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The RESISTO project, a pioneer innovation initiative in Europe, endeavors to enhance the resilience of electrical networks against extreme weather events and associated risks. Emphasizing intelligence and flexibility within distribution networks, RESISTO aims to address climatic and physical incidents comprehensively, fostering resilience across planning, response, recovery, and adaptation phases. Leveraging advanced technologies including AI, IoT sensors, and aerial robots, RESISTO integrates prediction, detection, and mitigation strategies to optimize network operation. This article summarizes the main technical aspects of the proposed solutions to meet the aforementioned objectives, including the development of a climate risk detection platform, an IoT-based monitoring and anomaly detection network, and a fleet of intelligent aerial robots. Each contributing to the project's overarching objectives of enhancing network resilience and operational efficiency.

Content moderation on a global scale must navigate a complex array of local cultural distinctions, which can hinder effective enforcement. While global policies aim for consistency and broad applicability, they often miss the subtleties of regional language interpretation, cultural beliefs, and local legislation. This work introduces a flexible framework that enhances foundation language models with cultural knowledge. Our approach involves fine-tuning encoder-decoder models on media-diet data to capture cultural nuances, and applies a continued training regime to effectively integrate these models into a content moderation pipeline. We evaluate this framework in a case study of an online podcast platform with content spanning various regions. The results show that our culturally adapted models improve the accuracy of local violation detection and offer explanations that align more closely with regional cultural norms. Our findings reinforce the need for an adaptable content moderation approach that remains flexible in response to the diverse cultural landscapes it operates in and represents a step towards a more equitable and culturally sensitive framework for content moderation, demonstrating what is achievable in this domain., Comment: 7 pages, 7 Figures. Supplementary material

We show that for two doubling measures $\sigma$ and $\omega$ on $\mathbb{R}^{n}$ and any fixed dyadic grid $\mathcal{D}$ in $\mathbb{R}^{n}$, \[ \mathfrak{N}_{\mathbf{R}^{\lambda, n}}\left( \sigma,\omega\right) \approx\mathfrak{H}_{\mathbf{R}^{\lambda, n}}^{\mathcal{D},\operatorname*{glob}}\left( \sigma,\omega\right) +\mathfrak{H}_{\mathbf{R}^{\lambda, n}}^{\mathcal{D},\operatorname*{glob}}\left( \omega, \sigma\right) \ , \] where $\mathfrak{N}_{\mathbf{R}^{\lambda, n}} (\sigma, \omega)$ denotes the $L^2 (\sigma) \to L^2 (\omega)$ operator norm of the vector-Riesz transform $\mathbf{R}^{\lambda, n}$ of fractional order $\lambda \neq 1$, and \[ \mathfrak{H}_{\mathbf{R}^{\lambda,n}}^{\mathcal{D},\operatorname*{glob}}\left( \sigma,\omega\right) \equiv\sup_{I\in\mathcal{D}}\left\Vert \mathbf{R}^{\lambda,n} h_{I}^{\sigma}\right\Vert _{L^{2}\left( \omega\right) }\ , \] is the global Haar testing characteristic for $\mathbf{R}^{\lambda,n}$ on the grid $\mathcal{D}$, and $\left\{ h_{I}^{\sigma}\right\} _{I\in\mathcal{D}}$ is the weighted Haar orthonormal basis of $L^{2}\left( \sigma\right) $ arising in the work of Nazarov, Treil and Volberg. We also show this theorem extends more generally to weighted Alpert wavelets which replace the weighted Haar wavelets in the proofs of some recent two-weight $T1$ theorems. Finally, we briefly pose these questions in the context of orthonormal bases in arbitrary Hilbert spaces., Comment: 22 pages + references. Due to a gap in a previous version of [SaWi], main results weakened to only consider p=2 and the vector Riesz transform. We also carry out a similar analysis for the Alpert wavelets

