Miracle-dz/UniFAR-FTUs huggingface dataset:
A Unifying and Canonical Description of Measure-Preserving Diffusions

A complete recipe of measure-preserving diffusions in Euclidean space was recently derived unifying several MCMC algorithms into a single framework. In this paper, we develop a geometric theory that improves and generalises this construction to any manifold. We thereby demonstrate that the completeness result is a direct consequence of the topology of the underlying manifold and the geometry induced by the target measure $P$; there is no need to introduce other structures such as a Riemannian metric, local coordinates, or a reference measure. Instead, our framework relies on the intrinsic geometry of $P$ and in particular its canonical derivative, the deRham rotationnel, which allows us to parametrise the Fokker--Planck currents of measure-preserving diffusions using potentials. The geometric formalism can easily incorporate constraints and symmetries, and deliver new important insights, for example, a new complete recipe of Langevin-like diffusions that are suited to the construction of samplers. We also analyse the reversibility and dissipative properties of the diffusions, the associated deterministic flow on the space of measures, and the geometry of Langevin processes. Our article connects ideas from various literature and frames the theory of measure-preserving diffusions in its appropriate mathematical context.
Front Propagation of a Sexual Population with Evolution of Dispersion: A Formal Analysis

The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the context of invasions, when considering the evolution of a heritable trait that encodes the dispersive ability of individuals, the trait distribution develops a particular spatial structure that leads to the acceleration of the front propagation. That phenomenon is known as spatial sorting. Many biological examples can be cited like the bush cricket in Britain, the cane toad invasion in Australia or the common myna one in South Africa. Adopting this framework, recent mathematical studies have led to highlight the influence of the reproductive mode on the front propagation. Asexual populations have been shown to spread with an asymptotic rate of t3/2 in a minimal reactiondiffusion model, whereas the analogous rate for sexual populations is of t5/4 (where t denotes the time). However, the precise description of the behaviour of the front propagation in the sexual case is still an open question. The aim of this paper is to give precise approximations for large times of its position, as well as some features of the local trait distribution at the front. To do so, we solve explicitly the asymptotic problem derived formally. Numerical simulations are shown to confirm these calculations.
Disintegration of Long-period Comet C/2019 Y4 (ATLAS). I. Hubble Space Telescope Observations

The near-Sun comet C/2019 Y4 (ATLAS) is the first member of a long-period comet group observed to disintegrate well before perihelion. Here we present our investigation into this disintegration event using images obtained in a three-day Hubble Space Telescope campaign. We identify two fragment clusters produced by the initial disintegration event, corresponding to fragments C/2019 Y4-A and C/2019 Y4-B identified in ground-based data. These two clusters started with similar integrated brightness but exhibit different evolutionary behavior. C/2019 Y4-A was much shorter-lived compared to C/2019 Y4-B and showed signs of significant mass loss and changes in size distribution throughout the three-day campaign. The cause of the initial fragmentation is undetermined by the limited evidence but crudely compatible with either the spin-up disruption of the nucleus or runaway sublimation of subsurface supervolatile ices, either of which would lead to the release of a large amount of gas as inferred from the significant bluing of the comet observed shortly before its disintegration. Gas can only be produced by the sublimation of volatile ices, which must have survived at least one perihelion passage at a perihelion distance of q = 0.25 au. We speculate that Comet ATLAS is derived from the ice-rich interior of a nonuniform, kilometer-wide progenitor that split during its previous perihelion. This suggests that comets down to a few kilometers in diameter can still possess complex, nonuniform interiors that can protect ices against intense solar heating.
Uncovering the socioeconomic structure of spatial and social interactions in cities

