Miracle-dz/UniFAR-FTUs huggingface dataset:
Crossover from interaction to driven regimes in quantum vortex reconnections

Significance Vortex reconnections are fundamental events in fluid motion, randomizing the velocity field, changing the topology, and redistributing energy across length scales. In superfluid helium and atomic Bose–Einstein condensates, vortices are effectively one-dimensional lines called quantum vortices (akin to minitornadoes of a fixed strength). Individual reconnections happen when two vortices collide and subsequently recoil, exchanging heads and tails. Recent experimental progress opens the possibility of answering the important question as to whether reconnections obey a universal behavior. Here we show that the intervortex distance between reconnecting vortices obeys two fundamental scaling laws, which we identify in experimental data and numerical simulations, across homogeneous superfluids and trapped condensates. Reconnections of coherent filamentary structures play a key role in the dynamics of fluids, redistributing energy and helicity among the length scales, triggering dissipative effects, and inducing fine-scale mixing. Unlike ordinary (classical) fluids where vorticity is a continuous field, in superfluid helium and in atomic Bose–Einstein condensates (BECs) vorticity takes the form of isolated quantized vortex lines, which are conceptually easier to study. New experimental techniques now allow visualization of individual vortex reconnections in helium and condensates. It has long being suspected that reconnections obey universal laws, particularly a universal scaling with time of the minimum distance between vortices δ. Here we perform a comprehensive analysis of this scaling across a range of scenarios relevant to superfluid helium and trapped condensates, combining our own numerical simulations with the previous results in the literature. We reveal that the scaling exhibits two distinct fundamental regimes: a δ∼t1/2 scaling arising from the mutual interaction of the reconnecting strands and a δ∼t scaling when extrinsic factors drive the individual vortices.
String percolation in AA and p+p collisions

A brief review of the string percolation model and its results are presented together with the comparison to experimental data. First, it is done an introduction to the quark-gluon phase diagram and the lattice results concerning the connement and the percolation of center domains. It is studied the interaction of the strings produced in nucleus-nucleus and proton-proton collisions showing how the string percolation arises. The main consequences of the string percolation, concerning the dependence on the energy and centrality, on the multiplicities and the mean transverse momentum are obtained comparing with experimental data. It is emphasized the non-abelian character of the color eld of the strings forming the cluster to reproduce the rise of the transverse momentum with multiplicity and the relative suppression of multiplicities. It is also studied dierent observables like multiplicity and transverse momentum distributions, dependence with multiplicity and transverse momentum correlations, forward-backward correlations, the strength of the Bose-Einstein correlations, dependence on the multiplicity of J/ψ production and its possible suppression in pp collisions at high multiplicity, strangeness enhancement, elliptic ow, and ridge structure. The comparison with the data shows an overall agreement. The thermodynamical properties of the extended cluster formed in the collision are discussed computingits energy and entropy density, shear viscosity over entropy density ratio, bulk viscosity, sound speed and trace anomaly as a function of temperature, showing a remarkable agreement with lattice QCD evaluations. The string percolation can be regarded as the initial frame able to describe the collective behavior produced in AA and pp collisions.
Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense

Recent works have shown that random triangulations decorated by critical ($p=1/2$) Bernoulli site percolation converge in the scaling limit to a $\sqrt{8/3}$-Liouville quantum gravity (LQG) surface (equivalently, a Brownian surface) decorated by SLE$_6$ in two different ways: 1. The triangulation, viewed as a curve-decorated metric measure space equipped with its graph distance, the counting measure on vertices, and a single percolation interface converges with respect to a version of the Gromov-Hausdorff topology. 2. There is a bijective encoding of the site-percolated triangulation by means of a two-dimensional random walk, and this walk converges to the correlated two-dimensional Brownian motion which encodes SLE$_6$-decorated $\sqrt{8/3}$-LQG via the mating-of-trees theorem of Duplantier-Miller-Sheffield (2014); this is sometimes called $\textit{peanosphere convergence}$. We prove that one in fact has $\textit{joint}$ convergence in both of these two senses simultaneously. We also improve the metric convergence result by showing that the map decorated by the full collection of percolation interfaces (rather than just a single interface) converges to $\sqrt{8/3}$-LQG decorated by CLE$_6$ in the metric space sense. This is the first work to prove simultaneous convergence of any random planar map model in the metric and peanosphere senses. Moreover, this work is an important step in an ongoing program to prove that random triangulations embedded into $\mathbb C$ via the so-called $\textit{Cardy embedding}$ converge to $\sqrt{8/3}$-LQG.
Inexact Newton Methods for Stochastic Non-Convex Optimization with Applications to Neural Network Training

