Miracle-dz/UniFAR-FTUs huggingface dataset:
Geometry of learning neural quantum states

Combining insights from machine learning and quantum Monte Carlo, the stochastic reconfiguration method with neural network Ansatz states is a promising new direction for high precision ground state estimation of quantum many body problems. At present, the method is heuristic, lacking a proper theoretical foundation. We initiate a thorough analysis of the learning landscape, and show that it reveals universal behavior reflecting a combination of the underlying physics and of the learning dynamics. In particular, the spectrum of the quantum Fisher matrix of complex restricted Boltzmann machine states can dramatically change across a phase transition. In contrast to the spectral properties of the quantum Fisher matrix, the actual weights of the network at convergence do not reveal much information about the system or the dynamics. Furthermore, we identify a new measure of correlation in the state by analyzing entanglement the eigenvectors. We show that, generically, the learning landscape modes with least entanglement have largest eigenvalue, suggesting that correlations are encoded in large flat valleys of the learning landscape, favoring stable representations of the ground state.
Instantons and Bar-Natan homology

A spectral sequence is established whose $E_{2}$ page is Bar-Natan's variant of Khovanov homology and which abuts to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral sequence whose $E_{2}$ page is a characteristic-2 version of $F_{5}$ homology in Khovanov's classification.
Augmented virtual double categories.

In this article the notion of virtual double category [Cruttwell-Shulman, 2010] (also known as ($\mathsf{fc}$-)multicategory [Burroni, 1971; Leinster, 2004]) is extended as follows. While cells in a virtual double category classically have a horizontal multi-source and single horizontal target, the notion of augmented virtual double category introduced here extends the latter notion by including cells with empty horizontal target as well. Any augmented virtual double category comes with a built-in notion of "locally small object" and we describe advantages of using augmented virtual double categories as a setting for formal category rather than 2-categories, which are classically equipped with a notion of "admissible object" by means of a yoneda structure [Street-Walters, 1978]. An object is locally small precisely if it admits a horizontal unit, and we show that the notions of augmented virtual double category and virtual double category coincide in the presence of all horizontal units. Without assuming the existence of horizontal units we show that most of the basic theory for virtual double categories, such as that of restriction and composition of horizontal morphisms, extends to augmented virtual double categories. We introduce and study in augmented virtual double categories the notion of "pointwise" composition of horizontal morphisms, which formalises the classical composition of profunctors given by the coend formula.
Superposition as Data Augmentation using LSTM and HMM in Small Training Sets

Considering audio and image data as having quantum nature (data are represented by density matrices), we achieved better results on training architectures such as 3-layer stacked LSTM and HMM by mixing training samples using superposition augmentation and compared with plain default training and mix-up augmentation. This augmentation technique originates from the mix-up approach but provides more solid theoretical reasoning based on quantum properties. We achieved 3% improvement (from 68% to 71%) by using 38% lesser number of training samples in Russian audio-digits recognition task and 7,16% better accuracy than mix-up augmentation by training only 500 samples using HMM on the same task. Also, we achieved 1.1% better accuracy than mix-up on first 900 samples in MNIST using 3-layer stacked LSTM.
An Optimal Restricted Isometry Condition for Exact Sparse Recovery with Orthogonal Least Squares

