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Understanding convective processes leading to severe weather hazards within Mediterranean cyclones is relevant for operational forecasters, insurance industry, and enhancing societal preparedness. In this work we examine the climatological link between Mediterranean cyclones and atmospheric conditions conducive to the formation of severe convection and convective hazards (convective precipitation, lightning and hail potential). Using ATDnet lightning detections we find that, from autumn to spring, 20 to 60% of lightning hours over the Mediterranean basin and adjacent land regions are associated with the presence of a nearby cyclone. Based on reanalysis data, severe convective environments, deep, moist convection (i.e., lightning potential) and related hazards are frequent in the warm sector of Mediterranean cyclones and to the north-east of their centres. In agreement with previous literature, convective processes and hazards peak approximately six hours prior to the time of minimum pressure of the cyclone centre. Moreover, severe convective environments are often detected in cyclone categories typical of transition seasons (especially autumn) and summer, while they are rarer in deep baroclinic cyclones with peak occurrence during winter. Finally, we show that dynamical cyclone features distinguish regions favourable to deep, moist convection. Warm conveyor belts of Mediterranean cyclones, characterised by large-scale ascent and located in regions of high thermodynamic instability, have the largest lightning potential. The potential is only half as intense along the cyclones' cold fronts.

In computational physics, chemistry, and biology, the implementation of new techniques in a shared and open source software lowers barriers to entry and promotes rapid scientific progress. However, effectively training new software users presents several challenges. Common methods like direct knowledge transfer and in-person workshops are limited in reach and comprehensiveness. Furthermore, while the COVID-19 pandemic highlighted the benefits of online training, traditional online tutorials can quickly become outdated and may not cover all the software's functionalities. To address these issues, here we introduce ``PLUMED Tutorials'', a collaborative model for developing, sharing, and updating online tutorials. This initiative utilizes repository management and continuous integration to ensure compatibility with software updates. Moreover, the tutorials are interconnected to form a structured learning path and are enriched with automatic annotations to provide broader context. This paper illustrates the development, features, and advantages of PLUMED Tutorials, aiming to foster an open community for creating and sharing educational resources., Comment: 26 pages, 5 figures

This work introduces a self-learning protocol that incorporates measurement and feedback into variational quantum circuits for efficient quantum state preparation. By combining projective measurements with conditional feedback, the protocol learns state preparation strategies that extend beyond unitary-only methods, leveraging measurement-based shortcuts to reduce circuit depth. Using the spin-1 Affleck-Kennedy-Lieb-Tasaki state as a benchmark, the protocol learns high-fidelity state preparation by overcoming a family of measurement induced local minima through adjustments of parameter update frequencies and ancilla regularization. Despite these efforts, optimization remains challenging due to the highly non-convex landscapes inherent to variational circuits. The approach is extended to larger systems using translationally invariant ans\"atze and recurrent neural networks for feedback, demonstrating scalability. Additionally, the successful preparation of a specific AKLT state with desired edge modes highlights the potential to discover new state preparation protocols where none currently exist. These results indicate that integrating measurement and feedback into variational quantum algorithms provides a promising framework for quantum state preparation.

Many biological processes occur on time scales longer than those accessible to molecular dynamics simulations. Identifying collective variables (CVs) and introducing an external potential to accelerate them is a popular approach to address this problem. In particular, $\texttt{PLUMED}$ is a community-developed library that implements several methods for CV-based enhanced sampling. This chapter discusses two recent developments that have gained popularity in recent years. The first is the On-the-fly Probability Enhanced Sampling (OPES) method as a biasing scheme. This provides a unified approach to enhanced sampling able to cover many different scenarios: from free energy convergence to the discovery of metastable states, from rate calculation to generalized ensemble simulation. The second development concerns the use of machine learning (ML) approaches to determine CVs by learning the relevant variables directly from simulation data. The construction of these variables is facilitated by the $\texttt{mlcolvar}$ library, which allows them to be optimized in Python and then used to enhance sampling thanks to a native interface inside $\texttt{PLUMED}$. For each of these methods, in addition to a brief introduction, we provide guidelines, practical suggestions and point to examples from the literature to facilitate their use in the study of the process of interest.

