Miracle-dz/UniFAR-FTUs huggingface dataset:
On Kummer's test of convergence and its relation to basic comparison tests.

Testing convergence of infinite series is an important part of mathematics. A very basic test of convergence is to upper-bound a given series with a known series, term by term. In $19^{th}$ century, Kummer proposed a test of convergence for any positive series based on finding a suitable positive sequence $\{p_n\}$ and a suitable real constant $c$. It can be easily shown that by choosing appropriate sequence $\{p_n\}$, the Kummer's test yields other tests like Raabe's, Gauss' or Bertrand's as its special cases. In 1995, Samelson noted that there is another interesting relation between Kummer's test and basic comparison tests, particularly, that one can transform the sequence $\{p_n\}$ into a convergent bounding series, and he sketched a simple proof of this statement. In this paper, we fill the missing formal proof, although using a different approach, and we show how to construct a bounding series from the sequence $\{p_n\}$ and vice versa.
Causal Structural Hypothesis Testing and Data Generation Models

A vast amount of expert and domain knowledge is captured by causal structural priors, yet there has been little research on testing such priors for generalization and data synthesis purposes. We propose a novel model architecture, Causal Structural Hypothesis Testing, that can use nonparametric, structural causal knowledge and approximate a causal model’s functional relationships using deep neural networks. We use these architectures for comparing structural priors, akin to hypothesis testing, using a deliberate (non-random) split of training and testing data. Extensive simulations demonstrate the effectiveness of out-of-distribution generalization error as a proxy for causal structural prior hypothesis testing and offers a statistical baseline for interpreting results. We show that the variational version of the architecture, Causal Structural Variational Hypothesis Testing can improve performance in low SNR regimes. Due to the simplicity and low parameter count of the models, practitioners can test and compare structural prior hypotheses on small dataset and use the priors with the best generalization capacity to synthesize much larger, causally-informed datasets. Finally, we validate our methods on a synthetic pendulum dataset, and show a use-case on a real-world trauma surgery ground-level falls dataset. Our code is available on GitHub. 2
Tri-Polarized Holographic MIMO Surface in Near-Field: Channel Modeling and Precoding Design

This paper investigates the utilization of triple polarization (TP) for multi-user (MU) holographic multiple-input multi-output surface (HMIMOS) wireless communication systems, targeting capacity boosting and diversity exploitation without enlarging the antenna array sizes. We specifically consider that both the transmitter and receiver are both equipped with an HMIMOS consisting of compact sub-wavelength TP patch antennas within the near-field (NF) regime. To characterize TP MU-HMIMOS systems, a TP NF channel model is constructed using the dyadic Green's function, whose characteristics are leveraged to design two precoding schemes for mitigating the cross-polarization and inter-user interference contributions. Specifically, a user-cluster-based precoding scheme assigns different users to one of three polarizations at the expense of the system's diversity, and a two-layer precoding scheme removes interference using the Gaussian elimination method at a high computational cost. The theoretical correlation analysis for HMIMOS in the NF region is also investigated, revealing that both the spacing of transmit patch antennas and user distance impact transmit correlation factors. Our numerical results show that the users far from transmitting HMIMOS experience higher correlation than those closer within the NF regime, resulting in a lower channel capacity. Meanwhile, in terms of channel capacity, TP HMIMOS can almost achieve 1.25 times gain compared with dual-polarized HMIMOS, and 3 times compared with conventional HMIMOS. In addition, the proposed two-layer precoding scheme combined with two-layer power allocation realizes a higher spectral efficiency than other schemes without sacrificing diversity.
Local selectivity of orders in central simple algebras

