Miracle-dz/UniFAR-FTUs huggingface dataset:
Foldover-free maps in 50 lines of code

Mapping a triangulated surface to 2D space (or a tetrahedral mesh to 3D space) is an important problem in geometry processing. In computational physics, untangling plays an important role in mesh generation: it takes a mesh as an input, and moves the vertices to get rid of foldovers. In fact, mesh untangling can be considered as a special case of mapping where the geometry of the object is to be defined in the map space and the geometric domain is not explicit, supposing that each element is regular. In this paper, we propose a mapping method inspired by the untangling problem and compare its performance to the state of the art. The main advantage of our method is that the untangling aims at producing locally injective maps, which is the major challenge of mapping. In practice, our method produces locally injective maps in very difficult settings, both in 2D and 3D. We demonstrate it on a large reference database as well as on more difficult stress tests. For a better reproducibility, we publish the code in Python for a basic evaluation, and in C++ for more advanced applications.
Bounds and Heuristics for Multi-Product Personalized Pricing

We present tight bounds and heuristics for personalized, multi-product pricing problems. Under mild conditions we show that offering a non-personalize price in the direction of a positive vector (factor) has a tight profit guarantee relative to optimal personalized pricing. An optimal non-personalized price is the choice factor, when known. Using a factor vector with equal components results in uniform pricing and has exceedingly mild sufficient conditions for the bound to hold. A robust factor is presented that achieves the best possible performance guarantee. As an application, our model yields a tight lower-bound on the performance of linear pricing relative to personalized non-linear pricing, and suggests effective non-linear price heuristics relative to personalized solutions. Additionally, our model provides guarantees for simple strategies such as bundle-size pricing and component-pricing with respect to personalized mixed bundling policies. Heuristics to cluster customer types are also developed with the goal of improving performance by allowing each cluster to price along its own factor. Numerical results are presented for a variety of demand models, factors and clustering heuristics. In our experiments, economically motivated factors coupled with machine learning clustering heuristics performed best.
Fusion of neural networks, for LIDAR‐based evidential road mapping

LIDAR sensors are usually used to provide autonomous vehicles with three‐dimensional representations of their environment. In ideal conditions, geometrical models could detect the road in LIDAR scans, at the cost of a manual tuning of numerical constraints, and a lack of flexibility. We instead propose an evidential pipeline, to accumulate road detection results obtained from neural networks. First, we introduce RoadSeg, a new convolutional architecture that is optimized for road detection in LIDAR scans. RoadSeg is used to classify individual LIDAR points as either belonging to the road, or not. Yet, such point‐level classification results need to be converted into a dense representation, that can be used by an autonomous vehicle. We thus second present an evidential road mapping algorithm, that fuses consecutive road detection results. We benefitted from a reinterpretation of logistic classifiers, which can be seen as generating a collection of simple evidential mass functions. An evidential grid map that depicts the road can then be obtained, by projecting the classification results from RoadSeg into grid cells, and by handling moving objects via conflict analysis. The system was trained and evaluated on real‐life data. A python implementation maintains a 10 Hz framerate. Since road labels were needed for training, a soft labeling procedure, relying lane‐level HD maps, was used to generate coarse training and validation sets. An additional test set was manually labeled for evaluation purposes. So as to reach satisfactory results, the system fuses road detection results obtained from three variants of RoadSeg, processing different LIDAR features.
Self-similar fault slip in response to fluid injection

Abstract There is scientific and industrial interest in understanding how geologic faults respond to transient sources of fluid. Natural and artificial sources can elevate pore fluid pressure on the fault frictional interface, which may induce slip. We consider a simple boundary value problem to provide an elementary model of the physical process and to provide a benchmark for numerical solution procedures. We examine the slip of a fault that is an interface of two elastic half-spaces. Injection is modelled as a line source at constant pressure and fluid pressure is assumed to diffuse along the interface. The resulting problem is an integro-differential equation governing fault slip, which has a single dimensionless parameter. The expansion of slip is self-similar and the rupture front propagates at a factor $\lambda$ of the diffusive length scale $\sqrt {\alpha t}$. We identify two asymptotic regimes corresponding to $\lambda$ being small or large and perform a perturbation expansion in each limit. For large $\lambda$, in the regime of a so-called critically stressed fault, a boundary layer emerges on the diffusive length scale, which lags far behind the rupture front. We demonstrate higher-order matched asymptotics for the integro-differential equation, and in doing so, we derive a multipole expansion to capture successive orders of influence on the outer problem for fault slip for a driving force that is small relative to the crack dimensions. Asymptotic expansions are compared with accurate numerical solutions to the full problem, which are tabulated to high precision.
Backyard Worlds: Planet 9 Discovery of an Unusual Low-mass Companion to an M Dwarf at 80 pc

