Miracle-dz/UniFAR-FTUs huggingface dataset:
Survivability of amorphous ice in comets depends on the latent heat of crystallization of impure water ice

Comets are believed to have amorphous rather than crystalline ice at the epoch of their accretion. Cometary ice contains some impurities that govern the latent heat of ice crystallization, Lcry. However, it is still controversial whether the crystallization process is exothermic or endothermic. In this study, we perform one-dimensional simulations of the thermal evolution of kilometer-sized comets and investigate the effect of the latent heat. We find that the depth at which amorphous ice can survive significantly depends on the latent heat of ice crystallization. Assuming the cometary radius of 2 km, the depth of the amorphous ice mantle is approximately 100 m when the latent heat is positive (i.e., the exothermic case with Lcry = +9 × 104 J kg−1). In contrast, when we consider the impure ice representing the endothermic case with Lcry = −9 × 104 J kg−1, the depth of the amorphous ice mantle could exceed 1 km. Although our numerical results indicate that these depths depend on the size and the accretion age of comets, the depth in a comet with the negative latent heat is a few to several times larger than in the positive case for a given comet size. This work suggests that the spatial distribution of the ice crystallinity in a comet nucleus depends on the latent heat, which can be different from the previous estimates assuming pure water ice.
Synthetic spectra for Lyman-$\alpha$ forest analysis in the Dark Energy Spectroscopic Instrument

Synthetic data sets are used in cosmology to test analysis procedures, to verify that systematic errors are well understood and to demonstrate that measurements are unbiased. In this work we describe the methods used to generate synthetic datasets of Lyman-$\alpha$ quasar spectra aimed for studies with the Dark Energy Spectroscopic Instrument (DESI). In particular, we focus on demonstrating that our simulations reproduces important features of real samples, making them suitable to test the analysis methods to be used in DESI and to place limits on systematic effects on measurements of Baryon Acoustic Oscillations (BAO). We present a set of mocks that reproduce the statistical properties of the DESI early data set with good agreement. Additionally, we use full survey synthetic data to forecast the BAO scale constraining power with DESI.
Representing maps for semibounded forms and their Lebesgue type decompositions

For a semibounded sesquilinear form ${\mathfrak t}$ in a Hilbert space ${\mathfrak H}$ there exists a representing map $Q$ from ${\mathfrak H}$ to another Hilbert space ${\mathfrak K}$, such that ${\mathfrak t}[\varphi, \psi]-c(\varphi, \psi)=(Q\varphi,Q\psi)$, $\varphi,\psi \in {\rm dom\,}{\mathfrak t}$, with $c \in {\mathbb R}$ a lower bound of ${\mathfrak t}$. Representing maps offer a simplifying tool to study general semibounded forms. By means of representing maps closedness, closability, and singularity of ${\mathfrak t}$ are immediately translated into the corresponding properties of the operator $Q$, and vice versa. Also properties of sum decompositions ${\mathfrak t}={\mathfrak t}_1+{\mathfrak t}_2$ of a nonnegative form ${\mathfrak t}$ with two other nonnegative forms ${\mathfrak t}_1$ and ${\mathfrak t}_2$ in ${\mathfrak H}$ can be analyzed by means of associated nonnegative contractions $K\in {\mathbf B}({\mathfrak K})$. This helps, for instance, to establish an explicit operator theoretic characterization for the summands ${\mathfrak t}_1$ and ${\mathfrak t}_2$ to be, or not to be, mutually singular. Such sum decompositions are used to study characteristic properties of the so-called Lebesgue type decompositions of semibounded forms ${\mathfrak t}$, where ${\mathfrak t}_1$ is closable and ${\mathfrak t}_2$ singular; in particular, this includes the Lebesgue decomposition of a semibounded form due to B. Simon. Furthermore, for a semibounded form ${\mathfrak t}$ with its representing map $Q$ it will be shown that the corresponding semibounded selfadjoint relation $Q^*Q^{**} +c$ is uniquely determined by a limit version of the classical representation theorem for the form ${\mathfrak t}$, being studied by W. Arendt and T. ter Elst in a sectorial context. Via representing maps a full treatment is given of the convergence of monotone sequences of semibounded forms.
A note on the $L^p$-Sobolev inequality

