Miracle-dz/UniFAR-FTUs huggingface dataset:
Estimation in Tensor Ising Models

The $p$-tensor Ising model is a one-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic is a multi-linear form of degree $p \geq 2$. This is a natural generalization of the matrix Ising model, that provides a convenient mathematical framework for capturing higher-order dependencies in complex relational data. In this paper, we consider the problem of estimating the natural parameter of the $p$-tensor Ising model given a single sample from the distribution on $N$ nodes. Our estimate is based on the maximum pseudo-likelihood (MPL) method, which provides a computationally efficient algorithm for estimating the parameter that avoids computing the intractable partition function. We derive general conditions under which the MPL estimate is $\sqrt N$-consistent, that is, it converges to the true parameter at rate $1/\sqrt N$. In particular, we show the $\sqrt N$-consistency of the MPL estimate in the $p$-spin Sherrington-Kirkpatrick (SK) model, spin systems on general $p$-uniform hypergraphs, and Ising models on the hypergraph stochastic block model (HSBM). In fact, for the HSBM we pin down the exact location of the phase transition threshold, which is determined by the positivity of a certain mean-field variational problem, such that above this threshold the MPL estimate is $\sqrt N$-consistent, while below the threshold no estimator is consistent. Finally, we derive the precise fluctuations of the MPL estimate in the special case of the $p$-tensor Curie-Weiss model. An interesting consequence of our results is that the MPL estimate in the Curie-Weiss model saturates the Cramer-Rao lower bound at all points above the estimation threshold, that is, the MPL estimate incurs no loss in asymptotic efficiency, even though it is obtained by minimizing only an approximation of the true likelihood function for computational tractability.
The SAGA Survey. II. Building a Statistical Sample of Satellite Systems around Milky Way–like Galaxies

We present the Stage II results from the ongoing Satellites Around Galactic Analogs (SAGA) Survey. Upon completion, the SAGA Survey will spectroscopically identify satellite galaxies brighter than M r,o = −12.3 around 100 Milky Way (MW) analogs at z ∼ 0.01. In Stage II, we have more than quadrupled the sample size of Stage I, delivering results from 127 satellites around 36 MW analogs with an improved target selection strategy and deep photometric imaging catalogs from the Dark Energy Survey and the Legacy Surveys. We have obtained 25,372 galaxy redshifts, peaking around z = 0.2. These data significantly increase spectroscopic coverage for very low redshift objects in 17 < r o < 20.75 around SAGA hosts, creating a unique data set that places the Local Group in a wider context. The number of confirmed satellites per system ranges from zero to nine and correlates with host galaxy and brightest satellite luminosities. We find that the number and luminosities of MW satellites are consistent with being drawn from the same underlying distribution as SAGA systems. The majority of confirmed SAGA satellites are star-forming, and the quenched fraction increases as satellite stellar mass and projected radius from the host galaxy decrease. Overall, the satellite quenched fraction among SAGA systems is lower than that in the Local Group. We compare the luminosity functions and radial distributions of SAGA satellites with theoretical predictions based on cold dark matter simulations and an empirical galaxy–halo connection model and find that the results are broadly in agreement.
HittER: Hierarchical Transformers for Knowledge Graph Embeddings

This paper examines the challenging problem of learning representations of entities and relations in a complex multi-relational knowledge graph. We propose HittER, a Hierarchical Transformer model to jointly learn Entity-relation composition and Relational contextualization based on a source entity’s neighborhood. Our proposed model consists of two different Transformer blocks: the bottom block extracts features of each entity-relation pair in the local neighborhood of the source entity and the top block aggregates the relational information from outputs of the bottom block. We further design a masked entity prediction task to balance information from the relational context and the source entity itself. Experimental results show that HittER achieves new state-of-the-art results on multiple link prediction datasets. We additionally propose a simple approach to integrate HittER into BERT and demonstrate its effectiveness on two Freebase factoid question answering datasets.
Estimation of separable direct and indirect effects in continuous time

Many research questions involve time‐to‐event outcomes that can be prevented from occurring due to competing events. In these settings, we must be careful about the causal interpretation of classical statistical estimands. In particular, estimands on the hazard scale, such as ratios of cause‐specific or subdistribution hazards, are fundamentally hard to interpret causally. Estimands on the risk scale, such as contrasts of cumulative incidence functions, do have a clear causal interpretation, but they only capture the total effect of the treatment on the event of interest; that is, effects both through and outside of the competing event. To disentangle causal treatment effects on the event of interest and competing events, the separable direct and indirect effects were recently introduced. Here we provide new results on the estimation of direct and indirect separable effects in continuous time. In particular, we derive the nonparametric influence function in continuous time and use it to construct an estimator that has certain robustness properties. We also propose a simple estimator based on semiparametric models for the two cause‐specific hazard functions. We describe the asymptotic properties of these estimators and present results from simulation studies, suggesting that the estimators behave satisfactorily in finite samples. Finally, we reanalyze the prostate cancer trial from Stensrud et al. (2020).
TATL at WNUT-2020 Task 2: A Transformer-based Baseline System for Identification of Informative COVID-19 English Tweets

