Miracle-dz/UniFAR-FTUs huggingface dataset:
Smallest Percolating Sets in Bootstrap Percolation on Grids

In this paper we fill in a fundamental gap in the extremal bootstrap percolation literature, by providing the first proof of the fact that for all $d \geq 1$, the size of the smallest percolating sets in $d$-neighbour bootstrap percolation on $[n]^d$, the $d$-dimensional grid of size $n$, is $n^{d-1}$. Additionally, we prove that such sets percolate in time at most $c_d n^2$, for some constant $c_d >0 $ depending on $d$ only.
Quantum Information Dynamics of Spacetime and Matter

It was known long ago that quantum theory and general relativity, two pillars of modern physics, are in sharp conflict in their foundations. Their fundamental inconsistencies render a consistent theory of quantum gravity the most challenging problem in physics. Here we propose an information-complete quantum field theory (ICQFT), which describes elementary fermions, their gauge fields, and gravity (together, called the trinary fields) as an elementary trinity without any conceptual inconsistency of existing theories. We then argue that the ICQFT provides a coherent picture and conceptual framework of unifying matter and spacetime (gravity) as information via spacetime-matter entanglement and gives a compelling solution to the problem of time and time's arrow. The trinary fields are characterized by dual entanglement and dual dynamics. Spacetime-matter entanglement encodes complete physical predictions of the theory and allows us to give a quantum information definition of dark energy. We consider two particular forms of spacetime-matter entangled states and their physical consequences. One of them\ is consistent with the variational holographic relation and another results in an universal relation between entanglement entropy and geometry (area and volume). This latter relation allows us to determine the cosmological constant term in the classical Einstein equation and implies that our Universe is not strictly holographic due to dark energy (related to an universal negative pressure). We predict the interior quantum state of a Schwarzschild black hole to be maximally information-complete. As a concrete quantum formulation of gravity coupled with matter, the ICQFT is about quantum information dynamics for spacetime and matter and eliminates the conceptual obstacles of existing quantum gravity theory.
The relation between the turbulent Mach number and observed fractal dimensions of turbulent clouds

Supersonic turbulence is a key player in controlling the structure and star formation potential of molecular clouds (MCs). The three-dimensional (3D) turbulent Mach number, $\operatorname{\mathcal {M}}$, allows us to predict the rate of star formation. However, determining Mach numbers in observations is challenging because it requires accurate measurements of the velocity dispersion. Moreover, observations are limited to two-dimensional (2D) projections of the MCs and velocity information can usually only be obtained for the line-of-sight component. Here we present a new method that allows us to estimate $\operatorname{\mathcal {M}}$ from the 2D column density, Σ, by analysing the fractal dimension, $\mathcal {D}$. We do this by computing $\mathcal {D}$ for six simulations, ranging between 1 and 100 in $\operatorname{\mathcal {M}}$. From this data we are able to construct an empirical relation, $\log \operatorname{\mathcal {M}}(\mathcal {D}) = \xi _1(\operatorname{erfc}^{-1} [(\mathcal {D}-\operatorname{\mathcal {D}_\text{min}})/\Omega ] + \xi _2),$ where $\operatorname{erfc}^{-1}$ is the inverse complimentary error function, $\operatorname{\mathcal {D}_\text{min}}= 1.55 \pm 0.13$ is the minimum fractal dimension of Σ, Ω = 0.22 ± 0.07, ξ1 = 0.9 ± 0.1, and ξ2 = 0.2 ± 0.2. We test the accuracy of this new relation on column density maps from Herschel observations of two quiescent subregions in the Polaris Flare MC, ‘saxophone’ and ‘quiet’. We measure $\operatorname{\mathcal {M}}\sim 10$ and $\operatorname{\mathcal {M}}\sim 2$ for the subregions, respectively, which are similar to previous estimates based on measuring the velocity dispersion from molecular line data. These results show that this new empirical relation can provide useful estimates of the cloud kinematics, solely based upon the geometry from the column density of the cloud.
Diagnosing quantum chaos in many-body systems using entanglement as a resource

Classical chaotic systems exhibit exponentially diverging trajectories due to small differences in their initial state. The analogous diagnostic in quantum many-body systems is an exponential growth of out-of-time-ordered correlation functions (OTOCs). These quantities can be computed for various models, but their experimental study requires the ability to evolve quantum states backward in time, similar to the canonical Loschmidt echo measurement. In some simple systems, backward time evolution can be achieved by reversing the sign of the Hamiltonian; however in most interacting many-body systems, this is not a viable option. Here we propose a new family of protocols for OTOC measurement that do not require backward time evolution. Instead, they rely on ordinary time-ordered measurements performed in the thermofield double (TFD) state, an entangled state formed between two identical copies of the system. We show that, remarkably, in this situation the Lyapunov chaos exponent $\lambda_L$ can be extracted from the measurement of an ordinary two-point correlation function. As an unexpected bonus, we find that our proposed method yields the so-called "regularized" OTOC -- a quantity that is believed to most directly indicate quantum chaos. According to recent theoretical work, the TFD state can be prepared as the ground state of two weakly coupled identical systems and is therefore amenable to experimental study. We illustrate the utility of these protocols on the example of the maximally chaotic Sachdev-Ye-Kitaev model and support our findings by extensive numerical simulations.
Lattice dynamics and Raman spectrum of 
BaZrO3
 single crystals

