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Based on ab initio calculations, we demonstrate that a Mott insulator LaTiO$_3$ (LTO), not inspected previously as an altermagnetic material, shows the characteristic features of altermagnets, i.e., (i) fully compensated antiferromagnetism and (ii) $\mathbf{k}$-dependent spin-split electron bands in the absence of spin-orbit coupling. The altermagnetic ground state of LTO is protected by the crystal symmetry and specifically ordered $d$-orbitals of Ti ions with the orbital momentum $l=2.$ The altermagnetism occurs when sites of Ti pair in the unit cell are occupied by single electrons with $m=-1,s_{z}=+1/2$ and $m=+1,s_{z}=-1/2$ per site, with $m$ and $s_{z}-$ being the $z-$ component of the orbital momentum and spin, respectively. By further simulating orbital disorder within the Green's function method, we disclose its damaging character on the spin splitting and the resulting altermagnetism. When the single-electron spin-polarized state at each Ti site is contributed almost equally by two or three $t_{2g}$ orbitals, LTO becomes antiferromagnetic. The effect of the spin-orbit coupling, which can cause orbital disorder and suppress altermagnetism, is discussed., Comment: 6 pages, 7 figures

We present the results of the "Fast Calorimeter Simulation Challenge 2022" - the CaloChallenge. We study state-of-the-art generative models on four calorimeter shower datasets of increasing dimensionality, ranging from a few hundred voxels to a few tens of thousand voxels. The 31 individual submissions span a wide range of current popular generative architectures, including Variational AutoEncoders (VAEs), Generative Adversarial Networks (GANs), Normalizing Flows, Diffusion models, and models based on Conditional Flow Matching. We compare all submissions in terms of quality of generated calorimeter showers, as well as shower generation time and model size. To assess the quality we use a broad range of different metrics including differences in 1-dimensional histograms of observables, KPD/FPD scores, AUCs of binary classifiers, and the log-posterior of a multiclass classifier. The results of the CaloChallenge provide the most complete and comprehensive survey of cutting-edge approaches to calorimeter fast simulation to date. In addition, our work provides a uniquely detailed perspective on the important problem of how to evaluate generative models. As such, the results presented here should be applicable for other domains that use generative AI and require fast and faithful generation of samples in a large phase space., Comment: 204 pages, 100+ figures, 30+ tables

Understanding the variation of the optimal value with respect to change in the data is an old problem of mathematical optimisation. This paper focuses on the linear problem $f(\lambda) = \min c^t x$ such that $(A+\lambda D)x \leq b$, where $\lambda$ is an unknown parameter that varies within an interval and $D$ is a matrix modifying the coefficients of the constraint matrix $A$. This problem is used to analyse the impact of multiple affine changes in the constraint matrix on the objective function. The function $f(\lambda)$ can have an erratic behaviour and computing it for a large number of points is computationally heavy while not providing any guarantees in between the computed points. As a new approach to the problem, we derive several bounding methods that provide guarantees on the objective function's behaviour. Those guarantees can be exploited to avoid recomputing the problem for numerous $\lambda$. The bounding methods are based on approaches from robust optimisation or Lagrangian relaxations. For each approach, we derive three methods of increasing complexity and precision, one that provides constant bounds, one that provides $\lambda$-dependant bounds and envelope bounds. We assess each bounding method in terms of precision, availability and timing. We show that for a large number of problems, the bound approach outperforms the naive sampling approach considered with 100 points while still providing a good precision and stronger guarantees on a large dataset of problems. We also introduce an iterative algorithm that uses these bounds to compute an approximation of the original function within a given error threshold and discuss its performances.

In the modelling of stochastic phenomena, such as quasi-reaction systems, parameter estimation of kinetic rates can be challenging, particularly when the time gap between consecutive measurements is large. Local linear approximation approaches account for the stochasticity in the system but fail to capture the nonlinear nature of the underlying process. At the mean level, the dynamics of the system can be described by a system of ODEs, which have an explicit solution only for simple unitary systems. An analytical solution for generic quasi-reaction systems is proposed via a first order Taylor approximation of the hazard rate. This allows a nonlinear forward prediction of the future dynamics given the current state of the system. Predictions and corresponding observations are embedded in a nonlinear least-squares approach for parameter estimation. The performance of the algorithm is compared to existing SDE and ODE-based methods via a simulation study. Besides the increased computational efficiency of the approach, the results show an improvement in the kinetic rate estimation, particularly for data observed at large time intervals. Additionally, the availability of an explicit solution makes the method robust to stiffness, which is often present in biological systems. An illustration on Rhesus Macaque data shows the applicability of the approach to the study of cell differentiation.

