Miracle-dz/UniFAR-FTUs huggingface dataset:
On a Free-Endpoint Isoperimetric Problem in $\mathbb{R}^2$

Inspired by a planar partitioning problem involving multiple improper chambers, this article investigates using classical techniques what can be said of the existence, uniqueness, and regularity of minimizers in a certain free-endpoint isoperimetric problem. By restricting to curves which are expressible as graphs of functions, a full existence-uniqueness-regularity result is proved using a convexity technique inspired by work of Talenti. The problem studied here can be interpreted physically as the identification of the equilibrium shape of a sessile liquid drop in half-space (in the absence of gravity). This is a well-studied variational problem whose full resolution requires the use of geometric measure theory, in particular the theory of sets of finite perimeter, but here we present a more direct, classical geometrical approach. Conjectures on improper planar partitioning problems are presented throughout.
Negative superinflating bipartite fluctuations near exceptional points in $\mathcal{PT}$-symmetric models

We investigate bipartite particle number fluctuations near the rank-$2$ exceptional points (EPs) of $\mathcal{PT}$-symmetric Su-Schrieffer-Heeger models. Beyond a conformal field theory of massless fermions, fluctuations or equivalently compressibility is negative definite and exhibits superinflation in leading order at EPs, due to the defectiveness in the biorthogonal Hilbert space. Associated with the bipartite von Neumann entanglement entropy, a parameter in an anomalous correspondence referencing from a purely non-Hermitian limit helps characterize two inequivalent EP sets. Our work paves the way for understanding the singularity of fluctuations relevant to EPs, more promisingly detectable in experiments.
Can ChatGPT support prospective teachers in physics task development?

The recent advancement of large language models presents numerous opportunities for teaching and learning. Despite widespread public debate regarding the use of large language models, empirical research on their opportunities and risks in education remains limited. In this work, we demonstrate the qualities and shortcomings of using ChatGPT 3.5 for physics task development by prospective teachers. In a randomized controlled trial, 26 prospective physics teacher students were divided into two groups: the first group used ChatGPT 3.5 to develop text-based physics tasks for four different concepts in the field of kinematics for 10th grade high school students, while the second group used a classical textbook to create tasks for the same concepts and target group. The results indicate no difference in task correctness, but students using the textbook achieved a higher clarity and more frequently embedded their questions in a meaningful context. Both groups adapted the level of task difficulty easily to the target group but struggled strongly with sufficient task specificity, i.e., relevant information to solve the tasks were missing. Students using ChatGPT for problem posing rated high system usability but experienced difficulties with output quality. These results provide insights into the opportunities and pitfalls of using large language models in education.
Deep-Learning-based Vasculature Extraction for Single-Scan Optical Coherence Tomography Angiography

Optical coherence tomography angiography (OCTA) is a non-invasive imaging modality that extends the functionality of OCT by extracting moving red blood cell signals from surrounding static biological tissues. OCTA has emerged as a valuable tool for analyzing skin microvasculature, enabling more accurate diagnosis and treatment monitoring. Most existing OCTA extraction algorithms, such as speckle variance (SV)- and eigen-decomposition (ED)-OCTA, implement a larger number of repeated (NR) OCT scans at the same position to produce high-quality angiography images. However, a higher NR requires a longer data acquisition time, leading to more unpredictable motion artifacts. In this study, we propose a vasculature extraction pipeline that uses only one-repeated OCT scan to generate OCTA images. The pipeline is based on the proposed Vasculature Extraction Transformer (VET), which leverages convolutional projection to better learn the spatial relationships between image patches. In comparison to OCTA images obtained via the SV-OCTA (PSNR: 17.809) and ED-OCTA (PSNR: 18.049) using four-repeated OCT scans, OCTA images extracted by VET exhibit moderate quality (PSNR: 17.515) and higher image contrast while reducing the required data acquisition time from ~8 s to ~2 s. Based on visual observations, the proposed VET outperforms SV and ED algorithms when using neck and face OCTA data in areas that are challenging to scan. This study represents that the VET has the capacity to extract vascularture images from a fast one-repeated OCT scan, facilitating accurate diagnosis for patients.
Phase transition in magic with random quantum circuits

Magic is a property of quantum states that enables universal fault-tolerant quantum computing using simple sets of gate operations. Understanding the mechanisms by which magic is created or destroyed is, therefore, a crucial step towards efficient and practical fault-tolerant computation. We observe that a random stabilizer code subject to coherent errors exhibits a phase transition in magic, which we characterize through analytic, numeric and experimental probes. Below a critical error rate, stabilizer syndrome measurements remove the accumulated magic in the circuit, effectively protecting against coherent errors; above the critical error rate syndrome measurements concentrate magic. A better understanding of such rich behavior in the resource theory of magic could shed more light on origins of quantum speedup and pave pathways for more efficient magic state generation.
Convergence of the pruning processes of stable Galton-Watson trees and other $\mathbb{R}$-trees

