Miracle-dz/UniFAR-FTUs huggingface dataset:
Efficient average-case population recovery in the presence of insertions and deletions

Several recent works have considered the \emph{trace reconstruction problem}, in which an unknown source string $x\in\{0,1\}^n$ is transmitted through a probabilistic channel which may randomly delete coordinates or insert random bits, resulting in a \emph{trace} of $x$. The goal is to reconstruct the original string~$x$ from independent traces of $x$. While the best algorithms known for worst-case strings use $\exp(O(n^{1/3}))$ traces \cite{DOS17,NazarovPeres17}, highly efficient algorithms are known \cite{PZ17,HPP18} for the \emph{average-case} version, in which $x$ is uniformly random. We consider a generalization of this average-case trace reconstruction problem, which we call \emph{average-case population recovery in the presence of insertions and deletions}. In this problem, there is an unknown distribution $\cal{D}$ over $s$ unknown source strings $x^1,\dots,x^s \in \{0,1\}^n$, and each sample is independently generated by drawing some $x^i$ from $\cal{D}$ and returning an independent trace of $x^i$. Building on \cite{PZ17} and \cite{HPP18}, we give an efficient algorithm for this problem. For any support size $s \leq \smash{\exp(\Theta(n^{1/3}))}$, for a $1-o(1)$ fraction of all $s$-element support sets $\{x^1,\dots,x^s\} \subset \{0,1\}^n$, for every distribution $\cal{D}$ supported on $\{x^1,\dots,x^s\}$, our algorithm efficiently recovers ${\cal D}$ up to total variation distance $\epsilon$ with high probability, given access to independent traces of independent draws from $\cal{D}$. The algorithm runs in time poly$(n,s,1/\epsilon)$ and its sample complexity is poly$(s,1/\epsilon,\exp(\log^{1/3}n)). $ This polynomial dependence on the support size $s$ is in sharp contrast with the \emph{worst-case} version (when $x^1,\dots,x^s$ may be any strings in $\{0,1\}^n$), in which the sample complexity of the most efficient known algorithm \cite{BCFSS19} is doubly exponential in $s$.
On the Bruhat-Tits stratification of a quaternionic unitary Shimura variety

In this note we study the special fiber of the Rapoport-Zink space attached to a quaternionic unitary group. The special fiber is described using the so called Bruhat-Tits stratification and is intimately related to the Bruhat-Tits building of a split symplectic group. As an application we describe the supersingular locus of the related Shimura variety.
Topological magnetic-spin textures in two-dimensional van der Waals Cr2Ge2Te6.

Two-dimensional (2D) van der Waals (vdW) materials show a range of profound physical properties that can be tailored through their incorporation in heterostructures and manipulated with external forces1-5. The recent discovery of long-range ferromagnetic order down to atomic layers provides an additional degree of freedom in engineering 2D materials and their heterostructure devices for spintronics, valleytronics and magnetic tunnel junction switches6-9. Here, using direct imaging by cryo-Lorentz transmission electron microscopy we show that topologically nontrivial magnetic-spin states, skyrmionic bubbles, can be realized in exfoliated insulating 2D vdW Cr2Ge2Te6. Due to the competition between dipolar interactions and uniaxial magnetic anisotropy, hexagonally-packed nanoscale bubble lattices emerge by field cooling with magnetic field applied along the out-of-plane direction. Despite a range of topological spin textures in stripe domains arising due to pair formation and annihilation of Bloch lines, bubble lattices with single chirality are prevalent. Our observation of topologically-nontrivial homochiral skyrmionic bubbles in exfoliated vdW materials provides a new avenue for novel quantum states in atomically-thin insulators for magneto-electronic and quantum devices.
Efficient Video Generation on Complex Datasets

