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The definition of an action functional for the Jacobi sigma models, known for Jacobi brackets of functions, is generalized to \emph{Jacobi bundles}, i.e., Lie brackets on sections of (possibly nontrivial) line bundles, with the particular case of contact manifolds. Different approaches are proposed, but all of them share a common feature: the presence of a \emph{homogeneity structure} appearing as a principal action of the Lie group $\mathbb{R}^{\times}=\mathrm{GL}(1;\mathbb{R})$. Consequently, solutions of the equations of motions are morphisms of certain \emph{Jacobi algebroids}, i.e., principal $\mathbb{R}^{\times}$-bundles equipped additionally with a compatible Lie algebroid structure. Despite the different approaches we propose, there is a one-to-one correspondence between the space of solutions of the different models. The definition can be immediately extended to \emph{almost Poisson} and \emph{almost Jacobi brackets}, i.e., to brackets that do not satisfy the Jacobi identity. Our sigma models are geometric and fully covariant., Comment: 35 pages

We define the gauge potentials of Poisson electrodynamics as sections of a symplectic realization of the spacetime manifold and infinitesimal gauge transformations as a representation of the associated Lie algebroid acting on the symplectic realization. Finite gauge transformations are obtained by integrating the sections of the Lie algebroid to bisections of a symplectic groupoid, which form a one-parameter group of transformations, whose action on the fields of the theory is realized in terms of an action groupoid. A covariant electromagnetic two-form is obtained, together with a dual two-form, invariant under gauge transformations. The duality appearing in the picture originates from the existence of a pair of orthogonal foliations of the symplectic realization, which produce dual quotient manifolds, one related with space-time, the other with momenta., Comment: 23 pages. No figures. Revised version: contains a comparison with ref. [9]. References added

This study explores the use of Federated Learning (FL) for stenosis detection in coronary angiography images (CA). Two heterogeneous datasets from two institutions were considered: Dataset 1 includes 1219 images from 200 patients, which we acquired at the Ospedale Riuniti of Ancona (Italy); Dataset 2 includes 7492 sequential images from 90 patients from a previous study available in the literature. Stenosis detection was performed by using a Faster R-CNN model. In our FL framework, only the weights of the model backbone were shared among the two client institutions, using Federated Averaging (FedAvg) for weight aggregation. We assessed the performance of stenosis detection using Precision (P rec), Recall (Rec), and F1 score (F1). Our results showed that the FL framework does not substantially affects clients 2 performance, which already achieved good performance with local training; for client 1, instead, FL framework increases the performance with respect to local model of +3.76%, +17.21% and +10.80%, respectively, reaching P rec = 73.56, Rec = 67.01 and F1 = 70.13. With such results, we showed that FL may enable multicentric studies relevant to automatic stenosis detection in CA by addressing data heterogeneity from various institutions, while preserving patient privacy.

Software Heritage is the largest public archive of software source code and associated development history, as captured by modern version control systems. As of July 2023, it has archived more than 16 billion unique source code files coming from more than 250 million collaborative development projects. In this chapter, we describe the Software Heritage ecosystem, focusing on research and open science use cases.On the one hand, Software Heritage supports empirical research on software by materializing in a single Merkle direct acyclic graph the development history of public code. This giant graph of source code artifacts (files, directories, and commits) can be used-and has been used-to study repository forks, open source contributors, vulnerability propagation, software provenance tracking, source code indexing, and more.On the other hand, Software Heritage ensures availability and guarantees integrity of the source code of software artifacts used in any field that relies on software to conduct experiments, contributing to making research reproducible. The source code used in scientific experiments can be archived-e.g., via integration with open-access repositories-referenced using persistent identifiers that allow downstream integrity checks and linked to/from other scholarly digital artifacts.

An extension of Cencov's categorical description of classical inference theory to the domain of quantum systems is presented. It provides a novel categorical foundation to the theory of quantum information that embraces both classical and quantum information theory in a natural way, while also allowing to formalise the notion of quantum environment. A first application of these ideas is provided by extending the notion of statistical manifold to incorporate categories, and investigating a possible, uniparametric Cramer-Rao inequality in this setting., Comment: 20 pages, comments are welcome!

Declarative Distributed Systems (DDSs) are distributed systems grounded in logic programming. Although DDS model-checking is undecidable in general, we detect decidable cases by tweaking the data-source bounds, the message expressiveness, and the channel type., Comment: Published in the online proceedings of the ESSLLI 2021 Student Session

We discuss how to exploit the recent formulation of classical and quantum information geometry in terms of normal states on $W^{*}$-algebras to formulate a problem that unifies Cencov's theorem and Petz's theorem., Comment: 9 pages - Comments are welcome!

