A state-dependent lifetime process of individuals subject to external perturbations

1980 ◽  
Vol 17 (4) ◽  
pp. 922-938
Author(s):  
Wolfgang Mergenthaler
Keyword(s):  
Ionizing Radiation ◽  
State Space ◽  
Lifetime Distribution ◽  
The State ◽  
Time Dependent ◽  
Biological Cell ◽  
Regeneration Time ◽  
External Perturbations ◽  
State Dependent ◽  
The Mean

We consider an individual which ultimately dies or divides, and whose state is subject to drift and jumps caused by external perturbations. The mortality and division rates being state-dependent, the present paper deals with the time-dependent distribution of the individual's position in the state-space and with its lifetime distribution. The results are applied to a model of a biological cell which is exposed to ionizing radiation. Under certain conditions on the parameters of the type of perturbation one can show that the division probability decreases and the mean regeneration time increases with increasing frequency and ‘effect' of the perturbations.

A state-dependent lifetime process of individuals subject to external perturbations

1980 ◽  
Vol 17 (04) ◽  
pp. 922-938
Author(s):  
Wolfgang Mergenthaler
Keyword(s):  
Ionizing Radiation ◽  
State Space ◽  
Lifetime Distribution ◽  
The State ◽  
Time Dependent ◽  
Biological Cell ◽  
Regeneration Time ◽  
External Perturbations ◽  
State Dependent ◽  
The Mean

We consider an individual which ultimately dies or divides, and whose state is subject to drift and jumps caused by external perturbations. The mortality and division rates being state-dependent, the present paper deals with the time-dependent distribution of the individual's position in the state-space and with its lifetime distribution. The results are applied to a model of a biological cell which is exposed to ionizing radiation. Under certain conditions on the parameters of the type of perturbation one can show that the division probability decreases and the mean regeneration time increases with increasing frequency and ‘effect' of the perturbations.

scholarly journals SOME FEATURES OF THE STATE-SPACE TRAJECTORIES FOLLOWED BY ROBUST ENTANGLED FOUR-QUBIT STATES DURING DECOHERENCE

2010 ◽  
Vol 08 (03) ◽  
pp. 505-515 ◽  
Author(s):  
A. P. MAJTEY ◽  
A. BORRAS ◽  
A. R. PLASTINO ◽  
M. CASAS ◽  
A. PLASTINO
Keyword(s):  
State Space ◽  
Recent Work ◽  
Mixed State ◽  
Pure State ◽  
The State ◽  
Time Dependent ◽  
Space Trajectories ◽  
Geometrical Features ◽  
Initial States ◽  
Qubit States

In a recent work (Borras et al., Phys. Rev. A79 (2009) 022108), we have determined, for various decoherence channels, four-qubit initial states exhibiting the most robust possible entanglement. Here, we explore some geometrical features of the trajectories in state space generated by the decoherence process, connecting the initially robust pure state with the completely decohered mixed state obtained at the end of the evolution. We characterize these trajectories by recourse to the distance between the concomitant time-dependent mixed state and different reference states.

New results on semi-explicit and almost explicit MPC algorithms

2017 ◽  
Vol 65 (4) ◽  
Author(s):  
Gregor Goebel ◽  
Frank Allgöwer
Keyword(s):  
Model Predictive Control ◽  
State Space ◽  
Predictive Control ◽  
Closed Loop ◽  
Space Dimension ◽  
The State ◽  
Online Optimization ◽  
Numerical Examples ◽  
State Dependent ◽  
Common Framework

AbstractNew results on a particular type of state-dependent parameterization for model predictive control (MPC) are presented. Based on such parameterizations efficient MPC algorithms can be formulated, which combine the advantages of explicit and online optimization-based MPC. The new results comprise an offline stability check for the parameterizations to decide if a closed-loop MPC scheme applying the parameterizations is asymptotically stabilizing. Second, a novel way of computing the parameterizations with improved scalability in the state space dimension is included. Furthermore, new results and simplifications of almost explicit MPC schemes based on univariate parameterizations are contributed. The results are presented in a common framework and are illustrated in numerical examples including an almost explicit controller for an eight-dimensional spring-damper system.

scholarly journals Existence and non-existence for time-dependent mean field games with strong aggregation

2021 ◽  
Author(s):  
Marco Cirant ◽  
Daria Ghilli
Keyword(s):  
Population Density ◽  
State Space ◽  
Time Horizon ◽  
Existence Of Solutions ◽  
Mean Field ◽  
The State ◽  
Time Dependent ◽  
Classical Solutions ◽  
Mean Field Games ◽  
Quadratic Mean

AbstractWe investigate the existence of classical solutions to second-order quadratic Mean-Field Games systems with local and strongly decreasing couplings of the form $$-\sigma m^\alpha $$ - σ m α ,$$\alpha \ge 2/N$$ α ≥ 2 / N , where m is the population density and N is the dimension of the state space. We prove the existence of solutions under the assumption that $$\sigma $$ σ is small enough. For large $$\sigma $$ σ , we show that existence may fail whenever the time horizon T is large.

