We present ELENA (EvaLuator of tunnElliNg Actions), an open-source Python package designed to compute the full evolution of first-order phase transitions in the early Universe generated by particle physics models, taking into account several refinements that go beyond commonly assumed simplifications. The core of ELENA is based on a vectorized implementation of the tunnelling potential formalism, which allows for a fast computation of the finite-temperature tunnelling action. This, in turn, enables the sampling of the full range of temperatures where two phases coexist and the use of integral expressions that track the complete evolution of the transition, providing a comprehensive picture of it. In addition, ELENA provides all the tools to compute the resulting stochastic gravitational waves spectrum, allowing for the full chain of computations - from the Lagrangian parameter inputs to the final gravitational waves spectrum - in a fast and self-contained implementation.

Extreme mass ratio inspirals, compact objects spiraling into massive black holes, represent key sources for future space-based gravitational-wave detectors such as LISA. The inspirals will occur within rich astrophysical environments containing gravitating matter. Motivated by this, we develop a fully relativistic framework for inspirals under the gravitational influence of matter environments. Our approach employs a two-parameter perturbation expansion in the mass ratio and an environmental parameter. This yields a modified Teukolsky equation capturing the leading cross-order. We then implement a simple pole-dipole approximation of an axisymmetric environment through a thin matter shell and restrict to non-rotating black holes. As a result, we obtain a piecewise type D spacetime. This enables the use of Teukolsky-based methods while accounting for junction physics. The presence of the matter shell leads to effectively non-separable boundary conditions for the Teukolsky scalar and introduces mode mixing between adjacent multipoles. Additionally, the shell oscillates under the wave perturbation of the inspiral, contributing to the overall flux. The framework provides novel insights into the global dynamics of gravitational radiation in tidal environments. Furthermore, it represents a complete theoretical foundation for a future computation of inspirals and waveforms in our environmental model.

The evidence of a Stochastic Gravitational Wave Background (SGWB) in the nHz frequency range is posed to open a new window on the Universe. A preferred explanation relies on a supercooled first order phase transition at the 100 MeV - GeV scale. In this article, we address the feasibility going from the particle physics model to the production of the gravitational waves. We take a minimal approach for the dark sector model introducing the fewest ingredients required, namely a new U(1) gauge group and a dark scalar that dynamically breaks the symmetry. Supercooling poses challenges in the analysis that put under question the feasibility of this explanation: we address them, going beyond previous studies by carefully considering the effects of a vacuum domination phase and explicitly tracking the phase transition from its onset to its completion. We find that the proposed model can successfully give origin to the observed PTA SGWB signal. The strong supercooling imposes a correlation between the new gauge coupling and the scalar quartic one, leading to a significant hierarchy between the (heavier) gauge boson and the dark scalar. Ultimately, information on phase transitions from SGWB observations could provide a direct probe of the microphysics of the Early Universe and be used to guide future searches of dark sector in laboratories.

Despite their popularity in non-English NLP, multilingual language models often underperform monolingual ones due to inter-language competition for model parameters. We propose Cross-lingual Expert Language Models (X-ELM), which mitigate this competition by independently training language models on subsets of the multilingual corpus. This process specializes X-ELMs to different languages while remaining effective as a multilingual ensemble. Our experiments show that when given the same compute budget, X-ELM outperforms jointly trained multilingual models across all considered languages and that these gains transfer to downstream tasks. X-ELM provides additional benefits over performance improvements: new experts can be iteratively added, adapting X-ELM to new languages without catastrophic forgetting. Furthermore, training is asynchronous, reducing the hardware requirements for multilingual training and democratizing multilingual modeling.

