Search

The method of complex Langevin simulations is a tool that can be used to tackle the complex-action problem encountered, for instance, in finite-density lattice quantum chromodynamics or real-time lattice field theories. The method is based on a stochastic evolution of the dynamical degrees of freedom via (complex) Langevin equations, which, however, sometimes converge to the wrong equilibrium distributions. While the convergence properties of the evolution can to some extent be assessed by studying so-called boundary terms, we demonstrate in this contribution that boundary terms on their own are not sufficient as a correctness criterion. Indeed, in their absence complex Langevin simulation results might still be spoiled by unwanted so-called integration cycles. In particular, we elaborate on how the introduction of a kernel into the complex Langevin equation can - in principle - be used to control which integration cycles are sampled in a simulation such that correct convergence is restored., Comment: 7 pages, 3 figures; Proceedings of the 41st International Symposium on Lattice Field Theory (LATTICE 2024), 28th July - 3rd August 2024, Liverpool, United Kingdom

Decoupling charge and heat transport is essential for optimizing thermoelectric materials. Strategies to inhibit lattice-driven heat transport, however, also compromise carrier mobility, limiting the performance of most thermoelectrics, including Fe$_2$VAl Heusler compounds. Here, we demonstrate an innovative approach, which bypasses this tradeoff: via liquid-phase sintering, we incorporate the archetypal topological insulator Bi$_{1-x}$Sb$_{x}$ between Fe$_2$V$_{0.95}$Ta$_{0.1}$Al$_{0.95}$ grains. Structural investigations alongside extensive thermoelectric and magneto-transport measurements reveal distinct modifications in the microstructure, and a reduced lattice thermal conductivity and enhanced carrier mobility are simultaneously found. This yields a huge performance boost $-$ far beyond the effective-medium limit $-$ and results in one of the highest figure of merits among both half- and full-Heusler compounds, $z\approx 1.6\times 10^{-3}\,$K$^{-1}$ ($zT\approx 0.5$) at 295 K. Our findings highlight the potential of secondary phases to decouple charge and heat transport and call for more advanced theoretical studies of multiphase composites.

Machine Learning (ML) is crucial in many sectors, including computer vision. However, ML models trained on sensitive data face security challenges, as they can be attacked and leak information. Privacy-Preserving Machine Learning (PPML) addresses this by using Differential Privacy (DP) to balance utility and privacy. This study identifies image dataset characteristics that affect the utility and vulnerability of private and non-private Convolutional Neural Network (CNN) models. Through analyzing multiple datasets and privacy budgets, we find that imbalanced datasets increase vulnerability in minority classes, but DP mitigates this issue. Datasets with fewer classes improve both model utility and privacy, while high entropy or low Fisher Discriminant Ratio (FDR) datasets deteriorate the utility-privacy trade-off. These insights offer valuable guidance for practitioners and researchers in estimating and optimizing the utility-privacy trade-off in image datasets, helping to inform data and privacy modifications for better outcomes based on dataset characteristics.

In this article we show that the empirical measure of certain continuous time random walks satisfies a strong large deviation principle with respect to a topology introduced in~\cite{MV2016} by Mukherjee and Varadhan. This topology is natural in models which exhibit an invariance with respect to spatial translations. Our result applies in particular to the case of simple random walk and complements the results obtained in~\cite{MV2016} in which the large deviation principle has been established for the empirical measure of Brownian motion., Comment: 20 pages

In this work, we establish a Trotter-Kato type theorem. More precisely, we characterize the convergence in distribution of Feller processes by examining the convergence of their generators. The main novelty lies in providing quantitative estimates in the vague topology at any fixed time. As important applications, we deduce functional central limit theorems for random walks on the positive integers with boundary conditions, which converge to Brownian motions on the positive half-line with boundary conditions at zero., Comment: 31 pages, 12 figures

We prove several results on reductive group schemes over LG-rings, e.g., existence of maximal tori and conjugacy of parabolic subgroups. These were proven in SGA3 for the special case of semilocal rings. We apply these results to establish cancellation theorems for hermitian and quadratic forms over LG-rings and show that the Brauer classes of Azumaya algebras over connected LG-rings have a unique representative and allow Brauer decomposition.

Characteristic shock effects in silica serve as a key indicator of historical impacts at geological sites. Despite this geological significance, atomistic details of structural transformations under high pressure and shock compression remain poorly understood. This ambiguity is evidenced by conflicting experimental observations of both amorphization and crystallization transitions. Utilizing a newly developed machine-learning interatomic potential, we examine the response of $\alpha$-quartz to shock compression with a peak pressure of 60 GPa over nano-second timescales. We initially observe amorphization before recrystallization into a d-NiAs-structured silica with disorder on the silicon sublattice, accompanied by the formation of domains with partial order of silicon. Investigating a variety of strain conditions enables us to identify the non-hydrostatic stress and strain states that allow the direct diffusionless formation of rosiaite-structured silica.

