Miracle-dz/UniFAR-FTUs huggingface dataset:
Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles

We study the behaviour of extremal eigenvalues of the Dirichlet biharmonic operator over rectangles with a given fixed area. We begin by proving that the principal eigenvalue is minimal for a rectangle for which the ratio between the longest and the shortest side lengths does not exceed $1.066459$. We then consider the sequence formed by the minimal $k^{\rm th}$ eigenvalue and show that the corresponding sequence of minimising rectangles converges to the square as $k$ goes to infinity.
Virasoro symmetries of Drinfeld-Sokolov hierarchies and equations of Painlev\'{e} type

We construct a tau cover of the generalized Drinfeld-Sokolov hierarchy associated to an arbitrary affine Kac-Moody algebra with gradations $\mathrm{s}\le\mathds{1}$ and derive its Virasoro symmetries. By imposing the Virasoro constraints we obtain solutions of the Drinfeld-Sokolov hierarchy of Witten-Kontsevich and of Brezin-Gross-Witten types, and of those characterized by certain ordinary differential equations of Painleve type. We also show the existence of affine Weyl group actions on solutions of such Painleve type equations, which generalizes the theory of Noumi and Yamada on affine Weyl group symmetries of the Painleve type equations.
The Heintze-Karcher inequality for metric measure spaces

In this note we prove the Heintze-Karcher inequality in the context of essentially non-branching metric measure spaces satisfying a lower Ricci curvature bound in the sense of Lott-Sturm-Villani. The proof is based on the the needle decomposition technique for metric measure spaces introduced by Cavalletti-Mondino. Moreover, in the class of spaces satisfying a Riemannian curvature-dimension condition with positive curvature the equality case is characterized.
On the Double Roman Domination Number of Generalized Sierpinski Graphs

In this paper, we study the double Roman domination number of generalized Sierpinski graphs $S(G,t)$. More precisely, we obtain a bound for the double Roman domination number of $S(G, t)$. We also find the exact value of $\gamma_{dR}(S(K_{n}, 2))$.
Direct comparison of high voltage breakdown measurements in liquid argon and liquid xenon

As noble liquid time projection chambers grow in size their high voltage requirements increase, and detailed, reproducible studies of dielectric breakdown and the onset of electroluminescence are needed to inform their design. The Xenon Breakdown Apparatus (XeBrA) is a 5-liter cryogenic chamber built to characterize the DC high voltage breakdown behavior of liquid xenon and liquid argon. Electrodes with areas up to 33 cm2 were tested while varying the cathode-anode separation from 1 to 6 mm with a voltage difference up to 75 kV. A power-law relationship between breakdown field and electrode area was observed. The breakdown behavior of liquid argon and liquid xenon within the same experimental apparatus was comparable.
Driving white dwarf metal pollution through unstable eccentric periodic orbits

Context. Planetary debris is observed in the atmospheres of over 1000 white dwarfs, and two white dwarfs are now observed to contain orbiting minor planets. Exoasteroids and planetary core fragments achieve orbits close to the white dwarf through scattering with major planets. However, the architectures that allow for this scattering to take place are time-consuming to explore with N-body simulations lasting ∼1010 yr; these long-running simulations restrict the amount of phase space that can be investigated. Aims. Here we use planar and three-dimensional (spatial) elliptic periodic orbits, as well as chaotic indicators through dynamical stability maps, as quick scale-free analytic alternatives to N-body simulations in order to locate and predict instability in white dwarf planetary systems that consist of one major and one minor planet on very long timescales. We then classify the instability according to ejection versus collisional events. Methods. We generalized our previous work by allowing eccentricity and inclination of the periodic orbits to increase, thereby adding more realism but also significantly more degrees of freedom to our architectures. We also carried out a suite of computationally expensive 10 Gyr N-body simulations to provide comparisons with chaotic indicators in a limited region of phase space. Results. We compute dynamical stability maps that are specific to white dwarf planetary systems and that can be used as tools in future studies to quickly estimate pollution prospects and timescales for one-planet architectures. We find that these maps also agree well with the outcomes of our N-body simulations. Conclusions. As observations of metal-polluted white dwarfs mount exponentially, particularly in the era of Gaia, tools such as periodic orbits can help infer dynamical histories for ensembles of systems.
Orbital dynamics of circumbinary planets