Future autonomous mobile systems will greatly benefit from cooperation and real-time sensor data exchange using V2X communication. In such applications, wireless communication has to cope with stringent real-time and safety constraints, a huge challenge given the inherently lossy wireless communication with highly dynamic channel and error conditions. To meet the safety and real-time goals, the use of state-of-the-art (5G and 802.11) V2X technologies focuses on reliable exchange of small data objects, as in URLLC. In contrast, reliable low-latency exchange of large data, such as camera frames, has received little attention, despite its predicted benefits in safe perception and cooperation. The LOTUS project, outlined in this paper, exploits the specific properties of large application data objects to develop novel, application-aware mechanisms for low-latency reliable large data exchange on top of existing and future V2X technologies. Evaluation with statistical analysis, simulation, and physical prototypes demonstrates the feasibility of low-latency large data object exchange at unprecedented levels of reliability.

A version control system, such as Git, requires a way to integrate changes from different developers or branches. Given a merge scenario, a merge tool either outputs a clean integration of the changes, or it outputs a conflict for manual resolution. A clean integration is correct if it preserves intended program behavior, and is incorrect otherwise (e.g., if it causes a test failure). Manual resolution consumes valuable developer time, and correcting a defect introduced by an incorrect merge is even more costly. New merge tools have been proposed, but they have not yet been evaluated against one another. Prior evaluations do not properly distinguish between correct and incorrect merges, are not evaluated on a realistic set of merge scenarios, and/or do not compare to state-of-the-art tools. We have performed a more realistic evaluation. The results differ significantly from previous claims, setting the record straight and enabling better future research. Our novel experimental methodology combines running test suites, examining merges on deleted branches, and accounting for the cost of incorrect merges. Based on these evaluations, we created a merge tool that out-performs all previous tools under most assumptions. It handles the most common merge scenarios in practice., Comment: ASE 2024

Path planning is an essential component of autonomous driving. A global planner is responsible for the high-level planning. It basically performs a shortest-path search on a known map, thereby defining waypoints used to control the local (low-level) planner. Local planning is a runtime verification method which is repeatedly run on the vehicle itself in real-time, so as to find the optimal short-horizon path which leads to the desired waypoint in a way which is both efficient and safe. The challenge is that the local planner has to take into account repeatedly incoming updates about the information available of the environment. In addition, it performs a complex task, as it has to take into account a large variety of requirements, originating from the necessity of collision avoidance with obstacles, respecting traffic rules, sticking to regulatory requirements, and lastly to reach the next waypoint efficiently. In this paper, we describe a logic-based specification mechanism which fulfills all these requirements., Comment: 10 pages, 5 Figures, 1 Table, Accepted as a short paper at 27th Brazilian Symposium on Formal Methods (SBMF 2024)

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.

The Euler Characteristic Transform (ECT) is a powerful invariant for assessing geometrical and topological characteristics of a large variety of objects, including graphs and embedded simplicial complexes. Although the ECT is invertible in theory, no explicit algorithm for general data sets exists. In this paper, we address this lack and demonstrate that it is possible to learn the inversion, permitting us to develop a novel framework for shape generation tasks on point clouds. Our model exhibits high quality in reconstruction and generation tasks, affords efficient latent-space interpolation, and is orders of magnitude faster than existing methods.

Calibrating verbalized probabilities presents a novel approach for reliably assessing and leveraging outputs from black-box Large Language Models (LLMs). Recent methods have demonstrated improved calibration by applying techniques like Platt scaling or temperature scaling to the confidence scores generated by LLMs. In this paper, we explore the calibration of verbalized probability distributions for discriminative tasks. First, we investigate the capability of LLMs to generate probability distributions over categorical labels. We theoretically and empirically identify the issue of re-softmax arising from the scaling of verbalized probabilities, and propose using the invert softmax trick to approximate the "logit" by inverting verbalized probabilities. Through extensive evaluation on three public datasets, we demonstrate: (1) the robust capability of LLMs in generating class distributions, and (2) the effectiveness of the invert softmax trick in estimating logits, which, in turn, facilitates post-calibration adjustments., Comment: 21 pages

The rising interest in leveraging higher-order interactions present in complex systems has led to a surge in more expressive models exploiting high-order structures in the data, especially in topological deep learning (TDL), which designs neural networks on high-order domains such as simplicial complexes. However, progress in this field is hindered by the scarcity of datasets for benchmarking these architectures. To address this gap, we introduce MANTRA, the first large-scale, diverse, and intrinsically high order dataset for benchmarking high-order models, comprising over 43,000 and 249,000 triangulations of surfaces and three-dimensional manifolds, respectively. With MANTRA, we assess several graph- and simplicial complex-based models on three topological classification tasks. We demonstrate that while simplicial complex-based neural networks generally outperform their graph-based counterparts in capturing simple topological invariants, they also struggle, suggesting a rethink of TDL. Thus, MANTRA serves as a benchmark for assessing and advancing topological methods, leading the way for more effective high-order models., Comment: 26 pages, 2 figures, 22 tables

Many-body interactions in metal-organic frameworks are fundamental for emergent quantum physics. Unlike their solution counterpart, magnetization at surfaces in low-dimensional analogues is strongly influenced by magnetic anisotropy induced by the substrate and still not well understood. Here, we use on-surface coordination chemistry to synthesize on Ag(111) and superconducting Pb(111) an iron-based spin chain by using pyrene-4,5,9,10-tetraone precursors as ligands. Using low-temperature scanning probe microscopy, we compare their structures and low-energy spin excitations of coordinated Fe atoms with high S = 2 spin-state. Although the chain and coordination centers are identical on both substrates, the long-range spin-spin coupling due to a superexchange through the ligand observed on Ag is absent on Pb(111). We ascribe this reduction of spin-spin interactions on Pb to the depletion of electronic states around the Fermi level in the Pb(111) superconductor as compared to silver.

