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As multiple crises threaten the sustainability of our societies and pose at risk the planetary boundaries, complex challenges require timely, updated, and usable information. Natural-language processing (NLP) tools enhance and expand data collection and processing and knowledge utilization capabilities to support the definition of an inclusive, sustainable future. In this work, we apply different NLP techniques, tools and approaches to climate and sustainability documents to derive policy-relevant and actionable measures. We focus on general and domain-specific large language models (LLMs) using a combination of static and prompt-based methods. We find that the use of LLMs is successful at processing, classifying and summarizing heterogeneous text-based data. However, we also encounter challenges related to human intervention across different workflow stages and knowledge utilization for policy processes. Our work presents a critical but empirically grounded application of LLMs to complex policy problems and suggests avenues to further expand Artificial Intelligence-powered computational social sciences., Comment: 15 pages; 4 figures

We present a detailed numerical study of ultrashort pulse compression using a three-stage hybrid all-bulk multipass cell scheme. By operating in the enhanced frequency chirp regime, we achieve the compression of pulses from around 180 fs to 4 fs pulse duration (a total compression factor above 45), with side lobes contributing with intensity values lower than 0.2 % of the peak intensity. Optimal conditions for the enhanced frequency chirp regime propagation have been identified, enabling smooth spectral broadening and high-quality temporal profiles. The first two stages are based on bulk multipass cells to achieve a controlled spectral broadening, while the third stage consists of a thin plate to reach the spectral broadening needed for few cycle pulses without leaving the enhanced frequency chirp regime.

Isolated attosecond pulses (IAPs) generated by few-cycle femtosecond lasers are essential for capturing ultrafast dynamics in atoms, molecules, and solids. Nonetheless, the advancement of attosecond science critically depends on achieving stable, high-temporal-contrast IAPs. Our study reveals a universal scenario in which self-compression of the infrared driver in high harmonic generation in extended gas media leads to high-contrast high-frequency IAP generation. Our experimental and theoretical results reveal that filamentation in a semi-infinite gas cell not only shapes the infrared driving pulse spatially and temporally, but also creates a stable propagation region where high harmonic generation is phase-matched, leading to the production of bright IAPs. In an argon-filled gas cell, filamentation notably reduces the pulse duration of Yb-based 1030 nm pulses from 4.7 fs to 3.5 fs, while simultaneously generating high-contrast 200-attosecond IAPs at 70 eV. We demonstrate the universality of filamentation-assisted IAP generation, showing that post-compressed Yb-based laser filaments in neon and helium yield even shorter IAPs: 69-attoseconds at 100 eV, and 65-attoseconds IAPs at 135 eV, respectively. This spatiotemporal reshaping of few-cycle pulses through filamentation possesses immediate impacts on both post-compression techniques and attosecond-based technologies.

We prove several results regarding the homology and homotopy type of images of real maps and their complexification. In particular, we study the local behavior of singular points after deformations. In this context, we prove a restrictive necessary condition for a real perturbation to have the same homology than its complexification, which is known as good real perturbation. We prove the conjecture of Marar and Mond stating that for singularities from $\mathbb{C}^n$ to $\mathbb{C}^{n+1}$, a good real perturbation is homotopy equivalent to its complexification, and show a generalization in other dimensions. Applications to $M$-deformations and other concepts as well as examples are given., Comment: Comments are welcomed!

In this paper we present a multi-criteria classification of Vocational and Educational Programs in Extremadura (Spain) during the period 2009-2016. This ranking has been carried out through the integration into a complete database of the detailed information of individuals finishing such studies together with their labor data. The multicriteria method used is TOPSIS together with a new decision support method for assessing the influence of each criterion and its dependence on the weights assigned to them. This new method is based on a worst-best case scenario analysis and it is compared to a well known global sensitivity analysis technique based on the Pearson's correlation ratio., Comment: 18 pages, 7 figures