We investigate the dynamics of a non-zero mass, circular orbit planet around an eccentric orbit binary for various values of the binary eccentricity, binary mass fraction, planet mass, and planet semimajor axis by means of numerical simulations. Previous studies investigated the secular dynamics mainly by approximate analytic methods. In the stationary inclination state, the planet and binary precess together with no change in relative tilt. For both prograde and retrograde planetary orbits, we explore the conditions for planetary orbital libration versus circulation and the conditions for stationary inclination. As was predicted by analytic models, for sufficiently high initial inclination, a prograde planet’s orbit librates about the stationary tilted state. For a fixed binary eccentricity, the stationary angle is a monotonically decreasing function of the ratio of the planet-to-binary angular momentum j. The larger j, the stronger the evolutionary changes in the binary eccentricity and inclination. We also calculate the critical tilt angle that separates the circulating from the librating orbits for both prograde and retrograde planet orbits. The properties of the librating orbits and stationary angles are quite different for prograde versus retrograde orbits. The results of the numerical simulations are in very good quantitative agreement with the analytic models. Our results have implications for circumbinary planet formation and evolution.
On symmetry of traveling solitary waves for dispersion generalized NLS

We consider dispersion generalized nonlinear Schrödinger equations (NLS) of the form where denotes a (pseudo)-differential operator of arbitrary order. As a main result, we prove symmetry results for traveling solitary waves in the case of powers . The arguments are based on Steiner type rearrangements in Fourier space. Our results apply to a broad class of NLS-type equations such as fourth-order (biharmonic) NLS, fractional NLS, square-root Klein–Gordon and half-wave equations.
A Study of BERT for Non-Factoid Question-Answering under Passage Length Constraints

We study the use of BERT for non-factoid question-answering, focusing on the passage re-ranking task under varying passage lengths. To this end, we explore the fine-tuning of BERT in different learning-to-rank setups, comprising both point-wise and pair-wise methods, resulting in substantial improvements over the state-of-the-art. We then analyze the effectiveness of BERT for different passage lengths and suggest how to cope with large passages.
Concurrent Parsing of Constituency and Dependency

Constituent and dependency representation for syntactic structure share a lot of linguistic and computational characteristics, this paper thus makes the first attempt by introducing a new model that is capable of parsing constituent and dependency at the same time, so that lets either of the parsers enhance each other. Especially, we evaluate the effect of different shared network components and empirically verify that dependency parsing may be much more beneficial from constituent parsing structure. The proposed parser achieves new state-of-the-art performance for both parsing tasks, constituent and dependency on PTB and CTB benchmarks.
Deep Learning Based Channel Estimation for Massive MIMO With Mixed-Resolution ADCs

In this letter, deep learning is applied to estimate the uplink channels for mixed analog-to-digital converters (ADCs) massive multiple-input multiple-output (MIMO) systems, where a portion of antennas are equipped with high-resolution ADCs while others employ low-resolution ones at the base station. A direct-input deep neural network (DI-DNN) is first proposed to estimate channels by using the received signals of all antennas. To eliminate the adverse impact of the coarsely quantized signals, a selective-input prediction DNN (SIP-DNN) is developed, where only the signals received by the high-resolution ADC antennas are exploited to predict the channels of other antennas as well as to estimate their own channels. Numerical results show the superiority of the proposed DNN based approaches over the existing methods, especially with mixed one-bit ADCs, and the effectiveness of the proposed approaches on different ADC resolution patterns.
Self-Attention Based Molecule Representation for Predicting Drug-Target Interaction

Predicting drug-target interactions (DTI) is an essential part of the drug discovery process, which is an expensive process in terms of time and cost. Therefore, reducing DTI cost could lead to reduced healthcare costs for a patient. In addition, a precisely learned molecule representation in a DTI model could contribute to developing personalized medicine, which will help many patient cohorts. In this paper, we propose a new molecule representation based on the self-attention mechanism, and a new DTI model using our molecule representation. The experiments show that our DTI model outperforms the state of the art by up to 4.9% points in terms of area under the precision-recall curve. Moreover, a study using the DrugBank database proves that our model effectively lists all known drugs targeting a specific cancer biomarker in the top-30 candidate list.
Contact Skill Imitation Learning for Robot-Independent Assembly Programming

Robotic automation is a key driver for the advancement of technology. The skills of human workers, however, are difficult to program and seem currently unmatched by technical systems. In this work we present a data-driven approach to extract and learn robot-independent contact skills from human demonstrations in simulation environments, using a Long Short Term Memory (LSTM) network. Our model learns to generate error-correcting sequences of forces and torques in task space from object-relative motion, which industrial robots carry out through a Cartesian force control scheme on the real setup. This scheme uses forward dynamics computation of a virtually conditioned twin of the manipulator to solve the inverse kinematics problem. We evaluate our methods with an assembly experiment, in which our algorithm handles part tilting and jamming in order to succeed. The results show that the skill is robust towards localization uncertainty in task space and across different joint configurations of the robot. With our approach, non-experts can easily program force-sensitive assembly tasks in a robot-independent way.
Time dynamics with matrix product states: Many-body localization transition of large systems revisited

