Miracle-dz/UniFAR-FTUs huggingface dataset:
Integral equation methods for acoustic scattering by fractals

We study sound-soft time-harmonic acoustic scattering by general scatterers, including fractal scatterers, in 2D and 3D space. For an arbitrary compact scatterer $\Gamma$ we reformulate the Dirichlet boundary value problem for the Helmholtz equation as a first kind integral equation (IE) on $\Gamma$ involving the Newton potential. The IE is well-posed, except possibly at a countable set of frequencies, and reduces to existing single-layer boundary IEs when $\Gamma$ is the boundary of a bounded Lipschitz open set, a screen, or a multi-screen. When $\Gamma$ is uniformly of $d$-dimensional Hausdorff dimension in a sense we make precise (a $d$-set), the operator in our equation is an integral operator on $\Gamma$ with respect to $d$-dimensional Hausdorff measure, with kernel the Helmholtz fundamental solution, and we propose a piecewise-constant Galerkin discretization of the IE, which converges in the limit of vanishing mesh width. When $\Gamma$ is the fractal attractor of an iterated function system of contracting similarities we prove convergence rates under assumptions on $\Gamma$ and the IE solution, and describe a fully discrete implementation using recently proposed quadrature rules for singular integrals on fractals. We present numerical results for a range of examples and make our software available as a Julia code.
Automated CVE Analysis for Threat Prioritization and Impact Prediction

The Common Vulnerabilities and Exposures (CVE) are pivotal information for proactive cybersecurity measures, including service patching, security hardening, and more. However, CVEs typically offer low-level, product-oriented descriptions of publicly disclosed cybersecurity vulnerabilities, often lacking the essential attack semantic information required for comprehensive weakness characterization and threat impact estimation. This critical insight is essential for CVE prioritization and the identification of potential countermeasures, particularly when dealing with a large number of CVEs. Current industry practices involve manual evaluation of CVEs to assess their attack severities using the Common Vulnerability Scoring System (CVSS) and mapping them to Common Weakness Enumeration (CWE) for potential mitigation identification. Unfortunately, this manual analysis presents a major bottleneck in the vulnerability analysis process, leading to slowdowns in proactive cybersecurity efforts and the potential for inaccuracies due to human errors. In this research, we introduce our novel predictive model and tool (called CVEDrill) which revolutionizes CVE analysis and threat prioritization. CVEDrill accurately estimates the CVSS vector for precise threat mitigation and priority ranking and seamlessly automates the classification of CVEs into the appropriate CWE hierarchy classes. By harnessing CVEDrill, organizations can now implement cybersecurity countermeasure mitigation with unparalleled accuracy and timeliness, surpassing in this domain the capabilities of state-of-the-art tools like ChaptGPT.
Continual Improvement of Threshold-Based Novelty Detection

When evaluated in dynamic, open-world situations, neural networks struggle to detect unseen classes. This issue complicates the deployment of continual learners in realistic environments where agents are not explicitly informed when novel categories are encountered. A common family of techniques for detecting novelty relies on thresholds of similarity between observed data points and the data used for training. However, these methods often require manually specifying (ahead of time) the value of these thresholds, and are therefore incapable of adapting to the nature of the data. We propose a new method for automatically selecting these thresholds utilizing a linear search and leave-one-out cross-validation on the ID classes. We demonstrate that this novel method for selecting thresholds results in improved total accuracy on MNIST, Fashion MNIST, and CIFAR-10.
Resilient VAE: Unsupervised Anomaly Detection at the SLAC Linac Coherent Light Source

