65 research outputs found
Predicting the Distribution of Spiral Waves from Cell Properties in a Developmental-Path Model of Dictyostelium Pattern Formation
The slime mold Dictyostelium discoideum is one of the model systems of biological pattern formation. One of the most successful answers to the challenge of establishing a spiral wave pattern in a colony of homogeneously distributed D. discoideum cells has been the suggestion of a developmental path the cells follow (Lauzeral and coworkers). This is a well-defined change in properties each cell undergoes on a longer time scale than the typical dynamics of the cell. Here we show that this concept leads to an inhomogeneous and systematic spatial distribution of spiral waves, which can be predicted from the distribution of cells on the developmental path. We propose specific experiments for checking whether such systematics are also found in data and thus, indirectly, provide evidence of a developmental path
On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment
de Angelis T, Federico S, Ferrari G. On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment. Center for Mathematical Economics Working Papers. Vol 509. Bielefeld: Center for Mathematical Economics; 2014.This paper examines a Markovian model for the optimal irreversible investment
problem of a firm aiming at minimizing total expected costs of production. We model market
uncertainty and the cost of investment per unit of production capacity as two independent
one-dimensional regular diffusions, and we consider a general convex running cost function.
The optimization problem is set as a three-dimensional degenerate singular stochastic control
problem.
We provide the optimal control as the solution of a Skorohod reflection problem at a suitable
free-boundary surface. Such boundary arises from the analysis of a family of two-dimensional
parameter-dependent optimal stopping problems and it is characterized in terms of the family of
unique continuous solutions to parameter-dependent nonlinear integral equations of Fredholm
type
Advantages of Randomization in Coherent Quantum Dynamical Control
Control scenarios have been identified where the use of randomized design may
substantially improve the performance of dynamical decoupling methods [L. F.
Santos and L. Viola, Phys. Rev. Lett. {\bf 97}, 150501 (2006)]. Here, by
focusing on the suppression of internal unwanted interactions in closed quantum
systems, we review and further elaborate on the advantages of randomization at
long evolution times. By way of illustration, special emphasis is devoted to
isolated Heisenberg-coupled chains of spin-1/2 particles. In particular, for
nearest-neighbor interactions, two types of decoupling cycles are contrasted:
inefficient averaging, whereby the number of control actions increases
exponentially with the system size, and efficient averaging associated to a
fixed-size control group. The latter allows for analytical and numerical
studies of efficient decoupling schemes created by exploiting and merging
together randomization and deterministic strategies, such as symmetrization,
concatenation, and cyclic permutations. Notably, sequences capable to remove
interactions up to third order are explicitly constructed. The consequences of
faulty controls are also analyzed.Comment: 27 pages, 7 figure
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