Opinion influence and evolution in social networks: a Markovian agents model

In this paper, the effect on collective opinions of filtering algorithms managed by social network platforms is modeled and investigated. A stochastic multi-agent model for opinion dynamics is proposed, that accounts for a centralized tuning of the strength of interaction between individuals. The evolution of each individual opinion is described by a Markov chain, whose transition rates are affected by the opinions of the neighbors through influence parameters. The properties of this model are studied in a general setting as well as in interesting special cases. A general result is that the overall model of the social network behaves like a high-dimensional Markov chain, which is viable to Monte Carlo simulation. Under the assumption of identical agents and unbiased influence, it is shown that the influence intensity affects the variance, but not the expectation, of the number of individuals sharing a certain opinion. Moreover, a detailed analysis is carried out for the so-called Peer Assembly, which describes the evolution of binary opinions in a completely connected graph of identical agents. It is shown that the Peer Assembly can be lumped into a birth-death chain that can be given a complete analytical characterization. Both analytical results and simulation experiments are used to highlight the emergence of particular collective behaviours, e.g. consensus and herding, depending on the centralized tuning of the influence parameters.Comment: Revised version (May 2018

A Hamilton-Jacobi setup for the static output feedback stabilization of nonlinear systems

Published versio

Modeling vaccination rollouts, SARS-CoV-2 variants and the requirement for non-pharmaceutical interventions in Italy

Despite progress in clinical care for patients with coronavirus disease 2019 (COVID-19)1, population-wide interventions are still crucial to manage the pandemic, which has been aggravated by the emergence of new, highly transmissible variants. In this study, we combined the SIDARTHE model2, which predicts the spread of SARS-CoV-2 infections, with a new data-based model that projects new cases onto casualties and healthcare system costs. Based on the Italian case study, we outline several scenarios: mass vaccination campaigns with different paces, different transmission rates due to new variants and different enforced countermeasures, including the alternation of opening and closure phases. Our results demonstrate that non-pharmaceutical interventions (NPIs) have a higher effect on the epidemic evolution than vaccination alone, advocating for the need to keep NPIs in place during the first phase of the vaccination campaign. Our model predicts that, from April 2021 to January 2022, in a scenario with no vaccine rollout and weak NPIs (R = 1.27), as many as 298,000 deaths associated with COVID-19 could occur. However, fast vaccination rollouts could reduce mortality to as few as 51,000 deaths. Implementation of restrictive NPIs (R = 0.9) could reduce COVID-19 deaths to 30,000 without vaccinating the population and to 18,000 with a fast rollout of vaccines. We also show that, if intermittent open\u2013close strategies are adopted, implementing a closing phase first could reduce deaths (from 47,000 to 27,000 with slow vaccine rollout) and healthcare system costs, without substantive aggravation of socioeconomic losses

Vertex results for the robust analysis of uncertain biochemical systems

We consider the problem of assessing the sensitivity of uncertain biochemical systems in the presence of input perturbations (either constant or periodic) around a stable steady state. In particular, we propose approaches for the robust sensitivity analysis of systems with uncertain parameters assumed to take values in a hyper-rectangle. We highlight vertex results, which allow us to check whether a property is satisfied for all parameter choices in the hyper-rectangle by simply checking whether it is satisfied for all parameter choices at the vertices of the hyper-rectangle. We show that, for a vast class of systems, including (bio)chemical reaction networks with mass-action kinetics, the system Jacobian has a totally multiaffine structure (namely, all minors of the Jacobian matrix are multiaffine functions of the uncertain parameters), which can be exploited to obtain several vertex results. We consider different problems: robust non-singularity; robust stability of the steady-state; robust steady-state sensitivity analysis, in the case of constant perturbations; robust frequency-response sensitivity analysis, in the presence of periodic perturbations; and robust adaptation analysis. The developed theory is then applied to gain insight into some examples of uncertain biochemical systems, including the incoherent feed-forward loop, the coherent feed-forward loop, the Brusselator oscillator and the Goldbeter oscillator

Essentially Negative News About Positive Systems

In this paper the discretisation of switched and non-switched linear positive systems using Padé approximations is considered. Padé approximations to the matrix exponential are sometimes used by control engineers for discretising continuous time systems and for control system design. We observe that this method of approximation is not suited for the discretisation of positive dynamic systems, for two key reasons. First, certain types of Lyapunov stability are not, in general, preserved. Secondly, and more seriously, positivity need not be preserved, even when stability is. Finally we present an alternative approximation to the matrix exponential which preserves positivity, and linear and quadratic stability

Computing upper-bounds of the minimum dwell time of linear switched systems via homogenous polynomial lyapunov functions