Preliminary version of a course in univariate real analysis, with 14 chapters and 1 appendix (Chapters 1-8 complete at present). 1. Infinite sums. Real numbers; 2. Limits of sequences and subsequences; 3. Arithmetic of limits. AK series; 4. Infinite series. Elementary functions; 5. Limits of functions. Asymptotic notation; 6. Continuous functions; 7. Derivatives; 8. Applications of mean value theorems; 9. Taylor polynomials and series. Real analytic functions; 10. Primitives of uniformly continuous functions; 11. Newton integral. Primitives of rational functions; 12. Riemann integral. Transcendence of the number e; 13. Riemann integral. Henstock--Kurzweil integral; 14. More applications of Riemann integral and A. Solutions to exercises.

We present a comparison of our results from ground-based observations of asteroid (21) Lutetia with imaging data acquired during the flyby of the asteroid by the ESA Rosetta mission. This flyby provided a unique opportunity to evaluate and calibrate our method of determination of size, 3-D shape, and spin of an asteroid from ground-based observations. We present our 3-D shape-modeling technique KOALA which is based on multi-dataset inversion. We compare the results we obtained with KOALA, prior to the flyby, on asteroid (21) Lutetia with the high-spatial resolution images of the asteroid taken with the OSIRIS camera on-board the ESA Rosetta spacecraft, during its encounter with Lutetia. The spin axis determined with KOALA was found to be accurate to within two degrees, while the KOALA diameter determinations were within 2% of the Rosetta-derived values. The 3-D shape of the KOALA model is also confirmed by the spectacular visual agreement between both 3-D shape models (KOALA pre- and OSIRIS post-flyby). We found a typical deviation of only 2 km at local scales between the profiles from KOALA predictions and OSIRIS images, resulting in a volume uncertainty provided by KOALA better than 10%. Radiometric techniques for the interpretation of thermal infrared data also benefit greatly from the KOALA shape model: the absolute size and geometric albedo can be derived with high accuracy, and thermal properties, for example the thermal inertia, can be determined unambiguously. We consider this to be a validation of the KOALA method. Because space exploration will remain limited to only a few objects, KOALA stands as a powerful technique to study a much larger set of small bodies using Earth-based observations.

High-precision angle-resolved dc magnetization and magnetic torque studies were performed on a single-crystalline sample of URhGe, an orthorhombic Ising ferromagnet with the $c$ axis being the magnetization easy axis, in order to investigate the phase diagram around the ferromagnetic (FM) reorientation transition in a magnetic field near the $b$ axis. We have clearly detected first-order transition in both the magnetization and the magnetic torque at low temperatures, and determined detailed profiles of the wing structure of the three-dimensional $T$-$H_{b}$-$H_{c}$ phase diagram, where $H_{c}$ and $H_{b}$ denotes the field components along the $c$ and the $b$ axes, respectively. The quantum wing critical points are located at $\mu_0H_c\sim\pm$1.1 T and $\mu_0H_b\sim$13.5 T. Two second-order transition lines at the boundaries of the wing planes rapidly tend to approach with each other with increasing temperature up to $\sim 3$ K. Just at the zero conjugate field ($H_c=0$), however, a signature of the first-order transition can still be seen in the field derivative of the magnetization at $\sim 4$ K, indicating that the tricritical point exists in a rather high temperature region above 4 K. This feature of the wing plane structure is consistent with the theoretical expectation that three second-order transition lines merge tangentially at the triciritical point.

In this letter, we study tree-level scattering amplitudes of scalar particles in the context of effective field theories. We use tools similar to the soft bootstrap to build an ansatz for cyclically ordered amplitudes and impose the Bern-Carrasco-Johansson (BCJ) relations as a constraint. We obtain a set of BCJ-satisfying amplitudes as solutions to our procedure, which can be thought of as special higher-derivative corrections to SU(N) non-linear sigma model amplitudes satisfying BCJ relations to arbitrary multiplicity at leading order. The surprising outcome of our analysis is that BCJ conditions on higher-point amplitudes impose constraints on lower-point amplitudes, and they relate coefficients at different orders in the derivative expansion. This shows that BCJ conditions are much more restrictive than soft limit behavior, allowing only for a very small set of solutions.

