Miracle-dz/UniFAR-FTUs huggingface dataset:
Random Perturbation of Sparse Graphs

In the model of randomly perturbed graphs we consider the union of a deterministic graph $\mathcal{G}_\alpha$ with minimum degree $\alpha n$ and the binomial random graph $\mathbb{G}(n,p)$. This model was introduced by Bohman, Frieze, and Martin and for Hamilton cycles their result bridges the gap between Dirac's theorem and the results by Pósa and Korshunov on the threshold in $\mathbb{G}(n,p)$. In this note we extend this result in $\mathcal{G}_\alpha\cup\mathbb{G}(n,p)$ to sparser graphs with $\alpha=o(1)$. More precisely, for any $\varepsilon>0$ and $\alpha \colon \mathbb{N} \mapsto (0,1)$ we show that a.a. s. $\mathcal{G}_\alpha\cup \mathbb{G}(n,\beta /n)$ is Hamiltonian, where $\beta = -(6 + \varepsilon) \log(\alpha)$. If $\alpha>0$ is a fixed constant this gives the aforementioned result by Bohman, Frieze, and Martin and if $\alpha=O(1/n)$ the random part $\mathbb{G}(n,p)$ is sufficient for a Hamilton cycle. We also discuss embeddings of bounded degree trees and other spanning structures in this model, which lead to interesting questions on almost spanning embeddings into $\mathbb{G}(n,p)$.
MuTual: A Dataset for Multi-Turn Dialogue Reasoning

Non-task oriented dialogue systems have achieved great success in recent years due to largely accessible conversation data and the development of deep learning techniques. Given a context, current systems are able to yield a relevant and fluent response, but sometimes make logical mistakes because of weak reasoning capabilities. To facilitate the conversation reasoning research, we introduce MuTual, a novel dataset for Multi-Turn dialogue Reasoning, consisting of 8,860 manually annotated dialogues based on Chinese student English listening comprehension exams. Compared to previous benchmarks for non-task oriented dialogue systems, MuTual is much more challenging since it requires a model that be able to handle various reasoning problems. Empirical results show that state-of-the-art methods only reach 71%, which is far behind human performance of 94%, indicating that there is ample room for improving reasoning ability.
Injecting Numerical Reasoning Skills into Language Models

Large pre-trained language models (LMs) are known to encode substantial amounts of linguistic information. However, high-level reasoning skills, such as numerical reasoning, are difficult to learn from a language-modeling objective only. Consequently, existing models for numerical reasoning have used specialized architectures with limited flexibility. In this work, we show that numerical reasoning is amenable to automatic data generation, and thus one can inject this skill into pre-trained LMs, by generating large amounts of data, and training in a multi-task setup. We show that pre-training our model, GenBERT, on this data, dramatically improves performance on DROP (49.3 –> 72.3 F1), reaching performance that matches state-of-the-art models of comparable size, while using a simple and general-purpose encoder-decoder architecture. Moreover, GenBERT generalizes well to math word problem datasets, while maintaining high performance on standard RC tasks. Our approach provides a general recipe for injecting skills into large pre-trained LMs, whenever the skill is amenable to automatic data augmentation.
STOCHASTIC SPECTRAL EMBEDDING

Constructing approximations that can accurately mimic the behavior of complex models at reduced computational costs is an important aspect of uncertainty quantification. Despite their flexibility and efficiency, classical surrogate models such as Kriging or polynomial chaos expansions tend to struggle with highly non-linear, localized or non-stationary computational models. We hereby propose a novel sequential adaptive surrogate modeling method based on recursively embedding locally spectral expansions. It is achieved by means of disjoint recursive partitioning of the input domain, which consists in sequentially splitting the latter into smaller subdomains, and constructing a simpler local spectral expansions in each, exploiting the trade-off complexity vs. locality. The resulting expansion, which we refer to as "stochastic spectral embedding" (SSE), is a piece-wise continuous approximation of the model response that shows promising approximation capabilities, and good scaling with both the problem dimension and the size of the training set. We finally show how the method compares favorably against state-of-the-art sparse polynomial chaos expansions on a set of models with different complexity and input dimension.
Volumetric star formation prescriptions in vertically resolved edge-on galaxies

