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Supernova remnants (SNRs) provide insights into cosmic-ray acceleration and magnetic field dynamics at shock fronts. Recent X-ray polarimetric measurements by the Imaging X-ray Polarimetry Explorer (IXPE) have revealed radial magnetic fields near particle acceleration sites in young SNRs, including Cassiopeia A, Tycho, and SN 1006. We present here the spatially-resolved IXPE X-ray polarimetric observation of the northwestern rim of SNR RX J1713.7-3946. For the first time, our analysis shows that the magnetic field in particle acceleration sites of this SNR is oriented tangentially with respect to the shock front. Because of the lack of precise Faraday-rotation measurements in the radio band, this was not possible before. The average measured polarization degree (PD) of the synchtrotron emission is 12.5 {\pm} 3.3%, lower than the one measured by IXPE in SN 1006, comparable to the Tycho one, but notably higher than the one in Cassiopeia A. On sub-parsec scales, localized patches within RX J1713.7-3946 display PD up to 41.5 {\pm} 9.5%. These results are compatible with a shock-compressed magnetic field. However, in order to explain the observed PD, either the presence of a radial net magnetic field upstream of the shock, or partial reisotropization of the turbulence downstream by radial magneto-hydrodynamical instabilities, can be invoked. From comparison of PD and magnetic field distribution with {\gamma}-rays and 12 CO data, our results provide new inputs in favor of a leptonic origin of the {\gamma}-ray emission., Comment: 18 pages, 6 figures, 2 tables, published in ApJ Letters

Semispaces of a convexity space $(X,C)$ are maximal convex sets missing a point. The separation axiom $S_3$ asserts that any point $x_0\in X$ and any convex set $A$ not containing $x_0$ can be separated by complementary halfspaces (convex sets with convex complements) or, equivalently, that all semispaces are halfspaces. In this paper, we study $S_3$ for geodesic convexity in graphs and the structure of semispaces in $S_3$-graphs. We characterize $S_3$-graphs and their semispaces in terms of separation by halfspaces of vertices $x_0$ and special sets, called maximal $x_0$-proximal sets and in terms of convexity of their mutual shadows $x_0/K$ and $K/x_0$. In $S_3$-graphs $G$ satisfying the triangle condition (TC), maximal proximal sets are the pre-maximal cliques of $G$ (i.e., cliques $K$ such that $K\cup\{ x_0\}$ are maximal cliques). This allows to characterize the $S_3$-graphs satisfying (TC) in a structural way and to enumerate their semispaces efficiently. In case of meshed graphs (an important subclass of graphs satisfying (TC)), the $S_3$-graphs have been characterized by excluding five forbidden subgraphs. On the way of proving this result, we also establish some properties of meshed graphs, which maybe of independent interest. In particular, we show that any connected, locally-convex set of a meshed graph is convex. We also provide several examples of $S_3$-graphs, including the basis graphs of matroids. Finally, we consider the (NP-complete) halfspace separation problem, describe two methods of its solution, and apply them to particular classes of graphs and graph-convexities., Comment: 59 pages, 2 figures

We propose a method for reducing the spatial discretization error of coarse computational fluid dynamics (CFD) problems by enhancing the quality of low-resolution simulations using deep learning. We feed the model with fine-grid data after projecting it to the coarse-grid discretization. We substitute the default differencing scheme for the convection term by a feed-forward neural network that interpolates velocities from cell centers to face values to produce velocities that approximate the down-sampled fine-grid data well. The deep learning framework incorporates the open-source CFD code OpenFOAM, resulting in an end-to-end differentiable model. We automatically differentiate the CFD physics using a discrete adjoint code version. We present a fast communication method between TensorFlow (Python) and OpenFOAM (c++) that accelerates the training process. We applied the model to the flow past a square cylinder problem, reducing the error from 120% to 25% in the velocity for simulations inside the training distribution compared to the traditional solver using an x8 coarser mesh. For simulations outside the training distribution, the error reduction in the velocities was about 50%. The training is affordable in terms of time and data samples since the architecture exploits the local features of the physics.