Geometric description of time-dependent finite-dimensional mechanical systems

2020 ◽  
Vol 25 (11) ◽  
pp. 2050-2075
Author(s):  
Simon R. Eugster ◽  
Giuseppe Capobianco ◽  
Tom Winandy
Keyword(s):  
State Space ◽  
Degrees Of Freedom ◽  
Vector Fields ◽  
Mechanical Systems ◽  
Second Order ◽  
The State ◽  
Time Dependent ◽  
Finite Dimensional ◽  
Affine Bundle ◽  
Time Position

Using the non-standard geometric structure proposed by Loos, we present a coordinate-free formulation of the theory for time-dependent finite-dimensional mechanical systems with n degrees of freedom. The state space containing the system’s information on time, position and velocity is defined as a (2 n+1)-dimensional affine bundle over an ( n+1)-dimensional generalized space-time. The main goal is to present a geometric postulate that characterizes a second-order vector field whose integral curves describe the motions of a time-dependent finite-dimensional mechanical system. The core objects of the postulate are differential two-forms on the state space, called action forms, which are in a bijective relation with second-order vector fields. The requirements for a differential two-form to be an action form allow for a coordinate-free definition of non-potential forces, which may depend on time, position and velocity. Finally, we show that not only Lagrange’s equations but also Hamilton’s equations follow directly as mere coordinate representations of the same coordinate-free postulate.

Refining Mean-field Approximations by Dynamic State Truncation

2021 ◽  
Vol 5 (2) ◽  
pp. 1-30
Author(s):  
Francesca Randone ◽  
Luca Bortolussi ◽  
Mirco Tribastone
Keyword(s):  
State Space ◽  
Mean Field ◽  
Field Approximation ◽  
The State ◽  
Mean Field Approximation ◽  
Dynamic State ◽  
Field Equations ◽  
Mean Field Equations ◽  
The Mean ◽  
Mean Field Approximations

Mean-field models are an established method to analyze large stochastic systems with N interacting objects by means of simple deterministic equations that are asymptotically correct when N tends to infinity. For finite N, mean-field equations provide an approximation whose accuracy is model- and parameter-dependent. Recent research has focused on refining the approximation by computing suitable quantities associated with expansions of order $1/N$ and $1/N^2$ to the mean-field equation. In this paper we present a new method for refining mean-field approximations. It couples the master equation governing the evolution of the probability distribution of a truncation of the original state space with a mean-field approximation of a time-inhomogeneous population process that dynamically shifts the truncation across the whole state space. We provide a result of asymptotic correctness in the limit when the truncation covers the state space; for finite truncations, the equations give a correction of the mean-field approximation. We apply our method to examples from the literature to show that, even with modest truncations, it is effective in models that cannot be refined using existing techniques due to non-differentiable drifts, and that it can outperform the state of the art in challenging models that cause instability due orbit cycles in their mean-field equations.

MEAN-FIELD DYNAMICAL SEMIGROUPS ON C*-ALGEBRAS

1992 ◽  
Vol 04 (03) ◽  
pp. 383-424 ◽  
Author(s):  
N.G. DUFFIELD ◽  
R.F. WERNER
Keyword(s):  
State Space ◽  
Mean Field ◽  
Liapunov Function ◽  
The State ◽  
Mean Field Limit ◽  
Lattice Systems ◽  
C Algebra ◽  
C Algebras ◽  
Dynamical Semigroup ◽  
The Mean

We study a notion of the mean-field limit of a sequence of dynamical semigroups on the n-fold tensor products of a C*-algebra [Formula: see text] with itself. In analogy with the theory of semigroups on Banach spaces we give abstract conditions for the existence of these limits. These conditions are verified in the case of semigroups whose generators are determined by the successive resymmetrizations of a fixed operator, as well as generators which can be approximated by generators of this type. This includes the time evolutions of the mean-field versions of quantum lattice systems. In these cases the limiting dynamical semigroup is given by a continuous flow on the state space of [Formula: see text]. For a class of such flows we show stability by constructing a Liapunov function. We also give examples where the limiting evolution is given by a diffusion, rather than a flow on the state space of [Formula: see text].

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