The countless applications of ultrashort laser pulses in very different scientific areas explain the ongoing efforts to develop new strategies for the generation of light pulses with increasingly better characteristics. In this work, we theoretically study the application of the nonlinear reverse propagation method to produce few-cycle pulses with clean temporal profiles from standard post-compression setups based in hollow capillary fibers. By numerically solving the propagation of a desired goal pulse in the backward direction, we are able to predict the structure of the ideal input pulse that could be perfectly compressed in a given setup. Although the goal pulse cannot be chosen in a simple manner due to the fundamental symmetries of the nonlinear propagation equation, our analysis shows that the ideal pulse presents a recurring form and that, in general, both its intensity profile and phase must be shaped to recover the optimized goal output., Comment: 15 pages, 10 figures

We compute the signature of the Milnor fiber of certain type of non-isolated complex surface singularities, namely, images of finitely determined holomorphic germs. An explicit formula is given in algebraic terms. As a corollary we show that the signature of the Milnor fiber is a topological invariant for these singularities. The proof combines complex analytic and smooth topological techniques. The main tools are Thom-Mather theory of map germs and the Ekholm-Sz\H{u}cs-Takase-Saeki formula for immersions. We give a table with many examples for which the signature is computed using our formula., Comment: 36 pages, 7 figures, 1 table

High-order harmonic generation (HHG) arising from the non-perturbative interaction of intense light fields with matter constitutes a well-established tabletop source of coherent extreme-ultraviolet and soft X-ray radiation, which is typically emitted as attosecond pulse trains. However, ultrafast applications increasingly demand isolated attosecond pulses (IAPs), which offer great promise for advancing precision control of electron dynamics. Yet, the direct generation of IAPs typically requires the synthesis of near-single-cycle intense driving fields, which is technologically challenging. In this work, we theoretically demonstrate a novel scheme for the straightforward and compact generation of IAPs from multi-cycle infrared drivers using hollow capillary fibers (HCFs). Starting from a standard, intense multi-cycle infrared pulse, a light transient is generated by extreme soliton self-compression in a HCF with decreasing pressure, and is subsequently used to drive HHG in a gas target. Owing to the sub-cycle confinement of the HHG process, high-contrast IAPs are continuously emitted almost independently of the carrier-envelope phase (CEP) of the optimally self-compressed drivers. This results in a CEP-robust scheme which is also stable under macroscopic propagation of the high harmonics in a gas target. Our results open the way to a new generation of integrated all-fiber IAP sources, overcoming the efficiency limitations of usual gating techniques for multi-cycle drivers., Comment: 18 pages, 5 figures

We prove that, if two germs of plane curves $(C,0)$ and $(C',0)$ with at least one singular branch are equivalent by a (real) smooth diffeomorphism, then $C$ is complex isomorphic to $C'$ or to $\overline{C'}$. A similar result was shown by Ephraim for irreducible hypersurfaces before, but his proof is not constructive. Indeed, we show that the complex isomorphism is given by the Taylor series of the diffeomorphism. We also prove an analogous result for the case of non-irreducible hypersurfaces containing an irreducible component of zero-dimensional isosingular locus. Moreover, we provide a general overview of the different classifications of plane curve singularities.

We show how machine learning methods can unveil the fractional and delayed nature of discrete dynamical systems. In particular, we study the case of the fractional delayed logistic map. We show that given a trajectory, we can detect if it has some delay effect or not, and also to characterize the fractional component of the underlying generation model., Comment: 14 pages, 9 figures

Anomalous diffusion is present at all scales, from atomic to large scales. Some exemplary systems are; ultra-cold atoms, telomeres in the nucleus of cells, moisture transport in cement-based materials, the free movement of arthropods, and the migration patterns of birds. The characterization of the diffusion gives critical information about the dynamics of these systems and provides an interdisciplinary framework with which to study diffusive transport. Thus, the problem of identifying underlying diffusive regimes and inferring the anomalous diffusion exponent {$\alpha$} with high confidence is critical to physics, chemistry, biology, and ecology. Classification and analysis of raw trajectories combining machine learning techniques with statistics extracted from them have widely been studied in the Anomalous Diffusion Challenge ge (Munoz-Gil et al., 2021). Here we present a new data-driven method for working with diffusive trajectories. This method utilizes Gramian Angular Fields (GAF) to encode one-dimensional trajectories as images (Gramian Matrices), while preserving their spatiotemporal structure for input to computer-vision models. This allows us to leverage two well-established pre-trained computer-vision models, ResNet and MobileNet, to characterize the underlying diffusive regime, and infer the anomalous diffusion exponent {$\alpha$}. Short raw trajectories, of lengths between 10 and 50, are commonly encountered in single-particle tracking experiments and are the most difficult to characterize. We show that by using GAF images, we can outperform the current state-of-the-art while increasing accessibility to machine learning methods in an applied setting., Comment: 19 pages, 15 figures