Since the work of Aldous and Pitman (1998), several authors have studied the pruning processes of Galton-Watson trees and their continuous analogue L\'evy trees. L\"ohr, Voisin and Winter (2015) introduced the space of bi-measure $\mathbb{R}$-trees equipped with the so-called leaf sampling weak vague topology which allows them to unify the discrete and the continuous picture by considering them as instances of the same Feller-continuous Markov process with different initial conditions. Moreover, the authors show that these so-called pruning processes converge in the Skorokhod space of c\`adl\`ag paths with values in the space of bi-measure $\mathbb{R}$-trees, whenever the initial bi-measure $\mathbb{R}$-trees converge. In this paper we first provide an example to the above principle by verifying that a sequence of suitably rescaled critical conditioned Galton-Watson trees whose offspring distributions lie in the domain of attraction of a stable law of index $\alpha \in (1,2]$ converge to the $\alpha$-stable L\'evy-tree in the leaf-sampling weak converge. Secondly, we strengthen the results of L\"ohr et al. (2015) and show that the convergence holds in the Skorokhod space of c\`adl\`ag (rooted measure) $\mathbb{R}$-tree-valued functions equipped with the Gromov-Hausdorff weak topology.
A minimal physical model for curvotaxis driven by curved protein complexes at the cell’s leading edge

Cells often migrate on curved surfaces inside the body, such as curved tissues, blood vessels or highly curved protrusions of other cells. Recent in-vitro experiments provide clear evidence that motile cells are affected by the curvature of the substrate on which they migrate, preferring certain curvatures to others, termed “curvotaxis”. The origin and underlying mechanism that gives rise to this curvature sensitivity are not well understood. Here, we employ a “minimal cell” model which is composed of a vesicle that contains curved membrane protein complexes, that exert protrusive forces on the membrane (representing the pressure due to actin polymerization). This minimal-cell model gives rise to spontaneous emergence of a motile phenotype, driven by a lamellipodia-like leading edge. By systematically screening the behaviour of this model on different types of curved substrates (sinusoidal, cylinder and tube), we show that minimal ingredients and energy terms capture the experimental data. The model recovers the observed migration on the sinusoidal substrate, where cells move along the grooves (minima), while avoiding motion along the ridges. In addition, the model predicts the tendency of cells to migrate circumferentially on convex substrates and axially on concave ones. Both of these predictions are verified experimentally, on several cell types. Altogether, our results identify the minimization of membrane-substrate adhesion energy and binding energy between the membrane protein complexes as key players of curvotaxis in cell migration.
Efficient Deep Reinforcement Learning Requires Regulating Overfitting

Deep reinforcement learning algorithms that learn policies by trial-and-error must learn from limited amounts of data collected by actively interacting with the environment. While many prior works have shown that proper regularization techniques are crucial for enabling data-efficient RL, a general understanding of the bottlenecks in data-efficient RL has remained unclear. Consequently, it has been difficult to devise a universal technique that works well across all domains. In this paper, we attempt to understand the primary bottleneck in sample-efficient deep RL by examining several potential hypotheses such as non-stationarity, excessive action distribution shift, and overfitting. We perform thorough empirical analysis on state-based DeepMind control suite (DMC) tasks in a controlled and systematic way to show that high temporal-difference (TD) error on the validation set of transitions is the main culprit that severely affects the performance of deep RL algorithms, and prior methods that lead to good performance do in fact, control the validation TD error to be low. This observation gives us a robust principle for making deep RL efficient: we can hill-climb on the validation TD error by utilizing any form of regularization techniques from supervised learning. We show that a simple online model selection method that targets the validation TD error is effective across state-based DMC and Gym tasks.
On the Independence of Association Bias and Empirical Fairness in Language Models

The societal impact of pre-trained language models has prompted researchers to probe them for strong associations between protected attributes and value-loaded terms, from slur to prestigious job titles. Such work is said to probe models for bias or fairness—or such probes ‘into representational biases’ are said to be ‘motivated by fairness’—suggesting an intimate connection between bias and fairness. We provide conceptual clarity by distinguishing between association biases [11] and empirical fairness [56] and show the two can be independent. Our main contribution, however, is showing why this should not come as a surprise. To this end, we first provide a thought experiment, showing how association bias and empirical fairness can be completely orthogonal. Next, we provide empirical evidence that there is no correlation between bias metrics and fairness metrics across the most widely used language models. Finally, we survey the sociological and psychological literature and show how this literature provides ample support for expecting these metrics to be uncorrelated.
Full-field, quasi-3D hygroscopic characterization of paper inter-fiber bonds