The usual Sobolev inequality in $\mathbb{R}^N$, asserts that $\|\nabla u\|_{L^p(\mathbb{R}^N)} \geq \mathcal{S}\|u\|_{L^{p^*}(\mathbb{R}^N)}$ for $1<p<N$ and $p^*=\frac{pN}{N-p}$, with $\mathcal{S}$ being the sharp constant. This note is concerned, instead, with function restricted to bounded domain $\Omega\subset \mathbb{R}^N$. Based on the recent work of Figalli and Zhang [Duke Math. J., 2022], a remainder term with weak norm is established \[ \frac{\|\nabla u\|_{L^p(\Omega)}}{\|u\|_{L^{p^*}(\Omega)}} -\mathcal{S} \geq \mathcal{C} \left(\frac{\|u\|_{L^{\bar{p}}_w(\Omega)}} {\|u\|_{L^{p^*}(\Omega)}}\right)^{\max\{2,p\}},\quad \forall u\in C^\infty_0(\Omega)\setminus\{0\}, \] for some $\mathcal{C}=\mathcal{C}(N,p,\Omega)>0$, where $\bar{p}=p^*(p-1)/p$ and $\|\cdot\|_{L^{\bar{p}}_w(\Omega)}$ denotes the weak $L^{\bar{p}}$-norm. Furthermore, the weak norm can not be replaced by the strong norm. This result answers the long-standing open problem raised by Bianchi and Egnell [J. Funct. Anal. , 1991].
Evaluation is all you need. Prompting Generative Large Language Models for Annotation Tasks in the Social Sciences. A Primer using Open Models

This paper explores the use of open generative Large Language Models (LLMs) for annotation tasks in the social sciences. The study highlights the challenges associated with proprietary models, such as limited reproducibility and privacy concerns, and advocates for the adoption of open (source) models that can be operated on independent devices. Two examples of annotation tasks, sentiment analysis in tweets and identification of leisure activities in childhood aspirational essays are provided. The study evaluates the performance of different prompting strategies and models (neural-chat-7b-v3-2, Starling-LM-7B-alpha, openchat_3.5, zephyr-7b-alpha and zephyr-7b-beta). The results indicate the need for careful validation and tailored prompt engineering. The study highlights the advantages of open models for data privacy and reproducibility.
Learn to integrate parts for whole through correlated neural variability

Sensory perception originates from the responses of sensory neurons, which react to a collection of sensory signals linked to various physical attributes of a singular perceptual object. Unraveling how the brain extracts perceptual information from these neuronal responses is a pivotal challenge in both computational neuroscience and machine learning. Here we introduce a statistical mechanical theory, where perceptual information is first encoded in the correlated variability of sensory neurons and then reformatted into the firing rates of downstream neurons. Applying this theory, we illustrate the encoding of motion direction using neural covariance and demonstrate high-fidelity direction recovery by spiking neural networks. Networks trained under this theory also show enhanced performance in classifying natural images, achieving higher accuracy and faster inference speed. Our results challenge the traditional view of neural covariance as a secondary factor in neural coding, highlighting its potential influence on brain function.
DiffMorph: Text-less Image Morphing with Diffusion Models

Text-conditioned image generation models are a prevalent use of AI image synthesis, yet intuitively controlling output guided by an artist remains challenging. Current methods require multiple images and textual prompts for each object to specify them as concepts to generate a single customized image. On the other hand, our work, \verb|DiffMorph|, introduces a novel approach that synthesizes images that mix concepts without the use of textual prompts. Our work integrates a sketch-to-image module to incorporate user sketches as input. \verb|DiffMorph| takes an initial image with conditioning artist-drawn sketches to generate a morphed image. We employ a pre-trained text-to-image diffusion model and fine-tune it to reconstruct each image faithfully. We seamlessly merge images and concepts from sketches into a cohesive composition. The image generation capability of our work is demonstrated through our results and a comparison of these with prompt-based image generation.
Inferring community structure in attributed hypergraphs using stochastic block models