As the COVID-19 outbreak continues to spread throughout the world, more and more information about the pandemic has been shared publicly on social media. For example, there are a huge number of COVID-19 English Tweets daily on Twitter. However, the majority of those Tweets are uninformative, and hence it is important to be able to automatically select only the informative ones for downstream applications. In this short paper, we present our participation in the W-NUT 2020 Shared Task 2: Identification of Informative COVID-19 English Tweets. Inspired by the recent advances in pretrained Transformer language models, we propose a simple yet effective baseline for the task. Despite its simplicity, our proposed approach shows very competitive results in the leaderboard as we ranked 8 over 56 teams participated in total.
Unpaired Deep Learning for Accelerated MRI Using Optimal Transport Driven CycleGAN

Recently, deep learning approaches for accelerated MRI have been extensively studied thanks to their high performance reconstruction in spite of significantly reduced run-time complexity. These neural networks are usually trained in a supervised manner, so matched pairs of subsampled, and fully sampled <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-space data are required. Unfortunately, it is often difficult to acquire matched fully sampled <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-space data, since the acquisition of fully sampled <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-space data requires long scan time, and often leads to the change of the acquisition protocol. Therefore, unpaired deep learning without matched label data has become a very important research topic. In this article, we propose an unpaired deep learning approach using a optimal transport driven cycle-consistent generative adversarial network (OT-cycleGAN) that employs a single pair of generator, and discriminator. The proposed OT-cycleGAN architecture is rigorously derived from a dual formulation of the optimal transport formulation using a specially designed penalized least squares cost. The experimental results show that our method can reconstruct high resolution MR images from accelerated <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-space data from both single, and multiple coil acquisition, without requiring matched reference data.
Broadcasted Nonparametric Tensor Regression

We propose a novel broadcasting idea to model the nonlinearity in tensor regression non-parametrically. Unlike existing non-parametric tensor regression models, the resulting model strikes a good balance between flexibility and interpretability. A penalized estimation and corresponding algorithm are proposed. Our theoretical investigation, which allows the dimensions of the tensor covariate to diverge, indicates that the proposed estimation enjoys desirable convergence rate. Numerical experiments are conducted to confirm the theoretical finding and show that the proposed model has advantage over existing linear counterparts.
Determination of the light exposure on the photodiodes of a new instrumented baffle for the Virgo input mode cleaner end-mirror

As part of the upgrade program of the advanced Virgo interferometer, the installation of new instrumented baffles surrounding the main test masses is foreseen. As a demonstrator, and to validate the technology, the existing baffle in the area of the input mode cleaner end-mirror will be first replaced by a baffle equipped with photodiodes. This paper presents detailed simulations of the light distribution on the input mode cleaner baffle. They served to validate the proposed layout of the sensors in the baffle, and determine the light exposure of the photodiodes under different scenarios of the interferometer operations, in order to define mitigation strategies for preserving the detector integrity.
Photon Spheres, ISCOs, and OSCOs: Astrophysical Observables for Regular Black Holes with Asymptotically Minkowski Cores

Classical black holes contain a singularity at their core. This has prompted various researchers to propose a multitude of modified spacetimes that mimic the physically observable characteristics of classical black holes as best as possible, but that crucially do not contain singularities at their cores. Due to recent advances in near-horizon astronomy, the ability to observationally distinguish between a classical black hole and a potential black hole mimicker is becoming increasingly feasible. Herein, we calculate some physically observable quantities for a recently proposed regular black hole with an asymptotically Minkowski core—the radius of the photon sphere and the extremal stable timelike circular orbit (ESCO). The manner in which the photon sphere and ESCO relate to the presence (or absence) of horizons is much more complex than for the Schwarzschild black hole. We find situations in which photon spheres can approach arbitrarily close to (near extremal) horizons, situations in which some photon spheres become stable, and situations in which the locations of both photon spheres and ESCOs become multi-valued, with both ISCOs (innermost stable circular orbits) and OSCOs (outermost stable circular orbits). This provides an extremely rich phenomenology of potential astrophysical interest.
Cyclotron line energy in Hercules X-1: stable after the decay

