14, Dem16, CDM17, Dem18]. Log canonical centers are seminormal by [Amb03, Fuj17], even Du Bois by [KK10, KK20]. This has important applications to birational geometry and moduli theory; see [KK10, KK20] or [Kol22, Sec.2. 5]. We recall the concept of Du Bois singularities in Definition–Theorem 4. An unusual aspect is that this notion makes sense for complex spaces that have irreducible components of different dimension. This is crucial even for the statement of our theorem. In this note we generalize the results of [KK10, KK20] by showing that if a closed subset V ⊂ X is ‘close enough’ to being a union of log canonical centers, then it is Du Bois. The minimal log discrepancy—denoted by mld(V,X,∆) as in Definition 2—is a nonnegative rational number, that measures the deviation from being a union of log canonical centers. The log canonical gap in dimension n—denoted by lcg(n) as in Definition 3—gives the precise notion of ‘closeness. ’
Combinatorics of Vogan diagrams for almost-Kähler manifolds

Let [Formula: see text] be a non-compact classical semisimple Lie group and let [Formula: see text] be the adjoint orbit with respect to a fixed element in [Formula: see text]. These manifolds can be equipped with an almost-Kähler structure and we provide explicit formulae for the existence of special almost-complex structures on [Formula: see text] purely in terms of the combinatorics of the associated Vogan diagram. The formulae are given separately for Lie groups whose Lie algebras are of type [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], where [Formula: see text] denotes the rank of the Lie algebra.
Pulsar and cosmic variances of pulsar timing-array correlation measurements of the stochastic gravitational wave background

Pulsar timing-array correlation measurements offer an exciting opportunity to test the nature of gravity in the cosmologically novel nanohertz gravitational wave regime. The stochastic gravitational wave background is assumed Gaussian and random, while there are limited pulsar pairs in the sky. This brings theoretical uncertainties to the correlation measurements, namely the pulsar variance due to pulsar samplings and the cosmic variance due to Gaussian signals. We demonstrate a straightforward calculation of the mean and the variances on the Hellings-Downs correlation relying on a power spectrum formalism. We keep arbitrary pulsar distances and consider gravitational wave modes beyond Einstein gravity as well as off the light cone throughout, thereby presenting the most general and, most importantly, numerically efficient calculation of the variances.
ROBUST OPTICAL RICHNESS ESTIMATION WITH REDUCED SCATTER

Reducing the scatter between cluster mass and optical richness is a key goal for cluster cosmology from photometric catalogs. We consider various modifications to the red-sequence-matched filter richness estimator of Rozo et al. implemented on the maxBCG cluster catalog and evaluate the impact of these changes on the scatter in X-ray luminosity (LX) at fixed richness, using LX from the ROSAT All-Sky Catalog as the best mass proxy available for the large area required. Most significantly, we find that deeper luminosity cuts can reduce the recovered scatter, finding that for clusters with M500c ≳ 1.6 × 1014 h−170 M☉. The corresponding scatter in mass at fixed richness is σln M|λ ≈ 0.2–0.3 depending on the richness, comparable to that for total X-ray luminosity. We find that including blue galaxies in the richness estimate increases the scatter, as does weighting galaxies by their optical luminosity. We further demonstrate that our richness estimator is very robust. Specifically, the filter employed when estimating richness can be calibrated directly from the data, without requiring a priori calibrations of the red sequence. We also demonstrate that the recovered richness is robust to up to 50% uncertainties in the galaxy background, as well as to the choice of photometric filter employed, so long as the filters span the 4000 Å break of red-sequence galaxies. Consequently, our richness estimator can be used to compare richness estimates of different clusters, even if they do not share the same photometric data. Appendix A includes “easy-bake” instructions for implementing our optimal richness estimator, and we are releasing an implementation of the code that works with Sloan Digital Sky Survey data, as well as an augmented maxBCG catalog with the λ richness measured for each cluster.
On the Input-Output Behavior of a Geothermal Energy Storage: Approximations by Model Order Reduction