Generative models of natural images have progressed towards high fidelity samples by the strong leveraging of scale. We attempt to carry this success to the field of video modeling by showing that large Generative Adversarial Networks trained on the complex Kinetics-600 dataset are able to produce video samples of substantially higher complexity than previous work. Our proposed network, Dual Video Discriminator GAN (DVD-GAN), scales to longer and higher resolution videos by leveraging a computationally efficient decomposition of its discriminator. We evaluate on the related tasks of video synthesis and video prediction, and achieve new state of the art Frechet Inception Distance on prediction for Kinetics-600, as well as state of the art Inception Score for synthesis on the UCF-101 dataset, alongside establishing a number of strong baselines on Kinetics-600.
The Two-Sided Game of Googol and Sample-Based Prophet Inequalities

The secretary problem or the game of Googol are classic models for online selection problems that have received significant attention in the last five decades. We consider a variant of the problem and explore its connections to data-driven online selection. Specifically, we are given $n$ cards with arbitrary non-negative numbers written on both sides. The cards are randomly placed on $n$ consecutive positions on a table, and for each card, the visible side is also selected at random. The player sees the visible side of all cards and wants to select the card with the maximum hidden value. To this end, the player flips the first card, sees its hidden value and decides whether to pick it or drop it and continue with the next card. We study algorithms for two natural objectives. In the first one, as in the secretary problem, the player wants to maximize the probability of selecting the maximum hidden value. We show that this can be done with probability at least $0.45292$. In the second one, similar to the prophet inequality, the player maximizes the expectation of the selected hidden value. We show a guarantee of at least $0.63518$ with respect to the expected maximum hidden value. Our algorithms result from combining three basic strategies. One is to stop whenever we see a value larger than the initial $n$ visible numbers. The second one is to stop the first time the last flipped card's value is the largest of the currently $n$ visible numbers in the table. And the third one is similar to the latter but it additionally requires that the last flipped value is larger than the value on the other side of its card. We apply our results to the prophet secretary problem with unknown distributions, but with access to a single sample from each distribution. Our guarantee improves upon $1-1/e$ for this problem, which is the currently best known guarantee and only works for the i.i. d. case.
High HIV-1 Genetic Diversity in Patients from Northern Brazil

The HIV-1 epidemic in Brazil is driven by subtypes B, F1, and C and recombinants forms among those subtypes. The distribution of HIV-1 subtypes, however, may vary across different Brazilian regions and the molecular epidemiologic profile in Northern Brazil remains poorly explored. HIV-1 pol sequences were obtained from 305 patients failing antiretroviral therapy followed at outpatient clinics from five Northern Brazilian states. The most prevalent HIV-1 clade observed in the Northern Brazilian region was subtype B (81%), followed by BF1 recombinants (10%), subtype F1 (4%), subtype C (3%), BC recombinants (2%), and BU recombinants (1%). Although HIV-1 subtype B was the predominant HIV-1 clade in Northern Brazil, its prevalence greatly varies among different states, ranging from 63% in Rondônia to 92% in Acre. Among the 37 HIV-1 recombinant sequences detected in the Northern Brazilian region, nine (24%) displayed a unique recombinant form structure, five (14%) a CRF28/29_BF-like structure, and four (11%) a CRF31_BC-like structure. Two other BF1 recombinant patterns were identified in 16 (43%) and three (8%) samples that may correspond to two potentially new CRFs_BF characteristic of the Northern region. This study reveals that despite the low spatial connectivity with other Brazilian regions, the genetic complexity of the HIV-1 epidemic in Northern Brazil is very high and that the molecular epidemiologic pattern may vary across different northern states, reflecting a complex epidemic with multiple independent viral introductions into this Brazilian region.
Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: First-principles approach

Twisted bilayer graphene (TBLG) has emerged as an important platform for studying correlated phenomena, including unconventional superconductivity, in two-dimensional systems. The complexity of the atomic-scale structures in TBLG has made even the study of single-particle physics at low energies around the Fermi level, quite challenging. Our goal here is to provide a convenient and physically motivated picture of single-particle physics in TBLG using reduced models with the smallest possible number of localized orbitals. The reduced models exactly reproduce the low-energy bands of \textit{ab-initio} tight-binding models, including the effects of atomic relaxations. Furthermore, we obtain for the first time the corresponding Wannier orbitals that incorporate all symmetries of TBLG, which are also calculated as a function of angle, a requisite first step towards incorporating electron interaction effects. We construct eight-band and five-band models for the low-energy states for twist angles between $1.3^\circ$ and $0.6^\circ$. The models are created using a multi-step Wannier projection technique starting with appropriate $\textit{ab initio}$ $k \cdot p$ continuum hamiltonians. Our procedure can also readily capture the perturbative effects of substrates and external displacement fields while offering a significant reduction in complexity for studying electron-electron correlation phenomena in realistic situations.
The HST large programme on NGC 6752 – III. Detection of the peak of the white dwarf luminosity function