The state-of-the-art in paper mechanics calls for novel experimental data covering the full-field hygro-expansion of inter-fiber bonds in paper, i.e., the 3D morphological changes and inter-fiber interactions. Therefore, a recently developed full-field single fiber hygro-expansion measurement methodology based on global digital height correlation is extended to orthogonally bonded inter-fiber bonds, to investigate their full-field quasi-3D hygroscopic behavior. A sample holder has been developed which enables the quasi-3D characterization of the initial geometry of individual inter-fiber bonds, including the fiber thickness and width along the length of the fibers as well as the degree of wrap around and contact area of the bond, which are vital for understanding the inter-fiber bond hygro-mechanics. Full-field hygroscopic testing revealed novel insights on the inter-fiber interactions: (i) the transverse hygro-expansion of each fiber strongly reduces when approaching the bonded area, due to the significantly lower longitudinal hygro-expansion of the other bonded fiber. (ii) The relatively large transverse strain of one fiber stretches the other crossing fiber in its longitudinal direction, thereby significantly contributing to the sheet scale hygro-expansion. (iii) Out-of-plane bending is observed in the bonded region which is driven by the significant difference in transverse and longitudinal hygro-expansion of, respectively, the top and bottom fiber constituting the bond. A bi-layer laminate model is derived to rationalize the bending deformation and an adequate match is found with the experimental data. Under the assumption of zero bending, which represents constrained inter-fiber bonds inside a paper sheet, the model is able to predict the contribution of the transverse strain in the bonded regions to the sheet-scale hygro-expansion.
Solving the Kidney-Exchange Problem via Graph Neural Networks with No Supervision

This paper introduces a new learning-based approach for approximately solving the Kidney-Exchange Problem (KEP), an NP-hard problem on graphs. The problem consists of, given a pool of kidney donors and patients waiting for kidney donations, optimally selecting a set of donations to optimize the quantity and quality of transplants performed while respecting a set of constraints about the arrangement of these donations. The proposed technique consists of two main steps: the first is a Graph Neural Network (GNN) trained without supervision; the second is a deterministic non-learned search heuristic that uses the output of the GNN to find paths and cycles. To allow for comparisons, we also implemented and tested an exact solution method using integer programming, two greedy search heuristics without the machine learning module, and the GNN alone without a heuristic. We analyze and compare the methods and conclude that the learning-based two-stage approach is the best solution quality, outputting approximate solutions on average 1.1 times more valuable than the ones from the deterministic heuristic alone.
Methods for high-precision determinations of radiative-leptonic decay form factors using lattice QCD

We present a study of lattice-QCD methods to determine the relevant hadronic form factors for radiative leptonic decays of pseudoscalar mesons. We provide numerical results for $D_s^+ \to \ell^+ \nu \gamma$. Our calculation is performed using a domain-wall action for all quark flavors and on a single RBC/UKQCD lattice gauge-field ensemble. The first part of the study is how to best control two sources of systematic error inherent in the calculation, specifically the unwanted excited states created by the meson interpolating field, and unwanted exponentials in the sum over intermediate states. Using a 3d sequential propagator allows for better control over unwanted exponentials from intermediate states, while using a 4d sequential propagator allows for better control over excited states. We perform individual analyses of the 3d and 4d methods as well as a combined analysis using both methods, and find that the 3d sequential propagator offers good control over both sources of systematic uncertainties for the smallest number of propagator solves. From there, we further improve the use of a 3d sequential propagator by employing an infinite-volume approximation method, which allows us to calculate the relevant form factors over the entire allowed range of photon energies. We then study improvements gained by performing the calculation using a different three-point function, using ratios of three-point functions, averaging over positive and negative photon momentum, and using an improved method for extracting the structure-dependent part of the axial form factor. The optimal combination of methods yields results for the $D_s^+ \to \ell^+ \nu \gamma$ structure-dependent vector and axial form factors in the entire kinematic range with statistical plus fitting uncertainties of order 5%, using 25 gauge configurations with 64 samples per configuration.
Test-driving RISC-V Vector hardware for HPC

Whilst the RISC-V Vector extension (RVV) has been ratified, at the time of writing both hardware implementations and open source software support are still limited for vectorisation on RISC-V. This is important because vectorisation is crucial to obtaining good performance for High Performance Computing (HPC) workloads and, as of April 2023, the Allwinner D1 SoC, containing the XuanTie C906 processor, is the only mass-produced and commercially available hardware supporting RVV. This paper surveys the current state of RISC-V vectorisation as of 2023, reporting the landscape of both the hardware and software ecosystem. Driving our discussion from experiences in setting up the Allwinner D1 as part of the EPCC RISC-V testbed, we report the results of benchmarking the Allwinner D1 using the RAJA Performance Suite, which demonstrated reasonable vectorisation speedup using vendor-provided compiler, as well as favourable performance compared to the StarFive VisionFive V2 with SiFive's U74 processor.
Adaptive minimax optimality in statistical inverse problems via SOLIT—Sharp Optimal Lepskiĭ-Inspired Tuning