The orthogonal least squares (OLS) algorithm is popularly used in sparse recovery, subset selection, and function approximation. In this paper, we analyze the performance guarantee of OLS. Specifically, we show that if a sampling matrix $\mathbf{\Phi}$ has unit $\ell_{2}$-norm columns and satisfies the restricted isometry property (RIP) of order $K+1$ with \begin{align*} \delta_{K+1} &<C_{K} = \begin{cases} \frac{1}{\sqrt{K}}, & K=1, \frac{1}{\sqrt{K+\frac{1}{4}}}, & K=2, \frac{1}{\sqrt{K+\frac{1}{16}}}, & K=3, \frac{1}{\sqrt{K}}, & K \ge 4, \end{cases} \end{align*} then OLS exactly recovers any $K$-sparse vector $\mathbf{x}$ from its measurements $\mathbf{y} = \mathbf{\Phi} \mathbf{x}$ in $K$ iterations. Furthermore, we show that the proposed guarantee is optimal in the sense that OLS may fail the recovery under $\delta_{K+1} \ge C_{K}$. Additionally, we show that if the columns of a sampling matrix are $\ell_{2}$-normalized, then the proposed condition is also an optimal recovery guarantee for the orthogonal matching pursuit (OMP) algorithm. Also, we establish a recovery guarantee of OLS in the more general case where a sampling matrix might not have unit $\ell_{2}$-norm columns. Moreover, we analyze the performance of OLS in the noisy case. Our result demonstrates that under a suitable constraint on the minimum magnitude of nonzero elements in an input signal, the proposed RIP condition ensures OLS to identify the support exactly.
Utility of daily routine portable chest X-ray in mechanically ventilated patients in the pediatric intensive care unit

Abstract The utility of daily routine chest X-rays (CXRs) in mechanically ventilated patients in intensive care units is still controversial. The present study compared the diagnostic, therapeutic and outcome efficacy between daily routine and non-routine (clinically indicated) CXRs in children patients in pediatric intensive care unit (PICU). A prospective randomized study conducted in tertiary center 18-bed PICU, Riyadh Military Hospital, Riyadh, Kingdom of Saudi Arabia. The study selected 52 children, who were mechanically intubated for at least 48 hr. The children were randomized to receive either routine (29 patients) or non-routine (23 patients) CXRs and were followed until extubation or death. Demographic and outcome data were collected and analyzed as appropriate. Although children in the non-routine group received fewer CXRs, the lengths of stay (LOS) in intensive care unit and hospital and mortality rate were nearly the same compared with routine group. The percentage of CXRs with new findings was higher in the non-routine group (83%; 53 CXRs) compared to that in the routine group (69%; 156 CXRs) with an odds ratio (OR) of 2.10 (95% confidence interval [CI] = 0.60–8.11). Also, the percentage of CXRs with new findings that result in intervention was higher in non-routine group (78% vs. 69%; OR = 1.60; 95% CI = 0.50–5.70). The daily routine CXRs was not associated with a reduced effect on length of stay in PICU and hospital or mortality and it does not seem to add any advantages over non-routine CXRs in PICU. Large multicenter studies are needed to confirm these results.
Fluctuations of work in realistic equilibrium states of quantum systems with conserved quantities

The out-of-equilibrium dynamics of quantum systems is one of the most fascinating problems in physics, with outstanding open questions on issues such as relaxation to equilibrium. An area of particular interest concerns few-body systems, where quantum and thermal fluctuations are expected to be especially relevant. In this contribution, we present numerical results demonstrating the impact of conserved quantities (or ‘charges’) in the outcomes of out-of-equilibrium measurements starting from realistic equilibrium states on a few-body system implementing the Dicke model.
Poitou–Tate sequence for complex of tori over $p$-adic function fields

We complete the picture of local and global arithmetic duality theorems for short complexes of finite Galois modules and tori over $p$-adic function fields. In view of the duality theorems, we deduce a $12$-term Poitou--Tate exact sequence which relates global Galois cohomology groups to restricted topological products of local Galois cohomology groups.
The Star Formation Rate–Radius Connection: Data and Implications for Wind Strength and Halo Concentration

