Miracle-dz/UniFAR-FTUs huggingface dataset:
Nonequilibrium Flow Simulations Using Unified Gas-Kinetic Wave-Particle Method

Nonequilibrium flows are commonly encountered in aerospace engineering applications such as spacecraft reentry, rocket launch, and satellite attitude control. Numerical simulations help greatly in the understanding of nonequilibrium flow, multiscale effects, and the dynamics in these applications. Coupling particle transport and collision within the gas evolution process, the unified gas-kinetic wave-particle (UGKWP) method has been developed for multiscale flow simulation, offering a strategy that strikes a balance between accuracy and efficiency. In the present study, the UGKWP method simulates challenging flow problems with large Knudsen number variations, including supersonic flow around a sphere, hypersonic flow around a space vehicle, nozzle plume into vacuum, and side-jet impingement on the hypersonic flow. The UGKWP accurately captures complex flow structures and has been verified through experimental data or direct simulation Monte Carlo results. Regarding computational cost, the UGKWP method requires only 60 GiB of memory to simulate the three-dimensional space vehicle with 560,593 cells under various flow conditions, which is manageable even on personal workstations. Given its excellent efficiency and accuracy, the UGKWP method shows its substantial benefits in simulating multiscale flow for aerospace engineering applications.
The M-Theory Three-Form and Singular Geometries

While M- and F-theory compactifications describe a much larger class of vacua than perturbative string compactifications, they typically need singularities to generate non-abelian gauge fields and charged matter. The physical explanation involves M2-branes wrapped on vanishing cycles. Here we seek an alternative explanation that could address outstanding issues such as the description of nilpotent branches, stability walls, frozen singularities and so forth. To this end we use a model in which the three-form is related to the Chern-Simons form of a bundle. The model has a one-form non-abelian gauge symmetry which normally eliminates all the degrees of freedom associated to the bundle. However by restricting the transformations to preserve the bundle along the vanishing cycles, we may get new degrees of freedom associated to singularities, without appealing to wrapped M2-branes. The analysis can be simplified by gauge-fixing the one-form symmetry using higher-dimensional instanton equations. We explain how this mechanism leads to the natural emergence of phenomena such as enhanced ADE gauge symmetries, nilpotent branches, charged matter fields and their holomorphic couplings.
Planning to Go Out-of-Distribution in Offline-to-Online Reinforcement Learning

Offline pretraining with a static dataset followed by online fine-tuning (offline-to-online, or OtO) is a paradigm well matched to a real-world RL deployment process. In this scenario, we aim to find the best-performing policy within a limited budget of online interactions. Previous work in the OtO setting has focused on correcting for bias introduced by the policy-constraint mechanisms of offline RL algorithms. Such constraints keep the learned policy close to the behavior policy that collected the dataset, but we show this can unnecessarily limit policy performance if the behavior policy is far from optimal. Instead, we forgo constraints and frame OtO RL as an exploration problem that aims to maximize the benefit of online data-collection. We first study the major online RL exploration methods based on intrinsic rewards and UCB in the OtO setting, showing that intrinsic rewards add training instability through reward-function modification, and UCB methods are myopic and it is unclear which learned-component's ensemble to use for action selection. We then introduce an algorithm for planning to go out-of-distribution (PTGOOD) that avoids these issues. PTGOOD uses a non-myopic planning procedure that targets exploration in relatively high-reward regions of the state-action space unlikely to be visited by the behavior policy. By leveraging concepts from the Conditional Entropy Bottleneck, PTGOOD encourages data collected online to provide new information relevant to improving the final deployment policy without altering rewards. We show empirically in several continuous control tasks that PTGOOD significantly improves agent returns during online fine-tuning and avoids the suboptimal policy convergence that many of our baselines exhibit in several environments.
Groups with exotic finiteness properties from complex Morse theory

