Miracle-dz/UniFAR-FTUs huggingface dataset:
On the p-adic Birch and Swinnerton-Dyer conjecture for elliptic curves over number fields

We formulate a multi-variable p-adic Birch and Swinnerton-Dyer conjecture for p-ordinary elliptic curves A over number fields K. It generalises the one-variable conjecture of Mazur-Tate-Teitelbaum, who studied the case K=Q and the phenomenon of exceptional zeros. We discuss old and new theoretical evidence towards our conjecture and in particular we fully prove it, under mild conditions, in the following situation: K is imaginary quadratic, A=E_K is the base-change to K of an elliptic curve over the rationals, and the rank of A is either 0 or 1. The proof is naturally divided into a few cases. Some of them are deduced from the purely cyclotomic case of elliptic curves over Q, which we obtain from a refinement of recent work of Venerucci alongside the results of Greenberg-Stevens, Perrin-Riou, and the author. The only genuinely multi-variable case (rank 1, two exceptional zeros, three partial derivatives) is newly established here. Its proof generalises to show that the `almost-anticyclotomic' case of our conjecture is a consequence of conjectures of Bertolini-Darmon on families of Heegner points, and of (partly conjectural) p-adic Gross--Zagier and Waldspurger formulas in families.
Decomposability and Mordell-Weil ranks of Jacobians using Picard numbers

We use methods for computing Picard numbers of reductions of K3 surfaces in order to study the decomposability of Jacobians over number fields and the variance of Mordell-Weil ranks of families of Jacobians over different ground fields. For example, we give examples of surfaces whose Picard numbers jump in rank at all primes of good reduction using Mordell-Weil groups of Jacobians and show that the genus of curves over number fields whose Jacobians are isomorphic to a product of elliptic curves satisfying certain reduction conditions is bounded. The isomorphism result addresses the number field analogue of some questions of Ekedahl and Serre on decomposability of Jacobians of curves into elliptic curves.
Stream–orbit misalignment – I. The dangers of orbit-fitting

Tidal streams don't, in general, delineate orbits. A stream-orbit misalignment is expected to lead to biases when using orbit-fitting to constrain models for the Galactic potential. In this first of two papers we discuss the expected magnitude of the misalignment and the resulting dangers of using orbit-fitting algorithms to constrain the potential. We summarize data for known streams which should prove useful for constraining the Galactic potential, and compute their actions in a realistic Galactic potential. We go on to discuss the formation of tidal streams in angle-action space, and explain why, in general, streams do not delineate orbits. The magnitude of the stream-orbit misalignment is quantified for a logarithmic potential and a multi-component Galactic potential. Specifically, we focus on the expected misalignment for the known streams. By introducing a two-parameter family of realistic Galactic potentials we demonstrate that assuming these streams delineate orbits can lead to order one errors in the halo flattening and halo-to-disc force ratio at the Sun. We present a discussion of the dependence of these results on the progenitor mass, and demonstrate that the misalignment is mass-independent for the range of masses of observed streams. Hence, orbit-fitting does not yield better constraints on the potential if one uses narrower, lower-mass streams.
Stationary and discontinuous weak solutions of the Navier-Stokes equations.

We prove that there exists a nontrivial finite energy periodic stationary weak solution to the 3D Navier-Stokes equations (NSE). The construction relies on a convex integration scheme utilizing new stationary building blocks designed specifically for the NSE. The constructed family of approximate stationary solutions is also used to prove the existence of weak solutions of the NSE with energy profiles discontinuous on a dense set of positive Lebesgue measure.
Dark matter searches at LHC

Besides Standard Model measurements and other Beyond Standard Model studies, the ATLAS and CMS experiments at the LHC will search for Supersymmetry, one of the most attractive explanation for dark matter. The SUSY discovery potential with early data is presented here together with some first results obtained with 2010 collision data at 7 TeV. Emphasis is placed on measurements and parameter determination that can be performed to disentangle the possible SUSY models and SUSY look-alike and the interpretation of a possible positive supersymmetric signal as an explanation of dark matter.
Forming misaligned stellar disks around a massive black hole: cloud infall in the Galactic center