We survey sub-sampled inexact Newton methods and consider their application in non-convex settings. Under mild assumptions we derive convergence rates in expected value for sub-sampled low rank Newton methods, and sub-sampled inexact Newton Krylov methods. These convergence rates quantify the errors incurred in sub-sampling the Hessian and gradient, as well as in approximating the Newton linear solve, and in choosing regularization and step length parameters. We deploy these methods in training convolutional autoencoders for the MNIST, CIFAR10 and LFW data sets. These numerical results demonstrate that these sub-sampled inexact Newton methods are competitive with first order methods in computational cost, and can outperform first order methods with respect to generalization errors.
Convergence of Heuristic Parameter Choice Rules for Convex Tikhonov Regularization

We investigate the convergence theory of several known as well as new heuristic parameter choice rules for convex Tikhonov regularisation. The success of such methods is dependent on whether certain restrictions on the noise are satisfied. In the linear theory, such conditions are well understood and hold for typically irregular noise. In this paper, we extend the convergence analysis of heuristic rules using noise restrictions to the convex setting and prove convergence of the aforementioned methods therewith. The convergence theory is exemplified for the case of an ill-posed problem with a diagonal forward operator in $\ell^q$ spaces. Numerical examples also provide further insight.
The Pressure and Temperature Limits of Likely Rocky Exoplanets

The interior composition of exoplanets is not observable, limiting our direct knowledge of their structure, composition, and dynamics. Recently described observational trends suggest that rocky exoplanets, that is, planets without significant volatile envelopes, are likely limited to <1.5 Earth radii. We show that given this likely upper limit in the radii of purely rocky super‐Earth exoplanets, the maximum expected core‐mantle boundary pressure and adiabatic temperature are relatively moderate, 630 GPa and 5000 K, while the maximum central core pressure varies between 1.5 and 2.5 TPa. We further find that for planets with radii less than 1.5 Earth radii, core‐mantle boundary pressure and adiabatic temperature are mostly a function of planet radius and insensitive to planet structure. The pressures and temperatures of rocky exoplanet interiors, then, are less than those explored in recent shock‐compression experiments, ab initio calculations, and planetary dynamical studies. We further show that the extrapolation of relevant equations of state does not introduce significant uncertainties in the structural models of these planets. Mass‐radius models are more sensitive to bulk composition than any uncertainty in the equation of state, even when extrapolated to terapascal pressures.
Dynamically Fused Graph Network for Multi-hop Reasoning

Text-based question answering (TBQA) has been studied extensively in recent years. Most existing approaches focus on finding the answer to a question within a single paragraph. However, many difficult questions require multiple supporting evidence from scattered text among two or more documents. In this paper, we propose Dynamically Fused Graph Network (DFGN), a novel method to answer those questions requiring multiple scattered evidence and reasoning over them. Inspired by human’s step-by-step reasoning behavior, DFGN includes a dynamic fusion layer that starts from the entities mentioned in the given query, explores along the entity graph dynamically built from the text, and gradually finds relevant supporting entities from the given documents. We evaluate DFGN on HotpotQA, a public TBQA dataset requiring multi-hop reasoning. DFGN achieves competitive results on the public board. Furthermore, our analysis shows DFGN produces interpretable reasoning chains.
Learning to Regress 3D Face Shape and Expression From an Image Without 3D Supervision

