Miracle-dz/UniFAR-FTUs huggingface dataset:
On the connection between thin vortex layers and vortex sheets

The equations for the two-dimensional motion of a layer of uniform vorticity in an incompressible, inviscid fluid are examined in the limit of small thickness. Under the right circumstances, the limit is a vortex sheet whose strength is the vorticity multiplied by the local thickness of the layer. However, vortex sheets can develop singularities in finite time, and their subsequent nature is an open question. Vortex layers, on the other hand, have motions for all time, though they may develop singularities on their boundaries. Fortunately, a material curve within the layer does exist for all time. Under certain assumptions, its limiting motion is again the vortex sheet, and thus its behaviour may indicate the nature and possible existence of the vortex sheet after the singularity time. Similar asymptotic results are obtained also for the limiting behaviour of the centre curve as defined by Moore (1978). By examining the behaviour of a sequence of layers, some physical understanding of the formation of the curvature singularity for a vortex sheet is gained. A strain flow, induced partly by the periodic extension of the sheet, causes vorticity to be advected to a certain point on the sheet rapidly enough to form the singularity. A vortex layer, however, simply bulges outwards as a consequence of incompressibility and subsequently forms a core with trailing arms that wrap around it. The evidence indicates that no singularities form on the boundary curves of the layer. Beyond the singularity time of the vortex sheet, the limiting behaviour of the vortex layers is non-uniform. Away from the vortex core, the layers converge to a smooth curve which has the appearance of a doubly branched spiral. While the circulation around the core vanishes, approximations to the vortex sheet strength become unbounded, indicating a complex, local structure whose precise nature remains undetermined.
The mathematics of sex and marriage, revisited

We analyze the problem of modeling marriages in a two‐sex model of population dynamics. We first deal with the problem of incomplete and inconsistent census data and then use a simulator to compare the performance of a variety of marriage functions in modeling births and couples during the ten‐year period between consecutive U.S. censuses. Unlike most empirical methods for comparing marriage functions based on goodness of fit, the differences in the projections of the various functions in our method are of the same magnitude (or even smaller) than the errors between the projected and real data. We observe that for the population of the United States, the harmonic mean function frequently found and used in the literature is a quite poor performer when compared with many other functions in the family we use.
ESO large program about transneptunian objects: surface variations on (47171) 1999 TC36

Aims. We investigate the surface composition of the Plutino (47171) 1999 TC36. Methods. We completed near-infrared photometric and spectroscopic observations of (47171) 1999 TC36 with the adaptive optics instrument NACO at the ESO VLT during 12 October 2006, and present these data with ISAAC and SINFONI spectroscopic observations carried out about one month later on 9 November 2006 and 8 November 2006, respectively. The ISAAC and SINFONI spectroscopic observations were combined with a visible spectrum obtained by FORS1 on 9 November 2006. Composition and properties of the compounds present on the surface of the target are investigated by applying a Hapke radiative transfer model to the measured spectra and to previously published observations. Results. We present the relative reflectance spectrum of (47171) 1999 TC36 in the wavelength range (0.37–2.33) μm. An intimate mixture of Triton tholin, Titan tholin, serpentine, and Triton tholin diluted in water ice represents the best-fit model description of the measured spectrum. Any significant differences from the published spectra of (47171) 1999 TC36 taken on 2001 and 2003 could be due to surface heterogeneity.
“Negative magnetic buoyancy” effects and reconstruction of toroidal field in the solar convection zone

Abstract This investigation is devoted to study the turbulent convective transport of mean (large-scale) magnetic field in the solar convection zone (SCZ). For the SCZ model by Stix (1989) the reconstruction of the toroidal field was calculated as a result of the balance of mean-field magnetic buoyancy and two “negative magnetic buoyancy” effects: i) macroscopic turbulent diamagnetism and ii) the ∇ρ effect. It is shown that at high latitudes negative buoyancy effects block the magnetic fields, about 3000 – 4000 G, near the bottom of the SCZ. This may be the most plausible reason why a deep-seated field here could not become as apparent at the solar surface as sunspots. However, at the near equatorial domain in the deep layers the ∇ρ effect, with allowance for rotation, causes the upward magnetic transport, that facilitates penetration of strong fields to the surface where they emerge as sunspot patters in the “royal zone”.
Entire Space Learning Framework: Unbias Conversion Rate Prediction in Full Stages of Recommender System

