Search

Adversarial training is arguably the most popular way to provide empirical robustness against specific adversarial examples. While variants based on multi-step attacks incur significant computational overhead, single-step variants are vulnerable to a failure mode known as catastrophic overfitting, which hinders their practical utility for large perturbations. A parallel line of work, certified training, has focused on producing networks amenable to formal guarantees of robustness against any possible attack. However, the wide gap between the best-performing empirical and certified defenses has severely limited the applicability of the latter. Inspired by recent developments in certified training, which rely on a combination of adversarial attacks with network over-approximations, and by the connections between local linearity and catastrophic overfitting, we present experimental evidence on the practical utility and limitations of using certified training towards empirical robustness. We show that, when tuned for the purpose, a recent certified training algorithm can prevent catastrophic overfitting on single-step attacks, and that it can bridge the gap to multi-step baselines under appropriate experimental settings. Finally, we present a novel regularizer for network over-approximations that can achieve similar effects while markedly reducing runtime.

The world is moving towards clean and renewable energy sources, such as wind energy, in an attempt to reduce greenhouse gas emissions that contribute to global warming. To enhance the analysis and storage of wind data, we introduce a deep learning framework designed to simultaneously enable effective dimensionality reduction and continuous representation of multi-altitude wind data from discrete observations. The framework consists of three key components: dimensionality reduction, cross-modal prediction, and super-resolution. We aim to: (1) improve data resolution across diverse climatic conditions to recover high-resolution details; (2) reduce data dimensionality for more efficient storage of large climate datasets; and (3) enable cross-prediction between wind data measured at different heights. Comprehensive testing confirms that our approach surpasses existing methods in both super-resolution quality and compression efficiency., Comment: arXiv admin note: text overlap with arXiv:2401.16936

In this work the Coulomb effects (Coulomb correlations) in $\pi^+\pi^-$ pairs produced in p + Ni collisions at 24 GeV/$c$, are studied using experimental $\pi^+\pi^-$ pair distributions in $Q$, the relative momentum in the pair center of mass system (c.m.s), and its projections $Q_L$ (longitudinal component) and $Q_t$ (transverse component) relative to the pair direction in the laboratory system (l.s.). The $Q$, $Q_L$, and $Q_t$ distributions of the {\sl Coulomb pairs} in the c.m.s. have been simulated assuming they are described by the phase space modified by the known point-like Coulomb correlation function $A_C(Q)$, corrected for small effects due to the nonpoint-like pair production and the strong two-pion interaction. The same distributions of {\sl non-Coulomb pairs} have been simulated according to the phase space, but without $A_C(Q)$. It is shown that the number of {\sl Coulomb pairs} in all $Q_t$ intervals, including the small $Q_t$ (small opening angles $\theta$ in the l.s.) is calculated with the theoretical precision better than 2\%. The comparison of the simulated and experimental numbers of {\sl Coulomb pairs} at small $Q_t$ allows us to check and correct the detection efficiency for the pairs with small $\theta$ (0.06 mrad and smaller). It is shown that {\sl Coulomb pairs} can be used as a new physical tool to check and correct the quality of the simulated events. The special property of the {\sl Coulomb pairs} is the possibility of checking and correcting the detection efficiency, especially for the pairs with small opening angles.

Sterile neutrinos are a minimal extension of the Standard Model of particle physics and a promising candidate for dark matter if their mass is in the keV-range. The Karlsruhe Tritium Neutrino experiment (KATRIN), equipped with a novel multi-pixel silicon drift detector array, the TRISTAN detector, will be capable of searching for these keV-scale sterile neutrinos by investigating the kinematics of the tritium $\beta$-decay. This measurement will be performed after the completion of the neutrino mass measurement campaign. To detect a sterile neutrino signal with a high sensitivity, a profound understanding of the detector response is required. In this work, we report on the characterization of a 7-pixel TRISTAN prototype detector with a laser system. We present the experimental results obtained in high-resolution scans of the detector surface with a focused laser beam and demonstrate how the charge collection and the timing of the signals generated in the detector is related to the detector geometry. A comparison of the experimental data with simulations shows a good agreement., Comment: 23 pages, 12 figures

This document contains an educational introduction to the problem of sparsifying parametric models with L0 regularization. We utilize this approach together with dictionary learning to learn sparse polynomial policies for deep reinforcement learning to control parametric partial differential equations. The code and a tutorial are provided here: https://github.com/nicob15/Sparsifying-Parametric-Models-with-L0.

In this work we considerably improve the state-of-the-art SMT solving on first-order quantified problems by efficient machine learning guidance of quantifier selection. Quantifiers represent a significant challenge for SMT and are technically a source of undecidability. In our approach, we train an efficient machine learning model that informs the solver which quantifiers should be instantiated and which not. Each quantifier may be instantiated multiple times and the set of the active quantifiers changes as the solving progresses. Therefore, we invoke the ML predictor many times, during the whole run of the solver. To make this efficient, we use fast ML models based on gradient boosting decision trees. We integrate our approach into the state-of-the-art cvc5 SMT solver and show a considerable increase of the system's holdout-set performance after training it on a large set of first-order problems collected from the Mizar Mathematical Library.