This paper presents and evaluates a framework for the coupling of subdomain-local projection-based reduced order models (PROMs) using the Schwarz alternating method following a domain decomposition (DD) of the spatial domain on which a given problem of interest is posed. In this approach, the solution on the full domain is obtained via an iterative process in which a sequence of subdomain-local problems are solved, with information propagating between subdomains through transmission boundary conditions (BCs). We explore several new directions involving the Schwarz alternating method aimed at maximizing the method's efficiency and flexibility, and demonstrate it on three challenging two-dimensional nonlinear hyperbolic problems: the shallow water equations, Burgers' equation, and the compressible Euler equations. We demonstrate that, for a cell-centered finite volume discretization and a non-overlapping DD, it is possible to obtain a stable and accurate coupled model utilizing Dirichlet-Dirichlet (rather than Robin-Robin or alternating Dirichlet-Neumann) transmission BCs on the subdomain boundaries. We additionally explore the impact of boundary sampling when utilizing the Schwarz alternating method to couple subdomain-local hyper-reduced PROMs. Our numerical results suggest that the proposed methodology has the potential to improve PROM accuracy by enabling the spatial localization of these models via domain decomposition, and achieve up to two orders of magnitude speedup over equivalent coupled full order model solutions and moderate speedups over analogous monolithic solutions.

A definable choice is a semialgebraic selection of one point in every fiber of the projection of a semialgebraic set. Definable choices exist by semialgebraic triviality, but their complexity depends exponentially on the number of variables. By allowing the selection to be approximate (in the Hausdorff sense), we quantitatively improve this result. In particular, we construct an approximate selection with degree that is linear in the complexity of the original set, and independent on the number of variables. This work is motivated by infinite-dimensional applications, in particular to the Sard conjecture in sub-Riemannian geometry. To prove these results, we develop a general quantitative theory for Hausdorff approximations in semialgebraic geometry, which has independent interest.

Human-robot physical interaction (pHRI) is a rapidly evolving research field with significant implications for physical therapy, search and rescue, and telemedicine. However, a major challenge lies in accurately understanding human constraints and safety in human-robot physical experiments without an IRB and physical human experiments. Concerns regarding human studies include safety concerns, repeatability, and scalability of the number and diversity of participants. This paper examines whether a physical approximation can serve as a stand-in for human subjects to enhance robot autonomy for physical assistance. This paper introduces the SHULDRD (Shoulder Haptic Universal Limb Dynamic Repositioning Device), an economical and anatomically similar device designed for real-time testing and deployment of pHRI planning tasks onto robots in the real world. SHULDRD replicates human shoulder motion, providing crucial force feedback and safety data. The device's open-source CAD and software facilitate easy construction and use, ensuring broad accessibility for researchers. By providing a flexible platform able to emulate infinite human subjects, ensure repeatable trials, and provide quantitative metrics to assess the effectiveness of the robotic intervention, SHULDRD aims to improve the safety and efficacy of human-robot physical interactions., Comment: Submitted to ICRA '25

The purpose of the paper is threefold: first, we prove optimal regularity results for the distance from $C^k$ submanifolds of general rank-varying sub-Riemannian structures. Then, we study the asymptotics of the volume of tubular neighbourhoods around such submanifolds. Finally, for the case of curves in the Heisenberg groups, we prove a Weyl's invariance result: the volume of small tubes around a curve does not depend on the way the curve is isometrically embedded, but only on its Reeb angle. The proof does not need the computation of the actual volume of the tube, and it is new even for the three-dimensional Heisenberg group., Comment: 25 pages, 1 figure

A spectral solution method is proposed to solve a previuously developed non-equilibrium statistical model describing partial thermalization of produced charged hadrons in relativistic heavy-ion collisions, thus improving the accuracy of the numerical solution. The particle's phase-space trajectories are treated as drift-diffusion stochastic process, leading to a Fokker-Planck equation (FPE) for the single-particle probability distribution function. The drift and diffusion coefficients are derived from the expected asymptotic states via appropriate fluctuation-dissipation relations, and the resulting FPE is then solved numerically using a spectral eigenfunction decomposition. The calculated time-dependent particle distributions are compared to Pb-Pb data from the ATLAS and ALICE collaborations at the Large Hadron Collider., Comment: 17 pages, 8 figures; submitted to Eur. Phys. J. A

In this work we discuss stability and nondegeneracy properties of some special families of minimal hypersurfaces embedded in $\mathbb{R}^m\times \mathbb{R}^n$ with $m,n\geq 2$. These hypersurfaces are asymptotic at infinity to a fixed Lawson cone $C_{m,n}$. In the case $m+n\ge 8$, we show that such hypersurfaces are strictly stable and we provide a full classification of their bounded Jacobi fields, which in turn allows us to prove the non-degeneracy of such surfaces. In the case $m+n\le 7$, we prove that such hypersurfaces have infinite Morse index.