Recommender system is an essential part of online services, especially for e-commerce platform. Conversion Rate (CVR) prediction in RS plays a significant role in optimizing Gross Merchandise Volume (GMV) goal of e-commerce. However, CVR suffers from well-known Sample Selection Bias (SSB) and Data Sparsity (DS) problems. Although existing methods ESMM and ESM2 train with all impression samples over the entire space by modeling user behavior paths, SSB and DS problems still exist. In real practice, the online inference space are samples from previous stage of RS process, rather than the impression space modeled by existing methods. Moreover, existing methods solve the DS problem mainly by building behavior paths of their own specific scene, ignoring the behaviors in various scenes of e-commerce platform. In this paper, we propose Entire Space Learning Framework: Unbias Conversion Rate Prediction in Full Stages of Recommender System, solving SSB and DS problems by reformulating GMV goal in a novel manner. Specifically, we rebuild the CVR on the entire data space with samples from previous stage of RS process, unifying training and online inference space. Moreover, we explicitly introduce purchase samples from other scenes of e-commerce platform in model learning process. Online A/B test and offline experiments show the superiority of our framework. Our framework has been deployed in rank stage of Taobao recommendation, providing recommendation service for hundreds of millions of consumers everyday.
Optimality-Based Discretization Methods for the Global Optimization of Nonconvex Semi-Infinite Programs

We use sensitivity analysis to design $\textit{optimality-based}$ discretization (cutting-plane) methods for the global optimization of nonconvex semi-infinite programs (SIPs). We begin by formulating the optimal discretization of SIPs as a max-min problem and propose variants that are more computationally tractable. We then use parametric sensitivity theory to design an efficient method for solving these max-min problems to local optimality and argue this yields valid discretizations without sacrificing global optimality guarantees. Finally, we formulate optimality-based $\textit{generalized}$ discretization of SIPs as max-min problems and design efficient local optimization algorithms to solve them approximately. Numerical experiments on test instances from the literature demonstrate that our new optimality-based discretization methods can significantly reduce the number of iterations for convergence relative to the classical feasibility-based method.
Counting independent sets in amenable groups

Given a locally finite graph $\Gamma $ , an amenable subgroup G of graph automorphisms acting freely and almost transitively on its vertices, and a G-invariant activity function $\unicode{x3bb} $ , consider the free energy $f_G(\Gamma ,\unicode{x3bb} )$ of the hardcore model defined on the set of independent sets in $\Gamma $ weighted by $\unicode{x3bb} $ . Under the assumption that G is finitely generated and its word problem can be solved in exponential time, we define suitable ensembles of hardcore models and prove the following: if $\|\unicode{x3bb} \|_\infty < \unicode{x3bb} _c(\Delta )$ , there exists a randomized $\epsilon $ -additive approximation scheme for $f_G(\Gamma ,\unicode{x3bb} )$ that runs in time $\mathrm {poly}((1+\epsilon ^{-1})\lvert \Gamma /G \rvert )$ , where $\unicode{x3bb} _c(\Delta )$ denotes the critical activity on the $\Delta $ -regular tree. In addition, if G has a finite index linearly ordered subgroup such that its algebraic past can be decided in exponential time, we show that the algorithm can be chosen to be deterministic. However, we observe that if $\|\unicode{x3bb} \|_\infty> \unicode{x3bb} _c(\Delta )$ , there is no efficient approximation scheme, unless $\mathrm {NP} = \mathrm {RP}$ . This recovers the computational phase transition for the partition function of the hardcore model on finite graphs and provides an extension to the infinite setting. As an application in symbolic dynamics, we use these results to develop efficient approximation algorithms for the topological entropy of subshifts of finite type with enough safe symbols, we obtain a representation formula of pressure in terms of random trees of self-avoiding walks, and we provide new conditions for the uniqueness of the measure of maximal entropy based on the connective constant of a particular associated graph.
Strong-coupling magnetophononics: Self-blocking, phonon-bitriplons, and spin-band engineering

