Miracle-dz/UniFAR-FTUs huggingface dataset:
On the effect of boundary conditions on the scalability of Schwarz methods

In contrast with classical Schwarz theory, recent results have shown that for special domain geometries, one-level Schwarz methods can be scalable. This property has been proved for the Laplace equation and external Dirichlet boundary conditions. Much less is known if mixed boundary conditions are considered. This short manuscript focuses on the convergence and scalability analysis of one-level parallel Schwarz method and optimized Schwarz method for several different external configurations of boundary conditions, i.e., mixed Dirichlet, Neumann and Robin conditions.
Zonal flow in a resonant precessing cylinder

Abstract A cylinder undergoes precession when it rotates around its axis and this axis itself rotates around another axis. In a precessing cylinder full of fluid, a steady and axisymmetric component of the azimuthal flow is generally present. This component is called a zonal flow. Although zonal flows have been often observed in experiments and numerical simulations, their origin has eluded theoretical approaches so far. Here, we develop an asymptotic analysis to calculate the zonal flow forced in a resonant precessing cylinder, that is when the harmonic response is dominated by a single Kelvin mode. We find that the zonal flow originates from three different sources: (1) the nonlinear interaction of the inviscid Kelvin mode with its viscous correction; (2) the steady and axisymmetric response to the nonlinear interaction of the Kelvin mode with itself; and (3) the nonlinear interactions in the end boundary layers. In a precessing cylinder, two additional sources arise due to the equatorial Coriolis force and the forced shear flow; however, they cancel exactly. The study thus generalises to any Kelvin mode, forced by precession or any other mechanism. The present theoretical predictions of the zonal flow are confirmed by comparison with numerical simulations and experimental results. We also show numerically that the zonal flow is always retrograde in a resonant precessing cylinder ($m=1$) or when it results from resonant Kelvin modes of azimuthal wavenumbers $m=2$, $3$ and, presumably, higher.
Do the Rich Get Richer? Fairness Analysis for Blockchain Incentives

Proof-of-Work (PoW) is the most widely adopted incentive model in current blockchain systems, which unfortunately is energy inefficient. Proof-of-Stake (PoS) is then proposed to tackle the energy issue. The rich-get-richer concern of PoS has been heavily debated in the blockchain community. The debate is centered around the argument that whether rich miners possessing more stakes will obtain higher staking rewards and further increase their potential income in the future. In this paper, we define two types of fairness, i.e., expectational fairness and robust fairness, that are useful for answering this question. In particular, expectational fairness illustrates that the expected income of a miner is proportional to her initial investment, indicating that the expected return on investment is a constant. To better capture the uncertainty of mining outcomes, robust fairness is proposed to characterize whether the return on investment concentrates to a constant with high probability as time evolves. Our analysis shows that the classical PoW mechanism can always preserve both types of fairness as long as the mining game runs for a sufficiently long time. Furthermore, we observe that current PoS blockchains implement various incentive models and discuss three representatives, namely ML-PoS, SL-PoS and C-PoS. We find that (i) ML-PoS (e.g., Qtum and Blackcoin) preserves expectational fairness but may not achieve robust fairness, (ii) SL-PoS (e.g., NXT) does not protect any type of fairness, and (iii) C-PoS (e.g., Ethereum 2.0) outperforms ML-PoS in terms of robust fairness while still maintaining expectational fairness. Finally, massive experiments on real blockchain systems and extensive numerical simulations are performed to validate our analysis.
Structure of Multiple Mirror System From Kaleidoscopic Projections of Single 3D Point

