Enantiomorph-dependent probability distributions of origin-invariant phases

1984 ◽  
Vol 40 (6) ◽  
pp. 688-695
Author(s):  
W. M. G. F. Pontenagel ◽  
H. Krabbendam ◽  
J. J. L. Heinerman
Keyword(s):  
Probability Distributions ◽  
Dependent Probability

Generalizations of the elementary renewal theorem to distributions defined by concave recurrence relations

1977 ◽  
Vol 14 (3) ◽  
pp. 516-526
Author(s):  
W. Reh
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Probability Distributions ◽  
Branching Processes ◽  
General Procedure ◽  
Renewal Function ◽  
Renewal Theorem ◽  
Probability Generating Functions ◽  
Dependent Probability

The paper examines the renewal function associated with a sequence of probability distributions, which is defined by concave recurrence relations or by an even more general procedure. The elementary renewal theorem is generalized to such sequences. The results can be used to establish renewal theorems for first death in branching processes, if only the possibly generation dependent probability generating functions converge to a limit.

scholarly journals Postponing production exponentially enhances the molecular memory of a stochastic switch

2020 ◽  
Author(s):  
Pavol Bokes
Keyword(s):  
Probability Distributions ◽  
Protein Molecule ◽  
Toggle Switch ◽  
Feedback Systems ◽  
Qualitative Behaviour ◽  
Burst Frequency ◽  
Large Delay ◽  
Copy Numbers ◽  
Large Production ◽  
Dependent Probability

AbstractDelayed production can substantially alter the qualitative behaviour of feedback systems. Motivated by stochastic mechanisms in gene expression, we consider a protein molecule which is produced in randomly timed bursts, requires an exponentially distributed time to activate, and then partakes in positive regulation of its burst frequency. Asymptotically analysing the underlying master equation in the large-delay regime, we provide tractable approximations to time-dependent probability distributions of molecular copy numbers. Importantly, the presented analysis demonstrates that positive feedback systems with large production delays can constitute a stable toggle switch even if they operate with low copy numbers of active molecules.

scholarly journals Postponing production exponentially enhances the molecular memory of a stochastic switch

2021 ◽  
pp. 1-18
Author(s):  
PAVOL BOKES
Keyword(s):  
Probability Distributions ◽  
Protein Molecule ◽  
Toggle Switch ◽  
Feedback Systems ◽  
Qualitative Behaviour ◽  
Burst Frequency ◽  
Large Delay ◽  
Copy Numbers ◽  
Large Production ◽  
Dependent Probability

Delayed production can substantially alter the qualitative behaviour of feedback systems. Motivated by stochastic mechanisms in gene expression, we consider a protein molecule which is produced in randomly timed bursts, requires an exponentially distributed time to activate and then partakes in positive regulation of its burst frequency. Asymptotically analysing the underlying master equation in the large-delay regime, we provide tractable approximations to time-dependent probability distributions of molecular copy numbers. Importantly, the presented analysis demonstrates that positive feedback systems with large production delays can constitute a stable toggle switch even if they operate with low copy numbers of active molecules.

Generalizations of the elementary renewal theorem to distributions defined by concave recurrence relations

1977 ◽  
Vol 14 (03) ◽  
pp. 516-526
Author(s):  
W. Reh
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Probability Distributions ◽  
Branching Processes ◽  
General Procedure ◽  
Renewal Function ◽  
Renewal Theorem ◽  
Probability Generating Functions ◽  
Dependent Probability

The paper examines the renewal function associated with a sequence of probability distributions, which is defined by concave recurrence relations or by an even more general procedure. The elementary renewal theorem is generalized to such sequences. The results can be used to establish renewal theorems for first death in branching processes, if only the possibly generation dependent probability generating functions converge to a limit.

scholarly journals Probability Representation of Quantum Mechanics Where System States Are Identified with Probability Distributions

2020 ◽  
Vol 2 (1) ◽  
pp. 64-79 ◽  
Author(s):  
Vladimir Chernega ◽  
Olga Man'ko ◽  
Vladimir Man'ko
Keyword(s):  
Quantum Mechanics ◽  
Probability Distributions ◽  
Random Variables ◽  
Time Dependent ◽  
Continuous Variables ◽  
Probability Representation ◽  
Classical Statistics ◽  
Quantum Observables ◽  
System States ◽  
Dependent Probability

The probability representation of quantum mechanics where the system states are identified with fair probability distributions is reviewed for systems with continuous variables (the example of the oscillator) and discrete variables (the example of the qubit). The relation for the evolution of the probability distributions which determine quantum states with the Feynman path integral is found. The time-dependent phase of the wave function is related to the time-dependent probability distribution which determines the density matrix. The formal classical-like random variables associated with quantum observables for qubit systems are considered, and the connection of the statistics of the quantum observables with the classical statistics of the random variables is discussed.

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