We provide a self-contained introduction to Gr\"obner bases of submodules of $R[x_1, \ldots, x_n]^k$, where $R$ is a Euclidean domain, and explain how to use these bases to solve linear systems over $R[x_1, \ldots, x_n]$., Comment: Survey paper

Efficient, reliable and easy-to-use structure recognition of atomic environments is essential for the analysis of atomic scale computer simulations. In this work, we train two neuronal network (NN) architectures, namely PointNet and dynamic graph convolutional NN (DG-CNN) using different hyperparameters and training regimes to assess their performance in structure identification tasks of atomistic structure data. We show benchmarks on simple crystal structures, where we can compare against established methods. The approach is subsequently extended to structurally more complex SiO$_2$ phases. By making use of this structure recognition tool, we are able to achieve a deeper understanding of the crystallization process in amorphous SiO$_2$ under shock compression. Lastly, we show how the NN based structure identification workflows can be integrated into OVITO using its python interface.

We consider the (discrete) parabolic Anderson model $\partial u(t,x)/\partial t=\Delta u(t,x) +\xi_t(x) u(t,x)$, $t\geq 0$, $x\in \mathbb{Z}^d$. Here, the $\xi$-field is $\mathbb{R}$-valued, acting as a dynamic random environment, and $\Delta$ represents the discrete Laplacian. We focus on the case where $\xi$ is given by a rescaled symmetric simple exclusion process which converges to an Ornstein--Uhlenbeck process. By scaling the Laplacian diffusively and considering the equation on a torus, we demonstrate that in dimension $d=2$, when a suitably renormalized version of the above equation is considered, the sequence of solutions converges in law. This resolves an open problem from~\cite{EH23}, where a similar result was shown in the three-dimensional case. The novel contribution in the present work is the establishment of a gradient bound on the transition probability of a fixed but arbitrary number of labelled exclusion particles., Comment: arXiv admin note: text overlap with arXiv:2103.13479

The results of a recent simulation with a complex global climate model suggest that the overturning component of the freshwater transport at the southern boundary of the Atlantic could be used as an early-warning indicator of an AMOC collapse. However, there are two shortcomings. Firstly, the simulation is based on some implausible assumptions. It is therefore not clear whether this new indicator will still be helpful in a more realistic setting. Secondly, the statistical methods employed in the simulation work only for time series that are much longer than the currently available historical series. As not much can be done in the short term about the first issue, this paper focuses on the second issue. It is shown that it is possible to use alternative statistical methods that can do the job at least as well and, moreover, are also suitable for short series. Applying these more appropriate methods to historical data obtained with an ocean reanalysis system, no indication of an imminent AMOC collapse is found., Comment: 7 pages, 2 figures

We construct a globalization of Ferrand's norm functor over rings which generalizes it to the setting of a finite locally free morphism of schemes $T\to S$ of constant rank. It sends quasi-coherent modules over $T$ to quasi-coherent modules over $S$. These functors restrict to the category of quasi-coherent algebras. We also assemble these functors into a norm morphism from the stack of quasi-coherent modules over a finite locally free of constant rank extension of the base scheme into the stack of quasi-coherent modules. This morphism also restricts to the analogous stacks of algebras. Restricting our attention to finite \'etale covers, we give a cohomological description of the norm morphism in terms of the Segre embedding. Using this cohomological description, we show that the norm gives an equivalence of stacks of algebras $A_1^2 \equiv D_2$, akin to the result shown in The Book of Involutions., Comment: 89 pages

Cluster repair methods aim to determine errors in clusters and modify them so that each cluster consists of records representing the same entity. Current cluster repair methodologies primarily assume duplicate-free data sources, where each record from one source corresponds to a unique record from another. However, real-world data often deviates from this assumption due to quality issues. Recent approaches apply clustering methods in combination with link categorization methods so they can be applied to data sources with duplicates. Nevertheless, the results do not show a clear picture since the quality highly varies depending on the configuration and dataset. In this study, we introduce a novel approach for cluster repair that utilizes graph metrics derived from the underlying similarity graphs. These metrics are pivotal in constructing a classification model to distinguish between correct and incorrect edges. To address the challenge of limited training data, we integrate an active learning mechanism tailored to cluster-specific attributes. The evaluation shows that the method outperforms existing cluster repair methods without distinguishing between duplicate-free or dirty data sources. Notably, our modified active learning strategy exhibits enhanced performance when dealing with datasets containing duplicates, showcasing its effectiveness in such scenarios.

