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Register a new userRepeated measurements with unintended feedback: The Dutch new herring scandals
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Added by
Richard D. Gill
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
Authors
Richard D. Gill
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An econometric analysis of consumer research data which hit newspaper headlines in the Netherlands illustrates almost everything that can go wrong when statistical models are fit to the superficial characteristics of a data-set with no attention paid to the data generation mechanism. This paper is dedicated to Ornulf Borgan on the occasion of his virtual 65th birthday celebrations.
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In this paper the TileShuffle method is evaluated as a search method for candidate lncRNAs at 8q24.2. The method is run on three microarrays. Microarrays which all contained the same sample and repeated copies of tiled probes. This allows the coherence of the selection method within and between microarrays to be estimated by Monte Carlo simulations on the repeated probes.
We investigate the effect of conditional null measurements on a quantum system and find a rich variety of behaviors. Specifically, quantum dynamics with a time independent $H$ in a finite dimensional Hilbert space are considered with repeated strong null measurements of a specified state. We discuss four generic behaviors that emerge in these monitored systems. The first arises in systems without symmetry, along with their associated degeneracies in the energy spectrum, and hence in the absence of dark states as well. In this case, a unique final state can be found which is determined by the largest eigenvalue of the survival operator, the non-unitary operator encoding both the unitary evolution between measurements and the measurement itself. For a three-level system, this is similar to the well known shelving effect. Secondly, for systems with built-in symmetry and correspondingly a degenerate energy spectrum, the null measurements dynamically select the degenerate energy levels, while the non-degenerate levels are effectively wiped out. Thirdly, in the absence of dark states, and for specific choices of parameters, two or more eigenvalues of the survival operator match in magnitude, and this leads to an oscillatory behavior controlled by the measurement rate and not solely by the energy levels. Finally, when the control parameters are tuned, such that the eigenvalues of the survival operator all coalesce to zero, one has exceptional points that corresponds to situations that violate the null measurement condition, making the conditional measurement process impossible.
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