Hypergraphs are a representation of complex systems involving interactions among more than two entities and allow to investigation of higher-order structure and dynamics in real-world complex systems. Community structure is a common property observed in empirical networks in various domains. Stochastic block models have been employed to investigate community structure in networks. Node attribute data, often accompanying network data, has been found to potentially enhance the learning of community structure in dyadic networks. In this study, we develop a statistical framework that incorporates node attribute data into the learning of community structure in a hypergraph, employing a stochastic block model. We demonstrate that our model, which we refer to as HyperNEO, enhances the learning of community structure in synthetic and empirical hypergraphs when node attributes are sufficiently associated with the communities. Furthermore, we found that applying a dimensionality reduction method, UMAP, to the learned representations obtained using stochastic block models, including our model, maps nodes into a two-dimensional vector space while largely preserving community structure in empirical hypergraphs. We expect that our framework will broaden the investigation and understanding of higher-order community structure in real-world complex systems.
Stochastic Optimization under Hidden Convexity

In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from optimal control, revenue and inventory management, to convex reinforcement learning all admit such a hidden convex structure. Unfortunately, in the majority of applications considered, the map $c(\cdot)$ is unavailable or implicit; therefore, directly solving the convex reformulation is not possible. On the other hand, the stochastic gradients with respect to the original variable are often easy to obtain. Motivated by these observations, we examine the basic projected stochastic (sub-) gradient methods for solving such problems under hidden convexity. We provide the first sample complexity guarantees for global convergence in smooth and non-smooth settings. Additionally, in the smooth setting, we improve our results to the last iterate convergence in terms of function value gap using the momentum variant of projected stochastic gradient descent.
A Survey on Graph Neural Networks in Intelligent Transportation Systems

Intelligent Transportation System (ITS) is vital in improving traffic congestion, reducing traffic accidents, optimizing urban planning, etc. However, due to the complexity of the traffic network, traditional machine learning and statistical methods are relegated to the background. With the advent of the artificial intelligence era, many deep learning frameworks have made remarkable progress in various fields and are now considered effective methods in many areas. As a deep learning method, Graph Neural Networks (GNNs) have emerged as a highly competitive method in the ITS field since 2019 due to their strong ability to model graph-related problems. As a result, more and more scholars pay attention to the applications of GNNs in transportation domains, which have shown excellent performance. However, most of the research in this area is still concentrated on traffic forecasting, while other ITS domains, such as autonomous vehicles and urban planning, still require more attention. This paper aims to review the applications of GNNs in six representative and emerging ITS domains: traffic forecasting, autonomous vehicles, traffic signal control, transportation safety, demand prediction, and parking management. We have reviewed extensive graph-related studies from 2018 to 2023, summarized their methods, features, and contributions, and presented them in informative tables or lists. Finally, we have identified the challenges of applying GNNs to ITS and suggested potential future directions.
Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Laws

Large language model (LLM) scaling laws are empirical formulas that estimate changes in model quality as a result of increasing parameter count and training data. However, these formulas, including the popular DeepMind Chinchilla scaling laws, neglect to include the cost of inference. We modify the Chinchilla scaling laws to calculate the optimal LLM parameter count and pre-training data size to train and deploy a model of a given quality and inference demand. We conduct our analysis both in terms of a compute budget and real-world costs and find that LLM researchers expecting reasonably large inference demand (~1B requests) should train models smaller and longer than Chinchilla-optimal.
Stochastic Gradient Descent for Additive Nonparametric Regression

