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We consider a drift-diffusion process of $N$ stochastic particles and show that its empirical measure converges, as $N\rightarrow \infty$, to the solution of the Landau equation. We work in the regime of very soft and Coulomb potentials using a tightness/uniqueness method. To claim uniqueness, we need high integrability estimates that we obtain by crucially exploiting the dissipation of the Fisher information at the level of the particle system. To be able to exploit these estimates as $N\rightarrow \infty$, we prove the affinity in infinite dimension of the entropy production and Fisher information dissipation (and other first and second-order versions of the Fisher information through a general theorem), results which were up to now only known for the entropy and the usual Fisher information.

We prove that the pseudoautomorphism group of a blow-up of $\mathbb{P}^3$ at $8$ very general points is trivial. We also establish the injectivity of the Coble representation associated to blow-ups of $\mathbb{P}^3$ at $r\ge 8$ general points, answering a question of Dolgachev--Ortland.

In this paper, we prove that a very general cubic threefold does not admit a universal codimension-two cycle and hence is stably irrational.

This summary of the second Terrestrial Very-Long-Baseline Atom Interferometry (TVLBAI) Workshop provides a comprehensive overview of our meeting held in London in April 2024, building on the initial discussions during the inaugural workshop held at CERN in March 2023. Like the summary of the first workshop, this document records a critical milestone for the international atom interferometry community. It documents our concerted efforts to evaluate progress, address emerging challenges, and refine strategic directions for future large-scale atom interferometry projects. Our commitment to collaboration is manifested by the integration of diverse expertise and the coordination of international resources, all aimed at advancing the frontiers of atom interferometry physics and technology, as set out in a Memorandum of Understanding signed by over 50 institutions.

It is impossible today to pretend that the practice of machine learning is always compatible with the idea that training and testing data follow the same distribution. Several authors have recently used ensemble techniques to show how scenarios involving multiple data distributions are best served by representations that are both richer than those obtained by regularizing for the best in-distribution performance, and richer than those obtained under the influence of the implicit sparsity bias of common stochastic gradient procedures. This contribution investigates the use of very high dropout rates instead of ensembles to obtain such rich representations. Although training a deep network from scratch using such dropout rates is virtually impossible, fine-tuning a large pre-trained model under such conditions is not only possible but also achieves out-of-distribution performances that exceed those of both ensembles and weight averaging methods such as model soups. This result has practical significance because the importance of the fine-tuning scenario has considerably grown in recent years. This result also provides interesting insights on the nature of rich representations and on

Very flat and contradjusted modules naturally arise in algebraic geometry in the study of contraherent cosheaves over schemes. Here, we investigate the structure and approximation properties of these modules over commutative noetherian rings. Using an analogy between projective and flat Mittag-Leffler modules on one hand, and very flat and locally very flat modules on the other, we prove that each of the following statements are equivalent to the finiteness of the Zariski spectrum Spec(R) of a noetherian domain R: (i) the class of all very flat modules is covering, (ii) the class of all locally very flat modules is precovering, and (iii) the class of all contraadjusted modules is enveloping. We also prove an analog of Pontryagin's criterion for locally very flat modules over Dedekind domains.

Context: In the context of Galactic archaeology, the outer halo remains relatively unexplored with respect to its metallicity distribution, merger debris, and the abundance of known very/extremely metal-poor ([Fe/H]<-2.5) stars. Aim: We utilize the Pristine survey's publicly available, Pristine data release 1 (PDR1) and Pristine-Gaia synthetic (PGS) catalogues of photometric metallicities, to select Red Giant Branch (RGB) stars in the outer halo. Methods: The RGB selection pipeline selects giants based on the absence of a well-measured parallax in the brightness range where dwarfs have reasonable parallax estimate from Gaia DR3 data. The photometric distances are calculated using a BaSTI-isochrone fitting code and the photometric metallicities. Results: Photometric distances derived from PDR1- and PGS-giants show typical uncertainties of 12% and a scatter of up to 20% and 40% respectively, when validated against inverted-parallax and Starhorse-code distances. The PDR1-giants catalogue provides a low-to-no bias view of the metallicity structure versus distance compared to the PGS-giants catalogue (with a distance-metallicity selection bias), while the PGS-giants catalogue provide

