Miracle-dz/UniFAR-FTUs huggingface dataset:
Optimal estimation of Gaussian DAG models

We study the optimal sample complexity of learning a Gaussian directed acyclic graph (DAG) from observational data. Our main results establish the minimax optimal sample complexity for learning the structure of a linear Gaussian DAG model in two settings of interest: 1) Under equal variances without knowledge of the true ordering, and 2) For general linear models given knowledge of the ordering. In both cases the sample complexity is $n\asymp q\log(d/q)$, where $q$ is the maximum number of parents and $d$ is the number of nodes. We further make comparisons with the classical problem of learning (undirected) Gaussian graphical models, showing that under the equal variance assumption, these two problems share the same optimal sample complexity. In other words, at least for Gaussian models with equal error variances, learning a directed graphical model is statistically no more difficult than learning an undirected graphical model. Our results also extend to more general identification assumptions as well as subgaussian errors.
Neural Manifold Clustering and Embedding

Given a union of non-linear manifolds, non-linear subspace clustering or manifold clustering aims to cluster data points based on manifold structures and also learn to parameterize each manifold as a linear subspace in a feature space. Deep neural networks have the potential to achieve this goal under highly non-linear settings given their large capacity and flexibility. We argue that achieving manifold clustering with neural networks requires two essential ingredients: a domain-specific constraint that ensures the identification of the manifolds, and a learning algorithm for embedding each manifold to a linear subspace in the feature space. This work shows that many constraints can be implemented by data augmentation. For subspace feature learning, Maximum Coding Rate Reduction (MCR$^2$) objective can be used. Putting them together yields {\em Neural Manifold Clustering and Embedding} (NMCE), a novel method for general purpose manifold clustering, which significantly outperforms autoencoder-based deep subspace clustering. Further, on more challenging natural image datasets, NMCE can also outperform other algorithms specifically designed for clustering. Qualitatively, we demonstrate that NMCE learns a meaningful and interpretable feature space. As the formulation of NMCE is closely related to several important Self-supervised learning (SSL) methods, we believe this work can help us build a deeper understanding on SSL representation learning.
RW Aur A: SpeX Spectral Evidence for Differentiated Planetesimal Formation, Migration, and Destruction in an ∼3 Myr Old Excited CTTS System

We present 2007–2020 SpeX VISNIR spectral monitoring of the highly variable RW Aur A CTTS. We find direct evidence for a highly excited, IR-bright, asymmetric, and time-variable system. Comparison of the spectral and temporal trends found determines five different components: (1) a stable continuum from 0.7 to 1.3 μm, with color temperature ∼4000 K, produced by the CTTS photospheric surface; (2) variable hydrogen emission lines emitted from hot excited hydrogen in the CTTS’s protostellar atmosphere/accretion envelope; (3) hot CO gas in the CTTS’s protostellar atmosphere/accretion envelope; (4) highly variable 1.8–5.0 μm thermal continuum emission with color temperature ranging from 1130 to 1650 K, due to a surrounding accretion disk that is spatially variable and has an inner wall at r ∼ 0.04 au and T ∼ 1650 K and outer edges at ∼1200 K; and (5) transient, bifurcated signatures of abundant Fe ii + associated S i, Si i, and Sr i in the system’s jet structures. The bifurcated signatures first appeared in 2015, but these collapsed and disappeared into a small single-peaked protostellar atmosphere feature by late 2020. The temporal evolution of RW Aur A’s spectral signatures is consistent with a dynamically excited CTTS system forming differentiated Vesta-sized planetesimals in an asymmetric accretion disk and migrating them inward to be destructively accreted. By contrast, nearby coeval binary companion RW Aur B evinces only a stable WTTS photospheric continuum from 0.7 to 1.3 μm + cold CO gas in absorption + stable 1.8–5.0 μm thermal disk continuum emission with color temperature ∼1650 K.
On module categories related to Sp(N-1) \subset Sl(N)