BaZrO3 is a perovskite that remains in the simple cubic phase at all temperatures, hence with no first-order Raman-active phonon mode allowed by symmetry. Yet, it exhibits an intense Raman spectrum with sharp and well-defined features. Here, we report the evolution of the Raman spectrum of BaZrO3 single crystals in a broad temperature range (4--1200~K) and discuss its origin with the support of detailed first-principle calculations of the lattice dynamics. Phonon calculations are performed not only for the cubic phase of BaZrO3, but also for the low-symmetry phases with octahedra tilts that have been suspected to exist at the nanoscale. We show that the Raman spectrum shows no direct evidence for these nanodomains, but can instead be explained by classical second-order Raman scattering. We provide an assignment of the dominant features to phonon modes combinations. In particular, we show that the high frequency range of the spectrum is dominated by overtones and shows an image of the phonon density of states corresponding to the stretching modes of the oxygen octahedra.
Query-based Interactive Recommendation by Meta-Path and Adapted Attention-GRU

Recently, interactive recommender systems are becoming increasingly popular. The insight is that, with the interaction between users and the system, (1) users can actively intervene the recommendation results rather than passively receive them, and (2) the system learns more about users so as to provide better recommendation. We focus on the single-round interaction, i.e. the system asks the user a question (Step 1), and exploits his feedback to generate better recommendation (Step 2). A novel query-based interactive recommender system is proposed in this paper, where personalized questions are accurately generated from millions of automatically constructed questions in Step 1, and the recommendation is ensured to be closely-related to users' feedback in Step 2. We achieve this by transforming Step 1 into a query recommendation task and Step 2 into a retrieval task. The former task is our key challenge. We firstly propose a model based on Meta-Path to efficiently retrieve hundreds of query candidates from the large query pool. Then an adapted Attention-GRU model is developed to effectively rank these candidates for recommendation. Offline and online experiments on Taobao, a large-scale e-commerce platform in China, verify the effectiveness of our interactive system. The system has already gone into production in the homepage of Taobao App since Nov. 11, 2018 (see https://youtu.be/hAkXDOf2dDU on how it works online). Our code is public in https://github.com/zyody/QueryQR.
Control-Oriented Model Reduction for Minimizing Transient Energy Growth in Shear Flows

A linear non-modal mechanism for transient amplification of perturbation energy is known to trigger sub-critical transition to turbulence in many shear flows. Feedback control strategies for minimizing this transient energy growth can be formulated as convex optimization problems based on linear matrix inequalities. Unfortunately, solving the requisite linear matrix inequality problem can be computationally prohibitive within the context of high-dimensional fluid flows. In this work, we investigate the utility of control-oriented reduced-order models to facilitate the design of feedback flow control strategies that minimize the maximum transient energy growth. An output projection onto proper orthogonal decomposition modes is used to faithfully capture the system energy. Subsequently, a balanced truncation is performed to reduce the state dimension, while preserving the system's input-output properties. The model reduction and control approaches are studied within the context of a linearized channel flow with blowing and suction actuation at the walls. Controller synthesis for this linearized channel flow system becomes tractable through the use of the proposed control-oriented reduced-order models. Further, the resulting controllers are found to reduce the maximum transient energy growth compared with more conventional linear quadratic optimal control strategies.
Dirac Magnons in a Honeycomb Lattice Quantum 
XY
 Magnet 
CoTiO3

The discovery of massless Dirac electrons in graphene and topological Dirac-Weyl materials has prompted a broad search for bosonic analogues of such Dirac particles. Recent experiments have found evidence for Dirac magnons above an Ising-like ferromagnetic ground state in a two-dimensional (2D) kagome lattice magnet and in the van der Waals layered honeycomb crystal CrI$_3$, and in a 3D Heisenberg magnet Cu$_3$TeO$_6$. Here we report on our inelastic neutron scattering investigation on large single crystals of a stacked honeycomb lattice magnet CoTiO$_3$, which is part of a broad family of ilmenite materials. The magnetically ordered ground state of CoTiO$_3$ features ferromagnetic layers of Co$^{2+}$, stacked antiferromagnetically along the $c$-axis. We discover that the magnon dispersion relation exhibits strong easy-plane exchange anisotropy and hosts a clear gapless Dirac cone along the edge of the 3D Brillouin zone. Our results establish CoTiO$_3$ as a model pseudospin-$1/2$ material to study interacting Dirac bosons in a 3D quantum XY magnet.
Multi-object Tracking in Unknown Detection Probability with the PMBM Filter