Significant advances in utilizing deep learning for anomaly detection have been made in recent years. However, these methods largely assume the existence of a normal training set (i.e., uncontaminated by anomalies) or even a completely labeled training set. In many complex engineering systems, such as particle accelerators, labels are sparse and expensive; in order to perform anomaly detection in these cases, we must drop these assumptions and utilize a completely unsupervised method. This paper introduces the Resilient Variational Autoencoder (ResVAE), a deep generative model specifically designed for anomaly detection. ResVAE exhibits resilience to anomalies present in the training data and provides feature-level anomaly attribution. During the training process, ResVAE learns the anomaly probability for each sample as well as each individual feature, utilizing these probabilities to effectively disregard anomalous examples in the training data. We apply our proposed method to detect anomalies in the accelerator status at the SLAC Linac Coherent Light Source (LCLS). By utilizing shot-to-shot data from the beam position monitoring system, we demonstrate the exceptional capability of ResVAE in identifying various types of anomalies that are visible in the accelerator.
Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields

Neural Radiance Fields (NeRFs) have shown promise in applications like view synthesis and depth estimation, but learning from multiview images faces inherent uncertainties. Current methods to quantify them are either heuristic or computationally demanding. We introduce BayesRays, a post-hoc framework to evaluate uncertainty in any pre-trained NeRF without modifying the training process. Our method establishes a volumetric uncertainty field using spatial perturbations and a Bayesian Laplace approximation. We derive our algorithm statistically and show its superior performance in key metrics and applications. Additional results available at: https://bayesrays.github. io.
Euler Characteristics and Homotopy Types of Definable Sublevel Sets

Given a continuous definable function $f: S \to \mathbb{R}$ on a definable set $S$, we study sublevel sets of the form $S^f_t = \{x \in S: f(x) \leq t\}$ for all $t \in \mathbb{R}$. Using o-minimal structures, we prove that the Euler characteristic of $S^f_t$ is right continuous with respect to $t$. Furthermore, when $S$ is compact, we show that $S^f_{t+\delta}$ deformation retracts to $S^f_t$ for all sufficiently small $\delta>0$. Applying these results, we also characterize the relationship between the concepts of Euler characteristic transform and smooth Euler characteristic transform in topological data analysis.
Harmonic chain far from equilibrium: single-file diffusion, long-range order, and hyperuniformity

In one-dimensional many-particle systems, diffusion is strongly suppressed because particles cannot bypass each other. For this reason, the mean-square displacement (MSD) increases in proportion to the square of time, ${\rm MSD}(t)\sim t^{1/2}$ in equilibrium. This phenomenon is called single-file diffusion. Single-file diffusion is observed even in the harmonic lattice, which prevents the existence of long-range order in one dimension. We here study single-file diffusion of the harmonic chain far from equilibrium. We consider the following four types of driving forces that do not satisfy the detailed balance: (i) temporally correlated noise with the power-low Fourier-spectrum $D(\omega)\sim \omega^{-2\alpha}$, (ii) center-of-mass conserving noise, (iii) periodic driving force, and (iv) periodic deformations of particles. For the driving force (i) with $\alpha>-1/4$, we observe ${\rm MSD}(t)\sim t^{1/2+2\alpha}$ for large $t$. On the other hand, for the driving forces (i) with $\alpha<-1/4$ and (ii)-(iv), ${\rm MSD}$ remains finite. As a consequence, the harmonic chain exhibits the long-range order even in one dimension, which is prohibited by the Mermin-Wagner theorem in equilibrium. We also discuss that the model shows hyperuniformity when driven by the driving forces (i) with $\alpha<0$ and (ii)-(iv).
Rubric-Specific Approach to Automated Essay Scoring with Augmentation Training

Neural based approaches to automatic evaluation of subjective responses have shown superior performance and efficiency compared to traditional rule-based and feature engineering oriented solutions. However, it remains unclear whether the suggested neural solutions are sufficient replacements of human raters as we find recent works do not properly account for rubric items that are essential for automated essay scoring during model training and validation. In this paper, we propose a series of data augmentation operations that train and test an automated scoring model to learn features and functions overlooked by previous works while still achieving state-of-the-art performance in the Automated Student Assessment Prize dataset.
Incorporating Dictionaries into a Neural Network Architecture to Extract COVID-19 Medical Concepts From Social Media

