Miracle-dz/UniFAR-FTUs huggingface dataset:
Fitting Metrics and Ultrametrics with Minimum Disagreements

Given $x\in(\mathbb{R}_{\geqslant 0})(_{2}^{[n]})$ recording pairwise distances, the Metric Violation Distance problem asks to compute the $\ell_{0}$ distance between x and the metric cone; i.e., modify the minimum number of entries of x to make it a metric. Due to its large number of applications in various data analysis and optimization tasks, this problem has been actively studied recently. We present an $O(\log n)$-approximation algorithm for METRIC VIOLATION Distance, exponentially improving the previous best approximation ratio of $O(OPT^{1/3})$ of Fan, Raichel, and Van Buskirk [SODA, 2018]. Furthermore, a major strength of our algorithm is its simplicity and running time. We also study the related problem of Ultrametric Violation Distance, where the goal is to compute the $\ell_{0}$ distance to the cone of ultrametrics, and achieve a constant factor approximation algorithm. The ULTRAMETRIC VIOLATION DISTANCE problem can be regarded as an extension of the problem of fitting ultrametrics studied by Ailon and Charikar [SIAM J. Computing, 2011] and by Cohen-Addad, Das, Kipouridis, Parotsidis, and Thorup [FOCS, 2021] from $\ell_{1}$ norm to $\ell_{0}$ norm. We show that this problem can be favorably interpreted as an instance of CORRELATION CLUSTERING with an additional hierarchical structure, which we solve using a new $O(1)$-approximation algorithm for correlation clustering that has the structural property that it outputs a refinement of the optimum clusters. An algorithm satisfying such a property can be considered of independent interest. We also provide an $O(\log n\log\log n)$ approximation algorithm for weighted instances. Finally, we investigate the complementary version of these problems where one aims at choosing a maximum number of entries of x forming an (ultra-)metric. In stark contrast with the minimization versions, we prove that these maximization versions are hard to approximate within any constant factor assuming the Unique Games Conjecture.
Uncertainty-Induced Transferability Representation for Source-Free Unsupervised Domain Adaptation

Source-free unsupervised domain adaptation (SFUDA) aims to learn a target domain model using unlabeled target data and the knowledge of a well-trained source domain model. Most previous SFUDA works focus on inferring semantics of target data based on the source knowledge. Without measuring the transferability of the source knowledge, these methods insufficiently exploit the source knowledge, and fail to identify the reliability of the inferred target semantics. However, existing transferability measurements require either source data or target labels, which are infeasible in SFUDA. To this end, firstly, we propose a novel Uncertainty-induced Transferability Representation (UTR), which leverages uncertainty as the tool to analyse the channel-wise transferability of the source encoder in the absence of the source data and target labels. The domain-level UTR unravels how transferable the encoder channels are to the target domain and the instance-level UTR characterizes the reliability of the inferred target semantics. Secondly, based on the UTR, we propose a novel Calibrated Adaption Framework (CAF) for SFUDA, including i) the source knowledge calibration module that guides the target model to learn the transferable source knowledge and discard the non-transferable one, and ii) the target semantics calibration module that calibrates the unreliable semantics. With the help of the calibrated source knowledge and the target semantics, the model adapts to the target domain safely and ultimately better. We verified the effectiveness of our method using experimental results and demonstrated that the proposed method achieves state-of-the-art performances on the three SFUDA benchmarks. Code is available at https://github.com/SPIresearch/UTR.
Strain engineering a persistent spin helix with infinite spin lifetime

Persistent spin textures (PSTs) in solid-state materials arise from a unidirectional spin-orbit field in momentum space and offer a route to deliver long carrier spin lifetimes sought for future quantum microelectronic devices. Nonetheless, few three-dimensional materials are known to host PSTs owing to crystal symmetry and chemical requirements. There are even fewer examples demonstrated experimentally. Here we report that high-quality persistent spin textures can be obtained in the polar point groups containing an odd number of mirror operations. We use representation theory analysis and electronic structure calculations to formulate general discovery principles to identify PSTs hidden in known complex ternary layered and perovskite structures with large electric polarizations. We then show some of these materials exhibit PSTs without requiring any special crystalline symmetries. This finding removes the limitation imposed by mirror-symmetry protected PSTs that has limited compound discovery. Our general design approach enables the pursuit of persistent spin helices in materials exhibiting the $C_{3v}$ crystal class adopted by many quantum materials exhibiting large Rashba coefficients.
Atomistic nature of amorphous graphite