This paper is one in a series that explores the importance of radius as a second parameter in galaxy evolution. The topic investigated here is the relationship between star formation rate (SFR) and galaxy radius ( ) for main-sequence star-forming galaxies. The key observational result is that, over a wide range of stellar mass and redshift in both CANDELS and SDSS, there is little correlation between SFR and at fixed stellar mass. The Kennicutt–Schmidt law, or any similar density-related star formation law, then implies that smaller galaxies must have lower gas fractions than larger galaxies (at fixed ), and this is supported by observations of gas in local star-forming galaxies. We investigate the implications by adopting the equilibrium “bathtub” model: the ISM gas mass is assumed to be constant over time, and the net SFR is the difference between the accretion rate of gas onto the galaxy from the halo and the outflow rate due to winds. To match the observed null correlation between SFR and radius, the bathtub model requires that smaller galaxies at fixed mass have weaker galactic winds. Our hypothesis is that galaxies are a two-parameter family whose properties are set mainly by halo mass and concentration. These determine the radius and gas accretion rate, which in turn predict how wind strength needs to vary with to keep the SFR constant.
A contextual understanding of Mainland Chinese parent involvement in their children’s primary school years’ education

Although parent involvement has received long-standing attention in the literature, there is limited research about Chinese parent involvement, especially, in mainland, China. With Chinese immigrant students’ high academic success having been repeatedly reported, more attention has been given to Chinese parent involvement, however it was restricted to Chinese overseas, or in Taiwan and Hong Kong. It is unclear whether findings obtained accurately described Chinese parent involvement, and can be generalized to Chinese in Mainland. This research attempts to add an in-depth contextual understanding of mainland Chinese parent involvement. Based on face-to-face interviews, this study investigated Chinese parents’ involvement in, expectations for and perceptions of their children’s education. Participants were 30 parents, randomly selected from 5 primary schools in Changsha, China. Results indicated that parents: 1) are highly involved in their children’s education, with daily homework supervising; frequently communicating school issues to their children and generously investing time and money in children’s extra-curricular training; 2) hold high expectations for their children with more than 70% parents expecting their children to complete “at least” university education; 3) mostly attribute their educational involvement to the realistic need of well preparing their children for the fierce workforce competition, and passing the university-entry exams.
Diversifying Topic-Coherent Response Generation for Natural Multi-turn Conversations

Although response generation (RG) diversification for single-turn dialogs has been well developed, it is less investigated for natural multi-turn conversations. Besides, past work focused on diversifying responses without considering topic coherence to the context, producing uninformative replies. In this paper, we propose the Topic-coherent Hierarchical Recurrent Encoder-Decoder model (THRED) to diversify the generated responses without deviating the contextual topics for multi-turn conversations. In overall, we build a sequence-to-sequence net (Seq2Seq) to model multi-turn conversations. And then we resort to the latent Variable Hierarchical Recurrent Encoder-Decoder model (VHRED) to learn global contextual distribution of dialogs. Besides, we construct a dense topic matrix which implies word-level correlations of the conversation corpora. The topic matrix is used to learn local topic distribution of the contextual utterances. By incorporating both the global contextual distribution and the local topic distribution, THRED produces both diversified and topic-coherent replies. In addition, we propose an explicit metric (\emph{TopicDiv}) to measure the topic divergence between the post and generated response, and we also propose an overall metric combining the diversification metric (\emph{Distinct}) and \emph{TopicDiv}. We evaluate our model comparing with three baselines (Seq2Seq, HRED and VHRED) on two real-world corpora, respectively, and demonstrate its outstanding performance in both diversification and topic coherence.
Analyzing ASR Pretraining for Low-Resource Speech-to-Text Translation

Previous work has shown that for low-resource source languages, automatic speech-to-text translation (AST) can be improved by pre-training an end-to-end model on automatic speech recognition (ASR) data from a high-resource language. However, it is not clear what factors—e.g., language relatedness or size of the pretraining data— yield the biggest improvements, or whether pretraining can be effectively combined with other methods such as data augmentation. Here, we experiment with pretraining on datasets of varying sizes, including languages related and unrelated to the AST source language. We find that the best predictor of final AST performance is the word error rate of the pretrained ASR model, and that differences in ASR/AST performance correlate with how phonetic information is encoded in the later RNN layers of our model. We also show that pretraining and data augmentation yield complementary benefits for AST.
Weak lensing analysis of codex clusters using dark energy camera legacy survey: mass–richness relation