This paper focuses on the joint multi-object tracking (MOT) and the estimate of detection probability with the \emph{Poisson multi-Bernoulli mixture} (PMBM) filter. In a majority of multi-object scenarios, the knowledge of detection probability is usually uncertain, which is often estimated offline from the training data. In such cases, online filtering is not allowed or believable, otherwise, significate parameter mismatch will result in biased estimates (state and cardinality of objects). Consequently, the ability of adaptively estimating the detection probability is essential in practice. In this paper, we detail how the detection probability can be estimated accompanied with the state estimates. Besides, closed-form solutions to the proposed method are derived by approximating the intensity of Poisson random finite set (RFS) to a Beta-Gaussian mixture form and density of Bernoulli RFS to a single Beta-Gaussian form. Simulation results show the effectiveness and superiority of the proposed method.
Continuous Integration Theater

Background: Continuous Integration (CI) systems are now the bedrock of several software development practices. Several tools such as TravisCI, CircleCI, and Hudson, that implement CI practices, are commonly adopted by software engineers. However, the way that software engineers use these tools could lead to what we call “Continuous Integration Theater”, a situation in which software engineers do not employ these tools effectively, leading to unhealthy CI practices. Aims: The goal of this paper is to make sense of how commonplace are these unhealthy continuous integration practices being employed in practice. Method: By inspecting 1,270 open-source projects that use TravisCI, the most used CI service, we quantitatively studied how common is to use CI (1) with infrequent commits, (2) in a software project with poor test coverage, (3) with builds that stay broken for long periods, and (4) with builds that take too long to run. Results: We observed that $748 (\sim 60$%) projects face infrequent commits, which essentially makes the merging process harder. Moreover, we were able to find code coverage information for 51 projects. The average code coverage was 78%, although Ruby projects have a higher code coverage than Java projects (86% and 63%, respectively). However, some projects with very small coverage $(\sim 4$%) were found. Still, we observed that 85% of the studied projects have at least one broken build that take more than four days to be fixed. Interestingly, very small projects (up to 1,000 lines of code) are the ones that take the longest to fix broken builds. Finally, we noted that, for the majority of the studied projects, the build is executed under the 10 minutes rule of thumb. Conclusions: Our results are important to an increasing community of software engineers that employ CI practices on daily basis but may not be aware of bad practices that are eventually employed.
Bounding quantiles of Wasserstein distance between true and empirical measure

Consider the empirical measure, $\hat{\mathbb{P}}_N$, associated to $N$ i.i. d. samples of a given probability distribution $\mathbb{P}$ on the unit interval. For fixed $\mathbb{P}$ the Wasserstein distance between $\hat{\mathbb{P}}_N$ and $\mathbb{P}$ is a random variable on the sample space $[0,1]^N$. Our main result is that its normalised quantiles are asymptotically maximised when $\mathbb{P}$ is a convex combination between the uniform distribution supported on the two points $\{0,1\}$ and the uniform distribution on the unit interval $[0,1]$. This allows us to obtain explicit asymptotic confidence regions for the underlying measure $\mathbb{P}$. We also suggest extensions to higher dimensions with numerical evidence.
A new weak-field magnetic DA white dwarf in the local 20 pc volume

We report the discovery of a new magnetic DA white dwarf (WD), WD 0011 − 721, which is located within the very important 20 pc volume-limited sample of the closest WDs to the Sun. This star has a mean field modulus ⟨|B|⟩ of 343 kG, and from the polarisation signal we deduce a line-of-sight field component of 75 kG. The magnetic field is sufficiently weak to have escaped detection in classification spectra. We then present a preliminary exploration of the data concerning the frequency of such fields among WDs with hydrogen-rich atmospheres (DA stars). We find that 20 ± 5% of the DA WDs in this volume have magnetic fields, mostly weaker than 1 MG. Unlike the slow field decay found among the magnetic Bp stars of the upper main sequence, the WDs in this sample show no evidence of magnetic field or flux changes over several Gyr.
Taut foliations from double-diamond
 replacements