The estimation of 3D face shape from a single image must be robust to variations in lighting, head pose, expression, facial hair, makeup, and occlusions. Robustness requires a large training set of in-the-wild images, which by construction, lack ground truth 3D shape. To train a network without any 2D-to-3D supervision, we present RingNet, which learns to compute 3D face shape from a single image. Our key observation is that an individual’s face shape is constant across images, regardless of expression, pose, lighting, etc. RingNet leverages multiple images of a person and automatically detected 2D face features. It uses a novel loss that encourages the face shape to be similar when the identity is the same and different for different people. We achieve invariance to expression by representing the face using the FLAME model. Once trained, our method takes a single image and outputs the parameters of FLAME, which can be readily animated. Additionally we create a new database of faces “not quite in-the-wild” (NoW) with 3D head scans and high-resolution images of the subjects in a wide variety of conditions. We evaluate publicly available methods and find that RingNet is more accurate than methods that use 3D supervision. The dataset, model, and results are available for research purposes at http://ringnet.is. tuebingen.mpg. de.
The Inflation Technique Completely Solves the Causal Compatibility Problem

Abstract The causal compatibility question asks whether a given causal structure graph — possibly involving latent variables — constitutes a genuinely plausible causal explanation for a given probability distribution over the graph’s observed categorical variables. Algorithms predicated on merely necessary constraints for causal compatibility typically suffer from false negatives, i.e. they admit incompatible distributions as apparently compatible with the given graph. In 10.1515/jci-2017-0020, one of us introduced the inflation technique for formulating useful relaxations of the causal compatibility problem in terms of linear programming. In this work, we develop a formal hierarchy of such causal compatibility relaxations. We prove that inflation is asymptotically tight, i.e., that the hierarchy converges to a zero-error test for causal compatibility. In this sense, the inflation technique fulfills a longstanding desideratum in the field of causal inference. We quantify the rate of convergence by showing that any distribution which passes the nth-order inflation test must be On−1/2$\begin{array}{} \displaystyle {O}{\left(n^{{{-}{1}}/{2}}\right)} \end{array}$-close in Euclidean norm to some distribution genuinely compatible with the given causal structure. Furthermore, we show that for many causal structures, the (unrelaxed) causal compatibility problem is faithfully formulated already by either the first or second order inflation test.
Vector hidden-bottom tetraquark candidate: Y(10750)

In this article, we take the scalar diquark and antidiquark as the basic constituents, construct the $C\gamma_5\otimes\stackrel{\leftrightarrow}{\partial}_\mu\otimes \gamma_5C$ type tetraquark current to study the $Y(10750)$ with the QCD sum rules. The predicted mass $M_{Y}=10.75\pm0.10\,\rm{GeV}$ supports assigning the $Y(10750)$ to be the diquark-antidiquark type vector hidden-bottom tetraquark state with a relative P-wave between the diquark pair.
Graphical Models in Loopy Distribution Grids: Topology estimation, change detection and limitation

Graphical models are a succinct way to represent the structure in probability distributions. This article analyzes the graphical model of nodal voltages in non-radial power distribution grids. Using algebraic and structural properties of graphical models, algorithms exactly determining topology and detecting line changes for distribution grids are presented along with their theoretical limitations. We show that if distribution grids have cycles/loops of size greater than three, then nodal voltages are sufficient for efficient topology estimation without additional assumptions on system parameters. In contrast, line failure or change detection using nodal voltages does not require any structural assumption. Under noisy measurements, we provide the first non-trivial bounds on the maximum noise that the system can tolerate for asymptotically correct topology recovery. The performance of the designed algorithms is validated with nonlinear AC power flow samples generated by Matpower on test grids, including scenarios with injection correlations and system noise.
Single and double nonlinear Compton scattering