In this paper some reflections on the concept of transition are presented: groupoids are introduced as models for the construction of a ``generalized logic'' whose basic statements involve pairs of propositions which can be conditioned. In this sense, we could distinguish between classical probability theory where propositions can be conditioned if they have a non-zero intersection, from cases where ``non-local'' conditioning are allowed. The algebraic and geometrical properties of groupoids can be exploited to construct models of such non-local description., Comment: 9 pages - Submitted to conference GSI 23

It is well known that certain features of a quantum theory cannot be described in the standard picture on a Hilbert space. In particular, this happens when we try to formally frame a quantum field theory, or a thermodynamic system with finite density. This forces us to introduce different types of algebras, more general than the ones we usually encounter in a standard course of quantum mechanics. We show how these algebras naturally arise in the Schwinger description of the quantum mechanics of an infinite spin chain. In particular, we use the machinery of Dirac-Feynman-Schwinger (DFS) states developed in recent works to introduce a dynamics based on the modular theory by Tomita-Takesaki, and consequently we apply this approach to describe the Ising model., Comment: 42 pages, 1 figure

We go on with the program started in the companion paper [CDI+] of defining a Poisson bracket structure on the space of solutions of the equations of motion of first order Hamiltonian field theories. The case of non-Abelian gauge theories is addressed by using a suitable version of the coisotropic embedding theorem.

We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamiltonian mechanical point systems (as a (0 + 1)-dimensional field) and more general field theories without gauge symmetries are addressed by showing the existence of a symplectic (and, thus, a Poisson) structure on the space of solutions. Also the easiest case of gauge theory, namely free electrodynamics, is considered: within this problem, a pre-symplectic tensor on the space of solutions is introduced, and a Poisson structure is induced in terms of a flat connection on a suitable bundle associated to the theory.

Given a real, finite-dimensional, smooth parallelizable Riemannian manifold $(\mathcal{N},G)$ endowed with a teleparallel connection $\nabla$ determined by a choice of a global basis of vector fields on $\mathcal{N}$, we show that the $G$-dual connection $\nabla^{*}$ of $\nabla$ in the sense of Information Geometry must be the teleparallel connection determined by the basis of $G$-gradient vector fields associated with a basis of differential one-forms which is (almost) dual to the basis of vector fields determining $\nabla$. We call any such pair $(\nabla,\nabla^{*})$ a $G$-dual teleparallel pair. Then, after defining a covariant $(0,3)$ tensor $T$ uniquely determined by $(\mathcal{N},G,\nabla,\nabla^{*})$, we show that $T$ being symmetric in the first two entries is equivalent to $\nabla$ being torsion-free, that $T$ being symmetric in the first and third entry is equivalent to $\nabla^{*}$ being torsion free, and that $T$ being symmetric in the second and third entries is equivalent to the basis vectors determining $\nabla$ ($\nabla^{*}$) being parallel-transported by $\nabla^{*}$ ($\nabla$). Therefore, $G$-dual teleparallel pairs provide a generalization of the notion of Statistical Manifolds usually employed in Information Geometry, and we present explicit examples of $G$-dual teleparallel pairs arising both in the context of both Classical and Quantum Information Geometry., Comment: version 2: minor revisions following reviews, and minor cosmetic changes. Comments are welcome!

Starting from the canonical symmetroid $\mathcal{S}(G)$ associated with a groupoid $G$, the issue of describing dynamical maps in the groupoidal approach to Quantum Mechanics is addressed. After inducing a Haar measure on the canonical symmetroid $\mathcal{S}(G)$, the associated von-Neumann groupoid algebra is constructed. It is shown that the left-regular representation allows to define linear maps on the groupoid-algebra of the groupoid $G$ and given subsets of functions are associated with completely positive maps. Some simple examples are also presented., Comment: 21 pages