This paper proposes a novel algorithm of discovering the structure of a kaleidoscopic imaging system that consists of multiple planar mirrors and a camera. The kaleidoscopic imaging system can be recognized as the virtual multi-camera system and has strong advantages in that the virtual cameras are strictly synchronized and have the same intrinsic parameters. In this paper, we focus on the extrinsic calibration of the virtual multi-camera system. The problems to be solved in this paper are two-fold. The first problem is to identify to which mirror chamber each of the 2D projections of mirrored 3D points belongs. The second problem is to estimate all mirror parameters, i.e., normals, and distances of the mirrors. The key contribution of this paper is to propose novel algorithms for these problems using a single 3D point of unknown geometry by utilizing a kaleidoscopic projection constraint, which is an epipolar constraint on mirror reflections. We demonstrate the performance of the proposed algorithm of chamber assignment and estimation of mirror parameters with qualitative and quantitative evaluations using synthesized and real data.
Signatures of r-process Elements in Kilonova Spectra

Binary neutron star (NS) mergers have been expected to synthesize r-process elements and emit radioactively powered radiation, called kilonovae. Although r-process nucleosynthesis was confirmed by the observations of GW170817/AT2017gfo, no trace of individual elements has been identified except for strontium. In this paper, we perform systematic calculations of line strength for bound–bound transitions and radiative transfer simulations in NS merger ejecta toward element identification in kilonova spectra. We find that Sr ii triplet lines appear in the spectrum of a lanthanide-poor model, which is consistent with the absorption feature observed in GW170817/AT2017gfo. The synthetic spectrum also shows the strong Ca ii triplet lines. This is natural because Ca and Sr are coproduced in the material with relatively high electron fraction and their ions have similar atomic structures with only one s-electron in the outermost shell. The line strength, however, highly depends on the abundance distribution and temperature in the ejecta. For our lanthanide-rich model, the spectra show the features of doubly ionized heavy elements, such as Ce, Tb, and Th. Our results suggest that the line-forming region of GW170817/AT2017gfo was lanthanide-poor. We show that the Sr ii and Ca ii lines can be used as a probe of physical conditions in NS merger ejecta. Absence of the Ca ii line features in GW170817/AT2017gfo implies that the Ca/Sr ratio is <0.002 in mass fraction, which is consistent with nucleosynthesis for electron fraction ≥0.40 and entropy per nucleon (in units of Boltzmann constant) ≥25.
Knowing What VQA Does Not: Pointing to Error-Inducing Regions to Improve Explanation Helpfulness

Attention maps, a popular heatmap-based explanation method for Visual Question Answering (VQA), are supposed to help users understand the model by highlighting portions of the image/question used by the model to infer answers. However, we see that users are often misled by current attention map visualizations that point to relevant regions despite the model producing an incorrect answer. Hence, we propose Error Maps that clarify the error by highlighting image regions where the model is prone to err. Error maps can indicate when a correctly attended region may be processed incorrectly leading to an incorrect answer, and hence, improve users’ understanding of those cases. To evaluate our new explanations, we further introduce a metric that simulates users’ interpretation of explanations to evaluate their potential helpfulness to understand model correctness. We ﬁnally conduct user studies to see that our new explanations help users understand model correctness better than baselines by an expected 30% and that our proxy helpfulness metrics correlate strongly ( ρ > 0 . 97 ) with how well users can predict model correctness.
Fields interpretable in $P$-minimal fields

