Miracle-dz/UniFAR-FTUs huggingface dataset:
Rigid connections on P1 via the Bruhat–Tits building

We apply the theory of fundamental strata of Bremer and Sage to find cohomologically rigid G ‐connections on the projective line, generalising the work of Frenkel and Gross. In this theory, one studies the leading term of a formal connection with respect to the Moy–Prasad filtration associated to a point in the Bruhat–Tits building. If the leading term is regular semisimple with centraliser a (not necessarily split) maximal torus S , then we have an S ‐toral connection. In this language, the irregular singularity of the Frenkel–Gross connection gives rise to the homogeneous toral connection of minimal slope associated to the Coxeter torus C . In the present paper, we consider connections on Gm which have an irregular homogeneous C ‐toral singularity at zero of slope i/h , where h is the Coxeter number and i is a positive integer coprime to h , and a regular singularity at infinity with unipotent monodromy. Our main result is the characterisation of all such connections which are rigid.
Joint Estimation of the Non-parametric Transitivity and Preferential Attachment Functions in Scientific Co-authorship Networks

We propose a statistical method to estimate simultaneously the non-parametric transitivity and preferential attachment functions in a growing network, in contrast to conventional methods that either estimate each function in isolation or assume some functional form for them. Our model is shown to be a good fit to two real-world co-authorship networks and be able to bring to light intriguing details of the preferential attachment and transitivity phenomena that would be unavailable under traditional methods. We also introduce a method to quantify the amount of contributions of those phenomena in the growth process of a network based on the probabilistic dynamic process induced by the model formula. Applying this method, we found that transitivity dominated PA in both co-authorship networks. This suggests the importance of indirect relations in scientific creative processes. The proposed methods are implemented in the R package FoFaF.
Limit theorems for out-of-sample extensions of the adjacency and Laplacian spectral embeddings

Graph embeddings, a class of dimensionality reduction techniques designed for relational data, have proven useful in exploring and modeling network structure. Most dimensionality reduction methods allow out-of-sample extensions, by which an embedding can be applied to observations not present in the training set. Applied to graphs, the out-of-sample extension problem concerns how to compute the embedding of a vertex that is added to the graph after an embedding has already been computed. In this paper, we consider the out-of-sample extension problem for two graph embedding procedures: the adjacency spectral embedding and the Laplacian spectral embedding. In both cases, we prove that when the underlying graph is generated according to a latent space model called the random dot product graph, which includes the popular stochastic block model as a special case, an out-of-sample extension based on a least-squares objective obeys a central limit theorem about the true latent position of the out-of-sample vertex. In addition, we prove a concentration inequality for the out-of-sample extension of the adjacency spectral embedding based on a maximum-likelihood objective. Our results also yield a convenient framework in which to analyze trade-offs between estimation accuracy and computational expense, which we explore briefly.
Additional Shared Decoder on Siamese Multi-View Encoders for Learning Acoustic Word Embeddings

Acoustic word embeddings — fixed-dimensional vector representations of arbitrary-length words — have attracted increasing interest in query-by-example spoken term detection. Recently, on the fact that the orthography of text labels partly reflects the phonetic similarity between the words' pronunciation, a multi-view approach has been introduced that jointly learns acoustic and text embeddings. It showed that it is possible to learn discriminative embeddings by designing the objective which takes text labels as well as word segments. In this paper, we propose a network architecture that expands the multi-view approach by combining the Siamese multiview encoders with a shared decoder network to maximize the effect of the relationship between acoustic and text embeddings in embedding space. Discriminatively trained with multi-view triplet loss and decoding loss, our proposed approach achieves better performance on acoustic word discrimination task with the WSJ dataset, resulting in 11.1% relative improvement in average precision. We also present experimental results on cross-view word discrimination and word level speech recognition tasks.
CFAR Feature Plane: A Novel Framework for the Analysis and Design of Radar Detectors