We realize every closed flat 3-manifold as a cusp section of a complete, finite-volume hyperbolic 4-manifold whose symmetry group acts transitively on the set of cusps. Moreover, for every such 3-manifold, a dense subset of its flat metrics can be realized as cusp sections of a cusp-transitive 4-manifold. Finally, we prove that there are a lot of 4-manifolds with pairwise isometric cusps, for any given cusp type., Comment: 18 pages, 7 figures. Added acknowledgments

The Extreme Energy Events (EEE) Project, a joint project of the Centro Fermi (Museo Storico della Fisica e Centro Studi e Ricerche "E.Fermi") and INFN, has a dual purpose: a scientific research program on cosmic rays at ground level and an intense outreach and educational program. The project consists in a network of about 60 tracking detectors, called telescopes, mostly hosted in Italian High Schools. Each telescope is made by three Multigap Resistive Plate Chambers, operated so far with a gas mixture composed by 98% C$_2$H$_2$F$_4$ and 2% SF$_6$. Due to its high Global Warming Potential, a few years ago the EEE collaboration has started an extensive R&D on alternative mixtures environmentally sustainable and compatible with the current experimental setup and operational environment. Among other gas mixtures, the one with helium and hydrofluoroolefin R1234ze gave the best result during the preliminary tests performed with two of the network telescopes. The detector has proved to reach performance levels comparable to those obtained with previous mixtures, without any modification of the hardware. We will discuss the first results obtained with the new mixture, tested with different percentages of the two components., Comment: 14 pages, 6 figures, submitted to JINST

Path-like collective variables can be very effective for accurately modeling complex biomolecular processes in molecular dynamics simulations. Recently, we introduced DeepLNE, a machine learning-based path-like CV that provides a progression variable s along the path as a non-linear combination of several descriptors, effectively approximating the reaction coordinate. However, DeepLNE is computationally expensive for realistic systems needing many descriptors and limited in its ability to handle multi-state reactions. Here we present DeepLNE++, which uses a knowledge distillation approach to significantly accelerate the evaluation of DeepLNE, making it feasible to compute free energy landscapes for large and complex biomolecular systems. In addition, DeepLNE++ encodes system-specific knowledge within a supervised multitasking framework, enhancing its versatility and effectiveness.

Deconfined quantum critical points are exotic transition points not predicted by the Landau-Ginzburg-Wilson symmetry-breaking paradigm. They are associated to a one-point gap closing between distinct locally ordered phases, thus to a continuous phase transition. Because of this intrinsic criticality, at deconfined quantum critical points algebraic decay of all the correlation functions is expected. Here, we show that it is possible to go beyond this assumption. Specifically, we consider one dimensional interacting fermions where the phenomenon of spin-charge separation arises. We first explore the low energy regimes where a sine-Gordon Hamiltonian can provide accurate results. By means of a field theory approach we find that continuous phase transitions between different locally ordered phases can occur. As a consequence of the decoupled spin and charge degrees of freedom, we find that in two cases only one gap vanishes while the other remains finite. We then derive a microscopic model where such phase transitions take place. By performing a numerical analysis, we unambiguously find that deconfined quantum critical points can indeed be further characterized by the long-range order of a parity operator signaling the presence of a finite gap. Our results provide new interesting insights on the widely investigated topic of quantum phase transitions., Comment: 12 pages, 6 figures