Taming the instabilities inherent to many nonlinear optical phenomena is of paramount importance for modern photonics. In particular, the so-called snake instability is universally known to severely distort localized wave stripes, leading to the occurrence of transient, short-lived dynamical states that eventually decay. The phenomenon is ubiquitous in nonlinear science, from river meandering to superfluids, and to date it remains apparently uncontrollable. However, here we show that optical snake instabilities can be harnessed by a process that leads to the formation of stationary and robust two-dimensional zigzag states. We find that such new type of nonlinear waves exists in the hyperbolic regime of cylindrical micro-resonators and it naturally corresponds to two-dimensional frequency combs featuring spectral heterogeneity and intrinsic synchronization. We uncover the conditions of the existence of such spatiotemporal photonic snakes and confirm their remarkable robustness against perturbations. Our findings represent a new paradigm for frequency comb generation, thus opening the door to a whole range of applications in communications, metrology, and spectroscopy., Comment: 6 figures, 11 pages

Infrared spectroscopic observations from the ground must be corrected from telluric contamination to make them ready for scientific analyses. However, telluric correction is often a tedious process that requires significant expertise to yield accurate results in a reasonable time frame. To solve these inconveniences, we present a new method for telluric correction that employs a roughly simultaneous observation of a Vega analog to measure atmospheric transmission. After continuum reconstruction and spectral fitting, the stellar features are removed from the observed Vega-type spectrum and the result is used for cancelling telluric absorption features on science spectra. This method is implemented as TelCorAl (Telluric Correction from Alicante), a Python-based web application with a user-friendly interface, whose beta version will be released soon., Comment: 6 pages, 2 figures. To be published in Highlights of Spanish Astrophysics XI, Proceedings of the XV Scientific Meeting of the Spanish Astronomical Society

The 2030 Agenda of the United Nations (UN) revolves around the Sustainable Development Goals (SDGs). A critical step towards that objective is identifying whether scientific production aligns with the SDGs' achievement. To assess this, funders and research managers need to manually estimate the impact of their funding agenda on the SDGs, focusing on accuracy, scalability, and objectiveness. With this objective in mind, in this work, we develop ASDG, an easy-to-use artificial-intelligence (AI)-based model for automatically identifying the potential impact of scientific papers on the UN SDGs. As a demonstrator of ASDG, we analyze the alignment of recent aerospace publications with the SDGs. The Aerospace data set analyzed in this paper consists of approximately 820,000 papers published in English from 2011 to 2020 and indexed in the Scopus database. The most-contributed SDGs are 7 (on clean energy), 9 (on industry), 11 (on sustainable cities) and 13 (on climate action). The establishment of the SDGs by the UN in the middle of the 2010 decade did not significantly affect the data. However, we find clear discrepancies among countries, likely indicative of different priorities. Also, different trends can be seen in the most and least cited papers, with clear differences in some SDGs. Finally, the number of abstracts the code cannot identify is decreasing with time, possibly showing the scientific community's awareness of SDG.