We present the weak-lensing analysis of 279 CODEX clusters using imaging data from 4200 deg2 of the DECam Legacy Survey (DECaLS) Data Release 3. The cluster sample results from a joint selection in X-ray, optical richness in the range 20 ≤ λ < 110, and redshift in the range 0.1 ≤ z ≤ 0.2. We model the cluster mass (M200c) and the richness relation with the expression $\left\langle M_{\rm 200c} | \lambda \right\rangle \propto M_{0} \, (\lambda / 40)^{F_{\lambda }}$. By measuring the CODEX cluster sample as an individual cluster, we obtain the best-fitting values, $M_{0} = 3.24^{+0.29}_{-0.27} \times 10^{14} \text{M}_{\odot }$, and $F_{\lambda } = 1.00 ^{+0.22}_{-0.22}$ for the richness scaling index, consistent with a power-law relation. Moreover, we separate the cluster sample into three richness groups; λ = 20–30, 30–50, and 50–110, and measure the stacked excess surface mass density profile in each group. The results show that both methods are consistent. In addition, we find an excellent agreement between our weak lensing based scaling relation and the relation obtained with dynamical masses estimated from cluster member velocity dispersions measured by the SDSS-IV/SPIDERS team. This suggests that the cluster dynamical equilibrium assumption involved in the dynamical mass estimates is statistically robust for a large sample of clusters.
Meta-World: A Benchmark and Evaluation for Multi-Task and Meta Reinforcement Learning

Meta-reinforcement learning algorithms can enable robots to acquire new skills much more quickly, by leveraging prior experience to learn how to learn. However, much of the current research on meta-reinforcement learning focuses on task distributions that are very narrow. For example, a commonly used meta-reinforcement learning benchmark uses different running velocities for a simulated robot as different tasks. When policies are meta-trained on such narrow task distributions, they cannot possibly generalize to more quickly acquire entirely new tasks. Therefore, if the aim of these methods is to enable faster acquisition of entirely new behaviors, we must evaluate them on task distributions that are sufficiently broad to enable generalization to new behaviors. In this paper, we propose an open-source simulated benchmark for meta-reinforcement learning and multi-task learning consisting of 50 distinct robotic manipulation tasks. Our aim is to make it possible to develop algorithms that generalize to accelerate the acquisition of entirely new, held-out tasks. We evaluate 6 state-of-the-art meta-reinforcement learning and multi-task learning algorithms on these tasks. Surprisingly, while each task and its variations (e.g., with different object positions) can be learned with reasonable success, these algorithms struggle to learn with multiple tasks at the same time, even with as few as ten distinct training tasks. Our analysis and open-source environments pave the way for future research in multi-task learning and meta-learning that can enable meaningful generalization, thereby unlocking the full potential of these methods.
The effects of varying depth in cosmic shear surveys

We present a semi-analytic model for the shear two-point correlation function of a cosmic shear survey with non-uniform depth. Ground-based surveys are subject to depth variations that primarily arise through varying atmospheric conditions. For a survey like the Kilo-Degree Survey (KiDS), we find that the measured depth variation increases the amplitude of the observed shear correlation function at the level of a few percent out to degree-scales, relative to the assumed uniform-depth case. The impact on the inferred cosmological parameters is shown to be insignificant for a KiDS-like survey. For next-generation cosmic shear experiments, however, we conclude that variable depth should be accounted for.
The triangulation complexity of fibred 3-manifolds

The triangulation complexity of a closed orientable 3-manifold is the minimal number of tetrahedra in any triangulation of the manifold. The main theorem of the paper gives upper and lower bounds on the triangulation complexity of any closed orientable hyperbolic 3-manifold that fibres over the circle. We show that the triangulation complexity of the manifold is equal to the translation length of the monodromy action on the mapping class group of the fibre, up to a bounded factor, where the bound depends only on the genus of the fibre.
Surface density of states in superconductors with inhomogeneous pairing constant: Analytical results