Let V = C with N odd. We construct a q-deformation of EndSp(N−1)(V ) which contains EndUqslN (V ). It is a quotient of an abstract two-variable algebra which is defined by adding one more generator to the generators of the Hecke algebras Hn. These results suggest the existence of module categories of Rep(UqslN ) which may not come from already known coideal subalgebras of UqslN . We moreover indicate how this can be used to construct module categories of the associated fusion tensor categories as well as subfactors, along the lines of previous work for inclusions Sp(N) ⊂ SL(N). IN MEMORIAM OF VAUGHAN JONES WITH GRATITUDE The problem of classifying module categories of a given tensor category arises in different contexts such as conformal field theory and the study of subfactors. A lot of progress has been made for module categories of fusion categories coming from quantum groups (or WessZumino-Witten models) in recent work by Edie-Michell (see [4]), building on work of Jones, Ocneanu, Gannon, Schopieray, Evans and Pugh and others. But in many cases, a detailed description of those module categories such as fusion rules, algebras etc is still not available. It is well-known that Rep(H) is a module category of Rep(G) for an inclusion of groups H ⊂ G. The basic idea here is to find a subgroup H of a Lie group G for which one can find analogs of the module Rep(H) in fusion categories related to G. This was successfully carried out in [24] and [25] for inclusions Sp(N) ⊂ SL(N), N even, and O(N) ⊂ SL(N) × Z2 for arbitrary N > 1. It allowed a detailed description of these module categories in terms of the well-known combinatorics of these groups (see Section 5). The current paper roughly contains the analogous results of the paper [24] for the inclusions Sp(N − 1) ⊂ SL(N) for N odd. Here is our approach in more detail, formulated for the group G = SL(N) for simplicity. We denote the quotient tensor category of tilting modules of the quantum group UqslN modulo negligible modules for q a root of unity by Rep(UqslN ). It is often also denoted by SU(N)k for q2 a primitive (N + k)th root of unity. We study the following questions: Find a subgroup H ⊂ SL(N) for which we can find (a) a q-deformation of Rep(H) which is a module category of Rep(UqslN ), (b) a quotient of said q-deformation for q a root of unity which is a module category of Rep(UqslN ), (c) a subfactor corresponding to the module category in (b) if it is unitarizable. Before describing the results in this paper in more detail, we would like to make a few general remarks about this approach. It is known that Question (a) can be solved if H is the group of
A nested error regression model with high-dimensional parameter for small area estimation

In this paper, we propose a flexible nested error regression small area model with high-dimensional parameter that incorporates heterogeneity in regression coefficients and variance components. We develop a new robust small area-specific estimating equations method that allows appropriate pooling of a large number of areas in estimating small area-specific model parameters. We propose a parametric bootstrap and jackknife method to estimate not only the mean squared errors but also other commonly used uncertainty measures such as standard errors and coefficients of variation. We conduct both model-based and design-based simulation experiments and real-life data analysis to evaluate the proposed methodology.
Heisenberg models and Schur--Weyl duality

We present a detailed analysis of certain quantum spin systems with inhomogeneous (non-random) mean-field interactions. Examples include, but are not limited to, the interchange- and spin singlet projection interactions on complete bipartite graphs. Using two instances of the representation theoretic framework of Schur--Weyl duality, we can explicitly compute the free energy and other thermodynamic limits in the models we consider. This allows us to describe the phase-transition, the ground-state phase diagram, and the expected structure of extremal states.
MOORe: Model-based Offline-to-Online Reinforcement Learning

