Miracle-dz/UniFAR-FTUs huggingface dataset:
A Study of Stellar Spins in 15 Open Clusters

We analyze spectroscopic and photometric data to determine the projected inclinations of stars in 11 open clusters, placing constraints on the spin-axis distributions of six clusters. We combine these results with four additional clusters studied by Healy & McCullough and Healy et al. to perform an ensemble analysis of their spins. We find that eight out of 10 constrained clusters (80%) have spin-axis orientations consistent with isotropy, and we establish a lower limit of four out of 10 (40%) isotropic clusters at 75% confidence, assuming no correlation of spins between clusters. We also identify two clusters whose spin-axis distributions can be better described by a model consisting of an aligned fraction of stars combined with an isotropic distribution. However, the inclination values of these stars may be influenced by systematic error, and the small number of stars modeled as aligned in these two clusters precludes the interpretation that their stellar subsets are physically aligned. Overall, no cluster displays an unambiguous signature of spin alignment, and 97% of the stars in our sample are consistent with isotropic orientations in their respective clusters. Our results offer support for the dominance of turbulence over ordered rotation in clumps and do not suggest the alignment of rotation axes and magnetic fields in protostars.
What are the Machine Learning best practices reported by practitioners on Stack Exchange?

Machine Learning (ML) is being used in multiple disciplines due to its powerful capability to infer relationships within data. In particular, Software Engineering (SE) is one of those disciplines in which ML has been used for multiple tasks, like software categorization, bugs prediction, and testing. In addition to the multiple ML applications, some studies have been conducted to detect and understand possible pitfalls and issues when using ML. However, to the best of our knowledge, only a few studies have focused on presenting ML best practices or guidelines for the application of ML in different domains. In addition, the practices and literature presented in previous literature (i) are domain-specific (e.g., concrete practices in biomechanics), (ii) describe few practices, or (iii) the practices lack rigorous validation and are presented in gray literature. In this paper, we present a study listing 127 ML best practices systematically mining 242 posts of 14 different Stack Exchange (STE) websites and validated by four independent ML experts. The list of practices is presented in a set of categories related to different stages of the implementation process of an ML-enabled system; for each practice, we include explanations and examples. In all the practices, the provided examples focus on SE tasks. We expect this list of practices could help practitioners to understand better the practices and use ML in a more informed way, in particular newcomers to this new area that sits at the intersection of software engineering and machine learning.
Learning to Rank Normalized Entropy Curves with Differentiable Window Transformation

Recent automated machine learning systems often use learning curves ranking models to inform decisions about when to stop unpromising trials and identify better model configurations. In this paper, we present a novel learning curve ranking model specifically tailored for ranking normalized entropy (NE) learning curves, which are commonly used in online advertising and recommendation systems. Our proposed model, self-Adaptive Curve Transformation augmented Relative curve Ranking (ACTR 2 ), features an adaptive curve transformation layer that transforms raw lifetime NE curves into composite window NE curves with the window sizes adaptively optimized based on both the position on the learning curve and the curve’s dynamics. We also introduce a novel differentiable indexing method for the proposed adaptive curve transformation, which allows gradients with respect to the discrete indices to flow freely through the curve transformation layer, enabling the learned window sizes to be updated flexibly during training. Additionally, we propose a pairwise curve ranking architecture that directly models the difference between the two learning curves and is better at capturing subtle changes in relative performance that may not be evident when modeling each curve individually as the existing approaches did. Our extensive experiments on a real-world NE curve dataset demonstrate the effectiveness of each key component of ACTR 2 and its improved performance over the state-of-the-art.
Direct observation of magnon BEC in an out-of-plane magnetized yttrium iron garnet film

Bose-Einstain condensation occurs at an appropriate density of bosonic particles, depending on their mass and temperature. We were able to experimentally observe the transition from the spin wave regime to the magnon Bose-Einstein condensed state (mBEC) with increasing magnon density by a microwave pumping. We used optical methods to register the spatial distribution of the magnon density and phase. For the first time, a coherent state of stationary magnons was demonstrated far from the region of their excitation.
Lagrangian and Hamiltonian formulations of asymmetric rigid body, considered as a constrained system