The relationship between urban mobility, social networks, and socioeconomic status is complex and difficult to apprehend, notably due to the lack of data. Here we use mobile phone data to analyze the socioeconomic structure of spatial and social interaction in the Chilean urban system. Based on the concept of spatial and social events, we develop a methodology to assess the level of spatial and social interactions between locations according to their socioeconomic status. We demonstrate that people with the same socioeconomic status preferentially interact with locations and people with a similar socioeconomic status. We also show that this proximity varies similarly for both spatial and social interactions during the course of the week. Finally, we highlight that these preferential interactions appear to hold when considering city–city interactions.
Migrating Client Code without Change Examples

API developers evolve software libraries to fix bugs, add new features, or refactor code. To benefit from such library evolution, the programmers of client projects have to repetitively upgrade their library usages and adapt their codebases to any library API breaking changes (e.g., API renaming). Such adaptive changes can be tedious and error-prone. Existing tools provide limited support to help programmers migrate client projects from old library versions to new ones. For instance, some tools extract API mappings be-tween library versions and only suggest simple adaptive changes (i.e., statement updates); other tools suggest or automate more complicated edits (e.g., statement insertions) based on user-provided exemplar code migrations. However, when new library versions are available, it is usually cumbersome and time-consuming for users to provide sufficient human-crafted samples in order to guide automatic migration. In this paper, we propose a novel approach, AutoUpdate, to further improve the state of the art. Instead of learning from change examples, we designed AutoUpdate to automate migration in a compiler-directed way. Namely, given a compilation error triggered by upgrading libraries, AutoUpdate exploits 13 migration opera-tors to generate candidate edits, and tentatively applies each edit until the error is resolved or all edits are explored. We conducted two experiments. The first experiment involves migrating 371 tutorial examples between versions of 5 popular libraries. AutoUpdate reduced migration-related compilation errors for 92.7% of tasks. It eliminated such errors for 32.4% of tasks, and 33.9% of the tasks have identical edits to manual migrations. In the second experiment, we applied AutoUpdate to migrate two real client projects of lucene. AutoUpdate successfully migrated both projects, and the migrated code passed all tests.
Fermi's golden rule for heating in strongly driven Floquet systems

We study heating dynamics in isolated quantum many-body systems driven periodically at high frequency and large amplitude. Combining the high-frequency expansion for the Floquet Hamiltonian with Fermi's golden rule (FGR), we develop a master equation termed the Floquet FGR. Unlike the conventional one, the Floquet FGR correctly describes heating dynamics, including the prethermalization regime, even for strong drives, under which the Floquet Hamiltonian is significantly dressed, and nontrivial Floquet engineering is present. The Floquet FGR depends on system size only weakly, enabling us to analyze the thermodynamic limit with small-system calculations. Our results also indicate that, during heating, the system approximately stays in the thermal state for the Floquet Hamiltonian with a gradually rising temperature.
On the tangential cone condition for electrical impedance tomography

We state some sufﬁcient criteria for the tangential cone conditions to hold for the electrical impedance tomography problem. The results are based on Löwner convexity of the forward operator. As a consequence, we show that for conductivities that satisfy various properties, such as Hölder source conditions, ﬁnite-dimensionality, or certain monotonicity criteria, the tangential cone condition is veriﬁed.
Elliptic threefolds with high Mordell–Weil rank

We present the first examples of smooth elliptic Calabi-Yau threefolds with Mordell-Weil rank 10, the highest currently known value. They are given by the Schoen threefolds introduced by Namikawa; there are six isolated fibers of Kodaira Type IV. We explicitly compute the Shioda homomorphism for the generators of the Mordell-Weil group and their induced height pairing. Compactification of F-theory on these threefolds gives an effective theory in six dimensions which contains ten abelian gauge group factors. We compute the massless matter spectrum. In particular, we show that the charged singlet matter need not reside at enhancement loci of Type $I_2$, as previously believed. We relate the multiplicities of the massless spectrum to genus-zero Gopakumar-Vafa invariants and other geometric quantities of the Calabi-Yau. We show that the gravitational and abelian anomaly cancellation conditions are satisfied. We prove a Geometric Anomaly Cancellation equation and we deduce birational equivalence for the quantities in the spectrum. We explicitly describe a Weierstrass model over $\mathbb P^2$ of the Calabi-Yau threefolds as a log canonical model and compare it to a construction by Elkies and classical results of Burkhardt.
Effects of Dust Evolution on the Vertical Shear Instability in the Outer Regions of Protoplanetary Disks