With the success of offline reinforcement learning (RL), offline trained RL policies have the potential to be further improved when deployed online. A smooth transfer of the policy matters in safe real-world deployment. Besides, fast adaptation of the policy plays a vital role in practical online performance improvement. To tackle these challenges, we propose a simple yet efficient algorithm, Model-based Offline-to-Online Reinforcement learning (MOORe), which employs a prioritized sampling scheme that can dynamically adjust the offline and online data for smooth and efficient online adaptation of the policy. We provide a theoretical foundation for our algorithms design. Experiment results on the D4RL benchmark show that our algorithm smoothly transfers from offline to online stages while enabling sample-efficient online adaption, and also significantly outperforms existing methods.
Novel aspects of integrability for nonlinear sigma models in symmetric spaces

We obtained the formal solution of the auxiliary system of Non Linear Sigma Models, whose target space is a rank 1 symmetric space based on the indefinite orthogonal group O(p,q), corresponding to an arbitrary solution of the NLSM. This class includes Anti-de Sitter, de Sitter and Hyperbolic spaces, which are of interest in view of the AdS/CFT correspondence. The formal solution is related to the Pohlmeyer reduction of the NLSM, constituting another link between the NLSM and the reduced theory. Besides deriving the solution, we also review the Pohlmeyer reduction of such models. Finally, we comment on the implications for the monodromy matrix and its eigenvalues.
Probability estimation and structured output prediction for learning preferences in last mile delivery

We study the problem of learning the preferences of drivers and planners in the context of last mile delivery. Given a data set containing historical decisions and delivery locations, the goal is to capture the implicit preferences of the decision-makers. We consider two ways to use the historical data: one is through a probability estimation method that learns transition probabilities between stops (or zones). This is a fast and accurate method, recently studied in a VRP setting. Furthermore, we explore the use of machine learning to infer how to best balance multiple objectives such as distance, probability and penalties. Specifically, we cast the learning problem as a structured output prediction problem, where training is done by repeatedly calling the TSP solver. Another important aspect we consider is that for last-mile delivery, every address is a potential client and hence the data is very sparse. Hence, we propose a two-stage approach that first learns preferences at the zone level in order to compute a zone routing; after which a penalty-based TSP computes the stop routing. Results show that the zone transition probability estimation performs well, and that the structured output prediction learning can improve the results further. We hence showcase a successful combination of both probability estimation and machine learning, all the while using standard TSP solvers, both during learning and to compute the final solution; this means the methodology is applicable to other, real-life, TSP variants, or proprietary solvers.
Toward Parallel in Time for Chaotic Dynamical Systems

As CPU clock speeds have stagnated, and high performance computers continue to have ever higher core counts, increased parallelism is needed to take advantage of these new architectures. Traditional serial time-marching schemes are a significant bottleneck, as many types of simulations require large numbers of time-steps which must be computed sequentially. Parallel in Time schemes, such as the Multigrid Reduction in Time (MGRIT) method, remedy this by parallelizing across time-steps, and have shown promising results for parabolic problems. However, chaotic problems have proved more difficult, since chaotic initial value problems are inherently ill-conditioned. MGRIT relies on a hierarchy of successively coarser time-grids to iteratively correct the solution on the finest time-grid, but due to the nature of chaotic systems, subtle inaccuracies on the coarser levels can lead to poor coarse-grid corrections. Here we propose a modification to nonlinear FAS multigrid, as well as a novel time-coarsening scheme, which together better capture long term behavior on coarse grids and greatly improve convergence of MGRIT for chaotic initial value problems. We provide supporting numerical results for the Lorenz system model problem.
RFMask: A Simple Baseline for Human Silhouette Segmentation With Radio Signals