This paper focuses on the structural, electronic, and vibrational features of amorphous graphite [R. Thapa et al, Phys. Rev. Lett. , 2022, 128, 236402]. The structural order in amorphous graphite is discussed and compared with graphite and amorphous carbon. The electronic density of states and localization in these phases were analyzed. Spatial projection of charge densities in the π bands showed a high charge concentration on participating atoms in connecting hexagons. A vibrational density of states was computed and is potentially an experimentally testable fingerprint of the material. An analysis of the vibrational modes was carried out using the phase quotient, and the mode stretching character. The average thermal conductivity calculated for aG was 0·85 and 0·96 W/cmK at room temperature and 1000 K, respectively.
Remarks on Different Notions on Output Stability for Nonlinear Delay Systems

Motivated by the regulator theory and adaptive controls, several notions on output stability in the framework of input-to-state stability (iss) were introduced for finite-dimensional systems. It turned out that these output stability notions are intrinsically different, reflecting different manners of how state variables may affect the transient behavior of output variables. In this work, we consider these output stability properties for delay systems. Our main objective is to illustrate how the various notions are related for delay systems and to provide the Razumikhin criteria for the output stability properties. The main results are also critical in developing the converse Lyapunov theorems of the output stability properties for delay systems
Empirical stability boundary for hierarchical triples

Abstract The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be divided into separate two-body orbits with distinct time and length scales, such that one orbit is only mildly affected by the gravitation of the other bodies. Previous work has mapped the stability of such systems at varying resolutions over a limited range of parameters, and attempts have been made to derive analytic and semi-analytic stability boundary fits to explain the observed phenomena. Certain regimes are understood relatively well. However, there are large regions of the parameter space which remain unmapped, and for which the stability boundary is poorly understood. We present a comprehensive numerical study of the stability boundary of hierarchical triples over a range of initial parameters. Specifically, we consider the mass ratio of the inner binary to the outer third body ( $q_\mathrm{out}$ ), mutual inclination (i), initial mean anomaly and eccentricity of both the inner and outer binaries ( $e_\mathrm{in}$ and $e_\mathrm{out}$ respectively). We fit the dependence of the stability boundary on $q_\mathrm{ out}$ as a threshold on the ratio of the inner binary’s semi-major axis to the outer binary’s pericentre separation $a_\mathrm{in}/R_\mathrm{p, out} \leq 10^{-0.6 + 0. 04q_\mathrm{out}}q_\mathrm{out}^{0.32+0. 1q_\mathrm{out}}$ for coplanar prograde systems. We develop an additional factor to account for mutual inclination. The resulting fit predicts the stability of $10^4$ orbits randomly initialised close to the stability boundary with $87.7\%$ accuracy.
Variance-Based Bregman Extragradient Algorithm with Line Search for Solving Stochastic Variational Inequalities

The main purpose of this paper is to propose a variance-based Bregman extragradient algorithm with line search for solving stochastic variational inequalities, which is robust with respect an unknown Lipschitz constant. We prove the almost sure convergence of the algorithm by a more concise and effective method instead of using the supermartingale convergence theorem. Furthermore, we obtain not only the convergence rate $\mathcal{O}(1/k)$ with the gap function when $X$ is bounded, but also the same convergence rate in terms of the natural residual function when $X$ is unbounded. Under the Minty variational inequality condition, we derive the iteration complexity $\mathcal{O}(1/\varepsilon)$ and the oracle complexity $\mathcal{O}(1/\varepsilon^2)$ in both cases. Finally, some numerical results demonstrate the superiority of the proposed algorithm.
GRB 210619B optical afterglow polarization

We report on the follow-up of the extremely bright long gamma-ray burst GRB~210619B with optical polarimetry. We conducted optopolarimetric observations of the optical afterglow of GRB~210619B in the SDSS-r band in the time window ~ 5967 - 8245 seconds after the burst, using the RoboPol instrument at the Skinakas observatory. We report a $5\,\sigma$ detection of polarization $P=1.5\pm0.3$ at polarization angle $EVPA=8\pm6^\circ$. We find that during our observations the polarization is likely constant. These values are corrected for polarization induced by the interstellar medium of the Milky Way and host-induced polarization is likely negligible. Thus the polarization we quote is intrinsic to the GRB afterglow.
Biased Bytes: On the Validity of Estimating Food Consumption from Digital Traces

Given that measuring food consumption at a population scale is a challenging task, researchers have begun to explore digital traces (e.g., from social media or from food-tracking applications) as potential proxies. However, it remains unclear to what extent digital traces reflect real food consumption. The present study aims to bridge this gap by quantifying the link between dietary behaviors as captured via social media (Twitter) v.s. a food-tracking application (MyFoodRepo). We focus on the case of Switzerland and contrast images of foods collected through the two platforms, by designing and deploying a novel crowdsourcing framework for estimating biases with respect to nutritional properties and appearance. We find that the food type distributions in social media v.s. food tracking diverge; e.g., bread is 2.5 times more frequent among consumed and tracked foods than on Twitter, whereas cake is 12 times more frequent on Twitter. Controlling for the different food type distributions, we contrast consumed and tracked foods of a given type with foods shared on Twitter. Across food types, food posted on Twitter is perceived as tastier, more caloric, less healthy, less likely to have been consumed at home, more complex, and larger-portioned, compared to consumed and tracked foods. The fact that there is a divergence between food consumption as measured via the two platforms implies that at least one of the two is not a faithful representation of the true food consumption in the general Swiss population. Thus, researchers should be attentive and aim to establish evidence of validity before using digital traces as a proxy for the true food consumption of a general population. We conclude by discussing the potential sources of these biases and their implications, outlining pitfalls and threats to validity, and proposing actionable ways for overcoming them.
SSORN: Self-Supervised Outlier Removal Network for Robust Homography Estimation

