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Fontan, A. & Altafini, C. (2018). Multiequilibria analysis for a class of collective decision-making networked systems. IEEE Transactions on Control of Network Systems (4), 1931-1940
Open this publication in new window or tab >>Multiequilibria analysis for a class of collective decision-making networked systems
2018 (English)In: IEEE Transactions on Control of Network Systems, E-ISSN 2325-5870, no 4, p. 1931-1940Article in journal (Refereed) Published
Abstract [en]

The models of collective decision-making considered in this paper are nonlinear interconnected cooperative systems with saturating interactions. These systems encode the possible outcomes of a decision process into different steady states of the dynamics. In particular, they are characterized by two main attractors in the positive and negative orthant, representing two choices of agreement among the agents, associated to the Perron-Frobenius eigenvector of the system. In this paper we give conditions for the appearance of other equilibria of mixed sign. The conditions are inspired by Perron-Frobenius theory and are related to the algebraic connectivity of the network. We also show how all these equilibria must be contained in a solid disk of radius given by the norm of the equilibrium point which is located in the positive orthant.

Keywords
Symmetric matrices;Eigenvalues and eigenfunctions;Bifurcation;Neural networks;Decision making;Control systems;Cooperative systems;Collective decision-making;nonlinear cooperative systems;multiple equilibria;Perron-Frobenius theorem;algebraic connectivity
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-151688 (URN)10.1109/TCNS.2017.2774014 (DOI)000454245200038 ()
Note

Funding Agencies|Swedish Research Council [2015-04390]

Available from: 2018-10-02 Created: 2018-10-02 Last updated: 2019-01-11
Altafini, C. & Ceragioli, F. (2018). Signed bounded confidence models for opinion dynamics. Automatica, 93, 114-125
Open this publication in new window or tab >>Signed bounded confidence models for opinion dynamics
2018 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 93, p. 114-125Article in journal (Refereed) Published
Abstract [en]

The aim of this paper is to modify continuous-time bounded confidence opinion dynamics models so that "changes of opinion" (intended as changes of the sign of the initial states) are never induced during the evolution. Such sign invariance can be achieved by letting opinions of different sign localized near the origin interact negatively, or neglect each other, or even repel each other. In all cases, it is possible to obtain sign-preserving bounded confidence models with state-dependent connectivity and with a clustering behavior similar to that of a standard bounded confidence model. (C) 2018 Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
PERGAMON-ELSEVIER SCIENCE LTD, 2018
Keywords
Opinion dynamics; Bounded confidence models; Signed graphs; ODEs with discontinuous right-hand-side
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-149685 (URN)10.1016/j.automatica.2018.03.064 (DOI)000436916200014 ()
Note

Funding Agencies|Swedish Research Council [2015-04390]

Available from: 2018-07-25 Created: 2018-07-25 Last updated: 2018-08-14
Kärner Köhler, A., Nilsson, S., Jaarsma, T. & Tingström, P. (2017). Health beliefs about lifestyle habits differ between patients and spouses 1 year after a cardiac event – a qualitative analysis based on the Health Belief Model. Scandinavian Journal of Caring Sciences, 31(2), 332-341
Open this publication in new window or tab >>Health beliefs about lifestyle habits differ between patients and spouses 1 year after a cardiac event – a qualitative analysis based on the Health Belief Model
2017 (English)In: Scandinavian Journal of Caring Sciences, ISSN 0283-9318, E-ISSN 1471-6712, Vol. 31, no 2, p. 332-341Article in journal (Refereed) Published
Abstract [en]

BACKGROUND:

Spousal concordance on risk factors and lifestyle habits exists and can partly be explained by patients' and spouses' health beliefs and underuse of cardiac rehabilitation. However, there have been very few qualitative comparisons of health beliefs between patients and spouses after a cardiac event.

AIM:

To examine and qualitatively compare the health beliefs of patients with coronary heart disease and their spouses about lifestyle habits, 1 year after the cardiac event.

DESIGN:

Explorative and descriptive.

METHOD:

Semi-structured focus group interviews were conducted with patients (n = 14) 1 year after a cardiac event, as well as individual interviews with spouses (n = 8). The transcriptions underwent a deductive qualitative content analysis, within the framework of the Health Belief Model.