A novel approach to accounting for the influence of initial system-bath correlations on the dynamics of an open quantum system, based on the conventional projection operator technique, is suggested. To avoid the difficulties of treating the initial correlations, the conventional Nakajima-Zwanzig inhomogeneous generalized master equations (GMEs) for a system's reduced statistical operator and correlation function are exactly converted into the homogeneous GMEs (HGMEs), which take into account the initial correlations in the kernel governing the evolution of these HGMEs. In the second order (Born) approximation in the system-bath interaction, the obtained HGMEs are local in time and valid at all timescales. They are further specialized for a realistic equilibrium Gibbs initial (at $t=t_0$) system+bath state (for a system reduced statistical operator an external force at $t>t_0$ is applied) and then for a bath of oscillators (Boson field). As an example, the evolution of a selected quantum oscillator (a localized mode) interacting with a Boson field (Fano-like model) is considered at different timescales. It is shown explicitly how the initial correlations influence the oscillator evolution process. In particular, it is shown that the equilibrium system's correlation function acquires at the large timescale the additional constant phase factor conditioned by survived initial system-bath correlations., Comment: 24 pages

Let $(R,\mathfrak{m},k)$ be a Noetherian local ring and let $M$ be a finitely generated $R$-module. The main focus of this paper is to give positive answers for some long-standing homological conjectures over the idealization ring $R\ltimes M$. First, if $N$ is a $R\ltimes k$-module, we show that the vanishing of $\operatorname{Ext}_{R\ltimes k}^{i}(N,N\oplus (R\ltimes k))$ for $i=1,2,3$ gives that $N$ is free, and this provides a sharpened version of the Auslander-Reiten conjecture over $R\ltimes k$. Also, we give a characterization of the Betti numbers of an $R$-module over the idealization ring $R\ltimes M$ and, as a biproduct, we derive that the Jorgensen-Leuschke conjecture holds true for $R\ltimes M$. Further, we show that the true of Buchsbaum-Eisenbud-Horrocks and Total Rank conjectures over $R$ implies the true over $R\ltimes M$. This establishes particular answers for both conjectures for modules with infinite projective dimension, especially when $R$ is regular or a complete intersection ring. As applications of the idealization ring theory, we show that the Zariski-Lipman conjecture holds for any ring $R$ provided the Betti numbers of the $R$-derivation module $\operatorname{Der}_k(R)$, seen as $R\ltimes k$-module, satisfy the inequality $\beta_{n}^{R\ltimes k}(\operatorname{Der}_k(R))\leq\beta_{n-1}^{R\ltimes k}(\operatorname{Der}_k(R))$ for some $n>0$. Some implications regarding the Herzog-Vasconcelos conjecture are also provided., Comment: 17 pages, 0 figures

The quantified Boolean formula (QBF) problem is an important decision problem generally viewed as the archetype for PSPACE-completeness. Many problems of central interest in AI are in general not included in NP, e.g., planning, model checking, and non-monotonic reasoning, and for such problems QBF has successfully been used as a modelling tool. However, solvers for QBF are not as advanced as state of the art SAT solvers, which has prevented QBF from becoming a universal modelling language for PSPACE-complete problems. A theoretical explanation is that QBF (as well as many other PSPACE-complete problems) lacks natural parameters} guaranteeing fixed-parameter tractability (FPT). In this paper we tackle this problem and consider a simple but overlooked parameter: the number of existentially quantified variables. This natural parameter is virtually unexplored in the literature which one might find surprising given the general scarcity of FPT algorithms for QBF. Via this parameterization we then develop a novel FPT algorithm applicable to QBF instances in conjunctive normal form (CNF) of bounded clause length. We complement this by a W[1]-hardness result for QBF in CNF of unbounded clause length as well as sharper lower bounds for the bounded arity case under the (strong) exponential-time hypothesis.

In certain situations, neural networks will represent environment states in their hidden activations. Our goal is to visualize what environment states the networks are representing. We experiment with a recurrent neural network (RNN) architecture with a decoder network at the end. After training, we apply the decoder to the intermediate representations of the network to visualize what they represent. We define a quantitative interpretability metric and use it to demonstrate that hidden states can be highly interpretable on a simple task. We also develop autoencoder and adversarial techniques and show that benefit interpretability.

