5,385 research outputs found
The SIC Question: History and State of Play
Recent years have seen significant advances in the study of symmetric
informationally complete (SIC) quantum measurements, also known as maximal sets
of complex equiangular lines. Previously, the published record contained
solutions up to dimension 67, and was with high confidence complete up through
dimension 50. Computer calculations have now furnished solutions in all
dimensions up to 151, and in several cases beyond that, as large as dimension
844. These new solutions exhibit an additional type of symmetry beyond the
basic definition of a SIC, and so verify a conjecture of Zauner in many new
cases. The solutions in dimensions 68 through 121 were obtained by Andrew
Scott, and his catalogue of distinct solutions is, with high confidence,
complete up to dimension 90. Additional results in dimensions 122 through 151
were calculated by the authors using Scott's code. We recap the history of the
problem, outline how the numerical searches were done, and pose some
conjectures on how the search technique could be improved. In order to
facilitate communication across disciplinary boundaries, we also present a
comprehensive bibliography of SIC research.Comment: 16 pages, 1 figure, many references; v3: updating bibliography,
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Toward bio-inspired information processing with networks of nano-scale switching elements
Unconventional computing explores multi-scale platforms connecting
molecular-scale devices into networks for the development of scalable
neuromorphic architectures, often based on new materials and components with
new functionalities. We review some work investigating the functionalities of
locally connected networks of different types of switching elements as
computational substrates. In particular, we discuss reservoir computing with
networks of nonlinear nanoscale components. In usual neuromorphic paradigms,
the network synaptic weights are adjusted as a result of a training/learning
process. In reservoir computing, the non-linear network acts as a dynamical
system mixing and spreading the input signals over a large state space, and
only a readout layer is trained. We illustrate the most important concepts with
a few examples, featuring memristor networks with time-dependent and history
dependent resistances
The Quality-Quantity Trade-off in the Principal-Agent Framework
This paper uses the principal-agent theory to analytically investigate the optimal incentive-based compensation contract that a processor should offer to a grower performing efforts in quantity and quality. In this process, we contribute to the substantive literature on multi-task principal-agent models by analyzing the quality-quantity trade-off and studying the implications of such a relationship in the principal-agent framework. One striking result of these effects is that, under appropriate incentive-based grower’s compensation, the processor may encourage grower’s effort in quality without crowding out grower’s effort in quantity.quality, quantity, trade-off, incentive contract, principal-agent framework, uncertainty, Agribusiness, Agricultural and Food Policy, D86,
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