text
stringlengths 0
190k
|
|---|
0705.1667.txt |@word gr:2 caused:1 lack:1 results:1 existing:2 four:1 known:4 gb:1 grateful:1 gm:6 contributions:3 consider:3 whose:1 certainly:1 iorio:3 calculate:2 mismodeling:1 finally:1 analogous:3 deruelle:6 1pn:29 very:1 induce:1 perihelion:3 putting:1 decide:1 affect:1 level:9 did:1 turns:1 try:1 science:2 manchester:2 equation:1 measuring:7 measurable:1 approximation:2 rate:12 evaluated:1 further:1 estimated:4 expressions:1 postnewtonian:1 errors:3 sum:7 axes:2 near:3 expressed:1 uniform:1 current:1 consistently:1 coles:3 referees:1 method:2 body:1 arcsec:1 component:4 here:3 perpendicular:1 reported:1 l25:1 address:2 based:1 strong:1 appears:1 logarithmic:1 obtained:3 larger:3 allows:1 amount:1 pick:1 action:1 hospitality:1 skepticism:1 der:1 via:6 useful:2 apr:1 barker:6 prefer:1 highly:1 apj:8 total:2 unit:1 use:4 gravitoelectric:5 would:11 1975b:2 1975a:4 m2:3 taken:1 today:1 more:7 introducing:1 emission:1 keplerian:15 confused:1 particular:1 eccentricity:2 must:4 account:2 ma:3 mb:4 recall:1 challenge:1 modified:2 dei:1 itself:2 values:1 meet:1 could:1 deg:21 challenging:1 cosmological:1 give:1 relativistic:2 neglected:1 purposes:1 effectively:2 assumptions:1 every:1 axis:12 goal:1 rather:2 discussion:1 means:2 feature:1 write:1 how:1 instead:2 parameter:9 sin:9 profile:1 l50:1 astroph:1 wissenschaften:1 may:1 after:2 derived:1 plane:2 inst:2 date:1 law:4 data:3 barycentric:2 attempt:1 dynamical:1 third:4 light:1 quoted:2 bulik:1 negligible:2 allow:2 tall:1 scintillation:3 order:8 pulsed:1 anonymous:1 indeed:3 pointed:2 insight:1 years:1 paper:1 same:1 argued:1 poincar:2 its:3 delay:4 thank:1 maps:1 masses:8 relativity:2 better:8 texas:1 correspondence:1 them:1 haensel:1 affected:2 number:1 effects:4 they:1 symposium:1 now:8 day:3 easily:1 meas:6 university:1 presented:2 identified:2 sufficiently:1 magnitude:8 each:1 found:1 constraints:1 square:1 directly:1 doing:1 related:4 investigated:1 entering:2 measurement:8 our:4 eq:9 out:4 shown:1 nuovo:1 since:1 crucial:2 projected:8 istituto:1 induced:1 lorentzinvariant:1 m2a:1 m2b:1 theory:1 fisica:1 possibility:3 completely:1 besides:1 estimate:2 remainder:1 j0737:13 e2:6 advance:1 geometry:1 determining:3 just:1 used:3 feasible:2 motion:3 turn:1 massive:1 consequence:1 lincei:1 first:6 major:4 xb:15 xa:20 primary:2 spinning:1 improvements:1 done:3 adopted:1 quadrupole:2 pulsar:8 precisely:1 angular:2 size:1 mercury:2 given:2 introduction:1 achieved:1 system:14 least:3 their:4 listed:1 gives:1 way:2 continuous:1 took:1 released:1 authors:2 stairs:2 than:7 december:1 observed:1 22nd:1 double:2 l49:1 cimento:1 second:2 submitted:1 matter:2 determined:5 prospect:1 prd:3 prl:1 correction:1 kepler:4 unlikely:1 orders:5 angle:2 built:1 min:1 connell:8 gravity:3 note:2 extracted:1 potential:1 so:3 l113:1 accuracy:7 even:1 sereno:2 measures:1 reach:1 most:2 abc:5 preliminary:1 measured:9 bound:1 deviations:1 kg:1 subtracted:2 considered:4 calculated:1 face:1 definitely:1 principle:3 exp:1 conservatively:2 constrain:2 sigma:1 fact:3 quantity:1 precise:1 show:2 text:1 radio:2 inconsistent:1 carefully:1 lense:1 find:1 impact:4 slow:2 ratio:3 knowledge:1 parameters:16 should:9 being:1 only:5 lorenzo:3 thompson:2 kramer:12 di:3 dependent:1 overall:1 δxb:1 δxa:2 orbiting:2 cannot:1 words:1 timing:9 osterreichische:1 graz:1 precession:20 arxiv:4 acknowledgments:1 qc:2 predicted:2 pulsars:2 analytical:1 jetzer:2 inside:1 view:3 shapiro:5 computed:1 phenomenologically:6 correlations:1 relative:7 see:4 individual:2 result:1 bari:1 best:1 mismodelling:2 gravitomagnetic:11 currently:1 pisa:1 µs:1 written:2 future:4 various:3 between:3 affecting:3 conditions:1 email:1 discovery:1 knowing:1 terms:6 nature:2 importance:3 weak:3 however:6 gratefully:1 enters:1 key:1 jd:1 come:1 inertia:10 2pn:3 both:1 prospects:1 improved:1 many:1 uncertainty:12 according:3 propagation:1 context:1 contribution:3 among:1 relevant:2 3039a:12 reasons:2 sky:1 period:3 cxa:2 cy:1 table:2 viale:1 source:3 cqg:1 due:5 been:2 pb:13 much:2 change:1 basic:1 expected:3 pk:2 ph:2 ann:2 schutz:5 corresponding:1 lichtenegger:1 covariance:1 reaching:1 determination:1 systematic:5 c3:1 spin:9 present:4 c4:2 case:4 uncertain:1 pacs:1 reliable:1 value:4 will:7 while:3 error:5 b1913:1 vectors:1 undetectable:1 thus:6 equal:2 confound:1 bias:7 ia:2 orbital:7 binary:3 italy:1 author:1 make:2 precessional:1 any:2 potentially:2 largest:3 neutron:6 difficult:1 literature:1 effect:3 akademie:1 constraining:1 moment:11 v4:1 bejger:3 nucleare:1 acknowledge:1 well:3 analysis:4 severe:1 consistency:1 quantitative:1 model:1 binaries:1 latest:1 damour:21 semimajor:14 accurate:2 competitive:1 sources:3 shape:1 intervals:1 summed:1 speed:1 alignment:1 previous:1 yr:21 conclusions:1 point:1 seems:2 improvement:1 pericentre:1 lett:2 wex:6 momentum:2 aspects:1 possible:3 five:2 lyutikov:2 psr:11 using:1 intersection:1 moreover:1 apart:1 like:2 particle:2 δr:1 δs:3 yields:3 sezione:1 δe:1 δa:9 because:4 often:2 some:2 barycenter:1 sight:1 respect:2 duration:1 indirect:1 describing:1 realistic:1 measurements:2 exceeding:1 comments:1 conservative:1 contributing:1 accademia:1 lattimer:5 does:1 linearly:1 expressing:1 assuming:1 inclination:1 limitations:1 s19:1 schaefer:9 ba:1 bc:1 agreement:1 post:16 super:1 periastron:24 about:7 central:1 getting:2 o:11 referred:1 presence:1 into:4 interstellar:1 three:2 references:1 nonnegligible:1 determine:2 einstein:2 institut:1 support:1 there:1 start:1 italia:1 l135:1 stars:2 astrophysics:1 was:3 purposely:1 morrison:3 speculate:1 medium:1 newtonian:6 regard:2 but:3 astro:1 solar:2 mnras:2 line:1 true:1 infn:1 stanford:1 wish:1 lyne:3 variations:1 up:3 us:7 ur:1 below:1 limit:1 similar:1 aa:1 taylor:4 constant:1 defined:1 abstract:1 measure:6 am:1 general:4 examine:1 nazionale:2 burgay:4 amounts:4 percent:3 envisaged:1 field:3 other:10 details:2 test:2 conclusion:1 node:1 star:4 models:2 thirring:1 precision:4 a3:1 important:3 a7:1 included:1 dense:1 aware:1 gravitomagnetism:2 independently:1 implies:1 coupling:1 physics:1 proposed:1 required:4 orbit:7 eos:1 mass:3 time:5 far:1 |
0705.1668.txt |@word consider:6 remarkable:2 rev:30 magnetic:4 thouless:1 results:2 leads:2 gc:1 computation:1 kc2:1 constants:2 remarkably:1 denotes:2 whose:1 dimensionality:1 depend:3 pedri:1 pfau:3 environment:4 quasi:21 monotonically:2 preserved:1 46a:1 dressing:1 dramatically:2 divergent:1 stuhler:1 shielding:1 very:4 dell:2 induce:1 wave:4 affect:1 condition:3 severely:1 dominate:1 hamiltonian:2 anisotropy:1 solution:3 occurs:2 large:11 small:3 smaller:1 lewenstein:3 prediction:1 l3:4 approximation:2 zero:2 further:2 chem:2 linear:1 even:10 will:1 interatomic:1 plays:1 trapping:2 trivial:1 near:1 uniform:1 current:1 axial:6 above:1 boundary:1 new:3 contributes:1 ever:1 consisting:1 3d:13 satisfy:1 agreement:1 ibid:1 ranged:1 modify:1 atoms:2 growing:1 explore:1 cylindrical:3 box:1 bodo:1 bergemann:1 along:6 strong:1 change:3 obtained:3 property:1 osch:1 larger:1 allows:1 approaches:1 resonance:4 fourier:1 changes:1 elongated:1 via:1 orienting:1 castin:1 private:1 logarithmic:3 condensates:5 should:2 shlyapnikov:6 vef:1 use:2 eψ:1 would:4 positive:2 negative:2 giamarchi:1 france:1 calculation:2 approach:1 therefore:2 maxon:1 until:1 molecules:3 becomes:6 under:1 corrected:1 odinger:2 controlling:1 particular:6 known:3 rotons:1 must:2 rotational:1 integrating:1 equation:4 averaged:1 modified:5 minimum:2 values:10 following:3 im:1 modifies:1 control:1 f1:1 wang:1 scan:1 process:2 2ld:2 india:1 involve:1 anihilation:1 o:3 allowed:1 tan:1 quasi1d:1 end:1 dalgarno:1 g1d:31 off:2 shortrange:1 far:1 kolkata:1 axis:5 parameter:1 simplicity:1 product:1 mat:2 may:18 after:2 dx2:1 hence:7 plane:1 αd2:1 physik:1 choice:1 types:1 2l2:1 hannover:2 effective:10 sech:1 acknowledged:1 maintain:1 so:2 allow:2 increase:1 order:1 over:1 produced:1 thermal:1 experiments:3 including:2 lasers:1 experimentally:1 y1:1 existence:2 cold:4 still:1 excitations:2 its:1 condensation:1 ld:7 ospelkaus:1 energies:1 solving:1 vicinity:1 coordinates:2 absence:2 systems:2 dxψ:1 derivative:3 main:1 eur:1 maximal:1 eventually:4 non:2 good:2 affected:2 combination:3 prevented:1 conversations:1 greiner:1 fig:6 modification:2 yz:1 repulsive:7 effects:4 oxford:1 discuss:1 teller:1 2t:1 represents:1 several:1 fully:3 university:1 presented:1 by1:1 2d:4 sufficiently:9 l2:7 trap:3 radial:4 found:1 universit:1 characterized:2 homogeneous:5 bright:2 significantly:1 formulate:1 instability:1 energy:4 sinha:1 frequency:1 static:1 quantum:5 our:3 beyond:2 eq:1 special:1 mv0:2 shown:1 dominates:3 meijer:1 fundamentally:1 space:1 since:4 crucial:1 rz:1 research:1 particles:4 attracted:1 dxdx:1 formula:1 induced:5 ref:1 correct:2 sma:6 shows:3 theory:2 barrier:1 interactions:9 maintains:1 ewski:1 