We investigate the potential benefit of incorporating dictionary information into a neural network architecture for natural language processing. In particular, we make use of this architecture to extract several concepts related to COVID-19 from an on-line medical forum. We use a sample from the forum to manually curate one dictionary for each concept. In addition, we use MetaMap, which is a tool for extracting biomedical concepts, to identify a small number of semantic concepts. For a supervised concept extraction task on the forum data, our best model achieved a macro $F_1$ score of 90\%. A major difficulty in medical concept extraction is obtaining labelled data from which to build supervised models. We investigate the utility of our models to transfer to data derived from a different source in two ways. First for producing labels via weak learning and second to perform concept extraction. The dataset we use in this case comprises COVID-19 related tweets and we achieve an $F_1$ score 81\% for symptom concept extraction trained on weakly labelled data. The utility of our dictionaries is compared with a COVID-19 symptom dictionary that was constructed directly from Twitter. Further experiments that incorporate BERT and a COVID-19 version of BERTweet demonstrate that the dictionaries provide a commensurate result. Our results show that incorporating small domain dictionaries to deep learning models can improve concept extraction tasks. Moreover, models built using dictionaries generalize well and are transferable to different datasets on a similar task.
Signatures of Bayesian inference emerge from energy efficient synapses

Biological synaptic transmission is unreliable, and this unreliability likely degrades neural circuit performance. While there are biophysical mechanisms that can increase reliability, for instance by increasing vesicle release probability, these mechanisms cost energy. We examined four such mechanisms along with the associated scaling of the energetic costs. We then embedded these energetic costs for reliability in artificial neural networks (ANN) with trainable stochastic synapses, and trained these networks on standard image classification tasks. The resulting networks revealed a tradeoff between circuit performance and the energetic cost of synaptic reliability. Additionally, the optimised networks exhibited two testable predictions consistent with pre-existing experimental data. Specifically, synapses with lower variability tended to have 1) higher input firing rates and 2) lower learning rates. Surprisingly, these predictions also arise when synapse statistics are inferred through Bayesian inference. Indeed, we were able to find a formal, theoretical link between the performance-reliability cost tradeoff and Bayesian inference. This connection suggests two incompatible possibilities: evolution may have chanced upon a scheme for implementing Bayesian inference by optimising energy efficiency, or alternatively, energy efficient synapses may display signatures of Bayesian inference without actually using Bayes to reason about uncertainty.
Magnetic Navigation Using Attitude-Invariant Magnetic Field Information for Loop Closure Detection

Indoor magnetic fields are a combination of Earth's magnetic field and disruptions induced by ferromag-netic objects, such as steel structural components in buildings. As a result of these disruptions, pervasive in indoor spaces, mag-netic field data is often omitted from navigation algorithms in indoor environments. This paper leverages the spatially-varying disruptions to Earth's magnetic field to extract positional information for use in indoor navigation algorithms. The algorithm uses a rate gyro and an array of four magnetometers to estimate the robot's pose. Additionally, the magnetometer array is used to compute attitude-invariant measurements associated with the magnetic field and its gradient. These measurements are used to detect loop closure points. Experimental results indicate that the proposed approach can estimate the pose of a ground robot in an indoor environment within meter accuracy.
Thermal Degradation Characteristics of Rapeseed Biodiesel And Its Blends With Petroleum Diesel

Abstract Biodiesel is always blended with petroleum diesel to serve as the transport fuel, to obtain the specific impact of petroleum diesel addition on thermal degradation for biodiesel; in this study, the thermal degradation characteristics of biodiesel and biodiesel blends with diesel are investigated by thermogravimetric analysis at heating rates of 10, 15, and 20 K min−1 in the temperature range of 298 to 873 K. The kinetic parameters of activation energy are calculated based on the iso-conversional method, namely the Friedman method and Flynn–Wall–Ozawa method, and the reaction order is determined by Avrami theory. In addition, the thermodynamic parameters of enthalpy, entropy, and Gibbs-free energy are also calculated.
On statistical arbitrage under a conditional factor model of equity returns