We show that for an individual Riesz transform in the setting of doubling measures, the scalar $T1$ theorem fails when $p \neq 2$: for each $ p \in (1, \infty) \setminus \{2\}$, we construct a pair of doubling measures $(\sigma, \omega)$ on $\mathbb{R}^2$ with doubling constant close to that of Lebesgue measure that also satisfy the scalar $\mathcal{A}_p$ condition and the full scalar $L^p$-testing conditions for an individual Riesz transform $R_j$, and yet $\left ( R_j \right )_{\sigma} : L^p (\sigma) \not \to L^p (\omega)$. On the other hand, a quadratic, or vector-valued, $T1$ theorem holds when $p \neq 2$ on pairs of doubling measures. Namely, we improve upon the quadratic $T1$ theorem of Sawyer-Wick and dispense with their vector-valued weak boundedness property to show that for pairs of doubling measures, the two-weight $L^p$ norm inequality for the vector Riesz transform is characterized by a quadratic Muckenhoupt condition $A_{p} ^{\ell^2, \operatorname{local}}$, and a quadratic testing condition. Finally, in the appendix, we use constructions of \cite{KaTr} to show that the two-weight norm inequality for the maximal function cannot be characterized solely by the $A_p$ condition when the measures are doubling, contrary to reports in the literature., Comment: 43 pages, 7 figures. Corrected statement of theorem of Sawyer-Wick, and hence our improvement of their result. Main construction unchanged, while new T1 theorem only concerns the vector Riesz transform

This is the final part of a series of papers where we study perturbations of divergence form second order elliptic operators $-\operatorname{div} A \nabla$ by first and zero order terms, whose complex coefficients lie in critical spaces, via the method of layer potentials. In particular, we show that the $L^2$ well-posedness (with natural non-tangential maximal function estimates) of the Dirichlet, Neumann and regularity problems for complex Hermitian, block form, or constant-coefficient divergence form elliptic operators in the upper half-space are all stable under such perturbations. Due to the lack of the classical De Giorgi-Nash-Moser theory in our setting, our method to prove the non-tangential maximal function estimates relies on a completely new argument: We obtain a certain weak-$L^p$ ''$N

Given p between 1 and infinity, but not 2, we show that the T1 theorem for the Hilbert transform fails for L^{p}, despite holding for p equal to 2, Comment: 4 pages. Misprints corrected, introduction modified to accurately reflect updated results in references. To appear in Journal d'Analyse Math\'ematique

We show that while individual Riesz transforms are two weight norm stable under biLipschitz change of variables on $A_{\infty}$ weights, they are two weight norm unstable under even rotational change of variables on doubling weights. More precisely, we show that individual Riesz transforms are unstable under a set of rotations having full measure, which includes rotations arbitrarily close to the identity. This provides an operator theoretic distinction between $A_{\infty}$ weights and doubling weights. More generally, all iterated Riesz transforms of odd order are rotationally unstable on pairs of doubling weights, thus demonstrating the need for characterizations of iterated Riesz transform inequalities using testing conditions for doubling measures, as opposed to the typically stable 'bump' conditions., Comment: 43 pages, followed by 8 pages of appendices and references. Several proofs are corrected, including circumventing an error found in a previous version of the T1 theorem of[AlSaUr]. Futhermore, an additional subsection is added to the appendix relating stability and sparse operators. Main results unchanged. To appear in Revista Matem\'atica Iberoamericana

Rising wind energy integration, accompanied by a decreasing level of system inertia, requires additional sources of ancillary services. Wind turbines based on doubly fed induction generators (DFIG) can provide inertial and primary frequency support, when equipped with specific controls. This paper investigates the effect of frequency support provision by DFIGs on the small-signal stability of power systems. To this end, a modified version of the Kundur two-area test system is employed to analyze different scenarios. Wind energy generation is either added to the existing system or displaces part of the synchronous generation. Simulations show that primary frequency support tends to improve the damping of electromechanical oscillations and deteriorate it for converter control-based ones. On the other hand, inertial response may be either beneficial, detrimental or negligible to damping, depending on the tuning of control parameters.

We establish $L^2$ boundedness of all "nice" parabolic singular integrals on "Good Parabolic Graphs", aka {\em regular} Lip(1,1/2) graphs. The novelty here is that we include non-homogeneous kernels, which are relevant to the theory of parabolic uniform rectifiability. Previously, the third named author had treated the case of homogeneous kernels. The present proof combines the methods of that work (which in turn was based on methods described in Christ's CBMS lecture notes), with the techniques of Coifman-David-Meyer. This is a very preliminary draft. Eventually, these results will be part of a more extensive work on parabolic uniform rectifiability and singular integrals., Comment: This is a preliminary draft. Eventually, these results will be part of a more extensive work on parabolic uniform rectifiability and singular integrals. We post the file in its current form now, in response to several queries about the result and methods

Let $E \subset \mathbb R^{n+1}$ be a parabolic uniformly rectifiable set. We prove that every bounded solution $u$ to $$\partial_tu- \Delta u=0, \quad \text{in} \quad \mathbb R^{n+1}\setminus E$$ satisfies a Carleson measure estimate condition. An important technical novelty of our work is that we develop a corona domain approximation scheme for $E$ in terms of regular Lip(1/2,1) graph domains. This approximation scheme has an analogous elliptic version which is an improvement of the known results in that setting.