This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates or assumptions about the behavior of the rigid body. All the basic quantities and characteristics of a rigid body, as well as the equations of motion and integrals of motion, are obtained from the variational problem by direct and unequivocal calculations within the framework of standard methods of classical mechanics. Several equivalent forms for the equations of motion of rotational degrees of freedom are deduced and discussed on this basis. Using the resulting formulation, we revise some cases of integrability, and discuss a number of peculiar properties, that are not always taken into account when formulating the laws of motion of a rigid body.
Effect of swarm density on collective tracking performance

How does the size of a swarm affect its collective action? Despite being arguably a key parameter, no systematic and satisfactory guiding principles exist to select the number of units required for a given task and environment. Even when limited by practical considerations, system designers should endeavor to identify what a reasonable swarm size should be. Here, we show that this fundamental question is closely linked to that of selecting an appropriate swarm density. Our analysis of the influence of density on the collective performance of a target tracking task reveals different ‘phases’ corresponding to markedly distinct group dynamics. We identify a ‘transition’ phase, in which a complex emergent collective response arises. Interestingly, the collective dynamics within this transition phase exhibit a clear trade-off between exploratory actions and exploitative ones. We show that at any density, the exploration–exploitation balance can be adjusted to maximize the system’s performance through various means, such as by changing the level of connectivity between agents. While the density is the primary factor to be considered, it should not be the sole one to be accounted for when sizing the system. Due to the inherent finite-size effects present in physical systems, we establish that the number of constituents primarily affects system-level properties such as exploitation in the transition phase. These results illustrate that instead of learning and optimizing a swarm’s behavior for a specific set of task parameters, further work should instead concentrate on learning to be adaptive, thereby endowing the swarm with the highly desirable feature of being able to operate effectively over a wide range of circumstances.
Freezing transition and moments of moments of the Riemann zeta function

Moments of moments of the Riemann zeta function, defined by \[ \text{MoM}_T (k,\beta) = \frac{1}{T} \int_T^{2T} \left( \int_{ |h|\leq (\log T)^\theta}|\zeta(\tfrac{1}{2} + i t + ih)|^{2\beta} dh \right)^k dt \] where $k,\beta \geq 0$ and $\theta>-1$, were introduced by Fyodorov and Keating when comparing extreme values of zeta in short intervals to those of characteristic polynomials of random unitary matrices. We study the $k = 2$ case as $T \rightarrow \infty$ and obtain sharp upper bounds for $\text{MoM}_T(2,\beta)$ for all real $0\leq \beta \leq 1$ as well as lower bounds of the conjectured order for all $\beta \geq 0$. In particular, we show that the second moment of moments undergoes a freezing phase transition with critical exponent $\beta = \tfrac{1}{\sqrt{2}}$.
A test of water vapor radiometer‐based troposphere calibration using very long baseline interferometry observations on a 21‐km baseline

Simultaneous very long baseline interferometry (VLBI) and water vapor radiometer (WVR) measurements on a 21-km baseline showed that calibration by WVRs removed a significant fraction of the effect of tropospheric delay fluctuations for these experiments. From comparison of the residual delay variations within scans and between scans, the total tropospheric contribution to the delay residuals for each of the three 5–20 hour sessions was estimated as 1%, 17%, and 10%, with the first value being very uncertain. The observed improvement in rms residual delay from WVR calibration during these three sessions was 4%, 16%, and 2%, respectively. The improvement is consistent with the estimated 2–3 mm path delay precision of current WVRs. The VLBI measurements of natural radio sources were conducted in April and May 1993 at Goldstone, California. Dual-frequency (2.3 and 8.4 GHz) observations were employed to remove the effects of charged particles from the data. Measurements with copointed WVRs, located within 50 m of the axis of each antenna, were performed to test the ability of the WVRs to calibrate line-of-sight path delays. Factors which made WVR performance assessment difficult included the facts that (1) the level of tropospheric fluctuations was smaller than is typical for Goldstone during these experiments, and (2) VLBI delay variations on longer timescales (i.e., over multiple scans) contained uncalibrated instrumental effects (probably a result of slow temperature variations in the VLBI hardware) that were larger than the tropospheric effects.
Nonlinear wave loads on a slender vertical cylinder