Abstract The innermost parsec around Sgr A* has been found to play host to two disks or streamers of O and W-R stars. They are misaligned by an angle approaching 90°. That the stars are approximately coeval indicates that they formed in the same event rather than independently. We have performed smoothed particle hydrodynamic simulations of the infall of a single prolate cloud towards a massive black hole. As the cloud is disrupted, the large spread in angular momentum can, if conditions allow, lead to the creation of misaligned gas disks. In turn, stars may form within those disks. We are now investigating the origins of these clouds in the Galactic center (GC) region.
Prompt-photon plus jet associated photoproduction at HERA in the parton Reggeization approach

We study the photoproduction of isolated prompt photons associated with hadron jets in the framework of the parton Reggeization approach. The cross section distributions in the transverse energies and pseudorapidities of the prompt photon and the jet as well as the azimuthal decorrelation variables measured by the H1 and ZEUS collaborations at DESY HERA are nicely described by our predictions. The main improvements with respect to previous studies in the $k_T$-factorization framework include the application of the Reggeized-quark formalism, the generation of exactly gauge-invariant amplitudes with off-shell initial-state quarks, and the exact treatment of the $\gamma R\to \gamma g$ box contribution with off-shell initial-state gluons.
A Foreground Masking Strategy for [C ii] Intensity Mapping Experiments Using Galaxies Selected by Stellar Mass and Redshift

Intensity mapping provides a unique means to probe the epoch of reionization (EoR), when the neutral intergalactic medium was ionized by energetic photons emitted from the first galaxies. The [C ii] 158 μm fine-structure line is typically one of the brightest emission lines of star-forming galaxies and thus a promising tracer of the global EoR star formation activity. However, [C ii] intensity maps at 6 ≲ z ≲ 8 are contaminated by interloping CO rotational line emission (3 ≤ Jupp ≤ 6) from lower-redshift galaxies. Here we present a strategy to remove the foreground contamination in upcoming [C ii] intensity mapping experiments, guided by a model of CO emission from foreground galaxies. The model is based on empirical measurements of the mean and scatter of the total infrared luminosities of galaxies at z < 3 and with stellar masses M * > 10 8 M ⊙ selected in the K-band from the COSMOS/UltraVISTA survey, which can be converted to CO line strengths. For a mock field of the Tomographic Ionized-carbon Mapping Experiment, we find that masking out the “voxels” (spectral–spatial elements) containing foreground galaxies identified using an optimized CO flux threshold results in a z-dependent criterion m K AB ≲ 22 (or M * ≳ 10 9 M ⊙ ) at z < 1 and makes a [C ii]/COtot power ratio of ≳10 at k = 0.1 h/Mpc achievable, at the cost of a moderate ≲8% loss of total survey volume.
A simplification problem in manifold theory

Two smooth manifolds M and N are called R-diffeomorphic if their product with the real line are diffeomorphic. We consider the following simplification problem: does R-diffeomorphism imply diffeomorphism or homeomorphism? For compact manifolds, analysis of this problem relies on some of the main achievements of the theory of manifolds, in particular the h- and s-cobordism theorems in high dimensions and the spectacular more recent classification results in dimensions 3 and 4. This paper presents what is currently known about the subject as well as some new results about classifications of R-diffeomorphisms.
Cohomological construction of relative twists

Let g be a complex, semi-simple Lie algebra, h a Cartan subalgebra of g and D a subdiagram of the Dynkin diagram of g. Let g_D and l_D be the corresponding semi-simple and Levi subalgebras and consider two invariant solutions Phi, Phi_D of the pentagon equation for g and g_D respectively. Motivated by the theory of quasi-Coxeter quasitriangular quasibialgebras \cite{TL3}, we study in this paper the existence of a relative twist, that is an element F invariant under l_D such that the twist of Phi by F is Phi_D. Adapting the method of Donin and Shnider, who treated the case of an empty D, so that l_D=h and Phi_D=1, we give a cohomological construction of such an F under the assumption that Phi_D is the image of Phi under the generalised Harish-Chandra homomorphism. We also show that F is unique up to a gauge transformation if l_D is of corank 1 or F satisfies F^\Theta= F^{21} where \Theta is an involution of g acting as -1 on h.
A GAME CHARACTERIZING BAIRE CLASS 1 FUNCTIONS