The results of the Anomalous Diffusion Challenge (AnDi Challenge) have shown that machine learning methods can outperform classical statistical methodology at the characterization of anomalous diffusion in both the inference of the anomalous diffusion exponent alpha associated with each trajectory (Task 1), and the determination of the underlying diffusive regime which produced such trajectories (Task 2). Furthermore, of the five teams that finished in the top three across both tasks of the AnDi challenge, three of those teams used recurrent neural networks (RNNs). While RNNs, like the long short-term memory (LSTM) network, are effective at learning long-term dependencies in sequential data, their key disadvantage is that they must be trained sequentially. In order to facilitate training with larger data sets, by training in parallel, we propose a new transformer based neural network architecture for the characterization of anomalous diffusion. Our new architecture, the Convolutional Transformer (ConvTransformer) uses a bi-layered convolutional neural network to extract features from our diffusive trajectories that can be thought of as being words in a sentence. These features are then fed to two transformer encoding blocks that perform either regression or classification. To our knowledge, this is the first time transformers have been used for characterizing anomalous diffusion. Moreover, this may be the first time that a transformer encoding block has been used with a convolutional neural network and without the need for a transformer decoding block or positional encoding. Apart from being able to train in parallel, we show that the ConvTransformer is able to outperform the previous state of the art at determining the underlying diffusive regime in short trajectories (length 10-50 steps), which are the most important for experimental researchers., Comment: 20 pages, 13 figures

FV Time is a small-scale verification project developed in the Coq proof assistant using the Mathematical Components libraries. It is a library for managing conversions between time formats (UTC and timestamps), as well as commonly used functions for time arithmetic. As a library for time conversions, its novelty is the implementation of leap seconds, which are part of the UTC standard but usually not implemented in existing libraries. Since the verified functions of FV Time are reasonably simple yet non-trivial, it nicely illustrates our methodology for verifying software with Coq. In this paper we present a description of the project, emphasizing the main problems faced while developing the library, as well as some general-purpose solutions that were produced as by-products and may be used in other verification projects. These include a refinement package between proof-oriented MathComp numbers and computation-oriented primitive numbers from the Coq standard library, as well as a set of tactics to automatically prove certain decidable statements over finite ranges through brute-force computation.

Many of today's problems require techniques that involve the solution of arbitrarily large systems $A\mathbf{x}=\mathbf{b}$. A popular numerical approach is the so-called Greedy Rank-One Update Algorithm, based on a particular tensor decomposition. The numerical experiments support the fact that this algorithm converges especially fast when the matrix of the linear system is Laplacian-Like. These matrices that follow the tensor structure of the Laplacian operator are formed by sums of Kronecker product of matrices following a particular pattern. Moreover, this set of matrices is not only a linear subspace it is a a Lie sub-algebra of a matrix Lie Algebra. In this paper, we characterize and give the main properties of this particular class of matrices. Moreover, the above results allow us to propose an algorithm to explicitly compute the orthogonal projection onto this subspace of a given square matrix $A \in \mathbb{R}^{N\times N}.$

Developing complex biomolecular workflows is not always straightforward. It requires tedious developments to enable the interoperability between the different biomolecular simulation and analysis tools. Moreover, the need to execute the pipelines on distributed systems increases the complexity of these developments. To address these issues, we propose a methodology to simplify the implementation of these workflows on HPC infrastructures. It combines a library, the BioExcel Building Blocks (BioBBs), that allows scientists to implement biomolecular pipelines as Python scripts, and the PyCOMPSs programming framework which allows to easily convert Python scripts into task-based parallel workflows executed in distributed computing systems such as HPC clusters, clouds, containerized platforms, etc. Using this methodology, we have implemented a set of computational molecular workflows and we have performed several experiments to validate its portability, scalability, reliability and malleability., Comment: Accepted in IEEE eScience conference 2022

We present a method to study the dynamics of a quasi-two dimensional Bose-Einstein condensate which contains initially many vortices at arbitrary locations. We present first the analytical solution of the dynamics in a homogeneous medium and in a parabolic trap for the ideal non-interacting case. For the homogeneous case this was introduced in the context of photonics. Here we discuss this case in the context of Bose-Einstein condensates and extend the analytical solution to the trapped case, for the first time. This linear case allows one to obtain the trajectories of the position of phase singularities present in the initial condensate along with time. Also, it allows one to predict some quantities of interest, such as the time at which a vortex and an antivortex contained in the initial condensate will merge. Secondly, the method is complemented with numerical simulations of the non-linear case. We use a numerical split-step simulation of the non-linear Gross-Pitaevskii equation to determine how these trajectories and quantities of interest are changed by the presence of interactions. We illustrate the method with several simple cases of interest both in the homogeneous and parabolically trapped systems., Comment: 11 pages, 4 figures. Published in the Special Issue "Computational Methods for Quantum Matter", https://www.mdpi.com/journal/condensedmatter/special_issues/Comput_Quantum_Matter