Recent constructions have shown that interesting behaviours can be observed in the finiteness properties of K\"ahler groups and their subgroups. In this work, we push this further and exhibit, for each integer $k$, new hyperbolic groups admiting surjective homomorphisms to $\mathbb{Z}$ and to $\mathbb{Z}^{2}$, whose kernel is of type $\mathscr{F}_{k}$ but not of type $\mathscr{F}_{k+1}$. By a fibre product construction, we also find examples of nonnormal subgroups of K\"ahler groups with exotic finiteness properties.
Clifford algebras, symmetric spaces and cohomology rings of Grassmannians

We study various kinds of Grassmannians or Lagrangian Grassmannians over $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$, all of which can be expressed as $\mathbb{G}/\mathbb{P}$ where $\mathbb{G}$ is a classical group and $\mathbb{P}$ is a parabolic subgroup of $\mathbb{G}$ with abelian unipotent radical. The same Grassmannians can also be realized as (classical) compact symmetric spaces $G/K$. We give explicit generators and relations for the de Rham cohomology rings of $\mathbb{G}/\mathbb{P}\cong G/K$. At the same time we describe certain filtered deformations of these rings, related to Clifford algebras and spin modules. While the cohomology rings are of our primary interest, the filtered setting of $K$-invariants in the Clifford algebra actually provides a more conceptual framework for the results we obtain.
Cross-domain Robust Deepfake Bias Expansion Network for Face Forgery Detection

The rapid advancement of deepfake technologies raises significant concerns about the security of face recognition systems. While existing methods leverage the clues left by deepfake techniques for face forgery detection, malicious users may intentionally manipulate forged faces to obscure the traces of deepfake clues and thereby deceive detection tools. Meanwhile, attaining cross-domain robustness for data-based methods poses a challenge due to potential gaps in the training data, which may not encompass samples from all relevant domains. Therefore, in this paper, we introduce a solution - a Cross-Domain Robust Bias Expansion Network (BENet) - designed to enhance face forgery detection. BENet employs an auto-encoder to reconstruct input faces, maintaining the invariance of real faces while selectively enhancing the difference between reconstructed fake faces and their original counterparts. This enhanced bias forms a robust foundation upon which dependable forgery detection can be built. To optimize the reconstruction results in BENet, we employ a bias expansion loss infused with contrastive concepts to attain the aforementioned objective. In addition, to further heighten the amplification of forged clues, BENet incorporates a Latent-Space Attention (LSA) module. This LSA module effectively captures variances in latent features between the auto-encoder's encoder and decoder, placing emphasis on inconsistent forgery-related information. Furthermore, BENet incorporates a cross-domain detector with a threshold to determine whether the sample belongs to a known distribution. The correction of classification results through the cross-domain detector enables BENet to defend against unknown deepfake attacks from cross-domain. Extensive experiments demonstrate the superiority of BENet compared with state-of-the-art methods in intra-database and cross-database evaluations.
Assessing Dengue Risk Globally Using Non-Markovian Models

Dengue is a vector-borne disease transmitted by Aedes mosquitoes. The worldwide spread of these mosquitoes and the increasing disease burden have emphasized the need for a spatio-temporal risk map capable of assessing dengue outbreak conditions and quantifying the outbreak risk. Given that the life cycle of Aedes mosquitoes is strongly influenced by habitat temperature, numerous studies have utilized temperature-dependent development rates of these mosquitoes to construct virus transmission and outbreak risk models. In this study, we advance existing research by developing a mechanistic model for the mosquito life cycle that accurately accounts for the non-Markovian nature of the process. By fitting the model to data on human dengue cases, we estimate several model parameters, allowing the development of a global spatiotemporal dengue risk map. This risk model employs temperature and precipitation data to assess the environmental suitability for dengue outbreaks in a given area. Furthermore, we demonstrate how to reduce the model to the corresponding differential equations, enabling us to utilize existing methods for analyzing the system and fitting the model to observations. This approach can be further applied to similar non-Markovian processes that are currently described with less accurate Markovian models.
Anticyclotomic Iwasawa theory of abelian varieties of $\mathrm{GL}_2$-type at non-ordinary primes II