We present the discovery of CWISE J203546.35–493611.0, a peculiar M8 companion to the M4.5 star APMPM J2036−4936 discovered through the citizen science project Backyard Worlds: Planet 9. Given CWISE J203546.35–493611.0's proper motion (μ α , μ δ ) = (−126 ± 22, −478 ± 23) and angular separation of 342 from APMPM 2036−4936, we calculate a chance alignment probability of 1.15 × 10−6. Both stars in this system appear to be underluminous, and the spectrum obtained for CWISE J203546.35–493611.0 shows a triangular H band. Further study of this system is warranted to understand these peculiarities.
Train Track Maps and CTs on Graphs of Groups

In this paper we develop the theory of train track maps on graphs of groups. We prove the existence of CTs representing outer automorphisms of free products. We generalize an index inequality due to Feighn–Handel to the graph of groups setting, sharpening a result of Martino. A homotopy equivalence f : G→ G of a graph G is a train track map when the restriction of any iterate of f to an edge of G yields an immersion. (Relative) train track maps were introduced in [BH92]; they are perhaps the main tool for studying outer automorphisms of free groups. Choosing a basepoint ? in G and a path from ? to f(? ) determines an automorphism f] : π1(G, ? )→ π1(G, ? ) and a lift of f to the universal covering tree Γ of G. The map f̃ : Γ→ Γ is equivariant in the sense that for g ∈ π1(G, ? ) and x ∈ Γ, we have f̃(g.x) = f](g). f̃(x). The lift f̃ : Γ → Γ also satisfies the definition of a train track map. This formulation of train track maps as equivariant maps of trees can be adapted in a straightforward way to automorphisms of groups acting on trees. However, one is primarily interested in using train track maps to study outer automorphisms, for which it would be more convenient to be able to work directly in the quotient graph of groups. This is one purpose of this paper. Theorem A. Let G be a graph of groups. If an outer automorphism φ of π1(G) admits a topological representative, then there exists a relative train track map f : G′ → G′ representing φ. If φ is irreducible, then the relative train track map is a train track map. This is not the first construction of relative train track maps on graphs of groups, see [CT94], [FM15] and [Syk04], but it is the most general, allowing in particular for infinite edge groups. One class of groups acting on trees of particular interest are free products, which act with trivial edge stabilizers. This greater flexibility allows for stronger results. The other purpose of this paper is to extend Feighn–Handel’s completely split relative train track maps, CTs [FH11], to outer automorphisms of free products. Let F = A1 ∗ · · · ∗ An ∗ Fk be the free product of the groups Ai with a free group of rank k represented as the fundamental group of a graph of groups G, where the Ai are the nontrivial vertex groups of G, the edge groups of G are trivial, and the ordinary fundamental group of the (underlying graph of) G is free of rank k. Theorem B. Every φ ∈ Out(F ) which is represented by a rotationless relative train track map f : G → G on a G-marked graph of groups G is represented by a CT (see Section 6 for the definition) f ′ : G′ → G′ on a G-marked graph of groups. In [FH18], Feighn and Handel define an index j(φ) for an outer automorphism φ ∈ Out(Fn) (see Section 7 for a definition) and prove it satisfies an inequality strengthening an inequality due to Gaboriau, Jaeger, Levitt and Lutsig [GJLL98]. Our final result extends this definition and inequality to the free product setting, strengthening a result of Martino [Mar99]. 1 ar X iv :2 10 2. 02 84 8v 1 [ m at h. G R ] 4 F eb 2 02 1 Theorem C. If φ ∈ Out(F ) is represented on a G-marked graph of groups, then
Stable Online Computation Offloading via Lyapunov-guided Deep Reinforcement Learning

In this paper, we consider a multi-user mobile-edge computing (MEC) network with time-varying wireless channels and stochastic user task data arrivals in sequential time frames. In particular, we aim to design an online computation offloading algorithm to maximize the network data processing capability subject to the long-term data queue stability and average power constraints. The online algorithm is practical in the sense that the decisions for each time frame are made without the assumption of knowing future channel conditions and data arrivals. We formulate the problem as a multi-stage stochastic mixed integer non-linear programming (MINLP) problem that jointly determines the binary offloading (each user computes the task either locally or at the edge server) and system resource allocation decisions in sequential time frames. To address the coupling in the decisions of different time frames, we propose a novel framework, named LyDROO, that combines the advantages of Lyapunov optimization and deep reinforcement learning (DRL). Specifically, LyDROO first applies Lyapunov optimization to decouple the multi-stage stochastic MINLP into deterministic per-frame MINLP subproblems of much smaller size. Then, it integrates model-based optimization and model-free DRL to solve the per-frame MINLP problems with very low computational complexity. Simulation results show that the proposed LyDROO achieves optimal computation performance while satisfying all the long-term constraints. Besides, it induces very low execution latency that is particularly suitable for real-time implementation in fast fading environments.
Evidence of chromospheric molecular hydrogen emission in a solar flare observed by the IRIS satellite