We give a simple way to study the isotypical components of the homology of simplicial complexes with actions of finite groups, and use it for Milnor fibers of ICIS. We study the homology of images of mappings $f_t$ that arise as deformations of complex map germs $f:(\mathbb{C}^n,S)\to(\mathbb{C}^p,0)$, with $nn+1$: stable perturbations with contractible image and homology of $\text{im} f_t$ in unexpected dimensions. We show that Houston's conjecture, $\mu_I$ constant in a family implies excellency in Gaffney's sense, is false, but we give a correct modification of the statement of the conjecture which we also prove., Comment: 38 pages, 11 figures

We prove that a map germ $f:(\mathbb{C}^n,S)\to(\mathbb{C}^{n+1},0)$ with isolated instability is stable if and only if $\mu_I(f)=0$, where $\mu_I(f)$ is the image Milnor number defined by Mond. In a previous paper we proved this result with the additional assumption that $f$ has corank one. The proof here is also valid for corank $\ge 2$, provided that $(n,n+1)$ are nice dimensions in Mather's sense (so $\mu_I(f)$ is well defined). Our result can be seen as a weak version of a conjecture by Mond, which says that the $\mathcal{A}_e$-codimension of $f$ is $\le \mu_I(f)$, with equality if $f$ is weighted homogeneous. As an application, we deduce that the bifurcation set of a versal unfolding of $f$ is a hypersurface., Comment: 18 pages, 5 figures

We theoretically investigate the dynamics, bifurcation structure and stability of localized states in Kerr cavities driven at the pure fourth-order dispersion point. Both the normal and anomalous group velocity dispersion regimes are analysed, highlighting the main differences with the standard second order dispersion case. In the anomalous regime, single and multi-peak localised states exist and are stable over a much wider region of the parameter space. In the normal dispersion regime, stable narrow bright solitons exist. Some of our findings can be understood by a new scenario reported here for the spatial eigenvalues, which imposes oscillatory tails to all localised states. To be published in Optics Letters., Comment: To be published in Optics Letters

With the advent of more powerful Quantum Computers, the need for larger Quantum Simulations has boosted. As the amount of resources grows exponentially with size of the target system Tensor Networks emerge as an optimal framework with which we represent Quantum States in tensor factorizations. As the extent of a tensor network increases, so does the size of intermediate tensors requiring HPC tools for their manipulation. Simulations of medium-sized circuits cannot fit on local memory, and solutions for distributed contraction of tensors are scarce. In this work we present RosneT, a library for distributed, out-of-core block tensor algebra. We use the PyCOMPSs programming model to transform tensor operations into a collection of tasks handled by the COMPSs runtime, targeting executions in existing and upcoming Exascale supercomputers. We report results validating our approach showing good scalability in simulations of Quantum circuits of up to 53 qubits., Comment: 8 pages, 13 figures

Anomalous diffusion occurs at very different scales in nature, from atomic systems to motions in cell organelles, biological tissues or ecology, and also in artificial materials, such as cement. Being able to accurately measure the anomalous exponent associated with a given particle trajectory, thus determining whether the particle subdiffuses, superdiffuses or performs normal diffusion is of key importance to understand the diffusion process. Also, it is often important to trustingly identify the model behind the trajectory, as this gives a large amount of information on the system dynamics. Both aspects are particularly difficult when the input data are short and noisy trajectories. It is even more difficult if one cannot guarantee that the trajectories output in experiments is homogeneous, hindering the statistical methods based on ensembles of trajectories. We present a data-driven method able to infer the anomalous exponent and to identify the type of anomalous diffusion process behind single, noisy and short trajectories, with good accuracy. This model was used in our participation in the Anomalous Diffusion (AnDi) Challenge. A combination of convolutional and recurrent neural networks were used to achieve state-of-the-art results when compared to methods participating in the AnDi Challenge, ranking top 4 in both classification and diffusion exponent regression., Comment: 20 pages, 11 figures

We study germs of analytic maps $f:(X,S)\rightarrow(\mathbb{C}^p,0)$, when $X$ is an ICIS of dimension $n

