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Fast and sensitive detector arrays enable image scanning microscopy (ISM), overcoming the trade-off between spatial resolution and signal-to-noise ratio (SNR) typical of confocal microscopy. However, current ISM approaches cannot provide optical sectioning and fail with thick samples, unless the size of the detector is limited. Thus, another trade-off between optical sectioning and SNR persists. Here, we propose a method without drawbacks that combines uncompromised super-resolution, high SNR, and optical sectioning. Furthermore, our approach enables super-sampling of images, relaxing Nyquist's criterion by a factor of two. Based on the observation that imaging with a detector array inherently embeds axial information about the sample, we designed a straightforward reconstruction algorithm that inverts the physical model of ISM. We present the comprehensive theoretical framework and validate our method with synthetic and experimental images of biological samples captured using a custom setup equipped with a single-photon avalanche diode (SPAD) array detector. We demonstrate the feasibility of our approach exciting fluorescence emission both in the linear and non-linear regime. Moreover, we generalize the algorithm for fluorescence lifetime imaging, fully exploiting the single-photon timing ability of the SPAD array detector. Our method outperforms conventional approaches to ISM and can be extended to any LSM technique., Comment: 71 pages, 32 figures

Smart contract platforms based on the UTXO model face an efficiency bottleneck, in that any transaction sent to a contract must specify the entire updated contract state. This requirement becomes particularly burdensome when the contract state contains dynamic data structures, as needed in many use cases to track interactions between users and the contract. The problem is twofold: on the one hand, a large state in transactions implies a large transaction fee; on the other hand, a large centralized state is detrimental to the parallelization of transactions -- a feature that is often cited as a key advantage of UTXO-based blockchains over account-based ones. We propose a technique to efficiently execute smart contracts on an extended UTXO blockchain, which allows the contract state to be distributed across multiple UTXOs. In this way, transactions only need to specify the part of the state they need to access, reducing their size (and fees). We show how to exploit our model to parallelize the validation of transactions on multi-core CPUs. We implement our technique and provide an empirical validation of its effectiveness.

Intelligent Tutoring Systems (ITS) enhance personalized learning by predicting student answers to provide immediate and customized instruction. However, recent research has primarily focused on the correctness of the answer rather than the student's performance on specific answer choices, limiting insights into students' thought processes and potential misconceptions. To address this gap, we present MCQStudentBert, an answer forecasting model that leverages the capabilities of Large Language Models (LLMs) to integrate contextual understanding of students' answering history along with the text of the questions and answers. By predicting the specific answer choices students are likely to make, practitioners can easily extend the model to new answer choices or remove answer choices for the same multiple-choice question (MCQ) without retraining the model. In particular, we compare MLP, LSTM, BERT, and Mistral 7B architectures to generate embeddings from students' past interactions, which are then incorporated into a finetuned BERT's answer-forecasting mechanism. We apply our pipeline to a dataset of language learning MCQ, gathered from an ITS with over 10,000 students to explore the predictive accuracy of MCQStudentBert, which incorporates student interaction patterns, in comparison to correct answer prediction and traditional mastery-learning feature-based approaches. This work opens the door to more personalized content, modularization, and granular support., Comment: Accepted as a poster paper at EDM 2024: 17th International Conference on Educational Data Mining in Atlanta, USA

Digital twins require computationally-efficient reduced-order models (ROMs) that can accurately describe complex dynamics of physical assets. However, constructing ROMs from noisy high-dimensional data is challenging. In this work, we propose a data-driven, non-intrusive method that utilizes stochastic variational deep kernel learning (SVDKL) to discover low-dimensional latent spaces from data and a recurrent version of SVDKL for representing and predicting the evolution of latent dynamics. The proposed method is demonstrated with two challenging examples -- a double pendulum and a reaction-diffusion system. Results show that our framework is capable of (i) denoising and reconstructing measurements, (ii) learning compact representations of system states, (iii) predicting system evolution in low-dimensional latent spaces, and (iv) quantifying modeling uncertainties.

