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

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A AppendixDefinition A.17 (Solution Space).We call the union of all solutions of an optimization problem its solution space S.X ∗ ⊆ S ⊆ X(A.1)Definition A.18 (Search Space).The search space G of an optimization problem is the set of all elements g which can beprocessed by the search operations.Definition A.19 (Genotype).The elements g ∈ G of the search space G of a given optimization problem are called thegenotypes.Definition A.20 (Gene).The distinguishable units of information in a genotype that encode the phenotypical propertiesare called genes.Definition A.21 (Search Operations).The search operations searchOp are used by optimization algorithms in order to explorethe search space G.106
A.4 Definitions for OptimizationDefinition A.22 (Genotype-Phenotype Mapping).The genotype-phenotype mapping (GPM) gpm : G ↦→ X is a left-total binary relation which mapsthe elements of the search space G to elements in the problem space X.∀g ∈ G ∃x ∈ X : gpm(g) = x (A.2)Definition A.23 (Optimization Problem).An optimization problem is defined by a fivetuple (X, F, G, Op, gpm) specifying the problemspace X, the objective functions F, the search space G, the set of search operations Op, andthe genotype-phenotype mapping gpm. In theory, such an optimization problem can always besolved if Op is complete and the gpm is surjective.Definition A.24 (Completeness).A set Op of search operations searchOp is complete if and only if every point g 1 in thesearch space G can be reached <strong>from</strong> every other point g 2 ∈ G by applying only operationssearchOp ∈ Op.Definition A.25 (Individual).An individual p is a tuple (p.g, p.x) of an element p.g in the search space G and the correspondingelement p.x = gpm(p.g) in the problem space X.Definition A.26 (Population).A population Pop is a list of individuals used during an optimization process.Pop ⊆ G × X : ∀p = (p.g, p.x) ∈ Pop ⇒ p.x = gpm(p.g)(A.3)107
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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 67 and 68: 3.12 Artificial Test Examples for H
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 and 112: A AppendixA.1 From Copernicus to Ne
Page 113 and 114: A.2 Important Papers on the Rhodops
Page 115 and 116: A.3 Probability TheoryDefinition A.
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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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Diffusion Processes with Hidden States from ... - FU Berlin, FB MI

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