Deviations from Brownian motion leading to anomalous diffusion are ubiquitously found in transport dynamics, playing a crucial role in phenomena from quantum physics to life sciences. The detection and characterization of anomalous diffusion from the measurement of an individual trajectory are challenging tasks, which traditionally rely on calculating the mean squared displacement of the trajectory. However, this approach breaks down for cases of important practical interest, e.g., short or noisy trajectories, ensembles of heterogeneous trajectories, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. Aiming to perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams independently applied their own algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, the results revealed clear differences between the various approaches, providing practical advice for users and a benchmark for developers., Comment: 63 pages, 5 main figures, 1 table, 28 supplementary figures. Website: http://www.andi-challenge.org

We give the definition of the Thom condition and we show that given any germ of complex analytic function $f:(X,x)\to(\mathbb{C},0)$ on a complex analytic space $X$, there exists a geometric local monodromy without fixed points, provided that $f\in\mathfrak m_{X,x}^2$, where $\mathfrak m_{X,x}$ is the maximal ideal of $\mathcal O_{X,x}$. This result generalizes a well-known theorem of the second named author when $X$ is smooth and proves a statement by Tibar in his PhD thesis. It also implies the A'Campo theorem that the Lefschetz number of the monodromy is equal to zero. Moreover, we give an application to the case that $X$ has maximal rectified homotopical depth at $x$ and show that a family of such functions with isolated critical points and constant total Milnor number has no coalescing of singularities., Comment: 25 pages, 6 figures

We uncover a novel and robust phenomenon that causes the gradual self-replication of spatiotemporal Kerr cavity patterns in cylindrical microresonators. These patterns are inherently synchronised multi-frequency combs. Under proper conditions, the axially-localized nature of the patterns leads to a fundamental drift instability that induces transitions amongst patterns with a different number of rows. Self-replications, thus, result in the stepwise addition or removal of individual combs along the cylinder's axis. Transitions occur in a fully reversible and, consequently, deterministic way. The phenomenon puts forward a novel paradigm for Kerr frequency comb formation and reveals important insights into the physics of multi-dimensional nonlinear patterns., Comment: 13 pages, 9 figures, to appear in Physical Review Letters

Progress in science is deeply bound to the effective use of high-performance computing infrastructures and to the efficient extraction of knowledge from vast amounts of data. Such data comes from different sources that follow a cycle composed of pre-processing steps for data curation and preparation for subsequent computing steps, and later analysis and analytics steps applied to the results. However, scientific workflows are currently fragmented in multiple components, with different processes for computing and data management, and with gaps in the viewpoints of the user profiles involved. Our vision is that future workflow environments and tools for the development of scientific workflows should follow a holistic approach, where both data and computing are integrated in a single flow built on simple, high-level interfaces. The topics of research that we propose involve novel ways to express the workflows that integrate the different data and compute processes, dynamic runtimes to support the execution of the workflows in complex and heterogeneous computing infrastructures in an efficient way, both in terms of performance and energy. These infrastructures include highly distributed resources, from sensors and instruments, and devices in the edge, to High-Performance Computing and Cloud computing resources. This paper presents our vision to develop these workflow environments and also the steps we are currently following to achieve it., Comment: 10 pages, 6 figures, in proceedings of 2019 IEEE 39th International Conference on Distributed Computing Systems (ICDCS)

We show three basic properties on the image Milnor number $\mu_I(f)$ of a germ $f\colon(\mathbb{C}^{n},S)\rightarrow(\mathbb{C}^{n+1},0)$ with isolated instability. First, we show the conservation of the image Milnor number, from which one can deduce the upper semi-continuity and the topological invariance for families. Second, we prove the weak Mond's conjecture, which says that $\mu_I(f)=0$ if and only if $f$ is stable. Finally, we show a conjecture by Houston that any family $f_t\colon(\mathbb{C}^{n},S)\rightarrow(\mathbb{C}^{n+1},0)$ with $\mu_I(f_t)$ constant is excellent in Gaffney's sense. By technical reasons, in the two last properties we consider only the corank 1 case., Comment: Change in note after Theorem 3.9, a previous version was published in Quart. J. Math by error