We prove that parabolic uniformly rectifiable sets admit (bilateral) corona decompositions with respect to regular Lip(1,1/2) graphs. Together with our previous work, this allows us to conclude that if $\Sigma\subset\mathbb{R}^{n+1}$ is parabolic Ahlfors-David regular, then the following statements are equivalent. (1) $\Sigma$ is parabolic uniformly rectifiable. (2) $\Sigma$ admits a corona decomposition with respect to regular Lip(1,1/2) graphs. (3) $\Sigma$ admits a bilateral corona decomposition with respect to regular Lip(1,1/2) graphs. (4) $\Sigma$ is big pieces squared of regular Lip(1,1/2) graphs., Comment: We have improved the exposition in section 4. In particular, we have treated the case where `contact set' in the Whitney-type construction is empty. This case seemed to be overlooked in David and Semmes' original construction, but only required a modest fix. We have also corrected the (egregious) typo in what is now equation (4.42), which now has $\epsilon$ rather than $\delta$

Let $\Sigma$ be a closed subset of $\mathbb{R}^ {n+1}$ which is parabolic Ahlfors-David regular and assume that $\Sigma$ satisfies a 2-sided corkscrew condition. Assume, in addition, that $\Sigma$ is either time-forwards Ahlfors-David regular, time-backwards Ahlfors-David regular, or parabolic uniform rectifiable. We then first prove that $\Sigma$ satisfies a {\it weak synchronized two cube condition}. Based on this we are able to revisit the argument in \cite{NS} and prove that $\Sigma$ contains {\it uniform big pieces of Lip(1,1/2) graphs}. When $\Sigma$ is parabolic uniformly rectifiable the construction can be refined and in this case we prove that $\Sigma$ contains {\it uniform big pieces of regular parabolic Lip(1,1/2) graphs}. Similar results hold if $\Omega\subset\mathbb R^{n+1}$ is a connected component of $\mathbb R^{n+1}\setminus\Sigma$ and in this context we also give a parabolic counterpart of the main result in \cite{AHMNT} by proving that if $\Omega$ is a one-sided parabolic chord arc domain, and if $\Sigma$ is parabolic uniformly rectifiable, then $\Omega$ is in fact a parabolic chord arc domain. Our results give a flexible parabolic version of the classical (elliptic) result of G. David and D. Jerison concerning the existence of uniform big pieces of Lipschitz graphs for sets satisfying a two disc condition.

There are many scenarios where we may want to find pairs of textually similar documents in a large corpus (e.g. a researcher doing literature review, or an R&D project manager analyzing project proposals). To programmatically discover those connections can help experts to achieve those goals, but brute-force pairwise comparisons are not computationally adequate when the size of the document corpus is too large. Some algorithms in the literature divide the search space into regions containing potentially similar documents, which are later processed separately from the rest in order to reduce the number of pairs compared. However, this kind of unsupervised methods still incur in high temporal costs. In this paper, we present an approach that relies on the results of a topic modeling algorithm over the documents in a collection, as a means to identify smaller subsets of documents where the similarity function can then be computed. This approach has proved to obtain promising results when identifying similar documents in the domain of scientific publications. We have compared our approach against state of the art clustering techniques and with different configurations for the topic modeling algorithm. Results suggest that our approach outperforms (> 0.5) the other analyzed techniques in terms of efficiency., Comment: Accepted at the 9th International Conference on Knowledge Capture (K-CAP 2017)

