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Universal oscillations in counting statistics.

ABSTRACT: Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the correlations within a given noise source and its interaction with the environment, but they are often difficult to measure. Here we report measurements of the transient cumulants n(m) of the number n of passed charges to very high orders (up to m = 15) for electron transport through a quantum dot. For large m, the cumulants display striking oscillations as functions of measurement time with magnitudes that grow factorially with m. Using mathematical properties of high-order derivatives in the complex plane we show that the oscillations of the cumulants in fact constitute a universal phenomenon, appearing as functions of almost any parameter, including time in the transient regime. These ubiquitous oscillations and the factorial growth are system-independent and our theory provides a unified interpretation of previous theoretical studies of high-order cumulants as well as our new experimental data.

SUBMITTER: Flindt C

PROVIDER: S-EPMC2700917 | biostudies-literature | 2009 Jun

REPOSITORIES: biostudies-literature

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Universal oscillations in counting statistics.

Flindt C C Fricke C C Hohls F F Novotny T T Netocny K K Brandes T T Haug R J RJ

Proceedings of the National Academy of Sciences of the United States of America 20090610 25

Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the correlations within a given noise source and its interaction with the environment, but they are often difficult to measure. Here we report measurements of the transient cumulants n(m) of the number n of passed charges to very high orders (up to m = 15) for electron ...[more]

PMID: 19515823

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Project description:Magnetoencephalography and electroencephalography (MEG, EEG) are essential techniques for studying distributed signal dynamics in the human brain. In particular, the functional role of neural oscillations remains to be clarified. For that reason, imaging methods need to identify distinct brain regions that concurrently generate oscillatory activity, with adequate separation in space and time. Yet, spatial smearing and inhomogeneous signal-to-noise are challenging factors to source reconstruction from external sensor data. The detection of weak sources in the presence of stronger regional activity nearby is a typical complication of MEG/EEG source imaging. We propose a novel, hypothesis-driven source reconstruction approach to address these methodological challenges. The imaging with embedded statistics (iES) method is a subspace scanning technique that constrains the mapping problem to the actual experimental design. A major benefit is that, regardless of signal strength, the contributions from all oscillatory sources, which activity is consistent with the tested hypothesis, are equalized in the statistical maps produced. We present extensive evaluations of iES on group MEG data, for mapping 1) induced oscillations using experimental contrasts, 2) ongoing narrow-band oscillations in the resting-state, 3) co-modulation of brain-wide oscillatory power with a seed region, and 4) co-modulation of oscillatory power with peripheral signals (pupil dilation). Along the way, we demonstrate several advantages of iES over standard source imaging approaches. These include the detection of oscillatory coupling without rejection of zero-phase coupling, and detection of ongoing oscillations in deeper brain regions, where signal-to-noise conditions are unfavorable. We also show that iES provides a separate evaluation of oscillatory synchronization and desynchronization in experimental contrasts, which has important statistical advantages. The flexibility of iES allows it to be adjusted to many experimental questions in systems neuroscience.

Dataset Information

Universal oscillations in counting statistics.

Publications

Universal oscillations in counting statistics.

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