We report on the white dwarf (WD) cooling sequence of the old globular cluster NGC 6752, which is chemically complex and hosts a blue horizontal branch. This is one of the last globular cluster WD cooling sequences accessible to imaging by the Hubble Space Telescope. Our photometry and completeness tests show that we have reached the peak of the luminosity function of the WD cooling sequence, at a magnitude mF606W = 29.4 ± 0.1, which is consistent with a formal age of ∼14 Gyr. This age is also consistent with the age from fits to the main-sequence turn-off (13–14 Gyr), reinforcing our conclusion that we observe the expected accumulation of WDs along the cooling sequence.
Batch-Shaped Channel Gated Networks

We present a method for gating deep-learning architectures on a ﬁne-grained level. Individual convolutional maps are turned on/off conditionally on features in the network. This method allows us to train neural networks with a large capacity, but lower inference time than the full network. To achieve this, we introduce a new residual block architecture that gates convolutional channels in a ﬁne-grained manner. We also introduce a generally applicable tool batch-shaping that matches the marginal aggregate posteriors of features in a neural network to a pre-speciﬁed prior distribution. We use this novel technique to force gates to be more conditional on the data. We present results on CIFAR-10 and ImageNet datasets for image classiﬁcation and Cityscapes for semantic segmentation. Our results show that our method can slim down large architectures conditionally, such that the average computational cost on the data is on par with a smaller architecture, but with higher accuracy. In particular, our ResNet34 gated network achieves a performance of 72.55% top-1 accuracy compared to the 69.76% accuracy of the baseline ResNet18 model, for similar complexity. We also show that the resulting networks automatically learn to use more features for difﬁcult examples and fewer features for simple examples.
Contribution to the study of the use of brain-computer interfaces in virtual and augmented reality

The objective of this PhD thesis is to study the use of Brain- Computer Interfaces (BCIs) within Virtual Reality (VR) and Augmented Reality (AR). Our goal is to evaluate the compatibility between systems based on a BCI and VR/AR, to design new tools for the visualization of the brain activity based on VR/AR, and finally to propose new uses for the BCIs, and especially in combination with smart clothes. In order to fulfil these objectives, we have first designed and performed a feasibility study concerning the combination of a BCI and VR. Our objective was to study the influence of motor activity on a BCI. We have designed a system similar to a video game, serving as a base for a user study showing that this BCI can be successfully used, even when participants are performing a demanding muscular activity. We have also proposed three visualization tools for the brain activity based on VR/AR. Our first system called the «Mind- Mirror» which enables the visualization of our own brain activity «inside our own head» by superimposition. A user study has shown that no significant drop in BCI performance occurred, even with the additional complexity due to our AR-based display. Our second contribution is called «Mind- Window» and extends the Mind-Mirror’s possibilities by enabling one or multiple users to visualize the brain activity of another person as if her skull was transparent. Our last contribution is called «Mind-Inside» and allows users to visualize their brain activity in real-time while being immersed in a virtual brain. Finally, we have studied how BCIs and the VR/AR can be applied to smart clothes. We have designed an experimental platform comprising a dressing room integrating a BCI. Following this work, we proposed an «invisibility cloak» inspired by the Harry Potter universe. This virtual cloak allows users to camouflage themselves in AR using their mental state. Results from a preliminary study based on a simple videogame inspired by the Harry Potter universe could notably show that, compared to a standard control made with a keyboard, controlling the optical camouflage directly with the BCI could enhance the user experience and the feeling of «having a super-power».
On the Global Convergence of Actor-Critic: A Case for Linear Quadratic Regulator with Ergodic Cost