The diffraction of water waves by a vertical circular cylinder is considered in the regime where the wave amplitude A and cylinder radius a are of the same order, and both are small compared to the wavelength. The wave slope is small, and a conventional linear analysis applies in the outer domain far from the cylinder. Significant nonlinear effects exist in the complementary inner domain close to the cylinder, associated with the free-surface boundary condition. Using inner coordinates scaled with respect to a, it is shown that the leading-order nonlinear contribution to the velocity potential includes terms proportional to both A2a and A3. The wave load which acts on the cylinder near the free surface includes second- and third-harmonic components which are proportional respectively to A2a2 and A3a. In a conventional perturbation analysis, where A [Lt ] a, these components would be ordered in magnitude corresponding to the different powers of A, but here they are of the same order. The second- and third-order components of the total force are of comparable magnitude for practical values of the wave slope.
Exact Fractional Inference via Re-Parametrization & Interpolation between Tree-Re-Weighted- and Belief Propagation- Algorithms

Inference efforts -- required to compute partition function, $Z$, of an Ising model over a graph of $N$ ``spins"-- are most likely exponential in $N$. Efficient variational methods, such as Belief Propagation (BP) and Tree Re-Weighted (TRW) algorithms, compute $Z$ approximately minimizing respective (BP- or TRW-) free energy. We generalize the variational scheme building a $\lambda$-fractional-homotopy, $Z^{(\lambda)}$, where $\lambda=0$ and $\lambda=1$ correspond to TRW- and BP-approximations, respectively, and $Z^{(\lambda)}$ decreases with $\lambda$ monotonically. Moreover, this fractional scheme guarantees that in the attractive (ferromagnetic) case $Z^{(TRW)}\geq Z^{(\lambda)}\geq Z^{(BP)}$, and there exists a unique (``exact") $\lambda_*$ such that, $Z=Z^{(\lambda_*)}$. Generalizing the re-parametrization approach of \citep{wainwright_tree-based_2002} and the loop series approach of \citep{chertkov_loop_2006}, we show how to express $Z$ as a product, $\forall \lambda:\ Z=Z^{(\lambda)}{\cal Z}^{(\lambda)}$, where the multiplicative correction, ${\cal Z}^{(\lambda)}$, is an expectation over a node-independent probability distribution built from node-wise fractional marginals. Our theoretical analysis is complemented by extensive experiments with models from Ising ensembles over planar and random graphs of medium- and large- sizes. The empirical study yields a number of interesting observations, such as (a) ability to estimate ${\cal Z}^{(\lambda)}$ with $O(N^4)$ fractional samples; (b) suppression of $\lambda_*$ fluctuations with increase in $N$ for instances from a particular random Ising ensemble.
Low regularity error estimates for the time integration of 2D NLS

A filtered Lie splitting scheme is proposed for the time integration of the cubic nonlinear Schr\"odinger equation on the two-dimensional torus $\mathbb{T}^2$. The scheme is analyzed in a framework of discrete Bourgain spaces, which allows us to consider initial data with low regularity; more precisely initial data in $H^s(\mathbb{T}^2)$ with $s>0$. In this way, the usual stability restriction to smooth Sobolev spaces with index $s>1$ is overcome. Rates of convergence of order $\tau^{s/2}$ in $L^2(\mathbb{T}^2)$ at this regularity level are proved. Numerical examples illustrate that these convergence results are sharp.
Energy-Delay Tradeoff in Helper-Assisted NOMA-MEC Systems: A Four-Sided Matching Algorithm

