Miracle-dz/UniFAR-FTUs huggingface dataset:
A new theory of the coefficient of earth pressure at rest

One of the well-known and widely applied parameters in soil mechanics is the so-called coefficient of earth pressure at rest (denoted by a K0). Field and laboratory investigations show that this parameter is correlated with the friction angle and the overconsolidation ratio of the soil deposit. For normally consolidated clays, the semi-emprical expression developed by Jaky is considered to hold good. The extension of Jaky's equation for overconsolidated soils is built entirely on empirical data; and there is lack of a theoretical framework that satisfactorily explains the relationships. In this paper, these relationships are investigated from the nature of energy dissipation of soil aggregates. For the same, the cyclic stress-dilatancy relationship proposed by the author is employed, here for a plane strain condition. Then, the relationship between the stress ratio and the mobilized friction angle that maximizes the plastic dissipation is obtained; the value of the stress ratio at this state is shown to be reasonably close to the relationship proposed by Jaky. An exponential relationship between K0 and OCR is derived, and for a special case, the exponent is shown to be the sine of the critical state friction angle. Finally, some generalizations are given and aspects which need further investigation are highlighted.
No-Substitution k -means Clustering with Optimal Center Complexity and Low Memory

We consider k -means clustering in the online no-substitution setting where one must decide whether to take each data point x t as a center immediately upon streaming it and cannot remove centers once taken. Our work is focused on the arbitrary-order assumption where there are no restrictions on how the points X are ordered or generated. Algorithms in this setting are evaluated with respect to their approximation ratio compared to optimal clustering cost, the number of centers they select, and their memory usage. Recently, Bhattacharjee and Moshkovitz (2020) deﬁned a parameter, Lower α,k ( X ) that governs the minimum number of centers any α -approximationclustering algorithm, allowed any amount of memory, must take given input X . To complement their result, we give the ﬁrst algorithm that takes ˜ O ( Lower α,k ( X )) centers (hiding factors of k, log n ) while simultaneously achieving a constant approximation and using ˜ O ( k ) memory in addition to the memory required to save the centers. Our algorithm shows that it in the no-substitution setting, it is possible to take an order-optimal number of centers while using little additional memory.
Selection Effects in Periodic X-Ray Data from Maximizing Detection Statistics

The Neutron Star Interior Composition Explorer (NICER) records exceptional data on pulsars’ energy-dependent X-ray pulse profiles. However, in searching for evidence of pulsations, Guillot et al. (2019) introduce a procedure to select an ordered subset of data that maximizes a detection statistic (the H-test). I show that this can degrade subsequent analyses using an idealized model with stationary expected count rates from both noise and signal. Specifically, the data-selection procedure biases the inferred mean count rate to be too low and the inferred pulsation amplitude to be too high, and the size of these biases scales strongly with the amount of data that is rejected and the true signal amplitude. The procedure also alters the H-test’s null distribution, rendering nominal significance estimates overly optimistic. While the idealized model does not capture all the complexities of real NICER data, it suggests that these biases could be important for NICER’s observations of J0740+6620 and other faint pulsars (observations of J0030+0451 are likely less affected). I estimate that these effects may introduce a bias of (10%) on average in the inferred modulation depth of lightcurves like J0740+6620's, and may be as large as (50%) for fainter pulsars. However, the change for a single data set like J0740+6620 is expected to be a shift between −5% and +20%. This could imply that the lower limit on J0740+6620's radius is slightly larger than it should be, although preliminary investigations suggest the radius constraints shift to larger radii by (1%) with the same overall statistical precision using real J0740+6620 data.
Local Quantum Measurement Demands Type-Sensitive Information Principles for Global Correlations