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction of a deep neural network model that approximates the solution manifold through a continuously adaptive local basis. In contrast to global methods, such as Principal Orthogonal Decomposition (POD), the adaptivity allows the DOD to overcome the Kolmogorov barrier, making the approach applicable to a wide spectrum of parametric problems. Furthermore, due to its hybrid linear-nonlinear nature, the DOD can accommodate both intrusive and nonintrusive techniques, providing highly interpretable latent representations and tighter control on error propagation. For this reason, the proposed approach stands out as a valuable alternative to other nonlinear techniques, such as deep autoencoders. The methodology is discussed both theoretically and practically, evaluating its performances on problems featuring nonlinear PDEs, singularities, and parametrized geometries.

Confocal laser scanning microscopy (CLSM) stands out as one of the most widely used microscopy techniques, thanks to its three-dimensional imaging capability and its sub-diffraction spatial resolution, achieved through the closure of a pinhole in front of a single-element detector. However, the pinhole also rejects useful photons and beating the diffraction limit comes at the price of irremediably compromising the signal-to-noise ratio (SNR) of the data. Image scanning microscopy (ISM) emerged as the natural evolution of CLSM, exploiting a small array detector in place of the pinhole and the single-element detector. Each sensitive element is small enough to achieve sub-diffraction resolution through the confocal effect, but the size of the whole detector is large enough to guarantee excellent collection efficiency and SNR. However, the raw data produced by an ISM setup consists of a 4D dataset which can be seen as a set of confocal-like images. Thus, fusing the dataset into a single super-resolved image requires a dedicated reconstruction algorithm. Conventional methods are multi-image deconvolution, which requires prior knowledge of the system point spread functions (PSF), or adaptive pixel reassignment (APR), which is effective only on a limited range of experimental conditions. In this work, we describe and validate a novel concept for ISM image reconstruction based on autocorrelation inversion. We leverage unique properties of the autocorrelation to discard low-frequency components and maximize the resolution of the reconstructed image, without any assumption on the image or any knowledge of the PSF. Our results push the quality of the ISM reconstruction beyond the level provided by APR and open new perspectives for multi-dimensional image processing., Comment: 21 pages, 5 figures

Smart contracts have played a pivotal role in the evolution of blockchains and Decentralized Applications (DApps). As DApps continue to gain widespread adoption, multiple smart contract languages have been and are being made available to developers, each with its distinctive features, strengths, and weaknesses. In this paper, we examine the smart contract languages used in major blockchain platforms, with the goal of providing a comprehensive assessment of their main properties. Our analysis targets the programming languages rather than the underlying architecture: as a result, while we do consider the interplay between language design and blockchain model, our main focus remains on language-specific features such as usability, programming style, safety and security. To conduct our assessment, we propose an original benchmark which encompasses a wide, yet manageable, spectrum of key use cases that cut across all the smart contract languages under examination.

Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing and applying these tools, their use has been predominantly limited to structured datasets such as time series or images. Here, we introduce the k-nearest neighbor permutation entropy, an innovative extension of the permutation entropy tailored for unstructured data, irrespective of their spatial or temporal configuration and dimensionality. Our approach builds upon nearest neighbor graphs to establish neighborhood relations and uses random walks to extract ordinal patterns and their distribution, thereby defining the k-nearest neighbor permutation entropy. This tool not only adeptly identifies variations in patterns of unstructured data, but also does so with a precision that significantly surpasses conventional measures such as spatial autocorrelation. Additionally, it provides a natural approach for incorporating amplitude information and time gaps when analyzing time series or images, thus significantly enhancing its noise resilience and predictive capabilities compared to the usual permutation entropy. Our research substantially expands the applicability of ordinal methods to more general data types, opening promising research avenues for extending the permutation entropy toolkit for unstructured data., Comment: 14 two-column pages, 6 figures

We consider the execution of smart contracts on Bitcoin. There, every contract step corresponds to appending to the blockchain a new transaction that spends the output representing the old contract state, creating a new one for the updated state. This standard procedure requires the contract participants to pay transaction fees for every execution step. In this paper, we introduce a protocol that moves most of the execution of a Bitcoin contract off-chain. When all participants follow this protocol, they are able to save on transaction fees. By contrast, in the presence of adversaries, any honest participant is still able to enforce the correct execution of the contract, according to its original semantics.