We have carried out the first comprehensive investigation of enhanced line emission from molecular hydrogen, H2 at 1333.79 Å, observed at flare ribbons in SOL2014-04-18T13:03. The cool H2 emission is known to be fluorescently excited by Si iv 1402.77 Å UV radiation and provides a unique view of the temperature minimum region (TMR). Strong H2 emission was observed when the Si iv 1402.77 Å emission was bright during the flare impulsive phase and gradual decay phase, but it dimmed during the GOES peak. H2 line broadening showed non-thermal speeds in the range 7–18 $\rm {km\,s}^{-1}$, possibly corresponding to turbulent plasma flows. Small red (blue) shifts, up to 1.8 (4.9) $\rm {km\,s}^{-1}$ were measured. The intensity ratio of Si iv 1393.76 Å and Si iv 1402.77 Å confirmed that plasma was optically thin to Si iv (where the ratio = 2) during the impulsive phase of the flare in locations where strong H2 emission was observed. In contrast, the ratio differs from optically thin value of 2 in parts of ribbons, indicating a role for opacity effects. A strong spatial and temporal correlation between H2 and Si iv emission was evident supporting the notion that fluorescent excitation is responsible.
A Collaborative Visual SLAM Framework for Service Robots

We present a collaborative visual simultaneous localization and mapping (SLAM) framework for service robots. With an edge server maintaining a map database and performing global optimization, each robot can register to an existing map, update the map, or build new maps, all with a unified interface and low computation and memory cost. We design an elegant communication pipeline to enable real-time information sharing between robots. With a novel landmark organization and retrieval method on the server, each robot can acquire landmarks predicted to be in its view, to augment its local map. The framework is general enough to support both RGB-D and monocular cameras, as well as robots with multiple cameras, taking the rigid constraints between cameras into consideration. The proposed framework has been fully implemented and verified with public datasets and live experiments.
Emissions of ammonia, nitrous oxide and methane from different types of dairy manure during storage as affected by dietary protein content

In a storage experiment with dairy cow manure, the effects of dietary protein content and manure type on ammonia, nitrous oxide and methane volatilization as well as overall nitrogen (N) loss from manure were investigated. Early-lactating cows received rations with 175, 150 and 125 g crude protein/kg dry matter. Each ration was tested in four manure storage systems reflecting typical farm conditions. These either contained total excreta with high amounts of straw (deep litter manure) or no straw (slurry) or, proportionately, 0·9 of urine and 0·1 of faeces (urine-rich slurry) complemented by the residuals with a low amount of straw (farmyard manure). Manure samples were stored for 7 weeks under controlled conditions and trace gas emission was repeatedly measured. Reduction of N intake decreased daily N excretion and urine N proportion and, on average, led to 0·7-fold lower storage ammonia emission rates on average. Total storage N loss was simultaneously reduced with the extent depending on urine N proportion of the respective manures. A lower dietary protein content furthermore reduced nitrous oxide emission rates in most manure types but increased methane emission from urine-rich slurry; however, global warming potential (based on trace gas output) of all manures was similar with low and high dietary protein content. In deep litter manure, characterized by the highest C:N ratio, emission rates of total N, ammonia and methane were lowest, whereas nitrous oxide values were intermediate. Substantial emission of nitrous oxide occurred with farmyard manure which also had the highest methane values and, consequently, by far the highest global warming potential. C:N ratio of manure was shown to be suitable to predict total N loss from manure during storage in all manure types whereas urine N proportion and manure pH were only of use with liquid manures.
Quantum computing hardware in the cloud: Should a computational chemist care?

Within the last decade much progress has been made in the experimental realisation of quantum computing hardware based on a variety of physical systems. Rapid progress has been fuelled by the conviction that sufficiently powerful quantum machines will herald enormous computational advantages in many elds, including chemical research. A quantum computer capable of simulating the electronic structures of complex molecules would be a game changer for the design of new drugs and materials. Given the potential implications of this technology, there is a need within the chemistry community to keep abreast with the latest developments as well as becoming involved in experimentation with quantum prototypes. To facilitate this, here we review the types of quantum computing hardware that have been made available to the public through cloud services. We focus on three architectures, namely superconductors, trapped ions and semiconductors. For each one we summarise the basic physical operations, requirements and performance. We discuss to what extent each system has been used for molecular chemistry problems and highlight the most pressing hardware issues to be solved for a chemistry-relevant quantum advantage to eventually emerge.
Linearized Learning with Multiscale Deep Neural Networks for Stationary Navier-Stokes Equations with Oscillatory Solutions

