Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

He pointed out that implicit in the early Buddhist concept of dependent origination is the lack of any substantial being ( anatta ) underlying the participants in origination, so that they have no independent existence, a state identified as emptiness ( śūnyatā ), or emptiness of a nature or essence ( svabhāva ).

Hypertext is the underlying concept defining the structure of the World Wide Web.

The philosophy of human rights attempts to examine the underlying basis of the concept of human rights and critically looks at its content and justification.

: The knowledge base underlying the INTERNIST system is composed of two basic types of elements: disease entities and manifestations .... also contains a ... hierarchy of disease categories, organized primarily around the concept of organ systems, having at the top level such categories as " liver disease ," " kidney disease ," etc.

The original surface micromachining concept was based on thin polycrystalline silicon layers patterned as movable mechanical structures and released by sacrificial etching of the underlying oxide layer.

The underlying concept of the poet as creator is not uncommon, and some modernist poets essentially do not distinguish between the creation of a poem with words, and creative acts in other media.

The underlying concept is that their head height may never be equal to that of their superior.

In the related concept of overfitting, excessively complex models are affected by statistical noise ( a problem also known as the bias-variance trade-off ), whereas simpler models may capture the underlying structure better and may thus have better predictive performance.

The underlying concept is that such students need specific guidance to be able to analyze case studies.

The underlying concept is that with enough practice ( hundreds of case analyses ) students develop intuitive skills for analyzing and resolving complex business situations.

There is no real difference in the genetic processes underlying artificial and natural selection, and the concept of artificial selection was used by Charles Darwin as an illustration of the wider process of natural selection.

The concept that insulin resistance may be the underlying cause of diabetes mellitus type 2 was first advanced by Prof. Wilhelm Falta and published in Vienna in 1931, and confirmed as contributary by Sir Harold Percival Himsworth of the University College Hospital Medical Centre in London in 1936.

This concept is largely fuzzy and unclear in earlier stories depicting very rudimentary robots who are only programmed to comprehend basic physical tasks, where the Three Laws act as an overarching safeguard, but by the era of The Caves of Steel featuring robots with human or beyond-human intelligence the Three Laws have become the underlying basic ethical worldview that determines the actions of all robots.

The tool's underlying concept and data were published in various scientific publications.

The primary concept underlying Dōgen's Zen practice is " oneness of practice-enlightenment " ( 修證一如 shushō-ittō / shushō-ichinyo ).

Because it was the first major typesetting program to incorporate the concept of an implicit " underlying page " frame, and one of the first to incorporate a strong " style sheet " concept, Ventura Publisher produces documents with a high degree of internal consistency, unless specifically overridden by the user.

The underlying concept is that early intervention through play with adapted toys and technology can teach disabled children to deal with the " normal " world.

If the concept of belief is incoherent, then any attempt to find the underlying neural processes that support it will fail.

The concept of ki underlying Reiki is speculative and there is no scientific evidence that it exists ; a 2008 systematic review of randomised clinical trials concluded that " the evidence is insufficient to suggest that reiki is an effective treatment for any condition.

This concept provided scholarly substance for explaining the underlying Indian-ness of apparently divergent cultural and linguistic patterns.

In his autobiographical work Ecce Homo, Nietzsche states that the book's underlying concept is discussed within " the penultimate section of the fourth book " of ' The Gay Science ' ( Ecce Homo, Kaufmann ).

The underlying concept behind the Unplugged series has been attributed to the popularity among musicians of a variety of informal musical performances on stage, film, television and record in earlier decades.

Anxiety can be a symptom of an underlying health issue such as chronic obstructive pulmonary disease ( COPD ), heart failure, or heart arrythmia.

Alone or together with anticonvulsants ( e. g., carbamazepine or valproate ), these medications can be used to treat attention-deficit hyperactivity disorder ( ADHD ) and substance abuse by addressing underlying depression.

* By focusing on symbolic patterns, images, and poetic mantras, the meditant can achieve consciously directed Imaginations that allow sensory phenomena to appear as the expression of underlying beings of a soul-spiritual nature.

Temporary withdrawal symptoms including insomnia, agitation, psychosis, and motor disorders may occur during dosage reduction of antipsychotics, and can be mistaken for a return of the underlying condition.

The psychological withdrawal symptoms can include psychosis, and can be mistaken for a relapse of the underlying disorder.

If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.

There are various norms that can be placed on the tensor product of the underlying vector spaces, amongst others the projective cross norm and injective cross norm.

The fundamental question underlying all computing is " What can be ( efficiently ) automated?

This first connotation can be further differentiated into ( a ) pure common law arising from the traditional and inherent authority of courts to define what the law is, even in absence of an underlying statute, e. g., most criminal law and procedural law before the 20th century, and even today, most of contract law and the law of torts, and ( b ) court decisions that interpret and decide the fine boundaries and distinctions in law promulgated by other bodies.

The most pervasive influence on these languages has been syntactical, and they tend to combine the recognizable expression and statement syntax of C with underlying type systems and data models that can be radically different.

Coyote kills can be distinguished from wolf kills by the fact that there is less damage to the underlying tissues.

If this goal is met by a DBMS, then the designers and builders of the specific database can concentrate on the application's aspects, and not deal with building and maintaining the underlying DBMS.

Provided the underlying scalars form a field ( more generally, a commutative ring with unity ), the definition below shows that such a function exists, and it can be shown to be unique.

" However, the DSM is based on an underlying structure that assumes discrete medical disorders that can be separated from each other by symptom patterns.

Although these guidelines have been widely implemented, opponents argue that even when a diagnostic criteria set is accepted across different cultures, it does not necessarily indicate that the underlying constructs have any validity within those cultures ; even reliable application can only demonstrate consistency, not legitimacy.

* provide leverage ( or gearing ), such that a small movement in the underlying value can cause a large difference in the value of the derivative ;

Also, the underlying name of the star system itself can follow several different systems.

Wavefunction collapse can be viewed as an epiphenomenon of quantum decoherence, which in turn is nothing more than an effect of the underlying local time evolution of the wavefunction of a system and all of its environment.

From the back left of the painting you can see the artist himself looking out at the viewer, and the painting behind the family depicts Lot and his daughters, thus once again echoing the underlying message of corruption and gat.

Such programs can evaluate expressions like "" exactly, because they " know " the underlying mathematics.

Thus we have the important result that when a discrete data sequence, s, is proportional to samples of an underlying continuous function, s ( t ), one can deduce something about the continuous Fourier transform, S ( ƒ ).

Because HTTPS piggybacks HTTP entirely on top of TLS, the entirety of the underlying HTTP protocol can be encrypted.

Although the resulting energy eigenfunctions ( the orbitals ) are not necessarily isotropic themselves, their dependence on the angular coordinates follows completely generally from this isotropy of the underlying potential: the eigenstates of the Hamiltonian ( that is, the energy eigenstates ) can be chosen as simultaneous eigenstates of the angular momentum operator.