We apply reduced-order modeling (ROM) techniques to single-phase flow in faulted porous media, accounting for changing rock properties and fault geometry variations using a radial basis function mesh deformation method. This approach benefits from a mixed-dimensional framework that effectively manages the resulting non-conforming mesh. To streamline complex and repetitive calculations such as sensitivity analysis and solution of inverse problems, we utilize the Deep Learning Reduced Order Model (DL-ROM). This non-intrusive neural network-based technique is evaluated against the traditional Proper Orthogonal Decomposition (POD) method across various scenarios, demonstrating DL-ROM's capacity to expedite complex analyses with promising accuracy and efficiency.

Forward uncertainty quantification (UQ) for partial differential equations is a many-query task that requires a significant number of model evaluations. The objective of this work is to mitigate the computational cost of UQ for a 3D-1D multiscale computational model of microcirculation. To this purpose, we present a deep learning enhanced multi-fidelity Monte Carlo (DL-MFMC) method that integrates the information of a multiscale full-order model (FOM) with that coming from a deep learning enhanced non-intrusive projection-based reduced order model (ROM). The latter is constructed by leveraging on proper orthogonal decomposition (POD) and mesh-informed neural networks (previously developed by the authors and co-workers), integrating diverse architectures that approximate POD coefficients while introducing fine-scale corrections for the microstructures. The DL-MFMC approach provides a robust estimator of specific quantities of interest and their associated uncertainties, with optimal management of computational resources. In particular, the computational budget is efficiently divided between training and sampling, ensuring a reliable estimation process suitably exploiting the ROM speed-up. Here, we apply the DL-MFMC technique to accelerate the estimation of biophysical quantities regarding oxygen transfer and radiotherapy outcomes. Compared to classical Monte Carlo methods, the proposed approach shows remarkable speed-ups and a substantial reduction of the overall computational cost.

We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which the constraint is given by mass conservation. Our approach employs classical neural network architectures and supervised learning, but it is constructed in such a way that the resulting Reduced Order Model (ROM) is guaranteed to satisfy the linear constraints exactly. The procedure is based on a splitting of the PDE solution into a particular solution satisfying the constraint and a homogenous solution. The homogeneous solution is approximated by mapping a suitable potential function, generated by a neural network model, onto the kernel of the constraint operator; for the particular solution, instead, we propose an efficient spanning tree algorithm. Starting from this paradigm, we present three approaches that follow this methodology, obtained by exploring different choices of the potential spaces: from empirical ones, derived via Proper Orthogonal Decomposition (POD), to more abstract ones based on differential complexes. All proposed approaches combine computational efficiency with rigorous mathematical interpretation, thus guaranteeing the explainability of the model outputs. To demonstrate the efficacy of the proposed strategies and to emphasize their advantages over vanilla black-box approaches, we present a series of numerical experiments on fluid flows in porous media, ranging from mixed-dimensional problems to nonlinear systems. This research lays the foundation for further exploration and development in the realm of model order reduction, potentially unlocking new capabilities and solutions in computational geosciences and beyond.

Human-robot interaction (HRI) has become a crucial enabler in houses and industries for facilitating operational flexibility. When it comes to mobile collaborative robots, this flexibility can be further increased due to the autonomous mobility and navigation capacity of the robotic agents, expanding their workspace and consequently, the personalizable assistance they can provide to the human operators. This however requires that the robot is capable of detecting and identifying the human counterpart in all stages of the collaborative task, and in particular while following a human in crowded workplaces. To respond to this need, we developed a unified perception and navigation framework, which enables the robot to identify and follow a target person using a combination of visual Re-Identification (Re-ID), hand gestures detection, and collision-free navigation. The Re-ID module can autonomously learn the features of a target person and use the acquired knowledge to visually re-identify the target. The navigation stack is used to follow the target avoiding obstacles and other individuals in the environment. Experiments are conducted with few subjects in a laboratory setting where some unknown dynamic obstacles are introduced., Comment: published in "2023 IEEE International Conference on Advanced Robotics and Its Social Impacts (ARSO)"