This paper introduces an iterative algorithm for training additive models that enjoys favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient descent, applied to the coefficients of a truncated basis expansion of the component functions. We show that the resulting estimator satisfies an oracle inequality that allows for model mis-specification. In the well-specified setting, by choosing the learning rate carefully across three distinct stages of training, we demonstrate that its risk is minimax optimal in terms of the dependence on the dimensionality of the data and the size of the training sample. We further illustrate the computational benefits by comparing the approach with traditional backfitting on two real-world datasets.
An Empirical Study of Scaling Law for OCR

The laws of model size, data volume, computation and model performance have been extensively studied in the field of Natural Language Processing (NLP). However, the scaling laws in Optical Character Recognition (OCR) have not yet been investigated. To address this, we conducted comprehensive studies that involved examining the correlation between performance and the scale of models, data volume and computation in the field of text recognition.Conclusively, the study demonstrates smooth power laws between performance and model size, as well as training data volume, when other influencing factors are held constant. Additionally, we have constructed a large-scale dataset called REBU-Syn, which comprises 6 million real samples and 18 million synthetic samples. Based on our scaling law and new dataset, we have successfully trained a scene text recognition model, achieving a new state-ofthe-art on 6 common test benchmarks with a top-1 average accuracy of 97.42%. The models and dataset are publicly available at https://github.com/large-ocr-model/large-ocr-model.github. io.
Directional flow in perivascular networks: Mixed finite elements for reduced-dimensional models on graphs

The flow of cerebrospinal fluid through the perivascular spaces of the brain is believed to play a crucial role in eliminating toxic waste proteins. While the driving forces of this flow have been enigmatic, experiments have shown that arterial wall motion is central. In this work, we present a network model for simulating pulsatile fluid flow in perivascular networks. We establish the well-posedness of this model in the primal and dual mixed variational settings, and show how it can be discretized using mixed finite elements. Further, we utilize this model to investigate fundamental questions concerning the physical mechanisms governing perivascular fluid flow. Notably, our findings reveal that arterial pulsations can induce directional flow in branching perivascular networks.
6D-Diff: A Keypoint Diffusion Framework for 6D Object Pose Estimation

Estimating the 6D object pose from a single RGB image often involves noise and indeterminacy due to challenges such as occlusions and cluttered backgrounds. Meanwhile, diffusion models have shown appealing performance in generating high-quality images from random noise with high indeterminacy through step-by-step denoising. Inspired by their denoising capability, we propose a novel diffusion-based framework (6D-Diff) to handle the noise and indeterminacy in object pose estimation for better performance. In our framework, to establish accurate 2D-3D correspondence, we formulate 2D keypoints detection as a reverse diffusion (denoising) process. To facilitate such a denoising process, we design a Mixture-of-Cauchy-based forward diffusion process and condition the reverse process on the object features. Extensive experiments on the LM-O and YCB-V datasets demonstrate the effectiveness of our framework.
Quantifying intra-tumoral genetic heterogeneity of glioblastoma toward precision medicine using MRI and a data-inclusive machine learning algorithm

Glioblastoma (GBM) is one of the most aggressive and lethal human cancers. Intra-tumoral genetic heterogeneity poses a significant challenge for treatment. Biopsy is invasive, which motivates the development of non-invasive, MRI-based machine learning (ML) models to quantify intra-tumoral genetic heterogeneity for each patient. This capability holds great promise for enabling better therapeutic selection to improve patient outcomes. We proposed a novel Weakly Supervised Ordinal Support Vector Machine (WSO-SVM) to predict regional genetic alteration status within each GBM tumor using MRI. WSO-SVM was applied to a unique dataset of 318 image-localized biopsies with spatially matched multiparametric MRI from 74 GBM patients. The model was trained to predict the regional genetic alteration of three GBM driver genes (EGFR, PDGFRA, and PTEN) based on features extracted from the corresponding region of five MRI contrast images. For comparison, a variety of existing ML algorithms were also applied. The classification accuracy of each gene was compared between the different algorithms. The SHapley Additive exPlanations (SHAP) method was further applied to compute contribution scores of different contrast images. Finally, the trained WSO-SVM was used to generate prediction maps within the tumoral area of each patient to help visualize the intra-tumoral genetic heterogeneity. This study demonstrated the feasibility of using MRI and WSO-SVM to enable non-invasive prediction of intra-tumoral regional genetic alteration for each GBM patient, which can inform future adaptive therapies for individualized oncology.
Two new mixture representations for the generalized inverse Gaussian distribution and their applications