We measure the gas disc thicknesses of the edge-on galaxy NGC 4013 and the less edge-on galaxies (NGC 4157 and 5907) using CO (CARMA/OVRO) and/or HI (EVLA) observations. We also estimate the scale heights of stars and/or the star formation rate (SFR) for our sample of five galaxies using Spitzer IR data (3.6 $\mu$m and 24 $\mu$m). We derive the average volume densities of the gas and the SFR using the measured scale heights along with radial surface density profiles. Using the volume density that is more physically relevant to the SFR than the surface density, we investigate the existence of a volumetric star formation law (SFL), how the volumetric SFL is different from the surface-density SFL, and how the gas pressure regulates the SFR based on our galaxy sample. We find that the volumetric and surface SFLs in terms of the total gas have significantly different slopes, while the volumetric and surface SFLs in terms of the molecular gas do not show any noticeable difference. The volumetric SFL for the total gas has a flatter power-law slope of 1.26 with a smaller scatter of 0.19 dex compared to the slope (2.05) and the scatter (0.25 dex) of the surface SFL. The molecular gas SFLs have similar slopes of 0.78 (volume density) and 0.77 (surface density) with the same rms scatter. We show that the interstellar gas pressure is strongly correlated with the SFR but find no significant difference between the correlations based on the volume and surface densities.
Masked GANs for Unsupervised Depth and Pose Prediction with Scale Consistency

Previous works have shown that adversarial learning can be used for unsupervised monocular depth and visual odometry (VO) estimation. However, the performance of pose and depth networks is limited by occlusions and visual field changes. Because of the incomplete correspondence of visual information between frames caused by motion, target images cannot be synthesized completely from source images via view reconstruction and bilinear interpolation. The reconstruction loss based on the difference between synthesized and real target images will be affected by the incomplete reconstruction. Besides, the data distribution of unreconstructed regions will be learned and help the discriminator distinguish between real and fake images, thereby causing the case that the generator may fail to compete with the discriminator. Therefore, a MaskNet is designed in this paper to predict these regions and reduce their impacts on the reconstruction loss and adversarial loss. The impact of unreconstructed regions on discriminator is tackled by proposing a boolean mask scheme, as shown in Fig. 1. Furthermore, we consider the scale consistency of our pose network by utilizing a new scale-consistency loss, therefore our pose network is capable of providing the full camera trajectory over the long monocular sequence. Extensive experiments on KITTI dataset show that each component proposed in this paper contributes to the performance, and both of our depth and trajectory prediction achieve competitive performance.
Statistical Identification of Penalizing Configurations in High-dimensional Thermal-hydraulic Numerical Experiments: The ICSCREAM Methodology

In the framework of risk assessment in nuclear accident analysis, best-estimate computer codes are used to estimate safety margins. Several inputs of the code can be uncertain, due to a lack of knowledge but also to the particular choice of accidental scenario being considered. The objective of this work is to identify the most penalizing (or critical) configurations (corresponding to extreme values of the code output) of several input parameters (called ``scenario inputs''), independently of the uncertainty of the other input parameters. However, complex computer codes, as the ones used in thermal-hydraulic accident scenario simulations, are often too CPU-time expensive to be directly used to perform these studies. A solution consists in fitting the code output by a metamodel, built from a reduced number of code simulations. When the number of input parameters is very large (e.g., around a hundred here), the metamodel building remains a challenge. To overcome this, we propose a methodology, called ICSCREAM (Identification of penalizing Configurations using SCREening And Metamodel), based on screening techniques and Gaussian process (Gp) metamodeling. The efficiency of this methodology is illustrated on a thermal-hydraulic industrial case simulating an accident of primary coolant loss in a Pressurized Water Reactor. This use-case includes 97 uncertain inputs, two scenario inputs to be penalized and 500 code simulations for the learning database. The study focuses on the peak cladding temperature (PCT) and critical configurations are defined by exceeding the 90%-quantile of PCT. For the screening step, statistical tests of independence based on the Hilbert-Schmidt independence criterion are used for global and target sensitivity analyses. They allow a significant reduction of inputs (from 97 to 20) and a ranking of these influential inputs by order of influence. Then, a Gp metamodel is sequentially built to reach a satisfactory predictivity of 82% of explained PTC variance, and a high capacity of identifying PTC critical areas (94% of good ranking rate above the threshold). Finally, the Gp is used to estimate, within a Bayesian framework, the conditional probabilities of exceeding the threshold, according to the two scenario inputs. The analysis reveals the strong interaction of the two scenario inputs in the occurrence of critical configurations, worst cases corresponding to medium values of both inputs.
Clogging transitions in constricted particle suspension flows.

