Instead, the feature space must be preprocessed ( often by an entropy analysis of some kind ) so that some guidance can be given as to how the discretization process should proceed.

Sampling is usually carried out in two stages, discretization and quantization.

This is often a problem because it amounts to changing the interval of discretization.

This is therefore another consequence of discretization, in this case of the energy in the electromagnetic field in terms of photons.

The discretization method tends to do better if there is a large amount of training data because it will learn to fit the distribution of the data.

Since naive Bayes is typically used when a large amount of data is available ( as more computationally expensive models can generally achieve better accuracy ), the discretization method is generally preferred over the distribution method.

This process of discretization or segmentation is often considered, as by Jean-Jacques Nattiez ( 1990 ), necessary for music to become accessible to analysis.

Fred Lerdahl ( 1992, 112-13 ) argues that discretization is necessary even for perception by learned listeners, thus making it a basis of his analyses, and finds pieces such as Artikulation by György Ligeti inaccessible ,( Lerdahl 1988, 235 ) while Rainer Wehinger ( 1970 ) created a " Hörpartitur " or " score for listening " for the piece, representing different sonorous effects with specific graphic symbols much like a transcription.

The digitalization of analog real-world data is known as digitizing, and involves sampling ( discretization ) and quantization.

An example of a continuum theory that is widely studied by lattice models is the QCD lattice model, a discretization of quantum chromodynamics.

The stability of the chosen discretization is generally established numerically rather than that of analytically as with simple linear problems.

And this is where the spectral element discretization begins.

which is an exact solution to the discretization problem.

The error in the pseudo-spectral method is overwhelmingly due to discretization error.

A histogram of an image is produced first by discretization of the colors in the image into a number of bins, and counting the number of image pixels in each bin.

In numerical analysis, computational physics, and simulation, discretization error ( or truncation error ) is error resulting from the fact that a function of a continuous variable is represented in the computer by a finite number of evaluations, for example, on a lattice.

When we define the derivative of as or, where is a finitely small number, the difference between the first formula and this approximation is known as discretization error.

In signal processing, the analog of discretization is sampling, and results in no loss if the conditions of the sampling theorem are satisfied, otherwise the resulting error is called aliasing.

Basic radiosity also has trouble resolving sudden changes in visibility ( e. g., hard-edged shadows ) because coarse, regular discretization into piecewise constant elements corresponds to a low-pass box filter of the spatial domain.

Lattice models are also ideal for study by the methods of computational physics, as the discretization of any continuum model automatically turns it into a lattice model.

In mathematics, discretization concerns the process of transferring continuous models and equations into discrete counterparts.

These classical methods run into problems: symbolic differentiation works at low speed, and faces the difficulty of converting a computer program into a single expression, while numerical differentiation can introduce round-off errors in the discretization process and cancellation.

The time symmetry inherent in the method reduces the level of local errors introduced into the integration by the discretization by removing all odd degree terms, here the terms in h of degree three.

" Redshift quantization " has also been called redshift periodicity, redshift discretization, preferred redshifts, and redshift-magnitude bands.

Dynamic programming has been coupled with ANNs ( Neuro dynamic programming ) by Bertsekas and Tsitsiklis and applied to multi-dimensional nonlinear problems such as those involved in vehicle routing or natural resources management because of the ability of ANNs to mitigate losses of accuracy even when reducing the discretization grid density for numerically approximating the solution of the original control problems.

As a result, usually, when a digital IIR filter is going to be implemented, an analog filter ( e. g. Chebyshev filter, Butterworth filter, Elliptic filter ) is first designed and then is converted to a digital filter by applying discretization techniques such as Bilinear transform or Impulse invariance.

TASCflow was a structured multi-block hexahedral grid code, with a co-located primitive variable formulation that utilized a control volume based finite element discretization scheme to create a linearized system of equations that was solved using a unique, highly effective proprietary coupled-multigrid solver.

The Waterloo office has maintained strong ties with the University of Waterloo and its initial, highly academic, focus led to the development of advanced discretization methods and solution algorithms.

In classical mechanics, with discretization in time,

Because direct discretization of the diffusion equation with only first order spatial central differences leads to checkerboard artifacts.

That is, although the local discretization error is of order 4, due to the second order of the differential equation the global error is of order 2, with a constant that grows exponentially in time.

Multigrid methods can be applied in combination with any of the common discretization techniques.

can be solved with the Crank – Nicolson discretization of

Discontinuity meshing uses knowledge of visibility events to generate a more intelligent discretization.

Jean Paul van Bendegem has argued that the Tile Argument can be resolved, and that discretization can therefore remove the paradox.