The traditional homography estimation pipeline consists of four main steps: feature detection, feature matching, outlier removal and transformation estimation. Recent deep learning models intend to address the homography estimation problem using a single convolutional network. While these models are trained in an end-to-end fashion to simplify the homography estimation problem, they lack the feature matching step and/or the outlier removal step, which are important steps in the traditional homography estimation pipeline. In this paper, we attempt to build a deep learning model that mimics all four steps in the traditional homography estimation pipeline. In particular, the feature matching step is implemented using the cost volume technique. To remove outliers in the cost volume, we treat this outlier removal problem as a denoising problem and propose a novel self-supervised loss to solve the problem. Extensive experiments on synthetic and real datasets demonstrate that the proposed model outperforms existing deep learning models.
Visual-Imagery-Based Analogical Construction in Geometric Matrix Reasoning Task

Raven's Progressive Matrices is a family of classical intelligence tests that have been widely used in both research and clinical settings. There have been many exciting efforts in AI communities to computationally model various aspects of problem solving such figural analogical reasoning problems. In this paper, we present a series of computational models for solving Raven's Progressive Matrices using analogies and image transformations. We run our models following three different strategies usually adopted by human testees. These models are tested on the standard version of Raven's Progressive Matrices, in which we can solve 57 out 60 problems in it. Therefore, analogy and image transformation are proved to be effective in solving RPM problems.
Correct-by-Construction Runtime Enforcement in AI - A Survey

Runtime enforcement refers to the theories, techniques, and tools for enforcing correct behavior with respect to a formal specification of systems at runtime. In this paper, we are interested in techniques for constructing runtime enforcers for the concrete application domain of enforcing safety in AI. We discuss how safety is traditionally handled in the field of AI and how more formal guarantees on the safety of a self-learning agent can be given by integrating a runtime enforcer. We survey a selection of work on such enforcers, where we distinguish between approaches for discrete and continuous action spaces. The purpose of this paper is to foster a better understanding of advantages and limitations of different enforcement techniques, focusing on the specific challenges that arise due to their application in AI. Finally, we present some open challenges and avenues for future work.
AVMiner: Expansible and Semantic-Preserving Anti-Virus Labels Mining Method

With the increase in the variety and quantity of malware, there is an urgent need to speed up the diagnosis and analysis of malware. Extracting the malware family-related tokens from AV (Anti-Virus) labels, provided by online antivirus engines, paves the way for pre-diagnosing the malware. Automatically extracting vital information from AV labels will greatly enhance the detection ability of security enterprises and equip the research ability of security analysts. Recent works like AVCLASS and AVCLASS2 try to extract the attributes of malware from AV labels and establish the taxonomy based on expert knowledge. However, due to the uncertain trend of complicated malicious behaviors, the system needs the following abilities to face the challenge: preserving vital semantics, being expansible, and being free from expert knowledge. In this work, we present AVMiner, an expansible malware tagging system that can mine the most vital tokens from AV labels. AVMiner adopts natural language processing techniques and clustering methods to generate a sequence of tokens without expert knowledge ranked by importance. AVMiner can self-update when new samples come. Finally, we evaluate AVMiner on over 8,000 samples from well-known datasets with manually labeled ground truth, which outperforms previous works.
Application of Convolutional Neural Networks with Quasi-Reversibility Method Results for Option Forecasting

This paper presents a novel way to apply mathematical finance and machine learning (ML) to forecast stock options prices. Following results from the paper Quasi-Reversibility Method and Neural Network Machine Learning to Solution of Black-Scholes Equations (appeared on the AMS Contemporary Mathematics journal), we create and evaluate new empirical mathematical models for the Black-Scholes equation to analyze data for 92,846 companies. We solve the Black-Scholes (BS) equation forwards in time as an ill-posed inverse problem, using the Quasi-Reversibility Method (QRM), to predict option price for the future one day. For each company, we have 13 elements including stock and option daily prices, volatility, minimizer, etc. Because the market is so complicated that there exists no perfect model, we apply ML to train algorithms to make the best prediction. The current stage of research combines QRM with Convolutional Neural Networks (CNN), which learn information across a large number of data points simultaneously. We implement CNN to generate new results by validating and testing on sample market data. We test different ways of applying CNN and compare our CNN models with previous models to see if achieving a higher profit rate is possible.
Planetary Structure&Dynamic in Science Fiction. Scientific Analysis&Review of Interstellar [UCM Bachelor Thesis, 2015]

