Miracle-dz/UniFAR-FTUs huggingface dataset:
A Bayesian Approach to Modeling Finite Element Discretization Error

In this work, the uncertainty associated with the finite element discretization error is modeled following the Bayesian paradigm. First, a continuous formulation is derived, where a Gaussian process prior over the solution space is updated based on observations from a finite element discretization. To avoid the computation of intractable integrals, a second, finer, discretization is introduced that is assumed sufficiently dense to represent the true solution field. A prior distribution is assumed over the fine discretization, which is then updated based on observations from the coarse discretization. This yields a posterior distribution with a mean that serves as an estimate of the solution, and a covariance that models the uncertainty associated with this estimate. Two particular choices of prior are investigated: a prior defined implicitly by assigning a white noise distribution to the right-hand side term, and a prior whose covariance function is equal to the Green's function of the partial differential equation. The former yields a posterior distribution with a mean close to the reference solution, but a covariance that contains little information regarding the finite element discretization error. The latter, on the other hand, yields posterior distribution with a mean equal to the coarse finite element solution, and a covariance with a close connection to the discretization error. For both choices of prior a contradiction arises, since the discretization error depends on the right-hand side term, but the posterior covariance does not. We demonstrate how, by rescaling the eigenvalues of the posterior covariance, this independence can be avoided.
Nonlinear multistate tunneling dynamics in a spinor Bose-Einstein condensate

We present an experimental realization of dynamic self-trapping and non-exponential tunneling in a multi-state system consisting of ultracold sodium spinor gases confined in moving optical lattices. Taking advantage of the fact that the tunneling process in the sodium spinor system is resolvable over a broader dynamic energy scale than previously observed in rubidium scalar gases, we demonstrate that the tunneling dynamics in the multi-state system strongly depends on an interaction induced nonlinearity and is influenced by the spin degree of freedom under certain conditions. We develop a rigorous multi-state tunneling model to describe the observed dynamics. Combined with our recent observation of spatially-manipulated spin dynamics, these results open up prospects for alternative multi-state ramps and state transfer protocols.
Lorentzian quantum cosmology from effective spin foams

Effective spin foams provide the computationally most efficient spin foam models yet and are therefore ideally suited for applications e.g. to quantum cosmology. We provide here the first effective spin foam computations of a finite time evolution step in a Lorentzian quantum de Sitter universe. We will consider a set-up which computes the no-boundary wave function, as well as a set-up describing the transition between two finite scale factors. A key property of spin foams is that they implement discrete spectra for the areas. We therefore study the effects that are induced by the discrete spectra. To perform these computations we had to identify a technique to deal with highly oscillating and slowly converging, or even diverging sums. We illustrate here that high order Shanks transformation work very well and are a promising tool for the evaluation of Lorentzian (gravitational) path integrals and spin foam sums.
Using extreme value theory to evaluate the leading pedestrian interval road safety intervention

Improving road safety is hugely important with the number of deaths on the world's roads remaining unacceptably high; an estimated 1.35 million people die each year as a result of road traffic collisions (WHO, 2020). Current practice for treating collision hotspots is almost always reactive: once a threshold level of collisions has been overtopped during some pre-determined observation period, treatment is applied (e.g. road safety cameras). Traffic collisions are rare, so prolonged observation periods are necessary. However, traffic conflicts are more frequent and are a margin of the social cost; hence, traffic conflict before/after studies can be conducted over shorter time periods. We investigate the effect of implementing the leading pedestrian interval (LPI) treatment (Van Houten et al. 2000) at signalised intersections as a safety intervention in a city in north America. Pedestrian-vehicle traffic conflict data were collected from treatment and control sites during the before and after periods. We implement a before/after study on post-encroachment times (PETs) where small PET values denote a near-miss. Hence, extreme value theory is employed to model extremes of our PET processes, with adjustments to the usual modelling framework to account for temporal dependence and treatment effects.
A Qualitative Analysis of Common Practices in Annotations: A Taxonomy and Design Space

Annotations are a vital component of data externalization and collaborative analysis, directing readers' attention to important visual elements. Therefore, it is crucial to understand their design space for effectively annotating visualizations. However, despite their widespread use in visualization, we have identified a lack of a design space for common practices for annotations. In this paper, we present two studies that explore how people annotate visualizations to support effective communication. In the first study, we evaluate how visualization students annotate bar charts when answering high-level questions about the data. Qualitative coding of the resulting annotations generates a taxonomy comprising enclosure, connector, text, mark, and color, revealing how people leverage different visual elements to communicate critical information. We then extend our taxonomy by performing thematic coding on a diverse range of real-world annotated charts, adding trend and geometric annotations to the taxonomy. We then combine the results of these studies into a design space of annotations that focuses on the key elements driving the design choices available when annotating a chart, providing a reference guide for using annotations to communicate insights from visualizations.
Laser-induced alignment of nanoparticles and macromolecules for single-particle-imaging applications