In today's Human-Robot Interaction (HRI) scenarios, a prevailing tendency exists to assume that the robot shall cooperate with the closest individual or that the scene involves merely a singular human actor. However, in realistic scenarios, such as shop floor operations, such an assumption may not hold and personalized target recognition by the robot in crowded environments is required. To fulfil this requirement, in this work, we propose a person re-identification module based on continual visual adaptation techniques that ensure the robot's seamless cooperation with the appropriate individual even subject to varying visual appearances or partial or complete occlusions. We test the framework singularly using recorded videos in a laboratory environment and an HRI scenario, i.e., a person-following task by a mobile robot. The targets are asked to change their appearance during tracking and to disappear from the camera field of view to test the challenging cases of occlusion and outfit variations. We compare our framework with one of the state-of-the-art Multi-Object Tracking (MOT) methods and the results show that the CARPE-ID can accurately track each selected target throughout the experiments in all the cases (except two limit cases). At the same time, the s-o-t-a MOT has a mean of 4 tracking errors for each video., Comment: Accepted to the International Conference on Robotics and Automation (ICRA) 2024

Deep Learning is having a remarkable impact on the design of Reduced Order Models (ROMs) for Partial Differential Equations (PDEs), where it is exploited as a powerful tool for tackling complex problems for which classical methods might fail. In this respect, deep autoencoders play a fundamental role, as they provide an extremely flexible tool for reducing the dimensionality of a given problem by leveraging on the nonlinear capabilities of neural networks. Indeed, starting from this paradigm, several successful approaches have already been developed, which are here referred to as Deep Learning-based ROMs (DL-ROMs). Nevertheless, when it comes to stochastic problems parameterized by random fields, the current understanding of DL-ROMs is mostly based on empirical evidence: in fact, their theoretical analysis is currently limited to the case of PDEs depending on a finite number of (deterministic) parameters. The purpose of this work is to extend the existing literature by providing some theoretical insights about the use of DL-ROMs in the presence of stochasticity generated by random fields. In particular, we derive explicit error bounds that can guide domain practitioners when choosing the latent dimension of deep autoencoders. We evaluate the practical usefulness of our theory by means of numerical experiments, showing how our analysis can significantly impact the performance of DL-ROMs.

Complex DeFi services are usually constructed by composing a variety of simpler smart contracts. The permissionless nature of the blockchains where these smart contracts are executed makes DeFi services exposed to security risks, since adversaries can target any of the underlying contracts to economically damage the compound service. We introduce a new notion of secure composability of smart contracts, which ensures that adversaries cannot economically harm the compound contract by interfering with its dependencies.

Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales in their data. However, these numerical solutions are often computationally expensive due to the need to capture fine details at small scales. As a result, simulating such phenomena becomes unaffordable for many-query applications, such as parametrized systems with multiple scale-dependent features. Traditional projection-based reduced order models (ROMs) fail to resolve these issues, even for second-order elliptic PDEs commonly found in engineering applications. To address this, we propose an alternative nonintrusive strategy to build a ROM, that combines classical proper orthogonal decomposition (POD) with a suitable neural network (NN) model to account for the small scales. Specifically, we employ sparse mesh-informed neural networks (MINNs), which handle both spatial dependencies in the solutions and model parameters simultaneously. We evaluate the performance of this strategy on benchmark problems and then apply it to approximate a real-life problem involving the impact of microcirculation in transport phenomena through the tissue microenvironment.

In the context of micro-circulation, the coexistence of two distinct length scales - the vascular radius and the tissue/organ scale - with a substantial difference in magnitude, poses significant challenges. To handle slender inclusions and simplify the geometry involved, a technique called topological dimensionality reduction is employed, which suppresses manifold dimensions associated with the smaller characteristic length. However, the resulting discretized system's algebraic structure presents a challenge in constructing efficient solution algorithms. This chapter addresses this challenge by developing a robust preconditioner for the 3d-1d problem using the operator preconditioning technique. Robustness of the preconditioner is demonstrated with respect to problem parameters, except for the vascular radius. The vascular radius, as demonstrated, plays a fundamental role in mathematical well-posedness of the problem and the preconditioner's effectiveness.