Instead of randomly acquiring training data points, Uncertainty-based Active Learning (UAL) operates by querying the label(s) of pivotal samples from an unlabeled pool selected based on the prediction uncertainty, thereby aiming at minimizing the labeling cost for model training. The efficacy of UAL critically depends on the model capacity as well as the adopted uncertainty-based acquisition function. Within the context of this study, our analytical focus is directed toward comprehending how the capacity of the machine learning model may affect UAL efficacy. Through theoretical analysis, comprehensive simulations, and empirical studies, we conclusively demonstrate that UAL can lead to worse performance in comparison with random sampling when the machine learning model class has low capacity and is unable to cover the underlying ground truth. In such situations, adopting acquisition functions that directly target estimating the prediction performance may be beneficial for improving the performance of UAL.

Objectives: Evaluating the effects and artifacts introduced by medical foreign bodies in clinical dark-field chest radiographs and assessing their influence on the evaluation of pulmonary tissue, compared to conventional radiographs. Material & Methods: This retrospective study analyzed data from subjects enrolled in clinical trials conducted between 2018 and 2021, focusing on chronic obstructive pulmonary disease (COPD) and COVID-19 patients. All patients obtained a radiograph using an in-house developed clinical prototype for grating-based dark-field chest radiography. The prototype simultaneously delivers a conventional and dark-field radiograph. Two radiologists independently assessed the clinical studies to identify patients with foreign bodies. Subsequently, an analysis was conducted on the effects and artifacts attributed to distinct foreign bodies and their impact on the assessment of pulmonary tissue. Results: Overall, 30 subjects with foreign bodies were included in this study (mean age, 64 years +/- 11 [standard deviation]; 15 men). Foreign bodies composed of materials lacking microstructure exhibited a diminished dark-field signal or no discernible signal. Foreign bodies with a microstructure, in our investigations the cementation of the kyphoplasty, produce a positive dark-field signal. Since most foreign bodies lack microstructural features, dark-field imaging revealed fewer signals and artifacts by foreign bodies compared to conventional radiographs. Conclusion: Dark-field radiography enhances the assessment of pulmonary tissue with overlaying foreign bodies compared to conventional radiography. Reduced interfering signals result in fewer overlapping radiopaque artifacts within the investigated regions. This mitigates the impact on image quality and interpretability of the radiographs and the projection-related limitations of radiography compared to CT.

A potential weakness of topological waveguides is that they act on a fixed narrow band of frequencies. However, by 3D printing samples from a photo-responsive polymer, we can obtain a device whose operating frequency can be fine-tuned dynamically using laser excitation. This greatly enhances existing static tunability strategies, typically based on modifying the geometry. We use a version of the classical Su-Schrieffer-Heeger model to demonstrate our approach., Comment: 5 pages, 3 figures

In the recently proposed Graph Vertex Model (GVM), cellular rearrangements are implemented as local graph transformations of the cell aggregate, represented by a knowledge graph [1]. This study extends GVM to incorporate cell division, a critical biological process involved in morphogenesis, homeostasis, and disease progression. Like cellular rearrangements, cell division in GVM begins by identifying a subgraph of nodes and links, involved in the division, by matching suitable graph patterns or templates within the full knowledge graph. The matched subgraph is then transformed to incorporate topological changes within the knowledge graph, caused by the division event. Importantly, when this transformation is applied to a polygon in a 2D tiling, it performs the transformation, required to divide a polygon, indicating that the 3D graph transformation is general and applicable also to 2D vertex models. Our extension of GVM enables the study of the dynamics of growing cell aggregates in 3D to offer new insights into developmental processes and cancer growth., Comment: 8 pages, 4 figures, 1 supplementary document, and 1 supplementary movie

The projected sensitivity of the effective electron neutrino-mass measurement with the KATRIN experiment is below 0.3 eV (90 % CL) after five years of data acquisition. The sensitivity is affected by the increased rate of the background electrons from KATRIN's main spectrometer. A special shifted-analysing-plane (SAP) configuration was developed to reduce this background by a factor of two. The complex layout of electromagnetic fields in the SAP configuration requires a robust method of estimating these fields. We present in this paper a dedicated calibration measurement of the fields using conversion electrons of gaseous $^\mathrm{83m}$Kr, which enables the neutrino-mass measurements in the SAP configuration., Comment: 19 pages, 11 figures

The rod phase as it is expected in the bottom layers of neutron-star crusts is analyzed within the Hartree-Fock-Bogoliubov framework. In order to well describe the interplay between band structure and superfluidity, periodicity of the lattice is taken into account using Bloch boundary conditions. A relative flow between the rods and the surrounding neutron gas is introduced in a time-independent way. This induces a non-trivial phase of the complex order parameter, leading to a counterflow between neutrons inside and outside the rods. With the resulting current, we compute the actual neutron superfluid fraction. For the latter our results are significantly larger than previous ones obtained in normal band theory, indicating that the normal band theory overestimates the entrainment effect., Comment: 11 pages, 6 figures

The "classical" (weak) greedy algorithm is widely used within model order reduction in order to compute a reduced basis in the offline training phase: An a posteriori error estimator is maximized and the snapshot corresponding to the maximizer is added to the basis. Since these snapshots are determined by a sufficiently detailed discretization, the offline phase is often computationally extremely costly. We suggest to replace the serial determination of one snapshot after the other by a parallel approach. In order to do so, we introduce a batch size $b$ and add $b$ snapshots to the current basis in every greedy iteration. These snapshots are computed in parallel. We prove convergence rates for this new batch greedy algorithm and compare them to those of the classical (weak) greedy algorithm in the Hilbert and Banach space case. Then, we present numerical results where we apply a (parallel) implementation of the proposed algorithm to the linear elliptic thermal block problem. We analyze the convergence rate as well as the offline and online wall-clock times for different batch sizes. We show that the proposed variant can significantly speed-up the offline phase while the size of the reduced problem is only moderately increased. The benefit of the parallel batch greedy increases for more complicated problems., Comment: 21 pages, 4 figures