Let B be a central simple algebra of degree n over a number field K, and L ⊂ B be a strictly maximal subfield. We say that the ring of integers 𝒪L is selective if there exists an isomorphism class of maximal orders in B no element of which contains 𝒪L. In the present work, we consider a local variant of the selectivity problem and applications. We first prove a theorem characterizing which maximal orders in a local central simple algebra contain the global ring of integers 𝒪L by leveraging the theory of affine buildings for SLr(D) where D is a local central division algebra. Then as an application, we use the local result and a local–global principle to show how to compute a set of representatives of the isomorphism classes of maximal orders in B, and distinguish those which are guaranteed to contain 𝒪L. Having such a set of representatives allows both algebraic and geometric applications. As an algebraic application, we recover a global selectivity result, and give examples which clarify the interesting role of partial ramification in the algebra.
The Cahn-Hilliard equation on an evolving surface

We study the asymptotic limit of the Cahn-Hilliard equation on an evolving surface with prescribed velocity. The method of formally matched asymptotic expansions is extended to account for the movement of the domain. We consider various forms for the mobility and potential functions, in particular, with regards to the scaling of the mobility with the interface thickness parameter. Mullins-Sekerka, but also surface diffusion type problems, can be derived featuring additional terms which are due to the domain evolution. The asymptotic behaviour is supported and further explored with some numerical simulations.
A first look at quasi-Monte Carlo for lattice field theory problems

In this project we initiate an investigation of the applicability of Quasi-Monte Carlo methods to lattice field theories in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Monte Carlo simulation behaves like N−1/2, where N is the number of observations. By means of Quasi-Monte Carlo methods it is possible to improve this behavior for certain problems to up to N−1. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling.
Asymptotics of the Sketched Pseudoinverse

We take a random matrix theory approach to random sketching and show an asymptotic first-order equivalence of the regularized sketched pseudoinverse of a positive semidefinite matrix to a certain evaluation of the resolvent of the same matrix. We focus on real-valued regularization and extend previous results on an asymptotic equivalence of random matrices to the real setting, providing a precise characterization of the equivalence even under negative regularization, including a precise characterization of the smallest nonzero eigenvalue of the sketched matrix, which may be of independent interest. We then further characterize the second-order equivalence of the sketched pseudoinverse. We also apply our results to the analysis of the sketch-and-project method and to sketched ridge regression. Lastly, we prove that these results generalize to asymptotically free sketching matrices, obtaining the resulting equivalence for orthogonal sketching matrices and comparing our results to several common sketches used in practice.
Simple Primitives With Feasibility- and Contextuality-Dependence for Open-World Compositional Zero-Shot Learning

The task of Open-World Compositional Zero-Shot Learning (OW-CZSL) is to recognize novel state-object compositions in images from all possible compositions, where the novel compositions are absent during the training stage. The performance of conventional methods degrades significantly due to the large cardinality of possible compositions. Some recent works consider simple primitives (i.e., states and objects) independent and separately predict them to reduce cardinality. However, it ignores the heavy dependence between states, objects, and compositions. In this paper, we model the dependence via feasibility and contextuality. Feasibility-dependence refers to the unequal feasibility of compositions, e.g., hairy is more feasible with cat than with building in the real world. Contextuality-dependence represents the contextual variance in images, e.g., cat shows diverse appearances when it is dry or wet. We design Semantic Attention (SA) to capture the feasibility semantics to alleviate impossible predictions, driven by the visual similarity between simple primitives. We also propose a generative Knowledge Disentanglement (KD) to disentangle images into unbiased representations, easing the contextual bias. Moreover, we complement the independent compositional probability model with the learned feasibility and contextuality compatibly. In the experiments, we demonstrate our superior or competitive performance, SA-and-kD-guided Simple Primitives (SAD-SP), on three benchmark datasets.
ProtoX: Explaining a Reinforcement Learning Agent via Prototyping