For a fixed prime power $q$, let $\text{GL}_\bullet(q)$ denote the family of groups $\text{GL}_N(q)$ for $N \in \mathbb{Z}_{\geq 0}$. In this paper we study the $\mathbb{C}$-algebra of "stable" class functions of $\text{GL}_\bullet(q)$, and show it admits four different linear bases, each arising naturally in different settings. One such basis is that of stable irreducible characters, namely, the class functions spanned by the characters corresponding to finitely generated simple $\mathrm{VI}$-modules in the sense of [arXiv:1408.3694,arXiv:1602.00654]. A second one comes from characters of parabolic representations. The final two, one originally defined in [arXiv:1803.04155] and the other in [arXiv:2110.11099], are more combinatorial in nature. As corollaries, we clarify many properties of these four bases and prove a conjecture from [arXiv:2106.11587]., Comment: 25 pages

This paper discusses some statistical aspects of the U.K. Covid-19 pandemic response, focussing particularly on cases where we believe that a statistically questionable approach or presentation has had a substantial impact on public perception, or government policy, or both. We discuss the presentation of statistics relating to Covid risk, and the risk of the response measures, arguing that biases tended to operate in opposite directions, overplaying Covid risk and underplaying the response risks. We also discuss some issues around presentation of life loss data, excess deaths and the use of case data. The consequences of neglect of most individual variability from epidemic models, alongside the consequences of some other statistically important omissions are also covered. Finally the evidence for full stay at home lockdowns having been necessary to reverse waves of infection is examined, with new analyses provided for a number of European countries.

Linking the fundamental physics of band structure and scattering theory with macroscopic features such as measurable bulk thermoelectric transport properties is indispensable to a thorough understanding of transport phenomena and ensures more targeted and efficient experimental research. Here, we introduce SeeBand, a highly efficient and interactive fitting tool based on Boltzmann transport theory. A fully integrated user interface and visualization tool enable real-time comparison and connection between the electronic band structure (EBS) and microscopic transport properties. It allows simultaneous analysis of data for the Seebeck coefficient $S$, resistivity $\rho$ and Hall coefficient $R_\text{H}$ to identify suitable EBS models and extract the underlying microscopic material parameters and additional information from the model. Crucially, the EBS can be obtained by directly fitting the temperature-dependent properties of a single sample, which goes beyond previous approaches that look into doping dependencies. Finally, the combination of neural-network-assisted initial guesses and an efficient subsequent fitting routine allows for a rapid processing of big datasets, facilitating high-throughput analyses to identify underlying, yet undiscovered dependencies, thereby guiding material design.

This paper introduces a systematic approach to address the topological path identification (TPI) problem in power distribution networks. Our approach starts by listing the DSO's raw information coming from several sources. The raw information undergoes a transformation process using a set of transformation functions. This process converts the raw information into well-defined information exploitable by an algorithm. Then a set of hypothetical paths is generated, considering any potential connections between the elements of the power distribution system. This set of hypothetical paths is processed by the algorithm that identifies the hypothetical paths that are compatible with the well-defined information. This procedure operates iteratively, adapting the set of transformation functions based on the result obtained: if the identified paths fail to meet the DSO's expectations, new data is collected, and/or the transformation functions found to be responsible for the discrepancies are modified. The systematic procedure offers practical advantages for DSOs, including improved accuracy in path identification and high adaptability to diverse network configurations, even with incomplete or inaccurate data. Consequently, it emerges as a useful tool for the construction of digital twins of power distribution networks that aligns with DSO expectations.

A customer topological path represents the sequence of network elements connecting an MV/LV transformer to a customer. Accurate knowledge of these paths is crucial for distribution system operators (DSOs) in digitalization, analysis, and network planning. This paper introduces an innovative approach to address the challenge of customer topological path identification (TPI) using only the limited and often inaccurate data available to DSOs. Specifically, our method relies only on geographic information system (GIS) data of network elements and the customer to MV/LV transformers connection information. We introduce an integer linear programming (ILP) optimization algorithm designed to identify customer topological paths that closely approximate the real electricity paths. The effectiveness of the proposed approach is demonstrated through its application to both an academic and a real-world electrical distribution network. Results show that the method effectively addresses data inaccuracies and successfully identifies customer topological paths, providing a valuable tool for DSOs in developing accurate digital twins of their distribution networks.

