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For most infinite lattice graphs, p c cannot be calculated exactly, though in some cases p c there is an exact value. For example: For example: for the square lattice ℤ 2 in two dimensions, p c = 1 / 2 for bond percolation, a fact which was an open question for more than 20 years and was finally resolved by Harry Kesten in the early ...
These diagrams are graphs of fixed points (or periodic points , as described below ) x as a function of a parameter a , with a on the horizontal axis and x on the vertical axis. To distinguish between stable and unstable fixed points, the former curves are sometimes drawn as solid lines and the latter as dotted lines .
The simplest kind of an orbit is a fixed point, or an equilibrium. If a mechanical system is in a stable equilibrium state then a small push will result in a localized motion, for example, small oscillations as in the case of a pendulum. In a system with damping, a stable equilibrium state is moreover asymptotically stable. On the other hand ...
The Nyquist plot for () = + + with s = jω.. In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker [] at Siemens in 1930 [1] [2] [3] and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, [4] is a graphical technique ...
It is used heavily in statistical physics, statistical analysis, information theory, data science, neural networks, finance and marketing. A sample path of a diffusion process models the trajectory of a particle embedded in a flowing fluid and subjected to random displacements due to collisions with other particles, which is called Brownian motion.
Line chart showing the population of the town of Pushkin, Saint Petersburg from 1800 to 2010, measured at various intervals. A line chart or line graph, also known as curve chart, [1] is a type of chart that displays information as a series of data points called 'markers' connected by straight line segments. [2]
Diffusion curves are vector graphic primitives for creating smooth-shaded images. Each diffusion curve partitions the 2D graphics space through which it is drawn, defining different colors on either side. When rendered, these colors then spread into the regions on either side of the curve in a way analogous to diffusion. The colors may also be ...
If the number of resulting edges is small compared to the original graph, then the partitioned graph may be better suited for analysis and problem-solving than the original. Finding a partition that simplifies graph analysis is a hard problem, but one that has applications to scientific computing, VLSI circuit design, and task scheduling in ...