Abstract Duparc introduced a two-player game for a function f between zero-dimensional Polish spaces in which Player II has a winning strategy iff f is of Baire class 1. We generalize this result by defining a game for an arbitrary function f : X → Y between arbitrary Polish spaces such that Player II has a winning strategy in this game iff f is of Baire class 1. Using the strategy of Player II, we reprove a result concerning first return recoverable functions.
Improved Landau gauge fixing and the suppression of finite-volume effects of the lattice gluon propagator

For the gluon propagator of pure SU(2) lattice gauge theory in the Landau gauge we investigate the effect of Gribov copies and finite-volume effects. Concerning gauge fixing, we enlarge the accessible gauge orbits by adding nonperiodic Z(2) gauge transformations and systematically employ the simulated annealing algorithm. Strategies to keep all Z(2) sectors under control within reasonable CPU time are discussed. We demonstrate that the finite-volume effects in the infrared regime become ameliorated. Reaching a physical volume of about (6.5 fm){sup 4}, we find that the propagator, calculated with the indicated improvements, becomes flat in the region of smallest momenta. There are first signs in four dimensions of a decrease towards vanishing momentum.
OUTFLOWS IN ρ OPHIUCHI AS SEEN WITH THE SPITZER INFRARED ARRAY CAMERA

Using the IRAC images from the Spitzer c2d program, we have made a survey of mid-infrared outflows in the ρ Ophiuchi molecular cloud. Extended objects that have prominent emission in IRAC channel 2 (4.5 μm) compared to IRAC channel 1 (3.6 μm) and stand out as green objects in the three-color images (3.6 μm in blue, 4.5 μm in green, 8.0 μm in red) are identified as mid-infrared outflows. As a result, we detected 13 new outflows in the ρ Ophiuchi molecular cloud that have not been previously observed in either the optical or the near-infrared. In addition, at the positions of previously observed HH objects or near-infrared emission, we detected 31 mid-infrared outflows, among which seven correspond to previously observed HH objects and 30 to near-infrared emission. Most of the mid-infrared outflows detected in the ρ Ophiuchi cloud are concentrated in the L1688 dense core region. In combination with the survey results for young stellar objects (YSOs) and millimeter and submillimeter sources, the distribution of mid-infrared outflows in the ρ Ophiuchi molecular complex hints a propagation of star formation in the cloud in the direction from the northwest to the southeast, as suggested by previous studies of the region.
TIME SERIES ANALYSIS OF GAMMA-RAY BLAZARS AND IMPLICATIONS FOR THE CENTRAL BLACK-HOLE MASS

Radiation from the blazar class of active galactic nuclei (AGNs) exhibits fast time variability which is usually ascribed to instabilities in the emission region near the central supermassive black hole. The variability time scale is generally faster in higher energy region, and data recently provided by the Fermi Gamma-ray Space Telescope in the GeV energy band enable a detailed study of the temporal behavior of AGN. Due to its wide field-of-view in the scanning mode, most sky regions are observed for several hours per day and daily light curves of many AGNs have been accumulated for more than 4 yr. In this paper we investigate the time variability of 15 well-detected AGNs by studying the normalized power spectrum density of their light curves in the GeV energy band. One source, 3C 454.3, shows a specific time scale of 6.8 × 105 s, and this value suggests, assuming the internal shock model, a mass for the central black hole of (108–1010) M☉ which is consistent with other estimates. It also indicates the typical time interval of ejected blobs is (7–70) times the light crossing time of the Schwarzschild radius.
Loss of halo triaxiality due to bar formation

