Quantum Time

We give a consistent quantum description of time, based on Page and Wootters' conditional probabilities mechanism, that overcomes the criticisms that were raised against similar previous proposals. In particular we show how the model allows to reproduce the correct statistics of sequential measurements performed on a system at different times.Comment: Final version accepted for publication on Phys. Rev.

On the performance of a hybrid genetic algorithm in dynamic environments

The ability to track the optimum of dynamic environments is important in many practical applications. In this paper, the capability of a hybrid genetic algorithm (HGA) to track the optimum in some dynamic environments is investigated for different functional dimensions, update frequencies, and displacement strengths in different types of dynamic environments. Experimental results are reported by using the HGA and some other existing evolutionary algorithms in the literature. The results show that the HGA has better capability to track the dynamic optimum than some other existing algorithms.Comment: This paper has been submitted to Applied Mathematics and Computation on May 22, 2012 Revised version has been submitted to Applied Mathematics and Computation on March 1, 201

Embedded model discrepancy: A case study of Zika modeling

Mathematical models of epidemiological systems enable investigation of and predictions about potential disease outbreaks. However, commonly used models are often highly simplified representations of incredibly complex systems. Because of these simplifications, the model output, of say new cases of a disease over time, or when an epidemic will occur, may be inconsistent with available data. In this case, we must improve the model, especially if we plan to make decisions based on it that could affect human health and safety, but direct improvements are often beyond our reach. In this work, we explore this problem through a case study of the Zika outbreak in Brazil in 2016. We propose an embedded discrepancy operator---a modification to the model equations that requires modest information about the system and is calibrated by all relevant data. We show that the new enriched model demonstrates greatly increased consistency with real data. Moreover, the method is general enough to easily apply to many other mathematical models in epidemiology.Comment: 9 pages, 7 figure

Black holes as mirrors: quantum information in random subsystems

We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the "half-way" point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.Comment: 18 pages, 2 figures. (v2): discussion of decoding complexity clarifie