possibility:1 completely:2 formation:1 gianturco:1 additional:1 interaction:16 r0:8 r2:2 created:1 geometry:5 aj1:1 transition:1 turn:1 length:10 erfc:2 isotropic:2 olshanii:2 consequence:3 top:1 first:2 origin:1 major:1 features:1 symmetry:4 rydberg:1 reaches:1 theoretische:1 channels:1 intuitively:1 employing:1 simplified:2 long:2 4d2:1 open:1 size:1 given:9 law:1 temperature:1 orlitz:2 leading:4 condensate:2 system:3 πl:1 imposing:1 intermediate:1 1d:37 calculations:2 realization:1 dfg:1 1l:2 dutta:1 acquire:1 transverse:1 short:19 authors:1 x2:2 x3:1 sign:3 separability:1 center:1 relative:3 roles:1 cyclic:1 bec:7 see:2 ranging:1 determined:1 solitonic:1 wildermuth:1 providing:1 solely:1 motivation:1 sal:1 spectrum:2 qualitatively:1 border:1 strength:3 angle:1 convenient:2 latter:3 stability:1 oriented:1 sciences:1 k1:1 potential:16 achieving:1 solve:2 degenerated:1 roton:6 play:1 towards:2 electric:2 centre:1 what:1 petrov:3 germany:1 significant:1 phase:1 analytically:1 sfb:1 kc:2 observation:1 considered:4 clear:1 kl:2 optical:1 exp:1 typically:1 fact:1 drastically:1 particularly:1 leibniz:1 sage:1 3x2:1 dimension:1 d2:9 overwhelmed:1 ground:1 knowledge:1 situations:2 writes:1 enough:1 than:1 moments:1 only:2 rich:1 αd:1 dominant:1 means:3 2a:1 cannot:1 dx:1 kurizki:1 lattices:1 twobody:1 v1d:9 girardeau:1 increasing:2 transversal:6 fields:2 arxiv:1 summary:1 paper:1 analytical:3 london:2 4πm:1 fixed:1 berezinskii:1 transforms:1 scanning:1 fascinating:1 physically:1 undergoes:1 national:1 j1:1 observed:1 differs:1 namely:2 result:2 enhanced:1 close:2 overwhelm:1 best:1 acquires:1 interacting:1 away:1 nature:4 dipole:12 santos:3 µl:4 state:1 various:1 gases:15 closed:1 between:1 justified:1 conditions:1 recently:4 complementary:1 attention:1 rezayi:1 however:6 vanishing:1 bose:2 configuration:1 suggested:1 both:1 super:2 condmat:1 σc:7 many:1 σe:1 chosen:2 osterloh:1 contribution:1 otherwise:1 inouye:1 gangardt:1 tong:1 asymptotically:1 thierry:1 harmonic:2 σc2:1 dimensional:4 written:1 decreases:1 giovanazzi:3 associated:1 chromium:1 considering:2 hadzibabic:1 geometries:5 addition:1 due:3 been:3 much:1 combined:1 basic:1 anisotropic:1 choose:1 interparticle:1 direction:1 corresponding:2 deeper:1 observable:2 formed:1 gas:6 precision:1 observe:1 irrelevant:1 present:1 case:3 novel:2 solid:2 appearance:1 engineering:1 value:10 employ:1 while:1 replaced:1 behavior:5 error:1 ultra:2 yi:1 studied:1 vd:2 orientation:1 thus:1 iv:1 dettmer:1 itself:1 cond:2 against:1 different:1 verified:1 pseudopotential:10 apparently:1 divergences:1 lett:22 highlighted:1 shifts:2 split:1 units:4 finite:4 evolve:1 wires:1 i1:1 numerical:2 v0:1 moment:3 waveguide:1 potentials:2 changing:2 paredes:1 schr:2 modes:1 well:3 kept:1 analysis:3 without:1 contact:7 feshbach:3 coordinate:1 position:4 model:1 chemistry:1 mic:1 usual:1 distances:4 being:2 rotated:1 obtain:2 shape:4 atomic:1 xdirection:1 scattering:23 note:7 cut:2 character:2 interested:1 attractive:3 stable:1 momentum:5 demands:1 read:1 evaluate:1 showing:1 thalhammer:1 increases:2 grid:2 press:1 using:1 part:1 displaced:1 strengths:1 imposed:1 like:1 particle:1 obvious:1 interestingly:3 unstable:3 become:3 qualitative:1 therein:1 parity:1 creation:1 some:1 back:1 understood:2 choosing:1 vsh:3 matching:1 obtaining:1 scale:1 griesmaier:1 lead:5 resonances:6 avoid:1 microwave:1 ddi:39 does:1 dipoles:5 assuming:1 bessel:2 mode:1 bold:1 detuned:1 pose:1 perpendicular:1 although:2 2m:2 tonks:4 properties:7 asymptotic:6 discussed:2 surround:1 range:22 uchler:2 plus:1 insufficient:1 introduced:2 letter:3 presence:1 communication:1 into:1 within:1 numerically:2 down:1 appropriate:1 references:1 einstein:1 operator:1 body:1 luttinger:1 institut:1 log:1 area:1 assumed:2 strictly:1 support:1 transform:1 fast:1 r3:1 dispersion:1 restricts:1 phonon:1 bosons:3 low:6 way:2 crucially:6 analyze:3 function:11 form:5 forming:1 but:2 expected:1 properly:2 delta:1 line:3 true:1 baranov:3 regularized:4 us:1 ur:1 cir:15 below:3 fermi:1 critical:1 fluctuations:1 problem:8 similar:4 called:1 demille:1 strongly:1 diverges:2 constant:5 moore:1 int:1 universal:2 describe:1 general:3 proper:1 single:1 scanned:1 ronen:2 flight:1 az:1 regime:2 again:2 functions:2 compared:3 dotted:2 no:1 dashed:2 whereas:3 wavefunction:6 when:7 vanishes:1 field:1 other:1 role:3 details:1 solitons:1 dipolar:23 you:1 polar:2 excitation:1 includes:1 important:1 cooper:1 bohn:1 opened:1 correlated:1 coupling:6 assume:2 physics:9 depth:1 confinement:7 mass:1 time:2 meystre:1 kosterlitz:1 oral:2 once:1 |
0705.1669.txt |@word gr:19 alternatives:1 results:1 scalar:5 edu:3 go:1 primes:1 denotes:1 cases:1 consider:4 whose:2 preserves:1 turkish:1 technique:1 tr:10 young:1 finally:1 present:1 excluded:1 under:1 analogous:1 include:3 supported:3 2ra:1 choice:1 ankara:1 fall:1 investigator:1 did:1 solution:13 solved:1 assurance:1 small:1 equation:1 work:1 slower:1 boulware:1 findings:1 sign:3 zero:1 further:1 expressions:1 3r:1 section:3 selected:1 birkhoff:1 above:2 values:4 3a:1 contributes:1 acknowledgments:1 exercise:1 ozg:1 full:1 led:2 arb:1 excludes:1 loose:1 here:7 ranges:1 desired:1 explore:1 ansatz:1 address:3 equations:7 implicit:1 obtained:1 institute:1 study:1 resulting:2 franklin:1 action:9 decouple:1 spacetime:1 glu:1 york:1 uniquely:1 palais:1 equivalence:1 useful:1 classification:2 forbid:1 total:2 derivatives:1 asymptotic:1 positive:2 stated:1 negative:1 going:1 dω2:1 taken:1 more:1 flat:4 itak:1 curvature:5 correspondingly:1 virtue:1 4ab:1 particular:1 known:1 hole:1 given:1 iii:1 must:1 tekin:2 keeping:1 valued:1 ma:1 deformed:1 g00:3 inertial:1 fµν:1 det:1 theories:2 obvious:1 caveat:1 cab:1 example:1 stimulating:1 numbers:1 cosmological:4 give:2 generically:1 rµναβ:13 dropped:1 council:1 allowed:1 unphysical:1 rescaling:1 guarantee:1 end:1 brandeis:2 acts:1 recovers:1 how:2 varies:1 pure:4 instead:1 parameter:1 may:1 informs:1 faculty:1 constants:2 natural:1 appreciate:1 provide:1 maintain:2 so:3 fundamental:1 order:8 gµν:1 bracketed:1 indeed:1 insight:1 displayed:1 course:2 including:2 still:2 its:4 ln:7 relativity:1 coordinates:1 labor:1 better:1 strange:1 derivative:6 defining:2 non:4 thereby:1 lambert:1 universality:1 solubility:1 they:1 singularity:4 gravities:1 nor:1 february:1 2r:1 invariants:4 university:2 2d:5 2a:4 2b:3 radial:1 found:3 weyl:13 metu:2 dωd:1 ef:1 reduce:1 static:1 our:10 ew:1 beyond:1 special:5 out:1 simplify:1 space:1 since:2 rev:1 research:1 fellowship:1 ra:1 rb:6 surprise:1 viable:1 math:1 theory:1 assured:1 divergence:1 differ:1 difficulty:1 california:1 term:7 forbids:1 enormous:1 r0:5 r2:4 geometry:1 could:1 conformally:2 ds2:2 keep:1 signature:1 retain:2 βn:2 generalizations:3 first:3 origin:4 already:1 xn:1 symmetry:1 number:1 bonnet:4 electronic:3 little:1 introduction:1 cµν:1 dt2:2 shell:2 2aa:1 schwarzschild:9 academy:1 immediate:1 part:2 somewhat:1 believe:1 than:2 horizons:3 depends:1 regulator:1 matter:3 exhibit:1 symmetries:1 generality:1 unchanged:1 say:1 substantial:1 seen:1 any:4 pursued:1 ideas:1 note:3 sciences:2 neither:1 new:2 sure:1 allow:1 metrics:1 algebraic:1 but:2 class:4 deviations:1 considered:1 later:1 principle:1 physics:3 fact:1 dover:1 particularly:1 show:1 probe:1 spaces:1 gauge:4 solutions:5 d4:2 trivial:1 deser:6 q2:3 knowledge:1 parameters:1 should:1 only:5 explicitly:1 black:1 removable:1 factor:1 local:1 do:1 notation:1 means:2 dd:1 overall:1 altogether:1 dr:6 justified:1 arxiv:4 grav:2 summary:1 qc:4 mapped:1 fixed:2 fair:1 ricci:4 physically:1 violated:1 flip:1 namely:1 result:1 best:1 tensor:4 succinctly:1 diverge:1 symmetric:6 written:1 various:1 simplest:2 invariant:1 boundary:1 preserve:1 terms:10 extend:1 nature:1 however:4 ln2:1 comm:1 tub:1 alters:1 jb:1 both:4 essentially:1 limits:1 demanded:1 etc:1 dated:1 tubitak:1 contribution:1 finds:1 behaviors:1 point:2 ca:1 cd:1 maintained:1 simply:1 exhibits:1 polynomial:3 moreover:1 turkey:2 arts:1 pq:1 geometries:3 addition:1 copies:1 much:1 interest:1 rather:2 scalars:1 technological:1 general:5 former:1 those:2 case:8 look:1 unlike:2 pacs:1 will:5 technical:1 while:3 behavior:1 conformal:1 a21:1 almost:1 endowed:1 metric:8 iv:1 ii:1 middle:1 reads:2 itself:2 exterior:1 vanish:4 technology:1 grant:2 generic:3 parts:1 quant:2 units:1 finite:3 independent:1 investigated:1 infinity:2 see:2 radically:1 hand:1 necessity:1 off:1 ryzhov:1 changes:2 no:3 well:1 without:3 components:1 ccd:1 model:5 arising:1 dimension:3 spherical:3 4rµν:1 enormously:1 just:2 being:1 obtain:2 actions:3 detail:1 thanks:1 spherically:6 now:1 4a2:1 surprises:1 ease:1 alternate:1 seems:1 except:1 source:2 add:1 pasadena:1 lett:1 easy:1 theorem:1 5d:1 east:1 remaining:1 real:1 presentable:1 loss:4 possible:2 usefully:1 department:2 immediately:1 bit:1 apart:3 insert:1 differentiations:1 reduces:2 performing:1 admitted:1 specific:1 arbitrary:3 degree:1 become:2 conrad:1 waltham:1 methods:1 some:3 b1:10 b2:2 provided:1 dimensions:1 integration:2 tuba:1 does:2 6a1:1 scientific:1 slight:1 properties:3 extension:1 most:1 industry:1 o:1 reduced:1 nonvanishing:1 range:1 extensions:2 horizon:4 mixed:1 introduced:1 contains:1 maxwell:5 into:1 obtaining:1 nsf:1 einstein:3 proportional:2 additions:3 story:1 additional:2 there:10 bianchi:1 was:2 function:3 complete:1 form:5 gauss:4 aµ:1 partially:2 made:1 qualitative:2 consist:1 gravitational:4 up:1 us:1 ur:1 limit:2 problem:1 ωd:1 ab:3 constant:3 defined:1 am:1 denote:1 single:2 identities:1 physical:1 functions:1 compared:1 grr:3 variety:1 fixing:1 when:1 vanishes:1 field:4 other:3 spatial:1 test:1 conclusion:1 models:3 a1:13 a0:4 a2:2 formal:1 4r:1 appendix:1 mass:2 time:3 cpq:1 original:1 augmented:1 |
