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When an inverted ensemble of atoms is tightly packed on the scale of its emission wavelength or when the atoms are collectively strongly coupled to a single cavity mode, their dipoles will align and decay rapidly via a superradiant burst. However, a spread-out dipole phase distribution theory predicts a required minimum threshold of atomic excitation for superradiance to occur. Here we experimentally confirm this predicted threshold for superradiant emission on a narrow optical transition when exciting the atoms transversely and show how to take advantage of the resulting sub- to superradiant transition. A $\pi/2$-pulse places the atoms in a subradiant state, protected from collective cavity decay, which we exploit during the free evolution period in a corresponding Ramsey pulse sequence. The final excited state population is read out via superradiant emission from the inverted atomic ensemble after a second $\pi/2$-pulse, and with minimal heating this allows for multiple Ramsey sequences within one experimental cycle. Our scheme is a fundamentally new approach to atomic state readout characterized by its speed, simplicity, and high sensitivity. It demonstrates the potential of sensors using collective effects in cavity-coupled quantum emitters., Comment: Removed a duplicate paragraph

Spider monkeys (genus Ateles) have a prehensile tail that functions as a flexible, multipurpose fifth limb, enabling them to navigate complex terrains, grasp objects of various sizes, and swing between supports. Inspired by the spider monkey tail, we present a life size hybrid soft-rigid continuum robot designed to imitate the function of the tail. Our planar design has a rigid skeleton with soft elements at its joints that achieve decreasing stiffness along its length. Five manually-operated wires along this central structure control the motion of the tail to form a variety of possible shapes in the 2D plane. Our design also includes a skin-like silicone and fabric tail pad that moves with the tail's tip and assists with object grasping. We quantify the force required to pull various objects out of the robot's grasp and demonstrate that this force increases with the object diameter and the number of edges in a polygonal object. We demonstrate the robot's ability to grasp, move, and release objects of various diameters, as well as to navigate around obstacles, and to retrieve an object after passing under a low passageway., Comment: 6 pages, 8 figures. Published in 2023 IEEE International Conference on Soft Robotics (RoboSoft)

Generative Pre-trained Transformer (GPT) models have exhibited exciting progress in their capabilities, capturing the interest of practitioners and the public alike. Yet, while the literature on the trustworthiness of GPT models remains limited, practitioners have proposed employing capable GPT models for sensitive applications such as healthcare and finance -- where mistakes can be costly. To this end, this work proposes a comprehensive trustworthiness evaluation for large language models with a focus on GPT-4 and GPT-3.5, considering diverse perspectives -- including toxicity, stereotype bias, adversarial robustness, out-of-distribution robustness, robustness on adversarial demonstrations, privacy, machine ethics, and fairness. Based on our evaluations, we discover previously unpublished vulnerabilities to trustworthiness threats. For instance, we find that GPT models can be easily misled to generate toxic and biased outputs and leak private information in both training data and conversation history. We also find that although GPT-4 is usually more trustworthy than GPT-3.5 on standard benchmarks, GPT-4 is more vulnerable given jailbreaking system or user prompts, potentially because GPT-4 follows (misleading) instructions more precisely. Our work illustrates a comprehensive trustworthiness evaluation of GPT models and sheds light on the trustworthiness gaps. Our benchmark is publicly available at https://decodingtrust.github.io/ ; our dataset can be previewed at https://huggingface.co/datasets/AI-Secure/DecodingTrust ; a concise version of this work is at https://openreview.net/pdf?id=kaHpo8OZw2 ., Comment: NeurIPS 2023 Outstanding Paper (Datasets and Benchmarks Track)

In this study, we introduce BEoRN (Bubbles during the Epoch of Reionisation Numerical Simulator), a publicly available Python code that generates three-dimensional maps of the 21-cm signal from the cosmic dawn and the epoch of reionisation. Built upon N-body simulation outputs, BEoRN populates haloes with stars and galaxies based on a flexible source model. It then computes the evolution of Lyman-$\alpha$ coupling, temperature, and ionisation profiles as a function of source properties, and paints these profiles around each source onto a three-dimensional grid. The code consistently deals with the overlap of ionised bubbles by redistributing photons around the bubble boundaries, thereby ensuring photon conservation. It accounts for the redshifting of photons and the source look-back effect for the temperature and Lyman-$\alpha$ coupling profiles which extend far into the intergalactic medium to scales of order 100 cMpc. We provide a detailed description of the code and compare it to results from the literature. After validation, we run three different benchmark models based on a cosmological N-body simulation. All three models agree with current observations from UV luminosity functions and estimates of the mean ionisation fraction. Due to different assumptions regarding the small-mass stellar-to-halo relation, the X-ray flux emission, and the ionising photon escape fraction, the models produce unique signatures ranging from a cold reionisation with deep absorption trough to an emission-dominated 21-cm signal, broadly encompassing the current uncertainties at cosmic dawn. The code BEoRN is publicly available at https://github.com/cosmic-reionization/BEoRN.