Despite the empirical success of the actor-critic algorithm, its theoretical understanding lags behind. In a broader context, actor-critic can be viewed as an online alternating update algorithm for bilevel optimization, whose convergence is known to be fragile. To understand the instability of actor-critic, we focus on its application to linear quadratic regulators, a simple yet fundamental setting of reinforcement learning. We establish a nonasymptotic convergence analysis of actor-critic in this setting. In particular, we prove that actor-critic finds a globally optimal pair of actor (policy) and critic (action-value function) at a linear rate of convergence. Our analysis may serve as a preliminary step towards a complete theoretical understanding of bilevel optimization with nonconvex subproblems, which is NP-hard in the worst case and is often solved using heuristics.
Genre-Based Approach to Teaching Writing in EFL Context

Writing is considered to be one of the most difficult skills that learners are expected to master. To write appropriately and effectively is a task that most ESL learners face despite years spending for learning and developing their writing skills. Genre-based approach is a teaching methodology that is believed to assist students in coping with this difficult task. Thus, this paper aims to examine the effects of genre-based approach to teaching writing in EFL contexts using an experimental approach. 40 EFL learners were selected from a private language institute; 20 of them were randomly selected to form the treatment group and the rest formed the control group. The experimental group was taught using the genre-based writing techniques and the other group was taught writing without it. The results showed considerable improvement in the treatment group compared with the control group.
Hybrid annihilation transformation (HAT) for pipelining QRD-based least-square adaptive filters

A novel transformation, referred to as hybrid annihilation transformation (HAT), for pipelining the QR decomposition (QRD) based least square adaptive filters has been developed. HAT provides a unified framework for the derivation of high-throughput/low-power VLSI architectures of three kinds of QRD adaptive filters, namely, QRD recursive least-square (LS) adaptive filters, QRD LS lattice adaptive filters, and QRD multichannel LS lattice adaptive filters. In this paper, HAT is presented as a solution to break the bottleneck of a high-throughput implementation introduced by the inherent recursive computation in the QRD based adaptive filters. The most important feature of the proposed solution is that it does not introduce any approximation in the entire filtering process. Therefore, it causes no performance degradation no matter how deep the filter is pipelined. It allows a linear speedup in the throughput rate by a linear increase in hardware complexity. The sampling rate can be traded off for power reduction with lower supply voltage for applications where high-speed is not required. The proposed transformation is addressed both analytically, with mathematical proofs, and experimentally, with computer simulation results on its applications in wireless code division multiple access (CDMA) communications, conventional digital communications and multichannel linear predictions.
ThirdEye: Triplet Based Iris Recognition without Normalization

Most iris recognition pipelines involve three stages: segmenting into iris/non-iris pixels, normalization the iris region to a fixed area, and extracting relevant features for comparison. Given recent advances in deep learning, it is prudent to ask which stages are required for accurate iris recognition. Lojez et al. (IWBF 2019) recently concluded that the segmentation stage is still crucial for good accuracy. We ask if normalization is beneficial? Towards answering this question, we develop a new iris recognition system called ThirdEye based on triplet convolutional neural networks (Schroff et al., ICCV 2015). ThirdEye directly uses segmented images without normalization.We observe equal error rates of 1.32%, 9.20%, and 0.59% on the ND-0405, UbirisV2, and IITD datasets respectively. For IITD, the most constrained dataset, this improves on the best prior work. However, for ND-0405 and UbirisV2, our equal error rate is slightly worse than prior systems. Our concluding hypothesis is that normalization is more important for less constrained environments.
Tackling Graphical NLP problems with Graph Recurrent Networks

