New Results - Temporal Logic Modeling of Dynamical Behaviors: First-Order Patterns and Solvers

1.1. Temporal Logic FO-LTL(Rlin) . . . . . . . . . . . . . . . . . . . . 12 1.1.1. Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.1.2. Semantics: Validity Domains of Free Variables . . . . . . . . 13 1.1.3. Generic Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.1.4. Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.1.5. Trace Simplification . . . . . . . . . . . . . . . . . . . . . . . . 17 1.1.6. Continuous Satisfaction Degree in [0,1] . . . . . . . . . . . . 17 1.2. Formula Patterns and Dedicated Solvers . . . . . . . . . . . . . . 19 1.2.1. Temporal Operator Patterns . . . . . . . . . . . . . . . . . . . 19 1.2.2. Thresholds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.2.3. Amplitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.2.4. Local Maxima . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.2.5. Monotony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.2.6. Peaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.2.7. Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.3. Study Case: Coupled Model of the Cell Cycle and the Circadian Clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.3.1. Circadian Molecular Clock Model . . . . . . . . . . . . . . . 29 1.3.2. Cell Cycle Model . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.3.3. Coupling of the Cell Cycle with the Circadian Clock through WEE1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.3.4. Successive Peak-to-Peak Distances . . . . . . . . . . . . . . . 32 1.3.5. Oscillations with Precise Phaseshifts and Imprecise Amplitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.3.6. Filtering out Damped Oscillations . . . . . . . . . . . . . . . 35 1.3.7. Phase Constraints . . . . . . . . . . . . . . . . . . . . . . . . . 35

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