In this work, we consider the $\mathcal{H}_2$ optimal model reduction of dynamical systems that are linear in the state equation and up to quadratic nonlinearity in the output equation. As our primary theoretical contributions, we derive gradients of the squared $\mathcal{H}_2$ system error with respect to the reduced model quantities and, from the stationary points of these gradients, introduce Gramian-based first-order necessary conditions for the $\mathcal{H}_2$ optimal approximation of a linear quadratic output (LQO) system. The resulting $\mathcal{H}_2$ optimality framework neatly generalizes the analogous Gramian-based optimality framework for purely linear systems. Computationally, we show how to enforce the necessary optimality conditions using Petrov-Galerkin projection; the corresponding projection matrices are obtained from a pair of Sylvester equations. Based on this result, we propose an iteratively corrected algorithm for the $\mathcal{H}_2$ model reduction of LQO systems, which we refer to as LQO-TSIA (linear quadratic output two-sided iteration algorithm). Numerical examples are included to illustrate the effectiveness of the proposed computational method against other existing approaches., Comment: 18 pages, 4 figures

The evolution of a thematic area undergoes various changes of perspective and adopts new theoretical approaches that arise from the interactions of the community and a wide range of social needs. The advent of digital technologies, such as social networks, underlines this factor by spreading knowledge and forging links between different communities. Web intelligence is now on the verge of raising questions that broaden the understanding of how artificial intelligence impacts the Web of People, Data, and Things, among other factors. To the best of our knowledge, there is no study that has conducted a longitudinal analysis of the evolution of this community. Thus, we investigate in this paper how Web intelligence has evolved in the last twenty years by carrying out a literature review and bibliometric analysis. Concerning the impact of this research study, increasing attention is devoted to determining which are the most influential papers in the community by referring to citation networks and discovering the most popular and pressing topics through a co-citation analysis and the keywords co-occurrence. The results obtained can guide the direction of new research projects in the area and update the scope and places of interest found in current trends and the relevant journals.

We have measured transition frequencies, isotope shifts and hyperfine structure splittings in the $3 d^{2}\left({ }^{3\!}F\right) 4 s\,{ }^{4} F_J\rightarrow 3 d^{2}\left({ }^{3\!} F\right) 4 p \,^{4} G_{J+1}$ transitions in Ti$^+$ ions for $J=\frac{3}{2},\, \frac{5}{2},\, \frac{7}{2}$ using collinear laser spectroscopy. Ions were generated by laser ablation in a buffer gas atmosphere and extracted into vacuum through a nozzle and a pair of radiofrequency (RF) funnels. The obtained results are of interest as reference values for on-line measurements of short-lived titanium isotopes and for astrophysical searches for temporal or spatial variations of the fine structure constant $\alpha$ using quasar absorption spectra.

Automating visual inspection in industrial production lines is essential for increasing product quality across various industries. Anomaly detection (AD) methods serve as robust tools for this purpose. However, existing public datasets primarily consist of images without anomalies, limiting the practical application of AD methods in production settings. To address this challenge, we present (1) the Valeo Anomaly Dataset (VAD), a novel real-world industrial dataset comprising 5000 images, including 2000 instances of challenging real defects across more than 20 subclasses. Acknowledging that traditional AD methods struggle with this dataset, we introduce (2) Segmentation-based Anomaly Detector (SegAD). First, SegAD leverages anomaly maps as well as segmentation maps to compute local statistics. Next, SegAD uses these statistics and an optional supervised classifier score as input features for a Boosted Random Forest (BRF) classifier, yielding the final anomaly score. Our SegAD achieves state-of-the-art performance on both VAD (+2.1% AUROC) and the VisA dataset (+0.4% AUROC). The code and the models are publicly available., Comment: Accepted to CVPR 2024

We compare two different numerical methods to integrate in time spatially delocalized initial densities using the Schr\"odinger-Poisson equation system as the evolution law. The basic equation is a nonlinear Schr\"odinger equation with an auto-gravitating potential created by the wave function density itself. The latter is determined as a solution of Poisson's equation modelling, e.g., non-relativistic gravity. For reasons of complexity, we treat a one-dimensional version of the problem whose numerical integration is still challenging because of the extreme long-range forces (being constant in the asymptotic limit). Both of our methods, a Strang splitting scheme and a basis function approach using B-splines, are compared in numerical convergence and effectivity. Overall, our Strang-splitting evolution compares favourably with the B-spline method. In particular, by using an adaptive time-stepper rather large one-dimensional boxes can be treated. These results give hope for extensions to two spatial dimensions for not too small boxes and large evolution times necessary for describing, for instance, dark matter formation over cosmologically relevant scales., Comment: Converged 1D solutions of Schr\"odinger-Poisson model including spatial expansion, comparison between various methods and optimisation of integrators

Differentiable particle filters are an emerging class of models that combine sequential Monte Carlo techniques with the flexibility of neural networks to perform state space inference. This paper concerns the case where the system may switch between a finite set of state-space models, i.e. regimes. No prior approaches effectively learn both the individual regimes and the switching process simultaneously. In this paper, we propose the neural network based regime learning differentiable particle filter (RLPF) to address this problem. We further design a training procedure for the RLPF and other related algorithms. We demonstrate competitive performance compared to the previous state-of-the-art algorithms on a pair of numerical experiments.