We prove several results giving new and stronger connections between learning, circuit lower bounds and pseudorandomness. Among other results, we show a generic learning speedup lemma, equivalences between various learning models in the exponential time and subexponential time regimes, a dichotomy between learning and pseudorandomness, consequences of non-trivial learning for circuit lower bounds, Karp-Lipton theorems for probabilistic exponential time, and NC$^1$-hardness for the Minimum Circuit Size Problem.

One of the major challenges of particle physics has been to gain an in-depth understanding of the role of quark flavor and measurements and theoretical interpretations of their results have advanced tremendously: apart from masses and quantum numbers of flavor particles, there now exist detailed measurements of the characteristics of their interactions allowing stringent tests of Standard Model predictions. Among the most interesting phenomena of flavor physics is the violation of the CP symmetry that has been subtle and difficult to explore. Till early 1990s observations of CP violation were confined to neutral $K$ mesons, but since then a large number of CP-violating processes have been studied in detail in neutral $B$ mesons. In parallel, measurements of the couplings of the heavy quarks and the dynamics for their decays in large samples of $K, D$, and $B$ mesons have been greatly improved in accuracy and the results are being used as probes in the search for deviations from the Standard Model. In the near future, there will be a transition from the current to a new generation of experiments, thus a review of the status of quark flavor physics is timely. This report summarizes the results of the current generation of experiments that is about to be completed and it confronts these results with the theoretical understanding of the field.

Electrical spin-current generation is among the core phenomena driving the field of spintronics. Using {\em ab initio} calculations we show that a room-temperature metallic collinear antiferromagnet RuO$_2$ allows for highly efficient spin-current generation, arising from anisotropically-split bands with conserved up and down spins along the N\'eel vector axis. The zero net moment antiferromagnet acts as an electrical spin-splitter with a 34$^\circ$ propagation angle between spin-up and spin-down currents. Correspondingly, the spin-conductivity is a factor of three larger than the record value from a survey of 20,000 non-magnetic spin-Hall materials. We propose a versatile spin-splitter-torque concept utilizing antiferromagnetic RuO$_2$ films interfaced with a ferromagnet.

Dynamical friction implies a consistency check on any system where dark matter particles are hypothesised to explain orbital dynamics requiring more mass under Newtonian gravity than is directly detectable. Introducing the assumption of a dominant dark matter halo will also imply a decay timescale for the orbits in question. A self-consistency constraint hence arises, such that the resulting orbital decay timescales must be longer than the lifetimes of the systems in question. While such constraints are often trivially passed, the combined dependencies of dynamical friction timescales on the mass and orbital radius of the orbital tracer and on the density and velocity dispersion of the assumed dark matter particles leads to the existence of a number of astronomical systems where such a consistency test is failed. Here, we review cases from stars in ultrafaint dwarf galaxies, galactic bars, satellite galaxies, and, particularly, the multi-period mutual orbits of the Magellanic Clouds, as recently inferred from the star formation histories of these two galaxies, as well as the nearby M81 group of galaxies, where introducing enough dark matter to explain observed kinematics leads to dynamical friction orbital decay timescales shorter than the lifetimes of the systems in question. Taken together, these observations exclude dark matter halos made of particles as plausible explanations for the observed kinematics of these systems.

We use the lightcurve inversion method to derive new shape models and spin states of asteroids from the sparse-in-time photometry compiled in the Lowell Photometric Database. To speed up the time-consuming process of scanning the period parameter space through the use of convex shape models, we use the distributed computing project Asteroids@home, running on the Berkeley Open Infrastructure for Network Computing (BOINC) platform. This way, the period-search interval is divided into hundreds of smaller intervals. These intervals are scanned separately by different volunteers and then joined together. We also use an alternative, faster, approach when searching the best-fit period by using a model of triaxial ellipsoid. By this, we can independently confirm periods found with convex models and also find rotation periods for some of those asteroids for which the convex-model approach gives too many solutions. From the analysis of Lowell photometric data of the first 100,000 numbered asteroids, we derived 328 new models. This almost doubles the number of available models. We tested the reliability of our results by comparing models that were derived from purely Lowell data with those based on dense lightcurves, and we found that the rate of false-positive solutions is very low. We also present updated plots of the distribution of spin obliquities and pole ecliptic longitudes that confirm previous findings about a non-uniform distribution of spin axes. However, the models reconstructed from noisy sparse data are heavily biased towards more elongated bodies with high lightcurve amplitudes.