We consider a superconductor with surface suppression of the BCS pairing constant $\lambda(x)$. We analytically find the gap in the surface density of states (DOS), behavior of the DOS $\nu(E)$ above the gap, a "vertical" peculiarity of the DOS around energy equal to the bulk order parameter $\Delta_0$, and perturbative correction to the DOS at higher energies. The surface gap in the DOS is parametrically different from the surface value of the order parameter due to difference between the spatial scale $r_c$, at which $\lambda(x)$ is suppressed, and coherence length. The vertical peculiarity implies infinite-derivative inflection point of the DOS curve at $E=\Delta_0$ with square-root behavior as $E$ deviates from $\Delta_0$. The coefficients of this dependence are different at $E \Delta_0$, so the peculiarity is asymmetric.
Probing Structure in Cold Gas at z ≲ 1 with Gravitationally Lensed Quasar Sight Lines

Absorption spectroscopy of gravitationally lensed quasars (GLQs) enables study of spatial variations in the interstellar and/or circumgalactic medium of foreground galaxies. We report observations of four GLQs, each with two images separated by 0. ″8–3. ″0, that show strong absorbers at redshifts 0.4 < zabs < 1.3 in their spectra, including some at the lens redshift with impact parameters 1.5–6.9 kpc. We measure H i Lyman lines along two sight lines each in five absorbers (10 sight lines in total) using Hubble Space Telescope Space Telescope Imaging Spectrograph, and metal lines using Magellan Echellette or Sloan Digital Sky Survey. Our data have doubled the lens galaxy sample with measurements of H i column densities (NH i) and metal abundances along multiple sight lines. Our data, combined with the literature, show no strong correlation between absolute values of differences in NH i, NFe ii, or [Fe/H] and the sight line separations at the absorber redshifts for separations of 0–8 kpc. The estimated abundance gradients show a tentative anticorrelation with abundances at galaxy centers. Some lens galaxies show inverted gradients, possibly suggesting central dilution by mergers or infall of metal-poor gas. [Fe/H] measurements and masses estimated from GLQ astrometry suggest the lens galaxies lie below the total mass–metallicity relation for early-type galaxies as well as measurements for quasar-galaxy pairs and gravitationally lensed galaxies at comparable redshifts. This difference may arise in part from the dust depletion of Fe. Higher resolution measurements of H and metals (especially undepleted elements) for more GLQ absorbers and accurate lens redshifts are needed to confirm these trends.
Fixed-Confidence Guarantees for Bayesian Best-Arm Identification

We investigate and provide new insights on the sampling rule called Top-Two Thompson Sampling (TTTS). In particular, we justify its use for fixed-confidence best-arm identification. We further propose a variant of TTTS called Top-Two Transportation Cost (T3C), which disposes of the computational burden of TTTS. As our main contribution, we provide the first sample complexity analysis of TTTS and T3C when coupled with a very natural Bayesian stopping rule, for bandits with Gaussian rewards, solving one of the open questions raised by Russo (2016). We also provide new posterior convergence results for TTTS under two models that are commonly used in practice: bandits with Gaussian and Bernoulli rewards and conjugate priors.
Instantons and some concordance invariants of knots

Concordance invariants of knots are derived from the instanton homology groups with local coefficients, as introduced in earlier work of the authors. These concordance invariants include a 1‐parameter family of homomorphisms fr , from the knot concordance group to R . Prima facie, these concordance invariants have the potential to provide independent bounds on the genus and number of double points for immersed surfaces with boundary a given knot.
A Recurrent Variational Autoencoder for Speech Enhancement

This paper presents a generative approach to speech enhancement based on a recurrent variational autoencoder (RVAE). The deep generative speech model is trained using clean speech signals only, and it is combined with a nonnegative matrix factorization noise model for speech enhancement. We propose a variational expectation-maximization algorithm where the encoder of the RVAE is finetuned at test time, to approximate the distribution of the latent variables given the noisy speech observations. Compared with previous approaches based on feed-forward fully-connected architectures, the proposed recurrent deep generative speech model induces a posterior temporal dynamic over the latent variables, which is shown to improve the speech enhancement results.