Sard's theorem asserts that the set of critical values of a smooth map from one Euclidean space to another one has measure zero. A version of this result for infinite-dimensional Banach manifolds was proven by Smale for maps with Fredholm differential. It is well-known, however, that when the domain is infinite dimensional and the range is finite dimensional, the result is not true -- even under the assumption that the map is ``polynomial'' -- and a general theory is still lacking. Addressing this issue, in this paper, we provide sharp quantitative criteria for the validity of Sard's theorem in this setting. Our motivation comes from sub-Riemannian geometry and, as an application of our results, we prove the sub-Riemannian Sard conjecture for the restriction of the Endpoint map of Carnot groups to the set of piece-wise real-analytic controls with large enough radius of convergence, and the strong Sard conjecture for the restriction to the set of piece-wise entire controls., Comment: 39 pages. V2: improved presentation, some of the main results have been tweaked

Through the use of sub-Riemannian metrics we provide quantitative estimates for the maximal tight neighbourhood of a Reeb orbit on a three-dimensional contact manifold. Under appropriate geometric conditions we show how to construct closed curves which are boundaries of overtwisted disks. We introduce the concept of contact Jacobi curve, and prove lower bounds of the so-called tightness radius (from a Reeb orbit) in terms of Schwarzian derivative bounds. We compare these results with the corresponding ones from [Etnyre, Komendarczyk, Massot - Invent. Math. 2012 and Trans. Amer. Math. Soc. 2016], and we show that our estimates are sharp for classical model structures. We also prove similar, but non-sharp, estimates in terms of sub-Riemannian canonical curvature bounds. We apply our results to K-contact sub-Riemannian manifolds. In this setting, we prove a contact analogue of the celebrated Cartan-Hadamard theorem.

Light activated local stimulation and sensing of biological cells offers enormous potential for minimally invasive bioelectronic interfaces. Organic semiconductors are a promising material class to achieve this kind of transduction due to their optoelectronic properties and biocompatibility. Here we investigate which material properties are necessary to keep the optical excitation localized. This is critical to single cell transduction with high spatial resolution. As a model system we use organic photocapacitors for cell stimulation made of the small molecule semiconductors H2Pc and PTCDI. We investigate the spatial broadening of the localized optical excitation with photovoltage microscopy measurements. Our experimental data combined with modelling show that resolution losses due to the broadening of the excitation are directly related to the effective diffusion length of charge carriers generated at the heterojunction. With additional transient photovoltage measurements we find that the H2Pc/PTCDI heterojunction offers a small diffusion length of lambda = 1.5 +/- 0.1 um due to the small mobility of charge carriers along the heterojunction. Instead covering the heterojunction with a layer of PEDOT:PSS improves the photocapacitor performance but increases the carrier diffusion length to lambda = 7.0 +/- 0.3 um due to longer lifetime and higher carrier mobility. Furthermore, we introduce electrochemical photocurrent microscopy experiments to demonstrate micrometric resolution with the pn-junction under realistic aqueous operation conditions. This work offers valuable insights into the physical mechanisms governing the excitation and transduction profile and provide design principles for future organic semiconductor junctions, aiming to achieve high efficiency and high spatial resolution.

In this paper we describe the set of ``New Worlds Simulations'', three very large cosmology simulations, Qo'noS, Vulcan, and Ferenginar, that were carried out on the Summit supercomputer with the Hardware/Hybrid Cosmology Code, HACC. The gravity-only simulations follow the evolution of structure in the Universe by each employing 12,288^3 particles in (3 Gpc/h)^3 volumes, leading to a mass resolution of m_p~10^9 Msun/h. The simulations cover three different cosmologies, one LambdaCDM model, consistent with measurements from Planck, one simulation with massive neutrinos, and one simulation with a varying dark energy equation of state. All simulations have the same phases to allow a detailed comparison of the results and the investigation of the impact of different cosmological parameters. We present measurements of some basic statistics, such as matter power spectra, correlation function, halo mass function and concentration-mass relation and investigate the differences due to the varying cosmologies. Given the large volume and high resolution, these simulations provide excellent bases for creating synthetic skies. A subset of the data is made publicly available as part of this paper., Comment: 10 pages, 13 figures, simulation data portal: https://cosmology.alcf.anl.gov/transfer/newworlds

