Daily Papers

In this article, we introduce and study singular foliations of b^k-type. These singular foliations formalize the properties of vector fields that are tangent to order k along a submanifold W subset M. Our first result is a classification of these foliations, relating them to geometric structures defined in a formal neighborhood of the submanifold, such as jets of distributions that are involutive up to order k-1. When W is a hypersurface, singular foliations of b^k-type are Lie algebroids. In this particular case, they are generalizations of the b^k-tangent bundles introduced by Scott. Indeed, they are always locally isomorphic to b^k-tangent bundles, but globally such an isomorphism is obstructed by a holonomy invariant. Our second main result is a Riemann-Hilbert-style classification of singular foliations of b^k-type in terms of holonomy representations. In this paper, we study singular foliations of b^k-type from several different perspectives. In particular: (1) We study the problem of extending a k-th-order foliation to a (k+1)-th order foliation and prove that this is obstructed by a characteristic class. (2) When W is a hypersurface, we give a detailed study of algebroid differential forms and extend Scott's calculation of the cohomology. (3) We study algebroid symplectic forms in terms of the geometric structures induced on W. In particular, we find that there is a close relationship between the above obstruction class for extensions and the symplectic variation of the symplectic foliation induced on W.

In neural text-to-speech (TTS), two-stage system or a cascade of separately learned models have shown synthesis quality close to human speech. For example, FastSpeech2 transforms an input text to a mel-spectrogram and then HiFi-GAN generates a raw waveform from a mel-spectogram where they are called an acoustic feature generator and a neural vocoder respectively. However, their training pipeline is somewhat cumbersome in that it requires a fine-tuning and an accurate speech-text alignment for optimal performance. In this work, we present end-to-end text-to-speech (E2E-TTS) model which has a simplified training pipeline and outperforms a cascade of separately learned models. Specifically, our proposed model is jointly trained FastSpeech2 and HiFi-GAN with an alignment module. Since there is no acoustic feature mismatch between training and inference, it does not requires fine-tuning. Furthermore, we remove dependency on an external speech-text alignment tool by adopting an alignment learning objective in our joint training framework. Experiments on LJSpeech corpus shows that the proposed model outperforms publicly available, state-of-the-art implementations of ESPNet2-TTS on subjective evaluation (MOS) and some objective evaluations.

We present the outflows detected in HOPS 373SW, a protostar undergoing a modest 30% brightness increase at 850 mum. Atacama Large Millimeter/submillimeter Array (ALMA) observations of shock tracers, including SiO 8--7, CH_3OH 7_{rm k}--6_{rm k}, and ^{12}CO 3--2 emission, reveal several outflow features around HOPS 373SW. The knots in the extremely high-velocity SiO emission reveal the wiggle of the jet, for which a simple model derives a 37^circ inclination angle of the jet to the plane of the sky, a jet velocity of 90 km s^{-1}, and a period of 50 years. The slow SiO and CH_3OH emission traces U-shaped bow shocks surrounding the two CO outflows. One outflow is associated with the high-velocity jets, while the other is observed to be close to the plane of the sky. The misaligned outflows imply that previous episodic accretion events have either reoriented HOPS 373SW or that it is an unresolved protostellar binary system with misaligned outflows.

The exact location of the gamma-ray emitting region in blazar jets has long been a matter of debate. However, the location has important implications about the emission processes, geometric and physical parameters of the jet, as well as the nature of interaction of the jet with the interstellar and intergalactic medium. Diverse conclusions have been drawn by various authors based on a variety of methods applied to different data sets of many blazars, e.g., the location is less than 0.1 pc from the central engine within the broad line region (BLR) or a few or tens of pc downstream beyond the dusty torus or at some intermediate distance. Here we use a method, established in a previous work, in which the location of the GeV/optical emission is determined using the ratio of energy dissipated during contemporaneous outbursts at those wave bands. We apply it to a total of 47 multi-wavelength outbursts in 10 blazars. We find that the location of the GeV/optical emission is beyond the BLR for all cases. This result is consistent with other studies, in which the location has been determined for a large sample of blazars. We compare the location determined by our method for several GeV outbursts of multiple blazars to that obtained by other authors using different methods. We find that our results are consistent in such one-to-one comparison in most cases, for which the required data were available.

Energy-energy correlators are constructed by averaging the number of charged particle pairs within jets, weighted by the product of their transverse momenta, as a function of the angular separation of the particles within a pair. They are sensitive to a multitude of perturbative and nonperturbative quantum chromodynamics phenomena in high-energy particle collisions. Using lead-lead data recorded with the CMS detector, energy-energy correlators inside high transverse momentum jets are measured in heavy ion collisions for the first time. The data are obtained at a nucleon-nucleon center-of-mass energy of 5.02 TeV and correspond to an integrated luminosity of 1.70 nb^{-1}. A similar analysis is done for proton-proton collisions at the same center-of-mass energy to establish a reference. The ratio of lead-lead to proton-proton energy-energy correlators reveals significant jet substructure modifications in the quark-gluon plasma. The results are compared to different models that incorporate either color coherence or medium response effects, where the two effects predict similar substructure modifications.

We use two-dimensional particle-in-cell simulations to investigate the generation and evolution of the magnetic field associated with the propagation of a jet for various initial conditions. We demonstrate that, in general, the magnetic field is initially grown by the Weibel and Mushroom instabilities. However, the field is saturated by the Alfv'en current limit. For initially non-magnetized plasma, we show that the growth of the magnetic field is delayed when the matter density of the jet environment is lower, which are in agreement with simple analytical predictions. We show that the higher Lorentz factor (gtrsim 2) prevents rapid growth of the magnetic fields. When the initial field is troidal, the position of the magnetic filaments moves away from the jet as the field strength increases. The axial initial field helps the jet maintain its shape more effectively than the troidal initial field.