In this paper we consider a geothermal energy storage in which the spatio-temporal temperature distribution is modeled by a heat equation with a convection term. Such storages often are embedded in residential heating systems and control and management require the knowledge of some aggregated characteristics of that temperature distribution in the storage. They describe the input-output behaviour of the storage and the associated energy flows and their response to charging and discharging processes. We aim to derive an efficient approximative description of these characteristics by a low-dimensional system of ODEs. This leads to a model order reduction problem for a large scale linear system of ODEs arising from the semi-discretization of the heat equation combined with a linear algebraic output equation. In a first step we approximate the non time-invariant system of ODEs by a linear time-invariant system. Then we apply Lyapunov balanced truncation model order reduction to approximate the output by a reduced-order system with only a few state equations but almost the same input-output behavior. The paper presents results of extensive numerical experiments showing the efficiency of the applied model order reduction methods. It turns out that only a few suitable chosen ODEs are sufficient to produce good approximations of the input-output behaviour of the storage.
Investigating 2M1155−79B: A Nearby, Young, Low-mass Star Actively Accreting from a Nearly Edge-on, Dusty Disk

We investigate the nature of an unusually faint member of the ϵ Cha association (D ∼ 100 pc, age ∼5 Myr), the nearest region of star formation of age <8 Myr. This object, 2MASS J11550336−7919147 (2M1155−79B), is a wide-separation (∼580 au), comoving companion to low-mass (M3) ϵ Cha association member 2MASS J11550485−7919108 (2M1155−79A). We present near-infrared (NIR) spectra of both components, along with analysis of photometry from Gaia Early Data Release 3, the Two Micron All Sky Survey, the Vista Hemisphere Survey, and the Wide-field Infrared Survey Explorer (WISE). The NIR spectrum of 2M1155−79B displays strong He i 1.083 emission, a sign of active accretion and/or accretion-driven winds from a circumstellar disk. Analysis of WISE archival data reveals that the mid-infrared excess previously associated with 2M1155−79A instead originates from the disk surrounding 2M1155−79B. Based on these results, as well as radiative transfer modeling of its optical/IR spectral energy distribution, we conclude that 2M1155−79B is most likely a young, late M star that is partially obscured by, and actively accreting from, a nearly edge-on circumstellar disk. This would place 2M1155−79B among the rare group of nearby (D ≲ 100 pc), young (age <10 Myr) mid-M stars that are orbited by and accreting from highly inclined protoplanetary disks. Like these systems, the 2M1155−79B system is a particularly promising subject for studies of star and planet formation around low-mass stars.
Probing early Universe supercooled phase transitions with gravitational wave data

We investigate the reach of the LIGO/Virgo/KAGRA detectors in the search for signatures of first-order phase transitions in the early Universe. Utilising data from the first three observing runs, we derive constraints on the parameters of the underlying gravitational-wave background, focusing on transitions characterised by strong supercooling. As an application of our analysis, we determine bounds on the parameter space of two representative particle physics models. We also comment on the expected reach of third-generation detectors in probing supercooled phase transitions.
GRB 090510: A GENUINE SHORT GRB FROM A BINARY NEUTRON STAR COALESCING INTO A KERR–NEWMAN BLACK HOLE

In a new classification of merging binary neutron stars (NSs) we separate short gamma-ray bursts (GRBs) into two subclasses. The ones with erg coalesce to form a massive NS and are indicated as short gamma-ray flashes (S-GRFs). The hardest, with erg, coalesce to form a black hole (BH) and are indicated as genuine short GRBs (S-GRBs). Within the fireshell model, S-GRBs exhibit three different components: the proper GRB (P-GRB) emission, observed at the transparency of a self-accelerating baryon- plasma; the prompt emission, originating from the interaction of the accelerated baryons with the circumburst medium; and the high-energy (GeV) emission, observed after the P-GRB and indicating the formation of a BH. GRB 090510 gives the first evidence for the formation of a Kerr BH or, possibly, a Kerr–Newman BH. Its P-GRB spectrum can be fitted by a convolution of thermal spectra whose origin can be traced back to an axially symmetric dyadotorus. A large value of the angular momentum of the newborn BH is consistent with the large energetics of this S-GRB, which reach in the 1–10,000 keV range erg and in the 0.1–100 GeV range erg, the most energetic GeV emission ever observed in S-GRBs. The theoretical redshift that we derive from the fireshell theory is consistent with the spectroscopic measurement , showing the self-consistency of the theoretical approach. All S-GRBs exhibit GeV emission, when inside the Fermi-LAT field of view, unlike S-GRFs, which never evidence it. The GeV emission appears to be the discriminant for the formation of a BH in GRBs, confirmed by their observed overall energetics.
Hierarchical Training of Deep Ensemble Policies for Reinforcement Learning in Continuous Spaces