FINDINGS:

Patients' and spouses' health beliefs about lifestyle habits qualitatively differed in most predetermined main analytical categories of the Health Belief Model. The patients relied more on their own capacity and the healthcare system than on collaboration with their spouses who instead emphasised the importance of mutual activities to establish lifestyle habits. The spouses therefore experienced problems with different family preferences compared to the patients' wishes. Moreover, only patients believed supervised exercise was beneficial for risk reduction of coronary heart disease and they related barriers for medication to a self-healing body and a meaningless life without relatives and old habits. Patients and spouses agreed that despite the severity of illness, life was captured and that normalisation to a life as usual was possible.

CONCLUSION:

The patients' and spouses' qualitatively different health beliefs regarding health-related behaviours imply a new approach. Nurses and associated professionals need to follow-up patients' and spouses' in primary health care to support them in a tailored way, for example in problem-based sessions. Recognition and understanding of their different views and otherness could lead to compromises and goals to work with.

Place, publisher, year, edition, pages
John Wiley & Sons, 2017
Keywords
Coronary Heart Disease, Primary Care, Health Psychology, Qualitative content analysis.
National Category
Health Care Service and Management, Health Policy and Services and Health Economy
Identifiers
urn:nbn:se:liu:diva-130771 (URN)10.1111/scs.12351 (DOI)000404644100014 ()27439667 (PubMedID)
Projects
The COR-PRIM study
Funder
Region Östergötland, Lio-433801
Note

Funding agencies: Swedish Heart and Lung Association [E103/13, E090/14]; Region Ostergotland, Sweden [LIO-433801]

Available from: 2016-08-23 Created: 2016-08-23 Last updated: 2018-07-02
Fontan, A. & Altafini, C. (2017). Investigating mixed-sign equilibria for nonlinear collective decision-making systems. In: : . Paper presented at 2017 IEEE 56th Annual Conference on Decision and Control (CDC), December 12-15, Melbourne, Australia (pp. 781-786).
Open this publication in new window or tab >>Investigating mixed-sign equilibria for nonlinear collective decision-making systems
2017 (English)Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we provide necessary conditions for the existence of multiple equilibrium points for a class of non-linear cooperative networked systems with saturating interactions which describe models of collective decision-making. The multiple steady states of the dynamics represent the possible outcomes of a decision process, and, except for one positive and one negative, have all mixed signs. The conditions we obtain can be formulated in terms of the algebraic connectivity of the network and are inspired by Perron-Frobenius arguments. It is also shown that the mixed-sign equilibria are contained in a ball of radius given by the norm of the positive equilibrium point and centered in the origin. Numerical examples are given to illustrate the results.

Series
IEEE Conference on Decision and Control, ISSN 0743-1546
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-145486 (URN)10.1109/CDC.2017.8263755 (DOI)000424696900122 ()978-1-5090-2873-3 (ISBN)
Conference
2017 IEEE 56th Annual Conference on Decision and Control (CDC), December 12-15, Melbourne, Australia
Note

Funding Agencies|Swedish Research Council [2015-04390]

Available from: 2018-03-02 Created: 2018-03-02 Last updated: 2018-10-01
Fontan, A. & Altafini, C. (2017). Investigating mixed-sign equilibria for nonlinear collective decision-making systems. In: Proceedings from the 2017 IEEE 56th Annual Conference on Decision and Control (CDC), December 12-15, 2017, Melbourne, Australia: . Paper presented at 2017 IEEE 56th Annual Conference on Decision and Control (CDC) December 12-15, 2017, Melbourne, Australia (pp. 781-786).
Open this publication in new window or tab >>Investigating mixed-sign equilibria for nonlinear collective decision-making systems
2017 (English)In: Proceedings from the 2017 IEEE 56th Annual Conference on Decision and Control (CDC), December 12-15, 2017, Melbourne, Australia, 2017, p. 781-786Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we provide necessary conditions for the existence of multiple equilibrium points for a class of non-linear cooperative networked systems with saturating interactions which describe models of collective decision-making. The multiple steady states of the dynamics represent the possible outcomes of a decision process, and, except for one positive and one negative, have all mixed signs. The conditions we obtain can be formulated in terms of the algebraic connectivity of the network and are inspired by Perron-Frobenius arguments. It is also shown that the mixed-sign equilibria are contained in a ball of radius given by the norm of the positive equilibrium point and centered in the origin. Numerical examples are given to illustrate the results.

