Space network, definition

Chaotic dynamics are by definition aperiodic dynamics in deterministic systems with sensitive dependence on initial conditions. Although many refer to chaotic dynamics in Eq. (3), this does not conform to standard nonlinear dynamics terminology since such systems have a finite state space and must necessarily cycle. However, in Eq. (5), chaotic dynamics are possible and have been demonstrated numerically and analytically in some example networks [42, 46]. We have no way to predict whether any particular logical structure is capable of generating chaotic dynamics for some set of parameters. A necessary condition for chaotic dynamics is that there is a vertex that lies on at least two... 

Enforcing stoichiometric, capacity, and thermodynamic constraints simultaneously leads to the definition of a solution space that contains all feasible steady-state flux vectors. Within this set, one can find a particular steady-state metabolic flux vector that optimizes the network behavior toward achieving one or more goals (e g., maximize or minimize the production of certain metabolites). Mathematically speaking, an objective function has to be defined that needs to be minimized or maximized subject to the imposed constraints. Such optimization problems are typically solved via linear programming techniques. 

For Markovian networks (with a discrete state space), there is a convenient definition of stabUity a stable network is one that is a positive recurrent Markov chain. This definition may be extended to more general networks, but doing this formally would require a mathematical digression. For a detailed discussion of stability, see Meyn and Tweedie (1993). 

The internal symmetry of a crystal structure is described. The concepts of the unit cell and lattice are developed, leading naturally to a definition of symmetry elements and, hence, to the crystallographic space groups. The relevance of space groups and symmetry elements to the formation of the extended networks found in supramo-lecular chemistry is summarized. A discussion of common crystal packing modes follows, and the relevance of space group symmetry is discussed in this context. 

Sari and Kubat (2012) describe a model that provides an index of intervention designed to save maximum life within shortest term and with limited economic resources in case of an earthquake. In the first phase of the model, the definition of the vulnerability and calculations of the number and locations of people in danger are provided. The second phase of the process is the evaluation of the blockage risks of the roads within a network because of the collapsed buildings. Afterwards, predictions of the major routes that people use frequently to reach the city main road network and major destinations in the urban configuration are estimated with space syntax theory. The outputs of the model are the road risk and the index of intervention . Each value provides information for total risk assessment and intervention priorities against the earthquake risk. The model is applied to a case study from Istanbul, Turkey. 

---