Magnetophononics, the modulation of magnetic interactions by driving infrared-active lattice excitations, is emerging as a key mechanism for the ultrafast dynamical control of both semiclassical and quantum spin systems by coherent light. We demonstrate that, in a quantum magnet with strong spin-phonon coupling, resonances between the driven phonon and the spin excitation frequencies exhibit an intrinsic self-blocking effect, whereby only a fraction of the available laser power is absorbed by the phonon. Using the quantum master equations governing the nonequilibrium steady states of the coupled spin-lattice system, we show how self-blocking arises from the self-consistent alteration of the resonance frequencies. We link this to the appearance of mutually repelling collective spin-phonon states, which in the regime of strong hybridization become composites of a phonon and two triplons. We then identify the mechanism and optimal phonon frequencies by which to control a global nonequilibrium renormalization of the lattice-driven spin excitation spectrum and demonstrate that this effect should be observable in ultrafast THz experiments on a number of known quantum magnetic materials.
Exploiting non-orthogonal eigenmodes in a non-Hermitian optical system to realize sub-100 MHz magneto-optical filters

Non-Hermitian physics is responsible for many of the counter-intuitive effects observed in optics research opening up new possibilities in sensing, polarization control and measurement. A hallmark of non-Hermitian matrices is the possibility of non-orthogonal eigenvectors resulting in coupling between modes. The advantages of propagation mode coupling have been little explored in magneto-optical filters and other devices based on birefringence. Magneto-optical filters select for ultra-narrow transmission regions by passing light through an atomic medium in the presence of a magnetic field. Passive filter designs have traditionally been limited by Doppler broadening of thermal vapors. Even for filter designs incorporating a pump laser, transmissions are typically less than 15\% for sub-Doppler features. Here we exploit our understanding of non-Hermitian physics to induce non-orthogonal propagation modes in a vapor and realize better magneto-optical filters. We construct two new filter designs with ENBWs and maximum transmissions of 181~MHz, 42\% and 140~MHz, 17\% which are the highest figure of merit and first sub-100~MHz FWHM passive filters recorded respectively. This work opens up a range of new filter applications including metrological devices for use outside a lab setting and commends filtering as a new candidate for deeper exploration of non-Hermitian physics such as exceptional points of degeneracy.
The asymptotics of the Ray-Singer analytic torsion of the symmetric powers of a positive vector bundle

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Lunar impact flash results and space surveillance activities at Kryoneri Observatory

We present current and future activities regarding lunar impact flash and NEO observations and satellite tracking from Kryoneri Observatory. In particular, we present results from the ESA-funded NELIOTA program, which has been monitoring the Moon for impact flashes since early 2017. Using the 1.2 m Kryoneri telescope, which is equipped with two high frame-rate cameras recording simultaneously in two optical bands, NELIOTA has recorded over 170 validated lunar impact flashes, while another ~90 have been characterized as suspected. We present statistical results concerning the sizes, the masses and the appearance frequency of the meteoroids in the vicinity of the Earth, as well as the temperatures developed during the impacts. Moreover, we present the capabilities of the Kryoneri telescope as a sensor for satellite tracking and the future plans regarding the provision of high-quality services for both the Planetary Defense activities of ESA (S2P/PDO) and the European Union's Space Surveillance and Tracking programme (EU/SST).
Computational assessment of subcritical and delayed onset in spiral Poiseuille flow experiments