While deep reinforcement learning has proven to be successful in solving control tasks, the"black-box"nature of an agent has received increasing concerns. We propose a prototype-based post-hoc policy explainer, ProtoX, that explains a blackbox agent by prototyping the agent's behaviors into scenarios, each represented by a prototypical state. When learning prototypes, ProtoX considers both visual similarity and scenario similarity. The latter is unique to the reinforcement learning context, since it explains why the same action is taken in visually different states. To teach ProtoX about visual similarity, we pre-train an encoder using contrastive learning via self-supervised learning to recognize states as similar if they occur close together in time and receive the same action from the black-box agent. We then add an isometry layer to allow ProtoX to adapt scenario similarity to the downstream task. ProtoX is trained via imitation learning using behavior cloning, and thus requires no access to the environment or agent. In addition to explanation fidelity, we design different prototype shaping terms in the objective function to encourage better interpretability. We conduct various experiments to test ProtoX. Results show that ProtoX achieved high fidelity to the original black-box agent while providing meaningful and understandable explanations.
Painlev\'e-II approach to binary black hole merger dynamics: universality from integrability

The binary black hole merger waveform is both simple and universal. Adopting an effective asymptotic description of the dynamics, we aim at accounting for such universality in terms of underlying (effective) integrable structures. More speciﬁcally, under a “wave-mean ﬂow” perspective, we propose that fast degrees of freedom corresponding to the observed waveform would be subject to effective linear dynamics, propagating on a slowly evolving background subject to (effective) non-linear integrable dynamics. The Painlev´e property of the latter would be implemented in terms of the so-called Painlev´e-II transcendent, providing a structural link between i) orbital (in particular, EMRI) dynamics in the inspiral phase, ii) self-similar solutions of non-linear dispersive Korteweg-de Vries-like equations (namely, the ‘modiﬁed Korteweg-de Vries’ equation) through the merger and iii) the matching with the isospectral features of black hole quasi-normal modes in late ringdown dynamics. Moreover, the Painlev´e-II equation provides also a ‘non-linear turning point’ problem, extending the linear discussion in the recently introduced Airy approach to binary black hole merger waveforms. Under the proposed integrability perspective, the simplicity and universality of the binary black hole merger waveform would be accounted to by the ‘hidden symmetries’ of the underlying integrable (effective) dynamics. In the spirit of asymptotic reasoning, and considering Ward’s conjecture linking integrability and self-dual Yang-Mills structures, it is tantalizing to question if such universal patterns would reﬂect the actual full integrability of a (self-dual) sector of general relativity, ultimately responsible for the binary black hole waveform patterns.
Decentralized Secondary Control Scheme for Frequency Restoration in Inverter-based Islanded Microgrids

—Inverter-dominated microgrids are quickly be- coming a key building block of future power systems. They rely on centralized controllers that can provide reliability and resiliency in extreme events. Nonetheless, communication failures due to cyber-physical attacks or natural disasters can make autonomous operation of islanded microgrids challenging. This paper examines a uniﬁed decentralized secondary control scheme that is robust to inverter clock synchronization errors and can be seamlessly applied to grid-following or grid-forming control architectures. The proposed scheme overcomes the well-known stability problem that arises from parallel operation of local integral controllers. Theoretical guarantees for stability are provided along with criteria to appropriately tune the secondary control gains to achieve good frequency regulation performance while ensuring fair power sharing. The efﬁcacy of our approach in eliminating the steady-state frequency deviation is demonstrated through simulations on a 5-bus microgrid with four grid-forming inverters.
Learning Fabric Manipulation in the Real World with Human Videos

Fabric manipulation is a long-standing challenge in robotics due to the enormous state space and complex dynamics. Learning approaches stand out as promising for this domain as they allow us to learn behaviours directly from data. Most prior methods however rely heavily on simulation, which is still limited by the large sim-to-real gap of deformable objects or rely on large datasets. A promising alternative is to learn fabric manipulation directly from watching humans perform the task. In this work, we explore how demonstrations for fabric manipulation tasks can be collected directly by humans, providing an extremely natural and fast data collection pipeline. Then, using only a handful of such demonstrations, we show how a pick-and-place policy can be learned and deployed on a real robot, without any robot data collection at all. We demonstrate our approach on a fabric folding task, showing that our policy can reliably reach folded states from crumpled initial configurations. Videos are available at: https://sites.google. com/view/foldingbyhand
THE X-RAY TRANSIENT 2XMMi J003833.3+402133: A CANDIDATE MAGNETAR AT HIGH GALACTIC LATITUDE