Usually, the strain-induced softening behaviour observed in the differential modulus $K(T,\gamma)$ of hydrogels has been attributed to the breakage of internal structures of the network, such as the cross-links that bind together the polymer chains. Here we consider a stress-strain relationship that we have recently derived from a coarse-grained model to demonstrate that no rupture of the network is needed for rubber-like gels to present such behaviour. In particular, we show that, in some cases, the decreasing of $K(T,\gamma)$ as a function of the strain $\gamma$ is closely related to the energy-related contribution to the elastic modulus that has been experimentally observed, e.g., for tetra-PEG hydrogels. Thus, our results suggest that, instead of the breakage of structures, the softening behaviour can be also related to the effective interaction between the chains in the network and their neighbouring solvent molecules. Comparison to experimental data determined for several hydrogels is included to illustrate that behaviour and to validate our approach., Comment: 10 pages, 4 figures

For any natural number $d$, a graph $G$ is a (disjoint) $d$-interval graph if it is the intersection graph of (disjoint) $d$-intervals, the union of $d$ (disjoint) intervals on the real line. Two important subclasses of $d$-interval graphs are unit and balanced $d$-interval graphs (where every interval has unit length or all the intervals associated to a same vertex have the same length, respectively). A celebrated result by Roberts gives a simple characterization of unit interval graphs being exactly claw-free interval graphs. Here, we study the generalization of this characterization for $d$-interval graphs. In particular, we prove that for any $d \geq 2$, if $G$ is a $K_{1,2d+1}$-free interval graph, then $G$ is a unit $d$-interval graph. However, somehow surprisingly, under the same assumptions, $G$ is not always a \emph{disjoint} unit $d$-interval graph. This implies that the class of disjoint unit $d$-interval graphs is strictly included in the class of unit $d$-interval graphs. Finally, we study the relationships between the classes obtained under disjoint and non-disjoint $d$-intervals in the balanced case and show that the classes of disjoint balanced 2-intervals and balanced 2-intervals coincide, but this is no longer true for $d>2$.

We study the quantum dynamics of the edge modes of lattice fractional quantum Hall liquids in response to time-dependent external potentials. We show that the nonlinear chiral Luttinger liquid theory provides a quantitatively accurate description even for the small lattice geometries away from the continuum limit that are available in state-of-the-art experiments. Experimentally accessible signatures of the quantized value of the bulk transverse Hall conductivity are identified both in the linear and the non-linear response to an external excitation. The strong nonlinearity induced by the open boundaries is responsible for sizable quantum blockade effects, leading to the generation of nonclassical states of the edge modes., Comment: 4+15 pages

The simulation of high-energy physics collision events is a key element for data analysis at present and future particle accelerators. The comparison of simulation predictions to data allows looking for rare deviations that can be due to new phenomena not previously observed. We show that novel machine learning algorithms, specifically Normalizing Flows and Flow Matching, can be used to replicate accurate simulations from traditional approaches with several orders of magnitude of speed-up. The classical simulation chain starts from a physics process of interest, computes energy deposits of particles and electronics response, and finally employs the same reconstruction algorithms used for data. Eventually, the data are reduced to some high-level analysis format. Instead, we propose an end-to-end approach, simulating the final data format directly from physical generator inputs, skipping any intermediate steps. We use particle jets simulation as a benchmark for comparing both discrete and continuous Normalizing Flows models. The models are validated across a variety of metrics to identify the most accurate. We discuss the scaling of performance with the increase in training data, as well as the generalization power of these models on physical processes different from the training one. We investigate sampling multiple times from the same physical generator inputs, a procedure we name oversampling, and we show that it can effectively reduce the statistical uncertainties of a dataset. This class of ML algorithms is found to be capable of learning the expected detector response independently of the physical input process. Their speed and accuracy, coupled with the stability of the training procedure, make them a compelling tool for the needs of current and future experiments., Comment: 35 pages, 19 figures, submitted to Machine Learning: Science and Technology. Added references

We realize 4 of the 6 closed orientable flat 3-manifolds as a cusp section of an orientable finite-volume hyperbolic 4-manifold whose symmetry group acts transitively on the set of cusps., Comment: 40 pages, 29 figures, 13 tables

Information visualization plays a key role in business intelligence analytics. With ever larger amounts of data that need to be interpreted, using the right visualizations is crucial in order to understand the underlying patterns and results obtained by analysis algorithms. Despite its importance, defining the right visualization is still a challenging task. Business users are rarely experts in information visualization, and they may not exactly know the most adequate visualization tools or patterns for their goals. Consequently, misinterpreted graphs and wrong results can be obtained, leading to missed opportunities and significant losses for companies. The main problem underneath is a lack of tools and methodologies that allow non-expert users to define their visualization and data analysis goals in business terms. In order to tackle this problem, we present an iterative goal-oriented approach based on the i* language for the automatic derivation of data visualizations. Our approach links non-expert user requirements to the data to be analyzed, choosing the most suited visualization techniques in a semi-automatic way. The great advantage of our proposal is that we provide non-expert users with the best suited visualizations according to their information needs and their data with little effort and without requiring expertise in information visualization.