Ice streams are major contributors to ice sheet mass loss and sea level rise. Effects of their dynamic behaviour are imprinted into seismic properties, such as wave speeds and anisotropy. Here we present results from the first Distributed Acoustic Sensing (DAS) experiment in a deep ice-core borehole in the onset region of the Northeast Greenland Ice Stream. A series of active surface sources produced clear recordings of the P and S wavefield, including internal reflections, along a 1500 m long fibre-optic cable that was lowered into the borehole. The combination of nonlinear traveltime tomography with a firn model constrained by multi-mode surface wave data, allows us to invert for P and S wave speeds with depth-dependent uncertainties on the order of only 10 m$/$s, and vertical resolution of 20--70 m. The wave speed model in conjunction with the regularly spaced DAS data enable a straightforward separation of internal upward reflections followed by a reverse-time migration that provides a detailed reflectivity image of the ice. While the differences between P and S wave speeds hint at anisotropy related to crystal orientation fabric, the reflectivity image seems to carry a pronounced climatic imprint caused by rapid variations in grain size. Currently, resolution is not limited by the DAS channel spacing. Instead, the maximum frequency of body waves below $\sim$200 Hz, low signal-to-noise ratio caused by poor coupling, and systematic errors produced by the ray approximation, appear to be the leading-order issues. Among these, only the latter has a simple existing solution in the form of full-waveform inversion. Improving signal bandwidth and quality, however, will likely require a significantly larger effort in terms of both sensing equipment and logistics., Comment: 15 pages, 14 figures

Geometric navigation is nowadays a well-established field of robotics and the research focus is shifting towards higher-level scene understanding, such as Semantic Mapping. When a robot needs to interact with its environment, it must be able to comprehend the contextual information of its surroundings. This work focuses on classifying and localising objects within a map, which is under construction (SLAM) or already built. To further explore this direction, we propose a framework that can autonomously detect and localize predefined objects in a known environment using a multi-modal sensor fusion approach (combining RGB and depth data from an RGB-D camera and a lidar). The framework consists of three key elements: understanding the environment through RGB data, estimating depth through multi-modal sensor fusion, and managing artifacts (i.e., filtering and stabilizing measurements). The experiments show that the proposed framework can accurately detect 98% of the objects in the real sample environment, without post-processing, while 85% and 80% of the objects were mapped using the single RGBD camera or RGB + lidar setup respectively. The comparison with single-sensor (camera or lidar) experiments is performed to show that sensor fusion allows the robot to accurately detect near and far obstacles, which would have been noisy or imprecise in a purely visual or laser-based approach., Comment: Accepted to the 11th European Conference on Mobile Robots (ECMR) 2023

Most blockchain platforms from Ethereum onwards render smart contracts as stateful reactive objects that update their state and transfer crypto-assets in response to transactions. A drawback of this design is that when users submit a transaction, they cannot predict in which state it will be executed. This exposes them to transaction-ordering attacks, a widespread class of attacks where adversaries with the power to construct blocks of transactions can extract value from smart contracts (the so-called MEV attacks). The UTXO model is an alternative blockchain design that thwarts these attacks by requiring new transactions to spend past ones: since transactions have unique identifiers, reordering attacks are ineffective. Currently, the blockchains following the UTXO model either provide contracts with limited expressiveness (Bitcoin), or require complex run-time environments (Cardano). We present ILLUM , an Intermediate-Level Language for the UTXO Model. ILLUM can express real-world smart contracts, e.g. those found in Decentralized Finance. We define a compiler from ILLUM to a bare-bone UTXO blockchain with loop-free scripts. Our compilation target only requires minimal extensions to Bitcoin Script: in particular, we exploit covenants, a mechanism for preserving scripts along chains of transactions. We prove the security of our compiler: namely, any attack targeting the compiled contract is also observable at the ILLUM level. Hence, the compiler does not introduce new vulnerabilities that were not already present in the source ILLUM contract. We evaluate the practicality of ILLUM as a compilation target for higher-level languages. To this purpose, we implement a compiler from a contract language inspired by Solidity to ILLUM, and we apply it to a benchmark or real-world smart contracts.