Cosmological N-body simulations indicate that the dark matter haloes of galaxies should be generally triaxial. Yet, the presence of a baryonic disc is believed to alter the shape of the haloes. Here we aim to study how bar formation is affected by halo triaxiality and how, in turn, the presence of the bar influences the shape of the halo. We perform a set of collisionless N-body simulations of disc galaxies with triaxial dark matter haloes, using elliptical discs as initial conditions. Such discs are much closer to equilibrium with their haloes than circular ones, and the ellipticity of the initial disc depends on the ellipticity of the halo gravitational potential. For comparison, we also consider models with initially circular discs, and find that the differences are very important. In all cases, the mass of the disc is grown quasi-adiabatically within the haloes, but the time-scale of growth is not very important. We study models of different halo triaxialities and, to investigate the behaviour of the halo shape in the absence of bar formation, we run models with different disc masses, halo concentrations, disc velocity dispersions and also models where the disc shape is kept artificially axisymmetric. We find that the introduction of a massive disc, even if this is not circular, causes the halo triaxiality to be partially diluted. Once the disc is fully grown, a strong stellar bar develops within the halo that is still non-axisymmetric, causing it to lose its remaining non-axisymmetry. In triaxial haloes in which the parameters of the initial conditions are such that a bar does not form, the halo is able to remain triaxial and the circularization of its shape on the plane of the disc is limited to the period of disc growth. We conclude that part of the circularization of the halo is due to disc growth, but part must be attributed to the formation of a bar. Bars in the halo component, which have already been found in axisymmetric haloes, are also found in triaxial ones. We find that initially circular discs respond excessively to the triaxial potential and become highly elongated. They also lose more angular momentum than the initially elliptical discs and thus form stronger bars. Because of that, the circularization that their bars induce on their haloes is also more rapid. We also analyse halo vertical shapes and observe that their vertical flattenings remain considerable, meaning that the haloes become approximately oblate by the end of the simulations. Finally, we also analyse the kinematics of a subset of halo particles that rotate in disc-like manner. These particles occupy a layer around the plane of the disc and their rotation is more important in the spherical halo than in triaxial ones. We also find that, even though the final shape of the halo is roughly independent of the initial shape, the initially triaxial ones are able to retain the anisotropy of their velocity dispersions.
Weighted Local Estimates for Singular Integral Operators

A local median decomposition is used to prove that a weighted local mean of a function is controlled by a weighted local mean of its local sharp maximal function. Together with (a local version of) the estimate $M^{\sharp}_{0,s}(Tf)(x) \le c\,Mf(x)$ for Calder\'{o}n-Zygmund singular integral operators, this allows us to express the local weighted integral control of $Tf$ by $Mf$. Similar estimates hold for $T$ replaced by singular integrals with kernels satisfying H\"{o}rmander-type conditions or integral operators with homogeneous kernels, and $M$ replaced by an appropriate maximal function $M_T$. Using sharper bounds in the local median decomposition we prove two-weight, $L^p_v$-$L^q_w$ estimates for singular integral operators for $1<p\le q<\infty$. In all cases, the results include weights that are not necessarily $A_{\infty}$. The local nature of these estimates leads to results involving weighted generalized Orlicz-Campanato and Orlicz-Morrey spaces.
A New Homotopy Proximal Variable-Metric Framework for Composite Convex Minimization

This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is to utilize a new parameterization strategy of the optimality condition to design a class of homotopy proximal variable-metric algorithms that can achieve linear convergence and finite global iteration-complexity bounds. We identify at least three subclasses of convex problems in which our approach can apply to achieve linear convergence rates. The second idea is a new primal-dual-primal framework for implementing proximal Newton methods that has attractive computational features for a subclass of nonsmooth composite convex minimization problems. We specialize the proposed algorithm to solve a covariance estimation problem in order to demonstrate its computational advantages. Numerical experiments on the four concrete applications are given to illustrate the theoretical and computational advances of the new methods compared with other state-of-the-art algorithms.
Time to negative throat culture following initiation of antibiotics for pharyngeal group A Streptococcus: a systematic review and meta-analysis to inform public health control measures