Many actor-critic deep reinforcement learning (DRL) algorithms have achieved cutting-edge performance in tackling various challenging reinforcement learning (RL) problems, including complex control tasks with high-dimensional continuous state and action spaces. Despite of widely reported success, existing DRL algorithms often suffer from the ineffective exploration issue, resulting in limited learning stability and performance. To address this limitation, several ensemble DRL algorithms have been proposed recently to boost exploration and stabilize the learning process. However, many existing ensemble algorithms are designed to train each base learner individually without controlling explicitly the collaboration among the trained base learners. In this paper, we propose a new technique to train an ensemble of base learners based on the multi-step integration methods. The new multi-step training technique enables us to develop a new hierarchical training algorithm for ensemble DRL that promotes inter-learner collaboration through explicit inter-learner parameter sharing. The design of our new algorithm is veri-ﬁed theoretically. The algorithm is also shown empirically to outperform several cutting-edge DRL algorithms on multiple benchmark RL problems.
A PAN-STARRS + UKIDSS SEARCH FOR YOUNG, WIDE PLANETARY-MASS COMPANIONS IN UPPER SCORPIUS

We have combined optical and NIR photometry from Pan-STARRS 1 and UKIDSS to search the young (5–10 Myr) star-forming region of Upper Scorpius for wide (≈400–4000 AU) substellar companions down to ∼5 MJup. Our search is ≈4 mag deeper than previous work based on the Two Micron All Sky Survey. We identified several candidates around known stellar members using a combination of color selection and spectral energy distribution fitting. Our follow-up spectroscopy has identified two new companions as well as confirmed two companions previously identified from photometry, with spectral types of M7.5–M9 and masses of ∼15–60 MJup, indicating a frequency for such wide substellar companions of ∼0.6% ± 0.3%. Both USco 1610−1913B and USco 1612−1800B are more luminous than expected for their spectral type compared with known members of Upper Sco. HIP 77900B has an extreme mass ratio (M2/M1 ≈ 0.005) and an extreme separation of 3200 AU. USco 1602−2401B also has a very large separation of 1000 AU. We have also confirmed a low-mass stellar companion, USco 1610−2502B (730 AU, M5.5). Our substellar companions appear both non-coeval with their primary stars according to evolutionary models and, as a group, are systematically more luminous than the Upper Sco cluster sequence. One possible reason for these luminosity discrepancies could be different formation processes or accretion histories for these objects.
The interplay between the dark matter axion and primordial black holes

If primordial black holes (PBHs) had come to dominate the energy density of the early Universe when oscillations in the axion field began, we show that the relic abundance and expected mass range of the QCD axion would be greatly modified. Since the QCD axion is a potential candidate for dark matter (DM), we refer to it as the DM axion. We predominantly explore PBHs in the mass range (106 - 5× 108)g. We investigate the relation between the relic abundance of DM axions and the parameter space of PBHs. We numerically solve the set of Boltzmann equations, that governs the cosmological evolution during both radiation and PBH-dominated epochs, providing the bulk energy content of the early Universe. We further solve the equation of motion of the DM axion field to obtain its present abundance. Alongside non-relativistic production mechanisms, light QCD axions are generated from evaporating PBHs through the Hawking mechanism and could make up a fraction of the dark radiation (DR). If the QCD axion is ever discovered, it will give us insight into the early Universe and probe into the physics of the PBH-dominated era. We estimate the bounds on the model from DR axions produced via PBH evaporation and thermal decoupling, and we account for isocurvature bounds for the period of inflation where the Peccei-Quinn symmetry is broken. We assess the results obtained against the available CMB data and we comment on the forecasts from gravitational wave searches. We briefly state the consequences of PBH accretion and the uncertainties this may further add to cosmology and astroparticle physics modeling.
Human Motion Diffusion Model