We summarize the results of a dedicated effort made between 2012 and 2019 to follow the evolution of the cyclotron line in Her X-1 through repeated NuSTAR observations. The previously observed nearly 20-year-long decay of the cyclotron line energy has ended in 2012: from then on, the pulse-phase-averaged flux-corrected cyclotron line energy has remained stable and constant at an average value of Ecyc = (37.44 ± 0.07) keV (normalized to a flux level of 6.8 RXTE/ASM-cts s−1). The flux dependence of Ecyc discovered in 2007 is now measured with high precision, giving a slope of (0.675 ± 0.075) keV/(ASM-cts s−1), corresponding to an increase of 6.5% of Ecyc for an increase in flux by a factor of two. We also find that all line parameters as well as the continuum parameters show a correlation with X-ray flux. While a correlation between Ecyc and X-ray flux (both positive and negative) is now known for several accreting binaries with various suggestions for the underlying physics, the phenomenon of a long-term decay has so far only been seen in Her X-1 and Vela X-1, with far less convincing explanations.
Residual torsion-free nilpotence, biorderability and pretzel knots

The residual torsion-free nilpotence of the commutator subgroup of a knot group has played a key role in studying the bi-orderability of knot groups. A technique developed by Mayland provides a sufficient condition for the commutator subgroup of a knot group to be residually-torsion-free nilpotent using work of Baumslag. In this paper, we apply Mayland's technique to several genus one pretzel knots and a family of pretzel knots with arbitrarily high genus. As a result, we obtain a large number of new examples of knots with bi-orderable knot groups. These are the first examples of bi-orderable knot groups for knots which are not fibered or alternating.
Habitat Preferences and the Distribution of Uta stansburiana and Sceloporus occidentalis in Coastal California

Uta stansburiana does not range west to the immediate coast north of Santa Barbara, California, whereas Sceloporus occidentalis occurs at maritime localities from Washington south. At the Hastings Reservation, Monterey County, California, 24 km NE of the Pacific Ocean, both species are found. U. stansburiana is almost entirely restricted to rocky situations there and S. occidentalis occurs mainly on standing or fallen trees where rocks are absent. Where both rocks and trees are present, Sceloporus occurs mainly on rocks when air temperatures are low and on trees when air temperatures are high. Comparison of Monterey, a central coastal locality where U. stansburiana is absent, and Santa Barbara, the northernmost coastal locality at which it occurs, indicates that sky cover is less at Santa Barbara in July and August and temperatures are higher there from May through October. Since U. stansburiana breeds following the first hibernation period, and is short-lived, it is possible that the less favorable climatic regime at Monterey delays maturity sufficiently to postpone breeding to a point at which it is not feasible. S. occidentalis, first breeding after the second hibernation period, and relatively long-lived, has more time in which to mature and can therefore tolerate the marine environment north of Santa Barbara. In support of this hypothesis, all the lizards for which breeding time is known and which reach the coast north of Santa Barbara are of the late-maturing type.
Modeling disk fragmentation and multiplicity in massive star formation

Context. There is growing evidence that massive stars grow by disk accretion in a similar way to their low-mass counterparts. Early in evolution, these disks can achieve masses that are comparable to the current stellar mass, and therefore the forming disks are highly susceptible to gravitational fragmentation. Aims. We investigate the formation and early evolution of an accretion disk around a forming massive protostar, focussing on its fragmentation physics. To this end, we follow the collapse of a molecular cloud of gas and dust, the formation of a massive protostar, the formation of its circumstellar disk, and the formation and evolution of the disk fragments. Methods. We used a grid-based, self-gravity radiation hydrodynamics code including a sub-grid module for stellar evolution and dust evolution. We purposely do not use a sub-grid module for fragmentation such as sink particles to allow for all paths of fragment formation and destruction, but instead we keep the spatial grid resolution high enough to properly resolve the physical length scales of the problem, namely the pressure scale height and Jeans length of the disk. Simulations are performed on a grid in spherical coordinates with a logarithmic spacing of the grid cells in the radial direction and a cosine distribution of the grid cells in the polar direction, focusing the spatial resolution on the disk midplane. As a consequence, roughly 25% of the total number of grid cells, corresponding to ~26 million grid cells, are used to model the disk physics. These constitute the highest resolution simulations performed up to now on disk fragmentation around a forming massive star with the physics considered here. For a better understanding of the effects of spatial resolution and to compare our high-resolution results with previous lower resolution studies in the literature, we perform the same simulation at five different resolutions, each run differing in resolution from its predecessor by a factor of two. Results. The cloud collapses and a massive (proto)star is formed in its center surrounded by a fragmenting Keplerian-like accretion disk with spiral arms. The fragments have masses of ~1 M⊙, and their continuous interactions with the disk, spiral arms, and other fragments result in eccentric orbits. Fragments form hydrostatic cores surrounded by secondary disks with spiral arms that also produce new fragments. We identified several mechanisms of fragment formation, interaction, and destruction. Central temperatures of the fragments can reach the hydrogen dissociation limit, form second Larson cores, and evolve into companion stars. Based on this, we study the multiplicity predicted by the simulations and find approximately six companions at different distances from the primary: from possible spectroscopic multiples, to companions at distances between 1000 and 2000 au.
Kähler spaces with zero first Chern class: Bochner principle, Albanese map and fundamental groups

