Transients in the Synchronization of Oscillator Arrays

The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped harmonic oscillators in R with completely decentralized nearest neighbor interaction. We then use the theory to establish that in a certain range of the parameters transients grow linearly in the number of agents (and faster outside that range). Finally, in the regime where this linear growth occurs we give the constant of proportionality as a function of the signal velocities (see [3]) in each of the two directions. As corollaries we show that symmetric interactions are far from optimal and that all these results independent of (reasonable) boundary conditions.Comment: 11 pages, 4 figure

Stability Conditions for Coupled Autonomous Vehicles Formations

In this paper, we give necessary conditions for stability of coupled autonomous vehicles in R. We focus on linear arrays with decentralized vehicles, where each vehicle interacts with only a few of its neighbors. We obtain explicit expressions for necessary conditions for stability in the cases that a system consists of a periodic arrangement of two or three different types of vehicles, i.e. configurations as follows: ...2-1-2-1 or ...3-2-1-3-2-1. Previous literature indicated that the (necessary) condition for stability in the case of a single vehicle type (...1-1-1) held that the first moment of certain coefficients of the interactions between vehicles has to be zero. Here, we show that that does not generalize. Instead, the (necessary) condition in the cases considered is that the first moment plus a nonlinear correction term must be zero

Diffusion and consensus on weakly connected directed graphs

Let $G$ be a weakly connected directed graph with asymmetric graph Laplacian ${\cal L}$. Consensus and diffusion are dual dynamical processes defined on $G$ by $\dot x=-{\cal L}x$ for consensus and $\dot p=-p{\cal L}$ for diffusion. We consider both these processes as well their discrete time analogues. We define a basis of row vectors $\{\bar \gamma_i\}_{i=1}^k$ of the left null-space of ${\cal L}$ and a basis of column vectors $\{\gamma_i\}_{i=1}^k$ of the right null-space of ${\cal L}$ in terms of the partition of $G$ into strongly connected components. This allows for complete characterization of the asymptotic behavior of both diffusion and consensus --- discrete and continuous --- in terms of these eigenvectors. As an application of these ideas, we present a treatment of the pagerank algorithm that is dual to the usual one. We further show that the teleporting feature usually included in the algorithm is not strictly necessary. This is a complete and self-contained treatment of the asymptotics of consensus and diffusion on digraphs. Many of the ideas presented here can be found scattered in the literature, though mostly outside mainstream mathematics and not always with complete proofs. This paper seeks to remedy this by providing a compact and accessible survey.Comment: 19 pages, Survey Article, 1 figur

The contribution of two funds of identity interventions to well-being related student outcomes in primary education

Drawing on students' ‘funds of identity’ is supposed to contribute to more equitable educational outcomes, both in terms of achievement and well-being-related outcomes. However, it is not obvious how teachers can uncover and use students' funds of identity (FoI) and little is known about the actual effects of an approach based on funds of identity theory. This study investigates the (perceived) effects on students' engagement, motivation for learning, school well-being, social initiative and self-efficacy of two different interventions in which four primary school teachers tried to uncover and use their students' FoI (N = 31). A mixed methods design was used. Observations were conducted before, during and after the FoI-interventions, teachers filled in questionnaires and semi-structured interviews were conducted with teachers and students. In order to track how the intervention was enacted, logbooks of teachers were collected. The quantitative results showed significant improvement of students' engagement and social initiative during the FoI-interventions, which was confirmed by the observations. In the interviews and logbooks teachers and students reported positive effects of the interventions on students' engagement, motivation for learning, school well-being and self-efficacy. The interventions from this study can serve as examples for other schools

The role of acquaintanceship in the perception of child behaviour problems

The role of acquaintanceship with the child on reports of child behaviour by different informants was examined within the framework of a general theory of personality judgment. Mothers of referred children and group-care workers rated videotaped behaviour samples of a well known and an unknown child in the clinic. Independent observers also rated the videotapes. In line with the acquaintanceship hypothesis, mothers were found to perceive more behaviour problems than independent observers when rating well known children but not unknown children. Contrary to the acquaintanceship hypothesis, however, the group-care workers in our study reported more behaviour problems than the other informants regardless of their acquaintance with the children. The clinical and methodological implications of these findings are discussed

Economic costs of chronic disease through lost productive life years (PLYs) among Australians aged 45–64 years from 2015 to 2030:Results from a microsimulation model

Objectives: To project the number of older workers with lost productive life years (PLYs) due to chronic disease and resultant lost income; and lost taxes and increased welfare payments from 2015 to 2030. Design, setting and participants: Using a microsimulation model, Health&WealthMOD2030, the costs of chronic disease in Australians aged 45–64 were projected to 2030. The model integrates household survey data from the Australian Bureau of Statistics Surveys of Disability, Ageing and Carers (SDACs) 2003 and 2009, output from long-standing microsimulation models (STINMOD (Static Incomes Model) and APPSIM (Australian Population and Policy Simulation Model)) used by various government departments, population and labour force growth data from Treasury, and disease trends data from the Australian Burden of Disease and Injury Study (2003). Respondents aged 45–64 years in the SDACs 2003 and 2009 formed the base population. Main outcome measures: Lost PLYs due to chronic disease; resultant lost income, lost taxes and increased welfare payments in 2015, 2020, 2025 and 2030. Results: We projected 380 000 (6.4%) people aged 45–64 years with lost PLYs in 2015, increasing to 462 000 (6.5%) in 2030—a 22% increase in absolute numbers. Those with lost PLYs experience the largest reduction in income than any other group in each year compared to those employed full time without a chronic disease, and this income gap widens over time. The total economic loss due to lost PLYs consisted of lost income modelled at $A12.6 billion in 2015, increasing to$A20.5 billion in 2030—a 62.7% increase. Additional costs to the government consisted of increased welfare payments at $A6.2 billion in 2015, increasing to$A7.3 billion in 2030—a 17.7% increase; and a loss of $A3.1 billion in taxes in 2015, increasing to$A4.7 billion in 2030—a growth of 51.6%. Conclusions: There is a need for greater investment in effective preventive health interventions which improve workers’ health and work capacity.Full Tex