* LMGC90 Open platform for modelling interaction problems between elements including multi-physics aspects based on an hybrid or extended FEM – DEM discretization, using various numerical strategies as MD or NSCD.

The timestep must be chosen small enough to avoid discretization errors ( i. e. smaller than the fastest vibrational frequency in the system ).

Special care must also be taken to ensure that the discretization handles discontinuous solutions gracefully.

* 1941: Alexander Hrennikoff submitted his D. Sc thesis in MIT on the discretization of plane elasticity problems using a lattice framework

This is specified by a distribution function Af such that the probability that Af lies in some region D of the stage space is Af.

Then Af, the maximization being over all admissible Af and the integration over the whole of stage space.

NASA later confirmed the object to be a piece of the first stage of the Saturn V rocket that launched Apollo 16 into space.

The band then set out on a nine-month, 92-date world tour, with an enormous set and a hugely expensive space ship stage with fog machines and a laser display.

As movies have overdone their explorations of the representation of violence, the intimate space of a theatre where actors hurt themselves and each other, at times with extra help from the theatrical illusion, might become again the most genuine stage of fears.

Faced with the dilemma of what to do with the empty space left behind by the lack of large amplifier cabinets, Lee chose to decorate his side of the stage with unusual items.

Berkeley's numbers typically begin on a stage but gradually transcend the limitations of theatrical space: his ingenious routines, involving human bodies forming patterns like a kaleidoscope, could never fit onto a real stage and the intended perspective is viewing from straight above.

This proposed rocket is dubbed " Ares ", which would utilize space shuttle Advanced Solid Rocket Boosters, a modified shuttle external tank, and a new Lox / LH2 third stage for the trans-Mars injection of the payload.

In Ancient Greece, the orchestra was the space between the auditorium and the proscenium ( or stage ), in which were stationed the chorus and the instrumentalists.

Because there was no orchestra, there was no space separating the audience from the stage.

Harrison Storms, the North American designer who was responsible for the X-15 rocket plane, and went on to head the effort to design the Apollo Command / Service Module and Saturn V launch vehicle's second stage was moved by the launch of Sputnik to think of space as being the next step for America.

The reusable first stage would be very large, nearly the size of a Saturn V to lift an orbiter the size of the space shuttle.

" Apollo X " would have replaced the LEM carried on the top of the S-IVB stage with a small space station slightly larger than the CSM's service area, containing supplies and experiments for missions between 15 and 45 days ' duration.

# The unity of place: a play should cover a single physical space and should not attempt to compress geography, nor should the stage represent more than one place.

Even at the height of its development as a chariot-racing circuit, the circus remained the most suitable space in Rome for religious processions on a grand scale, and was the most popular venue for large-scale venationes ; in the late 3rd century, the emperor Probus laid on a spectacular Circus show in which beasts were hunted through a veritable forest of trees, on a specially built stage.

Originally " drop-in " replacements were considered for higher performance, but a larger replacement for the S-IVB stage was later studied for missions to Mars and other high-load profiles, known as the S-N. Nuclear thermal space " tugs " were planned as part of the Space Transportation System to take payloads from a propellant depot in Low Earth Orbit to higher orbits, the Moon, and other planets.

In order to keep low frequency energy focused on the audience area and not on the stage, and to keep low frequencies from bothering people outside of the event space, a variety of techniques have been developed in concert sound to turn the naturally omnidirectional radiation of subwoofers into a more directional pattern.

This requires no light to shine on the background other than the LEDs, which use an extremely small amount of power and space unlike big stage lights, and require no rigging.

* Roman artists begin to extend the space of a room visually with painted scenes of figures on a shallow stage or with a landscape or cityscape.

The Death Star, a moon-sized space station ( the construction of which is in an early stage at the end of Revenge of the Sith ) with sufficient firepower to destroy an entire planet, is designed to be the supreme weapon of the Empire's power.

At the maturity stage, with competitive products occupying the space, new features are introduced (" auto-reverse ", " stereo with extra bass ", " shock proof for jogging ", " waterproof in the rain "... etc.

The introduction of semiconductors ( transistors ) allowed the output stage to change to a transistor, which soon lead to the elimination of the vibrator, and the use of " space charge " tubes that only required 6 or 12 volts on their plates without a high voltage plate power supply ( typical examples were the 6DR8 / EBF83, 6GM8 / ECC86, 6DS8 / ECH83, 6ES6 / EF97 and 6ET6 / EF98 ).

Centaur is a rocket stage designed for use as the upper stage of space launch vehicles.