0705.1670.txt |@word represent:3 secondly:1 results:6 leads:5 cooperative:1 edu:1 gk:6 localized:10 calculate:1 description:1 γk:5 does:1 dressing:4 include:1 tc:6 g1:2 2γk:1 far:2 bilinear:2 intriguing:1 splitting:13 δgk:1 difference:6 condition:6 mielke:1 obvious:1 presented:5 turns:3 tanh:4 solution:10 large:1 small:5 noted:4 gerlach:1 employing:1 foundation:1 dealing:2 consistent:16 thermo:1 cosh:3 approximation:5 zero:14 chen:8 further:3 chem:1 even:3 what:1 plays:1 sub:17 ˆx:3 d2:4 section:4 overwhelmed:1 lights:1 ˆb:11 above:19 ˆi:1 d1:3 method:2 body:1 condensed:1 lee:2 degree:1 respectively:4 guangzhou:1 here:3 understanding:1 reported:1 china:2 making:1 strong:5 equations:4 appears:2 change:1 deduced:1 obtained:2 property:1 study:2 larger:3 reason:2 controversy:3 trial:12 resulting:1 usually:1 suitable:1 makes:1 lowers:2 examining:1 extra:2 discontinuous:34 plenum:1 zwerger:2 addressed:1 decrease:1 fake:1 tools:1 existed:1 readily:1 environment:2 use:2 takes:1 beginning:1 stated:2 ψv:4 next:2 discrepancies:1 calculation:30 noting:1 therefore:2 shed:1 tell:1 more:3 successful:2 becomes:11 stable:5 correspondingly:1 known:6 cases:9 hold:1 iii:2 high:2 account:1 science:1 equation:22 work:2 oscillator:24 modified:1 worth:1 values:3 following:3 under:3 example:5 history:2 f0:7 renormalization:2 figure:2 give:4 process:2 numerator:1 organized:1 states:4 effectively:1 chin:4 numbers:1 sense:1 counting:1 needs:1 goal:1 provide:2 discussion:2 zhang:1 regions:4 how:3 larsen:1 βωk:1 answer:7 instead:1 parameter:7 mat:1 derived:2 them:1 fa:2 lay:1 law:1 physical:1 third:1 grant:2 lines:4 rather:1 shore:1 cannot:2 so:5 as12:1 taking:1 integrand:1 order:2 typical:2 serving:1 help:5 βk2:3 developed:1 mainly:1 stability:1 paper:2 including:1 omitting:1 mentioned:9 still:1 its:2 diagonalized:1 group:2 chosen:1 boson:13 better:1 hou:1 systems:12 main:2 deformation:2 eur:1 correspondence:1 non:11 good:3 combination:2 landau:2 yz:1 bogoliubov:1 now:4 yu:1 nor:1 ωk3:1 represents:4 term:3 always:9 university:2 hamiltonian:5 wong:3 mode:19 found:22 giving:1 side:1 characterized:1 arxiv:1 england:1 another:1 weight:5 energy:30 hard:1 displacement:2 applicable:1 frequency:28 quantum:4 wavelength:1 transitions:3 eq:11 out:4 try:1 shown:16 δγk:1 rep:1 since:8 rev:16 dss:14 increase:1 seriously:1 induced:6 issue:2 shows:14 sinh2:1 theory:2 localization:11 increasing:3 free:9 assures:1 approaches:2 perturbation:1 complicated:2 york:1 dorsey:1 rises:1 e1:5 e0:12 interaction:1 transition:52 keep:1 turn:2 due:5 hence:3 first:4 origin:2 pines:1 reaches:2 done:1 directly:5 reached:9 xp:1 clarity:1 vojta:3 divided:1 given:12 toy:1 temperature:5 introduction:1 leading:6 system:4 needed:1 too:1 calculations:16 2fk:2 oversimplified:1 scheme:40 speaking:1 gives:1 liang:2 trapped:1 tool:1 continuous:10 serve:2 artifact:7 because:2 natural:1 than:8 population:4 jump:9 kind:2 variational:170 determines:2 sc:5 roles:1 second:1 annihilation:1 matter:2 determined:7 kth:1 nie:1 were:1 dutta:1 treated:1 perturbative:1 behaviors:5 function:8 motivation:1 false:1 turned:2 curves:1 crossover:31 say:1 qualitatively:1 take:2 tells:1 lie:2 strength:5 studying:3 self:17 note:2 k2:5 k1:49 k0:14 generalized:3 online:7 new:1 explanation:3 spectral:6 play:1 exactly:2 shall:3 any:1 phases:9 most:1 boltzmann:1 phase:4 analytically:3 δet:2 why:9 kb:1 considered:2 clear:2 gk2:1 coincides:1 feynman:1 points:24 exp:14 dos:33 physics:5 ˆz:2 fact:5 show:5 silbey:1 supported:1 solutions:12 threshold:2 substituting:1 trivial:4 find:6 ground:76 based:33 parameters:3 true:7 state:81 should:10 only:8 factor:6 misidentified:5 equilibrium:1 do:1 predict:1 notation:1 dependent:4 de:1 gea:1 ones:1 words:2 despite:1 neither:1 coth:12 evolution:2 resolve:1 mahan:1 conditions:1 ohmic:43 acknowledgments:1 predicted:19 shi:1 fixed:4 explanations:1 approaching:1 bulla:2 grosso:1 exists:3 physically:1 generally:1 spohn:1 maximum:3 depends:3 sec:2 result:17 fail:68 analog:1 fails:11 phonons:1 clearing:1 yet:1 αc:27 closed:2 routine:1 c2k:2 boundary:8 before:4 approach:2 recently:1 however:11 zhi:1 wu:1 succeed:2 key:3 analyzed:2 banacloche:1 ωc:17 abruptly:1 both:21 last:2 many:2 region:8 according:2 against:1 called:7 dmrg:4 σz:3 σx:1 developing:1 leggett:1 contribution:9 otherwise:1 ck:10 tgs:1 σz2:1 δab:1 tong:2 point:50 color:7 jinan:1 corresponds:1 coincidence:1 ab:10 decreases:6 described:1 2cλ:1 three:7 been:3 whom:1 combined:1 basic:1 expected:2 sachdev:1 fk:6 fig:17 corresponding:4 observable:2 nrg:4 schwab:1 understand:3 spin:13 present:11 case:79 multi:4 pacs:1 solid:1 value:7 will:6 while:7 behavior:13 squeezed:3 situation:10 tunneling:13 couplings:3 very:4 δfk:1 coupled:1 almost:3 owen:1 surprisingly:1 discrepancy:1 iv:1 ii:1 reads:1 cond:1 seen:1 disappear:1 different:13 perhaps:1 righthand:1 author:1 perform:2 make:2 same:11 clearly:3 selfconsistent:1 parts:1 pauli:1 dimensionless:1 finite:2 used:8 parravicini:1 see:5 singapore:1 numerical:7 hang:1 effect:3 hand:1 v0:2 harris:1 totally:1 reference:1 lower:10 off:1 modes:21 nevertheless:3 well:3 analysis:23 obviously:1 academic:1 without:2 firstly:4 model:20 dimension:1 left:1 ny:1 just:6 less:1 when:21 accurate:1 rest:2 λc:11 questions:1 world:1 eigenstates:1 cn:1 k3:1 cut:1 density:2 percent:2 multimode:1 except:2 weiss:1 simple:1 setting:3 lett:3 easy:1 theorem:1 transformation:2 gave:2 around:1 easily:1 showing:6 possible:1 φph:5 increases:14 know:1 press:3 using:2 accepted:1 mod:2 displaced:26 like:5 particle:1 follows:4 adiabatic:1 illusion:3 unstable:6 characterizes:1 ˆbk:6 become:1 by4:1 mathematical:1 satisfactory:2 right:1 methods:2 creation:1 some:13 back:1 examples:1 extended:1 chakravarty:1 confusing:1 happens:7 scale:3 lead:3 demonstrates:1 opposite:1 critical:9 provides:2 prog:1 demonstrated:1 kehrein:1 scientific:1 power:1 martin:1 agreement:1 bk:6 jayannavar:1 analyses:2 super:4 between:8 stage:1 comparison:2 about:2 tracing:1 favorite:1 range:1 consequently:1 cambridge:2 presence:2 garg:1 into:1 integral:1 bound:5 bath:8 down:2 lies:3 appropriate:1 schemes:45 references:2 raises:1 determine:1 operator:1 k12:1 vˆ:2 comparing:2 assumed:1 there:13 question:3 approximate:1 long:3 start:1 low:22 way:5 delocalized:9 was:11 polaron:3 fk2:2 form:3 energies:2 jun:1 but:6 hu:1 failure:8 gain:2 line:1 level:1 dissipative:3 faster:1 made:1 whether:1 up:7 us:1 ωk:12 limit:4 continuously:5 sander:1 problem:3 ωd:40 irish:1 later:1 constant:1 ln:5 defined:1 flow:1 universal:1 contribute:1 general:2 single:13 our:3 controlled:1 regime:3 again:2 functions:2 ev:8 thermodynamical:15 ref:5 no:3 exciton:4 hybrid:8 invalid:1 application:2 other:12 role:1 details:3 department:1 misinterpreted:1 conclusion:4 nonzero:1 stat:1 kinds:1 convincing:1 variation:5 important:11 dissipation:5 fisher:1 matrix:2 implies:5 coupling:13 dω:5 phonon:31 4d:1 starting:2 having:6 once:1 |