Non-radial oscillation modes of a neutron star possess valuable information about its internal structure and nuclear physics. Starting from the quadrupolar order, such modes under general relativity are known as quasi-normal modes since they dissipate energy through gravitational radiation and their frequencies are complex. The stability of these modes is governed by the sign of the imaginary part of the frequency, which determines whether the mode would decay or grow over time. In this Letter, we develop a fully consistent framework in general relativity to study quasi-normal modes of neutron stars with anisotropic pressure, whose motivation includes strong internal magnetic fields and non-vanishing shear or viscosity. We employ parametrized models for the anisotropy and solve the perturbed Einstein field equations numerically. We find that, unlike the case for isotropic neutron stars, the imaginary parts of some of the pressure ($p$-)modes flip signs as the degree of anisotropy deviates from zero, depicting a transition from stable modes to unstable modes. This finding indicates that some anisotropic neutron star models are unstable, potentially restricting the form of sustained anisotropy., Comment: 8+6 pages, 2+1 figures, re-submitted to PRD

This work discusses a novel method for estimating the location of a gas source based on spatially distributed concentration measurements taken, e.g., by a mobile robot or flying platform that follows a predefined trajectory to collect samples. The proposed approach uses a Physics-Guided Neural Network to approximate the gas dispersion with the source location as an additional network input. After an initial offline training phase, the neural network can be used to efficiently solve the inverse problem of localizing the gas source based on measurements. The proposed approach allows avoiding rather costly numerical simulations of gas physics needed for solving inverse problems. Our experiments show that the method localizes the source well, even when dealing with measurements affected by noise., Comment: Submission to the International Symposium of Electronic Nose (ISOEN)

We explain how the (shifted) Ratios Conjecture for $L(s,\chi)$ would extend a randomization argument of Harper from a conductor-limited range to an unlimited range of ``beyond square-root cancellation'' for character twists of the Liouville function. As a corollary, the Liouville function would have nontrivial cancellation in arithmetic progressions of modulus just exceeding the well-known square-root barrier. Morally, the paper passes from random matrices to random multiplicative functions., Comment: 24 pages

Apportionment is the act of distributing the seats of a legislature among political parties (or states) in proportion to their vote shares (or populations). A famous impossibility by Balinski and Young (2001) shows that no apportionment method can be proportional up to one seat (quota) while also responding monotonically to changes in the votes (population monotonicity). Grimmett (2004) proposed to overcome this impossibility by randomizing the apportionment, which can achieve quota as well as perfect proportionality and monotonicity -- at least in terms of the expected number of seats awarded to each party. Still, the correlations between the seats awarded to different parties may exhibit bizarre non-monotonicities. When parties or voters care about joint events, such as whether a coalition of parties reaches a majority, these non-monotonicities can cause paradoxes, including incentives for strategic voting. In this paper, we propose monotonicity axioms ruling out these paradoxes, and study which of them can be satisfied jointly with Grimmett's axioms. Essentially, we require that, if a set of parties all receive more votes, the probability of those parties jointly receiving more seats should increase. Our work draws on a rich literature on unequal probability sampling in statistics (studied as dependent randomized rounding in computer science). Our main result shows that a sampling scheme due to Sampford (1967) satisfies Grimmett's axioms and a notion of higher-order correlation monotonicity.