Human silhouette segmentation, which is originally defined in computer vision, has achieved promising results for understanding human activities. However, the physical limitation makes existing systems based on optical cameras suffer from severe performance degradation under low illumination, smoke, and/or opaque obstruction conditions. To overcome such limitations, in this paper, we propose to utilize the radio signals, which can traverse obstacles and are unaffected by the lighting conditions to achieve silhouette segmentation. The proposed RFMask framework is composed of three modules. It first transforms RF signals captured by millimeter wave radar on two planes into spatial domain and suppress interference with the signal processing module. Then, it locates human reflections on RF frames and extract features from surrounding signals with human detection module. Finally, the extracted features from RF frames are aggregated with an attention based mask generation module. To verify our proposed framework, we collect a dataset containing 804,760 radio frames and 402,380 camera frames with human activities under various scenes. Experimental results show that the proposed framework can achieve impressive human silhouette segmentation even under the challenging scenarios (such as low light and occlusion scenarios) where traditional optical-camera-based methods fail. To the best of our knowledge, this is the first investigation towards segmenting human silhouette based on millimeter wave signals. We hope that our work can serve as a baseline and inspire further research that perform vision tasks with radio signals. The dataset and codes will be made in public.
Data-Driven Mutation Analysis for Cyber-Physical Systems

Cyber-physical systems (CPSs) typically consist of a wide set of integrated, heterogeneous components; consequently, most of their critical failures relate to the interoperability of such components. Unfortunately, most CPS test automation techniques are preliminary and industry still heavily relies on manual testing. With potentially incomplete, manually-generated test suites, it is of paramount importance to assess their quality. Though mutation analysis has demonstrated to be an effective means to assess test suite quality in some specific contexts, we lack approaches for CPSs. Indeed, existing approaches do not target interoperability problems and cannot be executed in the presence of black-box or simulated components, a typical situation with CPSs. In this article, we introduce data-driven mutation analysis, an approach that consists in assessing test suite quality by verifying if it detects interoperability faults simulated by mutating the data exchanged by software components. To this end, we describe a data-driven mutation analysis technique (DaMAT) that automatically alters the data exchanged through data buffers. Our technique is driven by fault models in tabular form where engineers specify how to mutate data items by selecting and configuring a set of mutation operators. We have evaluated DaMAT with CPSs in the space domain; specifically, the test suites for the software systems of a microsatellite and nanosatellites launched on orbit last year. Our results show that the approach effectively detects test suite shortcomings, is not affected by equivalent and redundant mutants, and entails acceptable costs.
Toward a Minecraft Mod for Early Detection of Alzheimer's Disease in Young Adults

This paper proposes a Minecraft-based system for early detection of Alzheimer’s disease in young adults. Early detection, where spatial navigation is a crucial key, is regarded as an important way to prevent the disease. The proposed system is compared with a recent existing and thoroughly studied system using a game called Sea Hero Quest (SHQ), by analyzing spatial navigational patterns of players. Our preliminaries results show that spatial navigational patterns in both systems are highly correlated, indicating that the proposed system is likely as effective as the SHQ system for the detection task.
Quasi-stationary distributions in reducible state spaces

We study quasi-stationary distributions and quasi-limiting behavior of Markov chains in general reducible state spaces with absorption. We propose a set of assumptions dealing with particular situations where the state space can be decomposed into three subsets between which communication is only possible in a single direction. These assumptions allow us to characterize the exponential order of magnitude and the exact polynomial correction, called polynomial convergence parameter, for the leading order term of the semigroup for large time. They also provide explicit convergence speeds to this leading order term. We apply these results to general Markov chains with finitely or denumerably many communication classes using a specific induction over the communication classes of the chain. We are able to explicitely characterize the polynomial convergence parameter, to determine the complete set of quasistationary distributions and to provide explicit estimates for the speed of convergence to quasi-limiting distributions in the case of finitely many communication classes. We conclude with an application of these results to the case of denumerable state spaces, where we are able to prove that, in general, there is existence of a quasi-stationary distribution without assuming irreducibility before absorption. This actually holds true assuming only aperiodicity, the existence of a Lyapunov function and the existence of a point in the state space from which the return time is finite with positive probability. 1Université de Lorraine, CNRS, Inria, IECL, F-54000 Nancy, France E-mail: Nicolas.Champagnat@inria.fr, Denis.Villemonais@univ-lorraine.fr 1 ar X iv :2 20 1. 10 15 1v 1 [ m at h. PR ] 2 5 Ja n 20 22
ShapeFormer: Transformer-based Shape Completion via Sparse Representation