In this paper, we present linearized learning methods to accelerate the convergence of training for stationary nonlinear Navier-Stokes (NS) equations. To solve the stationary nonlinear NS equation with deep neural networks, we integrate lineariza-tions of the nonlinear convection term in the NS equations into the training process of multi-scale deep neural network (DNN) approximations of the NS solution. Four forms of linearizations are considered. We solve highly oscillating stationary ﬂows in complex domains utilizing the proposed linearized learning with multiscale neural networks. The results show that multiscale deep neural network combined with the linearized schemes can be trained much faster and accurately than regular fully connected DNNs.
Learning Rate Optimization for Federated Learning Exploiting Over-the-air Computation

Federated learning (FL) as a promising edge-learning framework can effectively address the latency and privacy issues by featuring distributed learning at the devices and model aggregation in the central server. In order to enable efficient wireless data aggregation, over-the-air computation (Air-Comp) has recently attracted great attention. However, fading of wireless channels can produce aggregate distortions in an AirComp-based FL scheme. In this paper, we propose a modified federated averaging (FedAvg) algorithm by introducing the local learning rates and present the convergence analysis. To combat the distortion, the local learning rates are optimized to adapt the fading channel, which is termed as dynamic learning rate (DLR). We begin our discussion by considering multiple-input-single-output (MISO) scenario, since the underlying optimization problem is convex and has a closed-form solution. Our studies are extended to a more general multiple-input-multiple-output (MIMO) case and an iterative method is derived. We also present the asymptotic analysis and give a near-optimal and closed-form receive beamforming solution when the number of antennas approaches infinity. Extensive simulation results demonstrate the effectiveness of the proposed DLR scheme in reducing the aggregate distortion and guaranteeing the testing accuracy on the MNIST and CIFAR10 datasets. In addition, the asymptotic analysis and the close-form solution are verified through intensive numerical simulations.
sígame v3: Gas Fragmentation in Postprocessing of Cosmological Simulations for More Accurate Infrared Line Emission Modeling

We present an update to the framework called Simulator of Galaxy Millimeter/submillimeter Emission (sígame). sígame derives line emission in the far-infrared (FIR) for galaxies in particle-based cosmological hydrodynamics simulations by applying radiative transfer and physics recipes via a postprocessing step after completion of the simulation. In this version, a new technique is developed to model higher gas densities by parameterizing the probability distribution function (PDF) of the gas density in higher-resolution simulations run with the pseudo-Lagrangian, Voronoi mesh code arepo. The parameterized PDFs are used as a look-up table, and reach higher densities than in previous work. sígame v3 is tested on redshift z = 0 galaxies drawn from the simba cosmological simulation for eight FIR emission lines tracing vastly different phases of the interstellar medium. This version of sígame includes dust radiative transfer with Skirt and high-resolution photoionization models with Cloudy, the latter sampled according to the density PDF of the arepo simulations to augment the densities in the cosmological simulation. The quartile distributions of the predicted line luminosities overlap with the observed range for nearby galaxies of similar star formation rate (SFR) for all but two emission lines: [O i]63 and CO(3–2), which are overestimated by median factors of 1.3 and 1.0 dex, respectively, compared to the observed line–SFR relation of mixed-type galaxies. We attribute the remaining disagreement with observations to the lack of precise attenuation of the interstellar light on sub-grid scales (≲200 pc) and differences in sample selection.
Active flows on curved surfaces

We consider a numerical approach for a covariant generalised Navier-Stokes equation on general surfaces and study the influence of varying Gaussian curvature on anomalous vortex-network active turbulence. This regime is characterised by self-assembly of finitesize vortices into linked chains of anti-ferromagnet order, which percolate through the entire surface. The simulation results reveal an alignment of these chains with minimal curvature lines of the surface and indicate a dependency of this turbulence regime on the sign and the gradient in local Gaussian curvature. While these results remain qualitative and their explanations are still incomplete, several of the observed phenomena are in qualitative agreement with experiments on active nematic liquid crystals on toroidal surfaces and contribute to an understanding of the delicate interplay between geometrical properties of the surface and characteristics of the flow field, which has the potential to control active flows on surfaces via gradients in the spatial curvature of the surface.
Equivariant message passing for the prediction of tensorial properties and molecular spectra

Message passing neural networks have become a method of choice for learning on graphs, in particular the prediction of chemical properties and the acceleration of molecular dynamics studies. While they readily scale to large training data sets, previous approaches have proven to be less data efficient than kernel methods. We identify limitations of invariant representations as a major reason and extend the message passing formulation to rotationally equivariant representations. On this basis, we propose the polarizable atom interaction neural network (PaiNN) and improve on common molecule benchmarks over previous networks, while reducing model size and inference time. We leverage the equivariant atomwise representations obtained by PaiNN for the prediction of tensorial properties. Finally, we apply this to the simulation of molecular spectra, achieving speedups of 4-5 orders of magnitude compared to the electronic structure reference.