We present the first two-dimensional (2D) optical Thomson scattering measurements of electron density and temperature in laser-produced plasmas. The novel instrument directly measures $n_e(x,y)$ and $T_e(x,y)$ in two dimensions over large spatial regions (cm$^2$) with sub-mm spatial resolution, by automatically translating the scattering volume while the plasma is produced repeatedly by irradiating a solid target with a high-repetition-rate laser beam (10 J, $\sim$10$^{12}$ W/cm$^2$, 1 Hz). In this paper, we describe the design and auto-alignment of the instrument, and the computerized fitting algorithm of the spectral distribution function to large data-sets of measured scattering spectra, as they transition from the collective to the non-collective regime with distance from the target. As an example, we present 2D scattering measurements in laser driven shock waves in ambient nitrogen gas at a pressure of 95 mTorr., Comment: 8 pages, 4 figures

Recent work claims that large language models display emergent abilities, abilities not present in smaller-scale models that are present in larger-scale models. What makes emergent abilities intriguing is two-fold: their sharpness, transitioning seemingly instantaneously from not present to present, and their unpredictability, appearing at seemingly unforeseeable model scales. Here, we present an alternative explanation for emergent abilities: that for a particular task and model family, when analyzing fixed model outputs, emergent abilities appear due to the researcher's choice of metric rather than due to fundamental changes in model behavior with scale. Specifically, nonlinear or discontinuous metrics produce apparent emergent abilities, whereas linear or continuous metrics produce smooth, continuous predictable changes in model performance. We present our alternative explanation in a simple mathematical model, then test it in three complementary ways: we (1) make, test and confirm three predictions on the effect of metric choice using the InstructGPT/GPT-3 family on tasks with claimed emergent abilities; (2) make, test and confirm two predictions about metric choices in a meta-analysis of emergent abilities on BIG-Bench; and (3) show to choose metrics to produce never-before-seen seemingly emergent abilities in multiple vision tasks across diverse deep networks. Via all three analyses, we provide evidence that alleged emergent abilities evaporate with different metrics or with better statistics, and may not be a fundamental property of scaling AI models.

During brain tumour resection, localising cancerous tissue and delineating healthy and pathological borders is challenging, even for experienced neurosurgeons and neuroradiologists. Intraoperative imaging is commonly employed for determining and updating surgical plans in the operating room. Ultrasound (US) has presented itself a suitable tool for this task, owing to its ease of integration into the operating room and surgical procedure. However, widespread establishment of this tool has been limited because of the difficulty of anatomy localisation and data interpretation. In this work, we present a robotic framework designed and tested on a soft-tissue-mimicking brain phantom, simulating intraoperative US (iUS) scanning during brain tumour surgery.

Double descent is a surprising phenomenon in machine learning, in which as the number of model parameters grows relative to the number of data, test error drops as models grow ever larger into the highly overparameterized (data undersampled) regime. This drop in test error flies against classical learning theory on overfitting and has arguably underpinned the success of large models in machine learning. This non-monotonic behavior of test loss depends on the number of data, the dimensionality of the data and the number of model parameters. Here, we briefly describe double descent, then provide an explanation of why double descent occurs in an informal and approachable manner, requiring only familiarity with linear algebra and introductory probability. We provide visual intuition using polynomial regression, then mathematically analyze double descent with ordinary linear regression and identify three interpretable factors that, when simultaneously all present, together create double descent. We demonstrate that double descent occurs on real data when using ordinary linear regression, then demonstrate that double descent does not occur when any of the three factors are ablated. We use this understanding to shed light on recent observations in nonlinear models concerning superposition and double descent. Code is publicly available.

This paper proposes a Nonlinear Model-Predictive Control (NMPC) method capable of finding and converging to energy-efficient regular oscillations, which require no control action to be sustained. The approach builds up on the recently developed Eigenmanifold theory, which defines the sets of line-shaped oscillations of a robot as an invariant two-dimensional submanifold of its state space. By defining the control problem as a nonlinear program (NLP), the controller is able to deal with constraints in the state and control variables and be energy-efficient not only in its final trajectory but also during the convergence phase. An initial implementation of this approach is proposed, analyzed, and tested in simulation.