Generation, statistically steady state, and temporal decay of axially rotating thermal counterflow of superfluid $^4$He (He~II) in a square channel is probed using the second sound attenuation technique, measuring the density of quantized vortex lines. The array of rectilinear quantized vortices created by rotation strongly affects the development of quantum turbulence. At relatively slow angular velocities, the type of instability responsible for the destruction of the laminar counterflow qualitatively changes: the growth of seed vortex loops pinned on the channel wall becomes gradually replaced by the growth due to Donnelly-Glaberson instability, which leads to rapid growth of helical Kelvin waves on vortices parallel with applied counterflow. The initial transient growth of vortex line density that follows the sudden start of the counterflow appears self-similar, linear in dimensionless time, $\Omega t$. We show numerically that Kelvin waves of sufficiently strong amplitude reorient the vortices into more flattened shapes, which grow similarly to a free vortex ring. The observed steady state vortex line density at sufficiently high counterflow velocity and its early temporal decay after the counterflow is switched off is not appreciably affected by rotation. It is striking, however, that although the steady state of rotating counterflow is very different from rotating classical grid-generated turbulence, the late temporal decay of both displays similar features: the decay exponent decreases with the rotation rate $\Omega$ from -3/2 towards approximately -0.7, typical for two-dimensional turbulence, consistent with the transition to bidirectional cascade., Comment: 20 pages, 9 figures, 2 videos

We report an estimation of the injected mass composition of ultra-high energy cosmic rays (UHECRs) at energies higher than 10 EeV. The composition is inferred from an energy-dependent sky distribution of UHECR events observed by the Telescope Array surface detector by comparing it to the Large Scale Structure of the local Universe. In the case of negligible extra-galactic magnetic fields the results are consistent with a relatively heavy injected composition at E ~ 10 EeV that becomes lighter up to E ~ 100 EeV, while the composition at E > 100 EeV is very heavy. The latter is true even in the presence of highest experimentally allowed extra-galactic magnetic fields, while the composition at lower energies can be light if a strong EGMF is present. The effect of the uncertainty in the galactic magnetic field on these results is subdominant., Comment: 8 pages, 3 figures, accepted for publication in PRL

We use a new method to estimate the injected mass composition of ultrahigh cosmic rays (UHECRs) at energies higher than 10 EeV. The method is based on comparison of the energy-dependent distribution of cosmic ray arrival directions as measured by the Telescope Array experiment (TA) with that calculated in a given putative model of UHECR under the assumption that sources trace the large-scale structure (LSS) of the Universe. As we report in the companion letter, the TA data show large deflections with respect to the LSS which can be explained, assuming small extra-galactic magnetic fields (EGMF), by an intermediate composition changing to a heavy one (iron) in the highest energy bin. Here we show that these results are robust to uncertainties in UHECR injection spectra, the energy scale of the experiment and galactic magnetic fields (GMF). The assumption of weak EGMF, however, strongly affects this interpretation at all but the highest energies E > 100 EeV, where the remarkable isotropy of the data implies a heavy injected composition even in the case of strong EGMF. This result also holds if UHECR sources are as rare as $2 \times 10^{-5}$ Mpc$^{-3}$, that is the conservative lower limit for the source number density., Comment: 18 pages, 11 figures, accepted for publication in PRD

In this work, we prove over 3000 previously ATP-unproved Mizar/MPTP problems by using several ATP and AI methods, raising the number of ATP-solved Mizar problems from 75\% to above 80\%. First, we start to experiment with the cvc5 SMT solver which uses several instantiation-based heuristics that differ from the superposition-based systems, that were previously applied to Mizar,and add many new solutions. Then we use automated strategy invention to develop cvc5 strategies that largely improve cvc5's performance on the hard problems. In particular, the best invented strategy solves over 14\% more problems than the best previously available cvc5 strategy. We also show that different clausification methods have a high impact on such instantiation-based methods, again producing many new solutions. In total, the methods solve 3021 (21.3\%) of the 14163 previously unsolved hard Mizar problems. This is a new milestone over the Mizar large-theory benchmark and a large strengthening of the hammer methods for Mizar.

Mechanical stresses and strains in the microstructure of cathode materials evolving during charge/discharge cycles can reduce the long-term stability of intercalation-type alkali-metal-ion batteries. In this context, crystalline compounds exhibiting zero-strain (ZS) behavior are of particular interest. Near-ZS sodiation was experimentally measured in the tetragonal tungsten bronze (TTB) type compound Na$_x$FeF$\mathrm{_3}$. Using a first-principles method based on density functional theory, we investigate the potential of iron-based fluoride compounds with tungsten bronze (TB) structures as ZS cathode materials. Simulations were conducted to study the intercalation of the alkali metal ions Li$\mathrm{^+}$, Na$\mathrm{^+}$, and K$\mathrm{^+}$ into the TTB and two related TB structures of the cubic perovskite (PTB) and hexagonal (HTB) types. We describe compensating local volume effects that can explain the experimentally measured low volume change of Na$_x$FeF$\mathrm{_3}$. We discuss the structural and chemical prerequisites of the host lattice for ZS insertion mechanism for alkali ions in TB structures and present a qualitative descriptor to predict the local volume change, that provides a way for faster screening and discovery of novel ZS battery materials., Comment: 10 pages, 6 figures

