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   Liu, Yuan; Zhou, Jiawang; Wasielewski, Michael R.; Xing, Hang; Mirkin, Chad A. (October 2018, Chemical Communications)

   Four distinct fluorescent states are achieved in a single Weak-Link Approach (WLA) construct bearing pyrene and tetraphenylethene moieties. The fluorescence of the compound in both the solution and solid phases can be manipulated through reversible coordination chemistry at the Pt II center. 

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   null (Ed.)

   Traditional state estimation (SE) methods that are based on nonlinear minimization of the sum of localized measurement error functionals are known to suffer from nonconvergence and large residual errors. In this paper we propose an equivalent circuit formulation (ECF)-based SE approach that inherently considers the complete network topology and associated physical constraints. We analyze the mathematical differences between the two approaches and show that our approach produces a linear state-estimator that is mathematically a quadratic programming (QP) problem with closed-form solution. Furthermore, this formulation imposes additional topology-based constraints that provably shrink the feasible region and promote convergence to a more physically meaningful solution. From a probabilistic viewpoint, we show that our method applies prior knowledge into the estimate, thus converging to a more physics-based estimate than the traditional observation-driven maximum likelihood estimator (MLE). Importantly, incorporation of the entire system topology and underlying physics, while being linear, makes ECF-based SE advantageous for large-scale systems. 

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4. Learning from Neighbours about a Changing State

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   Abstract Agents learn about a changing state using private signals and their neighbours’ past estimates of the state. We present a model in which Bayesian agents in equilibrium use neighbours’ estimates simply by taking weighted sums with time-invariant weights. The dynamics thus parallel those of the tractable DeGroot model of learning in networks, but arise as an equilibrium outcome rather than a behavioural assumption. We examine whether information aggregation is nearly optimal as neighbourhoods grow large. A key condition for this is signal diversity: each individual’s neighbours have private signals that not only contain independent information, but also have sufficiently different distributions. Without signal diversity—e.g. if private signals are i.i.d.—learning is suboptimal in all networks and highly inefficient in some. Turning to social influence, we find it is much more sensitive to one’s signal quality than to one’s number of neighbours, in contrast to standard models with exogenous updating rules. 

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