We classify Sylow $p$-subgroups of finite groups whose principal $p$-blocks have precisely six ordinary irreducible characters., Comment: 18 pages, 1 table. The second version includes comments from Gunter Malle

The 21-cm power spectrum of reionization is a promising probe for cosmology and fundamental physics. Exploiting this new observable, however, requires fast predictors capable of efficiently scanning the very large parameter space of cosmological and astrophysical uncertainties. In this paper, we introduce the halo model of reionization (HMreio), a new analytical tool that combines the halo model of the cosmic dawn with the excursion-set bubble model for reionization, assuming an empirical correction factor to deal with overlapping ionization bubbles. First, HMreio is validated against results from the well-known semi-numerical code 21cmFAST, showing a good overall agreement for wave-modes of $k\lesssim 1$ h/Mpc. Based on this result, we perform a Monte-Carlo Markov-Chain (MCMC) forecast analysis assuming mock data from 1000-hour observations with the low-frequency part of the Square Kilometre Array (SKA) observatory. We simultaneously vary the six standard cosmological parameters together with seven astrophysical nuisance parameters quantifying the abundance and spectral properties of sources. Depending on the assumed theory error, we find very competitive constraints on cosmological parameters. In particular, it will be possible to conclusively test current cosmological tensions related to the Hubble parameter ($H_0$-tension) and the matter clustering amplitude ($S_8$-tension). Furthermore, the sum of the neutrino masses can be strongly constrained, making it possible to determine the neutrino mass hierarchy at the $\sim 90$ percent confidence level. However, these goals can only be achieved if the current modelling uncertainties are substantially reduced to below $\sim 3$ percent., Comment: 18 pages, 8 figures, comments welcome

Analysis of Electrochemical Impedance Spectroscopy (EIS) data for electrochemical systems often consists of defining an Equivalent Circuit Model (ECM) using expert knowledge and then optimizing the model parameters to deconvolute various resistance, capacitive, inductive, or diffusion responses. For small data sets, this procedure can be conducted manually; however, it is not feasible to manually define a proper ECM for extensive data sets with a wide range of EIS responses. Automatic identification of an ECM would substantially accelerate the analysis of large sets of EIS data. We showcase machine learning methods to classify the ECMs of 9,300 impedance spectra provided by QuantumScape for the BatteryDEV hackathon. The best-performing approach is a gradient-boosted tree model utilizing a library to automatically generate features, followed by a random forest model using the raw spectral data. A convolutional neural network using boolean images of Nyquist representations is presented as an alternative, although it achieves a lower accuracy. We publish the data and open source the associated code. The approaches described in this article can serve as benchmarks for further studies. A key remaining challenge is the identifiability of the labels, underlined by the model performances and the comparison of misclassified spectra., Comment: Manuscript: 17 pages, 9 figures; Supplementary Information: 9 pages, 6 figures

Fast-exploding plasmas traveling though magnetized, collisionless plasmas can occur in a variety of physical systems, such as supernova remnants, coronal mass ejections, and laser-driven laboratory experiments. To study these systems, it is important to understand the coupling process between the plasmas. In this work, we develop a semi-analytical model of the parameters that characterize the strong collisionless coupling between an unmagnetized driver plasma and a uniformly and perpendicularly magnetized background plasma. In particular, we derive analytical expressions that describe the characteristic diamagnetic cavity and magnetic compression of these systems, such as their corresponding velocities, the compression ratio, and the maximum size of the cavity. The semi-analytical model is compared with collisionless 1D particle-in-cell simulations and experimental results with laser-driven plasmas, showing good agreement. The model allows us to provide bounds for parameters that are otherwise difficult to diagnose in experiments with similar setups.

The aim of this paper is to introduce a robotic platform for autonomous iUS tissue scanning to optimise intraoperative diagnosis and improve surgical resection during robot-assisted operations. To guide anatomy specific robotic scanning and generate a representation of the robot task space, fast and accurate techniques for the recovery of 3D morphological structures of the surgical cavity are developed. The prototypic DLR MIRO surgical robotic arm is used to control the applied force and the in-plane motion of the US transducer. A key application of the proposed platform is the scanning of brain tissue to guide tumour resection.