Cavity electrodynamics offers a unique avenue for tailoring ground-state material properties, excited-state engineering, and versatile control of quantum matter. Merging these concepts with high-field physics in the terahertz (THz) spectral range opens the door to explore low-energy, field-driven cavity electrodynamics, emerging from fundamental resonances or order parameters. Despite this demand, leveraging the full potential of field-driven material control in cavities is hindered by the lack of direct access to the intra-cavity fields. Here, we demonstrate a new concept of active cavities, consisting of electro-optic Fabry-Perot resonators, which measure their intra-cavity electric fields on sub-cycle timescales. We thereby demonstrate quantitative retrieval of the cavity modes in amplitude and phase, over a broad THz frequency range. To enable simultaneous intra-cavity sampling alongside excited-state material control, we design a tunable multi-layer cavity, enabling deterministic design of hybrid cavities for polaritonic systems. Our theoretical models reveal the origin of the avoided crossings embedded in the intricate mode dispersion, and will enable fully-switchable polaritonic effects within arbitrary materials hosted by the hybrid cavity. Electro-optic cavities (EOCs) will therefore serve as integrated probes of light-matter interactions across all coupling regimes, laying the foundation for field-resolved intra-cavity quantum electrodynamics., Comment: main: 7 pages, 4 figurs; total: 34 pages, 20 figures

The fact that neutrinos carry a non-vanishing rest mass is evidence of physics beyond the Standard Model of elementary particles. Their absolute mass bears important relevance from particle physics to cosmology. In this work, we report on the search for the effective electron antineutrino mass with the KATRIN experiment. KATRIN performs precision spectroscopy of the tritium $\beta$-decay close to the kinematic endpoint. Based on the first five neutrino-mass measurement campaigns, we derive a best-fit value of $m_\nu^{2} = {-0.14^{+0.13}_{-0.15}}~\mathrm{eV^2}$, resulting in an upper limit of $m_\nu < {0.45}~\mathrm{eV}$ at 90 % confidence level. With six times the statistics of previous data sets, amounting to 36 million electrons collected in 259 measurement days, a substantial reduction of the background level and improved systematic uncertainties, this result tightens KATRIN's previous bound by a factor of almost two., Comment: 61 pages, 20 figures, 2 tables

Deconfined quantum critical points (DQCPs) are putative phase transitions beyond the Landau paradigm with emergent fractionalized degrees of freedom. The original example of a DQCP is the spin-1/2 quantum antiferromagnet on the square lattice which features a second order transition between valence bond solid (VBS) and N\'eel order. The VBS order breaks a lattice symmetry, and the corresponding VBS order parameter may couple to lattice distortion modes (phonons) at appropriate momenta. We investigate a field-theoretic description of the DQCP in the presence of such a spin-lattice coupling. We show that treating phonons as classical lattice distortions leads to a relevant monopole-phonon interaction inducing an instability towards a distorted lattice by an analogous mechanism to the spin-Peierls instability in one dimension. Consequently, there is a breakdown of the DQCP which generally becomes a strong first-order transition. Taking into account the full quantum nature of the phonons, we argue that the continuous DQCP persists above a critical phonon frequency. Lastly, we comment on the connection to general gapless, deconfined gauge theories., Comment: 12 pages, 3 figures

We report on an observation of the difference between northern and southern skies of the ultrahigh energy cosmic ray energy spectrum with a significance of ${\sim}8\sigma$. We use measurements from the two largest experiments$\unicode{x2014}$the Telescope Array observing the northern hemisphere and the Pierre Auger Observatory viewing the southern hemisphere. Since the comparison of two measurements from different observatories introduces the issue of possible systematic differences between detectors and analyses, we validate the methodology of the comparison by examining the region of the sky where the apertures of the two observatories overlap. Although the spectra differ in this region, we find that there is only a $1.8\sigma$ difference between the spectrum measurements when anisotropic regions are removed and a fiducial cut in the aperture is applied., Comment: 8 pages, 6 figures

In recent years, deep generative models have been successfully adopted for various molecular design tasks, particularly in the life and material sciences. A critical challenge for pre-trained generative molecular design (GMD) models is to fine-tune them to be better suited for downstream design tasks aimed at optimizing specific molecular properties. However, redesigning and training an existing effective generative model from scratch for each new design task is impractical. Furthermore, the black-box nature of typical downstream tasks$\unicode{x2013}$such as property prediction$\unicode{x2013}$makes it nontrivial to optimize the generative model in a task-specific manner. In this work, we propose a novel approach for a model uncertainty-guided fine-tuning of a pre-trained variational autoencoder (VAE)-based GMD model through performance feedback in an active learning setting. The main idea is to quantify model uncertainty in the generative model, which is made efficient by working within a low-dimensional active subspace of the high-dimensional VAE parameters explaining most of the variability in the model's output. The inclusion of model uncertainty expands the space of viable molecules through decoder diversity. We then explore the resulting model uncertainty class via black-box optimization made tractable by low-dimensionality of the active subspace. This enables us to identify and leverage a diverse set of high-performing models to generate enhanced molecules. Empirical results across six target molecular properties, using multiple VAE-based generative models, demonstrate that our uncertainty-guided fine-tuning approach consistently outperforms the original pre-trained models.