Since Kelly's pioneering work on GLRT-based adaptive detection, many solutions have been proposed to enhance either selectivity or robustness of radar detectors to mismatched signals. In this paper such a problem is addressed in a different space, called CFAR feature plane and given by a suitable maximal invariant, where observed data are mapped to clusters that can be analytically described. The characterization of the trajectories and shapes of such clusters is provided and exploited for both analysis and design purposes, also shedding new light on the behavior of several well-known detectors. Novel linear and non-linear detectors are proposed with diversified robust or selective behaviors, showing that through the proposed framework it is not only possible to achieve the same performance of well-known receivers obtained by a radically different design approach (namely GLRT), but also to devise detectors with unprecedented behaviors: in particular, our results show that the highest standard of selectivity can be achieved without sacrifying neither detection power under matched conditions nor CFAR property.
Robust Data-Driven Zero-Velocity Detection for Foot-Mounted Inertial Navigation

We present two novel techniques for detecting zero-velocity events to improve foot-mounted inertial navigation. Our first technique augments a classical zero-velocity detector by incorporating a motion classifier that adaptively updates the detector’s threshold parameter. Our second technique uses a long short-term memory (LSTM) recurrent neural network to classify zero-velocity events from raw inertial data, in contrast to the majority of zero-velocity detection methods that rely on basic statistical hypothesis testing. We demonstrate that both of our proposed detectors achieve higher accuracies than existing detectors for trajectories including walking, running, and stair-climbing motions. Additionally, we present a straightforward data augmentation method that is able to extend the LSTM-based model to different inertial sensors without the need to collect new training data.
Leaky Forcing: A New Variation of Zero Forcing

Zero forcing is a one-player game played on a graph. The player chooses some set of vertices to color, then iteratively applies a color change rule: If all but one of a colored vertex's neighbors are colored, color (i.e. "force") the remaining uncolored neighbor. Generally, the goal is to find the minimum number of vertices to initially color such that all vertices eventually become colored. Recently, equivalent formations of zero forcing have been developed in different settings including sensor allocation to solve linear systems (K.-Lin 2018), controllability in follower-leader dynamics (Monshizadeh-Zhang-Camlibel 2014), and edge covering in specific hypergraphs (Brimkov-Fast-Hicks 2016). While many variations of zero forcing are motivated by an associated minimum rank problem, these new formulations give new inspiration for new meaningful zero forcing variants. In our case, we study a new variation based on the linear algebraic interpretation mentioned above. In particular, what if there is a juncture in a network that has a leak, and, hence, is unreliable to facilitate solving a linear system on the network? In the context of zero forcing this corresponds to the following variation we call $\ell$-forcing: Given $\ell$, find a set of vertices such that for any set of $\ell$ vertices that are unable to force, all vertices will still be colored. We compute the $\ell$-forcing number for selected families of graphs including grid graphs. Perhaps surprisingly, we find examples where additional edges make the graph more "resilient" to these leaks. Further, we also implement known computational methods for our new leaky forcing variation.
Lorentz and CPT Tests Using Penning Traps

The theoretical prospects for quantum electrodynamics with Lorentz-violating operators of mass dimensions up to six are revisited in this work. The dominant effects due to Lorentz and CPT violation are studied in measurements of magnetic moments of particles confined in Penning traps. Using recently reported experimental results, new coefficients for Lorentz violation are constrained and existing bounds of various coefficients are improved.
Estimating Smooth GLM in Non-interactive Local Differential Privacy Model with Public Unlabeled Data