This paper designs a helper-assisted resource allocation strategy in non-orthogonal multiple access (NOMA)-enabled mobile edge computing (MEC) systems, in order to guarantee the quality of service (QoS) of the energy/delay-sensitive user equipments (UEs). To achieve a tradeoff between the energy consumption and the delay, we introduce a novel performance metric, called \emph{energy-delay tradeoff}, which is defined as the weighted sum of energy consumption and delay. The joint optimization of user association, resource block (RB) assignment, power allocation, task assignment, and computation resource allocation is formulated as a mixed-integer nonlinear programming problem with the aim of minimizing the maximal energy-delay tradeoff. Due to the non-convexity of the formulated problem with coupled and 0-1 variables, this problem cannot be directly solved with polynomial complexity. To tackle this challenge, we first decouple the formulated problem into a power allocation, task assignment and computation resource allocation (PATACRA) subproblem. Then, with the solution obtained from the PATACRA subproblem, we equivalently reformulate the original problem as a discrete user association and RB assignment (DUARA) problem. For the PATACRA subproblem, an iterative parametric convex approximation (IPCA) algorithm is proposed. Then, based on the solution obtained from the PATACRA subproblem, we first model the DUARA problem as a four-sided matching problem, and then propose a low-complexity four-sided UE-RB-helper-server matching (FS-URHSM) algorithm. Theoretical analysis demonstrates that the proposed algorithms are guaranteed to converge to stable solutions with polynomial complexity. Finally, simulation results are provided to show the superior performance of our proposed algorithm in terms of the energy consumption and the delay.
ClimaX: A foundation model for weather and climate

Most state-of-the-art approaches for weather and climate modeling are based on physics-informed numerical models of the atmosphere. These approaches aim to model the non-linear dynamics and complex interactions between multiple variables, which are challenging to approximate. Additionally, many such numerical models are computationally intensive, especially when modeling the atmospheric phenomenon at a fine-grained spatial and temporal resolution. Recent data-driven approaches based on machine learning instead aim to directly solve a downstream forecasting or projection task by learning a data-driven functional mapping using deep neural networks. However, these networks are trained using curated and homogeneous climate datasets for specific spatiotemporal tasks, and thus lack the generality of numerical models. We develop and demonstrate ClimaX, a flexible and generalizable deep learning model for weather and climate science that can be trained using heterogeneous datasets spanning different variables, spatio-temporal coverage, and physical groundings. ClimaX extends the Transformer architecture with novel encoding and aggregation blocks that allow effective use of available compute while maintaining general utility. ClimaX is pre-trained with a self-supervised learning objective on climate datasets derived from CMIP6. The pre-trained ClimaX can then be fine-tuned to address a breadth of climate and weather tasks, including those that involve atmospheric variables and spatio-temporal scales unseen during pretraining. Compared to existing data-driven baselines, we show that this generality in ClimaX results in superior performance on benchmarks for weather forecasting and climate projections, even when pretrained at lower resolutions and compute budgets. The source code is available at https://github.com/microsoft/ClimaX.
Modelling Long Range Dependencies in N-D: From Task-Specific to a General Purpose CNN

Performant Convolutional Neural Network (CNN) architectures must be tailored to specific tasks in order to consider the length, resolution, and dimensionality of the input data. In this work, we tackle the need for problem-specific CNN architectures. We present the Continuous Convolutional Neural Network (CCNN): a single CNN able to process data of arbitrary resolution, dimensionality and length without any structural changes. Its key component are its continuous convolutional kernels which model long-range dependencies at every layer, and thus remove the need of current CNN architectures for task-dependent downsampling and depths. We showcase the generality of our method by using the same architecture for tasks on sequential ($1{\rm D}$), visual ($2{\rm D}$) and point-cloud ($3{\rm D}$) data. Our CCNN matches and often outperforms the current state-of-the-art across all tasks considered.
Capitation funding in the public sector

