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Conversely, if the data are sparse — that is, if only K out of N Fourier coefficients are nonzero — then the complexity can be reduced to O ( K log N log ( N / K )), and this has been demonstrated to lead to practical speedups compared to an ordinary FFT for N / K > 32 in a large-N example ( N = 2 < sup > 22 </ sup >) using a probabilistic approximate algorithm ( which estimates the largest K coefficients to several decimal places ).

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## Some Related Sentences

Conversely and if

__Conversely__

**,**

__if__statistics were uncovered

**which**contradicted

**a**cherished theory

**,**

**the**sources were denounced as faulty.

__Conversely__

**,**experimenters would consider as impressive such statements as

**the**following

**,**

**which**

**,**

__if__they turned

**out**

**to**

**be**hits

**,**

**are**so unusual as

**to**

**be**really significant:

__Conversely__

**,**

__if__he gives

**a**heavy rating

**to**his own reading

**,**

**and**finds more accurate facts

**in**it than

**in**

**the**others

**,**

**a**point

**is**chalked up

**for**

**the**intrinsic

**,**objective meaningfulness

**of**

**this**type

**of**mediumistic material.

__Conversely__

**,**

**a**subset R defines

**a**binary function

__if__

**and**

**only**

__if__

**,**

**for**any x

**in**X

**and**y

**in**Y

**,**there exists

**a**unique z

**in**Z such

**that**

**(**x

**,**y

**,**z ) belongs

**to**R.

__Conversely__

**,**

__if__

**a**Boolean ring A

**is**given

**,**we

**can**turn it into

**a**Boolean algebra by defining x ∨ y := x + y +

**(**x · y )

**and**x ∧ y := x · y.

__Conversely__

**,**

__if__

**the**second theory

**is**correct

**,**

**then**

**the**Athenians were merely reacting

**to**

**the**Persians attacking them.

__Conversely__

**the**equilibrium position

**is**said

**to**

**be**" far

**to**

**the**left "

__if__hardly any product

**is**formed from

**the**reactants.

__Conversely__

**,**

__if__ƒ: C → C

**is**

**a**function

**which**

**is**differentiable when regarded as

**a**function on R

**<**

**sup**

**>**

**2**

**</**

**sup**>,

**then**ƒ

**is**complex differentiable

__if__

**and**

**only**

__if__

**the**Cauchy – Riemann equations hold.

__Conversely__

**,**

__if__

**the**amount

**of**fat

**is**increased

**,**increasing

**the**number

**of**calories ingested will

**only**add weight.

__Conversely__

**,**

__if__

**the**source

**of**waves

**is**moving away from

**the**observer

**,**each wave

**is**emitted from

**a**position farther from

**the**observer than

**the**previous wave

**,**so

**the**arrival time between successive waves

**is**increased

**,**reducing

**the**frequency.

__Conversely__every partition

**of**comes from

**an**equivalence relation

**in**

**this**way

**,**according

**to**

**which**

__if__

**and**

**only**

__if__

**and**belong

**to**

**the**same set

**of**

**the**partition.

If neither A nor B includes

**the**idea**of**existence**,****then**" some A**are**B " simply adjoins A**to**B.__Conversely__**,**__if__A or B do include**the**idea**of**existence**in****the**way**that**" triangle " contains**the**idea " three angles equal**to**two right angles ",**then**" A exists "**is**automatically true**,****and**we have**an**ontological proof**of**A's existence.__Conversely__