In this paper the problem of tomographic reconstruction of states is investigated within the so-called Schwinger's picture of Quantum Mechanics in which a groupoid is associated with every quantum system. The attention is focused on spin tomography: In this context the groupoid of interest is the groupoid of pairs over a finite set. In a nutshell, this groupoid is made up of transitions between all possible pairs of outcomes belonging to a finite set. In addition, these transitions possess a partial composition rule, generalizing the notion of groups. The main goal of the paper consists in providing a reconstruction formula for states on the groupoid-algebra associated with the observables of the system. Using the group of bisections of this groupoid, which are special subsets in one-to-one correspondence with the outcomes, a frame is defined and it is used to prove the validity of the tomographic reconstruction. The special case of the set of outcomes being the set of integers modulo n, with n odd prime, is considered in detail. In this case the subgroup of discrete affine linear transformations, whose graphs are linear subspaces of the groupoid, provides a \textit{quorum} in close analogy with the continuos case., Comment: 32 pages

We review some geometrical aspects pertaining to the world of monotone quantum metrics in finite dimensions. Particular emphasis is given to an unfolded perspective for quantum states that is built out of the spectral theorem and is naturally suited to investigate the comparison with the classical case of probability distributions., Comment: 45 pages

Deep-learning (DL) algorithms are becoming the standard for processing ultrasound (US) fetal images. Despite a large number of survey papers already present in this field, most of them are focusing on a broader area of medical-image analysis or not covering all fetal US DL applications. This paper surveys the most recent work in the field, with a total of 145 research papers published after 2017. Each paper is analyzed and commented on from both the methodology and application perspective. We categorized the papers in (i) fetal standard-plane detection, (ii) anatomical-structure analysis, and (iii) biometry parameter estimation. For each category, main limitations and open issues are presented. Summary tables are included to facilitate the comparison among the different approaches. Publicly-available datasets and performance metrics commonly used to assess algorithm performance are summarized, too. This paper ends with a critical summary of the current state of the art on DL algorithms for fetal US image analysis and a discussion on current challenges that have to be tackled by researchers working in the field to translate the research methodology into the actual clinical practice.

Noticing that the space of the solutions of a first order Hamiltonian field theory has a pre-symplectic structure, we describe a class of conserved charges on it associated to the momentum map determined by any symmetry group of transformations. Gauge theories are dealt with by using a symplectic regularization based on an application of Gotay's coisotropic embedding theorem. The analysis of Electrodynamics and of the Klein-Gordon theory illustrates the main results of the theory as well as the emergence of the energy-momentum tensor algebra of conserved currents.

A novel derivation of Feynman's sum-over-histories construction of the quantum propagator using the groupoidal description of Schwinger picture of Quantum Mechanics is presented. It is shown that such construction corresponds to the GNS representation of a natural family of states called Dirac-Feynman-Schwinger (DFS) states. Such states are obtained from a q-Lagrangian function $\ell$ on the groupoid of configurations of the system. The groupoid of histories of the system is constructed and the q-Lagrangian $\ell$ allow to define a DFS state on the algebra of the groupoid. The particular instance of the groupoid of pairs of a Riemannian manifold serves to illustrate Feynman's original derivation of the propagator for a point particle described by a classical Lagrangian $L$., Comment: 16 pages

Using the recently developed groupoidal description of Schwinger's picture of Quantum Mechanics, a new approach to Dirac's fundamental question on the role of the Lagrangian in Quantum Mechanics is provided. It is shown that a function $\ell$ on the groupoid of configurations (or kinematical groupoid) of a quantum system determines a state on the von Neumann algebra of the histories of the system. This function, which we call {\itshape q-Lagrangian}, can be described in terms of a new function $\mathcal{L}$ on the Lie algebroid of the theory. When the kinematical groupoid is the pair groupoid of a smooth manifold $M$, the quadratic expansion of $\mathcal{L}$ will reproduce the standard Lagrangians on $TM$ used to describe the classical dynamics of particles., Comment: 12 pages

Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced.It is shown that, given a groupoid $G\rightrightarrows \Omega$ associated with a (quantum) system, there are two possible descriptions of its symmetries, one "microscopic", the other one "global".The microscopic point of view leads to the introduction of an additional layer over the grupoid $G$, giving rise to a suitable algebraic structure of 2-groupoid.On the other hand, taking advantage of the notion of group of bisections of a given groupoid, the global perspective allows to construct a group of symmetries out of a 2-groupoid.The latter notion allows to introduce an analog of the Wigner's theorem for quantum symmetries in the groupoid approach to Quantum Mechanics., Comment: 25 pages, 2 figures

Schr\"{o}dinger's famous Gedankenexperiment involving a cat is used as a motivation to discuss the evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently. It is shown that the notion of classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. In accordance with Raggio's theorem, the impossibility of evolving the product state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution which is internal to the composite system itself is proved in the groupoid formalism., Comment: 24 pages. A slightly different version this work will has appeared in Entropy. The main difference is that in the version published in Entropy no mention is made of Schr\"{o}dinger's cat Gedankenexperiment. Comments and suggestions are more than welcome!