A fundamental requirement of government at all levels—national and local—is to distribute the limited funds that it wishes to spend on particular public services between geographical areas or institutions, which are effectively competitors for such funds. Increasing use is now being made of capitation methods for such purposes, in which a standard estimate of expected expenditure is attached to a citizen with given characteristics. Statistical methods are playing an important role in determining such capitations, but they give rise to profound methodological problems. This paper examines the rationale for capitation and discusses the associated methodological issues. It illustrates the issues raised with two examples taken from the UK public sector: in personal social services and hospital care. Severe limitations of the data mean that small area data are used as the unit of observation, giving rise to considerable complexity in the model to be estimated. As a result, a range of methodologies including two‐stage least squares and multilevel modelling methods are deployed. The paper concludes with a suggestion for an approach which would represent an improvement on current capitation methods, but which would require data on individuals rather than on small areas.
High-Degree Collisional Moments of Inelastic Maxwell Mixtures—Application to the Homogeneous Cooling and Uniform Shear Flow States

The Boltzmann equation for d-dimensional inelastic Maxwell models is considered to determine the collisional moments of the second, third and fourth degree in a granular binary mixture. These collisional moments are exactly evaluated in terms of the velocity moments of the distribution function of each species when diffusion is absent (mass flux of each species vanishes). The corresponding associated eigenvalues as well as cross coefficients are obtained as functions of the coefficients of normal restitution and the parameters of the mixture (masses, diameters and composition). The results are applied to the analysis of the time evolution of the moments (scaled with a thermal speed) in two different nonequilibrium situations: the homogeneous cooling state (HCS) and the uniform (or simple) shear flow (USF) state. In the case of the HCS, in contrast to what happens for simple granular gases, it is demonstrated that the third and fourth degree moments could diverge in time for given values of the parameters of the system. An exhaustive study on the influence of the parameter space of the mixture on the time behavior of these moments is carried out. Then, the time evolution of the second- and third-degree velocity moments in the USF is studied in the tracer limit (namely, when the concentration of one of the species is negligible). As expected, while the second-degree moments are always convergent, the third-degree moments of the tracer species can be also divergent in the long time limit.
Inverse Surfacelet Transform for Image Reconstruction With Constrained-Conjugate Gradient Methods

Image reconstruction is the transformation process from a reduced-order representation to the original image pixel form. In materials characterization, it can be utilized as a method to retrieve material composition information. In our previous work, a surfacelet transform was developed to efficiently represent boundary information in material images with surfacelet coefficients. In this paper, new constrained-conjugate-gradient based image reconstruction methods are proposed as the inverse surfacelet transform. With geometric constraints on boundaries and internal distributions of materials, the proposed methods are able to reconstruct material images from surfacelet coefficients as either lossy or lossless compressions. The results between the proposed and other optimization methods for solving the least-square error inverse problems are compared. [DOI: 10.1115/1.4026376]
The global signal of the 11-year sunspot cycle in the atmosphere: When do we need the QBO?

The global structure and the size of the signal of the 11-year sunspot cycle in the stratosphere and troposphere was examined in earlier studies. The correlations between the solar cycle and heights and temperatures of and at different pressure levels were mainly carried out with the whole data set and only during northern winters the years were separated according to the phase of the Quasi-Biennial Oscillation. Here, this work is expanded and it is shown that the Quasi-Biennial Oscillation must be introduced during northern summers, because the solar signal is very different in the respective phases of the Quasi-Biennial Oscillation, particularly over the tropics and subtropics. The structure of the solar signal in (northern) summer appears to indicate that the mean meridional circulations (Hadley and Brewer-Dobson Circulations) are influenced by the 11-year sunspot cycle, especially during the east phase of the Quasi-Biennial Oscillation. This result may help to find the mechanism through which the solar cycle (and the connected variation of the ultraviolet radiation) can influence the atmosphere.