**,**

__if__

**the**measured potential

**is**negative

**,**

**the**electrode

**is**more oxidizing than

**the**SHE

**(**such as Zn

**in**ZnSO

**<**sub

**>**4

**</**sub

**>**where

**the**standard electrode potential

**is**− 0. 76 V

**).**

__Conversely__

**,**

__if__

**the**firm

**is**able

**to**get bulk discounts

**of**

**an**input

**,**

**then**it could have economies

**of**scale

**in**some range

**of**output levels even

__if__it

**has**decreasing returns

**in**production

**in**

**that**output range.

__Conversely__

**,**daylight stock shot

**in**daylight will look normal

**,**but orange

__if__shot under tungsten lights.

Conversely and data

__Conversely__

**,**most realists

**(**specifically

**,**indirect realists ) hold

**that**perceptions or sense

__data__

**are**caused by mind-independent objects.

__Conversely__

**,**

**the**symbol width could

**be**set at 8

**,**even

**if**

**only**values 0

**and**1

**are**used ; these

__data__would

**only**require

**a**2-color table.

__Conversely__

**,**mapping

**the**

__data__flow between

**the**components determines

**the**logical topology

**of**

**the**network.

__Conversely__

**,**

**the**influence

**of**

**the**

__data__at any given point on

**the**initial line propagates with

**the**finite velocity c: there

**is**no effect outside

**a**triangle through

**that**point whose sides

**are**characteristic curves.

__Conversely__

**,**

**the**Tiahrt Amendment

**is**supported by

**the**Fraternal Order

**of**Police

**,**as it allows municipal police departments full access

**to**ATF trace

__data__

**in**any criminal investigation.

__Conversely__

**,**

**for**

**a**fossil

**of**known age

**,**

**the**paleomagnetic

__data__

**can**fix

**the**latitude at

**which**

**the**fossil was laid down.

__Conversely__

**,**

__data__must

**be**

**in**registers before it

**can**

**be**operated upon by

**the**other instructions

**in**

**the**computer's instruction set.

__Conversely__

**,**leads may

**be**delivered electronically

**,**such as by email

**,**SMS or

**a**ping

**/**post

**of**

**the**

__data__directly

**to**

**a**database.

__Conversely__

**,**

**the**histogram

**for**

**a**very bright image with few dark areas

**and**

**/**or shadows will have most

**of**its

__data__points on

**the**right side

**and**center

**of**

**the**graph.

Conversely and are

__Conversely__

**,**

**the**vowel marks

**of**

**the**Tigrinya abugida

**and**

**the**Amharic abugida

**(**ironically

**,**

**the**original source

**of**

**the**term " abugida ") have

**been**so completely assimilated into their consonants

**that**

**the**modifications

__are__no longer systematic

**and**have

**to**

**be**learned as

**a**syllabary rather than as

**a**segmental script.

__Conversely__

**,**most heat-treatable alloys

__are__precipitation hardening alloys

**,**

**which**produce

**the**opposite effects

**that**steel does.

__Conversely__

**the**use

**of**true brass seems

**to**have declined

**in**Western Europe during

**this**period

**in**favour

**of**gunmetals

**and**other mixed alloys but by

**the**end

**of**

**the**first Millennium AD brass artefacts

__are__found

**in**Scandinavian graves

**in**Scotland

**,**brass was being used

**in**

**the**manufacture

**of**coins

**in**Northumbria

**and**there

**is**archaeological

**and**historical evidence

**for**

**the**production

**of**brass

**in**Germany

**and**The Low Countries areas rich

**in**calamine ore

**which**would remain important centres

**of**brass making throughout

**the**medieval period

**,**especially Dinant – brass objects

__are__still collectively known as dinanterie

**in**French.

__Conversely__

**,**many fighter aircraft

**,**such as

**the**F-16

**,**

__are__often used as ' bomb trucks ,' despite being designed

**for**aerial combat.

__Conversely__

**,**

**the**Belgian Blue's meat tenderness

**has**

**been**argued

**to**

**be**just as tender because there

__are__

**a**large number

**of**smaller muscle fibers.

__Conversely__

**,**because space

**is**expanding

**,**

**and**more distant objects

__are__receding ever more quickly

**,**light emitted by us today may never " catch up "

**to**very distant objects.

__Conversely__

**,**certain general principles

**(**

**for**

**example**

**,**neighbourliness

**,**or charity )

__are__seen

**to**

**be**universal

**and**consistent.

__Conversely__

**,**modern biological sciences

**(**including even concepts such as molecular ecology )

__are__intimately entwined

**and**dependent on

**the**methods developed through biotechnology

**and**what

**is**commonly thought

**of**as

**the**life sciences industry.

__Conversely__beetles

__are__prey

**of**various invertebrates

**and**vertebrates including insects

**,**fish

**,**reptiles

**,**birds

**and**mammals.

__Conversely__

**,**factors

**that**favor plate columns

__are__: presence

**of**solids

**in**feed

**,**high liquid rates

**,**large column diameters

**,**complex columns

**,**columns with wide feed composition variation

**,**columns with

**a**chemical reaction

**,**absorption columns

**,**columns limited by foundation weight tolerance

**,**low liquid rate

**,**large turn-down ratio

**and**those processes subject

**to**process surges.

__Conversely__

**,**computer implementations

__are__significant

**in**applying ideas from discrete mathematics

**to**real-world problems

**,**such as

**in**operations research.

__Conversely__

**,**there

__are__other stars

**that**never rise above

**the**horizon

**,**as seen from any given point on

**the**Earth's surface

**(**except exactly on

**the**equator

**).**

__Conversely__

**,**Harris maintains

**that**

**the**fact-value distinction

**is**

**a**confusion

**,**proposing

**that**values

__are__really

**a**certain kind

**of**fact.

__Conversely__

**,**

**the**tiny meson mass mass differences responsible

**for**meson oscillations

__are__often expressed

**in**

**the**more convenient inverse picoseconds.

__Conversely__

**,**BBC critic Mark Kermode believes

**that**"

**the**movie industries

**of**Britain

**and**America

__are__inextricably intertwined ", citing numerous examples

**of**how Hollywood provides work

**to**British production staff

**and**studios

**,**whilst Britain enables Hollywood

**to**base their prestigious productions at UK studios.

__Conversely__

**,**

**in**functional code

**,**

**the**output value

**of**

**a**function depends

**only**on

**the**arguments

**that**

__are__input

**to**

**the**function

**,**so calling

**a**function f twice with

**the**same value

**for**

**an**argument x will produce

**the**same result f

**(**x ) both times.

__Conversely__

**,**

**the**bodies

**of**people who had certain medical conditions

__are__useful

**for**research into those conditions.

__Conversely__

**,**rifle bullets

**can**pierce light armor

**and**

__are__easier

**to**shoot accurately

**,**but even

**a**carbine such as

**the**Colt M4

**is**larger

**and**

**/**or longer than

**a**submachine gun

**,**making it harder

**to**maneuver

**in**close quarters.

__Conversely__

**,**

**if**either

**of**these last two expressions

**is**defined

**,**

**then**so

**is**

**the**other

**(**

**and**again they

__are__equal

**).**

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