Proton imaging has become a key diagnostic for measuring electromagnetic fields in high-energy-density (HED) laboratory plasmas. Compared to other techniques for diagnosing fields, proton imaging is a non-perturbative measurement that can simultaneously offer high spatial and temporal resolution and the ability to distinguish between electric and magnetic fields. Consequently, proton imaging has been used in a wide range of HED experiments, from inertial confinement fusion to laboratory astrophysics. An overview is provided on the state of the art of proton imaging, including detailed discussion of experimental considerations like proton sources and detectors, the theory of proton-imaging analysis, and a survey of experimental results demonstrating the breadth of applications. Topics at the frontiers of proton imaging development are also described, along with an outlook on the future of the field.

Operator learning trains a neural network to map functions to functions. An ideal operator learning framework should be mesh-free in the sense that the training does not require a particular choice of discretization for the input functions, allows for the input and output functions to be on different domains, and is able to have different grids between samples. We propose a mesh-free neural operator for solving parametric partial differential equations. The basis enhanced learning network (BelNet) projects the input function into a latent space and reconstructs the output functions. In particular, we construct part of the network to learn the ``basis'' functions in the training process. This generalized the networks proposed in Chen and Chen's universal approximation theory for the nonlinear operators to account for differences in input and output meshes. Through several challenging high-contrast and multiscale problems, we show that our approach outperforms other operator learning methods for these tasks and allows for more freedom in the sampling and/or discretization process.

Particle dynamics and multi-agent systems provide accurate dynamical models for studying and forecasting the behavior of complex interacting systems. They often take the form of a high-dimensional system of differential equations parameterized by an interaction kernel that models the underlying attractive or repulsive forces between agents. We consider the problem of constructing a data-based approximation of the interacting forces directly from noisy observations of the paths of the agents in time. The learned interaction kernels are then used to predict the agents behavior over a longer time interval. The approximation developed in this work uses a randomized feature algorithm and a sparse randomized feature approach. Sparsity-promoting regression provides a mechanism for pruning the randomly generated features which was observed to be beneficial when one has limited data, in particular, leading to less overfitting than other approaches. In addition, imposing sparsity reduces the kernel evaluation cost which significantly lowers the simulation cost for forecasting the multi-agent systems. Our method is applied to various examples, including first-order systems with homogeneous and heterogeneous interactions, second order homogeneous systems, and a new sheep swarming system.

In this note, we prove that if every character of a finite group $G$ fixed by an order-2 Galois automorphism has odd degree, then $G$ has a normal Sylow $2$-subgroup. On the way, we study extensions of characters of $GL_n(q)$, $q$ odd, to the group extended by the transpose-inverse automorphism and prove that unipotent characters of $PSL_n(q)$ extend to rational characters of its automorphism group., Comment: Thm. A, Cor. B, are incorrect as stated and would require additional assumptions on q (a result of a missing assumption in another paper). Withdrawn until I obtain a working solution

We complete the proof of the McKay--Navarro conjecture (also known as the Galois--McKay conjecture) for the prime 2, by completing the proof of the inductive McKay--Navarro conditions introduced by Navarro--Sp\"ath--Vallejo in this situation.

We consider the classical shadows task for pure states in the setting of both joint and independent measurements. The task is to measure few copies of an unknown pure state $\rho$ in order to learn a classical description which suffices to later estimate expectation values of observables. Specifically, the goal is to approximate $\mathrm{Tr}(O \rho)$ for any Hermitian observable $O$ to within additive error $\epsilon$ provided $\mathrm{Tr}(O^2)\leq B$ and $\lVert O \rVert = 1$. Our main result applies to the joint measurement setting, where we show $\tilde{\Theta}(\sqrt{B}\epsilon^{-1} + \epsilon^{-2})$ samples of $\rho$ are necessary and sufficient to succeed with high probability. The upper bound is a quadratic improvement on the previous best sample complexity known for this problem. For the lower bound, we see that the bottleneck is not how fast we can learn the state but rather how much any classical description of $\rho$ can be compressed for observable estimation. In the independent measurement setting, we show that $\mathcal O(\sqrt{Bd} \epsilon^{-1} + \epsilon^{-2})$ samples suffice. Notably, this implies that the random Clifford measurements algorithm of Huang, Kueng, and Preskill, which is sample-optimal for mixed states, is not optimal for pure states. Interestingly, our result also uses the same random Clifford measurements but employs a different estimator., Comment: 34 pages; v2 - journal version