The impact of the non-linear effects in the QCD dynamics on the observables is directly related to the magnitude of the saturation scale $Q_s$, which is predicted to increase with the energy, rapidity and multiplicity. In this paper, we investigate the $D^0$ meson production in $pp$ collisions at forward rapidities and/or high multiplicities considering the Color Glass Condensate (CGC) formalism and the solutions of the running coupling Balitsky - Kovchegov (BK) equation. The contributions of gluon - and charm - initiated processes are taken into account, and a comparison with the current LHCb data is performed. The impact of an intrinsic charm component in the proton's wave function is also estimated. Predictions for the self-normalized yields of $D^0$ mesons as a function of the multiplicity of coproduced charged hadrons are presented, considering $pp$ collisions at $\sqrt{s} = 13$ TeV and different values of the meson rapidity. A comparison with the predictions for the kaon and isolated photon production is performed. Our results indicate that a future experimental analysis of the $D^0$ meson production at forward rapidities and high multiplicities can be useful to probe the CGC formalism and to disentangle the contribution of initial - and final - state effects., Comment: 14 pages, 13 figures

Autonomous Vehicles (AVs) are prone to revolutionise the transportation industry. However, they must be thoroughly tested to avoid safety violations. Simulation testing plays a crucial role in finding safety violations of Automated Driving Systems (ADSs). This paper proposes PAFOT, a position-based approach testing framework, which generates adversarial driving scenarios to expose safety violations of ADSs. We introduce a 9-position grid which is virtually drawn around the Ego Vehicle (EV) and modify the driving behaviours of Non-Playable Characters (NPCs) to move within this grid. PAFOT utilises a single-objective genetic algorithm to search for adversarial test scenarios. We demonstrate PAFOT on a well-known high-fidelity simulator, CARLA. The experimental results show that PAFOT can effectively generate safety-critical scenarios to crash ADSs and is able to find collisions in a short simulation time. Furthermore, it outperforms other search-based testing techniques by finding more safety-critical scenarios under the same driving conditions within less effective simulation time., Comment: Pre-print from AST 2024 conference

The origin of multiple peaks in lightcurves of various wavelengths remains illusive during flares. Here we discuss the flare of SOL2023-05-09T03:54M6.5 with six flux peaks as recorded by a tandem of new microwave and Hard X-ray instruments. According to its microwave spectra, the flare represents a high-turnover frequency (>15 GHz) event. The rather-complete microwave and HXR spectral coverage provides a rare opportunity to uncover the origin of such event together with simultaneous EUV images. We concluded that (1) the microwave sources originates around the top section of the flaring loops with a trend of source spatial dispersion with frequency;(2) the visible movement of the microwave source from peak to peak originates from the process of new flaring loops appearing sequentially along the magnetic neutral line; 3) the optically-thin microwave spectra are hard with the indices varying from -1.2 to -0.4, and the turnover frequency always exceeds 15 GHz; 4) higher turnover/peak frequency corresponds to stronger peak intensity and harder optically-thin spectra. Using the Fokker-Planck and GX simulator codes we obtained a good fit to the observed microwave spectra and spatial distribution of the sources at all peaks, if assuming the radiating energetic electrons have the same spatial distribution and single-power-law spectra but with the number density varying in a range of 30%. We conclude that the particle acceleration in this flare happens in a compact region nearing the looptop. These results provide new constraints on the acceleration of energetic electrons and the underlying flare intermittent reconnection process., Comment: 23 pages, 11 figures

Industrial applications of plasma have significantly increased beyond semiconductor manufacturing in recent years. This necessitates training a skilled workforce in plasma science and technology. However, an essential challenge to this end stems from the high cost of plasma devices and diagnostics. The limited access to plasma devices has hindered plasma education, particularly in the least developed countries. To this end, this paper demonstrates how low-cost sensors and circuits can be developed to enable inexpensive plasma experiments in laboratory environments. In particular, we show how to measure high voltage, current, and power from a cold-atmospheric plasma discharge. Additionally, we develop a low-cost illuminance sensor and demonstrate how it can be used to estimate the corresponding plasma power. The low-cost sensors and electronics presented in this paper can aid educators in characterizing plasma power versus plasma illuminance.

The growing interest in vision-language models (VLMs) has been driven by improvements in large language models and vision transformers. Despite the abundance of literature on this subject, we observe that critical decisions regarding the design of VLMs are often not justified. We argue that these unsupported decisions impede progress in the field by making it difficult to identify which choices improve model performance. To address this issue, we conduct extensive experiments around pre-trained models, architecture choice, data, and training methods. Our consolidation of findings includes the development of Idefics2, an efficient foundational VLM of 8 billion parameters. Idefics2 achieves state-of-the-art performance within its size category across various multimodal benchmarks, and is often on par with models four times its size. We release the model (base, instructed, and chat) along with the datasets created for its training.