Physical theories with local structure similar to quantum theory can allow beyond-quantum global states that are in agreement with unentangled Gleason’s theorem. In a standard Bell experiment any such bipartite state produces correlations that are always quantum simulable. In this limited classical-input-classical-output Bell scenario, we show that there exist bipartite beyond-quantum states that produce correlations all of which are in-fact classically simulable. However, if the type of Bell scenario is generalized to consider quantum states as inputs, we then show that any such bipartite beyond-quantum state yields beyond-quantum input-output correlations. We also analyze the implication of this quantum input scenario while studying generic multipartite correlations obtained from local quantum theory but potentially allowing different global structure. Our study suggests the requirement of type sensitive information principles for isolating the quantum correlations from the beyond-quantum ones.
The Problem of Zombie Datasets: A Framework For Deprecating Datasets

What happens when a machine learning dataset is deprecated for legal, ethical, or technical reasons, but continues to be widely used? In this paper, we examine the public afterlives of several prominent deprecated or redacted datasets, including ImageNet, 80 Million Tiny Images, MS-Celeb-1M, Duke MTMC, Brainwash, and HRT Transgender, in order to inform a framework for more consistent, ethical, and accountable dataset deprecation. Building on prior research [27, 35, 61], we ﬁnd that there is a lack of consistency, transparency, and centralized sourcing of information on the deprecation of datasets, and as such, these datasets and their derivatives continue to be cited in papers and circulate online. These datasets that never die – which we term “zombie datasets” – continue to inform the design of production-levelsystems, causing technical, legal, and ethical challenges; in so doing, they risk perpetuating the harms that prompted their supposed withdrawal, including concerns around bias, discrimination, and privacy. Based on this analysis, we propose a Dataset Deprecation Framework that includes considerations of risk, mitigation of impact, appeal mechanisms, timeline, post-deprecation protocol, and publication checks that can be adapted and implemented by the machine learning community. Drawing on work on datasheets and checklists [29, 48], we further offer two sample dataset deprecation sheets and propose a centralized repository that tracks which datasets have been deprecated and could be incorporated into the publication protocols of venues like NeurIPS.
SustainBench: Benchmarks for Monitoring the Sustainable Development Goals with Machine Learning

Progress toward the United Nations Sustainable Development Goals (SDGs) has been hindered by a lack of data on key environmental and socioeconomic indicators, which historically have come from ground surveys with sparse temporal and spatial coverage. Recent advances in machine learning have made it possible to utilize abundant, frequently-updated, and globally available data, such as from satellites or social media, to provide insights into progress toward SDGs. Despite promising early results, approaches to using such data for SDG measurement thus far have largely evaluated on different datasets or used inconsistent evaluation metrics, making it hard to understand whether performance is improving and where additional research would be most fruitful. Furthermore, processing satellite and ground survey data requires domain knowledge that many in the machine learning community lack. In this paper, we introduce SustainBench, a collection of 15 benchmark tasks across 7 SDGs, including tasks related to economic development, agriculture, health, education, water and sanitation, climate action, and life on land. Datasets for 11 of the 15 tasks are released publicly for the first time. Our goals for SustainBench are to (1) lower the barriers to entry for the machine learning community to contribute to measuring and achieving the SDGs; (2) provide standard benchmarks for evaluating machine learning models on tasks across a variety of SDGs; and (3) encourage the development of novel machine learning methods where improved model performance facilitates progress towards the SDGs.
Prime values of $f(a,b^2)$ and $f(a,p^2)$, $f$ quadratic

We prove an asymptotic formula for primes of the shape f(a, b) with a, b integers and of the shape f(a, p) with p prime. Here f is a binary quadratic form with integer coefficients, irreducible over Q and has no local obstructions. This refines the seminal work of Friedlander and Iwaniec on primes of the form x + y and Heath-Brown and Li on primes of the form a + p, as well as earlier work of the author with Lam and Schindler on primes of the form f(a, p) with f a positive definite form.
Exploring Gravitationally Lensed z ≳ 6 X-Ray Active Galactic Nuclei Behind the RELICS Clusters