This erratum highlights a very serious error in a paper published by SIAM Review in 2011. The error is in Section 6.2 of [1]. It is very important to notify this error because of the following two reasons: (i) [1] is one of the most cited contributions in the field of identifiability of viral dynamics models, and (ii)the error is relevant because, as a result of it, a very popular viral model (perhaps the most popular in the field of HIV dynamics) has been classified as identifiable. In contrast, three of its parameters are not identifiable, even locally. This erratum first proves the non uniqueness of the three unidentifiable parameters by exhibiting infinitely many distinct but indistinguishable values of them. The non uniqueness is even local. Then, this erratum details the error made by the authors of [1] which produced the claimed (but false) local identifiability of all the model parameters.

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions.

This chapter concentrates on the deaths of very massive stars, the events leading up to their deaths, and how mass loss affects the resulting death. The previous three chapters emphasized the theory of wind mass loss, eruptions, and core collapse physics, but here we emphasize mainly the observational properties of the resulting death throes. Mass loss through winds, eruptions, and interacting binaries largely determines the wide variety of different types of supernovae that are observed, as well as the circumstellar environments into which the supernova blast waves expand. Connecting these observed properties of the explosions to the initial masses of their progenitor stars is, however, an enduring challenge and is especially difficult for very massive stars. Superluminous supernovae, pair instability supernovae, gamma ray bursts, and "failed" supernovae are all end fates that have been proposed for very massive stars, but the range of initial masses or other conditions leading to each of these (if they actually occur) are still very certain. Extrapolating to infer the role of very massive stars in the early universe is essentially unencumbered by observational constraints and sti

The Euclidean renormalization bundle considered in QFT by Connes, Kreimer, and Marcolli has been extended, in a remarkable series of papers by S Agarwala, to Riemannian manifolds $(X,g)$: in particular by the construction of a flat connection on that bundle, regarded as defined over a thickening of $X$ by an infinitesimal disk. The theory of Fourier integral operators on manifolds reconciles dimensional and zeta-function regularization by interpreting this disk as the germ of a neighborhood of a Jordan curve around $\infty$ on the Riemann sphere. Such fields $X \to ΩS^2$ were proposed in \cite{14} as useful in these contexts.

In this chapter, after a brief introduction and overview of stellar evolution, we discuss the evolution and nucleosynthesis of very massive stars (VMS: M>100 solar masses) in the context of recent stellar evolution model calculations. This chapter covers the following aspects: general properties, evolution of surface properties, late central evolution, and nucleosynthesis including their dependence on metallicity, mass loss and rotation. Since very massive stars have very large convective cores during the main-sequence phase, their evolution is not so much affected by rotational mixing, but more by mass loss through stellar winds. Their evolution is never far from a homogeneous evolution even without rotational mixing. All VMS at metallicities close to solar end their life as WC(-WO) type Wolf-Rayet stars. Due to very important mass loss through stellar winds, these stars may have luminosities during the advanced phases of their evolution similar to stars with initial masses between 60 and 120 solar masses. A distinctive feature which may be used to disentangle Wolf-Rayet stars originating from VMS from those originating from lower initial masses is the enhanced abundances of ne

We present a collection of results concerning the location and distribution of very triangular numbers among triangular numbers, including the twin very triangular number theorem, the existence of arbitrarily long gaps between -- and an analog of Bertrand's postulate for -- very triangular numbers.

