The synchronization of chaotic systems

(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

Nonlinear multivariate analysis of neurophysiological signals

https://www.dcs.warwick.ac.uk/~feng/papers/Analyzing%20multiple%20nonlinear%20time%20series.pdf

Analyzing multiple nonlinear time series with extended Granger causality

Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.

/pdf/kernel-method-for-nonlinear-granger-causality-3xyzdpzkmk.pdf

Kernel method for nonlinear granger causality.

1. History of Optics.- 2. The Main Areas of Optics.- 3. Fundamentals of Wave Optics.- 4. Coherence.- 5. Multiple-Beam Interference.- 6. Speckles.- 7. Holography.- 8. Interferometry.- 9. Fourier Optics.- 10. The Laser.- 11. Ultrafast Optics.- 12. Nonlinear Optics.- 13. Fiber Optics.- A. The Fourier Transform.- A.1 One-Dimensional Fourier Transform.- A.2 Two-Dimensional Fourier Transform.- A.3 Convolution and Autocorrelation.- A.4 Properties of the Fourier Transform.- A.5 Selected Functions and Their Fourier Transforms.- Problems.- B. Solutions of Problems.- References.

Coherent Optics: Fundamentals and Applications

A method is presented for detecting weak coupling between (chaotic) dynamical systems below the threshold of (generalized) synchronization. This approach is based on reconstruction of mixed states consisting of delayed samples taken from simultaneously measured time series of both systems.

Mixed state analysis of multivariate time series

Optics has developed from human sight. Sight is one of our most important faculties, whereby we interact with nature and gain knowledge of the physical world surrounding us. Therefore optical phenomena have attracted attention since ancient times.

History of Optics

When discussing the coherence properties of light, we mainly compared two light waves with each other. In the course of deriving the condition for spatial coherence, we in fact considered light sources comprising many independent point sources. Their waves, however, were incoherently summed by adding the intensities. We now consider phenomena occurring when many mutually coherent waves are superimposed: multiple-beam interference. To them belong Newton’s rings, the color of thin films, Bragg reflection, and also the principle underlying interference filters. An important instrument, whose operation is based on multiple superposition of light waves, is the Fabry-Perot interferometer.

Multiple-Beam Interference

Abstract Background  As a national effort to better understand the current pandemic, three cohorts collect sociodemographic and clinical data from coronavirus disease 2019 (COVID-19) patients from different target populations within the German National Pandemic Cohort Network (NAPKON). Furthermore, the German Corona Consensus Dataset (GECCO) was introduced as a harmonized basic information model for COVID-19 patients in clinical routine. To compare the cohort data with other GECCO-based studies, data items are mapped to GECCO. As mapping from one information model to another is complex, an additional consistency evaluation of the mapped items is recommended to detect possible mapping issues or source data inconsistencies. Objectives  The goal of this work is to assure high consistency of research data mapped to the GECCO data model. In particular, it aims at identifying contradictions within interdependent GECCO data items of the German national COVID-19 cohorts to allow investigation of possible reasons for identified contradictions. We furthermore aim at enabling other researchers to easily perform data quality evaluation on GECCO-based datasets and adapt to similar data models. Methods  All suitable data items from each of the three NAPKON cohorts are mapped to the GECCO items. A consistency assessment tool (dqGecco) is implemented, following the design of an existing quality assessment framework, retaining their - defined consistency taxonomies, including logical and empirical contradictions. Results of the assessment are verified independently on the primary data source. Results  Our consistency assessment tool helped in correcting the mapping procedure and reveals remaining contradictory value combinations within COVID-19 symptoms, vital signs, and COVID-19 severity. Consistency rates differ between the different indicators and cohorts ranging from 95.84% up to 100%. Conclusion  An efficient and portable tool capable of discovering inconsistencies in the COVID-19 domain has been developed and applied to three different cohorts. As the GECCO dataset is employed in different platforms and studies, the tool can be directly applied there or adapted to similar information models.

/pdf/consistency-as-a-data-quality-measure-for-german-corona-11urczte.pdf

Martin Wiesenfeldt

Papers

Coherent Optics: Fundamentals and Applications

Mixed state analysis of multivariate time series

History of Optics

Multiple-Beam Interference

Consistency as a Data Quality Measure for German Corona Consensus Items Mapped from National Pandemic Cohort Network Data Collections