Abstractly, the probability model for a classifier is a conditional model

Abstractly, we can say that D is a linear transformation from some vector space V to another one, W. We know that D ( c ) = 0 for any constant function c. We can by general theory ( mean value theorem ) identify the subspace C of V, consisting of all constant functions as the whole kernel of D. Then by linear algebra we can establish that D < sup >− 1 </ sup > is a well-defined linear transformation that is bijective on Im D and takes values in V / C.

Abstractly, this is equivalent to stabilising a flag: upper triangular matrices are precisely those that preserve the standard flag, which is given by the standard ordered basis and the resulting flag < math > 0 <

Abstractly, this circle is a cyclic group of order twelve, and may be identified with the residue classes modulo twelve.

Abstractly, it can be defined as the integer triples ( a, b, c ), associated to 3 < sup > a </ sup > 5 < sup > b </ sup > 7 < sup > c </ sup >, where the distance measure is not the usual Euclidean distance but rather the Euclidean distance deriving from the vector space norm

Abstractly, in trying to prove a proposition P, one assumes that it is false, and that therefore there is at least one counterexample.

Abstractly we can say that this is a projective line in the space of all conics, on which we take

Abstractly, these are the left adjoint and right adjoint, respectively, to the inclusion functors of in D. In addition, the truncation functors fit into a triangle, and this is in fact the unique triangle satisfying the third axiom above:

Abstractly it is assumed that the economy consists only of capitalist production and that the capitalist economy is equal to capitalist society.

Abstractly, the method is as follows:

Abstractly, if one starts with a complex vector space W and takes the complexification of the underlying real space, one obtains a space isomorphic to the direct sum of W and its conjugate:

Abstractly, a hierarchy can be modelled mathematically as a rooted tree: the root of the tree forms the top level, and the children of a given vertex are at the same level, below their common parent.

Abstractly, 1 / 8-schisma tuning may be considered the analog, among schismatic tunings, of 1 / 4-comma meantone among meantone tunings, as it also has pure interval ratios of 2: 1 and 5: 4, though with much more accurate interval ratios of 3: 2 and 6: 5 ( less than a quarter of a cent off from just intonation ) than its meantone counterpart.

Abstractly programmable toolpath guidance began with mechanical solutions, such as in musical box cams and Jacquard looms.

Abstractly, we can identify the chain rule as a 1-cocycle.

Abstractly, Weyl groups are finite Coxeter groups, and are important examples of these.

Abstractly, a parametric equation defines a relation as a set of equations.

Abstractly, the matrix exponential gives the connection between a matrix Lie algebra and the corresponding Lie group.

( This treats the array reference as a content-addressable data rather than an address of a value )

Taking a coordinate basis or frame of reference and applying the tensor to it results in an organized multidimensional array representing the tensor in that basis, or as it looks from that frame of reference.

When the loop variables index into an array, such a transformation can improve locality of reference, depending on the array's layout.

* Endoliths General Collection — This collection of online resources such as news articles, web sites, and reference pages provides a comprehensive array of information about endoliths.

It is wired with an array of window lights which can be used as a display for playing Tetris, in reference to a legendary ( but at the time of construction, apocryphal ) MIT hack.

However a reference may also be the offset ( difference ) between the datum's address and some fixed " base " address, or an index into an array.

Relational data and redundancy removal are displayed: the " ship-to " associative array content is copied from the " bill-to " associative array's content as indicated by the anchor ( & ) and reference ( * ) labels.

For instance, within the loop a reference to element I of an array would likely employ the auxiliary variable ( especially if it were held in a machine register ), but if I is a parameter to some routine ( for instance, a print-statement to reveal its value ), it would likely be a reference to the proper variable I instead.

Arrays are passed by reference, and this mechanism is an advertised feature of the language to pass data back out of a subroutine — but array slices are copied before being passed, so that data do not flow back into array ranges, violating the principle of least surprise.

Each array contains 140 ( one for each priority level ) pointers to doubly linked lists, which in turn reference all processes with the given priority.