0705.1671.txt |@word magnetically:2 limited:3 externally:1 consider:2 chain:2 represent:1 rev:1 magnetic:54 particular:3 amplifier:6 splitting:1 gf:2 quadrature:1 per:4 broader:1 op:1 consists:1 shot:2 disk:1 contributions:1 assembled:2 ptp:2 compact:2 hemmer:2 amplification:2 terms:1 re:2 producing:1 lasers:1 optimization:1 budker:2 contained:1 suspending:1 environment:2 finally:1 program:4 stable:2 visualizing:1 cm3:2 worth:2 sent:1 applied:2 updated:2 supported:1 amplitudes:2 consequently:2 very:11 frequencies:1 rise:1 agilent:1 wave:7 worst:1 axes:1 sidebands:1 resonant:7 difference:4 bringing:1 pumping:1 condition:2 squids:1 splitter:2 impressive:1 presented:7 ref:2 solution:1 large:6 shielded:1 vector:1 elsewhere:1 marinelli:1 small:5 biological:2 accumulation:1 degeneracy:1 prd:1 prevent:1 strongly:1 smaller:3 slower:1 specially:1 allred:1 foundation:1 consistent:1 direct:3 approximation:1 discriminated:1 second:3 fiber:6 evaluated:4 expense:1 selected:1 implemented:1 odd:3 rough:1 institute:1 even:3 index:5 what:1 nonlinear:2 trapping:5 rate:12 clock:1 saved:2 section:1 celebrated:1 dephasing:1 expressed:1 centers:1 cell:5 dynamical:1 experiment:1 above:6 replaced:1 principal:1 method:3 contrast:3 devoted:2 magnetometry:4 simultaneously:1 ms:2 q0:1 respectively:3 commercial:2 transferred:1 atoms:3 ranges:2 reported:3 cylindrical:1 free:2 separation:2 others:1 represented:1 ratio:3 along:1 rochester:2 respect:6 obtained:7 convert:2 stark:1 spite:1 suitably:1 technical:2 involved:2 vectors:1 allows:5 yˆ:1 amount:3 resulting:3 launched:1 permit:1 usually:1 resonance:44 suitable:5 makes:3 numerical:2 diameter:1 via:1 stabilization:4 photon:2 scales:4 offset:1 marked:1 highly:3 scaled:2 modulated:4 preventing:1 quenching:1 planck:1 unit:1 archaeology:1 interest:3 use:2 usb:3 working:5 lasing:2 contains:3 determined:2 arms:2 next:1 discrepancies:1 few:6 harmonics:1 noting:2 examination:1 averaging:1 taken:1 means:3 achieving:2 today:2 more:2 separated:3 flat:1 accuracy:1 gyromagnetic:2 conclusions:1 under:3 envelope:1 emission:2 tested:1 unresolved:1 geophysics:2 discussed:1 varying:1 actual:1 cases:2 iii:1 must:1 high:8 account:2 mf:3 locked:1 room:3 mm:1 science:1 setup:5 work:5 cm2:3 mt:1 mw:1 mv:1 values:6 mp:3 transparency:1 determining:2 following:1 making:2 ibs:3 root:1 example:2 control:2 dedicated:1 scan:8 lock:23 chip:1 preserving:1 belonging:1 states:5 effectively:1 application:3 rubidium:1 performed:5 sense:1 shielding:1 locking:3 calculated:1 axis:2 influenced:1 routines:1 monitoring:3 ahler:1 rather:4 di:4 feature:2 arrangement:1 far:2 pair:1 slow:2 adjacent:2 opt:3 instead:3 absolute:1 dominance:1 circular:2 profile:25 simplicity:1 monte:1 de:1 ft:2 inversion:2 coming:1 may:1 broad:2 oscillators:1 after:3 derived:2 containing:1 lab:1 dei:1 applications:4 produce:2 fe:16 demonstrating:1 waves:2 spectrometer:1 minimizes:1 choice:1 data:13 fm:4 consisting:1 times:1 acquisitions:1 short:1 natural:1 waist:1 third:3 sets:3 light:14 counter:1 capacitors:1 ghz:2 st:1 perform:1 so:5 ultimate:2 fundamental:1 representation:1 vapor:3 cnism:1 typical:5 operations:1 feedback:1 developed:1 over:7 mainly:3 kominis:1 meter:1 years:1 produced:5 raman:2 through:2 filters:3 left:1 linewidth:8 fwhm:3 its:7 ωrf:14 controllable:1 group:1 monitor:1 fit:10 located:2 chosen:1 procedures:1 vicinity:1 decreases:1 edge:1 better:1 detected:3 degrees:1 fig:24 torr:2 total:2 derivative:4 main:1 lies:1 versus:5 non:4 good:1 junction:2 university:1 dac:1 matches:2 bevilacqua:2 material:1 diodes:1 scaling:1 band:3 couples:3 detunings:1 effects:1 optimal:3 employed:1 rotation:2 nor:1 incoherent:1 represents:1 term:4 electro:1 2s:1 fully:2 reasonably:1 level:8 lifetime:1 fringes:2 transmitted:2 mode:3 each:10 found:1 universit:1 quarter:2 side:2 characterized:1 lasting:4 fp:1 differential:10 cost:1 significantly:1 generation:2 series:1 magneto:4 reduce:1 principles:1 related:2 interferometer:2 frequency:50 aim:2 measurement:10 quantum:3 laboratory:4 operation:11 transitions:9 eq:2 unaffected:1 out:2 shown:4 factors:1 gradient:1 sketched:1 furthermore:5 since:1 interference:1 publish:1 increase:5 modulation:17 rf:15 nominal:1 performs:3 siena:5 medicine:1 offline:1 size:2 sensor:16 occurs:1 red:1 shows:1 ecg:1 gate:1 doppler:13 linear:6 fisica:2 possibility:1 standard:3 signal:17 reason:2 formation:1 york:1 besides:2 counteracted:1 approach:1 sensors:3 inductive:1 e0:1 card:6 publication:1 interaction:4 hwhm:2 created:2 record:1 widths:1 roomtemperature:1 transition:6 mariotti:1 confocal:1 filter:4 turn:2 length:1 harris:1 pattern:1 circuit:2 hence:3 multichannel:1 view:3 dipartimento:1 waited:1 first:5 note:1 perturb:1 fg:11 number:2 kimball:2 minimum:2 devices:1 reflects:1 done:2 fast:5 another:1 reached:2 array:2 angular:1 synchronously:1 passes:1 given:4 perturbation:1 checked:1 temperature:5 needed:2 introduction:1 leading:1 interact:1 system:18 adopted:1 parallel:2 their:3 cooling:3 intermediate:1 fleischhauer:2 observations:1 passed:1 realization:1 scheme:1 htm:1 gives:3 excellent:1 reproducible:1 servo:1 trapped:1 ch:1 estimate:2 completed:1 exactly:1 contribute:2 wiley:1 rejected:1 environmental:3 optical:39 suitability:1 maxima:2 lobe:1 sublevels:2 maintaining:1 than:4 ocis:1 population:7 diffusion:1 wide:1 kind:3 polarized:3 determines:3 effective:1 double:2 cimento:2 see:3 submitted:1 preparation:1 compensation:1 classes:2 modulators:1 risks:1 amplitude:9 were:1 providing:1 acquisition:6 perspective:1 hz:15 modulating:1 register:1 symmetries:1 enhanced:1 nuovo:2 fluctuation:2 half:1 msec:2 spectrum:6 comfortable:1 discussions:1 increment:1 need:2 seen:2 obviously:1 any:2 relatively:2 instrumentation:1 geomagnetic:1 strength:2 bessel:1 built:2 zero:1 depending:3 unsuitable:1 essentially:1 latter:1 able:1 mechanism:2 indexes:1 polarization:2 extracted:1 fitting:4 materials:2 absorbed:1 take:1 performance:1 detector:2 strengths:2 modulus:2 tool:1 hyperfine:8 butterfly:1 spectral:5 continuous:3 multiple:1 electric:1 trace:3 opposite:3 buffer:2 measures:1 most:2 connected:2 but:3 preliminary:1 phase:7 coil:2 comparison:1 intrinsic:1 class:1 sub:3 kb:1 operate:2 advantageous:1 considered:2 performances:2 average:1 broadened:3 steady:1 inferred:2 drifts:3 order:15 ks:2 principle:2 exp:1 mechanical:2 thank:1 velocity:2 mrf:2 sd:8 physics:5 away:2 fitted:3 slope:6 thomas:1 selection:1 particularly:1 detection:6 automated:6 synchronous:1 anyway:1 rotating:1 rejecting:1 superimposed:1 earth:11 magnetometers:3 longer:1 find:1 ground:8 nominally:1 current:10 periodically:2 specifically:1 based:8 parameters:7 square:3 less:1 blue:2 written:1 controls:1 calibrated:1 phillips:1 only:4 factor:7 emitting:1 oct:2 coherences:1 bridge:4 plate:2 dl:1 establishes:1 get:2 spurious:1 calibration:1 routine:1 overall:3 dc:2 truly:1 beam:10 magnetooptical:1 nearly:1 new:4 dv:2 during:1 collisional:1 secondary:1 queried:1 stability:1 runs:1 contributes:1 querying:1 upper:2 fields:13 arxiv:1 bytes:1 tuned:3 appear:1 bison:2 common:4 expr:1 including:2 cells:3 thanks:1 bulky:2 magneton:1 bars:2 set:8 human:2 swept:1 achieved:1 acquired:2 generally:2 sensitivity:18 testing:1 lett:1 maximum:10 observed:4 intensity:8 sec:5 result:1 romalis:2 operated:1 close:4 arm:1 best:5 coils:1 phases:2 puts:1 labview:1 µt:1 µw:3 exchange:2 diode:5 pd2:1 pd1:1 symmetric:1 initially:1 state:6 converted:1 inset:1 closed:2 between:4 tens:1 supplied:1 neither:1 reading:5 conditions:10 available:1 comparable:2 recently:1 relative:1 adding:1 scanning:2 controllers:1 weak:6 jr:1 efficiency:1 reproduces:1 analyzed:1 configuration:6 interfaced:1 improve:1 both:11 cos:2 last:1 limits:2 desired:2 many:1 uncertainty:2 pds:1 according:2 zeeman:6 quantization:2 sensitive:3 involve:1 objects:1 picard:1 exceeds:1 contribution:5 estimation:3 whole:2 experimental:9 among:1 sodium:1 relevant:2 cm:4 supply:1 simple:1 perot:2 relaxation:1 narrower:1 sweep:1 2nd:1 distinguish:1 simply:1 scully:2 cs:11 table:1 rep:1 accordingly:2 expensive:3 considering:2 broadening:6 consuming:1 comb:5 described:4 tuning:2 pt:4 knappe:1 observing:1 ledbetter:1 three:3 been:4 strategy:1 rivera:1 pc:4 detuning:18 much:2 pd:2 prl:4 expected:1 ph:1 estimated:4 roc:1 systems:4 settling:2 direction:1 lived:1 corresponding:4 deeper:1 vapors:1 νopt:2 designed:1 formed:3 gas:1 precision:1 readings:4 coherent:9 determination:4 coherently:1 systematic:1 station:1 isolator:2 evidence:1 spin:2 present:1 lyman:1 case:14 p3:1 multi:3 laser:52 p7:1 external:2 reliable:2 expanded:1 voltage:2 lobes:2 value:6 will:2 invoking:1 while:5 dν:2 superposed:1 evaluating:2 error:3 expander:1 procedure:11 resolved:1 collimator:3 unitary:1 coupled:8 almost:2 characteristics:1 thus:2 them:1 discrepancy:1 iv:1 ii:2 canceled:2 itself:1 turns:1 shift:7 investigated:1 increased:2 acknowledgments:1 different:7 inside:1 italy:1 metrology:1 etc:1 circularly:2 media:1 make:5 radiation:2 accomplished:1 same:3 read:1 unity:1 complex:2 changed:1 evaluate:1 units:3 plates:1 several:1 couple:3 ac:4 higher:2 magnetometer:22 independent:1 used:10 http:2 applicative:1 pick:1 driver:2 effect:6 hand:1 v0:2 cesium:1 running:2 levels:4 uses:2 purpose:1 changing:1 totally:3 reference:4 keep:2 threelevel:1 lower:2 narrow:2 kept:1 modes:1 min:2 well:3 analysis:6 bohr:1 without:5 components:5 roma:1 position:4 model:1 sensing:1 cryogenic:1 usual:1 bellow:1 routinely:2 buffered:1 being:1 photo:3 accurate:2 adjustments:1 grynberg:1 obtain:3 db:3 sources:5 bandwidth:1 intervals:1 atomic:10 actually:2 immediately:1 useful:2 minimized:1 speed:1 oriented:2 comparisons:1 josa:3 generator:5 instance:2 absorption:11 excites:1 point:4 smith:1 improvement:2 signals:4 instrument:1 setting:1 transformed:1 adc:6 input:1 mod:1 excited:2 momentum:1 identical:1 insensitive:1 around:5 depends:1 rules:1 advances:1 breaks:1 decomposed:2 possible:4 psd:8 corresponds:3 dark:1 possibly:1 moi:3 caves:1 resistors:1 