Several enhanced sampling techniques rely on the definition of collective variables to effectively explore free energy landscapes. Existing variables that describe the progression along a reactive pathway offer an elegant solution but face a number of limitations. In this paper, we address these challenges by introducing a new path-like collective variable called the `Deep-locally-non-linear-embedding', which is inspired by principles of the locally linear embedding technique and is trained on a reactive trajectory. The variable mimics the ideal reaction coordinate by automatically generating a non-linear combination of features through a differentiable generalized autoencoder that combines a neural network with a continuous k-nearest-neighbor selection. Among the key advantages of this method is its capability to automatically choose the metric for searching neighbors and to learn the path from state A to state B without the need to handpick landmarks a priori. We demonstrate the effectiveness of DeepLNE by showing that the progression along the path variable closely approximates the ideal reaction coordinate in toy models such as the M\"uller-Brown-potential and alanine dipeptide. We then use it in molecular dynamics simulations of an RNA tetraloop, where we highlight its capability to accelerate transitions and converge the free energy of folding.

Efforts in the fight against Climate Change are increasingly oriented towards new energy efficiency strategies in Smart Grids (SGs). In 2018, with proper legislation, the European Union (EU) defined the Renewable Energy Community (REC) as a local electrical grid whose participants share their self-produced renewable energy, aiming at reducing bill costs by taking advantage of proper incentives. That action aspires to accelerate the spread of local renewable energy exploitation, whose costs could not be within everyone's reach. Since a REC is technically an SG, the strategies above can be applied, and specifically, practical Energy Management Systems (EMSs) are required. Therefore, in this work, an online Hierarchical EMS (HEMS) is synthesized for REC cost minimization to evaluate its superiority over a local self-consumption approach. EU technical indications (as inherited from Italy) are diligently followed, aiming for results that are as realistic as possible. Power flows between REC nodes, or Microgrids (MGs) are optimized by taking Energy Storage Systems (ESSs) and PV plant costs, energy purchase costs, and REC incentives. A hybrid Fuzzy Inference System - Genetic Algorithm (FIS-GA) model is implemented with the GA encoding the FIS parameters. Power generation and consumption, which are the overall system input, are predicted by a LSTM trained on historical data. The proposed hierarchical model achieves good precision in short computation times and outperforms the self-consumption approach, leading to about 20% savings compared to the latter. In addition, the Explainable AI (XAI), which characterizes the model through the FIS, makes results more reliable thanks to an excellent human interpretation level. To finish, the HEMS is parametrized so that it is straightforward to switch to another Country's technical legislation framework., Comment: 26 pages, 18 figures

This paper introduces for the first time the concepts of non-coherent interfaces and microstructure-driven interface forces in the framework of micromorphic elasticity. It is shown that such concepts are of paramount importance when studying the response of finite-size mechanical metamaterials at the homogenized macro-scale. The need of introducing interface forces is elucidated through numerical examples comparing reduced relaxed micromorphic simulations to their full-microstructured counterparts. These results provide a milestone for the understanding of metamaterials' modeling at the homogenized scale and for the use of micromorphic-type models to achieve an accurate upscaling towards larger-scale metamaterials' structures.

In a digraph, a quasi-kernel is a subset of vertices that is independent and such that the shortest path from every vertex to this subset is of length at most two. The ``small quasi-kernel conjecture,'' proposed by Erd\H{o}s and Sz\'ekely in 1976, postulates that every sink-free digraph has a quasi-kernel whose size is within a fraction of the total number of vertices. The conjecture is even more precise with a $1/2$ ratio, but even with larger ratio, this property is known to hold only for few classes of graphs. The focus here is on small quasi-kernels in split graphs. This family of graphs has played a special role in the study of the conjecture since it was used to disprove a strengthening that postulated the existence of two disjoint quasi-kernels. The paper proves that every sink-free split digraph $D$ has a quasi-kernel of size at most $\frac{2}{3}|V(D)|$, and even of size at most two when the graph is an orientation of a complete split graph. It is also shown that computing a quasi-kernel of minimal size in a split digraph is W[2]-hard.

