Minor Invertible Products Assignment and sparse hyperdeterminants

We consider an extension of Minor Assignment Problems derived from the determinantal expansion of matrix products, under the condition that the terms of the expansion are units of C(t). This restriction places constraints on the sparsity and the factorisation properties of a family of hyperdeterminants derived from Grassmann-Plucker relations. We find minimal conditions guaranteeing that allowed assignments returning a determinantal expansion are the trivial ones, i.e. those induced by the action of a diagonal matrix of monomials on a pair of constant matrices. Counterexamples are provided when such conditions do not hold.Comment: 15 pages, improved exposition, minor typos corrected. Comments are welcom

Bethe Ansatz techniques for quasilocal charges in quench problems of integrable models

Diamo un' introduzione sui due metodi fondamentali per risolvere sistemi integrabili in una dimensione: il Coordinate Bethe Ansatz e l'Algebraic Bethe Ansatz. Concentriamo particolarmente la nostra attenzione su due catene di Heisenberg ampiamente studiate: il modello XXX e il modello XXZ. Successivamente presentiamo una breve panoramica nell'ambito del quench (in inglese il verbo to quench significa spegnere), che ha portato negli ultimi dieci anni a grandi progressi nel campo della fisica del non-equilibrio. Le tecniche fondamentali usate per implementare l'idea del quench sono l' Ensemble di Gibbs Generalizzato e l'Azione Quench. Affrontiamo con più dettagli la tecnica dell' Ensemble di Gibbs Generalizzato, costruito attraverso l' insieme infinito di cariche conservate locali di un sistema integrabile. Recentemente la tecnica dell' Ensemble di Gibbs Generalizzato è stata migliorata, aggiungendo all'insieme di cariche conservate locali, le cosiddette cariche conservate quasilocali. Proponiamo infine un procedimento per costruire un insieme di cariche quasilocali per il modello XXZ nel regime critico, detto anche senza gap (salto), attraverso il cosiddetto Y-system, ovvero un sistema gerarchico di equazioni, che appare spesso nel contesto delle teorie integrabili

Sparse deformations of determinant expansions and extensionality of set functions

We introduce an algebraic criterion for the reduction of Z^d-valued maps of subsets to corresponding Z^d-valued maps of elements of a given set. The algebraic structure is given by the expansion of the determinant of two matrices, one of which is generic, where each term of the expansion is deformed through a monomial factor. It is proved that, in broad generality, the deformation is integrable, namely, it is induced by the action of a diagonal matrix on the rows of the generic matrix. This framework allows to extend previous results in the study of signed exponential sums and their applications in statistical physics (statistical amoebas of partition functions), tropical geometry, and integrable systems (soliton solutions of the Kadomtsev-Petviashvili II equation). Furthermore, the hypotheses entailing the integrability of these deformations provide new connections between sparse polynomials, element-set relations, and hyperdeterminants and their factorisation over the ring of Laurent polynomials.Comment: 40 page

Aware Adoption of Artificial Intelligence and Big Data: a Value Framework for Reusable Knowledge

Artificial Intelligence (AI) is changing the way decision-makers reason about complex systems: more information (re)sources, e.g. Big Data (BD), are now available, but decisions are not always based on reusable and explainable knowledge resulting from the direct interaction with data. Therefore, it is necessary to define new models to describe and manage this type of uncertainty. This contribution introduces a conceptual framework to deal with the notion of Value in AI-BD contexts, embracing both the multiplicity of Value dimensions and the uncertainty in their visibility as the foundations for a dynamic, relational representation of Value. The purpose is to provide ad hoc models to support Business Intelligence in assessing the impact of AI-BD projects. The framework design is based on abstract and highly scalable definitions to represent Value, even considering the interaction of different agents through comparison, combination, and update of states of knowledge. The focus on reusable knowledge is exploited in the relation between Human and Artificial intelligences, which is characterised by a non-classical form of uncertainty regarding data observability. The impact of the dynamic behaviour of Value dimensions on decision-making and potential application domains are discussed, with the aim to enhance the sustainability of AI-BD initiatives over time.Comment: 32 pages, 5 figures. Improved exposition, corrected typos. Comments are welcome

Il peso dell'osservare: il ruolo del soggetto nel Metodo Scientifico

Nel procedere del progresso scientifico, descriviamo i fenomeni o il nostro rapporto con essi? Lungi dal poter dare risposte definitive, questa domanda verrà discussa concentrandosi sul ruolo del soggetto/osservatore nell'ambito del Metodo Scientifico. Si evidenzieranno alcuni esempi di limite alla conoscibilità o comunicabilità dei fenomeni, così come la rilevanza delle assunzioni e il concetto di informazione nell'inferenza di verità scientifiche. Tali limiti possono rappresentare una risorsa, rendendo il Metodo dinamico e adattabile alla creazione di nuova conoscenza

A Reference Architecture Proposal for Secure Data Management in Mobile Health

Mobile health (mHealth) is becoming a prominent component of healthcare. As the border between wearable consumer devices and medical devices begins to thin, we extend the mHealth definition including sports, lifestyle, and wellbeing apps that may connect to smart bracelets and watches as well as medical device apps running on consumer platforms and dedicated connected medical devices. This trend raises security and privacy concerns, since these technologies collect data ubiquitously and continuously, both on the individual user and on the surroundings. Security issues include lack of authentication and authorization mechanisms, as well as insecure data transmission and storage. Privacy issues include users' lack of control on data flow, poor quality consent management, and limitations on the possibility to remain anonymous. In response to these threats, we propose an advanced reference platform, securing the use of wearables and mobile apps in the mHealth domains through citizens' active protection and information

Signatures of partition functions and their complexity reduction through the KP II equation

A statistical amoeba arises from a real-valued partition function when the positivity condition for pre-exponential terms is relaxed, and families of signatures are taken into account. This notion lets us explore special types of constraints when we focus on those signatures that preserve particular properties. Specifically, we look at sums of determinantal type, and main attention is paid to a distinguished class of soliton solutions of the Kadomtsev-Petviashvili (KP) II equation. A characterization of the signatures preserving the determinantal form, as well as the signatures compatible with the KP II equation, is provided: both of them are reduced to choices of signs for columns and rows of a coefficient matrix, and they satisfy the whole KP hierarchy. Interpretations in term of information-theoretic properties, geometric characteristics, and the relation with tropical limits are discussed.Comment: 42 pages, 11 figures. Section 7.1 has been added, the organization of the paper has been change