vacuum:2 confined:1 using:14 bit:3 unique:1 bloom:1 wings:3 color:1 plan:1 hours:1 necessary:4 like:1 shaped:1 sublevel:1 follows:1 reduces:1 performing:2 zoom:1 characterization:1 agreement:1 communications:1 mhz:14 either:1 alternatively:1 output:15 response:6 works:2 reduced:2 deviation:5 sketch:1 because:3 schematics:1 ramsey:2 rms:3 affects:2 successfully:1 some:2 dead:1 stimulated:1 wider:1 unshielded:3 mirror:1 oscillations:1 apparent:1 provided:4 scale:2 flux:1 broadband:1 resonances:3 willis:1 measurements:5 recorded:2 integration:2 microwave:1 polluted:2 waveform:1 does:4 linearly:1 provides:2 prog:1 gradiometer:2 mapping:2 beating:2 chains:4 demonstrated:4 lowest:1 biology:1 noise:22 averages:1 scientific:1 minimization:1 bc:2 seconds:1 coincides:1 δi:3 communicate:1 perpendicular:2 acosta:1 quantified:1 systematically:1 step:3 passive:2 yashchuk:1 2n:1 y2i:4 about:7 central:10 would:3 freedom:1 jm:3 introduces:1 dependence:3 o:2 essential:1 range:10 lorentzian:4 larmor:1 mean:1 slightly:1 automatically:1 fabry:2 aquila:2 real:1 presence:1 into:3 within:1 numerically:2 www:1 due:6 device:2 appropriate:3 geophysical:3 accounts:1 responds:1 determine:2 registration:8 balanced:2 accumulated:1 cohen:2 semiconductor:1 starts:1 additional:2 area:1 measured:5 housing:1 support:1 long:9 measuring:3 sampling:2 width:8 collimated:1 appl:4 low:4 subsequent:2 was:10 energy:2 iˆ:1 function:6 head:2 creation:2 complete:2 vanishing:1 registered:4 differences:1 removes:1 hundreds:1 volume:1 collected:1 neutral:3 ferromagnetic:1 atom:5 beat:2 line:9 highest:1 active:1 expanders:1 pra:2 made:2 rejection:2 evident:1 ωp:5 gravitational:1 variations:5 up:2 us:2 theoretical:2 placed:4 below:1 decays:1 limit:4 ωl:5 spectroscopy:3 pumped:1 observation:2 fluctuations:5 tannoudji:2 stages:1 called:3 nature:1 distance:1 detailed:2 ohm:1 khz:14 required:1 constant:6 6a:2 dof:2 measure:2 general:1 single:11 reliability:1 right:1 together:2 our:9 kocharovskaya:1 controlled:1 gradients:2 avoided:2 weis:3 nm:1 no:1 amounts:1 na:1 arimondo:2 when:15 vanishes:1 nf:2 power:3 field:56 other:3 role:1 department:1 finite:1 coherence:1 wing:1 nt:2 optically:2 elements:3 kinds:1 superposition:1 excitation:9 separate:1 excite:1 center:19 minute:2 update:1 variation:8 generated:7 important:1 allowing:3 additionally:1 variable:1 σi:2 structure:3 building:1 land:1 remote:2 coupling:1 fluorescence:2 resolution:1 interval:1 curve:2 daily:1 fsr:1 fact:2 time:26 n2:5 cpt:58 having:3 once:2 |
0705.1675.txt |@word fredenhagen:1 homomorphism:1 consider:3 remarkable:4 similarity:1 alg:1 copy:3 results:10 four:44 eds:1 thoughtful:1 grateful:1 consists:1 follow:4 expressions:24 λ1l:6 contributions:1 soc:1 devoted:3 content:1 inverse:32 depend:2 calculate:4 auf:1 γr:30 subjected:1 tr:3 gab:2 γk:5 finally:17 does:1 indicate:2 present:4 th:12 under:16 γc:15 γb:15 γa:10 presentation:3 worth:1 γe:4 ingredient:1 string:1 song:1 very:18 rise:1 exception:2 dokl:1 unchen:2 chaichian:3 additional:1 decide:1 entries:3 application:1 emphasized:2 difference:1 matrices:206 deformations:1 condition:1 leads:3 scholl:4 conjugating:1 went:1 presented:2 lorentzinvariant:1 notes:1 nucl:1 list:6 scalar:3 conforms:1 mm:1 k6:6 vector:7 phase:2 wolfram:1 gρµ:1 ml:1 indices:16 gσµ:1 majorana:1 inspection:1 der:5 schroeder:1 upper:1 mn:1 2k1:1 core:1 dealing:2 consistent:5 requirements:2 coefficient:1 direct:4 prevents:1 second:11 value:2 incidentally:1 further:4 differential:2 remarkably:1 linear:5 bilinear:19 index:6 what:4 3x:1 stands:5 brackets:1 schmidke:3 section:10 contracted:2 expressed:2 agrees:1 axial:1 version:5 suq:6 fiore:2 new:6 order:2 method:1 satisfy:2 compact:2 led:1 chose:1 respectively:5 promising:1 here:2 understanding:2 identifications:1 replacements:7 ansatz:1 groups:12 making:2 mlt:2 consideration:4 along:1 xα:2 equations:6 change:1 referring:1 obtained:6 remark:1 antisymmetric:7 vµ:8 institute:2 leaves:1 completely:2 experience:1 later:1 products:13 stressed:1 fakult:1 symmetrical:3 suitable:2 makes:1 montreal:1 live:1 via:3 useful:7 raise:1 muenchen:2 k5:6 app:4 substitution:1 ls:12 replace:3 summation:1 apply:5 establish:4 planck:2 unit:1 clifford:53 standing:2 use:6 projector:6 working:2 prove:7 sake:2 stated:1 charge:1 next:13 few:1 qca:1 explicitly:4 centre:1 recommend:1 taken:2 ψc:3 compactly:1 type:2 refs:8 minor:1 more:14 sort:1 lowering:3 israel:1 qdb:1 qdc:1 ange:1 started:1 becomes:3 γl:75 line:1 ematiques:1 validity:2 aware:1 gλλ:1 appendix:1 proceed:2 known:5 foundations:4 hold:1 dlt:13 account:1 eberhard:1 defines:1 concretely:2 quantized:2 mb:6 deformed:130 recall:5 equation:5 work:10 ρl:4 mk:6 theories:2 mt:4 remain:4 itself:1 obvious:4 columns:1 princeton:2 mr:4 following:19 fulfill:5 arrive:4 endow:1 example:13 proof:1 ihre:1 claim:1 qdeformed:6 indicated:1 give:10 calculation:5 relativistic:2 allowed:3 confused:1 ann:2 lorentz:28 numbers:1 want:2 sense:6 simple:3 coalgebra:1 end:4 provide:2 describes:1 discussion:5 get:10 theresienstr:1 feature:1 write:11 necessary:1 numerous:1 reducible:1 adjacent:1 answer:1 instead:9 verlag:3 obeys:1 wave:2 product:6 express:2 sommerfeld:1 mat:1 algebra:54 may:3 max:1 invitation:1 derived:3 lengthy:2 jhep:1 applications:2 plane:8 physik:4 reshetikhin:1 multiplication:6 representations:15 choice:2 doplicher:1 types:5 transposed:1 stress:1 short:8 remember:2 effective:1 computations:1 generalizations:2 supersymmetric:1 explicit:8 correspond:1 su:4 st:1 rather:5 ones:1 so:18 verify:1 representation:7 heisenberg:2 s1:1 gµν:4 invariance:1 ogievetsky:1 holds:3 interpretation:1 antipode:1 tµν:8 hierarchy:1 indeed:5 over:10 displayed:1 raised:2 characteristic:1 equality:6 course:1 mathematicians:1 paper:2 including:2 thesis:1 mentioned:7 antisymmetrizer:2 its:29 geom:1 discretizing:2 derive:3 group:30 thank:2 maps:1 chosen:1 manin:3 solving:1 lj:2 conjugation:11 li:1 forms:3 lt:1 choose:1 underpin:1 mail:2 schmidt:6 defining:6 deformation:5 supersymmetry:3 split:1 correspondence:1 non:12 good:3 return:1 lukierski:1 combination:3 seeking:1 coproducts:3 watamura:6 introduce:11 tureanu:1 scaling:5 flint:1 they:8 das:1 formulating:1 now:23 yu:4 discuss:9 εm:4 fields:1 easily:2 several:2 dirac:46 2q:75 coaction:8 undertaking:1 university:3 nowicki:1 2x:1 berlin:2 possibilities:1 proceeding:1 l2:5 reasonable:2 each:10 found:8 universit:3 difficult:3 traces:3 side:1 baxter:2 spinor:30 weyl:6 financial:1 directly:1 formulate:2 doing:5 ed:2 reduce:1 idea:1 related:2 conventions:1 constitute:3 contracting:1 literature:2 obtains:1 combining:1 quantum:106 our:23 based:1 differ:1 eq:3 special:2 out:4 respects:1 3k1:1 matrix:36 space:95 restricted:1 furthermore:7 since:5 crucial:1 qc:2 cancels:1 denotes:2 particles:1 replacing:1 adjust:2 multiply:1 hill:1 reader:8 denoted:2 formula:4 illustrate:2 ref:8 mθ:1 math:22 shows:2 uber:2 theory:16 mσ:1 kulish:3 dealt:1 little:2 possibility:1 trq:72 reason:5 universelle:1 ask:1 arraga:1 phd:1 remainder:1 generate:1 repeat:3 care:2 definition:10 derivation:2 βr:19 geometry:2 wachter:7 could:11 klimyk:1 phy:1 traceless:1 counterpart:1 turn:6 int:4 gordon:1 gµµ:7 leading:1 consequence:5 onto:1 assign:1 first:14 xj:5 already:2 features:1 striking:1 third:2 subtlety:1 pa:38 number:1 twisted:1 restrict:1 clear:5 alternatively:3 done:6 least:1 proposing:1 carry:2 calculational:1 γc1:1 γc0:3 udgen:1 γc2:1 counits:2 given:13 grimm:1 checked:3 rewritten:1 covariant:7 similarly:1 introduction:4 unknown:1 achieved:2 system:2 relations:75 their:34 attack:1 demichev:2 antisymmetrized:10 fierz:2 statement:1 convention:2 normalization:1 ordered:1 structures:9 1l:80 listed:2 free:2 γcl:7 calculations:1 relationship:3 compendium:1 bit:1 takhtadzhyan:1 γca:1 realized:1 γcb:1 part:34 too:1 consult:1 x2:3 details:1 theorie:2 representing:2 coefficients:4 γcr:3 spq:1 grassmann:1 kind:4 convenience:1 showed:1 sesquilinear:1 was:6 require:4 enabled:1 imply:2 contravariant:2 recording:1 appealing:1 determined:7 yang:3 were:5 bauer:1 enables:5 treated:2 springer:2 motivation:1 unchanged:1 mind:1 generalization:1 meyer:2 say:1 schladming:1 manner:7 conjugate:7 need:5 seen:2 seek:1 tells:4 contents:1 symmetrized:5 lie:3 built:1 zero:1 dilatation:1 check:1 studying:1 ruegg:1 able:3 ideas:2 pseudogroups:1 λgij:7 note:3 sciences:1 k1:12 take:8 analogy:14 k4:6 xi:8 wonder:1 analogs:12 oeckl:1 calculus:9 play:6 towards:1 trace:22 normal:2 attractiveness:1 3q2:8 sets:1 harmonic:1 plugging:1 most:2 bd:1 involving:2 germany:2 cyclicity:1 formulae:22 remarks:1 acknowledgements:1 inserted:1 why:1 gρρ:2 commutation:10 teilchenphysik:1 preˇsnajder:1 schm:1 observation:5 considered:1 behaves:2 ki:1 sometimes:2 implications:1 km:6 kl:12 takeuchi:1 qba:1 proceedings:2 lowered:1 rev:5 εjl:1 usual:5 physics:5 notion:3 fact:6 think:1 show:5 labels:2 bring:1 attempts:1 spaces:19 relation:10 