Keywords
Symmetric matrices, Eigenvalues and eigenfunctions, Bifurcation, Neural networks, Decision making, Steady-state, Cooperative systems
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-145192 (URN)10.1109/CDC.2017.8263755 (DOI)9781509028733 (ISBN)9781509028726 (ISBN)9781509028740 (ISBN)
Conference
2017 IEEE 56th Annual Conference on Decision and Control (CDC) December 12-15, 2017, Melbourne, Australia
Available from: 2018-03-22 Created: 2018-03-22 Last updated: 2019-05-09Bibliographically approved
Altafini, C. (2016). Minimal eventually positive realizations of externally positive systems. Automatica, 68, 140-147
Open this publication in new window or tab >>Minimal eventually positive realizations of externally positive systems
2016 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 68, p. 140-147Article in journal (Refereed) Published
Abstract [en]

It is a well-known fact that externally positive linear systems may fail to have a minimal positive realization. In order to investigate these cases, we introduce the notion of minimal eventually positive realization, for which the state update matrix becomes positive after a certain power. Eventually positive realizations capture the idea that in the impulse response of an externally positive system the state of a minimal realization may fail to be positive, but only transiently. As a consequence, we show that in discrete-time it is possible to use downsampling to obtain minimal positive realizations matching decimated sequences of Markov coefficients of the impulse response. In continuous-time, instead, if the sampling time is chosen sufficiently long, a minimal eventually positive realization leads always to a sampled realization which is minimal and positive.

Place, publisher, year, edition, pages
Pergamon Press, 2016
Keywords
Positive linear systems;Minimal realization;Eventually positive matrices;Perron–Frobenius theorem
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-127609 (URN)10.1016/j.automatica.2016.01.072 (DOI)000375507600016 ()
Note

Funding agencies: Swedish Research Council [2015-04390]

Available from: 2016-05-03 Created: 2016-05-03 Last updated: 2017-05-08Bibliographically approved
Lindmark, G. & Altafini, C. (2016). Positive Controllability of Large-Scale Networks. In: Proceedings of the 2016 European Control Conference: . Paper presented at European Control Conference, 2016, Aalborg, Denmark (pp. 819-824). Institute of Electrical and Electronics Engineers (IEEE)
Open this publication in new window or tab >>Positive Controllability of Large-Scale Networks
2016 (English)In: Proceedings of the 2016 European Control Conference, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 819-824Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, we study the problem of controlling large scale networks with controls which can assume only positive values. Given an adjacency matrix A, an algorithm is developed that constructs an input matrix B with a minimal number of columns such that the resulting system (A, B) is positively controllable. The algorithm combines the graphical methods used for structural controllability analysis with the theory of positive linear dependence. The number of control inputs guaranteeing positive controllability is near optimal.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2016
Keywords
Complex Networks, Controllability
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-130780 (URN)10.1109/ECC.2016.7810390 (DOI)000392695300137 ()978-1-5090-2591-6 (ISBN)978-1-5090-2592-3 (ISBN)978-1-5090-2590-9 (ISBN)
Conference
European Control Conference, 2016, Aalborg, Denmark
Available from: 2016-08-23 Created: 2016-08-23 Last updated: 2017-08-09
Precious, U. A., Ticozzi, F. & Altafini, C. (2015). Existence, uniqueness and stability properties of positive equilibria for a class of nonlinear cooperative systems. In: Proceedings of 54th IEEE Conference on Decision and Control (CDC): . Paper presented at IEEE Conference on Decision and Control. December 15-18, 2015 at the Osaka International Convention Center, Osaka, Japan (pp. 4406-4411). Institute of Electrical and Electronics Engineers (IEEE)
Open this publication in new window or tab >>Existence, uniqueness and stability properties of positive equilibria for a class of nonlinear cooperative systems
2015 (English)In: Proceedings of 54th IEEE Conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 4406-4411Conference paper, Published paper (Refereed)
Abstract [en]