Although observations of high-redshift quasars demonstrate that many supermassive black holes (BHs) reached large masses within one billion years after the Big Bang, the origin of the first BHs is still a mystery. A promising way to constrain the origin of the first BHs is to explore the average properties of z ≳ 6 BHs. However, typical BHs remain hidden from X-ray surveys, which is due to their relatively faint nature and the limited sensitivity of X-ray telescopes. Gravitational lensing provides an attractive way to study this unique galaxy population as it magnifies the faint light from these high-redshift galaxies. Here, we study the X-ray emission originating from 155 gravitationally lensed z ≳ 6 galaxies that were detected in the Reionization Lensing Cluster Survey. We utilize Chandra X-ray observations to search for active galactic nuclei (AGNs) in the individual galaxies and in the stacked galaxy samples. We did not identify an individual X-ray source that was undoubtedly associated with a high-redshift galaxy. We stack the signal from all galaxies and do not find a statistically significant detection. We split our sample based on stellar mass, star formation rate, and lensing magnification and stack these subsamples. We obtain a 2. 2σ detection for massive galaxies with an X-ray luminosity of (3.7 ± 1.6) × 1042 erg s−1, which corresponds to a (3.0 ± 1.3) × 105 M ⊙ BH accreting at its Eddington rate. Other stacks remain undetected and we place upper limits on the AGN emission. These limits imply that the bulk of BHs at z ≳ 6 either accrete at a few percent of their Eddington rate and/or are 1–2 orders of magnitude less massive than expected based on the stellar mass of their host galaxy.
Exponential dichotomy for noninvertible linear difference equations

In this article we study exponential dichotomies for noninvertible linear difference equations in finite dimensions. After giving the definition, we study the extent to which the projection in a dichotomy is unique. For equations on it is unique but for equations on only its range is unique and for only its nullspace. Here we strengthen Kalkbrenner's results and give a complete characterization of all possible projections. Next we study the possibility of extending the dichotomy to a larger interval. We reproduce the results of Pötzsche but also show exactly when the original projection remains unchanged. Next we prove that the roughness theorem, well known for additive perturbations, holds for multiplicative perturbations also. The proof uses ideas of Zhou, Lu and Zhang. Finally, following Ducrot, Magal and Seydi, we mention that the results by Palmer on finite time conditions on dichotomy for the invertible case can be extended to the noninvertible case.
Measuring the Properties of Active Galactic Nuclei Disks with Gravitational Waves

Active galactic nuclei (AGNs) are promising environments for the assembly of merging binary black hole (BBH) systems. Interest in AGNs as nurseries for merging BBHs is rising, following the detection of gravitational waves from a BBH system from the purported pair-instability mass gap, most notably GW190521. AGNs have also been invoked to explain the formation of the high-mass-ratio system GW190814. We draw on simulations of BBH systems in AGNs to propose a phenomenological model for the distribution of black hole spins of merging binaries in AGN disks. The model incorporates distinct features that make the AGN channel potentially distinguishable from other channels, such as assembly in the field and in globular clusters. The model parameters can be mapped heuristically to the age and density of the AGN disks. We estimate the extent to which different populations of mergers in AGNs can be distinguished. If the majority of merging black holes are assembled in AGNs, future gravitational-wave observations may provide insights into the dynamics of AGN disks.
Marchenko-Pastur law for a random tensor model

We study the limiting spectral distribution of large-dimensional sample covariance matrices associated with symmetric random tensors formed by $\binom{n}{d}$ different products of $d$ variables chosen from $n$ independent standardized random variables. We find optimal sufficient conditions for this distribution to be the Marchenko-Pastur law in the case $d=d(n)$ and $n\to\infty$. Our conditions reduce to $d^2=o(n)$ when the variables have uniformly bounded fourth moments. The proofs are based on a new concentration inequality for quadratic forms in symmetric random tensors and a law of large numbers for elementary symmetric random polynomials.
Smooth tensor estimation with unknown permutations