The errors that Purify discovers include array bounds reads and writes, trying to access unallocated memory, freeing unallocated memory ( usually due to freeing the same memory for the second time ), as well as memory leaks ( allocated memory with no pointer reference ).

if self has no attached array values then is a reference to this ( computer science ) | this object

if self has no attached array values then is a reference to this ( computer science ) | this object

During reading, the action of the reference beam and the stored interference pattern in the medium recreates this data beam which may be sensed by a detector array.

" As simple as this seems, it may have an inefficiency, in that the location of variable x has to be looked up twice if the compiler does not recognize that two parts of the expression are identical: x might be a reference to some array element or other complexity.

Creating a single integer value message ( which might be a reference to a string, array or data structure ) requires less overhead than creating a complicated message such as a SOAP message.

Leiden's Catalogue makes available a considerable array of digital scholarly information: more than 400 databases, > 40, 000 e-journals, > 5, 000 newspapers and newsmagazines, > 1, 000, 000 e-books and reference works, many hundreds of millions of journal articles, its digital special collections and repository materials.

When the loop variables index into an array, such a transformation can improve locality of reference, depending on the array's layout.

It is equal to one less than the number of elements contained in the array, as one element is used as a reference against which either constructive or destructive interference may be applied using each of the remaining antenna elements.

But is that not like going to a chemistry laboratory and blindly pouring out liquids and powders from an array of bottles and then, after stirring, expecting a new wonder drug inevitably to result??

The theme of The Walnut Trees Of Altenburg is most closely related to its immediate predecessor in Malraux's array of novels: Man's Hope ( 1937 ).

Turn off at any one of the marked picnic areas ( gasoline companies have touring service bureaus that issue booklets on national parks to tell you where you have barbecue facilities ) and -- with soft drinks cooled from morning loading up, hamburger, buns, an array of relishes, and fresh fruit -- your lunch is 75% cheaper than at a restaurant, and 100% more fun.

Your competition is now proportionately greater -- you are competing not only against manufacturers in the same field but also against a vast array of manufacturers of other appealing consumer products.

and it is again and again made clear that Utopian communism provides the institutional array indispensible to that best ordering.

For circular fibers in a closely packed hexagonal array, the packing efficiency is given by: Af where Af, and 0.906 is the ratio of the area of a circle to that of the circumscribed hexagon.

Assistive technology is the array of new devices created to enable sports enthusiasts who have disabilities to play.

Keem BayAchill Archaeological Field School is based at the Achill Archaeology Centre in Dooagh, which has served as a catalyst for a wide array of archaeological investigations on the island.

The array on the game board is arranged with lettered rows ( A through I ) and numbered columns ( 1 through 12 ).

The vast array of sensors available to the military is used for whatever tactical means required.

In computer science, an array data structure or simply an array is a data structure consisting of a collection of elements ( values or variables ), each identified by at least one array index or key.

An array is stored so that the position of each element can be computed from its index tuple by a mathematical formula.

Arrays are often used to implement tables, especially lookup tables ; the word table is sometimes used as a synonym of array.

In most modern computers and many external storage devices, the memory is a one-dimensional array of words, whose indices are their addresses.

The set of valid index tuples and the addresses of the elements ( and hence the element addressing formula ) are usually, but not always, fixed while the array is in use.

The term array is often used to mean array data type, a kind of data type provided by most high-level programming languages that consists of a collection of values or variables that can be selected by one or more indices computed at run-time.

The term is also used, especially in the description of algorithms, to mean associative array or " abstract array ", a theoretical computer science model ( an abstract data type or ADT ) intended to capture the essential properties of arrays.

They are known in this context as control tables and are used in conjunction with a purpose built interpreter whose control flow is altered according to values contained in the array.

When data objects are stored in an array, individual objects are selected by an index that is usually a non-negative scalar integer.

* 0 ( zero-based indexing ): The first element of the array is indexed by subscript of 0.