In this survey we revisit {\sc finite subtraction}, one-heap subtraction games on finite rulesets. The main purpose is to give a general overview of the development, and specifically to draw attention to Flammenkamp's thesis (1997), where he, contrary to other studies, experimentally observes exponential eventual period length of the outcomes, for a carefully selected subclass of games. In addition, we contribute an appendix on {\sc finite excluded subtraction} by Suetsugu., Comment: 15 pages, 2 figures, Appendix by Koki Suetsugu

Sterile neutrinos are hypothetical particles in the minimal extension of the Standard Model of Particle Physics. They could be viable dark matter candidates if they have a mass in the keV range. The Karlsruhe tritium neutrino (KATRIN) experiment, extended with a silicon drift detector focal plane array (TRISTAN), has the potential to search for keV-scale sterile neutrinos by measuring the kinematics of the tritium $\beta$-decay. The collaboration targets a sensitivity of $10^{-6}$ on the mixing amplitude $\sin^2{\Theta}$. For this challenging target, a precise understanding of the detector response is necessary. In this work, we report on the characterization of electron backscattering from the detector surface, which is one of the main effects that influence the shape of the observed energy spectrum. Measurements were performed with a tandem silicon drift detector system and a custom-designed electron source. The measured detector response and backscattering probability are in good agreement with dedicated backscattering simulations using the Geant4 simulation toolkit.

The interference gating is a novel method for robust time-resolved electron holographic measurements by directly switching the interference. Here, a new arrangement is presented in which a biprism in the condenser aperture as a fast electric phase shifter is used to control the interference pattern. High-frequency stimulation of the electric phase shifter in the gigahertz range are performed and observed via electron holography, proving the feasibility of interference gating in the upper picosecond range. Despite the bandwidth limitation of 180~MHz of the current signal generator, a time resolution of 100 nanoseconds is achieved through forward correction of the control signal. With this time resolution, it is already possible to measure the transient response of the biasing holder system. Our method paves the way towards a closer look on fast dynamic processes with high temporal and spatial resolution.

This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms significantly enhances the accuracy of the results. Simple modifications to the loss function may also improve precision, offering an additional avenue for enhancement. Despite optimization algorithms having a greater impact on convergence than adjustments to the loss function, practical considerations often favor tweaking the latter due to ease of implementation. On a global scale, the integration of an enhanced optimizer and a marginally adjusted loss function enables a reduction in the loss function by several orders of magnitude across diverse physical problems. Consequently, our results obtained using compact networks (typically comprising 2 or 3 layers of 20-30 neurons) achieve accuracies comparable to finite difference schemes employing thousands of grid points. This study encourages the continued advancement of PINNs and associated optimization techniques for broader applications across various fields., Comment: 46 pages, 13 figures, submitted for publication in JCP

Deep generative models have been accelerating the inverse design process in material and drug design. Unlike their counterpart property predictors in typical molecular design frameworks, generative molecular design models have seen fewer efforts on uncertainty quantification (UQ) due to computational challenges in Bayesian inference posed by their large number of parameters. In this work, we focus on the junction-tree variational autoencoder (JT-VAE), a popular model for generative molecular design, and address this issue by leveraging the low dimensional active subspace to capture the uncertainty in the model parameters. Specifically, we approximate the posterior distribution over the active subspace parameters to estimate the epistemic model uncertainty in an extremely high dimensional parameter space. The proposed UQ scheme does not require alteration of the model architecture, making it readily applicable to any pre-trained model. Our experiments demonstrate the efficacy of the AS-based UQ and its potential impact on molecular optimization by exploring the model diversity under epistemic uncertainty.

We investigate a mutual relationship between information and energy during early phase of LTP induction and maintenance in a large-scale system of mutually coupled dendritic spines, with discrete internal states and probabilistic dynamics, within the framework of nonequilibrium stochastic thermodynamics. In order to analyze this computationally intractable stochastic multidimensional system, we introduce a pair approximation, which allows us to reduce the spine dynamics into a lower dimensional manageable system of closed equations. It is found that the rates of information gain and energy attain their maximal values during an initial period of LTP (i.e. during stimulation), and after that they recover to their baseline low values, as opposed to a memory trace that lasts much longer. This suggests that learning phase is much more energy demanding than the memory phase. We show that positive correlations between neighboring spines increase both a duration of memory trace and energy cost during LTP, but the memory time per invested energy increases dramatically for very strong positive synaptic cooperativity, suggesting a beneficial role of synaptic clustering on memory duration. In contrast, information gain after LTP is the largest for negative correlations, and energy efficiency of that information generally declines with increasing synaptic cooperativity. We also find that dendritic spines can use sparse representations for encoding of long-term information, as both energetic and structural efficiencies of retained information and its lifetime exhibit maxima for low fractions of stimulated synapses during LTP. In general, our stochastic thermodynamics approach provides a unifying framework for studying, from first principles, information encoding and its energy cost during learning and memory in stochastic systems of interacting synapses., Comment: Corrected typo in Eq. (14). The paper is about information and its energy cost during synaptic plasticity (synaptic learning)

Normalizing flows are machine-learned maps between different lattice theories which can be used as components in exact sampling and inference schemes. Ongoing work yields increasingly expressive flows on gauge fields, but it remains an open question how flows can improve lattice QCD at state-of-the-art scales. We discuss and demonstrate two applications of flows in replica exchange (parallel tempering) sampling, aimed at improving topological mixing, which are viable with iterative improvements upon presently available flows., Comment: 9 pages, 5 figures, proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023)

We prove that the Lie algebra $\mathfrak{sl}_n(\textbf{F}_q)$ of traceless matrices over a finite field of characteristic $p$ can be generated by $2$ elements with exceptions when $(n, p)$ is $(3, 3)$ or $(4,2)$. In the latter cases, we establish curious identities that obstruct $2$-generation.