Christopher Nolan's latest blockbuster, Interstellar, has supposed a revolution not only from a cinematographically viewpoint, but also in the relation between current spectators and science. The aim of this report is to analyze some features presented in Interstellar. Basic Newtonian Physics shows how a planet orbiting a supermassive black hole like Gargantua must travel at 0.25 the speed of light in order to be in a stable orbit. Thus, this orbit is too far from the black hole to explain the time dilatation observed in Miller's Planet and an the orbit that could explain such a time dilatation is much more smaller that Roche's limit. Furthermore, I explain how enormous waves as Miller's Planet ones could appear by studying the tidal potential created by Gargantua, obtaining a wave of 200 kilometers high, but better results are obtained by considering a series of tsunamis in Miller's Planet. Finally, I present an explanation to Mann's Planet ice-covered landscape in which Snowball Earth Theory plays a fundamental role. No difficult General Relativity formulas will be used in order to make easier the comprehension of the research. Supervisors: M. L. Osete&J. Gorgas
Searching for the main powering outflow objects in Cepheus A East

We present (sub)millimeter line and continuum observations in a mosaicing mode of the massive star forming region Cepheus A East made with the Submillimeter Array (SMA). Our mosaic covers a total area of about 3$'$ $\times$ 12$'$ centered in the HW 2/3 region. For the first time, this observational study encloses a high angular resolution ($\sim$ 3$''$) together with a large scale mapping of Cepheus A East. We report compact and high velocity $^{12}$CO(2-1) emission associated with the multiple east-west bright H$_2$ condensations present in the region. Blueshifted and redshifted gas emission is found towards the east as well as west of HW 2/3. The observations suggest the presence of multiple large-scale east-west outflows that seems to be powered at smaller scales by radio sources associated with the young stars HW2, HW3c and HW3d. A kinematical study of part of the data suggests that the molecular outflow powered by HW2 is precesing with time as recently reported. Our data reveal five periodic ejections of material separated approximately every 10$^\circ$ as projected in the plane of the sky. The most recent ejections appear to move toward the plane of the sky. An energetic explosive event as the one that occurred in Orion BN/KL or DR21 does not explain the kinematics, and the dynamical times of the multiple ejections found here. The continuum observations only revealed a strong millimeter source associated with the HW 2/3 region. High angular resolution observations allow us to resolve this extended dusty object in only two compact sources (with spatial sizes of approximately 300 AU) associated with HW2 and HW3c. Finally, the bright optical/X-Ray HH 168 -- GDD37 object might be produced by strong shocks related with the outflow from HW3c.
Iterative solution methods

Preface Acknowledgements 1. Direct solution methods 2. Theory of matrix eigenvalues 3. Positive definite matrices, Schur complements, and generalized eigenvalue problems 4. Reducible and irreducible matrices and the Perron-Frobenius theory for nonnegative matrices 5. Basic iterative methods and their rates of convergence 6. M-matrices, convergent splittings, and the SOR method 7. Incomplete factorization preconditioning methods 8. Approximate matrix inverses and corresponding preconditioning methods 9. Block diagonal and Schur complement preconditionings 10. Estimates of eigenvalues and condition numbers for preconditional matrices 11. Conjugate gradient and Lanczos-type methods 12. Generalized conjugate gradient methods 13. The rate of convergence of the conjugate gradient method Appendices.
Detection of ultra-low protein concentrations with the simplest possible field effect transistor

Silicon nanowire (Si NW) sensors have attracted great attention due to their ability to provide fast, low-cost, label-free, real-time detection of chemical and biological species. Usually configured as field effect transistors (FETs), they have already demonstrated remarkable sensitivity with high selectivity (through appropriate functionalisation) towards a large number of analytes in both liquid and gas phases. Despite these excellent results, Si NW FET sensors have not yet been successfully employed to detect single molecules of either a chemical or biological target species. Here we show that sensors based on silicon junctionless nanowire transistors (JNTs), the simplest possible transistors, are capable of detecting the protein streptavidin at a concentration as low as 580 zM closely approaching the single molecule level. This ultrahigh detection sensitivity is due to the intrinsic advantages of junctionless devices over conventional FETs. Apart from their superior functionality, JNTs are much easier to fabricate by standard microelectronic processes than transistors containing p–n junctions. The ability of JNT sensors to detect ultra-low concentrations (in the zeptomolar range) of target species, and their potential for low-cost mass production, will permit their deployment in numerous environments, including life sciences, biotechnology, medicine, pharmacology, product safety, environmental monitoring and security.