We consider the problem of structured tensor denoising in the presence of unknown permutations. Such data problems arise commonly in recommendation system, neuroimaging, community detection, and multiway comparison applications. Here, we develop a general family of smooth tensor models up to arbitrary index permutations; the model incorporates the popular tensor block models and Lipschitz hypergraphon models as special cases. We show that a constrained least-squares estimator in the block-wise polynomial family achieves the minimax error bound. A phase transition phenomenon is revealed with respect to the smoothness threshold needed for optimal recovery. In particular, we find that a polynomial of degree up to $(m-2)(m+1)/2$ is sufficient for accurate recovery of order-$m$ tensors, whereas higher degree exhibits no further benefits. This phenomenon reveals the intrinsic distinction for smooth tensor estimation problems with and without unknown permutations. Furthermore, we provide an efficient polynomial-time Borda count algorithm that provably achieves optimal rate under monotonicity assumptions. The efficacy of our procedure is demonstrated through both simulations and Chicago crime data analysis.
Which metric on the space of collider events?

Which is the best metric for the space of collider events? Motivated by the success of the Energy Mover's Distance in characterizing collider events, we explore the larger space of unbalanced optimal transport distances, of which the Energy Mover's Distance is a particular case. Geometric and computational considerations favor an unbalanced optimal transport distance known as the Hellinger-Kantorovich distance, which possesses a Riemannian structure that lends itself to efficient linearization. We develop the particle linearized unbalanced Optimal Transport (pluOT) framework for collider events based on the linearized Hellinger-Kantorovich distance and demonstrate its efficacy in boosted jet tagging. This provides a flexible and computationally efficient optimal transport framework ideally suited for collider physics applications.
Rigid birational involutions of $\mathbb{P}^3$ and cubic threefolds

We construct families of birational involutions on $\mathbb{P}^3$ or a smooth cubic threefold which do not fit into a non-trivial elementary relation of Sarkisov links. As a consequence, we construct new homomorphisms from their group of birational transformations, effectively re-proving their non-simplicity. We also prove that these groups admit a free product structure. Finally, we produce automorphisms of these groups that are not generated by inner and field automorphisms.
Group-Aware Threshold Adaptation for Fair Classification

The fairness in machine learning is getting increasing attention, as its applications in different fields continue to expand and diversify. To mitigate the discriminated model behaviors between different demographic groups, we introduce a novel post-processing method to optimize over multiple fairness constraints through group-aware threshold adaptation. We propose to learn adaptive classification thresholds for each demographic group by optimizing the confusion matrix estimated from the probability distribution of a classification model output. As we only need an estimated probability distribution of model output instead of the classification model structure, our post-processing model can be applied to a wide range of classification models and improve fairness in a model-agnostic manner and ensure privacy. This even allows us to post-process existing fairness methods to further improve the trade-off between accuracy and fairness. Moreover, our model has low computational cost. We provide rigorous theoretical analysis on the convergence of our optimization algorithm and the trade-off between accuracy and fairness. Our method theoretically enables a better upper bound in near optimality than previous method under the same condition. Experimental results demonstrate that our method outperforms state-of-the-art methods and obtains the result that is closest to the theoretical accuracy-fairness trade-off boundary.
A Comparison of Deep Learning Architectures for Optical Galaxy Morphology Classification

The classification of galaxy morphology plays a crucial role in understanding galaxy formation and evolution. Traditionally, this process is done manually. The emergence of deep learning techniques has given room for the automation of this process. As such, this paper offers a comparison of deep learning architectures to determine which is best suited for optical galaxy morphology classification. Adapting the model training method proposed by Walmsley et al in 2021, the Zoobot Python library is used to train models to predict Galaxy Zoo DECaLS decision tree responses, made by volunteers, using EfficientNet B0, DenseNet121 and ResNet50 as core model architectures. The predicted results are then used to generate accuracy metrics per decision tree question to determine architecture performance. DenseNet121 was found to produce the best results, in terms of accuracy, with a reasonable training time. In future, further testing with more deep learning architectures could prove beneficial.
Flat-band Majorana bound states in topological Josephson junctions