Scale separation is an important physical principle that has previously enabled algorithmic advances such as multigrid solvers. Previous work on normalizing flows has been able to utilize scale separation in the context of scalar field theories, but the principle has been largely unexploited in the context of gauge theories. This work gives an overview of a new method for generating gauge fields using hierarchical normalizing flow models. This method builds gauge fields from the outside in, allowing different parts of the model to focus on different scales of the problem. Numerical results are presented for $U(1)$ and $SU(3)$ gauge theories in 2, 3, and 4 spacetime dimensions., Comment: Submitted as a proceedings to the 40th International Symposium on Lattice Field Theory (Lattice 2023)

We investigate nitrogen-vacancy center (NV) ensembles in diamond under the influence of strongly-correlated electron-spin baths. We thoroughly calculate the decoherence properties of the NV central spin for bath concentrations of 0.1-100 ppm using the cluster-correlation expansion (CCE) method. We systematically analyze possible origins of the significant deviations in the values of the $T_2$ coherence time reported in literature. We demonstrate that significant variations can originate from the choice of averaging and fitting procedures used for the ensemble average and we point out the respective aspects that need to be considered, when comparing the various theoretical studies. Our study may ease readers to perform reliable and fast simulations on the central spin problem. It provides an understanding and interpretation of the outcome parameters describing the dynamics of the local bath spins.

In a collinear antiferromagnet, spins tend to cant towards the direction of an applied magnetic field, thereby decreasing the energy of the system. The canting angle becomes negligible when the magnetic field is small so that the induced anisotropic energy is substantially lower than the exchange energy. However, this tiny anisotropy can play a significant role when the intrinsic anisotropy of the antiferromagnet is small. In our work, we conduct direct imaging of the N\'eel vector in a two-dimensional easy-plane antiferromagnet, MnPSe$_3$, with negligible spin canting under an external in-plane magnetic field. The small inherent in-plane anisotropy allows for the continuous rotation of the N\'eel vector by ramping up the magnetic field in samples from the bulk to the monolayer. In monolayer samples, the applied magnetic field elevates the N\'eel temperature 10$\%$ at 5 tesla, as the combination of intrinsic and field-induced anisotropies set a critical temperature scale for fluctuations of the otherwise disordered N\'eel vector field. Our study illuminates the contribution of field-induced anisotropy in two dimensional magnets with in-plane anisotropy. We also demonstrate that the strain can tune the spin flop transition field strength by one order of magnitude.

The TRISTAN detector is a new detector for electron spectroscopy at the Karlsruhe Tritium Neutrino (KATRIN) experiment. The semiconductor detector utilizes the silicon drift detector technology and will enable the precise measurement of the entire tritium beta decay electron spectrum. Thus, a significant fraction of the parameter space of potential neutrino mass eigenstates in the keV-mass regime can be probed. We developed a custom electron gun based on the effect of thermionic emission to characterize the TRISTAN detector modules with mono-energetic electrons before installation into the KATRIN beamline. The electron gun provides an electron beam with up to 25 keV kinetic energy and an electron rate in the order of 1E5 electrons per second. This manuscript gives an overview of the design and commissioning of the electron gun. In addition, we will shortly discuss a first measurement with the electron gun to characterize the electron response of the TRISTAN detector.

Worker-Robot Cooperation is a new industrial trend, which aims to sum the advantages of both the human and the industrial robot to afford a new intelligent manufacturing techniques. The cooperative manufacturing between the worker and the robot contains other elements such as the product parts and the manufacturing tools. All these production elements must cooperate in one manufacturing workcell to fulfill the production requirements. The manufacturing control system is the mean to connect all these cooperative elements together in one body. This manufacturing control system is distributed and autonomous due to the nature of the cooperative workcell. Accordingly, this article proposes the holonic control architecture as the manufacturing concept of the cooperative workcell. Furthermore, the article focuses on the feasibility of this manufacturing concept, by applying it over a case study that involves the cooperation between a dual-arm robot and a worker. During this case study, the worker uses a variety of hand gestures to cooperate with the robot to achieve the highest production flexibility

Cooperative manufacturing is a new trend in industry, which depends on the existence of a collaborative robot. A collaborative robot is usually a light-weight robot which is capable of operating safely with a human co-worker in a shared work environment. During this cooperation, a vast amount of information is exchanged between the collaborative robot and the worker. This information constructs the cooperative manufacturing knowledge, which describes the production components and environment. In this research, we propose a holonic control solution, which uses the ontology concept to represent the cooperative manufacturing knowledge. The holonic control solution is implemented as an autonomous multi-agent system that exchanges the manufacturing knowledge based on an ontology model. Ultimately, the research illustrates and implements the proposed solution over a cooperative assembly scenario, which involves two workers and one collaborative robot, whom cooperate together to assemble a customized product.

The integrated device of a perovskite solar cell with a Li-ion battery is an innovative solution for decentralized energy storage in smart electronic devices. In this study, we examine the stability of Li ions intercalated in a CsPbI$_3$ perovskite and their effect on the electronic structure of Li$_x$CsPbI$_3$ compounds using first-principles density functional theory. Our simulations demonstrate that the insertion of Li at concentrations up to $x$ = 1 into CsPbI$_3$ is energetically possible. Moreover, we identify that the distortion of the Pb-I octahedra has the strongest impact on the change in the electronic band gap. Specifically, an increase in the amount of intercalated Li causes larger structural distortions, which in turn lead to an increasing band gap as function of the Li content.