Regular Session - Switched Systems IIThis paper investigates the minimum dwell time for switched linear systems. It is shown that a sequence of upper bounds of the minimum dwell time can be computed by exploiting homogeneous polynomial Lyapunov functions and convex optimization based on LMIs. This sequence is obtained by adopting two possible representations of homogeneous polynomials, one based on Kronecker products, and the other on the square matrix representation. Some examples illustrate the use and the potentialities of the proposed approach.published_or_final_versionThe 2010 American Control Conference (ACC), Baltimore, MD., 30 June-2 July 2010. In Proceedings of the American Control Conference, 2010, p. 2487-249

A nonconservative LMI condition for stability of switched systems with guaranteed dwell time

Ensuring stability of switched linear systems with a guaranteed dwell time is an important problem in control systems. Several methods have been proposed in the literature to address this problem, but unfortunately they provide sufficient conditions only. This technical note proposes the use of homogeneous polynomial Lyapunov functions in the non-restrictive case where all the subsystems are Hurwitz, showing that a sufficient condition can be provided in terms of an LMI feasibility test by exploiting a key representation of polynomials. Several properties are proved for this condition, in particular that it is also necessary for a sufficiently large degree of these functions. As a result, the proposed condition provides a sequence of upper bounds of the minimum dwell time that approximate it arbitrarily well. Some examples illustrate the proposed approach. © 2012 IEEE.published_or_final_versio

Polythiophenes and oligothiophenes in zeolite hosts

The polymerization of different thiophenes in the channels of molecular sieve zeolite hosts is described. Thiophene, 3-methyIthiophene, 2,2'-bithiophene, and terthiophene were introduced into dehydrated proton-, Cu(II)- or Fe(III)-containing zeolites (NaY and Na-mordenite) from organic solvents or vapor-phase. In the large-pore hosts, green-black products are formed from the monomers within several minutes. Spectroscopic characterization (IR, UV-NIR) confirms the formation of oxidized polymer chains in the zeolite channels. UV-Near IR reflectance spectra of the zeolite/polythiophene samples exhibit a broad absorption from 500 to about 2500 nm as the bulk and not the resolved spectra of short oligomers, thus fairly long polymer chains are formed in the zeolites. Conducting polymers can be recovered after dissolution of the zeolite host in HF. 2, 2'-bithiophene and a-terthiophene in acidic H2Y and U^Y zeolites (2 and 6 protons per super cage/ß-cage) yield yellow-green and purple products, respectively. UV-NIR reflectance data indicate that the acidic zeolite hosts oxidize the thiophene oligomers to yield stable radical cations and dications in their channel systems

Almost sure stability of discrete-time Markov Jump Linear Systems

This paper deals with transient analysis and almost sure stability for discrete-time Markov Jump Linear System (MJLS). The expectation of sojourn time and activation number of any mode, and switching number between any two modes of discrete-time MJLS are presented firstly. Then a result on transient behavior analysis of discrete-time MJLS is given. Finally a new deterministically testable condition for the exponential almost sure stability of discrete-time MJLS is proposed

Growth attenuation under saline stress is mediated by the heterotrimeric G protein complex

BackgroundPlant growth is plastic, able to rapidly adjust to fluctuation in environmental conditions such as drought and salinity. Due to long-term irrigation use in agricultural systems, soil salinity is increasing; consequently crop yield is adversely affected. It is known that salt tolerance is a quantitative trait supported by genes affecting ion homeostasis, ion transport, ion compartmentalization and ion selectivity. Less is known about pathways connecting NaCl and cell proliferation and cell death. Plant growth and cell proliferation is, in part, controlled by the concerted activity of the heterotrimeric G-protein complex with glucose. Prompted by the abundance of stress-related, functional annotations of genes encoding proteins that interact with core components of the Arabidopsis heterotrimeric G protein complex (AtRGS1, AtGPA1, AGB1, and AGG), we tested the hypothesis that G proteins modulate plant growth under salt stress.ResultsNa+ activates G signaling as quantitated by internalization of Arabidopsis Regulator of G Signaling protein 1 (AtRGS1). Despite being components of a singular signaling complex loss of the Gβ subunit (agb1-2 mutant) conferred accelerated senescence and aborted development in the presence of Na+, whereas loss of AtRGS1 (rgs1-2 mutant) conferred Na+ tolerance evident as less attenuated shoot growth and senescence. Site-directed changes in the Gα and Gβγ protein-protein interface were made to disrupt the interaction between the Gα and Gβγ subunits in order to elevate free activated Gα subunit and free Gβγ dimer at the plasma membrane. These mutations conferred sodium tolerance. Glucose in the growth media improved the survival under salt stress in Col but not in agb1-2 or rgs1-2 mutants.ConclusionsThese results demonstrate a direct role for G-protein signaling in the plant growth response to salt stress. The contrasting phenotypes of agb1-2 and rgs1-2 mutants suggest that G-proteins balance growth and death under salt stress. The phenotypes of the loss-of-function mutations prompted the model that during salt stress, G activation promotes growth and attenuates senescence probably by releasing ER stress