Many physical problems involving heterogeneous spatial scales, such as the flow through fractured porous media, the study of fiber-reinforced materials, or the modeling of the small circulation in living tissues -- just to mention a few examples -- can be described as coupled partial differential equations defined in domains of heterogeneous dimensions that are embedded into each other. This formulation is a consequence of geometric model reduction techniques that transform the original problems defined in complex three-dimensional domains into more tractable ones. The definition and the approximation of coupling operators suitable for this class of problems is still a challenge. We develop a general mathematical framework for the analysis and the approximation of partial differential equations coupled by non-matching constraints across different dimensions, focusing on their enforcement using Lagrange multipliers. In this context, we address in abstract and general terms the well-posedness, stability, and robustness of the problem with respect to the smallest characteristic length of the embedded domain. We also address the numerical approximation of the problem and we discuss the inf-sup stability of the proposed numerical scheme for some representative configuration of the embedded domain. The main message of this work is twofold: from the standpoint of the theory of mixed-dimensional problems, we provide general and abstract mathematical tools to formulate coupled problems across dimensions. From the practical standpoint of the numerical approximation, we show the interplay between the mesh characteristic size, the dimension of the Lagrange multiplier space, and the size of the inclusion in representative configurations interesting for applications. The latter analysis is complemented with illustrative numerical examples., Comment: 41 pages, 11 Figures

The use of the probabilistic approach to solve inverse problems is becoming more popular in the geophysical community, thanks to its ability to address nonlinear forward problems and to provide uncertainty quantification. However, such strategy is often tailored to specific applications and therefore there is a lack of a common platform for solving a range of different geophysical inverse problems and showing potential and pitfalls. We demonstrate a common framework to solve such inverse problems ranging from, e.g, earthquake source location to potential field data inversion and seismic tomography. Within this approach, we can provide probabilities related to certain properties or structures of the subsurface. Thanks to its ability to address high-dimensional problems, the Hamiltonian Monte Carlo (HMC) algorithm has emerged as the state-of-the-art tool for solving geophysical inverse problems within the probabilistic framework. HMC requires the computation of gradients, which can be obtained by adjoint methods, making the solution of tomographic problems ultimately feasible. These results can be obtained with "HMCLab", a tool for solving a range of different geophysical inverse problems using sampling methods, focusing in particular on the HMC algorithm. HMCLab consists of a set of samplers and a set of geophysical forward problems. For each problem its misfit function and gradient computation are provided and, in addition, a set of prior models can be combined to inject additional information into the inverse problem. This allows users to experiment with probabilistic inverse problems and also address real-world studies. We show how to solve a selected set of problems within this framework using variants of the HMC algorithm and analyze the results. HMCLab is provided as an open source package written both in Python and Julia, welcoming contributions from the community., Comment: 21 pages, 4 figures

Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity when dealing with input-output maps involving the solution of nonlinear differential problems, because of the need to query expensive numerical solvers repeatedly. Projection-based reduced order models (ROMs), such as the Galerkin-reduced basis (RB) method, have been extensively developed in the last decades to overcome the computational complexity of high fidelity full order models (FOMs), providing remarkable speedups when addressing UQ tasks related with parameterized differential problems. Nonetheless, constructing a projection-based ROM that can be efficiently queried usually requires extensive modifications to the original code, a task which is non-trivial for nonlinear problems, or even not possible at all when proprietary software is used. Non-intrusive ROMs - which rely on the FOM as a black box - have been recently developed to overcome this issue. In this work, we consider ROMs exploiting proper orthogonal decomposition to construct a reduced basis from a set of FOM snapshots, and Gaussian process regression (GPR) to approximate the RB projection coefficients. Two different approaches, namely a global GPR and a tensor-decomposition-based GPR, are explored on a set of 3D time-dependent solid mechanics examples. Finally, the non-intrusive ROM is exploited to perform global sensitivity analysis (relying on both screening and variance-based methods) and parameter estimation (through Markov chain Monte Carlo methods), showing remarkable computational speedups and very good accuracy compared to high-fidelity FOMs.