Laser-induced alignment of particles and molecules was long envisioned to support three-dimensional structure determination using single-particle imaging with x-ray free-electron lasers [PRL 92, 198102 (2004)]. However, geometric alignment of isolated macromolecules has not yet been demonstrated. Using molecular modeling, we analyzed and demonstrated how the alignment of large nanorods and proteins is possible with standard laser technology, and performed a comprehensive analysis on the dependence of the degree of alignment on molecular properties and experimental details. Calculations of the polarizability anisotropy of about 150,000 proteins yielded a skew-normal distribution with a location of 1.2, which reveals that most of these proteins can be aligned using appropriate, realistic experimental parameters. Moreover, we explored the dependence of the degree of alignment on experimental parameters such as particle temperature and laser-pulse energy.
Secular dynamics of stellar spin driven by planets inside Kozai–Lidov resonance

In many exoplanetary systems with ‘hot Jupiters’, it is observed that the spin axes of host stars are highly misaligned to planetary orbital axes. In this study, a possible channel is investigated for producing such a misalignment under a hierarchical three-body system, where the evolution of stellar spin is subjected to the gravitational torque induced from the planet inside Kozai–Lidov (KL) resonance. In particular, two special configurations are explored in detail. The first one corresponds to the configuration with planets at KL fixed points, and the second one corresponds to the configurations with planets moving on KL librating cycles. When the planet is located at the KL fixed point, the corresponding Hamiltonian model is of one degree of freedom and there are three branches of libration centres for stellar spin. When the planet is moving on KL cycles, the technique of Poincaré section is taken to reveal global structures of stellar spin in phase space. To understand the complex structures, perturbative treatments are adopted to study rotational dynamics. It shows that analytical structures in phase portraits under the resonant model can agree well with numerical structures arising in Poincaré sections, showing that the complicated dynamics of stellar spin are governed by the primary resonance under the unperturbed Hamiltonian model in combination with the 2:1 (high-order and/or secondary) spin–orbit resonances.
Strategies to exploit XAI to improve classification systems

Explainable Artificial Intelligence (XAI) aims to provide insights into the decision-making process of AI models, allowing users to understand their results beyond their decisions. A significant goal of XAI is to improve the performance of AI models by providing explanations for their decision-making processes. However, most XAI literature focuses on how to explain an AI system, while less attention has been given to how XAI methods can be exploited to improve an AI system. In this work, a set of well-known XAI methods typically used with Machine Learning (ML) classification tasks are investigated to verify if they can be exploited, not just to provide explanations but also to improve the performance of the model itself. To this aim, two strategies to use the explanation to improve a classification system are reported and empirically evaluated on three datasets: Fashion-MNIST, CIFAR10, and STL10. Results suggest that explanations built by Integrated Gradients highlight input features that can be effectively used to improve classification performance.
Pressure consistency for binary hard-sphere mixtures from an integral equation approach

The site-site Ornstein-Zernike equation combined with the Verlet-modified bridge function has been applied to the binary hard sphere mixtures and pressure consistency has been tested. An equation of state has been computed for the case where a packing fraction is $\eta = 0.49$, diameter ratios are $\sigma_{2}/\sigma_{1} = 0.3$ and $0.6$, and the mole fractions are $x_{1} = 0.125, 0.5, 0.75$, and $1$. An excess chemical potential for each component has been obtained as well. Our findings for thermodynamic properties are in good agreement with available data in literature.
Extending Kernel PCA through Dualization: Sparsity, Robustness and Fast Algorithms

The goal of this paper is to revisit Kernel Principal Component Analysis (KPCA) through dualization of a difference of convex functions. This allows to naturally extend KPCA to multiple objective functions and leads to efficient gradient-based algorithms avoiding the expensive SVD of the Gram matrix. Particularly, we consider objective functions that can be written as Moreau envelopes, demonstrating how to promote robustness and sparsity within the same framework. The proposed method is evaluated on synthetic and real-world benchmarks, showing significant speedup in KPCA training time as well as highlighting the benefits in terms of robustness and sparsity.
Towards a Standard Definition of the Signal-to-Noise Ratio for Radio Signals of ultra-high-energy Particles

