21 research outputs found
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