We compare accuracy of two prime time evolution algorithms involving Matrix Product States - tDMRG (time-dependent density matrix renormalization group) and TDVP (time-dependent variational principle). The latter is supposed to be superior within a limited and fixed auxiliary space dimension. Surprisingly, we find that the performance of algorithms depends on the model considered. In particular, many-body localized systems as well as the crossover regions between localized and delocalized phases are better described by tDMRG, contrary to the delocalized regime where TDVP indeed outperforms tDMRG in terms of accuracy and reliability. As an example, we study many-body localization transition in a large size Heisenberg chain. We discuss drawbacks of previous estimates [Phys. Rev. B 98, 174202 (2018)] of the critical disorder strength for large systems.
Higher Equipments, Double Colimits and Homotopy Colimits

This document is centered around a main idea: simplicial categories, by which we mean simplicial objects in the category of categories, can be treated as a two-fold categorical structure and their double category theory is homotopically meaningful. The most well-known two-fold structures are double categories, typically used to organize bimodules in various contexts. However there is no double category of spaces even though notions of bimodule are conceivable. We first remedy this defect of double category theory by constructing a meaningful simplicial category of spaces. Then we develop the analogy with double categories by defining double colimits and by postulating an equipment property, which is promptly satisfied in the examples. As an application we prove that certain double colimits are naturally interpreted as homotopy colimits. Quite surprisingly this analogy unveils a principle: simplicial categories are to simplicially enriched categories what double categories are to 2-categories!
ShellNet: Efficient Point Cloud Convolutional Neural Networks Using Concentric Shells Statistics

Deep learning with 3D data has progressed significantly since the introduction of convolutional neural networks that can handle point order ambiguity in point cloud data. While being able to achieve good accuracies in various scene understanding tasks, previous methods often have low training speed and complex network architecture. In this paper, we address these problems by proposing an efficient end-to-end permutation invariant convolution for point cloud deep learning. Our simple yet effective convolution operator named ShellConv uses statistics from concentric spherical shells to define representative features and resolve the point order ambiguity, allowing traditional convolution to perform on such features. Based on ShellConv we further build an efficient neural network named ShellNet to directly consume the point clouds with larger receptive fields while maintaining less layers. We demonstrate the efficacy of ShellNet by producing state-of-the-art results on object classification, object part segmentation, and semantic scene segmentation while keeping the network very fast to train.
Unsupervised Learning of Landmarks by Descriptor Vector Exchange

Equivariance to random image transformations is an effective method to learn landmarks of object categories, such as the eyes and the nose in faces, without manual supervision. However, this method does not explicitly guarantee that the learned landmarks are consistent with changes between different instances of the same object, such as different facial identities. In this paper, we develop a new perspective on the equivariance approach by noting that dense landmark detectors can be interpreted as local image descriptors equipped with invariance to intra-category variations. We then propose a direct method to enforce such an invariance in the standard equivariant loss. We do so by exchanging descriptor vectors between images of different object instances prior to matching them geometrically. In this manner, the same vectors must work regardless of the specific object identity considered. We use this approach to learn vectors that can simultaneously be interpreted as local descriptors and dense landmarks, combining the advantages of both. Experiments on standard benchmarks show that this approach can match, and in some cases surpass state-of-the-art performance amongst existing methods that learn landmarks without supervision. Code is available at www.robots. ox.ac. uk/~vgg/research/DVE/.
Scattering of Energetic Electrons by Heat-flux-driven Whistlers in Flares

The scattering of electrons by heat-flux-driven whistler waves is explored with a particle-in-cell simulation relevant to the transport of energetic electrons in flares. This simulation is initiated with a large heat flux produced by using a kappa distribution of electrons with positive velocity and a cold return current beam. This system represents energetic electrons escaping from a reconnection-driven energy-release site. This heat-flux system drives large-amplitude oblique whistler waves propagating both along and against the heat flux, as well as electron acoustic waves. While the waves are dominantly driven by the low-energy electrons, including the cold return current beam, the energetic electrons resonate with and are scattered by the whistlers on timescales of the order of a hundred electron cyclotron times. Peak whistler amplitudes of and angles of ∼60° with respect to the background magnetic field are observed. Electron perpendicular energy is increased, while the field-aligned electron heat flux is suppressed. The resulting scattering mean-free-paths of energetic electrons are small compared with the typical scale size of energy-release sites in flares, which might lead to the effective confinement of energetic electrons required for the production of very energetic particles.
The influence of a top-heavy integrated galactic IMF and dust on the chemical evolution of high-redshift starbursts