The increasing adoption of distributed energy resources, particularly photovoltaic (PV) panels, has presented new and complex challenges for power network control. With the significant energy production from PV panels, voltage issues in the network have become a problem. Currently, PV smart inverters (SIs) are used to mitigate the voltage problems by controlling their active power generation and reactive power injection or absorption. However, reducing the active power output of PV panels can be perceived as unfair to some customers, discouraging future installations. To solve this issue, in this paper, a reinforcement learning technique is proposed to address voltage issues in a distribution network, while considering fairness in active power curtailment among customers. The feasibility of the proposed approach is explored through experiments, demonstrating its ability to effectively control voltage in a fair and efficient manner.

The Unit Commitment (UC) problem is a key optimization task in power systems to forecast the generation schedules of power units over a finite time period by minimizing costs while meeting demand and technical constraints. However, many parameters required by the UC problem are unknown, such as the costs. In this work, we estimate these unknown costs using simulation-based inference on an illustrative UC problem, which provides an approximated posterior distribution of the parameters given observed generation schedules and demands. Our results highlight that the learned posterior distribution effectively captures the underlying distribution of the data, providing a range of possible values for the unknown parameters given a past observation. This posterior allows for the estimation of past costs using observed past generation schedules, enabling operators to better forecast future costs and make more robust generation scheduling forecasts. We present avenues for future research to address overconfidence in posterior estimation, enhance the scalability of the methodology and apply it to more complex UC problems modeling the network constraints and renewable energy sources.

Light pulse atom interferometers (AIFs) are exquisite quantum probes of spatial inhomogeneity and gravitational curvature. Moreover, detailed measurement and calibration are necessary prerequisites for very-long-baseline atom interferometry (VLBAI). Here we present a method in which the differential signal of two co-located interferometers singles out a phase shift proportional to the curvature of the gravitational potential. The scale factor depends only on well controlled quantities, namely the photon wave number, the interferometer time and the atomic recoil, which allows the curvature to be accurately inferred from a measured phase. As a case study, we numerically simulate such a co-located gradiometric interferometer in the context of the Hannover VLBAI facility and prove the robustness of the phase shift in gravitational fields with complex spatial dependence. We define an estimator of the gravitational curvature for non-trivial gravitational fields and calculate the trade-off between signal strength and estimation accuracy with regard to spatial resolution. As a perspective, we discuss the case of a time-dependent gravitational field and corresponding measurement strategies., Comment: 6 pages of main text, 4 pages appendix, 6 figures

Interest in the study and analysis of dynamic processes in the social, behavioral, and health sciences has burgeoned in recent years due to the increased availability of intensive longitudinal data. However, how best to model and account for the persistent heterogeneity characterizing such processes remains an open question. The multi-VAR framework, a recent methodological development built on the vector autoregressive model, accommodates heterogeneous dynamics in multiple-subject time series through structured penalization. In the original multi-VAR proposal, individual-level transition matrices are decomposed into common and unique dynamics, allowing for generalizable and person-specific features. The current project extends this framework to allow additionally for the identification and penalized estimation of subgroup-specific dynamics; that is, patterns of dynamics that are shared across subsets of individuals. The performance of the proposed subgrouping extension is evaluated in the context of both a simulation study and empirical application, and results are compared to alternative methods for subgrouping multiple-subject, multivariate time series.

While COVID-19 has resulted in a significant increase in global mortality rates, the impact of the pandemic on mortality from other causes remains uncertain. To gain insight into the broader effects of COVID-19 on various causes of death, we analyze an Italian dataset that includes monthly mortality counts for different causes from January 2015 to December 2020. Our approach involves a generalized additive model enhanced with correlated random effects. The generalized additive model component effectively captures non-linear relationships between various covariates and mortality rates, while the random effects are multivariate time series observations recorded in various locations, and they embody information on the dependence structure present among geographical locations and different causes of mortality. Adopting a Bayesian framework, we impose suitable priors on the model parameters. For efficient posterior computation, we employ variational inference, specifically for fixed effect coefficients and random effects, Gaussian variational approximation is assumed, which streamlines the analysis process. The optimisation is performed using a coordinate ascent variational inference algorithm and several computational strategies are implemented along the way to address the issues arising from the high dimensional nature of the data, providing accelerated and stabilised parameter estimation and statistical inference.

Driven by applications in information technology, the search for new materials with stable, long-range magnetic ordering continues. Metalorganic magnets, involving the coordination of metal atoms with specific organic ligands, are a focus of intense research. These magnets offer customizable properties through synthetic adjustments to ligands or coordination chemistry. Here the synthesis, structural characterization, and magnetic properties of the 2D cyanocarbon magnet NiTCNE is reported. 2D-crystalline domains of this single-layered metalorganic network reach sizes exceeding 30 nanometers through co-deposition of the ligand TCNE (tetracyanoethylene) and Ni atoms on an Au(111) surface under ultrahigh vacuum conditions. Non-contact atomic force microscopy visualizes the structure with atomic resolution. X-ray magnetic circular dichroism establishes the 2D NiTCNE as a ferromagnet, with a very high magnetic remanence, a coercive field of around 1 tesla and a Curie temperature between 10 and 20 kelvin. As metalorganic chemistry opens a large variety of routes of synthesis, we anticipate that this materials research paves the way to new magnetic nanomaterials for spintronics applications.