We consider a conditional factor model for a multivariate portfolio of United States equities in the context of analysing a statistical arbitrage trading strategy. A state space framework underlies the factor model whereby asset returns are assumed to be a noisy observation of a linear combination of factor values and latent factor risk premia. Filter and state prediction estimates for the risk premia are retrieved in an online way. Such estimates induce filtered asset returns that can be compared to measurement observations, with large deviations representing candidate mean reversion trades. Further, in that the risk premia are modelled as time-varying quantities, non-stationarity in returns is de facto captured. We study an empirical trading strategy respectful of transaction costs, and demonstrate performance over a long history of 29 years, for both a linear and a non-linear state space model. Our results show that the model is competitive relative to the results of other methods, including simple benchmarks and other cutting-edge approaches as published in the literature. Also of note, while strategy performance degradation is noticed through time -- especially for the most recent years -- the strategy continues to offer compelling economics, and has scope for further advancement.
Deep Reinforcement Learning from Hierarchical Weak Preference Feedback

Reward design is a fundamental, yet challenging aspect of reinforcement learning (RL). Researchers typically utilize feedback signals from the environment to handcraft a reward function, but this process is not always effective due to the varying scale and intricate dependencies of the feedback signals. This paper shows by exploiting certain structures, one can ease the reward design process. Specifically, we propose a hierarchical reward modeling framework -- HERON for scenarios: (I) The feedback signals naturally present hierarchy; (II) The reward is sparse, but with less important surrogate feedback to help policy learning. Both scenarios allow us to design a hierarchical decision tree induced by the importance ranking of the feedback signals to compare RL trajectories. With such preference data, we can then train a reward model for policy learning. We apply HERON to several RL applications, and we find that our framework can not only train high performing agents on a variety of difficult tasks, but also provide additional benefits such as improved sample efficiency and robustness. Our code is available at \url{https://github.com/abukharin3/HERON}.
Dispersive analysis of the experimental data on the electromagnetic form factor of charged pions at spacelike momenta

The experimental data on the electromagnetic form factor of charged pions available at spacelike momenta are analyzed using the Dispersive Matrix (DM) approach, which describes the momentum dependence of hadronic form factors without introducing any explicit parameterization and includes properly the constraints coming from unitarity and analyticity. The unitary bound is evaluated nonperturbatively making use of the results of lattice QCD simulations of suitable two-point correlation functions contributing to the HVP term of the muon. Thanks to the DM method we determine the pion charge radius from existing spacelike data in a completely model-independent way and consistently with the unitary bound, obtaining $_{DM} = 0.703 \pm 0.027$ fm. This finding differs by $\simeq 1.6$ standard deviations from the latest PDG value $_{PDG} = 0.659 \pm 0.004$ fm, which is dominated by the very precise results of dispersive analyses of timelike data coming from measurements of the cross section of the $e^+ e^- \to \pi^+ \pi^-$ process. We have analyzed the spacelike data using also traditional $z$-expansions, like the Boyd-Grinstein-Lebed (BGL) or Bourrely-Caprini-Lellouch (BCL) fitting functions and adopting a simple procedure that incorporates ab initio the non-perturbative unitary bound in the fitting process. We get $_{BGL} = 0.711 \pm 0.039$ fm and $_{BCL} = 0.709 \pm 0.028$ fm in nice agreement with the DM result. We have addressed also the issue of the onset of perturbative QCD by performing a sensitivity study of the pion form factor at large spacelike momenta, based only on experimental spacelike data and unitarity. Hence, although the leading pQCD behaviour is found to set in only at very large momenta, our DM bands may provide information about the pre-asymptotic effects related to the scale dependence of the pion distribution amplitude.
Panic at the ISCO: the visible accretion disks powering optical variability in ZTF AGN