We consider statistical linear inverse problems in separable Hilbert spaces and filter-based reconstruction methods of the form fˆα=qαT∗TT∗Y , where Y is the available data, T the forward operator, qαα∈A an ordered filter, and α > 0 a regularization parameter. Whenever such a method is used in practice, α has to be appropriately chosen. Typically, the aim is to find or at least approximate the best possible α in the sense that mean squared error (MSE) E[∥fˆα−f†∥2] w.r. t. the true solution f† is minimized. In this paper, we introduce the Sharp Optimal Lepskiĭ-Inspired Tuning (SOLIT) method, which yields an a posteriori parameter choice rule ensuring adaptive minimax rates of convergence. It depends only on Y and the noise level σ as well as the operator T and the filter qαα∈A and does not require any problem-dependent tuning of further parameters. We prove an oracle inequality for the corresponding MSE in a general setting and derive the rates of convergence in different scenarios. By a careful analysis we show that no other a posteriori parameter choice rule can yield a better performance in terms of the order of the convergence rate of the MSE. In particular, our results reveal that the typical understanding of Lepskiĭ-type methods in inverse problems leading to a loss of a log factor is wrong. In addition, the empirical performance of SOLIT is examined in simulations.
Linear waves solutions of a stochastic shallow water model

In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind or coming as the feedback of the ocean on the atmosphere and leading in a very fast way to the selection of some wavelength. This interwoven, yet simple, mechanism explains the emergence of typical wavelength associated to near inertial waves. Ensemble-mean waves that are not in phase with the random forcing are damped at an exponential rate, whose magnitude depends on the random forcing variance. Geostrophic adjustment is also interpreted as a statistical homogenization process in which, in order to conserve potential vorticity, the small-scale component tends to align to the velocity ﬁelds to form a statistically homogeneous random ﬁeld.
Weakly Supervised Detection of Baby Cry

Detection of baby cries is an important part of baby monitoring and health care. Almost all existing methods use supervised SVM, CNN, or their varieties. In this work, we propose to use weakly supervised anomaly detection to detect a baby cry. In this weak supervision, we only need weak annotation if there is a cry in an audio file. We design a data mining technique using the pre-trained VGGish feature extractor and an anomaly detection network on long untrimmed audio files. The obtained datasets are used to train a simple CNN feature network for cry/non-cry classification. This CNN is then used as a feature extractor in an anomaly detection framework to achieve better cry detection performance.
Subsystem non-invertible symmetry operators and defects

We explore non-invertible symmetries in two-dimensional lattice models with subsystem \mathbb Z_2ℤ2 symmetry. We introduce a subsystem \mathbb Z_2ℤ2-gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes the ordinary Kramers-Wannier transformation. The corresponding duality operators and defects are constructed by gaugings on the whole or half of the Hilbert space. By gauging twice, we derive fusion rules of duality operators and defects, which enriches ordinary Ising fusion rules with subsystem features. Subsystem Kramers-Wannier duality defects are mobile in both spatial directions, unlike the defects of invertible subsystem symmetries. We finally comment on the anomaly of the subsystem Kramers-Wannier duality symmetry, and discuss its subtleties.
Contrastive Tuning: A Little Help to Make Masked Autoencoders Forget

Masked Image Modeling (MIM) methods, like Masked Autoencoders (MAE), efficiently learn a rich representation of the input. However, for adapting to downstream tasks, they require a sufficient amount of labeled data since their rich features code not only objects but also less relevant image background. In contrast, Instance Discrimination (ID) methods focus on objects. In this work, we study how to combine the efficiency and scalability of MIM with the ability of ID to perform downstream classification in the absence of large amounts of labeled data. To this end, we introduce Masked Autoencoder Contrastive Tuning (MAE-CT), a sequential approach that utilizes the implicit clustering of the Nearest Neighbor Contrastive Learning (NNCLR) objective to induce abstraction in the topmost layers of a pre-trained MAE. MAE-CT tunes the rich features such that they form semantic clusters of objects without using any labels. Notably, MAE-CT does not rely on hand-crafted augmentations and frequently achieves its best performances while using only minimal augmentations (crop & flip). Further, MAE-CT is compute efficient as it requires at most 10% overhead compared to MAE re-training. Applied to large and huge Vision Transformer (ViT) models, MAE-CT excels over previous self-supervised methods trained on ImageNet in linear probing, k-NN and low-shot classification accuracy as well as in unsupervised clustering accuracy. With ViT-H/16 MAE-CT achieves a new state-of-the-art in linear probing of 82.2%. Project page: github.com/ml-jku/MAE-CT.