Nodal topological superconductors characterized by px-wave pairing symmetry host flat-band Majorana bound states causing drastic anomalies in low-energy electromagnetic responses. Nevertheless, the study of flat-band Majorana bound states has been at a standstill owing to a serious lack of candidate materials for px-wave superconductors. In this paper, by expanding a scheme of planar topological Josephson junctions, we propose a promising device realizing an effective px-wave superconductor. Specifically, we consider a three-dimensional Josephson junction consisting of a thin-film semiconductor hosting a persistent spin-helix state and two conventional s-wave superconductors. We analytically obtain a topological phase diagram and numerically demonstrate the emergence of flat-band Majorana bound states by calculating the local density of states.
Universal and data-adaptive algorithms for model selection in linear contextual bandits

Model selection in contextual bandits is an important complementary problem to regret minimization with respect to a fixed model class. We consider the simplest non-trivial instance of model-selection: distinguishing a simple multi-armed bandit problem from a linear contextual bandit problem. Even in this instance, current state-of-the-art methods explore in a suboptimal manner and require strong"feature-diversity"conditions. In this paper, we introduce new algorithms that a) explore in a data-adaptive manner, and b) provide model selection guarantees of the form $\mathcal{O}(d^{\alpha} T^{1- \alpha})$ with no feature diversity conditions whatsoever, where $d$ denotes the dimension of the linear model and $T$ denotes the total number of rounds. The first algorithm enjoys a"best-of-both-worlds"property, recovering two prior results that hold under distinct distributional assumptions, simultaneously. The second removes distributional assumptions altogether, expanding the scope for tractable model selection. Our approach extends to model selection among nested linear contextual bandits under some additional assumptions.
Toward Learning Human-aligned Cross-domain Robust Models by Countering Misaligned Features

Machine learning has demonstrated remarkable prediction accuracy over i.i. d data, but the accuracy often drops when tested with data from another distribution. In this paper, we aim to offer another view of this problem in a perspective assuming the reason behind this accuracy drop is the reliance of models on the features that are not aligned well with how a data annotator considers similar across these two datasets. We refer to these features as misaligned features. We extend the conventional generalization error bound to a new one for this setup with the knowledge of how the misaligned features are associated with the label. Our analysis offers a set of techniques for this problem, and these techniques are naturally linked to many previous methods in robust machine learning literature. We also compared the empirical strength of these methods demonstrated the performance when these previous techniques are combined, with an implementation available at https://github.com/OoDBag/WR
Long exact sequences of homology groups of étale groupoids

<p style='text-indent:20px;'>When a pair of étale groupoids <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{G} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{G}' $\end{document}</tex-math></inline-formula> on totally disconnected spaces are related in some way, we discuss the difference of their homology groups. More specifically, we treat two basic situations. In the subgroupoid situation, <inline-formula><tex-math id="M3">\begin{document}$ \mathcal{G}' $\end{document}</tex-math></inline-formula> is assumed to be an open regular subgroupoid of <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{G} $\end{document}</tex-math></inline-formula>. In the factor groupoid situation, we assume that <inline-formula><tex-math id="M5">\begin{document}$ \mathcal{G}' $\end{document}</tex-math></inline-formula> is a quotient of <inline-formula><tex-math id="M6">\begin{document}$ \mathcal{G} $\end{document}</tex-math></inline-formula> and the factor map <inline-formula><tex-math id="M7">\begin{document}$ \mathcal{G}\to\mathcal{G}' $\end{document}</tex-math></inline-formula> is proper and regular. For each, we show that there exists a long exact sequence of homology groups. We present examples which arise from SFT groupoids and hyperplane groupoids. </p>