We present ShapeFormer, a transformer-based network that produces a distribution of object completions, conditioned on incomplete, and possibly noisy, point clouds. The resultant distribution can then be sampled to generate likely completions, each exhibiting plausible shape details while being faithful to the input. To facilitate the use of transformers for 3D, we introduce a compact 3D representation, vector quantized deep implicit function (VQDIF), that utilizes spatial sparsity to represent a close approximation of a 3D shape by a short sequence of discrete variables. Experiments demonstrate that ShapeFormer outperforms prior art for shape completion from ambiguous partial inputs in terms of both completion quality and diversity. We also show that our approach effectively handles a variety of shape types, incomplete patterns, and real-world scans.
Linear pair-creation damping of high-frequency plasma oscillation

We have studied the linear dispersion relation for Langmuir waves in plasmas of very high density, based on the Dirac–Heisenberg–Wigner formalism. The vacuum contribution to the physical observables leads to ultraviolet divergences, which are removed by a charge renormalization. The remaining vacuum contribution is small and is in agreement with previously derived expressions for the time-dependent vacuum polarization. The main new feature of the theory is a damping mechanism similar to Landau damping, but where the plasmon energy gives rise to creation of electron–positron pairs. The dependence of the damping rate (pair-creation rate) on the wavenumber, temperature, and density is analyzed. Finally, the analytical results of linearized theory are compared with numerical solutions.
Zero-Truncated Poisson Regression for Zero-Inflated Multiway Count Data

We propose a novel statistical inference paradigm for zero-inﬂated multiway count data that dispenses with the need to distinguish between true and false zero counts. Our approach ignores all zero entries and applies zero-truncated Poisson regression on the positive counts. Inference is accomplished via tensor completion that imposes low-rank structure on the Poisson parameter space. Our main result shows that an N -way rank- R parametric tensor M ∈ (0 , ∞ ) I ×···× I generating Poisson observations can be accurately estimated from approximately IR 2 log 22 ( I ) non-zero counts for a nonnegative canonical polyadic decomposition. Several numerical experiments are presented demonstrating that our zero-truncated paradigm is comparable to the ideal scenario where the locations of false zero counts are known a priori .
Has EU Accession Boosted Patent Performance in the EU-13? A Critical Evaluation Using Causal Impact Analysis with Bayesian Structural Time-Series Models

This paper provides new insights into the causal effects of the enlargement of the European Union (EU) on patent performance. The study focuses on the new EU member states (EU-13) and accession is considered as an intervention whose causal effect is estimated by the causal impact method using a Bayesian structural time-series model (proposed by Google). The empirical results based on data collected from the OECD database from 1985–2017 point towards a conclusion that joining the EU has had a significant impact on patent performance in Romania, Estonia, Poland, the Czech Republic, Croatia and Lithuania, although in the latter two countries, the impact was negative. For the rest of the EU-13 countries, there is no significant effect on patent performance. Whether the EU accession effect is significant or not, the EU-13 are far behind the EU-15 (countries which entered the EU before 2004) in terms of patent performance. The majority of patents (98.66%) are assigned to the EU-15, with just 1.34% of assignees belonging to the EU-13.
Characterisation for Exponential Stability of port-Hamiltonian Systems

Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for sufficient criteria in the literature by making regularity requirements for the Hamiltonian density largely obsolete. The key assumption for the characterisation (and thus the sufficient critera) to work is a uniform bound for a family of fundamental solutions for some non-autonomous, finite-dimensional ODEs. Regularity conditions on $\mathcal{H}$ for previously known criteria such as bounded variation are shown to imply the key assumption. Exponentially stable port-Hamiltonian systems with irregular $L_{\infty}$-densities are provided.