Satellite constellation systems are becoming more attractive to provide communication services worldwide, especially in areas without network connectivity. While optimizing satellite gateway placement is crucial for operators to minimize deployment and operating costs, reducing the number of gateways may require more inter-satellite link hops to reach the ground network, thereby increasing latency. Therefore, it is of significant importance to develop a framework that optimizes gateway placement, dynamic routing, and flow management in inter-satellite links to enhance network performance. To this end, we model an optimization problem as a mixed-integer problem with a cost function combining the number of gateways, flow allocation, and traffic latency, allowing satellite operators to set priorities based on their policies. Our simulation results indicate that the proposed approach effectively reduces the number of active gateways by selecting their most appropriate locations while balancing the trade-off between the number of gateways and traffic latency. Furthermore, we demonstrate the impact of different weights in the cost function on performance through comparative analysis.

Despite substantial progress in machine learning for scientific discovery in recent years, truly de novo design of small molecules which exhibit a property of interest remains a significant challenge. We introduce LambdaZero, a generative active learning approach to search for synthesizable molecules. Powered by deep reinforcement learning, LambdaZero learns to search over the vast space of molecules to discover candidates with a desired property. We apply LambdaZero with molecular docking to design novel small molecules that inhibit the enzyme soluble Epoxide Hydrolase 2 (sEH), while enforcing constraints on synthesizability and drug-likeliness. LambdaZero provides an exponential speedup in terms of the number of calls to the expensive molecular docking oracle, and LambdaZero de novo designed molecules reach docking scores that would otherwise require the virtual screening of a hundred billion molecules. Importantly, LambdaZero discovers novel scaffolds of synthesizable, drug-like inhibitors for sEH. In in vitro experimental validation, a series of ligands from a generated quinazoline-based scaffold were synthesized, and the lead inhibitor N-(4,6-di(pyrrolidin-1-yl)quinazolin-2-yl)-N-methylbenzamide (UM0152893) displayed sub-micromolar enzyme inhibition of sEH.

In this work we investigate the set of cubic Hamiltonian vector fields for which their associated Kahan-Hirota-Kimura maps preserve the original Hamiltonian function. We analyze these fields in $\mathbb{R}^2$ and $\mathbb{R}^4$. We also study a family of fields in $\mathbb{R}^6$. Additionally, we explore several properties like the existence of additional first integrals of specific type, the possibility that the initial Hamiltonian vector field is a Lie symmetry of the corresponding map, or the symplecticity of the considered maps., Comment: 30 pages, 1 Figure

We introduce WorkBench: a benchmark dataset for evaluating agents' ability to execute tasks in a workplace setting. WorkBench contains a sandbox environment with five databases, 26 tools, and 690 tasks. These tasks represent common business activities, such as sending emails and scheduling meetings. The tasks in WorkBench are challenging as they require planning, tool selection, and often multiple actions. If a task has been successfully executed, one (or more) of the database values may change. The correct outcome for each task is unique and unambiguous, which allows for robust, automated evaluation. We call this key contribution outcome-centric evaluation. We evaluate five existing ReAct agents on WorkBench, finding they successfully complete as few as 3% of tasks (Llama2-70B), and just 43% for the best-performing (GPT-4). We further find that agents' errors can result in the wrong action being taken, such as an email being sent to the wrong person. WorkBench reveals weaknesses in agents' ability to undertake common business activities, raising questions about their use in high-stakes workplace settings. WorkBench is publicly available as a free resource at https://github.com/olly-styles/WorkBench.

Research data sets are growing to unprecedented sizes and network modeling is commonly used to extract complex relationships in diverse domains, such as genetic interactions involved in disease, logistics, and social communities. As the number of nodes increases in a network, an increasing sparsity of edges is a practical limitation due to memory restrictions. Moreover, many of these sparse networks exhibit very large numbers of nodes with no adjacent edges, as well as disjoint components of nodes with no edges connecting them. A prevalent aim in network modeling is the identification of clusters, or communities, of nodes that are highly interrelated. Several definitions of strong community structure have been introduced to facilitate this task, each with inherent assumptions and biases. We introduce an intuitive objective function for quantifying the quality of clustering results in large sparse networks. We utilize a two-step method for identifying communities which is especially well-suited for this domain as the first step efficiently divides the network into the disjoint components, while the second step optimizes clustering of the produced components based on the new objective. Using simulated networks, optimization based on the new objective function consistently yields significantly higher accuracy than those based on the modularity function, with the widest gaps appearing for the noisiest networks. Additionally, applications to benchmark problems illustrate the intuitive correctness of our approach. Finally, the practicality of our approach is demonstrated in real-world data in which we identify complex genetic interactions in large-scale networks comprised of tens of thousands of nodes. Based on these three different types of trials, our results clearly demonstrate the usefulness of our two-step procedure and the accuracy of our simple objective.