The generalized inverse Gaussian, denoted $\mathrm{GIG}(p, a, b)$, is a flexible family of distributions that includes the gamma, inverse gamma, and inverse Gaussian distributions as special cases. In this article, we derive two novel mixture representations for the $\mathrm{GIG}(p, a, b)$: one that expresses the distribution as a continuous mixture of inverse Gaussians and another one that expresses it as a continuous mixture of truncated exponentials. Beyond their conceptual interest, these representations are useful for random number generation. We use the first representation to derive a geometrically ergodic Gibbs sampler whose stationary distribution is $\mathrm{GIG}(p, a, b)$, and the second one to define a recursive algorithm to generate exact independent draws from the distribution for half-integer $p$. Additionally, the second representation gives rise to a recursive algorithm for evaluating the cumulative distribution function of the $\mathrm{GIG}(p, a, b)$ for half-integer $p$. The algorithms are simple and can be easily implemented in standard programming languages.
Unsupervised Outlier Detection using Random Subspace and Subsampling Ensembles of Dirichlet Process Mixtures

Probabilistic mixture models are acknowledged as a valuable tool for unsupervised outlier detection owing to their interpretability and intuitive grounding in statistical principles. Within this framework, Dirichlet process mixture models emerge as a compelling alternative to conventional finite mixture models for both clustering and outlier detection tasks. However, despite their evident advantages, the widespread adoption of Dirichlet process mixture models in unsupervised outlier detection has been hampered by challenges related to computational inefficiency and sensitivity to outliers during the construction of detectors. To tackle these challenges, we propose a novel outlier detection method based on ensembles of Dirichlet process Gaussian mixtures. The proposed method is a fully unsupervised algorithm that capitalizes on random subspace and subsampling ensembles, not only ensuring efficient computation but also enhancing the robustness of the resulting outlier detector. Moreover, the proposed method leverages variational inference for Dirichlet process mixtures to ensure efficient and fast computation. Empirical studies with benchmark datasets demonstrate that our method outperforms existing approaches for unsupervised outlier detection.
Communication-Efficient Federated Learning for LEO Constellations Integrated with HAPs Using Hybrid NOMA-OFDM

—Space AI has become increasingly important and sometimes even necessary for government, businesses, and society. An active research topic under this mission is integrating federated learning (FL) with satellite communications (SatCom) so that numerous low Earth orbit (LEO) satellites can collab-oratively train a machine learning model. However, the special communication environment of SatCom leads to a very slow FL training process up to days and weeks. This paper proposes NomaFedHAP, a novel FL-SatCom approach tailored to LEO satellites, that (1) utilizes high-altitude platforms (HAPs) as distributed parameter servers ( PS s) to enhance satellite visibility, and (2) introduces non-orthogonal multiple access (NOMA) into LEO to enable fast and bandwidth-efficient model transmissions. In addition, NomaFedHAP includes (3) a new communication topology that exploits HAPs to bridge satellites among different orbits to mitigate the Doppler shift, and (4) a new FL model aggregation scheme that optimally balances models between different orbits and shells. Moreover, we (5) derive a closed-form expression of the outage probability for satellites in near and far shells, as well as for the entire system. Our extensive simulations have validated the mathematical analysis and demonstrated the superior performance of NomaFedHAP in achieving fast and efficient FL model convergence with high accuracy as compared to the state-of-the-art.