Natural and expressive human motion generation is the holy grail of computer animation. It is a challenging task, due to the diversity of possible motion, human perceptual sensitivity to it, and the difficulty of accurately describing it. Therefore, current generative solutions are either low-quality or limited in expressiveness. Diffusion models, which have already shown remarkable generative capabilities in other domains, are promising candidates for human motion due to their many-to-many nature, but they tend to be resource hungry and hard to control. In this paper, we introduce Motion Diffusion Model (MDM), a carefully adapted classifier-free diffusion-based generative model for the human motion domain. MDM is transformer-based, combining insights from motion generation literature. A notable design-choice is the prediction of the sample, rather than the noise, in each diffusion step. This facilitates the use of established geometric losses on the locations and velocities of the motion, such as the foot contact loss. As we demonstrate, MDM is a generic approach, enabling different modes of conditioning, and different generation tasks. We show that our model is trained with lightweight resources and yet achieves state-of-the-art results on leading benchmarks for text-to-motion and action-to-motion. https://guytevet.github. io/mdm-page/ .
Contrastive Unsupervised Learning of World Model with Invariant Causal Features

In this paper we present a world model , which learns causal features using the invariance principle. In particular, we use contrastive unsupervised learning to learn the invariant causal features, which enforces invariance across augmentations of irrelevant parts or styles of the observation. The world-model-based reinforcement learning methods independently optimize representation learning and the policy. Thus naïve contrastive loss implementation collapses due to a lack of supervisory signals to the representation learning module. We propose an intervention invariant auxiliary task to mitigate this issue. Specifically, we utilize depth prediction to explicitly enforce the invariance and use data augmentation as style intervention on the RGB observation space. Our design leverages unsupervised representation learning to learn the world model with invariant causal features. Our proposed method significantly outperforms current state-of-the-art model-based and model-free reinforcement learning methods on out-of-distribution point navigation tasks on the iGibson dataset. Moreover, our proposed model excels at the sim-to-real transfer of our perception learning module. 1
Correcting the Sub-optimal Bit Allocation

In this paper, we investigate the problem of bit allocation in Neural Video Compression (NVC). First, we reveal that a recent bit allocation approach claimed to be optimal is, in fact, sub-optimal due to its implementation. Specifically, we find that its sub-optimality lies in the improper application of semi-amortized variational inference (SAVI) on latent with non-factorized variational posterior. Then, we show that the corrected version of SAVI on non-factorized latent requires recursively applying back-propagating through gradient ascent, based on which we derive the corrected optimal bit allocation algorithm. Due to the computational in-feasibility of the corrected bit allocation, we design an efficient approximation to make it practical. Empirical results show that our proposed correction significantly improves the incorrect bit allocation in terms of R-D performance and bitrate error, and outperforms all other bit allocation methods by a large margin. The source code is provided in the supplementary material.
How good is your Laplace approximation of the Bayesian posterior? Finite-sample computable error bounds for a variety of useful divergences

The Laplace approximation is a popular method for providing posterior mean and variance estimates. But can we trust these estimates for practical use? One might consider using rate-of-convergence bounds for the Bayesian Central Limit Theorem (BCLT) to provide quality guarantees for the Laplace approximation. But the bounds in existing versions of the BCLT either: require knowing the true data-generating parameter, are asymptotic in the number of samples, do not control the Bayesian posterior mean, or apply only to narrow classes of models. Our work provides the first closed-form, finite-sample quality bounds for the Laplace approximation that simultaneously (1) do not require knowing the true parameter, (2) control posterior means and variances, and (3) apply generally to models that satisfy the conditions of the asymptotic BCLT. In fact, our bounds work even in the presence of misspecification. We compute exact constants in our bounds for a variety of standard models, including logistic regression, and numerically demonstrate their utility. We provide a framework for analysis of more complex models.