We present detailed analysis of the transient X-ray source 2XMMi J003833.3+402133 detected by XMM-Newton in 2008 January during a survey of M31. The X-ray spectrum is well fitted by either a steep power law plus a blackbody model or a double blackbody model. Prior observations with XMM-Newton, Chandra, Swift, and ROSAT spanning 1991–2007, as well as an additional Swift observation in 2011, all failed to detect this source. No counterpart was detected in deep optical imaging with the Canada–France–Hawaii Telescope down to a 3σ lower limit of g = 26.5 mag. This source has previously been identified as a black hole X-ray binary in M31. While this remains a possibility, the transient behavior, X-ray spectrum, and lack of an optical counterpart are equally consistent with a magnetar interpretation for 2XMMi J003833.3+402133. The derived luminosity and blackbody emitting radius at the distance of M31 argue against an extragalactic location, implying that if it is indeed a magnetar it is located within the Milky Way but 22° out of the plane. The high Galactic latitude could be explained if 2XMMi J003833.3+402133 were an old magnetar, or if its progenitor was a runaway star that traveled away from the plane prior to going supernova.
Max-Min Off-Policy Actor-Critic Method Focusing on Worst-Case Robustness to Model Misspecification

In the field of reinforcement learning, because of the high cost and risk of policy training in the real world, policies are trained in a simulation environment and transferred to the corresponding real-world environment. However, the simulation environment does not perfectly mimic the real-world environment, lead to model misspecification. Multiple studies report significant deterioration of policy performance in a real-world environment. In this study, we focus on scenarios involving a simulation environment with uncertainty parameters and the set of their possible values, called the uncertainty parameter set. The aim is to optimize the worst-case performance on the uncertainty parameter set to guarantee the performance in the corresponding real-world environment. To obtain a policy for the optimization, we propose an off-policy actor-critic approach called the Max-Min Twin Delayed Deep Deterministic Policy Gradient algorithm (M2TD3), which solves a max-min optimization problem using a simultaneous gradient ascent descent approach. Experiments in multi-joint dynamics with contact (MuJoCo) environments show that the proposed method exhibited a worst-case performance superior to several baseline approaches.
Predicting User-specific Future Activities using LSTM-based Multi-label Classification

User-specific future activity prediction in the healthcare domain based on previous activities can drastically improve the services provided by the nurses. It is challenging because, unlike other domains, activities in healthcare involve both nurses and patients, and they also vary from hour to hour. In this paper, we employ various data processing techniques to organize and modify the data structure and an LSTM-based multi-label classifier for a novel 2-stage training approach (user-agnostic pre-training and user-specific fine-tuning). Our experiment achieves a validation accuracy of 31.58\%, precision 57.94%, recall 68.31%, and F1 score 60.38%. We concluded that proper data pre-processing and a 2-stage training process resulted in better performance. This experiment is a part of the"Fourth Nurse Care Activity Recognition Challenge"by our team"Not A Fan of Local Minima".
Assisted chaotic inflation in brane-world cosmology

Assisted chaotic inflation in brane cosmology is discussed. We work in the framework of Randall-Sundrum (RS) II model, in which adopting the RS condition the only parameter is the five-dimensional Planck mass. Using the scalar spectral index and the amplitude of scalar perturbations we determine both the mass of the scalar fields responsible for inflation and the fundamental Planck mass of the higher-dimensional theory. We find that the mass of the scalars has the typical value of the inflaton mass in chaotic inflation (M{sub I}{approx}10{sup 13} GeV) and that the five-dimensional Planck mass is very close to the grand unified theories (GUT) scale (M{sub 5}{approx}(10{sup 16}-10{sup 17}) GeV). Furthermore, no matter how many scalar fields we use it is not possible to have chaotic inflation with field values below the fundamental Planck mass.
On the Irreducibility and Distribution of Arithmetic Divisors