When suspended particles are pushed by liquid flow through a constricted channel they might either pass the bottleneck without trouble or encounter a permanent clog that will stop them forever. But they might as well flow intermittently with great sensitivity to the neck-to-particle size ratio D/d. In this work, we experimentally explore the limits of the intermittent regime for a dense suspension through a single bottleneck as a function of this parameter. To this end, we make use of high time- and space-resolution experiments to obtain the distributions of arrest times between successive bursts, which display power-law tails with characteristic exponents. These exponents compare well with the ones found for as disparate situations as the evacuation of pedestrians from a room, the entry of a flock of sheep into a shed or the discharge of particles from a silo. Nevertheless, the intrinsic properties of our system seem to introduce a sharp transition from a clogged state (power-law exponent below two) to a continuous flow, where clogs do not develop at all. This contrasts with the results obtained in other systems where intermittent flow, with power-law exponents above two, were obtained.
Open spin chain realization of a topological defect in a one-dimensional Ising model: Boundary and bulk symmetry

We study the realizations of topological defects in 1d quantum Ising model with open boundary condition at criticality. Applying the construction discussed in [M. Hauru, G. Evenbly, W. W. Ho, D. Gaiotto, and G. Vidal, Phys. Rev. B 94, 115125 (2016)], we prove that the Ising model on an open chain with multiple topological defects can be transformed to the same model with boundary magnetic fields and noninteracting boundary degree of freedom. This results in the appearance of linear combination of Cardy states [J. L. Cardy, Nucl. Phys. B 324, 581 (1989)], which can be interpreted as an edge state of the spin or fermion chain. We show that this edge state with the large boundary entropy can be protected under bulk perturbation whereas it is fragile to a boundary perturbation. Our formulation suggests an existence of nontrivial edge physics under the existence of topological defects and opens many interesting questions for future analysis related to boundary and bulk physics.
Fundamental effective temperature measurements for eclipsing binary stars – I. Development of the method and application to AI Phoenicis

Stars with accurate and precise effective temperature (T$_{\rm eff}$) measurements are needed to test stellar atmosphere models and calibrate empirical methods to determine T$_{\rm eff}$. There are few standard stars currently available to calibrate temperature indicators for dwarf stars. Gaia parallaxes now make it possible, in principle, to measure T$_{\rm eff}$ for many dwarf stars in eclipsing binaries. We aim to develop a method that uses high-precision measurements of detached eclipsing binary stars, Gaia parallaxes and multi-wavelength photometry to obtain accurate and precise fundamental effective temperatures that can be used to establish a set of benchmark stars. We select the well-studied binary AI Phoenicis to test our method, since it has very precise absolute parameters and extensive archival photometry. The method uses the stellar radii and parallax for stars in eclipsing binaries. We use a Bayesian approach to obtain the integrated bolometric fluxes for the two stars from observed magnitudes, colours and flux ratios. The fundamental effective temperature of two stars in AI Phoenicis are $6199\pm22$ K for the F7V component and $5094\pm16$ K for the K0IV component. The zero-point error in the flux scale leads to a systematic error of only 0.2% ($\approx$ 11K) in T$_{\rm eff}$. We find that these results are robust against the details of the analysis, such as the choice of model spectra. Our method can be applied to eclipsing binary stars with radius, parallax and photometric measurements across a range of wavelengths. Stars with fundamental effective temperatures determined with this method can be used as benchmarks in future surveys.
Stochastic quantization of Liouville conformal field theory