Any two reduced expressions for the same Coxeter group element are related by a sequence of commutation and braid moves. Two reduced expressions are said to be braid equivalent if they are related via a sequence of braid moves. Braid equivalence is an equivalence relation and the corresponding equivalence classes are called braid classes. Each braid class can be encoded in terms of a braid graph in a natural way. In a recent paper, Awik et al.~proved that when a Coxeter system is simply laced and triangle free (i.e., the corresponding Coxeter graph has no three-cycles), the braid graph for a reduced expression is a partial cube (i.e., isometric to a subgraph of a hypercube). In this paper, we will provide an alternate proof of this fact, as well as determine the minimal dimension hypercube into which a braid graph can be isometrically embedded, which addresses an open question posed by Awik et al. For our main result, we prove that braid graphs in simply-laced triangle-free Coxeter systems are median, which is a strengthening of previous results., Comment: 24 pages, 19 figures

Radio-frequency pulses are widespread for the control of quantum bits and the execution of operations in quantum computers. The ability to tune key pulse parameters such as time-dependent amplitude, phase, and frequency is essential to achieve maximal gate fidelity and mitigate errors. As systems scale, a larger fraction of the control electronic processing will move closer to the qubits, to enhance integration and minimise latency in operations requiring fast feedback. This will constrain the space available in the memory of the control electronics to load time-resolved pulse parameters at high sampling rates. Cubic spline interpolation is a powerful and widespread technique that divides the pulse into segments of cubic polynomials. We show an optimised implementation of this strategy, using a two-stage curve fitting process and additional symmetry operations to load a high-sampling pulse output on an FPGA. This results in a favourable accuracy versus memory footprint trade-off. By simulating single-qubit population transfer and atom transport on a neutral atom device, we show that we can achieve high fidelities with low memory requirements. This is instrumental for scaling up the number of qubits and gate operations in environments where memory is a limited resource.

Magnetic impurities on superconductors present a viable platform for building advanced applications in quantum technologies. However, a controlled manipulation of their quantum states continues to pose a significant challenge, hindering the progress in the field. Here we show the manipulation of magnetic states in the radical molecule 4,5,9,10-tetrabromo-1,3,6,8-tetraazapyrene (TBTAP) on a Pb(111) superconducting surface using low-temperature scanning tunneling microscopy. Tunneling spectra reveal Yu-Shiba-Rusinov (YSR) states near the Fermi energy in isolated molecules. A quantum phase transition from singlet to doublet ground state is induced by changing the tip-molecule distance. Additionally, the presence of a second TBTAP molecule allows tuning of the YSR state position by altering the relative distance and can induce splitting of the YSR states for certain orientations. The construction of molecular chains up to pentamers shows periodic arrangements of charged and neutral molecules, with even-numbered chains forming a charged dimer structure at one end. Information can be encoded in these chains by switching the dimer position. These findings elucidate interactions between molecular assemblies and superconducting substrates, paving the way for advanced quantum-state engineering.

We developed SaludConectaMX as a comprehensive system to track and understand the determinants of complications throughout chemotherapy treatment for children with cancer in Mexico. SaludConectaMX is unique in that it integrates patient clinical indicators with social determinants and caregiver mental health, forming a social-clinical perspective of the patient's evolving health trajectory. The system is composed of a web application (for hospital staff) and a mobile application (for family caregivers), providing the opportunity for cooperative patient monitoring in both hospital and home settings. This paper presents the system's preliminary design and usability evaluation results from a 1.5-year pilot study. Our findings indicate that while the hospital web app demonstrates high completion rates and user satisfaction, the family mobile app requires additional improvements for optimal accessibility; statistical and qualitative data analysis illuminate pathways for system improvement. Based on this evidence, we formalize suggestions for health system development in LMICs, which HCI researchers may leverage in future work.