Dependency solving is a hard (NP-complete) problem in all non-trivial component models due to either mutually incompatible versions of the same packages or explicitly declared package conflicts. As such, software upgrade planning needs to rely on highly specialized dependency solvers, lest falling into pitfalls such as incompleteness-a combination of package versions that satisfy dependency constraints does exist, but the package manager is unable to find it. In this paper we look back at proposals from dependency solving research dating back a few years. Specifically, we review the idea of treating dependency solving as a separate concern in package manager implementations, relying on generic dependency solvers based on tried and tested techniques such as SAT solving, PBO, MILP, etc. By conducting a census of dependency solving capabilities in state-of-the-art package managers we conclude that some proposals are starting to take off (e.g., SAT-based dependency solving) while-with few exceptions-others have not (e.g., out-sourcing dependency solving to reusable components). We reflect on why that has been the case and look at novel challenges for dependency solving that have emerged since.

Aim of this paper is the description of a new tool to support institutions in the implementation of targeted countermeasures, based on quantitative and multi-scale elements, for the fight and prevention of emergencies, such as the current COVID-19 pandemic. The tool is a centralized system (web application), single multi-user platform, which relies on Artificial Intelligence (AI) algorithms for the processing of heterogeneous data, and which can produce an output level of risk. The model includes a specific neural network which will be first trained to learn the correlation between selected inputs, related to the case of interest: environmental variables (chemical-physical, such as meteorological), human activity (such as traffic and crowding), level of pollution (in particular the concentration of particulate matter), and epidemiological variables related to the evolution of the contagion. The tool realized in the first phase of the project will serve later both as a decision support system (DSS) with predictive capacity, when fed by the actual measured data, and as a simulation bench performing the tuning of certain input values, to identify which of them lead to a decrease in the degree of risk. In this way, the authors aim to design different scenarios to compare different restrictive strategies and the actual expected benefits, to adopt measures sized to the actual need, and adapted to the specific areas of analysis, useful to safeguard human health, but also the economic and social impact of the choices., Comment: 19 pages, 14 figures, 50 references, sottomesso ad una Special Issue di ISPRS International Journal of Geo-Information (https://www.mdpi.com/journal/ijgi/special_issues/Impacts_COVID-19 ), attualmente under review

A novel reduction procedure for covariant classical field theories, reflecting the generalized symplectic reduction theory of Hamiltonian systems, is presented. The departure point of this reduction procedure consists in the choice of a submanifold of the manifold of solutions of the equations describing a field theory. Then, the covariance of the geometrical objects involved, will allow to define equations of motion on a reduced space. The computation of the canonical geometrical structure is performed neatly by using the geometrical framework provided by the multisymplectic description of covariant field theories. The procedure is illustrated by reducing the D'Alembert theory on a five-dimensional Minkowski space-time to a massive Klein-Gordon theory in four dimensions and, more interestingly, to the Schr\"odinger equation in 3+1 dimensions., Comment: 14 pages

The analysis of the covariant brackets on the space of functions on the solutions to a variational problem in the framework of contact geometry initiated in the companion letter Ref.19 is extended to the case of the multisymplectic formulation of the free Klein-Gordon theory and of the free Schr\"{o}dinger equation., Comment: 16 pages

The formulation of covariant brackets on the space of solutions to a variational problem is analyzed in the framework of contact geometry. It is argued that the Poisson algebra on the space of functionals on fields should be read as a Poisson subalgebra within an algebra of functions equipped with a Jacobi bracket on a suitable contact manifold., Comment: 16 pages

An explicit Lagrangian description is given for the Heisenberg equation on the algebra of operators of a quantum system, and for the Landau-von Neumann equation on the manifold of quantum states which are isospectral with respect to a fixed reference quantum state., Comment: 13 pages

The groupoids description of Schwinger's picture of quantum mechanics is continued by discussing the closely related notions of composition of systems, subsystems, and their independence. Physical subsystems have a neat algebraic description as subgroupoids of the Schwinger's groupoid of the system. The groupoids picture offers two natural notions of composition of systems: Direct and free products of groupoids, that will be analyzed in depth as well as their universal character. Finally, the notion of independence of subsystems will be reviewed, finding that the usual notion of independence, as well as the notion of free independence, find a natural realm in the groupoids formalism. The ideas described in this paper will be illustrated by using the EPRB experiment. It will be observed that, in addition to the notion of the non-separability provided by the entangled state of the system, there is an intrinsic `non-separability' associated to the impossibility of identifying the entangled particles as subsystems of the total system., Comment: 32 pages. Comments are welcome!