We provide conditions that guarantee existence, uniqueness and stability of strictly positive equilibria for nonlinear cooperative systems associated to vector fields that are concave or subhomogeneous. This class of positive systems describes well interconnected dynamics that are of key interest for communication, biological, economical and neural network applications. These conditions can be formulated directly in terms of the spectral radius of the Jacobian of the system, and do not require to use constant inputs to move the equilibrium point from the origin to the interior of the positive orthant.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2015
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-127607 (URN)10.1109/CDC.2015.7402907 (DOI)000381554504096 ()9781479978861 (ISBN)9781479978847 (ISBN)9781479978854 (ISBN)
Conference
IEEE Conference on Decision and Control. December 15-18, 2015 at the Osaka International Convention Center, Osaka, Japan
Available from: 2016-05-03 Created: 2016-05-03 Last updated: 2018-08-24Bibliographically approved
Altafini, C. & Facchetti, G. (2015). Metabolic Adaptation Processes That Converge to Optimal Biomass Flux Distributions. PloS Computational Biology, 11(9), Article ID e1004434.
Open this publication in new window or tab >>Metabolic Adaptation Processes That Converge to Optimal Biomass Flux Distributions
2015 (English)In: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 11, no 9, article id e1004434Article in journal (Refereed) Published
Abstract [en]

In simple organisms like E. coli, the metabolic response to an external perturbation passes through a transient phase in which the activation of a number of latent pathways can guarantee survival at the expenses of growth. Growth is gradually recovered as the organism adapts to the new condition. This adaptation can be modeled as a process of repeated metabolic adjustments obtained through the resilencings of the non-essential metabolic reactions, using growth rate as selection probability for the phenotypes obtained. The resulting metabolic adaptation process tends naturally to steer the metabolic fluxes towards high growth phenotypes. Quite remarkably, when applied to the central carbon metabolism of E. coli, it follows that nearly all flux distributions converge to the flux vector representing optimal growth, i.e., the solution of the biomass optimization problem turns out to be the dominant attractor of the metabolic adaptation process.

Place, publisher, year, edition, pages
PUBLIC LIBRARY SCIENCE, 2015
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:liu:diva-122440 (URN)10.1371/journal.pcbi.1004434 (DOI)000362266400024 ()26340476 (PubMedID)
Available from: 2015-11-03 Created: 2015-11-02 Last updated: 2017-12-01
Altafini, C. & Lini, G. (2015). Predictable Dynamics of Opinion Forming for Networks With Antagonistic Interactions. IEEE Transactions on Automatic Control, 60(2), 342-357
Open this publication in new window or tab >>Predictable Dynamics of Opinion Forming for Networks With Antagonistic Interactions
2015 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 60, no 2, p. 342-357Article in journal (Refereed) Published
Abstract [en]

For communities of agents which are not necessarily cooperating, distributed processes of opinion forming are naturally represented by signed graphs, with positive edges representing friendly and cooperative interactions and negative edges the corresponding antagonistic counterpart. Unlike for nonnegative graphs, the outcome of a dynamical system evolving on a signed graph is not obvious and it is in general difficult to characterize, even when the dynamics are linear. In this paper, we identify a significant class of signed graphs for which the linear dynamics are however predictable and show many analogies with positive dynamical systems. These cases correspond to adjacency matrices that are eventually positive, for which the Perron-Frobenius property still holds and implies the existence of an invariant cone contained inside the positive orthant. As examples of applications, we determine cases in which it is possible to anticipate or impose unanimity of opinion in decision/voting processes even in presence of stubborn agents, and show how it is possible to extend the PageRank algorithm to include negative links.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2015
Keywords
Eventually positive matrices; invariant cones; opinion dynamics; Perron-Frobenius theorem; signed graphs; social networks
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:liu:diva-114571 (URN)10.1109/TAC.2014.2343371 (DOI)000348379000004 ()
Note

Funding Agencies|European Social Fund, through the SHARM project at SISSA

Available from: 2015-03-02 Created: 2015-02-26 Last updated: 2017-05-08Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-4142-6502

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