We introduce the notion of ǫ-irreducibility for arithmetic cycles meaning that the degree of its analytic part is small compared to the degree of its irreducible classical part. We will show that for every ǫ > 0 any sufficiently high tensor power of an arithmetically ample hermitian line bundle can be represented by an ǫ-irreducible arithmetic divisor. Our methods of proof also allow us to study the distribution of divisors of small sections of an arithmetically ample hermitian line bundle L. We will prove that for increasing tensor powers L ⊗n the normalized Dirac measures of these divisors almost always converge to c1(L) in the weak sense. Using geometry of numbers we will deduce this result from a distribution result on divisors of random sections of positive line bundles in complex analysis. As an application, we will give a new equidistribution result for the zero sets of integer polynomials. Finally, we will express the arithmetic intersection number of arithmetically ample hermitian line bundles as a limit of classical geometric intersection numbers over the finite fibers.
CRIPP-VQA: Counterfactual Reasoning about Implicit Physical Properties via Video Question Answering

Videos often capture objects, their visible properties, their motion, and the interactions between different objects. Objects also have physical properties such as mass, which the imaging pipeline is unable to directly capture. However, these properties can be estimated by utilizing cues from relative object motion and the dynamics introduced by collisions. In this paper, we introduce CRIPP-VQA, a new video question answering dataset for reasoning about the implicit physical properties of objects in a scene. CRIPP-VQA contains videos of objects in motion, annotated with questions that involve counterfactual reasoning about the effect of actions, questions about planning in order to reach a goal, and descriptive questions about visible properties of objects. The CRIPP-VQA test set enables evaluation under several out-of-distribution settings – videos with objects with masses, coefficients of friction, and initial velocities that are not observed in the training distribution. Our experiments reveal a surprising and significant performance gap in terms of answering questions about implicit properties (the focus of this paper) and explicit properties of objects (the focus of prior work).
LensWatch. I. Resolved HST Observations and Constraints on the Strongly Lensed Type Ia Supernova 2022qmx (“SN Zwicky”)

Supernovae (SNe) that have been multiply imaged by gravitational lensing are rare and powerful probes for cosmology. Each detection is an opportunity to develop the critical tools and methodologies needed as the sample of lensed SNe increases by orders of magnitude with the upcoming Vera C. Rubin Observatory and Nancy Grace Roman Space Telescope. The latest such discovery is of the quadruply imaged Type Ia SN 2022qmx (aka, “SN Zwicky”) at z = 0.3544. SN Zwicky was discovered by the Zwicky Transient Facility in spatially unresolved data. Here we present follow-up Hubble Space Telescope observations of SN Zwicky, the first from the multicycle “LensWatch (www.lenswatch.org)” program. We measure photometry for each of the four images of SN Zwicky, which are resolved in three WFC3/UVIS filters (F475W, F625W, and F814W) but unresolved with WFC3/IR F160W, and present an analysis of the lensing system using a variety of independent lens modeling methods. We find consistency between lens-model-predicted time delays (≲1 day), and delays estimated with the single epoch of Hubble Space Telescope colors (≲3.5 days), including the uncertainty from chromatic microlensing (∼1–1.5 days). Our lens models converge to an Einstein radius of θE=(0.168−0.005+0.009)″ , the smallest yet seen in a lensed SN system. The “standard candle” nature of SN Zwicky provides magnification estimates independent of the lens modeling that are brighter than predicted by ∼1.7−0.6+0.8 mag and ∼0.9−0.6+0.8 mag for two of the four images, suggesting significant microlensing and/or additional substructure beyond the flexibility of our image-position mass models.