For spiral Poiseuille flow with radius ratios $\eta \equiv R_i/R_o = 0.77$ and 0.95, we have computed complete linear stability boundaries, where $R_i$ and $R_o$ are the inner and outer cylinder radii, respectively. The analysis accounts for arbitrary disturbances of infinitesimal amplitude over the entire range of Reynolds numbers $Re$ for which the flow is stable for some range of Taylor number $Ta$, and extends previous work to several non-zero rotation rate ratios $\mu \equiv \Omega_o/\Omega_i$, where $\Omega_i$ and $\Omega_o$ are the (signed) angular speeds. For each combination of $\mu$ and $\eta$, there is a wide range of $Re$ for which the critical $Ta$ is nearly independent of $Re$, followed by a precipitous drop to $Ta = 0$ at the $Re$ at which non-rotating annular Poiseuille flow becomes unstable with respect to a Tollmien–Schlichting-like disturbance. Comparison is also made to a wealth of experimental data for the onset of instability. For $Re > 0$, we compute critical values of $Ta$ for most of the $\mu = 0$ data, and for all of the non-zero-$\mu$ data. For $\mu = 0$ and $\eta = 0.955$, agreement with data from an annulus with aspect ratio (length divided by gap) greater than 570 is within 3.2% for $Re \leq 325$ (based on the gap and mean axial speed), strongly suggesting that no finite-amplitude instability occurs over this range of $Re$. At higher $Re$, onset is delayed, with experimental values of $Ta_{\hbox{\scriptsize{\it crit}}}$ exceeding computed values. For $\mu = 0$ and smaller $\eta$, comparison to experiment (with smaller aspect ratios) at low $Re$ is slightly less good. For $\eta = 0.77$ and a range of $\mu$, agreement with experiment is very good for $Re < 135$ except at the most positive or negative $\mu$ (where $Ta_{\hbox{\scriptsize{\it crit}}}^{\hbox{\scriptsize{\it expt}}} > Ta_{\hbox{\scriptsize{\it crit}}}^{\hbox{\scriptsize{\it comp}}}$), whereas for $Re \geq 166$, $Ta_{\hbox{\scriptsize{\it crit}}}^{\hbox{\scriptsize{\it expt}}} > Ta_{\hbox{\scriptsize{\it crit}}}^{\hbox{\scriptsize{\it comp}}}$ for all but the most positive $\mu$. For $\eta = 0.9497$ and 0.959 and all but the most extreme values of $\mu$, agreement is excellent (generally within 2%) up to the largest $Re$ considered experimentally (200), again suggesting that finite-amplitude instability is unimportant.
Semiparametric analysis of clustered survival data under nonparametric frailty

In this article a novel approach to analyze clustered survival data that are subject to extravariation encountered through clustering of survival times is proposed. This is accomplished by extending the Cox proportional hazard model to a frailty model where the cluster‐specific shared frailty is modeled nonparametrically. We assume a nonparametric Dirichlet process for the distribution of frailty. In such a semiparametric setup, we propose a hybrid method to draw model‐based inferences. In the framework of the proposed hybrid method, the estimation of parameters is performed by implementing Monte Carlo expected conditional maximization algorithm. A simulation study is conducted to study the efficiency of our methodology. The proposed methodology is, thereafter, illustrated by a real‐life data on recurrence time to infections in kidney patient.
Guided Graph Generation: Evaluation of Graph Generators in Terms of Network Statistics, and a New Algorithm