A 3-manifold is foliar if it supports a codimension-one co-oriented taut foliation. Suppose $M$ is an oriented 3-manifold with connected boundary a torus, and suppose $M$ contains a properly embedded, compact, oriented, surface $R$ with a single boundary component that is Thurston norm minimizing in $H_2(M, \partial M)$. We define a readily recognizable type of sutured manifold decomposition, which for notational reasons we call double-diamond taut, and show that if $R$ admits a double-diamond taut sutured manifold decomposition, then every boundary slope except one is strongly realized by a co-oriented taut foliation; that is, the foliation intersects $\partial M$ transversely in a foliation by curves of that slope. In the case that $M$ is the complement of a knot $\kappa$ in $S^3$, the exceptional filling is the meridional one, and hence $\kappa$ is persistently foliar, by which we mean that every non-trivial slope is strongly realized; hence, restricting attention to rational slopes, every manifold obtained by non-trivial Dehn surgery along $\kappa$ is foliar. In particular, if $R$ is a Murasugi sum of surfaces $R_1$ and $R_2$, where $R_2$ is an unknotted band with an even number $2m\ge 4$ of half-twists, then $\kappa= \partial R$ is persistently foliar.
An adiabatic quantum algorithm for the Frobenius problem

The (Diophantine) Frobenius problem is a well-known NP-hard problem (also called the stamp problem or the chicken nugget problem) whose origins lie in the realm of combinatorial number theory. In this paper we present an adiabatic quantum algorithm which solves it, using the so-called Apery set of a numerical semigroup, via a translation into a QUBO problem. The algorithm has been specifically designed to run in a D-Wave 2X machine.
Combating the Filter Bubble: Designing for Serendipity in a University Course Recommendation System

Collaborative filtering based algorithms, including Recurrent Neural Networks (RNN), tend towards predicting a perpetuation of past observed behavior. In a recommendation context, this can lead to an overly narrow set of suggestions lacking in serendipity and inadvertently placing the user in what is known as a "filter bubble. " In this paper, we grapple with the issue of the filter bubble in the context of a course recommendation system in production at a public university. Most universities in the United States encourage students to explore developing interests while simultaneously advising them to adhere to course taking norms which progress them towards graduation. These competing objectives, and the stakes involved for students, make this context a particularly meaningful one for investigating real-world recommendation strategies. We introduce a novel modification to the skip-gram model applied to nine years of historic course enrollment sequences to learn course vector representations used to diversify recommendations based on similarity to a student's specified favorite course. This model, which we call multifactor2vec, is intended to improve the semantics of the primary token embedding by also learning embeddings of potentially conflated factors of the token (e.g., instructor). Our offline testing found this model improved accuracy and recall on our course similarity and analogy validation sets over a standard skip-gram. Incorporating course catalog description text resulted in further improvements. We compare the performance of these models to the system's existing RNN-based recommendations with a user study of undergraduates (N = 70) rating six characteristics of their course recommendations. Results of the user study show a dramatic lack of novelty in RNN recommendations and depict the characteristic trade-offs that make serendipity difficult to achieve.
Depth Growing for Neural Machine Translation

While very deep neural networks have shown effectiveness for computer vision and text classification applications, how to increase the network depth of the neural machine translation (NMT) models for better translation quality remains a challenging problem. Directly stacking more blocks to the NMT model results in no improvement and even drop in performance. In this work, we propose an effective two-stage approach with three specially designed components to construct deeper NMT models, which result in significant improvements over the strong Transformer baselines on WMT14 English\toGerman and English\toFrench translation tasks.
Distributed Learning in Non-Convex Environments—Part I: Agreement at a Linear Rate

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments. Most available works on distributed non-convex optimization problems focus on the deterministic setting where exact gradients are available at each agent. In this work and its Part II, we consider stochastic cost functions, where exact gradients are replaced by stochastic approximations and the resulting gradient noise persistently seeps into the dynamics of the algorithm. We establish that the diffusion learning strategy continues to yield meaningful estimates non-convex scenarios in the sense that the iterates by the individual agents will cluster in a small region around the network centroid. We use this insight to motivate a short-term model for network evolution over a finite-horizon. In Part II of this work, we leverage this model to establish descent of the diffusion strategy through saddle points in <inline-formula><tex-math notation="LaTeX">$O(1/\mu)$</tex-math></inline-formula> steps, where <inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> denotes the step-size, and the return of approximately second-order stationary points in a polynomial number of iterations.
Evaluation of Low Complexity Massive MIMO Techniques Under Realistic Channel Conditions

In this paper, a low complexity massive multiple-input multiple-output technique is studied with a geometry-based stochastic channel model, called COST 2100 model. We propose to exploit the discrete-time Fourier transform of the antenna correlation function to perform user scheduling. The proposed algorithm relies on a tradeoff between the number of occupied bins of the eigenvalue spectrum of the channel covariance matrix for each user and spectral overlap among the selected users. We next show that linear precoding design can be performed based only on the channel correlation matrix. The proposed scheme exploits the angular bins of the eigenvalue spectrum of the channel covariance matrix to build up an “approximate eigenchannels” for the users. We investigate the reduction of average system throughput with no channel state information at the transmitter (CSIT). Analysis and numerical results show that while the throughput slightly decreases due to the absence of CSIT, the complexity of the system is reduced significantly.