In the realm of Computational Fluid Dynamics (CFD), the demand for memory and computation resources is extreme, necessitating the use of leadership-scale computing platforms for practical domain sizes. This intensive requirement renders traditional checkpointing methods ineffective due to the significant slowdown in simulations while saving state data to disk. As we progress towards exascale and GPU-driven High-Performance Computing (HPC) and confront larger problem sizes, the choice becomes increasingly stark: to compromise data fidelity or to reduce resolution. To navigate this challenge, this study advocates for the use of in situ analysis and visualization techniques. These allow more frequent data "snapshots" to be taken directly from memory, thus avoiding the need for disruptive checkpointing. We detail our approach of instrumenting NekRS, a GPU-focused thermal-fluid simulation code employing the spectral element method (SEM), and describe varied in situ and in transit strategies for data rendering. Additionally, we provide concrete scientific use-cases and report on runs performed on Polaris, Argonne Leadership Computing Facility's (ALCF) 44 Petaflop supercomputer and J\"ulich Wizard for European Leadership Science (JUWELS) Booster, J\"ulich Supercomputing Centre's (JSC) 71 Petaflop High Performance Computing (HPC) system, offering practical insight into the implications of our methodology.

This work proposes the Two-headed DragoNet, a Transformer-based model for hierarchical multi-label classification of financial transactions. Our model is based on a stack of Transformers encoder layers that generate contextual embeddings from two short textual descriptors (merchant name and business activity), followed by a Context Fusion layer and two output heads that classify transactions according to a hierarchical two-level taxonomy (macro and micro categories). Finally, our proposed Taxonomy-aware Attention Layer corrects predictions that break categorical hierarchy rules defined in the given taxonomy. Our proposal outperforms classical machine learning methods in experiments of macro-category classification by achieving an F1-score of 93\% on a card dataset and 95% on a current account dataset.

Saturn is an innovative platform that assists Foundation Model (FM) building and its integration with IT operations (Ops). It is custom-made to meet the requirements of data scientists, enabling them to effectively create and implement FMs while enhancing collaboration within their technical domain. By offering a wide range of tools and features, Saturn streamlines and automates different stages of FM development, making it an invaluable asset for data science teams. This white paper introduces prospective applications of generative AI models derived from FMs in the financial sector.

In this paper we prove existence of normalized solutions $(u,\lambda)\subset H^1(\mathbb{R}^3)\times \mathbb{R}^+$ of the following Schr\"{o}dinger-Poisson equation \begin{equation} \begin{aligned} -\Delta u+V(x)u+\lambda u+(|x|^{-1}\ast|u|^2)u&=|u|^{p-2}u,&\text{in}~\mathbb{R}^{3},\\ \int_{\mathbb{R}^{3}}u^2dx&=a^2>0, \end{aligned} \end{equation} under suitable conditions on the potential $V(x)$, where $\lambda$ appears as a Lagrange multiplier. For $V(x)\geq0$ and $p\in(4,6)$, such solutions are obtained by using a linking argument introduced by Bartsch et al. \cite{bm}. For $V(x)\leq0$, a mountain pass argument leads to the existence of normalized solutions for any $p\in(\frac{10}{3},6)$.

We study the Bisognano-Wichmann Hamiltonian for fractional quantum Hall states defined on a sphere and explore its relationship with the entanglement Hamiltonian associated to the state. We present results for several examples, namely the bosonic Laughlin state stabilized by contact two-body interactions and the bosonic Moore-Read state by either three- or two-body interactions. Our findings demonstrate that the Bisognano-Wichmann Hamiltonian provides a reliable approximation of the entanglement Hamiltonian as a fully-local operator that can be written without any prior knowledge of the specific state under consideration.