In this paper, we study the problem of estimating smooth Generalized Linear Models (GLM) in the Non-interactive Local Differential Privacy (NLDP) model. Different from its classical setting, our model allows the server to access some additional public but unlabeled data. By using Stein's lemma and its variants, we first show that there is an $(\epsilon, \delta)$-NLDP algorithm for GLM (under some mild assumptions), if each data record is i.i. d sampled from some sub-Gaussian distribution with bounded $\ell_1$-norm. Then with high probability, the sample complexity of the public and private data, for the algorithm to achieve an $\alpha$ estimation error (in $\ell_\infty$-norm), is $O(p^2\alpha^{-2})$ and ${O}(p^2\alpha^{-2}\epsilon^{-2})$, respectively, if $\alpha$ is not too small ({\em i.e.,} $\alpha\geq \Omega(\frac{1}{\sqrt{p}})$), where $p$ is the dimensionality of the data. This is a significant improvement over the previously known quasi-polynomial (in $\alpha$) or exponential (in $p$) complexity of GLM with no public data. Also, our algorithm can answer multiple (at most $\exp(O(p))$) GLM queries with the same sample complexities as in the one GLM query case with at least constant probability. We then extend our idea to the non-linear regression problem and show a similar phenomenon for it. Finally, we demonstrate the effectiveness of our algorithms through experiments on both synthetic and real world datasets. To our best knowledge, this is the first paper showing the existence of efficient and effective algorithms for GLM and non-linear regression in the NLDP model with public unlabeled data.
Multi-season optical modulation phased with the orbit of the super-Earth 55 Cancri e

Context. 55 Cnc e is a transiting super-Earth orbiting a solar-like star with an orbital period of ~17.7 h. In 2011, using the Microvariability and Oscillations in Stars (MOST) space telescope, a quasi-sinusoidal modulation in flux was detected with the same period as the planetary orbit. The amplitude of this modulation was too large to be explained as the change in light reflected or emitted by the planet. Aims. The MOST telescope continued to observe 55 Cnc e for a few weeks per year over five years (from 2011 to 2015), covering 143 individual transits. This paper presents the analysis of the observed phase modulation throughout these observations and a search for the secondary eclipse of the planet. Methods. The most important source of systematic noise in MOST data is due to stray-light reflected from the Earth, which is modulated with both the orbital period of the satellite (101.4 min) and the Earth’s rotation period. We present a new technique to deal with this source of noise, which we combined with standard detrending procedures for MOST data. We then performed Markov chain Monte Carlo analyses of the detrended light curves, modeling the planetary transit and phase modulation. Results. We find phase modulations similar to those seen in 2011 in most of the subsequent years; however, the amplitude and phase of maximum light are seen to vary, from year to year, from 113 to 28 ppm and from 0.1 to 3.8 rad. The secondary eclipse is not detected, but we constrain the geometric albedo of the planet to less than 0.47 (2σ). Conclusions. While we cannot identify a single origin of the observed optical modulation, we propose a few possible scenarios. Those include star-planet interaction, such as coronal rains and spots rotating with the motion of the planet along its orbit, or the presence of a transiting circumstellar torus of dust. However, a detailed interpretation of these observations is limited by their photometric precision. Additional observations at optical wavelengths could measure the variations at higher precision, contribute to uncovering the underlying physical processes, and measure or improve the upper limit on the albedo of the planet.
GraphRQI: Classifying Driver Behaviors Using Graph Spectrums

We present a novel algorithm (GraphRQI) to identify driver behaviors from road-agent trajectories. Our approach assumes that the road-agents exhibit a range of driving traits, such as aggressive or conservative driving. Moreover, these traits affect the trajectories of nearby road-agents as well as the interactions between road-agents. We represent these inter-agent interactions using unweighted and undirected traffic graphs. Our algorithm classifies the driver behavior using a supervised learning algorithm by reducing the computation to the spectral analysis of the traffic graph. Moreover, we present a novel eigenvalue algorithm to compute the spectrum efficiently. We provide theoretical guarantees for the running time complexity of our eigenvalue algorithm and show that it is faster than previous methods by 2 times. We evaluate the classification accuracy of our approach on traffic videos and autonomous driving datasets corresponding to urban traffic. In practice, GraphRQI achieves an accuracy improvement of up to 25% over prior driver behavior classification algorithms. We also use our classification algorithm to predict the future trajectories of road-agents.
Effective spin distribution of black hole mergers in triples