Vertical shear instability (VSI) is a hydrodynamical instability that requires rapid gas cooling and has been suggested to operate in outer regions of protoplanetary disks. VSI drives turbulence with strong vertical motions, which could regulate dust growth and settling. However, dust growth and settling can regulate the VSI because dust depletion makes gas cooling inefficient in outer disk regions that are optically thin to their own thermal emission. In this study, we quantify these potentially stabilizing effects of dust evolution on the VSI based on linear analysis. We construct a model for calculating the cooling timescale, taking into account dust growth beyond micron sizes and size-dependent settling. Combining the model with linear stability analysis, we map the region where the VSI operates, which we call the VSI zone, and estimate the maximum growth rate at each radial position. We find that dust growth, as well as settling, makes the VSI zone more confined around the midplane. This causes a decrease in the growth rate because the vertical shear of the rotation velocity, which is the source of the instability, is weaker at lower altitudes. In our default disk model with 0.01 solar masses, dust growth from 10 μm to 1 mm causes a decrease in the growth rate by a factor of more than 10. The suppression of VSI-driven turbulence by dust evolution may promote further dust evolution in the outer regions and also explain the high degree of dust settling observed in the disk around HL Tau.
DiffSinger: Diffusion Acoustic Model for Singing Voice Synthesis

Singing voice synthesis (SVS) system is built to synthesize high-quality and expressive singing voice, in which the acoustic model generates the acoustic features ( e . g ., mel-spectrogram) given a music score. Previous singing acoustic models adopt simple loss ( e . g ., L1 and L2) or generative adversarial network (GAN) to reconstruct the acoustic features, while they suffer from over-smoothing and unstable training issues respectively, which hinder the naturalness of synthesized singing. In this work, we propose DiffSinger, an acoustic model for SVS based on the diffusion probabilistic model. DiffSinger is a parameterized Markov chain which iteratively converts the noise into mel-spectrogram conditioned on the music score. By implicitly optimizing variational bound, DiffSinger can be stably trained and generates realistic outputs. To further improve the voice quality, we introduce a shallow diffusion mechanism to make better use of the prior knowledge learned by the simple loss. Speciﬁcally, Diff-Singer starts generation at a shallow step smaller than the total number of diffusion steps, according to the intersection of the diffusion trajectories of the ground-truth mel-spectrogram and the one predicted by a simple mel-spectrogram decoder. Besides, we train a boundary prediction network to locate the intersection and determine the shallow step adaptively. The evaluations conducted on the Chinese singing dataset demonstrate that DiffSinger outperforms state-of-the-art SVS work with a notable margin (0.11 MOS gains). Our extensional experiments also prove the generalization of DiffSinger on text-to-speech task.
How to split the costs among travellers sharing a ride? Aligning system's optimum with users' equilibrium

How to form groups in a mobility system that offers shared rides, and how to split the costs within the travellers of a group, are non-trivial tasks, as two objectives conflict: 1) minimising the total costs of the system, and 2) making each user content with her assignment. Aligning both objectives is challenging, as users are not aware of the externalities induced to the rest of the system. In this paper, we propose protocols to share the costs within a ride so that optimal solutions can also constitute equilibria. To do this, we model the situation as a game. We show that the traditional notions of equilibrium in game theory (Nash and Strong) are not useful here, and prove that determining whether a Strong Equilibrium exists is an NP-Complete problem. Hence, we propose three alternative equilibrium notions (stronger than Nash and weaker than Strong), depending on how users can coordinate, that effectively represent stable ways to match the users. We then propose three cost-sharing protocols, for which the optimal solutions are an equilibrium for each of the mentioned intermediate notions of equilibrium. The game we study can be seen as a game-version of the well-known \textit{set cover problem}. Numerical simulations for Amsterdam reveal that our protocols can achieve stable solutions that are always close to the optimum, that there exists a trade-off between total users' costs and how equal do they distribute among them, and that having a central coordinator can have a large impact.
What’s in the Box? An Analysis of Undesirable Content in the Common Crawl Corpus