Let $p\ge 5$ be a prime number, $E/\mathbb{Q}$ an elliptic curve with good supersingular reduction at $p$, and $K$ an imaginary quadratic field such that the root number of $E$ over $K$ is $-1$. When $p$ is split in $K$, Castella and Wan formulated the plus and minus Heegner point main conjecture for $E$ along the anticyclotomic $\mathbb{Z}_p$-extension of $K$, and proved it for semistable curves. We generalize their results to two settings: 1. Under the assumption that $p$ is split in $K$ but without assuming $a_p(E)=0$, we study Sprung-type main conjectures for $\mathrm{GL}_2$-type abelian varieties at non-ordinary primes and prove it under some conditions. 2. We formulate, relying on the recent work of the first-named author with Kobayashi and Ota, plus and minus Heegner point main conjectures for elliptic curves when $p$ is inert in $K$, and prove the minus main conjecture for semistable elliptic curves. These results yield a $p$-converse to the Gross--Zagier and Kolyvagin theorem for $E$. Our method relies on Howard's framework of bipartite Euler system, Zhang's resolution of Kolyvagin's conjecture and the recent proof of Kobayashi's main conjecture.
The origin of a terrane: U/Pb zircon geochronology and tectonic evolution of the Xolapa Complex (sou

A repair device is used to restore a damaged dry wallboard, wherein a 2.5 inch or larger hole is cut out from the damaged wall. A cut out piece of wallboard of slightly smaller dimensions than the hole is used to effect the restoration in conjunction with the repair device. The repair device consists of a wallboard support member that inserts through the hole to be secured onto the inside surface of a rear drywall. The cut out piece of wallboard is secured to the board support member. A plurality of clip members are affixed onto the cutout piece of wallboard, wherein the clip members engage an inside surface of the damaged wall board. The cut out piece of wallboard is recessed inward from the front face of the damaged drywall. A user plasters material into the recess and onto the cut out piece of wallboard. The clip members and board support member become an integral part of the restored wallboard.
Validation of the self‐consistency of GOMOS NO3, NO2 and O3 data using chemical data assimilation

The NO3 measurement by the GOMOS instrument on board the ENVISAT platform is the first satellite measurements of this species. The simultaneous measurements of O3 and NO2, which are strongly coupled chemically to NO3, allow us to test the self‐consistency of the GOMOS measurements of the different species. In this paper, the self‐consistency of the nighttime measurements by GOMOS of O3, NO2 and NO3 are tested using chemical data assimilation. Measurements obtained between 25 and 55 km during two distinct periods are assimilated. Analyzed NO3 (i.e., NO3 calculated by the model after assimilation of GOMOS O3 and NO2 data) are then compared to corresponding GOMOS NO3 measurements in correlation plots (GOMOS NO3 versus analyzed NO3). Overall, the differences between the NO3 measurements and corresponding analyzed NO3 are found to be small, about 10% on average. The linear regressions for both periods are also found to be close to the 1‐to‐1 line with small standard errors. This agreement indicates that O3, NO2 and NO3 GOMOS measurements are self consistent chemically and that there is no substantial bias in GOMOS NO3 data. It also suggests that the nighttime NO3 chemistry is well understood.
The Mid-Oligocene Marshall Paraconformity, New Zealand: Coincidence with Global Eustatic Sea-Level Fall or Rise?

The Marshall Paraconformity is a regional mid-Oligocene unconformity that occurs widely in shelf sequences from the eastern New Zealand passive continental margin. The paraconformity represents a break in sedimentation of at least 3 m.y. and coincided with a regional sea-level highstand, in contrast to the prediction of global lowstand at 29 m.y. b.p. Similar paraconformities are widespread on other southern continents. Deep-sea hiatuses of similar age occurred in the adjacent southwest Pacific ocean basins; they may or may not have a common origin with the hiatus associated with the Marshall Paraconformity. Possible causes for the paraconformity and its associated glauconitic and bioclastic sediments are sea-level fluctuations, including those related to local geoidal effects, or erosive bottom waters stemming from the development of Antarctic glaciation or from splitting of the southern continents.
Differences in Atmospheric Circulation between the Development of Weak and Strong Warm Events in the Southern Oscillation