Software, and software source code in particular, is widely used in modern research. It must be properly archived, referenced, described and cited in order to build a stable and long lasting corpus of scientic knowledge. In this article we show how the Software Heritage universal source code archive provides a means to fully address the first two concerns, by archiving seamlessly all publicly available software source code, and by providing intrinsic persistent identifiers that allow to reference it at various granularities in a way that is at the same time convenient and effective. We call upon the research community to adopt widely this approach., Comment: arXiv admin note: substantial text overlap with arXiv:1909.10760

In this paper we will present tha main features of what can be called Schwinger's foundational approach to Quantum Mechanics. The basic ingredients of this formulation are the \textit{selective measurements}, whose algebraic composition rules define a mathematical structure called groupoid, which is associated with any physical system. After the introduction of the basic axioms of a groupoid, the concepts of observables and states, statistical interpretation and evolution are derived. An example is finally introduced to support the theoretical description of this approach., Comment: 14 pages, Proceedings PAFT 2019

Motivated by the geometrical structures of quantum mechanics, we introduce an almost-complex structure $J$ on the product $M\times M$ of any parallelizable statistical manifold $M$. Then, we use $J$ to extract a pre-symplectic form and a metric-like tensor on $M\times M$ from a divergence function. These tensors may be pulled back to $M$, and we compute them in the case of an N-dimensional symplex with respect to the Kullback-Leibler relative entropy, and in the case of (a suitable unfolding space of) the manifold of faithful density operators with respect to the von Neumann-Umegaki relative entropy., Comment: 19 pages, comments are welcome!

Among the entities involved in software citation, software source code requires special attention, due to the role it plays in ensuring scientific reproducibility. To reference source code we need identifiers that are not only unique and persistent, but also support \emph{integrity} checking intrinsically. Suitable identifiers must guarantee that denotedobjects will always stay the same, without relying on external third parties and administrative processes. We analyze the role of identifiers for digital objects (IDOs), whose properties are different from, and complementary to, those of the various digital identifiers of objects (DIOs) that are today popular building blocks of software and data citation toolchains.We argue that both kinds of identifiers are needed and detail the syntax, semantics, and practical implementation of the persistent identifiers (PIDs) adopted by the Software Heritage project to reference billions of softwaresource code artifacts such as source code files, directories, and commits., Comment: Computing in Science & Engineering, IEEE, In press

By fixing a reference frame in spacetime, it is possible to split the Euler-Lagrange equations associated with a degenerate Lagrangian into purely evolutionary equations and constraints on the allowed Cauchy data with respect to the notion of Space and Time associated with the given reference frame. In the context of Classical Electrodynamics, we introduce a "covariantization procedure" that allows to invert the perspective and to recover a full-fledged covariant formulation of Maxwell's equations starting only with constraint equations (i.e., Gauss' law and the local version of the law of conservation of magnetic flux) as perceived in a sufficient number of (inertial) reference frames on Minkowski spacetime.

In this paper a generalized form of relativistic dynamics is presented: A realization of the Poincar\'e algebra is provided in terms of vector fields on the tangent bundle of a simultaneity surface in $\mathbb{R}^4$. The construction of this realization is explicitly shown to clarify the role of the commutation relations of the Poincar\'e algebra versus their description in terms of Poisson brackets in the no-interaction theorem. Moreover, a geometrical analysis of the ``eleventh generator'' formalism introduced by Sudarshan and Mukunda is outlined, this formalism being at the basis of many proposals which evaded the no-interaction theorem., Comment: 15 pages

Software source code is an essential research output, and many research communities strongly encourage making the source code of the artefact available by archiving it in publicly-accessible long-term archives.Software Heritage is a non profit, long term universal archive specifically designed for software source code, and able to store not only a software artifact, but also its full development history. It provides the ideal place to preserve research software artifacts, and offers powerful mechanisms to enhance research articles with precise references to relevant fragments of your source code.Using Software Heritage for your research software artifacts is straightforward and involves three simple steps. This document details each of these three steps, providing guidelines for making the most out of Software Heritage for your research.