In recent years, there has been a push to understand how chemical composition affects the magnetic activity levels of main sequence low-mass stars. Results indicate that more metal-rich stars are more magnetically active for a given stellar mass and rotation period. This metallicity dependence has implications for how the rotation periods and activity levels of low-mass stars evolve over their lifetimes. Numerical modelling suggests that at late ages more metal-rich stars should be rotating more slowly and be more magnetically active. In this work, we study the rotation and activity evolution of low-mass stars using a sample of Kepler field stars. We use the gyro-kinematic age dating technique to estimate ages for our sample and use the photometric activity index as our proxy for magnetic activity. We find clear evidence that, at late ages, more metal-rich stars have spun down to slower rotation in agreement with the theoretical modeling. However, further investigation is required to definitively determine whether the magnetic activity evolution occurs in a metallicity dependent way., Comment: 10 pages, 9 figures. This paper has undergone peer review at MNRAS with only a very minor revision requested in the last round of comments

The Loewner framework is an interpolatory approach designed for approximating linear and nonlinear systems. The goal here is to extend this framework to linear parametric systems with an arbitrary number n of parameters. One main innovation established here is the construction of data-based realizations for any number of parameters. Equally importantly, we show how to alleviate the computational burden, by avoiding the explicit construction of large-scale n-dimensional Loewner matrices of size $N \times N$. This reduces the complexity from $O(N^3)$ to about $O(N^{1.4})$, thus taming the curse of dimensionality and making the solution scalable to very large data sets. To achieve this, a new generalized multivariate rational function realization is defined. Then, we introduce the n-dimensional multivariate Loewner matrices and show that they can be computed by solving a coupled set of Sylvester equations. The null space of these Loewner matrices then allows the construction of the multivariate barycentric transfer function. The principal result of this work is to show how the null space of the n-dimensional Loewner matrix can be computed using a sequence of 1-dimensional Loewner matrices, leading to a drastic computational burden reduction. Finally, we suggest two algorithms (one direct and one iterative) to construct, directly from data, multivariate (or parametric) realizations ensuring (approximate) interpolation. Numerical examples highlight the effectiveness and scalability of the method., Comment: 32 pages, 4 figures

This paper introduces v0.5 of the AI Safety Benchmark, which has been created by the MLCommons AI Safety Working Group. The AI Safety Benchmark has been designed to assess the safety risks of AI systems that use chat-tuned language models. We introduce a principled approach to specifying and constructing the benchmark, which for v0.5 covers only a single use case (an adult chatting to a general-purpose assistant in English), and a limited set of personas (i.e., typical users, malicious users, and vulnerable users). We created a new taxonomy of 13 hazard categories, of which 7 have tests in the v0.5 benchmark. We plan to release version 1.0 of the AI Safety Benchmark by the end of 2024. The v1.0 benchmark will provide meaningful insights into the safety of AI systems. However, the v0.5 benchmark should not be used to assess the safety of AI systems. We have sought to fully document the limitations, flaws, and challenges of v0.5. This release of v0.5 of the AI Safety Benchmark includes (1) a principled approach to specifying and constructing the benchmark, which comprises use cases, types of systems under test (SUTs), language and context, personas, tests, and test items; (2) a taxonomy of 13 hazard categories with definitions and subcategories; (3) tests for seven of the hazard categories, each comprising a unique set of test items, i.e., prompts. There are 43,090 test items in total, which we created with templates; (4) a grading system for AI systems against the benchmark; (5) an openly available platform, and downloadable tool, called ModelBench that can be used to evaluate the safety of AI systems on the benchmark; (6) an example evaluation report which benchmarks the performance of over a dozen openly available chat-tuned language models; (7) a test specification for the benchmark.