We prove that an infinite field interpretable in a p-adically closed field K is definably isomorphic to a finite extension of K. The result remains true in any P -minimal field where definable functions are generically differentiable. In [5], interpretable fields in various expansions of real closed valued fields were classified using analysis of one dimensional quotients which are definably embedded in the field. Here we use similar methods to classify interpretable fields in various expansions of p-adically closed fields. In [8] Pillay proved that any field definable in Qp is definably isomorphic to a finite extension of Qp, and asked whether the same result is true of interpretable fields. Our main theorem gives a positive answer to Pillay’s question. Theorem 1. Let K be a P -minimal field. If, additionally, definable functions in K are generically differentiable, then any infinite field interpretable in K is definably isomorphic to a finite extension of K . In particular, the result holds for p-adically closed fields. The proof does not use elimination of imaginaries (that is not known, in general, for P -minimal fields). It uses implicitly the fact that P -minimal fields are uniformities (see [13] for details). The results of Sections 4-5 do not use P -minimality beyond those consequences that are treated axiomatically in [13] (and even [2]). For that reason we expect that our methods can also be applied outside of the P -minimal context. Note that recently Walsberg showed, [15], that a positive answer to the above question of Pillay’s would provide an example of an NIP theory not interpreting an infinite field whose Shelah expansion does. We mention also that a positive answer to Pillay’s question on interpretable fields in Qp was announced also by E. Alouf, A. Fornasiero and J. de la Nuez Gonzalez. Acknowledgements We thank Immanuel Halupczok and Dugald Macpherson for several discussions during the preparation of the article. 1. BACKGROUND AND PRELIMINARIES The notion of P -minimal fields was introduced by Haskell and Macpherson in [4]. Recall that a valued field K is P -minimal if it is p-valued, its value group is a Z-group and in every structure elementary equivalent toK every definable subset ofK is quantifier-free definable in the Macintyre language for valued fields. We denote its value group by Γ and its valuation ring by O. It is one Date: March 30, 2021. The first author would like to thanks the Israel Science Foundation for its support of this research (grant No. 181/16) and the Kreitman foundation fellowship. The third author was partially supported by Israel Science Foundation grant number 290/19 .
Bridging Vision and Language from the Video-to-Text Perspective: A Comprehensive Review

Research in the area of Vision and Language encompasses challenging topics that seek to connect visual and textual information. The video-to-text problem is one of these topics, in which the goal is to connect an input video with its textual description. This connection can be mainly made by retrieving the most significant descriptions from a corpus or generating a new one given a context video. These two ways represent essential tasks for Computer Vision and Natural Language Processing communities, called text retrieval from video task and video captioning/description task. These two tasks are substantially more complex than predicting or retrieving a single sentence from an image. The spatiotemporal information present in videos introduces diversity and complexity regarding the visual content and the structure of associated language descriptions. This review categorizes and describes the state-of-the-art techniques for the video-to-text problem. It covers the main video-to-text methods and the ways to evaluate their performance. We analyze how the most reported benchmark datasets have been created, showing their drawbacks and strengths for the problem requirements. We also show the impressive progress that researchers have made on each dataset, and we analyze This work has been done as part of the Stic-AmSud Project 18-STIC-09, “Transforming multimedia data for indexing and retrieval purposes”. Jesus Perez-Martin is funded by ANID/Doctorado Nacional/2018-21180648. This work was partially supported by the ANID Millennium Science Initiative Program Code ICN17 002, the Department of Computer Science at University of Chile, and the Image and Multimedia Data Science Laboratory (IMScience) at PUC Minas. Jesus Perez-Martin, Benjamin Bustos, and Jorge Pérez IMFD, Department of Computer Science, University of Chile Beauchef 851, Santiago, Chile E-mail: jeperez@dcc.uchile. cl, bebustos@dcc.uchile. cl, jperez@dcc.uchile. cl Silvio Jamil F. Guimarães Computer Science Department, Pontifical Catholic University of Minas Gerais Belo Horizonte, Minas Gerais, Brazil E-mail: sjamil@pucminas.br Ivan Sipiran, and Grethel Coello Said Department of Computer Science, University of Chile Beauchef 851, Santiago, Chile E-mail: isipiran@dcc.uchile. cl, grethelyusel@gmail.com ar X iv :2 10 3. 14 78 5v 1 [ cs . C V ] 2 7 M ar 2 02 1 2 Jesus Perez-Martin et al. why, despite this progress, the video-to-text conversion is still unsolved. State-ofthe-art techniques are still a long way from achieving human-like performance in generating or retrieving video descriptions. We cover several significant challenges in the field and discuss future research directions.
The Statistics of Circular Optimal Transport