Smartwatch health sensor data are increasingly utilized in smart health applications and patient monitoring, including stress detection. However, such medical data often comprise sensitive personal information and are resource-intensive to acquire for research purposes. In response to this challenge, we introduce the privacy-aware synthetization of multi-sensor smartwatch health readings related to moments of stress, employing Generative Adversarial Networks (GANs) and Differential Privacy (DP) safeguards. Our method not only protects patient information but also enhances data availability for research. To ensure its usefulness, we test synthetic data from multiple GANs and employ different data enhancement strategies on an actual stress detection task. Our GAN-based augmentation methods demonstrate significant improvements in model performance, with private DP training scenarios observing an 11.90-15.48% increase in F1-score, while non-private training scenarios still see a 0.45% boost. These results underline the potential of differentially private synthetic data in optimizing utility-privacy trade-offs, especially with the limited availability of real training samples. Through rigorous quality assessments, we confirm the integrity and plausibility of our synthetic data, which, however, are significantly impacted when increasing privacy requirements., Comment: Published in the MDPI Sensors Journal

The weakly relational domain of Octagons offers a decent compromise between precision and efficiency for numerical properties. Here, we are concerned with the construction of non-numerical relational domains. We provide a general construction of weakly relational domains, which we exemplify with an extension of constant propagation by disjunctions. Since for the resulting domain of 2-disjunctive formulas, satisfiability is NP-complete, we provide a general construction for a further, more abstract weakly relational domain where the abstract operations of restriction and least upper bound can be efficiently implemented. In the second step, we consider a relational domain that tracks conjunctions of inequalities between variables, and between variables and constants for arbitrary partial orders of values. Examples are sub(multi)sets, as well as prefix, substring or scattered substring orderings on strings. When the partial order is a lattice, we provide precise polynomial algorithms for satisfiability, restriction, and the best abstraction of disjunction. Complementary to the constructions for lattices, we find that, in general, satisfiability of conjunctions is NP-complete. We therefore again provide polynomial abstract versions of restriction, conjunction, and join. By using our generic constructions, these domains are extended to weakly relational domains that additionally track disjunctions. For all our domains, we indicate how abstract transformers for assignments and guards can be constructed., Comment: 15 pages

We present the first hardware implementation of electrostatic interaction energies using a trapped-ion quantum computer. As test system for our computation, we focus on the reduction of $\mathrm{NO}$ to $\mathrm{N}_2\mathrm{O}$ catalyzed by a nitric oxide reductase (NOR). The quantum computer is used to generate an approximate ground state within the NOR active space. To efficiently measure the necessary one-particle density matrices, we incorporate fermionic basis rotations into the quantum circuit without extending the circuit length, laying the groundwork for further efficient measurement routines using factorizations. Measurements in the computational basis are then used as inputs for computing the electrostatic interaction energies on a classical computer. Our experimental results strongly agree with classical noise-less simulations of the same circuits, finding electrostatic interaction energies within chemical accuracy despite hardware noise. This work shows that algorithms tailored to specific observables of interest, such as interaction energies, may require significantly fewer quantum resources than individual ground state energies would in the straightforward supermolecular approach.

Witnesses record automated program analysis results and make them exchangeable. To validate correctness witnesses through abstract interpretation, we introduce a novel abstract operation unassume. This operator incorporates witness invariants into the abstract program state. Given suitable invariants, the unassume operation can accelerate fixpoint convergence and yield more precise results. We demonstrate the feasibility of this approach by augmenting an abstract interpreter with unassume operators and evaluating the impact of incorporating witnesses on performance and precision. Using manually crafted witnesses, we can confirm verification results for multi-threaded programs with a reduction in effort ranging from 7% to 47% in CPU time. More intriguingly, we discover that using witnesses from model checkers can guide our analyzer to verify program properties that it could not verify on its own., Comment: 29 pages, 4 figures, 2 tables, extended version of the paper which is to appear at VMCAI 2024

The rise of populism concerns many political scientists and practitioners, yet the detection of its underlying language remains fragmentary. This paper aims to provide a reliable, valid, and scalable approach to measure populist stances. For that purpose, we created an annotated dataset based on parliamentary speeches of the German Bundestag (2013 to 2021). Following the ideational definition of populism, we label moralizing references to the virtuous people or the corrupt elite as core dimensions of populist language. To identify, in addition, how the thin ideology of populism is thickened, we annotate how populist statements are attached to left-wing or right-wing host ideologies. We then train a transformer-based model (PopBERT) as a multilabel classifier to detect and quantify each dimension. A battery of validation checks reveals that the model has a strong predictive accuracy, provides high qualitative face validity, matches party rankings of expert surveys, and detects out-of-sample text snippets correctly. PopBERT enables dynamic analyses of how German-speaking politicians and parties use populist language as a strategic device. Furthermore, the annotator-level data may also be applied in cross-domain applications or to develop related classifiers.

