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We consider estimating the magnitude of a monochromatic AC signal that couples to a two-level sensor. For any detection protocol, the precision achieved depends on the signal's frequency and can be quantified by the quantum Fisher information. To study limitations in broadband sensing, we introduce the integrated quantum Fisher information and derive inequality bounds that embody fundamental tradeoffs in any sensing protocol. These inequalities show that sensitivity in one frequency range must come at a cost of reduced sensitivity elsewhere. For many protocols, including those with small phase accumulation and those consisting of π-pulses, we find the integrated Fisher information scales linearly with T. We also find protocols with substantial phase accumulation can have integrated QFI that grows quadratically with T, which is optimal. These protocols may allow the very rapid detection of a signal with unknown frequency over a very wide bandwidth. 

Summary Cluster analysis has proved to be an invaluable tool for the exploratory and unsupervised analysis of high-dimensional datasets. Among methods for clustering, hierarchical approaches have enjoyed substantial popularity in genomics and other fields for their ability to simultaneously uncover multiple layers of clustering structure. A critical and challenging question in cluster analysis is whether the identified clusters represent important underlying structure or are artifacts of natural sampling variation. Few approaches have been proposed for addressing this problem in the context of hierarchical clustering, for which the problem is further complicated by the natural tree structure of the partition, and the multiplicity of tests required to parse the layers of nested clusters. In this article, we propose a Monte Carlo based approach for testing statistical significance in hierarchical clustering which addresses these issues. The approach is implemented as a sequential testing procedure guaranteeing control of the family-wise error rate. Theoretical justification is provided for our approach, and its power to detect true clustering structure is illustrated through several simulation studies and applications to two cancer gene expression datasets. 

Understanding the nucleon spin structure in the regime where the strong interaction becomes truly strong poses a challenge to both experiment and theory. At energy scales below the nucleon mass of about 1 GeV, the intense interaction among the quarks and gluons inside the nucleon makes them highly correlated. Their coherent behaviour causes the emergence of effective degrees of freedom, requiring the application of non-perturbative techniques such as chiral effective field theory. Here we present measurements of the neutron’s generalized spin polarizabilities that quantify the neutron’s spin precession under electromagnetic fields at very low energy-momentum transfer squared down to 0.035 GeV2. In this regime, chiral effective field theory calculations are expected to be applicable. Our data, however, show a strong discrepancy with these predictions, presenting a challenge to the current description of the neutron’s spin properties.