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EN
A model to calculate the optimal work modes of train locomotives while serving train flows is proposed. The model is a further development of the dynamic transportation problem. Parameters of train movement and locomotive utilization are published. Both locomotive turnover and train schedules are produced. Useful utilization of locomotives increases from 70% to 90–95%. This allows the reduction of several thousands of train locomotives.
2
Content available remote Flexible and Robust Patterning by Centralized Gene Networks
EN
We investigate the possibility of programming arbitrarily complex space-time patterns, and transitions between such patterns, by gene networks. We consider networks with two types of nodes. The v-nodes, called centers, are hyperconnected and interact one to another via u-nodes, called satellites. This centralized architecture realizes a bow-tie scheme and possesses interesting properties. Namely, this organization creates feedback loops that are capable to generate any prescribed patterning dynamics, chaotic or periodic, or stabilize a number of prescribed equilibrium states. We show that activation or silencing of a node can sharply switch the network dynamics, even if the activated or silenced node is weakly connected. Centralized networks can keep their flexibility, and still be protected against environmental noises. Finding an optimized network that is both robust and flexible is a computationally hard problem in general, but it becomes feasible when the number of satellites is large. In theoretical biology, this class of models can be used to implement the Driesch-Wolpert program, allowing to go from morphogen gradients to multicellular organisms.
3
Content available remote Merging and interacting wave fronts for reaction - diffusion equations
EN
In this paper the merging and interacting kink-type solution for general reaction diffusion equations are considered. Both the analytical and numerical investigations are presented. In particular, the existence of the complicated merging, elliptic and hyperbolic fronts in two dimensions is shown.
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