Abstract In this study temporal and spatial aspects of El Nino (warm event) development are explored by comparing composite sequences of sea level pressure (SLP), surface wind, and sea surface temperature (SST) anomalies leading into strong and weak events. El Nino strength is found to be related to the magnitude and spatial extent of large-scale SLP anomalies that move in a low-frequency mode. In association with this, it is also intricately linked to the amplitude and wavelength of the Rossby waves in the southern midlatitudes. The primary signature of the Southern Oscillation is a more pronounced standing wave of pressure anomalies between southeastern Australia and the central South Pacific leading into stronger events. A strong reversal in the strength of the annual cycle between these two regions causes a stronger (weaker) SLP gradient that drives southwesterly (northwesterly) wind stress forcing toward (away from) the western equatorial Pacific in austral winter–spring of year 0 (−1). Thus, pressur.
An In-Context Learning Agent for Formal Theorem-Proving

We present an in-context learning agent for formal theorem-proving in environments like Lean and Coq. Current state-of-the-art models for the problem are finetuned on environment-specific proof data. By contrast, our approach, called COPRA, repeatedly asks a high-capacity, general-purpose large language model (GPT-4) to propose tactic applications from within a stateful backtracking search. Proposed tactics are executed in the underlying proof environment. Feedback from the execution is used to build the prompt for the next model query, along with selected information from the search history and lemmas retrieved from an external database. We evaluate our implementation of COPRA on the miniF2F benchmark for Lean and a set of Coq tasks from the CompCert project. On these benchmarks, COPRA significantly outperforms few-shot invocations of GPT-4. It also compares favorably against finetuning-based approaches, outperforming REPROVER, a state-of-the-art finetuned approach for Lean, in terms of the pass@1 metric. Our code and data are available at https://github.com/trishullab/copra.
On the Root Cause of the Host “Mass Step” in the Hubble Residuals of Type Ia Supernovae

It is well established that the Hubble residuals of Type Ia supernovae (SNe Ia) show the luminosity step with respect to their host galaxy stellar masses. This “mass step” is taken as an additional correction factor for the SN Ia luminosity standardization. Here we investigate the root cause of the mass step and propose that the bimodal nature of the host age distribution is responsible for the step. In particular, by using the empirical nonlinear mass-to-age relation of local galaxies, we convert the mass function of SN Ia hosts to their age distribution. We find that the age distribution shows clear bimodality: a younger (<6 Gyr) group with lower mass (∼109.5 M Sun) and an older (> 6 Gyr) group with higher mass (∼1010.5 M Sun). On the Hubble residual versus host-mass plane, the two groups create the mass step at ∼1010 M Sun. This leads us to conclude that the host galaxy mass step can be attributed to the bimodal age distribution in relation to a nonlinear relation between galaxy mass and age. We suggest that the mass step is another manifestation of the old “red sequence” and the young “blue cloud” observed in the galactic color–magnitude diagram.
Spectral norm bounds for high-dimensional realized covariance matrices and application to weak factor models

Motivated by statistical analysis of latent factor models for high-frequency financial data, we develop sharp upper bounds for the spectral norm of the realized covariance matrix of a high-dimensional It\^o semimartingale with possibly infinite activity jumps. For this purpose, we develop Burkholder-Gundy type inequalities for matrix martingales with the help of the theory of non-commutative $L^p$ spaces. The obtained bounds are applied to estimating the number of (relevant) common factors in a continuous-time latent factor model from high-frequency data in the presence of weak factors.
Transferable Deep Clustering Model