Silicon-oxygen compounds are among the most important ones in the natural sciences, occurring as building blocks in minerals and being used in semiconductors and catalysis. Beyond the well known silicon dioxide, there are phases with different stoichiometric composition and nanostructured composites. One of the key challenges in understanding the Si-O system is therefore to accurately account for its nanoscale heterogeneity beyond the length scale of individual atoms. Here we show that a unified computational description of the full Si-O system is indeed possible, based on atomistic machine learning coupled to an active-learning workflow. We showcase applications to very-high-pressure silica, to surfaces and aerogels, and to the structure of amorphous silicon monoxide. In a wider context, our work illustrates how structural complexity in functional materials beyond the atomic and few-nanometre length scales can be captured with active machine learning.

We consider the simple random walk on the Euclidean lattice, in three dimensions and higher, conditioned to visit fewer sites than expected, when the deviation from the mean scales like the mean. The associated large deviation principle was first derived in 2001 by van den Berg, Bolthausen and den Hollander in the continuous setting, that is for the volume of a Wiener sausage, and later taken up by Phetpradap in the discrete setting. One of the key ideas in their work is to condition the range of the random walk to a certain skeleton, that is a sub-sequence of the random walk path taken along an appropriate mesoscopic scale. In this paper we prove that (i) the rate function obtained by van den Berg, Bolthausen and den Hollander has a unique minimizer over the set of probability measures modulo shifts, at least for deviations of the range well below the mean, and (ii) the empirical measure of the skeleton converges under the conditioned law, in a certain manner, to this minimizer. To this end we use an adaptation of the topology recently introduced by Mukherjee and Varadhan to compactify the space of probability measures.

In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize equational domains, with respect to polynomial equations, inside congruence permutable varieties, and with respect to term equations, among all algebras of size two and all algebras of size three with a cyclic automorphism. Furthermore, for each size at least three, we prove that, modulo term equivalence, there is a continuum of equational domains of that size., Comment: 50 pages, 1 figure, 1 table

Wearables are widely used for health data collection due to their availability and advanced sensors, enabling smart health applications like stress detection. However, the sensitivity of personal health data raises significant privacy concerns. While user de-identification by removing direct identifiers such as names and addresses is commonly employed to protect privacy, the data itself can still be exploited to re-identify individuals. We introduce a novel framework for similarity-based Dynamic Time Warping (DTW) re-identification attacks on time series health data. Using the WESAD dataset and two larger synthetic datasets, we demonstrate that even short segments of sensor data can achieve perfect re-identification with our Slicing-DTW-Attack. Our attack is independent of training data and computes similarity rankings in about 2 minutes for 10,000 subjects on a single CPU core. These findings highlight that de-identification alone is insufficient to protect privacy. As a defense, we show that adding random noise to the signals significantly reduces re-identification risk while only moderately affecting usability in stress detection tasks, offering a promising approach to balancing privacy and utility.

A load sharing system has several components and the failure of one component can affect the lifetime of the surviving components. Since component failure does not equate to system failure for different system designs, the analysis of the dependency structure between components becomes a meaningful exercise. The Extended Sequential Order Statistics model allows us to model a dependence structure between heterogeneous components in load sharing systems. However, the results may suggest that the risk of failure decreases as components fail sequentially, which can be counterintuitive, especially when data is scarce. We propose to address this issue by imposing an order restriction on the model parameters that represent increasing failure risks. This assumption corresponds more realistically to the physical properties of the system in many applications. We discuss the advantages of the newly proposed estimates and describe situations where they should be used with caution.

We demonstrate the generation of unbalanced two-photon entanglement in the Laguerre-Gaussian (LG) transverse-spatial degree-of-freedom, where one photon carries a fundamental (Gauss) mode and the other a higher-order LG mode with a non-zero azimuthal ($\ell$) or radial ($p$) component. Taking a cue from the $N00N$ state nomenclature, we call these types of states $\ell 00 \ell$-entangled. They are generated by shifting one photon in the LG mode space and combining it with a second (initially uncorrelated) photon at a beamsplitter, followed by coincidence detection. In order to verify two-photon coherence, we demonstrate a two-photon ``twisted'' quantum eraser, where Hong-Ou-Mandel interference is recovered between two distinguishable photons by projecting them into a rotated LG superposition basis. Using an entanglement witness, we find that our generated states have fidelities of 95.31\% and 89.80\% to their respective ideal maximally entangled states. Besides being of fundamental interest, this type of entanglement will likely have a significant impact on tickling the average quantum physicist's funny bone., Comment: Written for submission to the AVS Quantum Science special issue in memory of Jon Dowling