Empirical optimal transport (OT) plans and distances provide effective tools to compare and statistically match probability measures defined on a given ground space. Fundamental to this are distributional limit laws and we derive a central limit theorem for the empirical OT distance of circular data. Our limit results require only mild assumptions in general and include prominent examples such as the von Mises or wrapped Cauchy family. Most notably, no assumptions are required when data are sampled from the probability measure to be compared with, which is in strict contrast to the real line. A bootstrap principle follows immediately as our proof relies on Hadamard differentiability of the OT functional. This paves the way for a variety of statistical inference tasks and is exemplified for asymptotic OT based goodness of fit testing for circular distributions. We discuss numerical implementation, consistency and investigate its statistical power. For testing uniformity, it turns out that this approach performs particularly well for unimodal alternatives and is almost as powerful as Rayleigh’s test, the most powerful invariant test for von Mises alternatives. For regimes with many modes the circular OT test is less powerful which is explained by the shape of the corresponding transport plan.
Conductance zeros in complex molecules and lattices from the interference set method

Destructive quantum interference (DQI) and its effects on electron transport is studied in chemical molecules and finite physical lattices that can be described by a discrete Hamiltonian. Starting from a bipartite system whose conductance zeros are known to exist between any two points of a specially designated set, the interference set, we use the Dyson equation to develop a general algorithm of determining the zero conductance points in complex systems, which are not necessarily bipartite. We illustrate this procedure as it applies to the fulvene molecule. The stability of the conductance zeros is analyzed in respect with external perturbations.
Cyclic Defense GAN Against Speech Adversarial Attacks

This letter proposes a new defense approach for counteracting state-of-the-art white and black-box adversarial attack algorithms. Our approach fits into the implicit reactive defense algorithm category since it does not directly manipulate the potentially malicious input signals. Instead, it reconstructs a similar signal with a synthesized spectrogram using a cyclic generative adversarial network. This cyclic framework helps to yield a stable generative model. Finally, we feed the reconstructed signal into the speech-to-text model for transcription. The conducted experiments on targeted and non-targeted adversarial attacks developed for attacking DeepSpeech, Kaldi, and Lingvo models demonstrate the proposed defense’s effectiveness in adverse scenarios.
Risk Bounds for Learning via Hilbert Coresets

We develop a formalism for constructing stochastic upper bounds on the expected full sample risk for supervised classification tasks via the Hilbert coresets approach within a transductive framework. We explicitly compute tight and meaningful bounds for complex datasets and complex hypothesis classes such as state-of-the-art deep neural network architectures. The bounds we develop exhibit nice properties: i) the bounds are non-uniform in the hypothesis space, ii) in many practical examples, the bounds become effectively deterministic by appropriate choice of prior and training data-dependent posterior distributions on the hypothesis space, and iii) the bounds become significantly better with increase in the size of the training set. We also lay out some ideas to explore for future research.
Contrastive Explanations of Plans Through Model Restrictions

In automated planning, the need for explanations arises when there is a mismatch between a proposed plan and the user’s expectation. We frame Explainable AI Planning as an iterative plan exploration process, in which the user asks a succession of contrastive questions that lead to the generation and solution of hypothetical planning problems that are restrictions of the original problem. The object of the exploration is for the user to understand the constraints that govern the original plan and, ultimately, to arrive at a satisfactory plan. We present the results of a user study that demonstrates that when users ask questions about plans, those questions are usually contrastive, i.e. “why A rather than B? ”. We use the data from this study to construct a taxonomy of user questions that often arise during plan exploration. Our approach to iterative plan exploration is a process of successive model restriction. Each contrastive user question imposes a set of constraints on the planning problem, leading to the construction of a new hypothetical planning problem as a restriction of the original. Solving this restricted problem results in a plan that can be compared with the original plan, admitting a contrastive explanation. We formally define model-based compilations in PDDL2.1 for each type of constraint derived from a contrastive user question in the taxonomy, and empirically evaluate the compilations in terms of computational complexity. The compilations were implemented as part of an explanation framework supporting iterative model restriction. We demonstrate its benefits in a second user study.
Multi-Scale Vision Longformer: A New Vision Transformer for High-Resolution Image Encoding

