1,720,998 research outputs found
Warning Signs of Impending Critical Transitions in Love Affairs
No full textPsychoanalysts and therapists have noticed that the increase of the reconciliation time, i.e., the period of dissatisfaction that two lovers need to return to their positive equilibrium after a dispute, is often a warning sign of an impending consistent drop of quality of the relationship, possibly followed by a breakup (e.g., a divorce). Here this rule is investigated and shown to be the logical consequence of the attitude of individuals (here called secure) who increase their reaction when their partners get more involved. The analysis is carried out with a well-known and repeatedly validated mathematical model composed of two nonlinear differential equations and the rule follows from the discovery that the model has catastrophic bifurcations with respect to the psychophysical traits of the partners. Thus, for example, negative trends in the appeal of the partners or in the reactiveness to it slowly but inevitably push couples toward a tipping point, from which a critical transition can originate. Since the rule is here justified only for couples composed of secure individuals, finding out if it holds also for other couples remains an interesting open problem
From Individual Traits to Couple Behavior
No full textMicro-macro links between individual psychophysical traits and couple behavior are established. The analysis is carried out through a simple idealized model that mimics couples not influenced by their social environment. The functions describing the traits, i.e. the reactions to the love and appeal of the partner, are quite general. In particular, they allow one to take into account relatively sophisticated characteristics like insecurity and bias. The results are interesting even if some of them have already been discovered in extremely special cases. Some features of the idealized model are also used to theoretically support important behaviors identified empirically by psychotherapists
Tree-based algorithms for the stability of discrete-time switched linear systems under arbitrary and constrained switching
No full textWe present a direct approach to study the stability of discrete-time switched linear systems that can be applied to arbitrary switching, as well as when switching is constrained by a switching automaton. We explore the tree of possible matrix products, by pruning the subtrees rooted at contractions and looking for unstable repeatable products. Generically, this simple strategy either terminates with all contracting leafs-showing the system's asymptotic stability-or finds the shortest unstable and repeatable matrix product. Although it behaves in the worst case as the exhaustive search, we show that its performance is greatly enhanced by measuring contractiveness w.r.t. sum-of-squares polynomial norms, optimized to minimize the largest expansion among the system's modes
Two-age-structured covid-19 epidemic model: Estimation of virulence parameters to interpret effects of national and regional feedback interventions and vaccination
Full text linkThe COVID-19 epidemic has recently led in Italy to the implementation of different external strategies in order to limit the spread of the disease in response to its transmission rate: strict national lockdown rules, followed first by a weakening of the social distancing and contact reduction feedback interventions and finally the implementation of coordinated intermittent regional actions, up to the application, in this last context, of an age-stratified vaccine prioritization strategy. This paper originally aims at identifying, starting from the available age-structured real data at the national level during the specific aforementioned scenarios, external-scenario-dependent sets of virulence parameters for a two-age-structured COVID-19 epidemic compartmental model, in order to provide an interpretation of how each external scenario modifies the age-dependent patterns of social contacts and the spread of COVID-19
Pinning Control of Hypergraphs
Full text linkA standard assumption in control of network dynamical systems is that its nodes interact through pairwise interactions, which can be described by means of a directed graph. However, in several contexts, multibody, directed interactions may occur, thereby requiring the use of directed hypergraphs rather then digraphs. For the first time, we propose a strategy, inspired by the classic pinning control on graphs, that is tailored for controlling network systems coupled through a directed hypergraph. By drawing an analogy with signed graphs, we provide sufficient conditions for controlling the network onto the desired trajectory provided by the pinner, and a dedicated algorithm to design the control hyperedges
An algorithm for finding equitable clusters in multi-layer networks
No full textThis paper is concerned with the analysis of multi-layer networks consisting of different kinds of oscillators and couplings. In particular, we propose an algorithm for finding equitable clusters in this general class of networks, thus generalizing an existing algorithm specific for networks with identical nodes and one kind of connections. The algorithm is suitable to analyze complex networks of particular interest for the scientific community, such as neuron networks and electrical networks. The algorithm is tested on a random heterogeneous network with 40 oscillators of two different kinds and couplings of two different kinds. The stability of the obtained clusters is checked in a two-dimensional parameter space by using brute-force simulations
Analyzing synchronized clusters in neuron networks
Full text linkThe presence of synchronized clusters in neuron networks is a hallmark of information transmission and processing. Common approaches to study cluster synchronization in networks of coupled oscillators ground on simplifying assumptions, which often neglect key biological features of neuron networks. Here we propose a general framework to study presence and stability of synchronous clusters in more realistic models of neuron networks, characterized by the presence of delays, different kinds of neurons and synapses. Application of this framework to two examples with different size and features (the directed network of the macaque cerebral cortex and the swim central pattern generator of a mollusc) provides an interpretation key to explain known functional mechanisms emerging from the combination of anatomy and neuron dynamics. The cluster synchronization analysis is carried out also by changing parameters and studying bifurcations. Despite some modeling simplifications in one of the examples, the obtained results are in good agreement with previously reported biological data
A theoretical analysis of complex armed conflicts
Full text linkThe introduction and analysis of a simple idealized model enables basic insights into how military characteristics and recruitment strategies affect the dynamics of armed conflicts, even in the complex case of three or more fighting groups. In particular, the model shows when never ending wars (stalemates) are possible and how initial conditions and interventions influence a conflict’s fate. The analysis points out that defensive recruitment policies aimed at compensating for suffered losses lead to conflicts with simple dynamics, while attack groups sensitive to the damages they inflict onto their enemies can give rise to conflicts with turbulent behaviours. Since non-governmental groups often follow attack strategies, the conclusion is that the evolution of conflicts involving groups of that kind can be expected to be difficult to forecast
Nonlinear pinning control of stochastic network systems
No full textWe propose a constructive method to design a pinning control law that synchronizes a network of stochastic dynamical systems. Different from traditional pinning control, we add to the standard proportional controller a nonlinear feedback term that, in the absence of coupling, would minimize a given cost functional. We then derive analytic guarantees that the proposed control law can effectively synchronize coupled noisy systems described by stochastic differential equations. Building on our theoretical results, we provide an algorithm for control design, whose effectiveness is illustrated on numerical testbeds. Finally, we perform extensive Monte Carlo simulations to evaluate the performance of the proposed nonlinear pinning strategy and compare it against the traditional proportional law
A simple tree-based algorithm for deciding the stability of discrete-time switched linear systems
No full textWe re-evaluate the direct approach to study the stability of discrete-time switched systems with finitely many linear modes. We explore the tree of possible matrix products by pruning the paths leading to contractions and looking for unstable repeatable products. Generically, this simple strategy either terminates with all contracting leafs-showing the asymptotic stability of the system-or finds the shortest unstable matrix product. Although it behaves in the worst-case as the exhaustive search, we show that its performance is greatly enhanced by measuring contractiveness w.r.t. sum-of-squares polynomial norms, optimized to minimize the largest expansion among the system's modes. We test our approach on several benchmark examples proposed to test switched Lyapunov function methods. Although these methods are mathematically elegant and efficient, they are more involved to apply and cannot decide the system's instability. Moreover, our algorithm is flexible. Adding/removing system's modes, setting mode-independent dwell-times, and constraining switching to finite automata can all be easily implemented and exploited in control design
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