We study single, double and higher-order nonlinear Compton scattering where an electron interacts nonlinearly with a high-intensity laser and emits one, two or more photons. We study, in particular, how double Compton is separated into one-step and two-step parts, where the latter is obtained from an incoherent product of two single-photon emissions. We include all contributions to double Compton and show that the previously neglected exchange term is in general on the same order of magnitude as the other one-step terms. Our approach reveals practically useful similarities between double Compton and the trident process, which allows us to transfer some of our previous results for trident to double Compton scattering. We provide a new gluing approach for obtaining the dominant contribution to higher-order Compton for long laser pulses. Unlike the standard gluing approach, our new approach does not require the intensity parameter $a_0$ to be much larger than one. For `hard' photons we obtain several saddle-point approximations for various field shapes.
Stroke Extraction for Offline Handwritten Mathematical Expression Recognition

Offline handwritten mathematical expression recognition is often considered much harder than its online counterpart due to the absence of temporal information. In order to take advantage of the more mature methods for online recognition and save resources, an oversegmentation approach is proposed to recover strokes from textual bitmap images automatically. The proposed algorithm first breaks down the skeleton of a binarized image into junctions and segments, then segments are merged to form strokes, finally stroke order is normalized by using recursive projection and topological sort. Good offline accuracy was obtained in combination with ordinary online recognizers, which were not specially designed for extracted strokes. Given a ready-made state-of-the-art online handwritten mathematical expression recognizer, the proposed procedure correctly recognized 58.22%, 65.65%, and 65.22% of the offline formulas rendered from the datasets of the Competitions on Recognition of Online Handwritten Mathematical Expressions (CROHME) in 2014, 2016, and 2019 respectively. Furthermore, given a trainable online recognition system, retraining it with extracted strokes resulted in an offline recognizer with the same level of accuracy. On the other hand, the speed of the entire pipeline was fast enough to facilitate on-device recognition on mobile phones with limited resources. To conclude, stroke extraction provides an attractive way to build optical character recognition software.
Effects of Carbon Monoxide on Myocardium: Ultrastructural Changes in Rabbits After Moderate, Chronic Exposure

Sixteen rabbits were placed in exposure chambers: eight were continuously exposed to 180 ppm of carbon monoxide and eight were exposed to atmospheric air for 2 weeks. The myocardial ultrastructure of all the rabbits was examined. In rabbits exposed to carbon monoxide, local areas of partial or total necrosis of the myofibrils and degenerative changes of the mitochondria were found. Extra- and intracellular edema, increases in the number of ribosomes and lipofuscin granules, and reparative fibrotic changes also occurred. Varying degrees of injury were noted in the blood vessels. Capillary edema, but never total stenosis, was seen in some areas. Stasis and occasional small perivascular hemorrhages were typical on the venous side; on the arterial side the characteristic picture was one of endothelial swelling, formation of subendothelial edema, and degenerative changes of the myocytes. The present study supports the hypothesis that chronic exposure to low levels of carboxyhemoglobin can produce myocardial damage and account for the increased risk of myocardial infarction and sudden death seen in heavy cigarette smokers.
Equivalences among the chi measure, Hoffman constant, and Renegar's distance to ill-posedness

We show the equivalence among the following three condition measures of a full column rank matrix $A$: the chi measure, the signed Hoffman constant, and the signed distance to ill-posedness. The latter two measures are constructed via suitable collections of matrices obtained by flipping the signs of some rows of $A$. Our results provide a procedure to estimate $\chi(A)$ thereby opening an avenue to identify classes of linear programs solvable in polynomial time in the real model of computation.
Plasmons in two-dimensional lattices of near-field coupled nanoparticles