Signal-to-noise ratios are a widely used concept for astroparticle radio detectors, such as air-shower radio arrays for cosmic-ray measurements or detectors searching for radio signals induced by neutrino interactions in ice. Nonetheless, no common standards or methods are established for the determination of the signal-to-noise ratio: values cannot be compared between experiments, and for the same signal and noise, various methods differ by large factors on the signal-to-noise ratio. This was the motivation to discuss a community-specific standardization at the ARENA conference 2022. No agreement on a common method to calculate signal-to-noise ratios was reached, however, awareness was raised that signal-to-noise ratios need to be well defined in any publications. This includes providing sufficient information on the procedure used to determine the signal-to-noise ratio, in addition to simply stating the formula. Even when using the same definition of the signal-to-noise ratio, there is still a significant dependence on the procedure of calculation, e.g., the signal-to-noise ratio of waveforms containing only background can vary significantly depending on the size of the time interval used as signal search window. To facilitate the interpretation of any signal-to-noise ratios in a specific study, the recommendation is to also state the mean value of the signal-to-noise ratio that the used method yields when applied to noise used in the study, e.g., the radio background measured by the corresponding experiment.
Hyper-Wiener Index of Unicyclic Graphs

The hyper–Wiener index is one of the distance–based graph invariants, used as a structure–descriptor for predicting physicochemical properties of organic compounds. We determine the n-vertex unicyclic graphs of cycle length r with the smallest and the largest hyper–Wiener indices for 3 ≤ r ≤ n, and the n-vertex unicyclic graphs with the smallest, the second smallest, the largest and the second largest hyper–Wiener indices for n ≥ 5.
How Sparse Can We Prune A Deep Network: A Geometric Viewpoint

Overparameterization constitutes one of the most significant hallmarks of deep neural networks. Though it can offer the advantage of outstanding generalization performance, it meanwhile imposes substantial storage burden, thus necessitating the study of network pruning. A natural and fundamental question is: How sparse can we prune a deep network (with almost no hurt on the performance)? To address this problem, in this work we take a first principles approach, specifically, by merely enforcing the sparsity constraint on the original loss function, we’re able to characterize the sharp phase transition point of pruning ratio, which corresponds to the boundary between the feasible and the infeasible, from the perspective of high-dimensional geometry. It turns out that the phase transition point of pruning ratio equals the squared Gaussian width of some convex body resulting from the l 1 -regularized loss function, normalized by the original dimension of parameters. As a byproduct, we provide a novel network pruning algorithm which is essentially a global one-shot pruning one. Furthermore, we provide efficient countermeasures to address the challenges in computing the involved Gaussian width, including the spectrum estimation of a large-scale Hessian matrix and dealing with the non-definite positiveness of a Hessian matrix. It is demonstrated that the predicted pruning ratio threshold coincides very well with the actual value obtained from the experiments and our proposed pruning algorithm can achieve competitive or even better performance than the existing pruning algorithms. All codes are available at: https://github.com/QiaozheZhang/Global-One-shot-Pruning
The Role of Diverse Replay for Generalisation in Reinforcement Learning

In reinforcement learning (RL), key components of many algorithms are the exploration strategy and replay buffer. These strategies regulate what environment data is collected and trained on and have been extensively studied in the RL literature. In this paper, we investigate the impact of these components in the context of generalisation in multi-task RL. We investigate the hypothesis that collecting and training on more diverse data from the training environments will improve zero-shot generalisation to new tasks. We motivate mathematically and show empirically that generalisation to tasks that are"reachable'' during training is improved by increasing the diversity of transitions in the replay buffer. Furthermore, we show empirically that this same strategy also shows improvement for generalisation to similar but"unreachable'' tasks which could be due to improved generalisation of the learned latent representations.
Teaching AI to Teach: Leveraging Limited Human Salience Data Into Unlimited Saliency-Based Training

Machine learning models have shown increased accuracy in classification tasks when the training process incorporates human perceptual information. However, a challenge in training human-guided models is the cost associated with collecting image annotations for human salience. Collecting annotation data for all images in a large training set can be prohibitively expensive. In this work, we utilize ''teacher'' models (trained on a small amount of human-annotated data) to annotate additional data by means of teacher models' saliency maps. Then, ''student'' models are trained using the larger amount of annotated training data. This approach makes it possible to supplement a limited number of human-supplied annotations with an arbitrarily large number of model-generated image annotations. We compare the accuracy achieved by our teacher-student training paradigm with (1) training using all available human salience annotations, and (2) using all available training data without human salience annotations. We use synthetic face detection and fake iris detection as example challenging problems, and report results across four model architectures (DenseNet, ResNet, Xception, and Inception), and two saliency estimation methods (CAM and RISE). Results show that our teacher-student training paradigm results in models that significantly exceed the performance of both baselines, demonstrating that our approach can usefully leverage a small amount of human annotations to generate salience maps for an arbitrary amount of additional training data.
Identifying the threshold to sustainable ridepooling

