Intuitively, this is why this algorithm works, and returns samples that follow the desired distribution.

Intuitively, this says that if one writes a function which is polynomial-time assuming that function calls are constant-time, and if those called functions themselves require polynomial time, then the entire algorithm takes polynomial time.

Intuitively, problem A is reducible to problem B if an algorithm for solving problem B efficiently ( if it existed ) could also be used as a subroutine to solve problem A efficiently.

Intuitively, the algorithm has been promised that the input does indeed belong to set of yes instances or no instances.

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

Intuitively HJB can be " derived " as follows.

Intuitively, it may be constructed as follows: Roll a 2-dimensional rectangle into a cylinder, so that its top and bottom edges meet.

Intuitively, this can be understood as follows: In quantum mechanics, the entropy of the joint system can be less than the sum of the entropy of its components because the components may be entangled.

Intuitively, NP is the set of all decision problems for which the instances where the answer is " yes " have efficiently verifiable proofs of the fact that the answer is indeed " yes ".

Intuitively then, the oracle machine can perform all of the usual operations of a Turing machine, and can also query the oracle for an answer to a specific question of the form " is x in A?

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 is because it required a choice, rigorously because any such choice of isomorphisms will not commute with all linear maps ; see for detailed discussion.

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

Intuitively, it states that the sum of all sources minus the sum of all sinks gives the net flow out of a region.

Intuitively we would expect it to be even more unlikely for all 5 marbles to be white.

Intuitively all dependencies are the result of keys.

Intuitively, we can think of this as being all meromorphic functions whose poles at every point are no worse than the corresponding coefficient in D ; if the coefficient in D at z is negative, then we require that h has a zero of at least that multiplicity at z – if the coefficient in D is positive, h can have a pole of at most that order.

Intuitively, one can think of the radical of I as obtained by taking all the possible roots of elements of I. Rad ( I ) turns out to be an ideal itself, containing I.

Intuitively, this is allowed in the antecedent because we can always restrict the scope of our proof ( if all cars have wheels, then it's safe to say that all black cars have wheels ); and in the succedent because we can always allow for alternative conclusions ( if all cars have wheels, then it's safe to say that all cars have either wheels or wings ).

If, for example, we simply look at a curve in the real affine plane there might be singular P modulo the stalk, or alternatively as the sum of m ( m − 1 )/ 2, where m is the multiplicity, over all infinitely near singular points Q lying over the singular point P. Intuitively, a singular point with delta invariant δ concentrates δ ordinary double points at P. For an irreducible and reduced curve and a point P we can define δ algebraically as the length of where is the local ring at P and is its integral closure.

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.

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 system simulates another system if it can match all of its moves.

Intuitively, the marginal probability of X is computed by examining the conditional probability of X given a particular value of Y, and then averaging this conditional probability over the distribution of all values of Y.

Intuitively, in a forward flow problem, it would be fastest if all

Intuitively, the theorem states that to build a VMM it is sufficient that all instructions that could affect the correct functioning of the VMM ( sensitive instructions ) always trap and pass control to the VMM.

Intuitively, the distinction is that the wavefronts of plane waves are truly planar ; all points on a given two-dimensional wavefront are equivalent.

Schubert wrote, " Intuitively, iterated limiting identification might be regarded as higher-order inductive inference performed collectively by an ever-growing community of lower order inductive inference machines.

Intuitively, an index falls into this set if and only if for every " there is an such that the Turing machine with index halts on input after steps ”.

In mathematics, especially in the area of algebra known as group theory, the Fitting subgroup F of a finite group G, named after Hans Fitting, is the unique largest normal nilpotent subgroup of G. Intuitively, it represents the smallest subgroup which " controls " the structure of G when G is solvable.

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, this map cuts the plane into 2 by 2 squares, then stacks the squares on top of each other.

Intuitively this seems to mean that the number of inputs and the number of outputs can always be equal in each subswitch, but intuition does not prove this can be done nor does it tell us how to do so.

Intuitively, a vector field is best visualized as an ' arrow ' attached to each point of a region, with variable length and direction.

Intuitively two systems are bisimilar if they match each other's moves.

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

Intuitively, the linking number represents the number of times that each curve winds around the other.

Intuitively, we can think of each characteristic line implying a solution to along itself.

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, this corresponds to finding the amount of output each sector should produce given that we want 7 units of good A and 4 units of good B.

Intuitively, we can view the hyperprior vector α as pseudocounts, i. e. as representing the number of observations in each category that we have already seen.

Intuitively, the procedure proceeds step by step, with a specific rule to cover what to do at each step of the calculation.

Intuitively, maximizing the function above is equivalent to pulling the points as far away from each other as possible and therefore " unfold " the manifold.

Intuitively we say two sets are close if they are arbitrarily near to each other.

Intuitively, the cost function encourages factories with high flows between each other to be placed close together.