solutions:1 carefully:2 substituting:2 counit:1 find:12 soq:3 help:3 gleason:1 o:1 q3:2 q2:30 q5:3 q4:4 q6:2 theoretischen:1 should:30 values:2 only:2 bases:10 generators:31 subsection:2 εij:1 factor:3 hopf:14 achieve:2 do:4 dl:8 his:3 above:15 notation:3 means:3 familiar:1 de:4 overall:1 antisymmetrization:1 da:1 aim:3 cannot:3 words:1 international:1 combinations:1 hartmut:2 amer:1 alexander:1 reveal:1 determinants:2 roles:1 die:2 conditions:4 arxiv:1 βl:32 yield:2 summary:3 qa:2 book:1 coproduct:4 slabospitsky:1 wish:1 through:3 fixed:1 valid:3 view:2 reveals:1 requirement:2 set:5 dobrev:1 xa:1 notational:2 clarified:1 cimento:1 accompanied:1 testing:1 lot:1 grosse:2 edition:1 see:17 computer:1 sec:12 result:3 close:1 cellular:1 theoretic:1 analog:5 subject:9 roberts:1 hilbert:1 tensor:14 purpose:1 subsequent:1 review:3 definite:1 supergravity:2 µm:1 written:9 various:2 bialgebras:1 between:8 sum:2 geometric:1 λl:12 approach:1 checks:1 gives:3 notice:15 realizations:1 terms:8 importance:1 εik:1 attention:3 lect:1 however:11 isoq:1 vanishing:5 maximilians:1 distinguish:3 article:10 axiom:2 come:6 tensors:1 antipodes:3 both:4 recherche:1 εki:1 last:8 2n:10 qft:1 many:2 taking:2 ilj:2 according:3 against:1 quantization:2 fulfilled:1 sensitive:1 objects:3 und:3 poincar:5 lifschitz:1 highlights:1 expand:2 uni:2 contribution:1 expression:3 otherwise:1 aa:5 relevant:1 co:1 cn:6 cm:3 conclude:2 reasons:1 seems:1 ca:1 leipzig:2 cf:11 cd:1 dimensional:55 xβ:1 ab:16 simply:4 coordinates:12 moreover:5 cq:4 throughout:1 pseudoscalar:3 mpi:1 ps:5 sine:1 described:1 transformations:8 basis:40 addition:4 invert:1 arbitrary:4 due:2 been:1 shortcuts:1 much:4 combined:3 interest:2 likewise:2 collected:1 ph:3 algebras:12 ak:5 λtr:1 define:5 concentrated:1 determinant:1 enable:1 corresponding:9 reasonings:14 going:2 concerning:8 cambridge:2 fortschr:1 qx:2 understand:1 deep:2 systematic:1 stems:2 gausterer:1 spin:23 former:1 those:7 case:22 anticommutes:2 p0:6 main:1 look:3 invariants:1 ina:1 starts:1 appearance:2 slq:32 arnold:1 remaining:3 will:7 euclidean:42 while:3 replaced:1 behavior:5 applies:2 situation:2 property:2 conformal:1 couplings:1 procedure:1 bin:1 majid:4 unitary:2 dieter:1 vol:1 detq:7 metric:17 thus:8 them:4 repeating:1 ψa:3 ii:5 reads:5 ij:21 dual:16 ready:1 peskin:1 rid:1 pseudovector:1 bispinor:3 different:6 any:2 verified:1 etc:1 perform:1 arguments:4 make:3 formulations:1 lett:5 same:17 clearly:2 εlj:1 read:9 viewed:6 pauli:29 castellani:1 constructed:2 ludwig:1 higher:2 independent:3 zumino:2 used:5 bristol:1 rmatrix:1 singapore:1 comprehensive:1 numerical:1 counterparts:7 hand:4 running:2 fabian:1 uses:2 delicate:1 student:1 hospitality:1 build:2 covariants:20 interested:1 totally:3 identity:5 nishijima:1 lower:3 task:2 off:4 center:1 koch:1 nevertheless:1 changes:1 page:1 well:13 love:1 thought:1 without:1 components:5 convenient:4 jetp:1 position:2 akademie:1 grounds:4 whereas:2 left:22 fand:1 world:1 4q2:1 λt:10 being:6 multiplied:1 λx:2 gravity:1 assigned:1 wess:8 formulated:1 drinfeld:2 transforms:3 correspondences:1 tilde:1 facts:1 uller:1 alternative:1 graduate:1 yet:1 succeeding:1 previous:2 k3:6 rs:14 conjugates:1 preprint:2 k2:14 etruy:1 similarities:1 had:1 assignment:1 realize:2 qx2:1 lattice:2 analogue:1 setting:1 conjugated:3 treatment:1 cb:4 eur:4 x1:4 mod:4 transformation:15 momentum:1 gave:4 identical:3 εt:8 symmetrizer:1 stein:1 iξ:1 rules:4 evaluate:1 decomposed:1 possible:1 spanned:1 corresponds:1 possibly:1 five:1 know:2 insert:1 press:4 using:4 dr:21 unique:1 variables:1 apart:1 noncommuting:1 appearing:1 like:13 c1l:2 exploiting:5 interestingly:1 continue:1 yields:3 bailin:1 always:3 rearrangement:5 become:10 conclusion:3 essential:1 gauge:1 δa:9 copies:5 right:17 variants:3 often:3 deal:5 discrete:2 oriented:1 some:18 begin:3 understood:5 deduce:1 a16:6 examples:1 choosing:1 respect:2 extended:1 sufficient:1 ourselves:1 girardi:1 cψ:1 describing:1 dimensions:6 lead:9 fourth:1 support:2 avoid:2 shall:2 ust:1 superfields:1 comments:1 everything:1 behave:1 decomposition:7 provides:1 3q:7 snyder:1 readily:2 refer:11 inserting:6 carow:3 faddeev:1 object:1 2q2:12 obey:4 bb:1 bc:2 c31:1 equivalent:3 l1:2 landau:1 agreement:1 expansion:9 cλ:5 how:3 step:1 substituted:1 although:1 qˆ:1 refers:2 cη:1 properties:28 westview:1 takes:3 monomials:1 comparison:1 about:4 works:1 would:11 gνν:3 commun:6 discussed:3 generated:1 recognized:3 δc:9 nonvanishing:1 recalling:1 nothing:1 stand:1 woronowicz:2 introduced:10 slightly:1 projectors:4 gamma:1 considerations:2 equally:2 contains:2 publishing:1 undeformed:22 maxwell:1 into:10 within:1 three:23 down:6 lies:3 hermitian:4 square:2 references:1 podle:2 determine:1 sov:3 operator:6 proportional:1 gσλ:1 substitutions:8 leningrad:1 jimbo:1 spinors:39 rows:1 hep:13 classical:4 kern:1 before:2 indispensable:1 there:15 question:2 transform:5 undotted:1 start:2 rept:1 dropping:1 internationale:1 way:10 series:1 scientific:1 xµ:1 sections:1 gij:2 axioms:1 scale:1 complete:5 form:21 epsilon:8 differences:1 but:5 sophisticated:1 ψb:2 repeated:1 construction:3 aµ:6 bagger:1 coactions:18 stating:1 ur:2 violate:1 raising:4 especially:5 gσσ:2 made:3 applying:7 intuitive:1 whether:1 minkowski:39 azc:1 uq:6 up:7 us:35 tell:1 commutative:3 planes:1 ansaetze:3 problem:2 similar:8 called:5 detailed:2 duals:5 ac:1 definitions:3 constant:2 ad:1 introducing:2 defined:8 certain:1 abstract:1 describe:2 am:3 lehrbuch:1 covers:1 denote:4 twist:1 examine:2 arises:1 exist:2 regularisation:1 formulation:1 follows:6 1k1:1 formalism:2 identities:19 calculated:1 physical:5 again:15 superanalysis:1 compared:2 completeness:7 dotted:1 no:1 qλ:9 mathematica:2 detail:1 qξ:3 field:13 zeidler:1 other:3 role:5 φa:1 braided:4 mathematics:1 theor:1 nu:1 regularizing:1 elements:16 congress:1 gol:1 finite:1 prepared:1 a0:12 ξj:1 important:5 a5:6 curvature:1 additionally:2 rqn:1 generalized:1 sides:2 structure:13 relativity:1 independently:1 topologie:1 implies:1 assume:3 starting:2 factors:2 tσ:2 together:13 4q:8 4n:1 noncommutative:2 time:12 far:2 requires:2 nuovo:1 once:5 |
0705.1676.txt |@word limited:3 concept:3 sci:1 consider:3 represent:6 rev:9 magnetic:4 lack:1 results:5 four:3 roy:2 england:1 commute:2 garching:1 computation:27 consists:2 gl:1 rectangles:1 whose:2 hold:1 spin:23 segments:1 deterministic:1 tr:1 rf:1 glaser:8 critical:1 th:2 under:3 ingredient:2 applied:7 probe:1 amplitudes:2 orthogonal:1 far:1 frequencies:1 rise:3 ρth:7 unchen:1 every:2 decide:1 entries:1 experimentally:3 matrices:2 condition:1 molar:1 entire:1 school:1 aliphatic:1 presented:2 ρu:1 try:1 solved:1 convenience:2 detected:5 uller:1 science:2 small:1 biological:1 align:1 programme:1 application:12 expanded:2 deutsch:9 pulse:21 filled:1 reson:6 gmbh:1 j24:1 j23:1 chen:1 further:2 implemented:13 sp:1 theory:1 even:3 what:1 sum:3 contributed:1 labeled:5 find:3 version:4 above:1 mosca:1 new:2 3a:1 increasing:1 method:1 contrast:2 margolus:1 bo:1 chose:2 respectively:3 never:2 here:9 atoms:1 desired:3 selective:8 threads:1 address:3 active:2 ratio:6 along:1 appears:1 obtained:1 institute:1 shift:1 study:1 losses:3 allows:4 orl:1 through:1 amount:1 products:5 knill:1 action:1 resonance:6 implement:2 boc:4 makes:2 der:1 f0:2 via:1 useful:3 extra:1 explained:1 logical:1 addressed:1 apply:3 total:1 propagators:3 manipulate:1 use:9 superpositions:8 usa:2 beginning:4 contains:4 finally:1 induction:1 next:2 popescu:1 taken:1 predictions:2 type:2 theoretical:3 more:3 linden:1 bennett:1 arvind:1 populations:1 composite:1 operators:4 γl:2 tested:1 known:1 cases:2 given:12 effort:1 must:2 sample:5 none:1 ρb:1 ma:2 thanks:2 avoiding:1 equation:1 london:2 remain:1 values:2 ms:2 concepts:2 following:9 coherences:1 example:8 decoupled:2 control:9 indicated:1 give:2 calculation:1 lock:2 permutations:2 neglected:1 implementations:1 states:27 indicates:1 performed:3 allowed:4 david:1 occur:1 tseng:1 information:7 respective:1 end:6 notation:1 rather:3 int:1 discussion:1 holds:1 chemical:1 how:2 numerous:2 pure:8 answer:1 gate:2 mccoy:1 ensemble:18 product:6 description:1 may:4 fz:10 after:4 derived:2 containing:2 scalable:2 independent:5 4th:1 offset:4 coming:1 spectrometer:1 wave:1 meaningful:1 parallel:3 qap:1 ramanathan:1 drop:1 fahmy:6 spectra:5 lines:1 correspond:4 element:2 switch:1 cannot:1 so:2 fundamental:1 representation:2 order:6 talk:1 operations:2 gershenfeld:1 pulsed:2 eigen:1 produces:2 indeed:1 over:4 spectral:1 soc:3 symbols:3 eiθk:2 thermal:14 experiments:7 including:1 holton:1 suffer:1 avenue:1 its:3 level:1 controllable:1 outer:7 thank:1 decay:1 chosen:5 interesting:1 solving:1 forms:1 subpopulation:1 systems:4 fid:3 covered:1 main:1 overcome:1 correspondence:1 freeman:4 non:9 good:1 pauli:1 thereby:1 matches:1 wolfgang:1 practice:1 runs:1 introduce:1 encouraging:1 scaling:4 