Abstract Let X be a compact Kähler space with klt singularities and vanishing first Chern class. We prove the Bochner principle for holomorphic tensors on the smooth locus of X: any such tensor is parallel with respect to the singular Ricci-flat metrics. As a consequence, after a finite quasi-étale cover X splits off a complex torus of the maximum possible dimension. We then proceed to decompose the tangent sheaf of X according to its holonomy representation. In particular, we classify those X which have strongly stable tangent sheaf: up to quasi-étale covers, these are either irreducible Calabi–Yau or irreducible holomorphic symplectic. As an application of these results, we show that if X has dimension four, then it satisfies Campana’s Abelianity Conjecture.
UvA-DARE (Digital Academic Repository) Large deviations for acyclic networks of queues with correlated Gaussian inputs

We consider an acyclic network of single-server queues with heterogeneous processing rates. It is assumed that each queue is fed by the superposition of a large number of i.i. d. Gaussian processes with stationary increments and positive drifts, which can be correlated across different queues. The ﬂow of work departing from each server is split deterministically and routed to its neighbors according to a ﬁxed routing matrix, with a fraction of it leaving the network altogether. We study the exponential decay rate of the probability that the steady-state queue length at any given node in the network is above any ﬁxed threshold, also referred to as the ‘overﬂow probability’. In particular, we ﬁrst leverage Schilder’s sample-path large deviations theorem to obtain a general lower bound for the limit of this exponential decay rate, as the number of Gaussian processes goes to inﬁnity. Then, we show that this lower bound is tight under additional technical conditions. Finally, we show that if the input processes to the different queues are nonnegatively correlated, non-short-range dependent fractional Brownian motions, and if the processing rates are large enough, then the asymptotic exponential decay rates of the queues coincide with the ones of isolated queues with appropriate Gaussian inputs.
AgNOR STAIN IN NORMAL, CIRRHOTIC AND CARCINOMATOUS LIVER

In this era of tumour marker AgNOR stain has still retained the diagnostic yield in tumour pathology. This study was conducted to evaluate the role of AgNOR number and morphological features in cirrhotic and carcinomatous liver. A total of one hundred liver biopsy specimens were included, twenty cases were of hepatocellular carcinoma, sixty were those of cirrhosis of the liver and twenty cases with normal histology as control. The mean AgNOR count, size and distribution were significantly of higher grade in hepatocellular carcinoma as compared to cirrhosis of liver. NORs (nucleolar organizer regions) are the structures present in the short arms of acrocentric chromosomes in human and were first detected on giemsa banding as” achromatic gaps” with much reduced staining. The areas are of course not geunine gaps but are, areas of specialized chromosome configuration number 13, 14, 15, 21&22 . It was shown that the achromatic gap areas on the achrocentric chromosomes were argyrophil and the silver method became a standard technique 1. NOR represent loops of DNA that possess the genes of ribosomal RNA and are associated with specific proteins including RNA polymerase 1 B 23 protien, and C23 protien 2-3. These proteins can be easily demonstrated by means of argyrophilic techniques for NORs 4 . Application of AgNOR staining to conventionally fixed and processed, paraffin sections has made this technique a useful tool in diagnosis of human malignancies 5 . Derezini et al in their study showed that higher number of interface AgNOR are associated with increased risk of hepatocellular carcinoma in patients with chronic liver disease 6.
The density of states and local eigenvalue statistics for random band matrices of fixed width

We prove that the local eigenvalue statistics for $d=1$ random band matrices with fixed bandwidth and, for example, Gaussian entries, is given by a Poisson point process and we identify the intensity of the process. The proof relies on an extension of the localization bounds of Schenker \cite{schenker} and the Wegner and Minami estimates. These two estimates are proved using averaging over the diagonal disorder. The new component is a proof of the uniform convergence and the smoothness of the density of states function. The limit function, known to be the semicircle law with a band-width dependent error \cite{bmp,dps,dl,mpk}, is identified as the intensity of the limiting Poisson point process. The proof of these results for the density of states relies on a new result that simplifies and extends some of the ideas used by Dolai, Krishna, and Mallick \cite{dkm}. These authors proved regularity properties of the density of states for random Schrodinger operators (lattice and continuum) in the localization regime. The proof presented here applies to the random Schrodinger operators on a class of infinite graphs treated by in \cite{dkm} and extends the results of \cite{dkm} to probability measures with unbounded support. The method also applies to fixed bandwidth RBM for $d=2,3$ provided certain localization bounds are known.