Given a flow network, the Minimum Flow Decomposition (MFD) problem is finding the smallest possible set of weighted paths whose superposition equals the flow. It is a classical, strongly NP-hard problem that is proven to be useful in RNA transcript assembly and applications outside of Bioinformatics. We improve an existing ILP (Integer Linear Programming) model by Dias et al. [RECOMB 2022] for DAGs by decreasing the solver's search space using solution safety and several other optimizations. This results in a significant speedup compared to the original ILP, of up to 55-90x on average on the hardest instances. Moreover, we show that our optimizations apply also to MFD problem variants, resulting in similar speedups, going up to 123x on the hardest instances. We also developed an ILP model of reduced dimensionality for an MFD variant in which the solution path weights are restricted to a given set. This model can find an optimal MFD solution for most instances, and overall, its accuracy significantly outperforms that of previous greedy algorithms while being up to an order of magnitude faster than our optimized ILP.

A variety of enhanced sampling methods predict multidimensional free energy landscapes associated with biological and other molecular processes as a function of a few selected collective variables (CVs). The accuracy of these methods is crucially dependent on the ability of the chosen CVs to capture the relevant slow degrees of freedom of the system. For complex processes, finding such CVs is the real challenge. Machine learning (ML) CVs offer, in principle, a solution to handle this problem. However, these methods rely on the availability of high-quality datasets -- ideally incorporating information about physical pathways and transition states -- which are difficult to access, therefore greatly limiting their domain of application. Here, we demonstrate how these datasets can be generated by means of enhanced sampling simulations in trajectory space via the metadynamics of paths [arXiv:2002.09281] algorithm. The approach is expected to provide a general and efficient way to generate efficient ML-based CVs for the fast prediction of free energy landscapes in enhanced sampling simulations. We demonstrate our approach with two numerical examples, a two-dimensional model potential and the isomerization of alanine dipeptide, using deep targeted discriminant analysis as our ML-based CV of choice.

The astronomical community is grappling with the increasing volume and complexity of data produced by modern telescopes, due to difficulties in reducing, accessing, analyzing, and combining archives of data. To address this challenge, we propose the establishment of a coordinating body, an "entity," with the specific mission of enhancing the interoperability, archiving, distribution, and production of both astronomical data and software. This report is the culmination of a workshop held in February 2023 on the Future of Astronomical Data Infrastructure. Attended by 70 scientists and software professionals from ground-based and space-based missions and archives spanning the entire spectrum of astronomical research, the group deliberated on the prevailing state of software and data infrastructure in astronomy, identified pressing issues, and explored potential solutions. In this report, we describe the ecosystem of astronomical data, its existing flaws, and the many gaps, duplication, inconsistencies, barriers to access, drags on productivity, missed opportunities, and risks to the long-term integrity of essential data sets. We also highlight the successes and failures in a set of deep dives into several different illustrative components of the ecosystem, included as an appendix., Comment: 59 pages; please send comments and/or questions to foadi@googlegroups.com

Modern hybrid superconductor-semiconductor Josephson junction arrays are a promising platform for analog quantum simulations. Their controllable and non-sinusoidal energy/phase relation opens the path to implement nontrivial interactions and study the emergence of exotic quantum phase transitions. Here, we propose the analysis of an array of hybrid Josephson junctions defining a 2-leg ladder geometry for the quantum simulation of the tricritical Ising phase transition. This transition provides the paradigmatic example of minimal conformal models beyond Ising criticality and its excitations are intimately related with Fibonacci non-Abelian anyons and topological order in two dimensions. We study this superconducting system and its thermodynamic phases based on bosonization and matrix-product-states techniques. Its effective continuous description in terms of a three-frequency sine-Gordon quantum field theory suggests the presence of the targeted tricritical point and the numerical simulations confirm this picture. Our results indicate which experimental observables can be adopted in realistic devices to probe the physics and the phase transitions of the model. Additionally, our proposal provides a useful one-dimensional building block to design exotic topological order in two-dimensional scalable Josephson junction arrays., Comment: 6 pages, 3 figures and Supplemental material

We derive the Green's functions (concentrated force and couple in an infinite space) for the isotropic planar relaxed micromorphic model. Since the relaxed micromorphic model particularises into the microstretch, Cosserat (micropolar), couple-stress, and linear elasticity model for certain choices of material parameters, we recover the fundamental solutions in all these cases.