In fifth generation (5G) wireless cellular networks, millimeter wave spectrum opens room for several potential improvements in throughput, reliability, latency, among other aspects. However, it also brings challenges, such as a higher influence of blockage which may significantly limit the coverage. In this context, network-controlled repeaters (NCRs) are network nodes with low complexity that represent a technique to overcome coverage problems. In this paper, we introduce the NCR concept and study its performance gains and deployment options. Particularly, presenting the main specifications of NCR as agreed in 3rd generation partnership project (3GPP) Rel-18, we analyze different NCR deployments in an urban scenario and compare its performance with alternative deployments. As demonstrated, with a proper network planning and beamforming design, NCR is an attractive solution to cover blind spots the base stations (BSs) may have., Comment: Submmited to IEEE Communications Standards Magazine

In this report, we introduce the Gemini 1.5 family of models, representing the next generation of highly compute-efficient multimodal models capable of recalling and reasoning over fine-grained information from millions of tokens of context, including multiple long documents and hours of video and audio. The family includes two new models: (1) an updated Gemini 1.5 Pro, which exceeds the February version on the great majority of capabilities and benchmarks; (2) Gemini 1.5 Flash, a more lightweight variant designed for efficiency with minimal regression in quality. Gemini 1.5 models achieve near-perfect recall on long-context retrieval tasks across modalities, improve the state-of-the-art in long-document QA, long-video QA and long-context ASR, and match or surpass Gemini 1.0 Ultra's state-of-the-art performance across a broad set of benchmarks. Studying the limits of Gemini 1.5's long-context ability, we find continued improvement in next-token prediction and near-perfect retrieval (>99%) up to at least 10M tokens, a generational leap over existing models such as Claude 3.0 (200k) and GPT-4 Turbo (128k). Finally, we highlight real-world use cases, such as Gemini 1.5 collaborating with professionals on completing their tasks achieving 26 to 75% time savings across 10 different job categories, as well as surprising new capabilities of large language models at the frontier; when given a grammar manual for Kalamang, a language with fewer than 200 speakers worldwide, the model learns to translate English to Kalamang at a similar level to a person who learned from the same content.

Higher-order topological insulators (HOTIs) are unique materials hosting topologically protected states, whose dimensionality is at least by a factor of 2 lower than that of the bulk. Topological states in such insulators may be strongly confined in their corners that leads to considerable enhancement of nonlinear processes involving such states. However, all nonlinear HOTIs demonstrated so far were built on periodic bulk lattice materials. Here we demonstrate first \textit{nonlinear photonic} HOTI with the fractal origin. Despite their fractional effective dimensionality, the HOTIs constructed here on two different types of the Sierpi\'nski gasket waveguide arrays, may support topological corner states for unexpectedly wide range of coupling strengths, even in parameter regions where conventional HOTIs become trivial. We demonstrate thresholdless solitons bifurcating from corner states in nonlinear fractal HOTIs and show that their localization can be efficiently controlled by the input beam power. We observe sharp differences in nonlinear light localization on outer and multiple inner corners and edges representative for these fractal materials. Our findings not only represent a new paradigm for nonlinear topological insulators, but also open new avenues for potential applications of fractal materials to control the light flow., Comment: 10 pages, 5 figures

Observations of linear polarization in the 2-8 keV energy range with the Imaging X-ray Polarimetry Explorer (IXPE) explore the magnetic field geometry and dynamics of the regions generating non-thermal radiation in relativistic jets of blazars. These jets, particularly in blazars whose spectral energy distribution peaks at X-ray energies, emit X-rays via synchrotron radiation from high-energy particles within the jet. IXPE observations of the X-ray selected BL Lac-type blazar 1ES 1959+650 in 2022 May 3-4 showed a significant linear polarization degree of $\Pi_\mathrm{x} = 8.0\% \pm 2.3\%$ at an electric-vector position angle $\psi_\mathrm{x} = 123^\circ \pm 8^\circ$. However, in 2022 June 9-12, only an upper limit of $\Pi_\mathrm{x} \leq 5.1\%$ could be derived (at the 99% confidence level). The degree of optical polarization at that time $\Pi_\mathrm{O} \sim 5\%$ is comparable to the X-ray measurement. We investigate possible scenarios for these findings, including temporal and geometrical depolarization effects. Unlike some other X-ray selected BL Lac objects, there is no significant chromatic dependence of the measured polarization in 1ES 1959+650, and its low X-ray polarization may be attributed to turbulence in the jet flow with dynamical timescales shorter than 1 day., Comment: 16 pages, 4 figures, accepted for publication in The Astrophysical Journal