Many astrophysical scenarios have been proposed to explain the several black hole (BH) and neutron star binary mergers observed via gravitational waves (GWs) by the LIGO–Virgo collaboration. Contributions from various channels can be statistically disentangled by mass, spin, eccentricity, and redshift distributions of merging binaries. In this paper, we investigate the signatures of BH–BH binary mergers induced by a third companion through the Lidov–Kozai mechanism in triple systems. We adopt different prescriptions for the supernovae natal kicks and consider different progenitor metallicities and initial orbital parameters. We show that the typical eccentricity in the LIGO band is 0.01–0.1 and that the merger rate is in the range 0.008−9 Gpc−3 yr−1, depending on the natal kick prescriptions and progenitor metallicity. Furthermore, we find that the typical distribution of effective projected spin is peaked at χeff ∼ 0 with significant tails. We show that the triple scenario could reproduce the distribution of χeff. We find that the triple channel may be strongly constrained by the misalignment angle between the binary component spins in future detections with spin precession.
Direct Comparison of Many-Body Methods for Realistic Electronic Hamiltonians

A large collaboration carefully benchmarks 20 first principles many-body electronic structure methods on a test set of 7 transition metal atoms, and their ions and monoxides. Good agreement is attained between the 3 systematically converged methods, resulting in experiment-free reference values. These reference values are used to assess the accuracy of modern emerging and scalable approaches to the many-electron problem. The most accurate methods obtain energies indistinguishable from experimental results, with the agreement mainly limited by the experimental uncertainties. Comparison between methods enables a unique perspective on calculations of many-body systems of electrons.
Multiple Antenna Technologies for Beyond 5G

Multiple antenna technologies have attracted large research interest for several decades and have gradually made their way into mainstream communication systems. Two main benefits are adaptive beamforming gains and spatial multiplexing, leading to high data rates per user and per cell, especially when large antenna arrays are used. Now that multiple antenna technology has become a key component of the fifth-generation (5G) networks, it is time for the research community to look for new multiple antenna applications to meet the immensely higher data rate, reliability, and traffic demands in the beyond 5G era. We need radically new approaches to achieve orders-of-magnitude improvements in these metrics and this will be connected to large technical challenges, many of which are yet to be identified. In this survey paper, we present a survey of three new multiple antenna related research directions that might play a key role in beyond 5G networks: Cell-free massive multiple-input multiple-output (MIMO), beamspace massive MIMO, and intelligent reflecting surfaces. More specifically, the fundamental motivation and key characteristics of these new technologies are introduced. Recent technical progress is also presented. Finally, we provide a list of other prospective future research directions.
Truth or Backpropaganda? An Empirical Investigation of Deep Learning Theory

We empirically evaluate common assumptions about neural networks that are widely held by practitioners and theorists alike. In this work, we: (1) prove the widespread existence of suboptimal local minima in the loss landscape of neural networks, and we use our theory to find examples; (2) show that small-norm parameters are not optimal for generalization; (3) demonstrate that ResNets do not conform to wide-network theories, such as the neural tangent kernel, and that the interaction between skip connections and batch normalization plays a role; (4) find that rank does not correlate with generalization or robustness in a practical setting.
MTab: Matching Tabular Data to Knowledge Graph using Probability Models

This paper presents the design of our system, namely MTab, for Semantic Web Challenge on Tabular Data to Knowledge Graph Matching (SemTab 2019). MTab combines the voting algorithm and the probability models to solve critical problems of the matching tasks. Results on SemTab 2019 show that MTab obtains promising performance for the three matching tasks.
Accuracy Prevents Robustness in Perception-based Control

