Operations between graphs include evaluating the direction of a subsumption relationship between two graphs, if any, and computing graph unification.

The unification of two argument graphs is defined as the most general graph ( or the computation thereof ) that is consistent with ( i. e. contains all of the information in ) the inputs, if such a graph exists ; efficient unification algorithms are known.

For contraint frameworks which are strictly compositional, graph unification is the sufficient satisfiability and combination function.

The usual assumed path of theories is given in the following graph, where each unification step leads one level up:

In computer science, the yo-yo problem is an anti-pattern that occurs when a programmer has to read and understand a program whose inheritance graph is so long and complicated that the programmer has to keep flipping between many different class definitions in order to follow the control flow of the program.

Such materials are characterized by a glass transition that occurs at a glass transition temperature, which may be roughly defined as the " knee " point of the material's density vs. temperature graph.

Every directed acyclic graph has a topological ordering, an ordering of the vertices such that the starting endpoint of every edge occurs earlier in the ordering than the ending endpoint of the edge.

If we imagine the light confined to a two-dimensional plane, the light from the flash spreads out in a circle after the event E occurs, and if we graph the growing circle with the vertical axis of the graph representing time, the result is a cone, known as the future light cone.

This occurs after point A in the graph.

There is often a cliff by which the first few steps in the graph are missing, so that there is no vesting at all for a period ( usually six or twelve months in the case of employee equity ), after which there is a cliff date upon which a large amount of vesting occurs all at once.

This is clear when examining a sketched graph of the cosine function ; the fixed point occurs where the cosine curve intersects the line.

For instance, such problems occurs very frequently in graph theory, where searching graphs for structures such as particular matching, cliques, independent set, etc.

The graph of f has at least one component whose support is the entire interval Aj.

We have shown that the graph of F contains at least one component whose inverse is the entire interval {0,T}, and whose multiplicity is odd.

The graph of this function does intersect the vertical asymptote once, at ( 0, 5 ).

While the numerical difference between the decimal and binary interpretations is relatively small for the prefixes kilo and mega, it grows to over 20 % for prefix yotta, illustrated in the linear-log graph ( at right ) of difference versus storage size.

A graph of a bandpass filter's gain magnitude, illustrating the concept of − 3 dB bandwidth at a gain of 0. 707.

When the functions J < sub > n </ sub >( x ) are plotted on the same graph, though, none of the zeros seem to coincide for different values of n except for the zero at x = 0.

For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point.

If x and y are real numbers, and if the graph of y is plotted against x, the derivative measures the slope of this graph at each point.

If the function f is not linear ( i. e. its graph is not a straight line ), however, then the change in y divided by the change in x varies: differentiation is a method to find an exact value for this rate of change at any given value of x.

In classical geometry, the tangent line to the graph of the function f at a real number a was the unique line through the point ( a, f ( a )) that did not meet the graph of f transversally, meaning that the line did not pass straight through the graph.

The derivative of y with respect to x at a is, geometrically, the slope of the tangent line to the graph of f at a.

If the limit exists, meaning that there is a way of choosing a value for Q ( 0 ) that makes the graph of Q a continuous function, then the function f is differentiable at a, and its derivative at a equals Q ( 0 ).

Hence the slope of the graph of the squaring function at the point ( 3, 9 ) is 6, and so its derivative at x

The most straightforward way of efficiently computing the Delaunay triangulation is to repeatedly add one vertex at a time, retriangulating the affected parts of the graph.

The PPF is a table or graph ( as at the right ) showing the different quantity combinations of the two goods producible with a given technology and total factor inputs, which limit feasible total output.

** In power engineering, a " bus " is any graph node of the single-line diagram at which voltage, current, power flow, or other quantities are to be evaluated.

This graph is planar ( it is important to note that we are talking about the graphs that have some limitations according to the map they are transformed from only ): it can be drawn in the plane without crossings by placing each vertex at an arbitrarily chosen location within the region to which it corresponds, and by drawing the edges as curves that lead without crossing within each region from the vertex location to each shared boundary point of the region.

In graph-theoretic terminology, the four-color theorem states that the vertices of every planar graph can be colored with at most four colors so that no two adjacent vertices receive the same color, or for short, " every planar graph is four-colorable " (; ).

According to this argument, the research around Dunbar's Number implies a limit on the number of inbound and outbound connections a human in a group-forming network can manage, so that the actual maximum-value structure is much sparser than the set-of-subsets measured by Reed's law or the complete graph measured by Metcalfe's Law.

< http :// www. weather. com / weather / wxclimatology / monthly / graph / USCT0161? from = month_bottomnav_undeclared >.</ ref > Temperatures are moderated not only by Long Island Sound, but also by the Connecticut River and the large system of marshes and tidal rivers in and around its delta.

* A streamgraph, a stacked, curvilinear area graph displaced around a central axis

In a real flat plate the fluid must turn around the sides, and full stagnation pressure is found only at the center, dropping off toward the edges as in the lower figure and graph.

The second graph clearly shows that for longer lines exceeding around 50 dB attenuation, ADSL2 and ADSL2 + bring no benefit in terms of speed.

* Circular layout methods place the vertices of the graph on a circle, choosing carefully the ordering of the vertices around the circle to reduce crossings and place adjacent vertices close to each other.

Intuitively speaking, part of the graph of a function is rotated around an axis, and is modelled by an infinite number of hollow pipes, all infinitely thin.

The idea of the ant colony algorithm is to mimic this behavior with " simulated ants " walking around the graph representing the problem to solve.

Nb: The y-axis in the accompanying graph is incorrectly labelled and should read " log of Minimum Alveolar Concentration or MAC "-The lesser the MAC the greater the potency ( Halothane has a MAC of slightly less than 1 while Nitrous oxide has a MAC of around 105, halothane is much more potent and it is because the log of the MAC is plotted on the y axis that halothane has a value of 0. 01 and nitrous oxide has a value of 1.

A cycle graph may have its edges colored with two colors if the length of the cycle is even: simply alternate the two colors around the cycle.

However, the region around the outside of the graph is not included as an area for this game.

This approach revolves around the use of an abstract dependency graph which is created from the system in question.

where B ( x, r ) denotes the ball of radius r around the point x in the Riemannian distance or in the graph distance.

This theme uses elements that make the interface look like it has been drawn in pencil on a drafting-board, including small " pencil marks " around the windows, a barely visible graph paper grid on the desktop, and " squarish " elements with low contrast.

In graphonomics, sloppiness space is a term introduced by Goldberg and Richardson to describe the shape space of all graph ( handwriting ) around an idealized allograph.

The surface and the embedding may be described combinatorially using a rotation system, a cyclic order of the edges surrounding each vertex of the graph that describes the order in which the edges would be crossed by a path that travels clockwise on the surface in a small loop around the vertex.