Optimal control of parametric partial differential equations (PDEs) is crucial in many applications in engineering and science. In recent years, the progress in scientific machine learning has opened up new frontiers for the control of parametric PDEs. In particular, deep reinforcement learning (DRL) has the potential to solve high-dimensional and complex control problems in a large variety of applications. Most DRL methods rely on deep neural network (DNN) control policies. However, for many dynamical systems, DNN-based control policies tend to be over-parametrized, which means they need large amounts of training data, show limited robustness, and lack interpretability. In this work, we leverage dictionary learning and differentiable L$_0$ regularization to learn sparse, robust, and interpretable control policies for parametric PDEs. Our sparse policy architecture is agnostic to the DRL method and can be used in different policy-gradient and actor-critic DRL algorithms without changing their policy-optimization procedure. We test our approach on the challenging tasks of controlling parametric Kuramoto-Sivashinsky and convection-diffusion-reaction PDEs. We show that our method (1) outperforms baseline DNN-based DRL policies, (2) allows for the derivation of interpretable equations of the learned optimal control laws, and (3) generalizes to unseen parameters of the PDE without retraining the policies.

Deep reinforcement learning (DRL) has shown significant promise for uncovering sophisticated control policies that interact in environments with complicated dynamics, such as stabilizing the magnetohydrodynamics of a tokamak fusion reactor or minimizing the drag force exerted on an object in a fluid flow. However, these algorithms require an abundance of training examples and may become prohibitively expensive for many applications. In addition, the reliance on deep neural networks often results in an uninterpretable, black-box policy that may be too computationally expensive to use with certain embedded systems. Recent advances in sparse dictionary learning, such as the sparse identification of nonlinear dynamics (SINDy), have shown promise for creating efficient and interpretable data-driven models in the low-data regime. In this work we introduce SINDy-RL, a unifying framework for combining SINDy and DRL to create efficient, interpretable, and trustworthy representations of the dynamics model, reward function, and control policy. We demonstrate the effectiveness of our approaches on benchmark control environments and challenging fluids problems. SINDy-RL achieves comparable performance to state-of-the-art DRL algorithms using significantly fewer interactions in the environment and results in an interpretable control policy orders of magnitude smaller than a deep neural network policy., Comment: 24 pages + 14 appendices (45 pages total). 25 figures, 7 tables. For code, see https://github.com/nzolman/sindy-rl

We present a theoretical study on the magnetic signals of structural surface defects like cracks or indents combined with rough surfaces or subsurface inclusions of soft ferromagnetic metals like body-centered cubic Fe or amorphous CoFeB. We discuss limits of early detection of small surface defects on the basis of calculated magnetic stray fields few tens of nm above the surface. The considered surface imperfections have extensions of a few nm which correspond to low multiples of the magnetic exchange lengths of Fe or CoFeB. The detection of such small inhomogeneities requires that the sensor is about as close to the surface as the size of the inhomogeneity is. Furthermore, the step width of a scanning sensor must be of the same size as well. Both these requirements may be fulfilled for instance by scanning microscopy with diamond nitrogen-vacancy-center quantum sensors., Comment: 8 pages, 7 figures

Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In practice, such systems however face large combinatorial explosion, and therefore include many heuristics and choice points that considerably influence their performance. This is an opportunity for trained machine learning predictors, which can guide the work of such reasoning systems. Conversely, deductive search supported by the notion of logically valid proof allows one to train machine learning systems on large reasoning corpora. Such bodies of proof are usually correct by construction and when combined with more and more precise trained guidance they can be boostrapped into very large corpora, with increasingly long reasoning chains and possibly novel proof ideas. In this paper we provide an overview of several automated reasoning and theorem proving domains and the learning and AI methods that have been so far developed for them. These include premise selection, proof guidance in several settings, AI systems and feedback loops iterating between reasoning and learning, and symbolic classification problems.

The melting temperature is important for materials design because of its relationship with thermal stability, synthesis, and processing conditions. Current empirical and computational melting point estimation techniques are limited in scope, computational feasibility, or interpretability. We report the development of a machine learning methodology for predicting melting temperatures of binary ionic solid materials. We evaluated different machine-learning models trained on a data set of the melting points of 476 non-metallic crystalline binary compounds, using materials embeddings constructed from elemental properties and density-functional theory calculations as model inputs. A direct supervised-learning approach yields a mean absolute error of around 180~K but suffers from low interpretability. We find that the fidelity of predictions can further be improved by introducing an additional unsupervised-learning step that first classifies the materials before the melting-point regression. Not only does this two-step model exhibit improved accuracy, but the approach also provides a level of interpretability with insights into feature importance and different types of melting that depend on the specific atomic bonding inside a material. Motivated by this finding, we used a symbolic learning approach to find interpretable physical models for the melting temperature, which recovered the best-performing features from both prior models and provided additional interpretability., Comment: 21 pages and 3 figures for the main manuscript, and 11 pages and 15 figures of supplementary information