Transverse thermoelectric power generation has emerged as a topic of immense interest in recent years owing to the orthogonal geometry which enables better scalability and fabrication of devices. Here, we investigate the thickness dependence of longitudinal and transverse responses in film-substrate systems i.e., the Seebeck coefficient, Hall coefficient, Nernst coefficient and anomalous Nernst coefficient in a unified and general manner based on the circuit model, which describes the system as the parallel setup. By solving the parallel circuit model, we show that the transverse responses exhibit a significant peak, indicating the importance of a cooperative effect between the film and the substrate, arising from circulating currents that occur in these multilayer systems in the presence of a temperature gradient. Finally, on the basis of realistic material parameters, we predict that the Nernst effect in bismuth thin films on doped silicon substrates is boosted to unprecedented values if the thickness ratio is tuned accordingly, motivating experimental validation., Comment: 11 pages, 6 figures

A Cayley permutation is a word of positive integers such that if a letter appears in this word, then all positive integers smaller than that letter also appear. We initiate a systematic study of pattern avoidance on Cayley permutations adopting a combinatorial species approach. Our methods lead to species equations, generating series, and counting formulas for Cayley permutations avoiding any pattern of length at most three. We also introduce the species of primitive structures as a generalization of Cayley permutations with no "flat steps". Finally, we explore various notions of Wilf equivalence arising in this context., Comment: 32 pages, 3 figures, 1 table

Let $M(n, k, p)$ denote the maximum probability of the event $X_1 = X_2 = \cdots = X_n=1$ under a $k$-wise independent distribution whose marginals are Bernoulli random variables with mean $p$. A long-standing question is to calculate $M(n, k, p)$ for all values of $n,k,p$. This question has been partially addressed by several authors, primarily with the goal of answering asymptotic questions. The present paper focuses on obtaining exact expressions for this probability. To this end, we provide closed-form formulas of $M(n,k,p)$ for $p$ near 0 as well as $p$ near 1.

We consider $k$ square integrable random variables $Y_1,...,Y_k$ and $k$ random (row) vectors of length $p$, $X_1,...,X_k$ such that $X_i(l)$ is square integrable for $1\le i\le k$ and $1\le l\le p$. No assumptions whatsoever are made of any relationship between the $X_i$:s and $Y_i$:s. We shall refer to each pairing of $X_i$ and $Y_i$ as an environment. We form the square risk functions $R_i(\beta)=\mathbb{E}\left[(Y_i-\beta X_i)^2\right]$ for every environment and consider $m$ affine combinations of these $k$ risk functions. Next, we define a parameter space $\Theta$ where we associate each point with a subset of the unique elements of the covariance matrix of $(X_i,Y_i)$ for an environment. Then we study estimation of the $\arg\min$-solution set of the maximum of a the $m$ affine combinations the of quadratic risk functions. We provide a constructive method for estimating the entire $\arg\min$-solution set which is consistent almost surely outside a zero set in $\Theta^k$. This method is computationally expensive, since it involves solving polynomials of general degree. To overcome this, we define another approximate estimator that also provides a consistent estimation of the solution set based on the bisection method, which is computationally much more efficient. We apply the method to worst risk minimization in the setting of structural equation models., Comment: arXiv admin note: substantial text overlap with arXiv:2307.15350

Prediction invariance of causal models under heterogeneous settings has been exploited by a number of recent methods for causal discovery, typically focussing on recovering the causal parents of a target variable of interest. When instrumental variables are not available, the causal Dantzig estimator exploits invariance under the more restrictive case of shift interventions. However, also in this case, one requires observational data from a number of sufficiently different environments, which is rarely available. In this paper, we consider a structural equation model where the target variable is described by a generalised additive model conditional on its parents. Besides having finite moments, no modelling assumptions are made on the conditional distributions of the other variables in the system. Under this setting, we characterise the causal model uniquely by means of two key properties: the Pearson residuals are invariant under the causal model and conditional on the causal parents the causal parameters maximise the population likelihood. These two properties form the basis of a computational strategy for searching the causal model among all possible models. Crucially, for generalised linear models with a known dispersion parameter, such as Poisson and logistic regression, the causal model can be identified from a single data environment.

With high equilibrium temperatures and tidally locked rotation, ultra-hot Jupiters (UHJs) are unique laboratories within which to probe extreme atmospheric physics and chemistry. In this paper, we present high-resolution dayside spectroscopy of the UHJ WASP-189b obtained with the new Gemini High-resolution Optical SpecTrograph (GHOST) at the Gemini South Observatory. The observations, which cover three hours of post-eclipse orbital phases, were obtained during the instrument's System Verification run. We detect the planet's atmosphere via the Doppler cross-correlation technique, and recover a detection of neutral iron in the planet's dayside atmosphere at a significance of 7.5$\sigma$ in the red-arm of the data, verifying the presence of a thermal inversion. We also investigate the presence of other species in the atmosphere and discuss the implications of model injection/recovery tests. These results represent the first atmospheric characterization of an exoplanet with GHOST's high-resolution mode, and demonstrate the potential of this new instrument in detecting and studying ultra-hot exoplanet atmospheres., Comment: 21 pages, 12 figures, 3 tables. Accepted for publication in The Astronomical Journal

Dynamic nuclear polarization (DNP) involves a polarization transfer from unpaired electrons to hyperfine coupled nuclei and can increase the sensitivity of nuclear magnetic resonance (NMR) signals by several orders of magnitude. The hyperfine coupling is considered to suppress nuclear dipolar flip-flop transitions, hindering the transport of nuclear hyperpolarization into the bulk (''spin-diffusion barrier''). Possible polarization-transfer pathways leading to DNP and subsequent spin diffusion between hypershifted nuclei in a two-electron two-nucleus four-spin system are investigated. The Schrieffer-Wolff transformation is applied to characterize transitions that are only possible as second-order effects. An energy-conserving electron-nuclear four-spin flip-flop is identified, which combines an electron dipolar with a nuclear dipolar flip-flop process, describing spin diffusion close to electrons. The relevance of this process is supported by two-compartment model fits of HypRes-on experimental data. This suggests that all nuclear spins can contribute to the hyperpolarization of the bulk and the concept of a spin-diffusion barrier has to be reconsidered for samples with significant electron and nuclear dipolar couplings.