Deep learning has shown remarkable success in the field of clustering recently. However, how to transfer a trained clustering model on a source domain to a target domain by leveraging the acquired knowledge to guide the clustering process remains challenging. Existing deep clustering methods often lack generalizability to new domains because they typically learn a group of fixed cluster centroids, which may not be optimal for the new domain distributions. In this paper, we propose a novel transferable deep clustering model that can automatically adapt the cluster centroids according to the distribution of data samples. Rather than learning a fixed set of centroids, our approach introduces a novel attention-based module that can adapt the centroids by measuring their relationship with samples. In addition, we theoretically show that our model is strictly more powerful than some classical clustering algorithms such as k-means or Gaussian Mixture Model (GMM). Experimental results on both synthetic and real-world datasets demonstrate the effectiveness and efficiency of our proposed transfer learning framework, which significantly improves the performance on target domain and reduces the computational cost.
Holographic description of Narain CFTs and their code-based ensembles

We provide a precise relation between an ensemble of Narain conformal field theories (CFTs) with central charge $c=n$, and a sum of $(U(1) \times U(1))^n$ Chern-Simons theories on different handlebody topologies. We begin by reviewing the general relation of additive codes to Narain CFTs. Then we describe a holographic duality between any given Narain theory and a pure Chern-Simons theory on a handlebody manifold. We proceed to consider an ensemble of Narain theories, defined in terms of an ensemble of codes of length $n$ over ${\mathbb Z}_k \times {\mathbb Z}_k$ for prime $k$. We show that averaging over this ensemble is holographically dual to a level-$k$ $(U(1) \times U(1))^n$ Chern-Simons theory, summed over a finite number of inequivalent classes of handlebody topologies. In the limit of large $k$ the ensemble approaches the ensemble of all Narain theories, and its bulk dual becomes equivalent to"U(1)-gravity"- the sum of the pertubative part of the Chern-Simons wavefunction over all possible handlebodies - providing a bulk microscopic definition for this theory. Finally, we reformulate the sum over handlebodies in terms of Hecke operators, paving the way for generalizations.
Influence of a realistic multiorbital band structure on conducting domain walls in perovskite ferroelectrics

Domain wall morphologies in ferroelectrics are believed to be largely shaped by electrostatic forces. Here, we show that for conducting domain walls, the morphology also depends on the details of the charge-carrier band structure. For concreteness, we focus on transition-metal perovskites like BaTiO$_3$ and SrTiO$_3$. These have a triplet of $t_{2g}$ orbitals attached to the Ti atoms that form the conduction bands when electron doped. We solve a set of coupled equations -- Landau-Ginzburg-Devonshire (LGD) equations for the polarization, tight-binding Schr\"odinger equations for the electron bands, and Gauss' law for the electric potential -- to obtain polarization and electron density profiles as a function of electron density. We find that at low electron densities, the electron gas is pinned to the surfaces of the ferroelectric by a Kittel-like domain structure. As the electron density increases, the domain wall evolves smoothly through a zigzag head-to-head structure, eventually becoming a flat head-to-head domain wall at high density. We find that the Kittel-like morphology is protected by orbital asymmetry at low electron densities, while at large electron densities the high density of states of the multiorbital band structure provides effective screening of depolarizing fields and flattens the domain wall relative to single-orbital models. Finally, we show that in the zigzag phase, the electron gas develops tails that extend away from the domain wall, in contrast to na\"{i}ve expectations.
Model Compression in Practice: Lessons Learned from Practitioners Creating On-device Machine Learning Experiences

On-device machine learning (ML) promises to improve the privacy, responsiveness, and proliferation of new, intelligent user experiences by moving ML computation onto everyday personal devices. However, today's large ML models must be drastically compressed to run efficiently on-device, a hurtle that requires deep, yet currently niche expertise. To engage the broader human-centered ML community in on-device ML experiences, we present the results from an interview study with 30 experts at Apple that specialize in producing efficient models. We compile tacit knowledge that experts have developed through practical experience with model compression across different hardware platforms. Our findings offer pragmatic considerations missing from prior work, covering the design process, trade-offs, and technical strategies that go into creating efficient models. Finally, we distill design recommendations for tooling to help ease the difficulty of this work and bring on-device ML into to more widespread practice.