With the ongoing growth in number of digital articles in a wider set of languages and the expanding use of different languages, we need annotation methods that enable browsing multi-lingual corpora. Multilingual probabilistic topic models have recently emerged as a group of semi-supervised machine learning models that can be used to perform thematic explorations on collections of texts in multiple languages. However, these approaches require theme-aligned training data to create a language-independent space. This constraint limits the amount of scenarios that this technique can offer solutions to train and makes it difficult to scale up to situations where a huge collection of multi-lingual documents are required during the training phase. This paper presents an unsupervised document similarity algorithm that does not require parallel or comparable corpora, or any other type of translation resource. The algorithm annotates topics automatically created from documents in a single language with cross-lingual labels and describes documents by hierarchies of multi-lingual concepts from independently-trained models. Experiments performed on the English, Spanish and French editions of JCR-Acquis corpora reveal promising results on classifying and sorting documents by similar content., Comment: Accepted at the 10th International Conference on Knowledge Capture (K-CAP 2019)

Multilingual BERT (mBERT) has shown reasonable capability for zero-shot cross-lingual transfer when fine-tuned on downstream tasks. Since mBERT is not pre-trained with explicit cross-lingual supervision, transfer performance can further be improved by aligning mBERT with cross-lingual signal. Prior work proposes several approaches to align contextualised embeddings. In this paper we analyse how different forms of cross-lingual supervision and various alignment methods influence the transfer capability of mBERT in zero-shot setting. Specifically, we compare parallel corpora vs. dictionary-based supervision and rotational vs. fine-tuning based alignment methods. We evaluate the performance of different alignment methodologies across eight languages on two tasks: Name Entity Recognition and Semantic Slot Filling. In addition, we propose a novel normalisation method which consistently improves the performance of rotation-based alignment including a notable 3% F1 improvement for distant and typologically dissimilar languages. Importantly we identify the biases of the alignment methods to the type of task and proximity to the transfer language. We also find that supervision from parallel corpus is generally superior to dictionary alignments., Comment: Accepted as a long paper in Findings of EMNLP 2020

We prove that coronizations with respect to arbitrary d-regular sets (not necessarily graphs) imply big pieces squared of these (approximating) sets. This is known (and due to David and Semmes in the case of sufficiently large co-dimension, and to Azzam and Schul in general) in the (classical) setting of Euclidean spaces with Hausdorff measure of integer dimension, where the approximating sets are Lipschitz graphs. Our result is a far reaching generalization of these results and we prove that coronizations imply big pieces squared is a generic property. In particular, our result applies, when suitably interpreted, in metric spaces having a fixed positive (perhaps non-integer) dimension, equipped with a Borel regular measure and with arbitrary approximating sets. As a novel application we highlight how to utilize this general setting in the context of parabolic uniform rectifiability., Comment: Observation 4.19 added

This is the first part of a series of two papers where we study perturbations of divergence form second order elliptic operators $-\mathop{\operatorname{div}} A \nabla$ by first and zero order terms, whose coefficients lie in critical spaces, via the method of layer potentials. In particular, we show that the $L^2$ well-posedness of the Dirichlet, Neumann and Regularity problems for complex Hermitian, block form, or constant-coefficient divergence form elliptic operators in the upper half-space are all stable under such perturbations. For instance, this allows us to claim the first results in the setting of an unbounded domain concerning the solvability of boundary value problems for the magnetic Schr\"odinger operator $-(\nabla-i{\bf a})^2+V$ when the magnetic potential ${\bf a}$ and the electric potential $V$ are accordingly small in the norm of a scale-invariant Lebesgue space. In the present paper, we establish $L^2$ control of the square function via a vector-valued $Tb$ theorem and abstract layer potentials, and use these square function bounds to obtain uniform slice bounds for solutions. The existence and uniqueness of solutions, as well as bounds for the non-tangential maximal operator, are considered in the upcoming paper., Comment: 71 pages, corrected some typographical errors

Cross-lingual annotations of legislative texts enable us to explore major themes covered in multilingual legal data and are a key facilitator of semantic similarity when searching for similar documents. Multilingual probabilistic topic models have recently emerged as a group of semi-supervised machine learning models that can be used to perform thematic explorations on collections of texts in multiple languages. However, these approaches require theme-aligned training data to create a language-independent space, which limits the amount of scenarios where this technique can be used. In this work, we provide an unsupervised document similarity algorithm based on hierarchies of multi-lingual concepts to describe topics across languages. The algorithm does not require parallel or comparable corpora, or any other type of translation resource. Experiments performed on the English, Spanish, French and Portuguese editions of JCR-Acquis corpora reveal promising results on classifying and sorting documents by similar content., Comment: IberLegal Workshop co-located with Jurix 2019