In calculations of the elementary scalar spectra of spontaneously broken gauge theories there is a number of subtleties which, though often unnecessary to deal with in the order-of-magnitude type of calculations, have to be taken into account if fully consistent results are sought for. Within the "canonical" effective-potential approach these are, for instance: the need to handle infinite series of nested commutators of derivatives of field-dependent mass matrices, the need to cope with spurious IR divergences emerging in the consistent leading-order approximation and, in particular, the need to account for the fine interplay between the renormalization effects in the one- and two-point Green's functions which, indeed, is essential for the proper stable vacuum identification and, thus, for the correct interpretation of the results. In this note we illustrate some of these issues in the realm of the minimal abelian Higgs model and two of its simplest extensions including extra heavy scalars in the spectrum in attempt to exemplify the key aspects of the usual "hierarchy problem" lore in a very specific and simple setting. We emphasise that, regardless of the omnipresent polynomial cut-off dependence in the one-loop corrections to the scalar two-point function, the physical Higgs boson mass is always governed by the associated symmetry-breaking VEV and, as such, it is generally as UV-robust as all other VEV-driven masses in the theory.

Let G be a planar graph with a list assignment L. Suppose a preferred color is given for some of the vertices. We prove that if G has girth at least six and all lists have size at least three, then there exists an L-coloring respecting at least a constant fraction of the preferences.

The stellar initial mass function (IMF) is the key to understanding the matter cycle in the Universe. Edwin Salpeter's paper of 1955 founded this research field. Evidence today, however, challenges the initial mass function as an invariant probability distribution function.

It is an open question whether the linear extension complexity of the Cartesian product of two polytopes P, Q is the sum of the extension complexities of P and Q. We give an affirmative answer to this question for the case that one of the two polytopes is a pyramid.

We present new constraints on neutrino secret interactions ($\nu$SI) by studying high-energy neutrinos from well-known astrophysical sources, such as SN1987A, the blazars TXS $0506+056$ and PKS $0735+178$, the active galaxy NGC 1068, and KM3-230213A neutrino event. We extend existing limits by covering a previously unconstrained region of the mediator mass parameter space. Our analysis focuses on Dirac neutrinos interacting with a massive spin-one boson as they propagate through the Cosmic Neutrino Background. We consider both ultra-relativistic and non-relativistic regimes, deriving bounds on the $\nu$SI coupling constant across the full $\nu$SI mediator mass range. Our results obtained using analytical methods, demonstrate significant constraints on the $\nu$SI coupling in the low-mass mediator mass region for a given cutoff parameter.

Metals enhance the cooling efficiency of molecular clouds, promoting fragmentation. Consequently, increasing the metallicity may boost the formation of low-mass stars. Within the integrated galaxy initial mass function (IGIMF) theory, this effect is empirically captured by a linear relation between the slope of the low-mass stellar IMF, $\alpha_1$, and the metal mass fraction, $Z$. This linear $\alpha_1$-$Z$ relation has been calibrated up to $\approx 2 \, Z_{\odot}$, though higher metallicity environments are known to exist. We show that if the linear $\alpha_1$-$Z$ relation extends to higher metallicities ($[Z] \gtrsim 0.5$), massive star formation is suppressed entirely. Alternatively, fragmentation efficiency may saturate beyond some metallicity threshold if gravitational collapse cascades rapidly enough. To model this behavior, we propose a logistic function describing the transition from metallicity-sensitive to metallicity-insensitive fragmentation regimes. We provide a user-friendly public code, pyIGIMF, which enables the instantaneous computation of the IGIMF theory with the logistic $\alpha_1$-$Z$ relation.