We study the effects of the integrated galactic initial mass function (IGIMF) and dust evolution on the abundance patterns of high redshift starburst galaxies. In our chemical models, the rapid collapse of gas clouds triggers an intense and rapid star formation episode, which lasts until the onset of a galactic wind, powered by the thermal energy injected by stellar winds and supernova explosions. Our models follow the evolution of several chemical elements (C, N, α-elements, and Fe) both in the gas and dust phases. We test different values of β, the slope of the embedded cluster mass function for the IGIMF, where lower β values imply a more top-heavy initial mass function (IMF). The computed abundances are compared to high-quality abundance measurements obtained in lensed galaxies and from composite spectra in large samples of star-forming galaxies in the redshift range 2 ≲ z ≲ 3. The adoption of the IGIMF causes a sensible increase of the rate of star formation with respect to a standard Salpeter IMF, with a strong impact on chemical evolution. We find that in order to reproduce the observed abundance patterns in these galaxies, either we need a very top-heavy IGIMF (β < 2) or large amounts of dust. In particular, if dust is important, the IGIMF should have β ≥ 2, which means an IMF slightly more top-heavy than the Salpeter one. The evolution of the dust mass with time for galaxies of different mass and IMF is also computed, highlighting that the dust amount increases with a top-heavier IGIMF.
API Misuse Correction: A Statistical Approach

Modern software development relies heavily on Application Programming Interface (API) libraries. However, there are often certain constraints on using API elements in such libraries. Failing to follow such constraints (API misuse) could lead to serious programming errors. Many approaches have been proposed to detect API misuses, but they still have low accuracy and cannot repair the detected misuses. In this paper, we propose SAM, a novel approach to detect and repair API misuses automatically. SAM uses statistical models to describe five factors involving in any API method call: related method calls, exceptions, pre-conditions, post-conditions, and values of arguments. These statistical models are trained from a large repository of high-quality production code. Then, given a piece of code, SAM verifies each of its method calls with the trained statistical models. If a factor has a sufficiently low probability, the corresponding call is considered as an API misuse. SAM performs an optimal search for editing operations to apply on the code until it has no API issue.
Language Features Matter: Effective Language Representations for Vision-Language Tasks

Shouldn't language and vision features be treated equally in vision-language (VL) tasks? Many VL approaches treat the language component as an afterthought, using simple language models that are either built upon fixed word embeddings trained on text-only data or are learned from scratch. We conclude that language features deserve more attention, which has been informed by experiments which compare different word embeddings, language models, and embedding augmentation steps on five common VL tasks: image-sentence retrieval, image captioning, visual question answering, phrase grounding, and text-to-clip retrieval. Our experiments provide some striking results; an average embedding language model outperforms a LSTM on retrieval-style tasks; state-of-the-art representations such as BERT perform relatively poorly on vision-language tasks. From this comprehensive set of experiments we can propose a set of best practices for incorporating the language component of vision-language tasks. To further elevate language features, we also show that knowledge in vision-language problems can be transferred across tasks to gain performance with multi-task training. This multi-task training is applied to a new Graph Oriented Vision-Language Embedding (GrOVLE), which we adapt from Word2Vec using WordNet and an original visual-language graph built from Visual Genome, providing a ready-to-use vision-language embedding: http://ai.bu. edu/grovle.
Learning Representations and Agents for Information Retrieval

A goal shared by artificial intelligence and information retrieval is to create an oracle, that is, a machine that can answer our questions, no matter how difficult they are. A more limited, but still instrumental, version of this oracle is a question-answering system, in which an open-ended question is given to the machine, and an answer is produced based on the knowledge it has access to. Such systems already exist and are increasingly capable of answering complicated questions. This progress can be partially attributed to the recent success of machine learning and to the efficient methods for storing and retrieving information, most notably through web search engines. One can imagine that this general-purpose question-answering system can be built as a billion-parameters neural network trained end-to-end with a large number of pairs of questions and answers. We argue, however, that although this approach has been very successful for tasks such as machine translation, storing the world's knowledge as parameters of a learning machine can be very hard. A more efficient way is to train an artificial agent on how to use an external retrieval system to collect relevant information. This agent can leverage the effort that has been put into designing and running efficient storage and retrieval systems by learning how to best utilize them to accomplish a task.
Koszul duality for non-graded derived categories

We are concerned with relating derived categories of all modules of two dual Koszul algebras defined by a locally bounded quiver. We first generalize the well known Acyclic Assembly Lemma and formalize an old method of extending a functor from an additive category into a complex category to its complex category. Applying this to the Koszul functor associated with a Koszul algebra defined by a gradable quiver, we obtain a Koszul complex functor, that descends to an equivalence of a continuous family of pairs of triangulated subcategories of doubly unbounded complexes of the respective derived categories of all modules of the Koszul algebra and its Koszul dual. Under this special setting, this extends Beilinson, Ginzburg and Soegel's Koszul duality. In case the Koszul algebra is right or left locally bounded and its Koszul dual is left or right locally bounded respectively (for instance, the quiver has no right infinite path or no left infinite path), our Koszul duality restricts to an equivalence of the bounded derived categories of finitely supported modules, and an equivalence of the bounded derived categories of finite dimensional modules.