Whereas much of the success of the current generation of neural language models has been driven by increasingly large training corpora, relatively little research has been dedicated to analyzing these massive sources of textual data. In this exploratory analysis, we delve deeper into the Common Crawl, a colossal web corpus that is extensively used for training language models. We find that it contains a significant amount of undesirable content, including hate speech and sexually explicit content, even after filtering procedures. We discuss the potential impacts of this content on language models and conclude with future research directions and a more mindful approach to corpus collection and analysis.
Parallelized sequential composition, pipelines, and hardware weak memory models

Since the introduction of the CDC 6600 in 1965 and its `scoreboarding' technique processors have not (necessarily) executed instructions in program order. Programmers of high-level code may sequence independent instructions in arbitrary order, and it is a matter of significant programming abstraction and computational efficiency that the processor can be relied upon to make sensible parallelizations/reorderings of low-level instructions to take advantage of, eg. , multiple ALUs. At the architectural level such reordering is typically implemented via a per-processor pipeline, into which instructions are fetched in order, but possibly committed out of order depending on local considerations, provided any reordering preserves sequential semantics from that processor's perspective. However multicore architectures, where several pipelines run in parallel, can expose these processor-level reorderings as unexpected, or `weak', behaviours. Such weak behaviours are hard to reason about, and (via speculative execution) underlie at least one class of widespread security vulnerability. In this paper we introduce a novel program operator, \emph{parallelized sequential composition}, which can be instantiated with a function that controls the reordering of atomic instructions. It generalises both sequential and parallel composition, and when appropriately instantiated exhibits many of the weak behaviours of well-known hardware weak memory models. Our framework admits the application of established compositional techniques (eg. Owicki-Gries) for reasoning about weak behaviours, and is convenient for abstractly expressing properties from the literature. The semantics and theory is encoded and verified in a theorem prover, and we give an implementation of the pipeline semantics which we use to empirically show conformance against established models of ARM and RISC-V.
Generalized Price’s law on fractional-order asymptotically flat stationary spacetimes

We obtain estimates on the rate of decay of a solution to the wave equation on a stationary spacetime that tends to Minkowski space at a rate $O(\lvert x \rvert^{-\kappa}),$ $\kappa \in (1,\infty) \backslash \mathbb{N}. $ Given suitably smooth and decaying initial data, we show a wave locally enjoys the decay rate $O(t^{-\kappa-2+\epsilon})$.
Electronic transport properties monitored by selective functionalization in Bernal bilayer graphene

Jouda Jemaa Khabthani, ∗ Ahmed Missaoui, 3, † Didier Mayou, ‡ and Guy Trambly de Laissardière § Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences de Tunis, Université de Tunis El Manar, Campus universitaire 1060 Tunis, Tunisia Laboratoire de Spectroscopie Atomique Moléculaire et Applications, Département de Physique, Faculté des Sciences de Tunis, Université de Tunis El Manar, Campus universitaire 1060 Tunis, Tunisia Laboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université, CNRS, 95302 Cergy-Pontoise, France Univ. Grenoble Alpes, Inst NEEL, F-38042 Grenoble, France CNRS, Inst NEEL, F-38042 Grenoble, France (Dated: May 7, 2021)
Adaptive Multigrid Strategy for Large-scale Molecular Mechanics Optimization ∗