About 3-10% of Type I active galactic nuclei (AGN) have double-peaked broad Balmer lines in their optical spectra originating from the motion of gas in their accretion disk. Double-peaked profiles arise not only in AGN, but occasionally appear during optical flares from tidal disruption events and changing-state AGN. In this paper we identify 250 double-peaked emitters (DPEs) amongst a parent sample of optically variable broad-line AGN in the Zwicky Transient Facility (ZTF) survey, corresponding to a DPE fraction of 19%. We model spectra of the broad H α emission line regions and provide a catalog of the fitted accretion disk properties for the 250 DPEs. Analysis of power spectra derived from the 5 year ZTF light curves finds that DPEs have similar amplitudes and power law indices to other broad-line AGN, but have lower turnover frequencies. Follow-up spectroscopy of 12 DPEs reveals that ∼ 50% display significant changes in the relative strengths of their red and blue peaks over long 10 − 20 year timescales, indicating that broad-line profile changes arising from spiral arm or hotspot rotation are common amongst optically variable DPEs. Analysis of the accretion disk parameters derived from spectroscopic modeling provides evidence that DPEs are not in a special accretion state, but are simply normal broad-line AGN viewed under the right conditions for the accretion disk to be easily visible. We compare the radio variability properties of the two samples and present radio jet imaging of 3 DPEs with disks of inclination angle ∼ 14 − 35 ° . We discuss some objects with notable light curves or unusual broad line profiles which are outliers amongst the variable DPE population. We include inspiraling SMBH binary candidate SDSSJ1430+2303 in our analysis, and discuss how its photometric and spectroscopic variability is consistent with the disk-emitting AGN population in ZTF.
Amortised Inference in Bayesian Neural Networks

Meta-learning is a framework in which machine learning models train over a set of datasets in order to produce predictions on new datasets at test time. Probabilistic meta-learning has received an abundance of attention from the research community in recent years, but a problem shared by many existing probabilistic meta-models is that they require a very large number of datasets in order to produce high-quality predictions with well-calibrated uncertainty estimates. In many applications, however, such quantities of data are simply not available. In this dissertation we present a significantly more data-efficient approach to probabilistic meta-learning through per-datapoint amortisation of inference in Bayesian neural networks, introducing the Amortised Pseudo-Observation Variational Inference Bayesian Neural Network (APOVI-BNN). First, we show that the approximate posteriors obtained under our amortised scheme are of similar or better quality to those obtained through traditional variational inference, despite the fact that the amortised inference is performed in a single forward pass. We then discuss how the APOVI-BNN may be viewed as a new member of the neural process family, motivating the use of neural process training objectives for potentially better predictive performance on complex problems as a result. Finally, we assess the predictive performance of the APOVI-BNN against other probabilistic meta-models in both a one-dimensional regression problem and in a significantly more complex image completion setting. In both cases, when the amount of training data is limited, our model is the best in its class.
A morphological segmentation approach to determining bar lengths

Bars are important drivers of galaxy evolution, influencing many physical processes and properties. Characterising bars is a difficult task, especially in large-scale surveys. In this work, we propose a novel morphological segmentation technique for determining bar lengths based on deep learning. We develop U-Nets capable of decomposing galaxy images into pixel masks highlighting the regions corresponding to bars and spiral arms. We demonstrate the versatility of this technique through applying our models to galaxy images from two different observational datasets with different source imagery, and to RGB colour and monochromatic galaxy imaging. We apply our models to analyse SDSS and Subaru HSC imaging of barred galaxies from the NA10 and SAMI catalogues in order to determine the dependence of bar length on stellar mass, morphology, redshift and the spin parameter proxy $\lambda _{R_e}$. Based on the predicted bar masks, we show that the relative bar scale length varies with morphology, with early type galaxies hosting longer bars. While bars are longer in more massive galaxies in absolute terms, relative to the galaxy disc they are actually shorter. We also find that the normalised bar length decreases with increasing redshift, with bars in early-type galaxies exhibiting the strongest rate of decline. We show that it is possible to distinguish spiral arms and bars in monochrome imaging, although for a given galaxy the estimated length in monochrome tends to be longer than in colour imaging. Our morphological segmentation technique can be efficiently applied to study bars in large-scale surveys and even in cosmological simulations.