Intuitively, one would expect systems which collect more than one type of data to be more useful than systems which collect only one type of information ( such as single-purpose laboratory or 911 call-center based systems ), and be less prone to false alarms, and this appears to be the case.

Intuitively, a minimal sufficient statistic most efficiently captures all possible information about the parameter θ.

Intuitively, homotopy groups record information about the basic shape, or holes, of a topological space.

Intuitively, mutual information measures the information that X and Y share: it measures how much knowing one of these variables reduces uncertainty about the other.

Intuitively, an ancillary complement " adds the missing information " ( without duplicating any ).

Intuitively, if entropy H ( X ) is regarded as a measure of uncertainty about a random variable, then H ( X | Y ) is a measure of what Y does not say about X.

Intuitively, one can reason that Hick's Law has a logarithmic form because people subdivide the total collection of choices into categories, eliminating about half of the remaining choices at each step, rather than considering each and every choice one-by-one, requiring linear time.

Intuitively, in such a case, starting from what we know about the parameter prior to observing the data point, we then can update our knowledge based on the data point and end up with a new distribution of the same form as the old one.

Intuitively, the parser attempts to locate the most basic elements, then the elements containing these, and so on.

Intuitively spoken, singular homology counts, for each dimension n, the n-dimensional holes of a space.

Intuitively, the fundamental group measures how the holes behave on a space ; if there are no holes, the fundamental group is trivial — equivalently, the space is simply connected.

In mathematics, the closure of a subset S in a topological space consists of all points in S plus the limit points of S. Intuitively, these are all the points that are " near " S. A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to the notion of interior.

Intuitively, this has the consequence that all points of the space are " lumped together " and cannot be distinguished by topological means ; it belongs to a pseudometric space in which the distance between any two points is zero.

Intuitively, a space is complete if there are no " points missing " from it ( inside or at the boundary ).

Intuitively, the distinction says merely that there is no canonical choice of where the origin should go in the space, because it can be translated anywhere.

Intuitively, the divergence ( denoted ∇•) of a vector field is a measure of flux diverging radially outwards from a point, so the negative is the amount piling up at a point, hence the rate of change of density in a region of space must be the amount of flux leaving or collecting in some region ( see main article for details ).

Intuitively, the first Betti number of a space counts the maximum number of cuts that can be made without dividing the space into two pieces.

In mathematics, an extreme point of a convex set S in a real vector space is a point in S which does not lie in any open line segment joining two points of S. Intuitively, an extreme point is a " vertex " of S.

Intuitively, a Sobolev space is a space of functions with sufficiently many derivatives for some application domain, such as partial differential equations, and equipped with a norm that measures both the size and regularity of a function.

Intuitively, the polar decomposition separates A into a component that stretches the space along a set of orthogonal axes, represented by P, and a rotation represented by U. The decomposition of the complex conjugate of is given by.

Intuitively, a contractible space is one that can be continuously shrunk to a point.

Intuitively, an algebraic space is a scheme modulo a " nice " equivalence relation ; the resulting category of algebraic spaces extends the category of schemes and allows to carry out several natural constructions that are needed for example in deformation theory or in the construction of moduli spaces but are not possible in the smaller category of schemes.

Intuitively, for two sets S and T to have the same cardinality means that it is possible to " pair off " elements of S with elements of T in such a fashion that every element of S is paired off with exactly one element of T and vice versa.

Intuitively, it is the " area so far " function of the probability distribution.

Intuitively, if we placed a small paddle wheel there, the larger " current " on its right side would cause the paddlewheel to rotate clockwise, which corresponds to a curl in the negative z direction.

Intuitively, the process can be pictured as follows: first shrink the real line to the open interval (- π, π ) on the x-axis ; then bend the ends of this interval upwards ( in positive y-direction ) and move them towards each other, until you get a circle with one point ( the topmost one ) missing.

Intuitively, an expander is a finite, undirected multigraph in which every subset of the vertices " which is not too large " has a " large " boundary.

Weather and GW Bridge traffic screen off other influences. Intuitively, this reduction in representation size is achieved simply because each variable depends only on a subset of the other variables.

Intuitively, one can say that the air follows the curve of the foil, but this is not very rigorous or precise.

Intuitively, a lambda abstraction represents an anonymous function that takes a single input, and the is said to bind in, and an application represents the application of input to some function.

Intuitively, if one pulled and stretched out the paths in the maze in the proper way, the result could be made to resemble a tree.

Intuitively, this means that the values x < sub > α </ sub > come and stay as close as we want to x for large enough α.

Intuitively, this means there are computational limits on what can be proven by computer programs.

Intuitively, the probability that any single number is divisible by a prime ( or any integer ), p is 1 / p.

) Intuitively, is a quine, a function that returns its own source code ( Gödel number ), except that rather than returning it directly, passes its Gödel number to and returns the result.

#: Intuitively, minimisation seeks -- beginning the search from 0 and proceeding upwards -- the smallest argument that causes the function to return zero ; if there is no such argument, the search never terminates.

Intuitively, a inherits the opposite orientation as b, as they are at opposite ends of the interval.

Intuitively, there are many cases where people do want to take the numbers involved into account.

Intuitively, theories of value must be important to ethics.

Intuitively, multiplying by a scalar r stretches a vector out by a factor of r. Geometrically, this can be visualized ( at least in the case when r is an integer ) as placing r copies of the vector in a line where the endpoint of one vector is the initial point of the next vector.

Intuitively, the reasoning is that, as web crawlers have a limit to how many pages they can crawl in a given time frame, ( 1 ) they will allocate too many new crawls to rapidly changing pages at the expense of less frequently updating pages, and ( 2 ) the freshness of rapidly changing pages lasts for shorter period than that of less frequently changing pages.

Intuitively, causation seems to require not just a correlation, but a counterfactual dependence.