In this paper, we present an eﬃcient adaptive multigrid strategy for large-scale molecular mechanics optimization. The oneway multigrid method is used with inexact approximations, such as the quasi-atomistic (QA) approximation [8] or the blended ghost force correction (BGFC) approximation [36] on each coarse level, combined with adaptive mesh reﬁnements based on the gradient-based a posteriori error estimator. For crystalline defects, like vacancies, micro-crack and dislocation, sublinear complexity is observed numerically when the adaptive BGFC method is employed. For systems with more than ten millions atoms, this strategy has a ﬁvefold acceleration in terms of CPU time
Multiple Scattering Enhanced Single Particle Sensing

Methods to increase the light scattered from small particles can help improve the sensitivity of many sensing techniques. Here, we investigate the role multiple scattering plays in perturbing the scattered signal when a particle is added to a random scattering environment. Three enhancement factors, parametrising the effect of different classes of multiple scattering trajectories on the field perturbation, are introduced and their mean amplitudes explored numerically in the context of surface plasmon polariton scattering. We demonstrate that there exists an optimum scatterer density at which the sensitivity enhancement is maximised, with factors on the order of 10 achievable. Dependence of the enhancement factors on scatterer properties are also studied.
Towards the Doran-Harder-Thompson conjecture via the Gross-Siebert program

The Doran-Harder-Thompson “gluing/splitting” conjecture unifies mirror symmetry conjectures for Calabi-Yau and Fano varieties, relating fibration structures on Calabi-Yau varieties to the existence of certain types of degenerations on their mirrors. This was studied for the case of Calabi-Yau complete intersections in toric varieties in [12] for the Hori-Vafa mirror construction. In this paper we prove one direction of the conjecture using a modified version of the Gross-Siebert program. This involves a careful study of the implications within tropical geometry and applying modern deformation theory for singular Calabi-Yau varieties. Mirror symmetry started with the study of Calabi-Yau manifolds, predicting a duality associating to any Calabi-Yau X a mirror partner X̌. As it grew it came to incorporate other statements, most notably it predicts a similar duality associating to any Fano variety and anti-canonical divisor pZ,Dq a Landau-Ginzburg model, a variety W̌ and a super-potential w : W̌ Ñ C. The theory of Landau-Ginzburg models was formalised in [1] where these were required to be a fibration of X̌ by lower dimensional Calabi-Yau varieties. The two worlds, Calabi-Yau and Fano, meet in the example of Tyurin degenerations. A Tyurin degeneration is a semi-stable degeneration Xt Ñ ∆ such that the central fibre is the union of two smooth components X0 “ Z1 Y Z2 meeting along a smooth divisor D. From the work of Kawamata-Nakayama D is an effective anti-canonical divisor on the components Zi, and the normal bundles are dual, ND{Z0 bND{Z0 – OD, and this is a necessary and sufficient condition for such smoothings to exist. This was expanded on by Kato in [13] where he proved that this condition is equivalent to the existence of a log structure of semi-stable type (in modern language locally free) on the central fibre, log smooth over the standard log point. This generalises the Kawamata-Nakayama condition since there are surgeries permitted by log geometry which produce central fibres necessarily smoothable but not of the type they consider, where the central fibre ∗The second author was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC)
XeroAlign: Zero-shot cross-lingual transformer alignment

The introduction of pretrained cross-lingual language models brought decisive improvements to multilingual NLP tasks. However, the lack of labelled task data necessitates a variety of methods aiming to close the gap to high-resource languages. Zero-shot methods in particular, often use translated task data as a training signal to bridge the performance gap between the source and target language(s). We introduce XeroAlign, a simple method for task-specific alignment of cross-lingual pretrained transformers such as XLM-R. XeroAlign uses translated task data to encourage the model to generate similar sentence embeddings for different languages. The XeroAligned XLM-R, called XLM-RA, shows strong improvements over the baseline models to achieve state-of-the-art zero-shot results on three multilingual natural language understanding tasks. XLM-RA's text classification accuracy exceeds that of XLM-R trained with labelled data and performs on par with state-of-the-art models on a cross-lingual adversarial paraphrasing task.