In this paper we prove the existence of a fundamental trade-off between accuracy and robustness in perception-based control, where control decisions rely solely on data-driven, and often incompletely trained, perception maps. In particular, we consider a control problem where the state of the system is estimated from measurements extracted from a high-dimensional sensor, such as a camera. We assume that a map between the camera’s readings and the state of the system has been learned from a set of training data of finite size, from which the noise statistics are also estimated. We show that algorithms that maximize the estimation accuracy (as measured by the mean squared error) using the learned perception map tend to perform poorly in practice, where the sensor’s statistics often differ from the learned ones. Conversely, increasing the variability and size of the training data leads to robust performance, however limiting the estimation accuracy, and thus the control performance, in nominal conditions. Ultimately, our work proves the existence and the implications of a fundamental trade-off between accuracy and robustness in perception-based control, which, more generally, affects a large class of machine learning and data-driven algorithms [1]–[4].
Rapid Escape of Ultra-hot Exoplanet Atmospheres Driven by Hydrogen Balmer Absorption

Atmospheric escape is key to explaining the long-term evolution of planets in our solar system and beyond, and in the interpretation of atmospheric measurements. Hydrodynamic escape is generally thought to be driven by the flux of extreme-ultraviolet photons that the planet receives from its host star. Here, we show that the escape from planets orbiting hot stars proceeds through a different yet complementary process: drawing its energy from the intense near-ultraviolet emission of the star that is deposited within an optically thin, high-altitude atmospheric layer of hydrogen excited into the lower state of the Balmer series. The ultra-hot exoplanet KELT-9b likely represents the first known instance of this Balmer-driven escape. In this regime of hydrodynamic escape, the near-ultraviolet emission from the star is more important at determining the planet mass loss than the extreme-ultraviolet emission, and uncertainties in the latter become less critical. Further, we predict that gas exoplanets around hot stars may experience catastrophic mass loss when they are less massive than 1–2 Jupiter masses and closer in than KELT-9b, thereby challenging the paradigm that all large exoplanets are stable to atmospheric escape. We argue that extreme escape will affect the demographics of close-in exoplanets orbiting hot stars.
Grassmann angles between real or complex subspaces

The Grassmann angle unifies and extends various concepts of angle between subspaces, being defined for equal or different dimensions, in real or complex inner product spaces. It is an angle in Grassmann algebra, gives the Fubini-Study distance in Grassmannians, and its cosine (squared, in the complex case) describes volume contraction in orthogonal projections. The angle is asymmetric when dimensions are different, giving a quasi-pseudometric on the total Grassmannian, and measuring Hausdorff distances between certain sets of simple multivectors. Odd features, present in similar angles but overlooked, are explained, like the angle with an orthogonal complement, and how the angle between complex subspaces is not the same as for the underlying real spaces. We use them to get an obstruction on complex structures for pairs of real subspaces.
The Next Generation Virgo Cluster Survey. XVII. A Search for Planetary Nebulae in Virgo Cluster Globular Clusters

The occurrence of planetary nebulae (PNe) in globular clusters (GCs) provides an excellent chance to study low-mass stellar evolution in a special (low-metallicity, high stellar density) environment. We report a systematic spectroscopic survey for the [O iii] 5007 Å emission line of PNe in 1469 Virgo GCs and 121 Virgo ultra-compact dwarfs (UCDs), mainly hosted in the giant elliptical galaxies M87, M49, M86, and M84. We detected zero PNe in our UCD sample and discovered one PN ( ) associated with an M87 GC. We used the [O iii] detection limit for each GC to estimate the luminosity-specific frequency of PNe, α, and measured α in the Virgo cluster GCs to be . The value of α in the Virgo GCs is among the lowest reported in any environment, due in part to the large sample size, and it is 5–6 times lower than that for the Galactic GCs. We suggest that α decreases toward brighter and more massive clusters, sharing a similar trend as the binary fraction, and the discrepancy between the Virgo and Galactic GCs can be explained by the observational bias in extragalactic surveys toward brighter GCs. This low but nonzero efficiency in forming PNe may highlight the important role played by binary interactions in forming PNe in GCs. We argue that a future survey of less massive Virgo GCs will be able to determine whether PN production in the Virgo GCs is governed by an internal process (mass, density, binary fraction) or if it is largely regulated by the external environment.