A type of dynamic network involves temporally ordered interactions between actors, where past network configurations may influence future ones. The relational event model can be used to identify the underlying dynamics that drive interactions among system components. Despite the rapid development of this model over the past 15 years, an ongoing area of research revolves around evaluating the goodness of fit of this model, especially when it incorporates time-varying and random effects. Current methodologies often rely on comparing observed and simulated events using specific statistics, but this can be computationally intensive, and requires various assumptions. We propose an additive mixed-effect relational event model estimated via case-control sampling, and introduce a versatile framework for testing the goodness of fit of such models using weighted martingale residuals. Our focus is on a Kolmogorov-Smirnov type test designed to assess if covariates are accurately modeled. Our approach can be easily extended to evaluate whether other features of network dynamics have been appropriately incorporated into the model. We assess the goodness of fit of various relational event models using synthetic data to evaluate the test's power and coverage. Furthermore, we apply the method to a social study involving 57,791 emails sent by 159 employees of a Polish manufacturing company in 2010. The method is implemented in the R package mgcv.

Attention-based models such as Transformers and recurrent models like state space models (SSMs) have emerged as successful methods for autoregressive sequence modeling. Although both enable parallel training, none enable parallel generation due to their autoregressiveness. We propose the variational SSM (VSSM), a variational autoencoder (VAE) where both the encoder and decoder are SSMs. Since sampling the latent variables and decoding them with the SSM can be parallelized, both training and generation can be conducted in parallel. Moreover, the decoder recurrence allows generation to be resumed without reprocessing the whole sequence. Finally, we propose the autoregressive VSSM that can be conditioned on a partial realization of the sequence, as is common in language generation tasks. Interestingly, the autoregressive VSSM still enables parallel generation. We highlight on toy problems (MNIST, CIFAR) the empirical gains in speed-up and show that it competes with traditional models in terms of generation quality (Transformer, Mamba SSM)., Comment: 4 pages, 11 pages total, 3 figures

Static analysis is sound in theory, but an implementation may unsoundly fail to analyze all of a program's code. Any such omission is a serious threat to the validity of the tool's output. Our work is the first to measure the prevalence of these omissions. Previously, researchers and analysts did not know what is missed by static analysis, what sort of code is missed, or the reasons behind these omissions. To address this gap, we ran 13 static analysis tools and a dynamic analysis on 1000 Android apps. Any method in the dynamic analysis but not in a static analysis is an unsoundness. Our findings include the following. (1) Apps built around external frameworks challenge static analyzers. On average, the 13 static analysis tools failed to capture 61% of the dynamically-executed methods. (2) A high level of precision in call graph construction is a synonym for a high level of unsoundness; (3) No existing approach significantly improves static analysis soundness. This includes those specifically tailored for a given mechanism, such as DroidRA to address reflection. It also includes systematic approaches, such as EdgeMiner, capturing all callbacks in the Android framework systematically. (4) Modeling entry point methods challenges call graph construction which jeopardizes soundness.

We present a method to directly detect the axion dark matter using nitrogen vacancy centers in diamonds. In particular, we use metrology leveraging the nuclear spin of nitrogen to detect axion-nucleus couplings. This is achieved through protocols designed for dark matter searches, which introduce a novel approach of quantum sensing techniques based on the nitrogen vacancy center. Although the coupling strength of the magnetic fields with nuclear spins is three orders of magnitude smaller than that with electron spins for conventional magnetometry, the axion interaction strength with nuclear spins is the same order of magnitude as that with electron spins. Furthermore, we can take advantage of the long coherence time by using the nuclear spins for the axion dark matter detection. We show that our method is sensitive to a broad frequency range $\lesssim 100\,\mathrm{Hz}$ corresponding to the axion mass $m_a \lesssim 4\times 10^{-13}\,\mathrm{eV}$. We present the detection limit of our method for both the axion-neutron and the axion-proton couplings and discuss its significance in comparison with other proposed ideas., Comment: 17 pages, 7 figures

In this paper we give local error estimates in Sobolev norms for the Galerkin method applied to strongly elliptic pseudodifferential equations on a polygon. By using the K-operator, an operator which averages the values of the Galerkin solution, we construct improved approximations., Comment: Dedicated to Prof. George C. Hsiao on the occasion of his 90th birthday