The phase transition layered Li$_{0.5}$NiO$_2$ to spinel Li(NiO$_2$)$_2$ is a potential degradation pathway in LiNiO$_2$-based lithium-ion battery cathodes. We investigated the mechanism of this phase transformation from first principles. Consistent with experimental observations reported in the literature, our results indicate a high energy barrier for the transformation due to high defect-formation energies, a complex charge-transfer mechanism, and electronic frustration. Our results suggest that partially inverse spinel phases are unlikely to form for Li$_{0.5}$NiO$_2$, a qualitative difference from the chemically similar Li$_{0.5}$MnO$_2$, in which the transformation occurs at room temperature. We show that Ni and Li atoms migrate concertedly towards their respective spinel sites for the layered-to-spinel transformation to occur. We investigated the charge ordering in layered phases along the LiNiO$_2$-NiO$_2$ composition line, finding a pronounced impact of the symmetry and space group on the layered-to-spinel transition in Li$_{0.5}$NiO$_2$. Finally, we evaluated the relative stability of different spinel space groups, finding that previously reported experimental observations are consistent with a temperature-averaged structure rather than the 0 Kelvin ground-state structure of Li(NiO$_2$)$_2$ spinel., Comment: 29 pages and 8 figures in the main manuscript, and 15 pages and 7 figures of supplementary information

Halide perovskites are highly promising light-harvesting materials with strong ionic character, enabling in principle the combination of a solar cell and a Li-ion battery in one integrated photo-battery device. Here, we investigate Li ions inside crystals of CsPbI$_3$, as a prototype compound, by means of density-functional-theory calculations. Our findings demonstrate that the interstitial location and migration of Li ions depend strongly on the dynamic nature of the crystal structure of the perovskite compound. We consider two limiting cases for Li in CsPbI$_{3}$,(i) the cubic-symmetry structure as a model for the limit of fast ion motion and (ii) a distorted cubic structure as a model for the limit of slow ion motion. For both limiting cases we obtain moderate energy barriers for migrating Li ions, which highlight the potential of halide perovskites like CsPbI$_3$ for applications in photo-battery devices.

The control of antiferromagnets with ultrashort optical pulses has emerged as a prominent field of research. Tailored laser excitation can launch coherent spin waves at terahertz frequencies, yet a comprehensive description of their generation mechanisms is still lacking despite extensive efforts. Using terahertz emission spectroscopy, we investigate the generation of a coherent magnon mode in the van der Waals antiferromagnet NiPS$_3$ under a range of photoexcitation conditions. By tuning the pump photon energy from transparency to resonant with a $d$-$d$ transition, we reveal a striking change in the coherent magnon's dependence on the pump polarization, indicating two distinct excitation mechanisms. Our findings provide a strategy for the manipulation of magnetic modes via photoexcitation around sub-gap electronic states., Comment: 15 pages, 14 figures

We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to speed up computation. The resulting method, Bayesian-SINDy, not only quantifies uncertainty in the parameters estimated but also is more robust when learning the correct model from limited and noisy data. Using both synthetic and real-life examples such as Lynx-Hare population dynamics, we demonstrate the effectiveness of the new framework in learning correct model equations and compare its computational and data efficiency with existing methods. Because Bayesian-SINDy can quickly assimilate data and is robust against noise, it is particularly suitable for biological data and real-time system identification in control. Its probabilistic framework also enables the calculation of information entropy, laying the foundation for an active learning strategy., Comment: 25 pages, 14 figures

We show that the maximal globally hyperbolic development of near-FLRW initial data for the Einstein scalar-field Vlasov system exhibits stable Big Bang formation in the collapsing direction, i.e., stable Kretschmann scalar blow-up, causing the spacetime to become past incomplete. This is the first stability result towards the collapsing direction in the presence of Vlasov matter. Furthermore, while the asymptotic behaviour of Vlasov matter is close to that of the FLRW solution up to a small change in asymptotic order controlled by initial data, generically, the distribution function itself asymptotically concentrates in certain preferred directions that are teleologically determined. To ensure that this behaviour is sufficiently mitigated by the scalar field, we crucially exploit a scaling hierarchy between horizontal and vertical derivatives in the Vlasov equation., Comment: 72 pages

There are many combinatorial games in which a move can terminate the game, such as a checkmate in chess. These moves give rise to diverse situations that fall outside the scope of the classical normal play structure. To analyze these games, an algebraic extension is necessary, including infinities as elements. In this work, affine normal play, the algebraic structure resulting from that extension, is analyzed. We prove that it is possible to compare two affine games using only their forms. Furthermore, affine games can still be reduced, although the reduced forms are not unique. We establish that the classical normal play is order-embedded in the extended structure, constituting its substructure of invertible elements. Additionally, as in classical theory, affine games born by day n form a lattice with respect to the partial order of games., Comment: 68 pages, 24 figures

Ultra-light dark matter perturbs the orbital motion of binary pulsars, in particular by causing peculiar time variations of a binary's orbital parameters, which then induce variations in the pulses' times-of-arrival. Binary pulsars have therefore been shown to be promising detectors of ultra-light dark matter. To date, the sensitivity of binary pulsars to ultra-light dark matter has only been studied for dark matter masses in a narrow resonance band around a multiple of the binary pulsar orbital frequency. In this study we devise a two-step, bayesian method that enables us to compute semi-analytically the sensitivity for all masses, also away from the resonance, and to combine several observed binaries into one global sensitivity curve. We then apply our method to the case of a universal, linearly-coupled, scalar ultra-light dark matter. We find that with next-generation radio observatories the sensitivity to the ultra-light dark matter coupling will surpass that of solar-system constraints for a decade in mass around $m\sim10^{-21}$ $\text{eV}$, even beyond resonance., Comment: 40 pages,15 figures