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Å. Pleijel (1956) has proved that in the case of the Laplacian with Dirichlet condition, the equality in the Courant nodal theorem (Courant sharp situation) can only be true for a finite number of eigenvalues when the dimension is ≥ 2. Recently Polterovich extended the result to the Neumann problem in two dimensions in the case when the boundary is piecewise analytic. A question coming from the th
Controllers with a diagonal-plus-low-rank structure constitute a scalable class of controllers for multi-agent systems. Previous research has shown that diagonal-plus-low-rank control laws appear as the optimal solution to a class of multi-agent H2 coordination problems, which arise in the control of wind farms. In this paper we show that this result extends to the case where the information excha
Closed-loop positivity of feedback interconnections of positive monotone nonlinear systems is investigated. It is shown that an instantaneous gain condition on the open-loop systems which implies feedback well-posedness also guarantees feedback positivity. Furthermore, the notion of integral linear constraints (ILC) is utilised as a tool to characterise uncertainty in positive feedback systems. Ro
This essay presents a speculative work on making distinctions among different equally valid types of research relevance. The work is innovative not only because it departs from the extant monistic perspectives, where only narrow forms of relevance are acknowledged, towards a pluralist perspective, but also because it recognizes and accounts for the plurality in the perceptions of relevance among d
Quadratic optimization subject to linear constraints is a fundamental building-block in many other branches of applied mathematics. However, for large-scale systems, where a common global objective function is neither naturally defined nor easily computable, it is natural to view economic equilibrium theory as an alternative approach to design and analysis. Stability and robustness of equilibria c
This study offers a method for empirically testing theories operationalized in the form of multivariate statistical models. An innovation of the method is that it distinguishes testing into three separate forms, “effect testing,” “prediction testing,” and “theory testing,”where statistical significance plays a separate role in each one. In another innovation, the researcher specifies not only his
Stable positive linear time-invariant autonomous systems admit diagonal quadratic Lyapunov functions. Such a property is known to be useful in distributed and scalable control of positive systems. In this paper, it is established that the same holds for exponentially stable positive discrete-time and continuous-time linear time-varying systems.
We consider a class of structured covariance completion problems which aim to complete partially known sample statistics in a way that is consistent with the underlying linear dynamics. The statistics of stochastic inputs are unknown and sought to explain the given correlations. Such inverse problems admit many solutions for the forcing correlations, but can be interpreted as an optimal low-rank a
Can local communities on the margins of society be charged with the responsibility of maintaining their own social order? What type of law (if any) can bring social order to these communities? Using semi-structured interviews with social workers, police officers, lawyers and other professionals familiar with the Tottenham riots, this chapter offers an inside view into what community means in a runCan local communities on the margins of society be charged with the responsibility of maintaining their own social order? What type of law (if any) can bring social order to these communities? Using semi-structured interviews with social workers, police officers, lawyers and other professionals familiar with the Tottenham riots, this chapter offers an inside view into what community means in a run