effects:3 they:1 instead:1 oxford:2 rotation:3 now:1 discuss:1 term:8 adjacent:1 fully:1 university:1 hamiltonian:8 2x:6 2z:2 magnitude:1 reasonable:1 each:17 found:2 universit:1 macchiavello:1 side:2 referred:2 domain:1 transforming:1 directly:5 ej:1 reference:1 series:1 energy:1 hard:2 reduce:1 gaussian:2 related:2 balanced:11 used:14 expect:2 measurement:6 quantum:36 our:4 approximated:1 transitions:1 extract:1 special:1 er:2 large:2 shown:6 actively:2 matrix:17 space:11 restricted:2 furthermore:1 since:2 crucial:1 cancels:1 fx:1 acting:3 ref:2 integrated:2 shows:1 earlier:1 linear:2 interactions:2 diagonal:21 free:2 standard:6 approaches:1 unwanted:1 jozsa:9 additional:10 magn:7 ρrs:2 created:1 starts:1 computers:4 fb:3 keep:1 turn:1 technische:1 uggen:1 place:2 exponentially:2 1x:1 hence:7 bodenhausen:1 lth:1 first:4 separable:1 initial:18 probability:1 powerful:3 number:30 lond:1 channels:1 clear:2 simplified:1 construct:2 another:1 4b:1 open:1 size:9 little:1 necessarily:2 temperature:3 indicate:2 introduction:1 leading:1 demonstration:3 behaves:2 system:16 least:1 needed:1 chem:2 realization:2 dfg:1 molecular:1 final:1 scans:2 shifted:1 implements:1 exactly:1 homonuclear:1 part:2 manipulation:1 x2:3 diminish:1 eliminated:1 ernst:1 representing:1 than:7 x4:3 havel:3 albeit:1 kind:1 scheme:1 decided:1 liquid:3 amide:1 was:13 require:1 imply:1 utilizing:1 preparation:6 compensation:1 individual:4 nonresonant:2 were:8 bauer:1 collins:2 gives:1 hz:6 obstacles:1 boston:2 topics:1 measure:1 spectrum:4 trilinear:4 discussions:1 say:1 angew:1 manner:1 eggenberger:1 concentration:1 unaffected:1 occupied:1 clearly:1 heff:2 strength:1 angle:2 boyd:1 zero:9 convenient:2 glycine:4 isolated:3 note:7 extracted:1 high:2 take:1 algorithms:5 bilinear:4 play:1 multiple:1 though:1 molecule:33 most:1 boltzmann:2 said:1 germany:2 phase:10 coil:1 measured:2 why:1 workshop:1 artefacts:1 observation:1 considered:2 medical:1 differ:1 deuterium:2 braunstein:1 exp:17 kt:7 physics:1 section:3 fact:2 shor:1 intensity:4 show:5 text:1 labels:1 rth:1 longitudinal:2 rotating:2 chuang:2 solutions:1 x3:3 availability:1 fifth:1 based:6 ensembles:2 implementation:6 explain:1 written:1 should:3 only:11 experiment:2 subsection:2 molecules:24 factor:2 local:2 equilibrium:8 brockett:1 do:1 waltz:1 pharmacology:1 get:1 de:1 overall:3 expectation:9 schematic:2 negative:1 3b:2 during:7 procedures:2 evolution:4 contributes:1 introduced:1 conditions:2 arxiv:1 acknowledgments:1 streamlined:4 contain:3 pulses:16 traceless:3 doublet:5 view:1 available:7 requirement:1 set:4 res:1 exists:1 sep:1 acquired:2 frame:1 detection:1 campbell:1 see:5 computer:8 result:1 eliminating:1 multiplet:3 operated:1 acts:1 best:1 techniques:1 permuted:1 still:2 capacity:1 nuclear:5 µs:4 initially:1 state:59 boulant:1 between:5 invariant:1 warren:1 approach:2 αl:6 preserve:1 barenco:1 terms:18 ability:2 vertical:1 qubits:15 inphase:1 however:6 scalability:1 implementing:1 harvard:1 comm:1 tum:1 key:3 distinguish:2 article:1 ket:1 distribution:1 topology:2 faced:1 both:3 2n:5 many:4 against:2 σz:2 sattler:1 receiver:1 distinction:1 qubit:14 argue:1 ilz:3 experimental:13 otherwise:1 unitarily:1 cj:3 impediments:1 ch:1 point:6 carbonyl:2 effective:6 relaxation:1 corresponds:2 exploit:1 simply:3 sequences:2 cs:4 constant:14 throughout:1 cu:4 cory:4 described:3 transformations:2 second:2 capable:1 addition:1 create:2 copies:2 been:6 imperfections:1 whom:1 much:1 combined:1 basic:1 expected:7 applying:3 ph:2 marx:4 fig:16 corresponding:14 observable:1 sufficient:2 coherence:1 coherent:5 c2:4 irrelevant:3 present:6 case:12 compatible:1 schmidt:1 exponential:11 straight:1 bruker:2 value:11 remaining:2 will:15 behavior:1 applies:2 gerhard:1 couplings:3 resolved:2 unitary:17 coupled:3 steffen:2 sleator:1 thus:1 vs:1 il:1 fonds:1 technology:1 inf:1 different:2 decoupling:4 combination:1 etc:1 saw:1 make:1 same:12 any:4 shifts:1 complex:1 quant:3 arguments:1 widely:1 myers:3 resulting:3 dα:4 grows:1 evolve:2 literature:2 upon:2 effect:1 doublets:1 natl:1 kim:1 decouple:1 infinite:1 yuan:1 identity:2 i2x:1 i2y:1 i2z:26 fourier:1 off:7 ekert:1 i1z:13 boxes:2 without:1 solve:2 ilx:1 thoroughly:1 very:1 entry:3 chemistry:2 dimension:1 usual:1 gates:1 magnetization:1 just:1 less:2 being:2 woodward:1 adjustments:1 wagner:1 obtain:1 vanishes:1 schack:1 transforms:3 questions:1 integer:2 facts:1 shorthand:1 multiples:2 previous:3 adv:1 5x:3 density:45 bell:2 except:1 signals:1 setting:1 keeler:2 lett:1 easy:1 technological:1 relevance:1 transformation:9 match:2 identical:3 evaluation:1 increased:1 read:1 possible:3 divincenzo:1 cf:1 test:4 increases:2 caves:1 five:3 entangled:1 similarly:1 press:1 using:8 τkl:2 amr:2 loss:3 necessary:2 shaped:2 follows:1 signal:15 qxi:1 shapes:1 steps:1 either:3 arbitrary:2 fluoride:4 reduced:1 spins:25 accessible:5 because:6 laflamme:1 classical:8 sequence:18 some:3 cancel:2 b0:1 cr:3 duration:5 nonzero:1 provided:1 scale:1 describing:1 dimensions:1 demonstrates:1 decision:1 shall:3 per:10 heitmann:1 does:6 decomposition:2 bra:1 provides:2 assuming:1 yields:3 proc:6 lucid:1 measuring:2 destroys:1 noise:2 nmr:18 ufb:2 processing:3 pp:1 step:3 although:1 explicitely:1 hadamard:1 cα:1 prepared:2 hilbert:1 cnot:3 1z:2 about:2 would:2 basis:22 discussed:2 factors:1 simulation:3 practical:3 mutually:1 nothing:1 act:2 mixed:4 importantly:1 mean:1 equally:1 computational:4 followed:1 presence:1 into:3 rotations:14 due:3 contrasts:1 hermitian:1 acad:1 operator:38 proportional:7 industrie:1 theoretically:1 log:1 prepare:1 synthesized:1 segment:14 support:2 there:6 question:2 transform:6 width:1 detectable:1 futile:1 way:3 ed:1 forward:1 formed:1 analyze:1 sections:2 propagator:5 synthesis:1 function:16 commutes:1 form:5 smolin:1 but:2 principles:1 underlined:2 line:1 removed:1 j12:2 j13:2 truncation:1 pseudopure:2 compute:1 4x:2 full:3 deterministically:1 whether:3 meeting:1 probabilistic:1 up:2 us:4 below:1 frequency:4 limit:1 ωl:3 suitable:1 demonstrate:3 problem:6 uf:4 similar:1 average:2 khz:3 associated:1 computing:9 defined:3 certain:1 describe:2 weinfurter:1 frames:1 general:5 levitt:2 eu:1 single:11 exist:1 promised:1 controlled:3 gradients:2 operation:1 constructed:1 functions:6 i1y:2 i1x:34 dotted:1 no:4 eq:4 νrf:1 gyromagnetic:1 when:2 inset:1 field:4 other:5 role:1 details:2 department:1 out:2 conclusion:2 happens:1 elements:12 superposition:8 separate:1 khaneja:2 durations:2 problems:5 includes:1 important:3 bounded:1 dissipation:1 transfers:1 4d:1 structure:2 jones:1 independently:1 implies:1 coupling:6 algorithm:19 assume:2 starting:5 required:2 4c:1 4n:2 eliminate:1 mimic:1 parallelism:4 time:5 cleve:2 decoherence:2 requires:2 avoid:1 4a:1 |
0705.1677.txt |@word holman:3 abundances:5 transitions:1 consider:1 remarkable:1 similarity:2 caused:1 excellent:1 gap:1 results:4 existing:1 leads:1 known:2 systemic:1 tycho:1 heliocentric:1 cameron:12 inflating:1 remarkably:1 disk:1 mp:1 rom:1 synthetic:10 whose:1 zone:1 brault:1 young:1 containing:1 environment:3 program:2 fischer:4 present:4 excluded:1 ti:2 atlas:1 characterised:1 indicating:1 2mass:1 brown:1 observatorio:1 very:8 multi:1 choice:4 indication:1 uncertain:1 difference:1 sme:5 treating:1 school:1 presented:2 solution:2 large:3 donovan:1 phase:1 bodenheimer:2 small:1 ree:1 dip:1 noted:1 inconsistent:2 upper:2 smaller:1 ten:1 contrasting:1 trend:3 bakos:3 consistent:4 among:1 balachandran:2 tex:1 likely:3 marcy:1 spectroscopy:1 spectrograph:5 follow:1 further:1 wings:5 even:2 established:1 what:1 errors:1 appear:1 testerman:1 giving:1 sun:3 section:1 selected:1 access:1 tyagi:1 melo:1 above:2 referees:1 shallis:2 method:2 temperatures:6 revealing:1 layers:1 agreement:5 full:2 simultaneously:2 lee:1 extrasolar:1 iraf:1 indicator:2 here:4 vald:1 l21:1 reported:2 tracks:2 andrews:3 others:1 macroturbulence:5 accretion:1 strong:6 respect:2 extreme:1 obtained:11 notably:1 instituto:1 dashed:1 supersolar:1 receive:1 fielding:1 study:2 larger:1 allows:1 commonly:1 leaving:2 kochukhov:1 suggests:2 amount:2 ikoma:2 published:1 dougados:1 history:1 studies:6 blackbody:1 useful:1 convolution:1 ftot:1 requiring:1 transit:1 fuhrmann:2 groenewegen:1 spanish:1 decrease:2 sestito:2 photospheric:2 total:1 tools:1 canarias:1 plot:1 use:4 wealth:1 would:5 dictated:1 contains:2 comparing:1 luminosity:2 9ss:1 type:2 theoretical:2 minor:1 more:5 flat:1 vmac:6 asterisks:1 successful:1 correlate:1 stable:1 corrected:1 om:1 instrumental:1 primarily:1 commissioned:1 profiles:4 particular:2 eccentricity:1 mounted:1 circle:1 insights:1 abundance:9 mg:24 rotational:3 integrating:1 science:1 challenge:1 mn:1 oscillator:1 modified:2 reproduce:3 ρp:1 allende:1 values:3 three:2 caveat:1 henry:2 growing:1 root:1 example:3 decoupled:1 sinusoidal:1 compare:2 finland:1 figure:5 give:1 calculation:1 