Air transportation is a complex system characterised by a plethora of interactions at multiple temporal and spatial scales; as a consequence, even simple dynamics like sequencing aircraft for landing can lead to the appearance of emergent behaviours, which are both difficult to control and detrimental to operational efficiency. We propose a model, based on a modulated Markov jitter, to represent ordinal pattern properties of real landing operations in European airports. The parameters of the model are tuned by minimising the distance between the probability distributions of ordinal patterns generated by the real and synthetic sequences, as estimated by the Permutation Jensen-Shannon Distance. We show that the correlation between consecutive hours in the landing flow changes between airports, and that it can be interpreted as a metric of efficiency. We further compare the dynamics pre and post COVID-19, showing how this has changed beyond what can be attributed to a simple reduction of traffic. We finally draw some operational conclusions, and discuss the applicability of these findings in a real operational environment., Comment: 12 pages, 11 figures, 2 tables

Extractable Value refers to a wide class of economic attacks to public blockchains, where adversaries with the power to reorder, drop or insert transactions in a block can "extract" value from smart contracts. Empirical research has shown that mainstream protocols, like e.g. decentralized exchanges, are massively targeted by these attacks, with detrimental effects on their users and on the blockchain network. Despite the growing impact of these attacks in the real world, theoretical foundations are still missing. We propose a formal theory of Extractable Value, based on a general, abstract model of blockchains and smart contracts. Our theory is the basis for proofs of security against Extractable Value attacks.

Confocal laser-scanning microscopy (CLSM) is one of the most popular optical architectures for fluorescence imaging. In CLSM, a focused laser beam excites the fluorescence emission from a specific specimen position. Some actuators scan the probed region across the sample and a photodetector collects a single intensity value for each scan point, building a two-dimensional image pixel-by-pixel. Recently, new fast single-photon array detectors have allowed the recording of a full bi-dimensional image of the probed region for each scan point, transforming CLSM into image scanning microscopy (ISM). This latter offers significant improvements over traditional imaging but requires an optimal processing tool to extract a super-resolved image from the four-dimensional dataset. Here we describe the image formation process in ISM from a statistical point of view, and we use the Bayesian framework to formulate a multi-image deconvolution problem. Notably, the single-photon detector suffers exclusively from the photon shot noise, enabling the development of an effective likelihood model. We derive an iterative likelihood maximization algorithm and test it on experimental and simulated data. Furthermore, we demonstrate that the ISM dataset is redundant, enabling the possibility of obtaining reconstruction sampled at twice the scanning step. Our results prove that in ISM, under appropriate conditions, the Nyquist-Shannon sampling criterium is effectively relaxed. This finding can be exploited to speed up the acquisition process by a factor of four, further improving the versatility of ISM systems.

Words are fundamental linguistic units that connect thoughts and things through meaning. However, words do not appear independently in a text sequence. The existence of syntactic rules induces correlations among neighboring words. Using an ordinal pattern approach, we present an analysis of lexical statistical connections for 11 major languages. We find that the diverse manners that languages utilize to express word relations give rise to unique pattern structural distributions. Furthermore, fluctuations of these pattern distributions for a given language can allow us to determine both the historical period when the text was written and its author. Taken together, our results emphasize the relevance of ordinal time series analysis in linguistic typology, historical linguistics and stylometry., Comment: 9 pages, 12 figures, 2 tables; v2: the section on universality has been removed because previous results were affected by spurious correlations. Published version

Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy and efficiency, the approaches available in the literature still lack a rigorous justification on their mathematical foundations. Motivated by this fact, in this paper we derive rigorous error bounds for the approximation of nonlinear operators by means of CNN models. More precisely, we address the case in which an operator maps a finite dimensional input $\boldsymbol{\mu}\in\mathbb{R}^{p}$ onto a functional output $u_{\boldsymbol{\mu}}:[0,1]^{d}\to\mathbb{R}$, and a neural network model is used to approximate a discretized version of the input-to-output map. The resulting error estimates provide a clear interpretation of the hyperparameters defining the neural network architecture. All the proofs are constructive, and they ultimately reveal a deep connection between CNNs and the Fourier transform. Finally, we complement the derived error bounds by numerical experiments that illustrate their application.