Diffusion Processes with Hidden States from ... - FU Berlin, FB MI

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A Appendixthe ideal of continuous accuracy in measurement and observation.The huge amount of observation data that Brahe has accumulated were published later by Keplerin the so called ”Rudolphine Tables”, named after Emperor Rudolf II. This position catalog ofplanets and fixed stars is forming the basis on which both Kepler’s model of planetary motion andIsaac Newton’s cosmological theory ground.Johannes Kepler (also: Ioannes Keplerus; * 27th December 1571 inWeil der Stadt; † 15th November 1630 in Regensburg) inherited thishuge amount of data, and in contrary to Brahe who only had the aimto accumulate more and more precise data, Kepler had the aim togive these data a sense. Here at last comes the role of the theoretician.Kepler who was a mathematician, astronomer and natural philosopherwas such a theoretician, and in contrary to Brahe also believed in thetruth of the heliocentric system.Kepler had the data from Brahe but the difficulty was to give sense tothem, and it took him nearly twenty years of trial and examination tofind his three rules of planetary motion around the sun.Johannes KeplerThe difficulty was the fact that the orbiting paths of the planets areobserved from the earth, while the earth itself is orbiting around thesun. This can lead to the apparently queer observation that the planetsare performing loops. By taking the position data of mars and the sun as basis, and withoutknowing the correct orbit form of mars, Kepler inversely derived the positions of the earth andfrom this the orbit of mars.It was the notion of the force action at a distance (”Anima Motrix”)together with the examination of Brahe’s data which brought Keplerto the discovery that the mars orbit is not a circle but an ellipse. Thisis not obvious since the elliptic paths of the big planets are nearly circular.That he anyway came to this insight is also due to Tycho Braheand the extraordinary accuracy of his data which allowed a distinctionbetween a circular and an elliptic path.Finally Kepler concluded that the planetary orbits are of elliptic formwhile the sun is in one of the two foci (1st Kepler law of planetarymotion). The second proposition of his model reveals that a line joininga planet and the sun sweeps out equal areas during equal intervalsof time (2nd Kepler law of planetary motion). Kepler published thesetwo laws in the year 1609 in his work ”Astronomia Nova”.Later Newton formulated in his work ”Philosophiae Naturalis PrincipiaMathematica” (1687) the universal theory of classical mechanicsthat combines the mechanical phenomena of normal day life withthe laws of gravitation from which also at least the laws of Kepler are following.Isaac Newton (Portraitby Godfrey Kneller from1689)100
A.2 Important Papers on the Rhodopsin-Transducin ProcessA.2 Important Papers on the Rhodopsin-Transducin ProcessThere are numerous papers, which are dealing with the analysis of the rhodopsin-transducin visualtransduction pathway (R-T-system):1. One of the early works on this topic is served by Michael J. Saxton and John C. Owicki in apaper from 1989 ([31]). Saxton and Owicki are investigating the question, how the concentrationof the numerous proteins affect the reaction rate of the rhodopsin-transducin-system.They are setting up a steady-state-diffusion model with concentration dependent diffusioncoefficients. They do this with the assumption of lateral diffusing transducin proteins on themembrane, and finally point out that there exists a maximum (optimal) reaction rate, andalong the way an optimal concentration. This conclusion grounds on the fact that on the onehand the reaction rate increases by the law of mass action, and on the other hand a higherconcentration would decrease the rate due to the decrease of the diffusion coefficients.2. A work from 1991 is [19], in which the authors deliver a model of transducin activationfrom its partial reactions, and solve the kinetic equations of the model both numerically, andfor small photo-activation, analytically.3. One year later, in the year 1992, a paper was published [6], in which the authors investigatethe activation of transducin by photo-excited rhodopsin in terms of the Michaelis-Mentenenzymologyand additionally by experiments.4. Lamb published his findings in a paper from 1996 [23], and in this work refers about asimulation of the diffusional interaction of the proteins by Monte Carlo techniques. Hisconclusion is that there exists a linear activation of many transducins by only one activatedrhodopsin.5. [15] is an experimental work from 1998, giving an account on the observation of transducinactivation with spatially and time resolved surface plasmon resonance.6. [11] deliver Master equation simulations of the diffusional protein interaction on a rectangular1µm 2 model membrane divided into 15 × 15 cells and with mono- and biomolecularreactions within cells and diffusional transitions between (neighboring) cells.101
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Diploma ThesisDepartment for Theore
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AbstractAnomalous diffusion is a ub
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Zusammenfassung 1Anomale Diffusion
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Contents1 Motivation 12 Visual Tran
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List of Figures2.1 Anatomy of the e
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1 Motivation„NEC FASCES, NEC OPES
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Theoretically we profit from enormo
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2 Visual Transduction”The eye owe
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(a)(b)(c)Figure 2.3: (a) The anatom
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effect of generating the photorecep
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3 Theory”The theory is the net, t
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3.2 Markov Chains, Markov Processes
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3.3 Hidden Markov ModelsP[X(t + τ)
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3.4 Maximum Likelihood Principlewit
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3.5 Optimization3.5 OptimizationAcc
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3.7 Baum-Welch-AlgorithmAlgorithm 3
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3.8 Two Approaches on Stochastic Sy
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3.9 DiffusionConsider a basin fille
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3.9 Diffusion169].Rearranging (3.34
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3.9 Diffusionwith τ = t −t ′ .
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3.9 DiffusionD = 2k2 B T 2σ . (3.4
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3.10 Hidden Markov Models with Stoc
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3.11 Hidden Markov Model - Vector A
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3.11 Hidden Markov Model - Vector A
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3.12 Artificial Test Examples for H
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Page 69 and 70: 3.13 Global Optimization Methods3.1
Page 71 and 72: 3.13 Global Optimization MethodsEve
Page 73 and 74: 4 Fluorescence Tracking Experiments
Page 75 and 76: 4.2 Fluorescence SpectroscopyAfter
Page 77 and 78: 4.3 Single Molecule Tracking via Wi
Page 79 and 80: 4.4 Total Internal Reflection Fluor
Page 81 and 82: 4.4 Total Internal Reflection Fluor
Page 83 and 84: 4.6 The expected range for the Tran
Page 85 and 86: 5 Modeling of the Experiment”The
Page 87 and 88: 5.1 Experimental Data(a)(b)(c)(d)Fi
Page 89 and 90: 5.2 Model Ansatz and Estimation of
Page 91 and 92: 5.2 Model Ansatz and Estimation of
Page 93 and 94: 5.3 Testing the Modelalgorithm was
Page 95 and 96: 5.5 Estimation of the Noise Intensi
Page 97 and 98: 5.6 Estimation on the Basis of Diff
Page 103 and 104: 6 Conclusion and OutlookThe main as
Page 105 and 106: 7 Bibliography[1] R. C. Aster, B. B
Page 107 and 108: [36] C. U. M. Smith: Elements of Mo
Page 109 and 110: Index11-cis retinal isomer, 87TM se
Page 111: A AppendixA.1 From Copernicus to Ne
Page 115 and 116: A.3 Probability TheoryDefinition A.
Page 117 and 118: A.4 Definitions for OptimizationDef
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Page 121 and 122: A.7 The Fluctuation-Dissipation-The
Page 123 and 124: A.7 The Fluctuation-Dissipation-The
Page 125 and 126: A.8 Kramers-Moyal Forward Expansion
Page 127 and 128: A.9 Deriving the Fokker-Planck Equa
Page 129 and 130: A.9 Deriving the Fokker-Planck Equa
Page 131 and 132: DanksagungenIch möchte folgenden M
Page 133: AffirmationHereby I, Arash Azhand,
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