This paper presents a new Vision Transformer (ViT) architecture Multi-Scale Vision Longformer, which significantly enhances the ViT of [12] for encoding high-resolution images using two techniques. The first is the multi-scale model structure, which provides image encodings at multiple scales with manageable computational cost. The second is the attention mechanism of Vision Long-former, which is a variant of Longformer [3], originally developed for natural language processing, and achieves a linear complexity w.r. t. the number of input tokens. A comprehensive empirical study shows that the new ViT significantly outperforms several strong baselines, including the existing ViT models and their ResNet counterparts, and the Pyramid Vision Transformer from a concurrent work [47], on a range of vision tasks, including image classification, object detection, and segmentation. The models and source code are released at https://github.com/microsoft/vision-longformer.
Neumann boundary optimal control problems governed by parabolic variational equalities

Abstract We consider a heat conduction problem S with mixed boundary conditions in an n-dimensional domain Ω with regular boundary and a family of problems Sα with also mixed boundary conditions in Ω, where α > 0 is the heat transfer coefficient on the portion of the boundary Γ1. In relation to these state systems, we formulate Neumann boundary optimal control problems on the heat flux q which is definite on the complementary portion Γ2 of the boundary of Ω. We obtain existence and uniqueness of the optimal controls, the first order optimality conditions in terms of the adjoint state and the convergence of the optimal controls, the system state and the adjoint state when the heat transfer coefficient α goes to infinity. Furthermore, we formulate particular boundary optimal control problems on a real parameter λ, in relation to the parabolic problems S and Sα and to mixed elliptic problems P and Pα. We find an explicit form for the optimal controls, we prove monotony properties and we obtain convergence results when the parameter time goes to infinity.
Constraining the Earth's Dynamical Ellipticity From Ice Age Dynamics

The dynamical ellipticity of a planet expresses the departure of its mass distribution from spherical symmetry. It enters as a parameter in the description of a planet's precession and nutation, as well as other rotational normal modes. In the case of the Earth, uncertainties in this quantity's history produce an uncertainty in the solutions for the past evolution of the Earth‐Moon system. Constraining this history has been a target of interdisciplinary efforts as it represents an astro‐geodetic parameter whose variation is shaped by geophysical processes, and whose imprints can be found in the geological signal. We revisit the classical problem of its variation during ice ages, where glacial cycles exerted a varying surface loading that had altered the shape of the geoid. In the framework of glacial isostatic adjustment, and with the help of a recent paleoclimatic proxy of ice volume, we present the evolution of the dynamical ellipticity over the Cenozoic ice ages. We map out the problem in full generality identifying major sensitivities to surface loading and internal variations in parameter space. This constrained evolution is aimed to be used in future astronomical computations of the orbital and insolation quantities of the Earth.
RESPONSE OF FRIJOLILLO RHYNCHOSIA MINIMA (L) DC. TO SUPPLEMENTARY PHOSPHORUS WITH THREE SOIL MOISTURE CONDITIONS: I. GROWTH AND DEVELOPMENT

This study was undertaken with the objective of evaluating the response of frijolillo, grown with three levels of soil moisture and supplemented with phosphorous (P). The experiment was carried out under greenhouse conditions without climate control. Plants were tested during the period from germination to vegetative growth stage. Three soil moisture levels (100, 50, and 25% of field capacity) combined with four levels of P (0, 50, 100, and 150 mg kg−1) were tested in a factorial arrangement with four replications. This species showed tolerance to drought stress since its leaf area, dry mass of stems and root mass did not decrease with 50% of constant moisture. Furthermore, with the highest concentrations of phosphorous (100 and 150 mg kg−1) there was more aerial mass accumulation. Finally, with maximum drought stress (25% moisture) growth of main stem decreased. However, root growth had a maximum length under the lowest moisture conditions.
Explaining the Road Not Taken

It is unclear if existing interpretations of deep neural network models respond effectively to the needs of users. This paper summarizes the common forms of explanations (such as feature attribution, decision rules, or probes) used in over 200 recent papers about natural language processing (NLP), and compares them against user questions collected in the XAI Question Bank. We found that although users are interested in explanations for the road not taken -- namely, why the model chose one result and not a well-defined, seemly similar legitimate counterpart -- most model interpretations cannot answer these questions.