This paper is the second part of our comprehensive study on the braid index problem of pretzel links. Our ultimate goal is to completely determine the braid indices of all pretzel links, alternating or non alternating. In our approach, we divide the pretzel links into three types as follows. Let $D$ be a standard diagram of an oriented pretzel link $\mathcal{L}$, $S(D)$ be the Seifert circle decomposition of $D$, and $C_1$, $C_2$ be the Seifert circles in $S(D)$ containing the top and bottom long strands of $D$ respectively, then $\mathcal{L}$ is classified as a Type 1 (Type 2) pretzel link if $C_1\not=C_2$ and $C_1$, $C_2$ have different (identical) orientations. In the case that $C_1=C_2$, then $\mathcal{L}$ is classified as a Type 3 pretzel link. In our previous paper, we succeeded in reaching our goal for all Type 1 and Type 2 pretzel links. That is, we successfully derived precise braid index formulas for all Type 1 and Type 2 pretzel links. In this paper, we present the results of our study on Type 3 pretzel links. In this case, we are very close to reaching our goal. More precisely, with the exception of a small percentage of Type 3 pretzel links, we are able to determine the precise braid indices for the majority of Type 3 pretzel links. Even for those exceptional ones, we are able to determine their braid indices within two consecutive integers. With some numerical evidence, we conjecture that in such a case, the braid index of the Type 3 pretzel link is given by the larger of the two consecutive integers given by our formulas., Comment: 29 pages, 13 figures

This study proposes a novel approach based on reinforcement learning (RL) to enhance the sorting efficiency of scrap metal using delta robots and a Pick-and-Place (PaP) process, widely used in the industry. We use three classical model-free RL algorithms (TD3, SAC and PPO) to reduce the time to sort metal scraps. We learn the release position and speed needed to throw an object in a bin instead of moving to the exact bin location, as with the classical PaP technique. Our contribution is threefold. First, we provide a new simulation environment for learning RL-based Pick-and-Throw (PaT) strategies for parallel grippers. Second, we use RL algorithms for learning this task in this environment resulting in 89% accuracy while speeding up the throughput by 51% in simulation. Third, we evaluate the performances of RL algorithms and compare them to a PaP and a state-of-the-art PaT method both in simulation and reality, learning only from simulation with domain randomisation and without fine tuning in reality to transfer our policies. This work shows the benefits of RL-based PaT compared to PaP or classical optimization PaT techniques used in the industry.

The anti-Stoner excitations are a spin-flips in which, effectively, an electron is promoted from a minority to a majority spin state, i.e., complementary to Stoner excitations and spin-waves. Since their spectral power is negligible in strong itinerant ferromagnets and they are identically absent in the ferromagnetic Heisenberg model, their properties and role in correlating electrons were hardly investigated so far. On the other hand, they are present in weak ferromagnets, fcc Ni being a prominent example, and both types of spin-flips (down-to-up and up-to-down) must be treated on the equal footing in systems with the degenerate spin up and down bands, in particular antiferromagnets in which case we choose CrSb as a model system. For these two materials we evaluate the strength of the effective interaction between the quasiparticles and the gas of virtual spin-flip excitations. To this end, we compute the corresponding self-energy taking advantage of our novel efficient \textit{ab initio} numerical scheme. We find that in Ni the band-structure renormalization due to the anti-Stoner processes is weaker than the one due to Stoner-type magnons in the majority spin channel but the two become comparable in the minority one. The effect can be traced back primarily to the spectral strength of the respective spin excitations and the densities of the final available quasiparticle states in the scattering process. For the antiferromagnet, the situation is more complex and we observe that the electron-magnon interaction is sensitive not only to these densities of states but critically to the spatial shapes of the coupling magnonic modes as well.

Bose-Einstein condensates (BECs) have been proposed for many applications in atom interferometry, as their coherence over long evolution times promises unprecedented sensitivity. To date, BECs can be efficiently created in devices using atom chips, but these are still complex and place high demands on size, weight and power. To further simplify these setups, we equipped an atom chip with a nano-structured diffraction-grating to derive all beams for the magneto-optical trap (MOT) from a single laser beam. Moreover, using a 2D$^+$-MOT as an atomic source and a beam with uniform intensity for the grating illumination, we capture $1\times10^9$ atoms in one second, cool them to $14\,\mu$K, and demonstrate magnetic trapping using the atom chip. This is a major step towards the simplification of portable BEC devices for quantum sensing on earth and in space., Comment: 12 pages, 3 figures

Traditional inference in relational event models from dynamic network data involves only dyadic and node-specific variables, as anything that is global, i.e. constant across dyads, drops out of the partial likelihood. We address this with the use of nested case-control sampling on a time-shifted version of the event process. This leads to a partial likelihood of a degenerate logistic additive model, enabling efficient estimation of global and non-global covariate effects. The method's effectiveness is demonstrated through a simulation study. An application to bike sharing data reveals significant influences of global covariates like weather and time of day on bike-sharing dynamics.