We consider the problem of graph generation guided by network statistics, i.e., the generation of graphs which have given values of various numerical measures that characterize networks, such as the clustering coefficient and the number of cycles of given lengths. Algorithms for the generation of synthetic graphs are often based on graph growth models, i.e., rules of adding (and sometimes removing) nodes and edges to a graph that mimic the processes present in real-world networks. While such graph generators are desirable from a theoretical point of view, they are often only able to reproduce a narrow set of properties of real-world networks, resulting in graphs with otherwise unrealistic properties. In this article, we instead evaluate common graph generation algorithms at the task of reproducing the numerical statistics of real-world networks, such as the clustering coefficient, the degree assortativity, and the connectivity. We also propose an iterative algorithm, the Guided Graph Generator, based on a greedy-like procedure that recovers realistic values over a large number of commonly used graph statistics, while at the same time allowing an efficient implementation based on incremental updating of only a small number of subgraph counts. We show that the proposed algorithm outperforms previous graph generation algorithms in terms of the error in the reconstructed graphs for a large number of graph statistics such as the clustering coefficient, the assortativity, the mean node distance, and also evaluate the algorithm in terms of precision, speed of convergence and scalability, and compare it to previous graph generators and models. We also show that the proposed algorithm generates graphs with realistic degree distributions, graph spectra, clustering coefficient distributions, and distance distributions.
Intuitive Telemanipulation of Hyper-Redundant Snake Robots within Locomotion and Reorientation using Task-Priority Inverse Kinematics

Snake robots offer considerable potential for endoscopic interventions due to their ability to follow curvilinear paths. Telemanipulation is an open problem due to hyper-redundancy, as input devices only allow a specification of six degrees of freedom. Our work addresses this by presenting a unified telemanipulation strategy which enables follow-the-leader locomotion and reorientation keeping the shape change as small as possible. The basis for this is a novel shape-fitting approach for solving the inverse kinematics in only a few milliseconds. Shape fitting is performed by maximizing the similarity of two curves using Fréchet distance while simultaneously specifying the position and orientation of the end effector. Telemanipulation performance is investigated in a study in which 14 participants controlled a simulated snake robot to locomote into the target area. In a final validation, pivot reorientation within the target area is addressed.
Sketch2Cloth: Sketch-Based 3D Garment Generation With Unsigned Distance Fields

3D model reconstruction from a single image has achieved great progress with the recent deep generative models. However, conventional reconstruction approaches with template mesh deformation and implicit fields have difficulty reconstructing non-watertight 3D mesh models, such as garments. In contrast to image-based modeling, the sketch-based approach can help users generate 3D models to meet the design intentions of hand-drawn sketches. In this study, we propose Sketch2Cloth, a sketch-based 3D garment generation system that uses the unsigned distance fields from the user’s sketch input. Sketch2Cloth first estimates the unsigned distance function of the target 3D model from the sketch input and then extracts the mesh from the estimated field with Marching Cubes. We also provide a model editing function to modify the generated mesh. We verified the proposed Sketch2Cloth with quantitative evaluations of garment generation and editing in comparison to a state-of-the-art approach.
Comprehensive Analysis of Over-smoothing in Graph Neural Networks from Markov Chains Perspective

The over-smoothing problem is an obstacle of developing deep graph neural network (GNN). Although many approaches to improve the over-smoothing problem have been proposed, there is still a lack of comprehensive understanding and conclusion of this problem. In this work, we analyze the over-smoothing problem from the Markov chain perspective. We focus on message passing of GNN and first establish a connection between GNNs and Markov chains on the graph. GNNs are divided into two classes of operator-consistent and operator-inconsistent based on whether the corresponding Markov chains are time-homogeneous. Next we attribute the over-smoothing problem to the convergence of an arbitrary initial distribution to a stationary distribution. Based on this, we prove that although the previously proposed methods can alleviate over-smoothing, but these methods cannot avoid the over-smoothing problem. In addition, we give the conclusion of the over-smoothing problem in two types of GNNs in the Markovian sense. On the one hand, operator-consistent GNN cannot avoid over-smoothing at an exponential rate. On the other hand, operator-inconsistent GNN is not always over-smoothing. Further, we investigate the existence of the limiting distribution of the time-inhomogeneous Markov chain, from which we derive a sufficient condition for operator-inconsistent GNN to avoid over-smoothing. Finally, we design experiments to verify our findings. Results show that our proposed sufficient condition can effectively improve over-smoothing problem in operator-inconsistent GNN and enhance the performance of the model.