Background: Public health guidance recommending isolation of individuals with group A streptococcal (GAS) infection or carriage for 12-24 hours from antibiotic initiation to prevent onward transmission requires a strong evidence-base. Methods: We conducted a systematic review (PROSPERO CRD42021290364) and meta-analysis to estimate the pooled proportion of individuals who remain GAS culture-positive at set intervals after initiation of antibiotics. We searched Ovid MEDLINE (1946-), EMBASE (1974-) and the Cochrane library. We included interventional or observational studies with ten or more participants reporting rates of GAS throat culture during antibiotics for culture confirmed GAS pharyngitis, scarlet fever, and asymptomatic pharyngeal GAS carriage. We did not apply age, language, or geographical restrictions. Findings: Of 5,058 unique records identified, 43 were included; 37 (86%) randomised controlled studies, three (7%) non-randomised controlled trials and three (7%) before-and-after studies. The proportion of individuals who remained culture-positive at day 1, day 2, and day 3-9 were 6.9% (95% CI 2.7-16.8%), 5.4% (95% CI 2.1-13.3%) and 2.6% (95% CI 1.6-4.2%). For penicillins and cephalosporins, day 1 positivity was 6.5% (95% CI 2.5-16.1%) and 1.6% (95% CI 0.04-42.9%) respectively. Overall, for 9.1% (95% CI 7.3-11.3), throat swabs collected after completion of therapy were GAS culture-positive. Interpretation: Our review provides evidence that antibiotics for pharyngeal GAS achieve a high rate of culture conversion within 24 hours but highlights the need for further research given the methodological limitations of published studies and imprecision of pooled estimates. Further evidence is needed for non-beta-lactam antibiotics and for asymptomatic individuals.
The open string McKay correspondence for type A singularities

We formulate a Crepant Resolution Correspondence for open Gromov-Witten invariants (OCRC) of toric Calabi-Yau orbifolds by viewing the open theories as sections of Givental's symplectic vector space and the correspondence as a linear map of Givental spaces which identifies them. We deduce a Bryan-Graber-type statement for disk invariants and extend it to arbitrary genus zero topologies in the Hard Lefschetz case. Upon leveraging Iritani's theory of integral structures to equivariant quantum cohomology, we conjecture a general form of the symplectomorphism entering the OCRC which arises from a geometric correspondence at the equivariant K-theory level. We give a complete proof of this in the case of minimal resolutions of threefold A_n singularities. Our methods rely on a new description of the equivariant quantum D-modules underlying the Gromov-Witten theory of this class of targets.
Markov approximations of Gibbs measures for long-range interactions on 1D lattices

We study one-dimensional lattice systems with pair-wise interactions of infinite range. We show projective convergence of Markov measures to the unique equilibrium state. For this purpose we impose a slightly stronger condition than summability of variations on the regularity of the interaction. With our condition we are able to explicitly obtain stretched exponential bounds for the rate of mixing of the equilibrium state. Finally we show convergence for the entropy of the Markov measures to that of the equilibrium state via the convergence of their topological pressure (free energy).
Internal Josephson effects in spinor dipolar Bose-Einstein condensates

We theoretically study the internal Josephson effect, which is driven by spin-exchange interactions and magnetic dipole-dipole interactions, in a three-level system for spin-1 Bose-Einstein condensates, obtaining novel spin dynamics. We introduce single spatial mode approximations into the Gross-Pitaevskii equations and derive the Josephson-type equations, which are analogous to tunneling currents through three junctions between three superconductors. From an analogy with two interacting nonrigid pendulums, we identify unique varied oscillational modes, called the 0-{pi}, 0-running, running-running, 2n{pi} and running-2{pi}, single nonrigid pendulum, and two rigid pendulums phase modes. These Josephson modes in the three states are expected to be found in real atomic Bose gas systems.
Determination of the lactose and galactose content of common foods: Relevance to galactosemia

Abstract Classical galactosemia (CG) is a disorder of galactose metabolism which results from deficiency of the enzyme galactose‐1‐phosphate uridylyl transferase (GALT). Treatment consists of immediately eliminating galactose from the diet in the new‐born and lifelong restriction of dietary galactose. The inclusion of a wider variety of foods for people with CG may provide many benefits, including improved nutritional adequacy and quality of life. Galactose plays an important role in glycosylation of glycoproteins and glycolipids. Moderate liberalization of galactose restriction has been shown to improve immunoglobulin G (IgG) glycosylation for some individuals with CG. Moreover, recent outcome research suggests that strict restriction of nondairy galactose may have more unfavorable outcomes than moderate liberalization in CG patients. In the current work, based on patient feedback, we have analyzed the lactose and galactose content of different foods available in Ireland. These include a range of cheeses, yogurts, pizzas, soups, biscuits, cakes, pastries, crackers, mayonnaises, salad creams, fat spreads, crisps, corn chips, salamis, and gravies. This work provides information to support the development of a practical food‐based approach to facilitate analysis of dietary galactose intake and to possibly increase overall variety of food choices for people with CG.