How to properly model graphs is a long-existing and important problem in NLP area, where several popular types of graphs are knowledge graphs, semantic graphs and dependency graphs. Comparing with other data structures, such as sequences and trees, graphs are generally more powerful in representing complex correlations among entities. For example, a knowledge graph stores real-word entities (such as "Barack_Obama" and "U.S.") and their relations (such as "live_in" and "lead_by"). Properly encoding a knowledge graph is beneficial to user applications, such as question answering and knowledge discovery. Modeling graphs is also very challenging, probably because graphs usually contain massive and cyclic relations. Recent years have witnessed the success of deep learning, especially RNN-based models, on many NLP problems. Besides, RNNs and their variations have been extensively studied on several graph problems and showed preliminary successes. Despite the successes that have been achieved, RNN-based models suffer from several major drawbacks on graphs. First, they can only consume sequential data, thus linearization is required to serialize input graphs, resulting in the loss of important structural information. Second, the serialization results are usually very long, so it takes a long time for RNNs to encode them. In this thesis, we propose a novel graph neural network, named graph recurrent network (GRN). We study our GRN model on 4 very different tasks, such as machine reading comprehension, relation extraction and machine translation. Some take undirected graphs without edge labels, while the others have directed ones with edge labels. To consider these important differences, we gradually enhance our GRN model, such as further considering edge labels and adding an RNN decoder. Carefully designed experiments show the effectiveness of GRN on all these tasks.
Delta-invariants for Fano varieties with large automorphism groups

For a variety $X$, a big $\mathbb{Q}$-divisor $L$ and a closed connected subgroup $G \subset \mathrm{Aut}(X, L)$ we define a $G$-invariant version of the $\delta$-threshold. We prove that for a Fano variety $(X, -K_X)$ and a connected subgroup $G \subset \mathrm{Aut}(X)$ this invariant characterizes $G$-equivariant uniform $K$-stability. We also use this invariant to investigate $G$-equivariant $K$-stability of some Fano varieties with large groups of symmetries, including spherical Fano varieties. We also consider the case of $G$ being a finite group.
One-dimensional minimizers for a diffuse interface generalized antiferromagnetic model in general dimension

In this paper we consider the diffuse interface version of the generalized antiferromagnetic model studied in its sharp interface limit as ε → 0 in [7, 8, 9] in the discrete and in [13] and [4] in the continuous setting. In any dimension d ≥ 1, denoting by τ the positive parameter measuring the deviation from the critical regime above which constant functions are optimal, as in [16] one expects that for ε small and τ small minimizing functions are one-dimensional periodic functions. In this paper we are able to prove such a characterization of minimizers, thus proving also the symmetry breaking as soon as the dimension d is strictly greater than one. Partial results on the periodicity of minimizers in dimension d = 1 were obtained for a more general class of reflection positive kernels in [6].
Rectification of energy and motion in non-equilibrium parity violating metamaterials

Uncovering new mechanisms for rectification of stochastic fluctuations has been a longstanding problem in non-equilibrium statistical mechanics. Here, using a model parity violating metamaterial that is allowed to interact with a bath of active energy consuming particles, we uncover new mechanisms for rectification of energy and motion. Our model active metamaterial can generate energy flows through an object in the absence of any temperature gradient. The nonreciprocal microscopic fluctuations responsible for generating the energy flows can further be used to power locomotion in, or exert forces on, a viscous fluid. Taken together, our analytical and numerical results elucidate how the geometry and inter-particle interactions of the parity violating material can couple with the non-equilibrium fluctuations of an active bath and enable rectification of energy and motion.
Subsystems of transitive subshifts with linear complexity

Abstract We bound the number of distinct minimal subsystems of a given transitive subshift of linear complexity, continuing work of Ormes and Pavlov [On the complexity function for sequences which are not uniformly recurrent. Dynamical Systems and Random Processes (Contemporary Mathematics, 736). American Mathematical Society, Providence, RI, 2019, pp. 125--137]. We also bound the number of generic measures such a subshift can support based on its complexity function. Our measure-theoretic bounds generalize those of Boshernitzan [A unique ergodicity of minimal symbolic flows with linear block growth. J. Anal. Math. 44(1) (1984), 77–96] and are closely related to those of Cyr and Kra [Counting generic measures for a subshift of linear growth. J. Eur. Math. Soc. 21(2) (2019), 355–380].