Ridepooling combines trips of multiple passengers in the same vehicle and may thereby provide a more sustainable option than transport by private cars. The efficiency and sustainability of ridepooling is typically quantified by key performance indicators such as the average vehicle occupancy or the total distance driven by all ridepooling vehicles relative to individual transport. However, even if the average occupancy is high and rides are shared, ridepooling services may increase the total distance driven due to additional detours and deadheading. Moreover, these key performance indicators are difficult to predict without large-scale simulations or actual ridepooling operation. Here, we propose a dimensionless parameter to estimate the sustainability of ridepooling by quantifying the load on a ridepooling service, relating characteristic timescales of demand and supply. The load bounds the relative distance driven and uniquely marks the break-even point above which the total distance driven by all vehicles of a ridepooling service falls below that of motorized individual transport. Detailed event-based simulations and a comparison with empirical observations from a ridepooling pilot project in a rural area of Germany validate the theoretical prediction. Importantly, the load follows directly from a small set of aggregate parameters of the service setting and is thus predictable a priori. The load may thus complement standard key performance indicators and simplify planning, operation and evaluation of ridepooling services.
The fundamental drivers of electrochemical barriers

We find that ionization dominates the behavior of electrochemical reaction barriers, through grand-canonical electronic structure calculations of proton-deposition on transition metal surfaces. We show that barriers respond to potential in a nonlinear manner and trace this to the continuous degree of electron transfer as an ion is created or destroyed. This explains both Marcus-like curvature and Hammond-like shifts. Across materials, we find the barrier energy to be driven primarily by the charge presented on the surface, which in turn is dictated by the native work function, a fundamentally different driving force than non-electrochemical systems.
On spectrum of sample covariance matrices from large tensor vectors

In this paper, we investigate the limiting empirical spectral distribution (LSD) of sums of independent rank-one $k$-fold tensor products of $n$-dimensional vectors as $k,n \to \infty$. Assuming that the base vectors are complex random variables with unit modular, we show that the LSD is the Mar\v{c}enko-Pastur law. Comparing with the existing results, our limiting setting allows $k$ to grow much faster than $n$. Consequently, we obtain the necessary and sufficient conditions for Mar\v{c}enko-Pastur law to serve as the LSD of our matrix model. Our approach is based on the moment method.
Machine learning the electronic structure of matter across temperatures

We introduce machine learning (ML) models that predict the electronic structure of materials across a wide temperature range. Our models employ neural networks and are trained on density functional theory (DFT) data. Unlike most other ML models that use DFT data, our models directly predict the local density of states (LDOS) of the electronic structure. This provides several advantages, including access to multiple observables such as the electronic density and electronic total free energy. Moreover, our models account for both the electronic and ionic temperatures independently, making them ideal for applications like laser-heating of matter. We validate the efficacy of our LDOS-based models on a metallic test system. They accurately capture energetic effects induced by variations in ionic and electronic temperatures over a broad temperature range, even when trained on a subset of these temperatures. These findings open up exciting opportunities for investigating the electronic structure of materials under both ambient and extreme conditions.
Coexistence of symmetry-protected topological order and Neel order in the spin-1/2 ladder antiferromagnet C9H18N2CuBr4

Topological phases of matter are beyond the paradigm of Landau's symmetry breaking and have challenged our understanding of condensed matter systems. Here we report a new type of symmetry-protected topological phase of matter in the spin-1/2 coupled two-leg ladder antiferromagnet C9H18N2CuBr4, DLCB for short. In this two-sublattice antiferromagnet with a weak easy-axis anisotropy, we find no evidence of a conventional spin-flop transition in the magnetization with the magnetic field applied parallel to the easy axis at T=0.4 K, well below TN=2.0 K. Moreover, the temperature dependence of the gapped transverse excitations across TN indicates that they are not the conventional S=1 magnons associated with explicit symmetry breaking. Instead, the thermal renormalization of the gap energy shows a remarkable agreement with a calculation for the three-dimensional O(3) nonlinear sigma model. Accordingly, the spin gap in DLCB is not due to the spin anisotropy but to the separation between a spin singlet state and a triplet excited state. Since an antiferromagnetic spin-1/2 ladder systems can be mapped onto the spin-1 chain, the notion of the Haldane gap is proposed to explain the opening of the spin gap in DLCB. Therefore, the ground state of DLCB is best described as a quantum superposition of a Haldane phase and a Neel-ordered phase, which resembles the quantum state of a qubit in quantum computing. Our results indicate the presence of a symmetry-protected topological order coexisting with an antiferromagnetic order in this material.