We consider a special form of state discrimination in which after the measurement we are given additional information that may help us identify the state. This task plays a central role in the analysis of quantum cryptographic protocols in the noisy-storage model, where the identity of the state corresponds to a certain bit string, and the additional information is typically a choice of encoding that is initially unknown to the cheating party. We first provide simple optimality conditions for measurements for any such problem and show upper and lower bounds on the success probability. For a certain class of problems, we furthermore provide tight bounds on how useful postmeasurement information can be. In particular, we show that for this class finding the optimal measurement for the task of state discrimination with postmeasurement information does in fact reduce to solving a different problem of state discrimination without such information. However, we show that for the corresponding classical state discrimination problems with postmeasurement information such a reduction is impossible, by relating the success probability to the violation of Bell inequalities. This suggests the usefulness of postmeasurement information as another feature that distinguishes the classical from a quantum world.

Clustering in wireless sensor networks plays a vital role in solving energy and scalability issues. Although multiple deployment structures and cluster shapes have been implemented, they sometimes fail to produce the expected outcomes owing to different geographical area shapes. This paper proposes a clustering algorithm with a complex deployment structure called radial-shaped clustering (RSC). The deployment structure is divided into multiple virtual concentric rings, and each ring is further divided into sectors called clusters. The node closest to the midpoint of each sector is selected as the cluster head. Each sector’s data are aggregated and forwarded to the sink node through angular inclination routing. We experimented and compared the proposed RSC performance against that of the existing fan-shaped clustering algorithm. Experimental results reveal that RSC outperforms the existing algorithm in scalability and network lifetime for large-scale sensor deployments.

Quantifying the speed of linguistic change is challenging because the historical evolution of languages is sparsely documented. Consequently, traditional methods rely on phylogenetic reconstruction. Here, we propose a model-based approach to the problem through the analysis of language change as a stochastic process combining vertical descent, spatial interactions, and mutations in both dimensions. A notion of linguistic temperature emerges naturally from this analysis as a dimensionless measure of the propensity of a linguistic feature to undergo change. We demonstrate how temperatures of linguistic features can be inferred from their present-day geospatial distributions, without recourse to information about their phylogenies. Thus, the evolutionary dynamics of language, operating across thousands of years, leave a measurable geospatial signature. This signature licenses inferences about the historical evolution of languages even in the absence of longitudinal data.

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