We study a nonlinear stochastic heat equation forced by a space-time white noise on closed surfaces, with nonlinearity $e^{\beta u}$. This equation corresponds to the stochastic quantization of the Liouville quantum gravity (LQG) measure. (i) We first revisit the construction of the LQG measure in Liouville conformal field theory (LCFT) in the $L^2$ regime $0 1$ respectively. Moreover, our argument shows that this measure is independent of the approximation procedure for a large class of smooth approximations. (ii) We prove almost sure global well-posedness of the parabolic stochastic dynamics, and invariance of the measure under this stochastic flow. In particular, our results improve previous results obtained by Garban (2020) in the cases of the sphere and the torus with their canonical metric, and are new in the case of closed surfaces with higher genus.
Calibrating Structured Output Predictors for Natural Language Processing

We address the problem of calibrating prediction confidence for output entities of interest in natural language processing (NLP) applications. It is important that NLP applications such as named entity recognition and question answering produce calibrated confidence scores for their predictions, especially if the applications are to be deployed in a safety-critical domain such as healthcare. However the output space of such structured prediction models are often too large to directly adapt binary or multi-class calibration methods. In this study, we propose a general calibration scheme for output entities of interest in neural network based structured prediction models. Our proposed method can be used with any binary class calibration scheme and a neural network model. Additionally, we show that our calibration method can also be used as an uncertainty-aware, entity-specific decoding step to improve the performance of the underlying model at no additional training cost or data requirements. We show that our method outperforms current calibration techniques for Named Entity Recognition, Part-of-speech tagging and Question Answering systems. We also observe an improvement in model performance from our decoding step across several tasks and benchmark datasets. Our method improves the calibration and model performance on out-of-domain test scenarios as well.
Inference in the Stochastic Block Model with a Markovian assignment of the communities

We tackle the community detection problem in the Stochastic Block Model (SBM) when the communities of the nodes of the graph are assigned with a Markovian dynamic. To recover the partition of the nodes, we adapt the relaxed K-means SDP program presented in [11]. We identify the relevant signal-to-noise ratio (SNR) in our framework and we prove that the misclassification error decays exponentially fast with respect to this SNR. We provide infinity norm consistent estimation of the parameters of our model and we discuss our results through the prism of classical degree regimes of the SBMs' literature. MSC 2010 subject classifications: Primary 68Q32; secondary 68R10, 90C35.
DeepCOVIDExplainer: Explainable COVID-19 Predictions Based on Chest X-ray Images

Amid the coronavirus disease(COVID-19) pandemic, humanity experiences a rapid increase in infection numbers across the world. Challenge hospitals are faced with, in the fight against the virus, is the effective screening of incoming patients. One methodology is the assessment of chest radiography(CXR) images, which usually requires expert radiologists' knowledge. In this paper, we propose an explainable deep neural networks(DNN)-based method for automatic detection of COVID-19 symptoms from CXR images, which we call 'DeepCOVIDExplainer'. We used 16,995 CXR images across 13,808 patients, covering normal, pneumonia, and COVID-19 cases. CXR images are first comprehensively preprocessed, before being augmented and classified with a neural ensemble method, followed by highlighting class-discriminating regions using gradient-guided class activation maps(Grad-CAM++) and layer-wise relevance propagation(LRP). Further, we provide human-interpretable explanations of the predictions. Evaluation results based on hold-out data show that our approach can identify COVID-19 confidently with a positive predictive value(PPV) of 89.61% and recall of 83%, improving over recent comparable approaches. We hope that our findings will be a useful contribution to the fight against COVID-19 and, in more general, towards an increasing acceptance and adoption of AI-assisted applications in the clinical practice.
Co-Robots as Care Robots