We consider plasmonic metasurfaces constituted by an arbitrary periodic arrangement of spherical metallic nanoparticles. Each nanoparticle supports three degenerate dipolar localized surface plasmon (LSP) resonances. In the regime where the interparticle distance is much smaller than the optical or near-infrared wavelength associated with the LSPs, the latter couple through the dipole-dipole interaction and form collective plasmonic modes which extend over the whole metasurface. Within a Hamiltonian model which we solve exactly, we derive general expressions which enable us to extract analytically the quasistatic plasmonic dispersion for collective modes polarized within the plane and perpendicular to the plane of the metasurface. Importantly, our approach allows us not only to consider arbitrary Bravais lattices, but also non-Bravais two-dimensional metacrystals featuring nontrivial topological properties, such as, e.g., the honeycomb or Lieb lattices. Additionally, using an open quantum system approach, we consider perturbatively the coupling of the collective plasmons to both photonic and particle-hole environments, which lead, respectively, to radiative and nonradiative frequency shifts and damping rates, for which we provide closed-form expressions. The radiative frequency shift, when added to the quasistatic dispersion relation, provides an approximate analytical description of the fully retarded band structure of the collective plasmons. While it is tempting to make a direct analogy between the various systems which we consider and their electronic tight-binding equivalents, we critically examine how the long-range retarded and anisotropic nature of the dipole-dipole interaction may quantitatively and qualitatively modify the underlying band structures and discuss their experimental observability.
Modern theory of hydraulic fracture modeling with using explicit and implicit schemes

The paper presents novel results, obtained on the basis of the modified theory of hydraulic fractures (HF). The theory underlines significance of the speed equation. When applied to numerical simulation of HF, the theory reveals three distinct issues: (i) modeling the central part of a HF; (ii) modeling the near-front zone; and (iii) tracing changes in the shape of a fracture contour. Modeling the central part leads to a stiff system of ODE in time, what strongly complicates its integration. For explicit schemes, it requires small time steps to meet the CFL condition. For implicit schemes, it requires proper preconditioners. The gains and flaws of the two strategies are discussed. It is noted that a rough spatial mesh may be used in the central part. Modeling the near-front zone reveals the vital role of the speed equation for HF modeling by any method. Its asymptotic analysis has resulted in the fundamental concept of the universal asymptotic umbrella. For the near-front zone, it is also established that a notable part of the zone adjacent to the front propagates virtually as a simple wave. This implies that the CFL condition of stability for this zone is much less restrictive than for the central part of the fracture. Of essence is also that the wave-like propagation of the near front zone makes preferable upwind schemes of time stepping. On whole, the analysis implies that explicit time stepping may be complementing, competitive and even superior over implicit integration. Tracing changes in the front shape appears merely in 3D problems when the contour changes its form. The problem, being essentially geometrical, it may be solved separately by various methods, including fast marching, level set and the simplest string/marker methods. In 1D cases, it does not arise at all. Quantitative estimations and numerical examples illustrate the theoretical conclusions.
SHARP – VI. Evidence for CO (1–0) molecular gas extended on kpc-scales in AGN star-forming galaxies at high redshift

We present a study of the stellar host galaxy, CO (1–0) molecular gas distribution and AGN emission on 50–500 pc-scales of the gravitationally lensed dust-obscured AGN MG J0751+2716 and JVAS B1938+666 at redshifts 3.200 and 2.059, respectively. By correcting for the lensing distortion using a grid-based lens modelling technique, we spatially locate the different emitting regions in the source plane for the first time. Both AGN host galaxies have 300–500 pc-scale size and surface brightness consistent with a bulge/pseudo-bulge, and 2 kpc-scale AGN radio jets that are embedded in extended molecular gas reservoirs that are 5–20 kpc in size. The CO (1–0) velocity fields show structures possibly associated with discs (elongated velocity gradients) and interacting objects (off-axis velocity components). There is evidence for a decrement in the CO (1–0) surface brightness at the location of the host galaxy, which may indicate radiative feedback from the AGN, or offset star formation. We find CO–H2 conversion factors of around αCO = 1.5 ± 0.5 (K km s−1 pc2)−1, molecular gas masses of >3 × 1010 M⊙, dynamical masses of ∼1011 M⊙, and gas fractions of around 60 per cent. The intrinsic CO line luminosities are comparable to those of unobscured AGN and dusty star-forming galaxies at similar redshifts, but the infrared luminosities are lower, suggesting that the targets are less efficient at forming stars. Therefore, they may belong to the AGN feedback phase predicted by galaxy formation models, because they are not efficiently forming stars considering their large amount of molecular gas.