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The dynamic behavior of the standard Cellular Neural Network (CNN) was studied via explicit solutions of the CNN vector state equations for certain piecewise linear domains Ω. The concepts of Ω-globally attractive domain, Ω-globally attractive equilibrium point, and Ω-globally expelling domain for the CNN state equations are presented. The terminology "Ω-global" indicates that the property is global relative to a domain Ω. It is shown that every "saturated domain" D (i.e. for every vector X∈ D, each corresponding component of X has the same sign as all others and its absolute value is greater than or equal to 1), is either Ω-globally attractive or Ω-globally expelling. Attractive equilibrium points in another special domain were also studied. Sufficient conditions for convergence to such equilibria are given, along with concrete new computer simulation examples which demonstrate this theory. Finally, several definitions and simulation results are given to explicate the complex dynamical relationships which were observed between initial states in the linear domain Ω (0) (i.e. every vector X∈Ω(0) has the property that the absolute value of each component is less that 1) and Ω-globally attractive equilibrium points in the saturated domain.
An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
In communication networks, such as the Internet or mobile ad-hoc networks, the actions taken by intermediate nodes or links are typically hidden from the communicating endpoints; all the endpoints can observe is whether or not the end-to-end transmission was successful. Therefore, in the absence of incentives to the contrary, rational (i.e., selfish) intermediaries may choose to forward messages at a low priority or simply not forward messages at all. Using a principal-agent model, we show how the hidden-action problem can be overcome through appropriate design of contracts in both the direct (the endpoints contract with each individual router directly) and the recursive (each router contracts with the next downstream router) cases. We further show that, depending on the network topology, per-hop or per-path monitoring may not necessarily improve the utility of the principal or the social welfare of the system.
Several new features arise in the ground-state phase diagram of a spin-1\ncondensate trapped in an optical trap when the magnetic dipole interaction\nbetween the atoms is taken into account along with confinement and spin\nprecession. The boundaries between the regions of ferromagnetic and polar\nphases move as the dipole strength is varied and the ferromagnetic phases can\nbe modulated. The magnetization of the ferromagnetic phase perpendicular to the\nfield becomes modulated as a helix winding around the magnetic field direction,\nwith a wavelength inversely proportional to the dipole strength. This\nmodulation should be observable for current experimental parameters in\n$^{87}$Rb. Hence the much-sought supersolid state, with broken continuous\ntranslation invariance in one direction and broken global U(1) invariance,\noccurs generically as a metastable state in this system as a result of dipole\ninteraction. The ferromagnetic state parallel to the applied magnetic field\nbecomes striped in a finite system at strong dipolar coupling.\n