Cooperation and collaboration robots, co-robots or cobots for short, are an integral part of factories. For example, they work closely with the fitters in the automotive sector, and everyone does what they do best. However, the novel robots are not only relevant in production and logistics, but also in the service sector, especially where proximity between them and the users is desired or unavoidable. For decades, individual solutions of a very different kind have been developed in care. Now experts are increasingly relying on co-robots and teaching them the special tasks that are involved in care or therapy. This article presents the advantages, but also the disadvantages of co-robots in care and support, and provides information with regard to human-robot interaction and communication. The article is based on a model that has already been tested in various nursing and retirement homes, namely Lio from F&P Robotics, and uses results from accompanying studies. The authors can show that co-robots are ideal for care and support in many ways. Of course, it is also important to consider a few points in order to guarantee functionality and acceptance.
Prune2Edge: A Multi-Phase Pruning Pipelines to Deep Ensemble Learning in IIoT

Most recently, with the proliferation of IoT devices, computational nodes in manufacturing systems IIoT(Industrial-Internet-of-things) and the lunch of 5G networks, there will be millions of connected devices generating a massive amount of data. In such an environment, the controlling systems need to be intelligent enough to deal with a vast amount of data to detect defects in a real-time process. Driven by such a need, artificial intelligence models such as deep learning have to be deployed into IIoT systems. However, learning and using deep learning models are computationally expensive, so an IoT device with limited computational power could not run such models. To tackle this issue, edge intelligence had emerged as a new paradigm towards running Artificial Intelligence models on edge devices. Although a considerable amount of studies have been proposed in this area, the research is still in the early stages. In this paper, we propose a novel edge-based multi-phase pruning pipelines to ensemble learning on IIoT devices. In the first phase, we generate a diverse ensemble of pruned models, then we apply integer quantisation, next we prune the generated ensemble using a clustering-based technique. Finally, we choose the best representative from each generated cluster to be deployed to a distributed IoT environment. On CIFAR-100 and CIFAR-10, our proposed approach was able to outperform the predictability levels of a baseline model (up to 7%), more importantly, the generated learners have small sizes (up to 90% reduction in the model size) that minimise the required computational capabilities to make an inference on the resource-constraint devices.
One-parameter groups of orthogonality preservers

We establish a more precise description of those surjective or bijective continuous linear operators preserving orthogonality between C$^*$-algebras. The new description is applied to determine all uniformly continuous one-parameter semigroups of orthogonality preserving operators on an arbitrary C$^*$-algebra. We prove that given a family $\{T_t: t\in \mathbb{R}_0^{+}\}$ of orthogonality preserving bounded linear bijections on a general C$^*$-algebra $A$ with $T_0=Id$, if for each $t\geq 0,$ we set $h_t = T_t^{**} (1)$ and we write $r_t$ for the range partial isometry of $h_t$ in $A^{**},$ and $S_t$ stands for the triple isomorphism on $A$ associated with $T_t$ satisfying $h_t^* S_t(x)$ $= S_t(x^*)^* h_t$, $h_t S_t(x^*)^* =$ $ S_t(x) h_t^*$, $h_t r_t^* S_t(x) =$ $S_t(x) r_t^* h_t$, and $$T_t(x) = h_t r_t^* S_t(x) = S_t(x) r_t^* h_t, \hbox{ for all } x\in A,$$ the following statements are equivalent: $(a)$ $\{T_t: t\in \mathbb{R}_0^{+}\}$ is a uniformly continuous one-parameter semigroup of orthogonality preserving operators on $A$; $(b)$ $\{S_t: t\in \mathbb{R}_0^{+}\}$ is a uniformly continuous one-parameter semigroup of surjective linear isometries (i.e. triple isomorphisms) on $A$ (and hence there exists a triple derivation $\delta$ on $A$ such that $S_t = e^{t \delta}$ for all $t\in \mathbb{R}$), the mapping $t\mapsto h_t $ is continuous at zero, and the identity $ h_{t+s} = h_t r_t^* S_t^{**} (h_s),$ holds for all $s,t\in \mathbb{R}. $ We also extend our study to the case of uniformly continuous one-parameter semigroups of orthogonality preserving operators on a general JB$^*$-algebra.