There are views prevalent in the noncovalent chemistry literature that i) the O atom in molecules cannot form a chalcogen bond, and ii) if formed, this bond is very weak. We have shown in this study that these views are not necessarily true since the attractive energy between the oxygen atom of some molecules and several electron rich anionic bases examined in a series of 34 ion-molecule complexes varied from the weak (ca -2.30 kcal/mol) to the ultrastrong (-90.10 kcal/mol). The [MP2/aug-cc-pVTZ] binding energies for several of these complexes were found to be comparable to or significantly larger than that of the well-known hydrogen bond complex [FH...F]- (roughly -40 kcal/mol). The nature of the intermolecular interactions was examined using the quantum theory of atoms in molecules, second order natural bond orbital and symmetric adaptive perturbation theory energy decomposition analyses. It was found that many of these interactions comprise mixed bonding character (ionic and covalent), especially manifest in the moderate to strongly bound complexes. All these can be explained by a bonding to an anti-bonding orbital type donor acceptor charge transfer delocalization. This study,

Let k be a field. A "field generator" is a polynomial F in k[X,Y] satisfying k(F,G) = k(X,Y) for some G in k(X,Y). If G can be chosen in k[X,Y], we call F a "good field generator"; otherwise, F is a "bad field generator". These notions were first studied by Abhyankar, Jan and Russell in the 1970s. The present paper introduces and studies the notions of "very good" and "very bad" field generators. We give theoretical results as well as new examples of bad and very bad field generators.

In this chapter I review theoretical models for the formation of very massive stars. After a brief overview of some relevant observations, I spend the bulk of the chapter describing two possible routes to the formation of very massive stars: formation via gas accretion, and formation via collisions between smaller stars. For direct accretion, I discuss the problems of how interstellar gas may be prevented from fragmenting so that it is available for incorporation into a single very massive star, and I discuss the problems presented for massive star formation by feedback in the form of radiation pressure, photoionization, and stellar winds. For collision, I discuss several mechanisms by which stars might be induced to collide, and I discuss what sorts of environments are required to enable each of these mechanisms to function. I then compare the direct accretion and collision scenarios, and discuss possible observational signatures that could be used to distinguish between them. Finally, I come to the question of whether the process of star formation sets any upper limits on the masses of stars that can form.

We perform simulations of the capabilities of the next generation Very Large Array to image stellar radio photospheres. For very large (in angle) stars, such as red supergiants within a few hundred parsecs, good imaging fidelity results can be obtained on radio photospheric structures at 38 GHz employing standard techniques, such as disk model fitting and subtraction, with hundreds of resolution elements over the star, even with just the ngVLA-classic baselines to 1000 km. Using the ngVLA Rev B plus long baseline configuration (with baselines out to 9000 km, August 2018), we find for main sequence stars within $\sim$ 10 pc, the photospheres can be easily resolved at 85 GHz, with accurate measures of the mean brightness and size, and possibly imaging large surface structures, as might occur on e.g., active M dwarf stars. For more distant main sequence stars, we find that measurements of sizes and brightnesses can be made using disk model fitting to the u,v-data down to stellar diameters $\sim$ 0.4 mas in a few hours. This size would include M0 V stars to a distance of 15 pc, A0 V stars to 60 pc, and Red Giants to 2.4 kpc. Based on the Hipparcos catalog, we estimate that there are at

Global return value estimates of significant wave height and 10-m neutral wind speed are estimated from very large aggregations of archived ECMWF ensemble forecasts at +240-h lead time from the period 2003-2012. The upper percentiles are found to match ENVISAT wind speed better than ERA-Interim (ERA-I), which tends to be biased low. The return estimates are significantly higher for both wind speed and wave height in the extratropics and the subtropics than what is found from ERA-I, but lower than what is reported by Caires and Sterl (2005) and Vinoth and Young (2011). The highest discrepancies between ERA-I and ENS240 are found in the hurricane-prone areas, suggesting that the ensemble comes closer than ERA-I in capturing the intensity of tropical cyclones. The width of the confidence intervals are typically reduced by 70% due to the size of the data sets. Finally, non-parametric estimates of return values were computed from the tail of the distribution. These direct return estimates compare very well with Generalized Pareto estimates.