pont:1 magnitudes:2 l45:1 high:10 ready:1 assumptions:2 council:1 allowed:1 orbits:1 hydrogen:1 forestini:1 swedish:1 xxxx:3 goal:1 provide:3 discussion:1 six:1 idl:1 regions:7 how:1 methodology:1 contrasts:1 possibly:1 optimal:1 parameter:9 sin:7 sato:4 astroph:1 de:3 galactic:1 description:1 may:4 reconciled:2 earlier:3 derived:7 santos:7 diagram:3 modest:1 plane:1 fe:5 cambridge:1 end:2 arhus:1 data:6 types:1 dynamical:1 effective:7 following:1 light:4 spectra:17 lines:11 st:3 149026b:4 si:2 cannot:2 winn:3 sect:4 fundamental:2 correlation:5 clusters:1 acknowledges:1 order:6 nearly:1 evolutionary:8 fife:1 burn:1 frandsen:3 soderblom:1 developed:2 pointed:2 spectral:6 mainly:1 pyraf:1 tamuz:1 outer:2 produced:1 paper:5 including:2 still:3 its:13 features:2 style:1 derive:2 group:1 thank:1 fit:2 located:1 interesting:1 masses:4 li:16 detected:2 complex:2 systems:2 mail:1 main:4 might:1 versus:1 non:1 good:4 marginally:1 greater:1 python:1 adopted:2 evolution:3 investigated:1 mccullough:3 often:1 process:1 astrofisica:1 subtraction:1 they:4 bressan:1 feature:2 scatter:1 thes:1 discuss:1 nor:1 continuum:2 represents:1 february:1 several:4 hereafter:1 january:1 university:3 routines:1 identified:1 establishing:1 magnitude:2 latham:2 2b:1 radial:8 inherent:1 spectroscopically:1 interpolation:1 ilyin:1 side:1 metalrich:1 reproducing:1 individually:2 square:1 telescope:3 weight:1 evolve:2 reference:1 hard:1 related:2 applicable:1 each:6 contracting:1 used:8 obtains:1 combining:1 substantially:2 our:16 inflated:1 randich:2 out:5 gonzalez:3 hcs:2 rp:2 space:1 open:1 since:2 projected:2 research:1 increase:1 atlas9:1 isochrones:1 dominated:1 photometrically:2 performs:1 surprise:1 newly:1 squares:1 cause:1 integrated:2 shows:5 fiber:1 theory:2 found:1 easily:1 frank:1 rjup:1 mechanisms:1 guess:1 standard:1 five:1 difficulty:1 proxy:1 estimate:6 beginning:1 compositions:1 additional:3 poses:1 unresolved:1 created:1 determining:3 could:4 similarly:1 so:3 times:2 demarque:1 place:1 massive:2 lte:4 hence:1 uses:2 marigo:1 first:2 ability:1 there:1 xo:2 wasp:50 number:2 ks:1 bertelli:1 done:1 relations:2 directly:1 robust:1 thick:2 fluxes:1 quality:3 salasnich:1 given:3 checked:2 transiting:5 st5:1 introduction:1 unknown:1 night:1 system:3 least:1 bensby:2 tanigawa:1 their:14 1b:8 observations:3 calculations:3 molecular:1 final:3 recovered:1 too:1 correlations:4 boesgaard:1 programs:1 reradiation:1 estimates:4 relative:1 accurately:1 lists:2 nearby:1 released:1 assumption:1 optical:3 gyr:10 apjs:2 authors:2 albedo:2 than:11 wide:2 l41:1 observatory:1 third:1 showed:2 mazeh:1 largely:2 namely:1 submitted:1 sweden:1 determined:12 were:5 sophie:1 gives:1 result:3 ribas:1 counter:2 remained:1 correction:2 conventional:1 ages:2 spectrum:16 curves:1 starkly:1 substantial:1 goodness:1 constrained:1 any:3 relatively:2 nights:1 apparent:1 zero:2 blueshift:1 efficient:1 lin:2 gravity:1 reddy:1 note:1 fitting:2 internal:2 analogy:2 interior:4 environ:1 smalley:3 strengths:1 coreless:2 accuracy:4 echelle:3 redetermined:1 differences:1 allow:1 investigations:1 quote:2 russel:2 who:1 reach:2 lodders:1 iceland:1 printed:1 significant:1 preliminary:1 remarks:1 l159:1 measured:2 inconsistency:1 latex:2 relates:1 redistribution:2 considered:1 clear:1 fies:4 metal:7 inferred:2 km:12 typeset:1 looked:1 part:1 inaccuracies:1 diagnostics:1 velocity:8 constrain:2 physics:3 fitted:1 laws:1 ecuvillon:1 planetary:2 atmosphere:3 saumon:1 vf05:9 show:3 text:2 scattered:2 furenlid:1 infrared:2 discovered:1 radii:4 relation:2 obliquity:1 petford:2 tentatively:1 earth:2 tend:1 fine:1 find:7 gilli:2 giant:7 slow:1 based:5 parameters:30 produces:1 enough:1 calibrated:1 only:4 rich:6 indeed:1 haugh:1 do:3 valenti:5 dominant:1 means:1 routine:1 yielded:1 methods:1 tens:1 deplete:3 listed:2 words:1 despite:1 during:2 suggest:1 saturn:2 freedman:1 reveal:1 processes:1 israelian:5 densities:4 covering:2 denmark:2 arxiv:4 yield:1 tuned:1 twice:1 contain:2 through:2 implication:1 fixed:3 sep:1 setup:1 blackwell:2 irradiation:1 set:4 art:1 pfeiffer:1 observer:1 higher:3 lifetimes:1 national:1 hα:2 turbulent:1 grey:1 observed:5 roque:1 see:14 individual:5 radius:13 mature:1 enhanced:3 operated:1 close:3 optimum:1 acts:1 best:4 techniques:1 closer:1 position:2 lejeune:1 mayor:5 cd:1 state:1 difficulties:1 various:1 between:11 orbiting:2 hebb:3 across:1 oversized:1 discovery:1 choose:1 comparable:2 triplet:2 recently:1 keele:1 parent:5 nature:1 initially:1 weak:5 however:5 sunspot:1 spectroscopic:8 efficiency:1 vrad:4 jointly:1 key:1 contamination:1 rapidly:1 improve:2 suggested:1 received:1 providing:1 always:1 many:1 region:7 uncertainty:4 staffordshire:1 against:2 called:1 sensitive:8 context:1 similarities:1 variance:1 finds:1 otherwise:1 strongly:5 adjusted:1 unclear:1 point:3 simple:2 ca:4 clues:1 corresponds:2 environments:1 prieto:1 dimensional:2 alone:1 table:7 broadening:5 marley:1 vmic:4 mara:3 second:1 basis:1 addition:2 absence:1 been:3 extraction:1 reduction:6 primordial:1 slowly:1 combined:1 interest:2 expected:2 ph:3 contraction:3 fig:3 rather:1 both:2 mind:1 formed:1 gas:5 requires:2 new:2 argument:1 underabundant:1 compromised:1 astron:1 those:3 reddening:1 applied:1 inhibit:1 atmospheric:5 solid:3 norway:1 empirical:3 value:17 piskunov:8 dept:1 while:3 5bg:1 encountered:1 error:2 muchachos:1 balance:1 temperature:13 yi:3 seven:7 file:2 mexico:1 simulations:1 thus:6 zucker:1 surface:1 heating:1 helped:1 itself:1 comparative:1 convection:1 ephemeris:2 iro:1 around:1 orbital:2 vogt:1 different:5 hubbard:1 indicate:2 author:1 perhaps:1 distributions:2 make:1 radiation:2 cross:1 same:1 check:1 shifts:1 parts:1 underestimate:1 widely:1 units:1 lithium:20 nightside:1 composition:2 difficult:1 status:3 independent:5 literature:1 imply:1 comprehensive:2 everett:1 numerical:1 primary:1 hand:1 average:1 v2:1 moving:1 purpose:1 kim:1 propagated:1 normalization:2 esquerdo:1 lower:2 off:2 database:1 los:1 changes:4 no:4 well:8 roughly:1 analysis:12 gsc:1 without:1 nordic:3 fixing:1 ky16:1 model:8 charbonneau:8 self:1 latest:1 distances:1 just:1 less:3 gehren:1 accurate:1 obtain:3 isolated:1 mardling:2 identify:1 atomic:2 followed:1 yet:2 previous:1 mjup:1 unique:1 candidate:1 density:6 absorption:1 extra:1 except:1 weiss:3 bench:1 5m:1 stempels:6 unambiguously:1 easy:1 structural:1 hat:2 exoplanet:4 identical:2 explained:1 increased:1 depends:1 format:1 conclude:2 bands:1 measurement:1 possible:1 smithsonian:1 early:2 photosphere:1 increases:1 grid:4 mon:1 background:1 destroy:1 press:2 using:7 accepted:1 unconstrained:1 formal:1 atmospheres:3 apj:13 necessary:1 like:2 cooler:2 should:1 signal:3 velocities:2 flux:4 steps:2 kupka:3 essential:1 del:1 barnes:1 because:5 teff:17 lundstr:1 sequence:4 some:1 showman:2 microturbulence:2 underabundances:1 warmer:1 accelerate:1 moreover:1 feltzing:1 little:1 jeffery:1 girardi:3 scale:1 dense:1 confirm:1 broad:1 measurements:3 ice:1 depletion:2 does:1 fortney:3 assuming:3 hosts:2 rebolo:1 propagating:2 core:6 varying:1 noise:4 scientific:1 minimization:1 slight:1 rock:1 aj:2 analysed:2 constructive:1 stellar:27 pressure:1 host:11 biases:1 although:4 209458b:2 tidal:1 analyses:1 super:1 properties:5 after:1 panel:2 comparison:3 about:1 ryabchikova:2 island:1 fringe:1 dependence:1 o:6 compatible:1 range:6 signalto:1 constraints:2 slightly:3 obs:1 ida:1 underabundance:1 soc:1 own:1 hubeny:1 nso:2 orders:1 into:2 within:1 obtaining:2 due:3 pair:1 references:1 determine:7 frames:1 factor:1 approximately:1 irfm:4 mental:1 uncertainties:10 log:24 assumed:3 support:2 initial:1 width:1 much:1 low:4 stars:20 astrophysics:1 was:6 synthesis:1 function:2 jones:2 north:1 form:1 offer:1 adjusting:1 irradiating:1 budaj:1 but:6 guillot:6 astro:3 taken:1 heat:2 solar:4 automated:1 mnras:2 line:17 highest:1 true:1 hd:14 butler:1 made:2 kurucz:6 understood:1 whether:2 la:1 gravitational:1 burrows:8 variations:2 up:1 us:2 planet:13 placed:1 below:1 astrophysical:1 limit:3 verification:1 uk:3 shporer:3 panels:1 similar:10 procyon:2 detailed:4 ac:1 associated:1 reconcile:1 minutes:1 abstract:1 describe:2 covers:1 balmer:3 diverse:1 au:1 planets:15 wavelength:7 collier:13 chiosi:1 ohp:1 eric:1 physical:1 ni:2 compared:4 dotted:1 calibration:2 na:3 when:1 elemental:4 acknowledgments:1 other:13 details:1 correlates:1 opacity:1 elements:2 star:16 reetz:1 models:7 envelope:2 prepared:1 metallicity:13 important:1 palma:1 allowing:2 included:1 astronomy:2 structure:2 exposure:1 building:1 correlated:3 exoplanets:2 described:1 resolution:1 age:13 bottom:1 speculations:1 orbit:2 together:1 original:1 siess:3 mass:11 fact:1 time:1 determination:2 starting:2 having:1 barklem:6 |
0705.1678.txt |@word ei:2 ej:8 ai:2 emax:1 nbu:4 ex:1 w0:2 2s:1 s2n:5 d2:1 elab:8 θlab:8 nel:4 mb:8 dbu:2 nb:2 σel:1 rx:5 l1:2 pb:5 nucl:1 ǫ2n:5 he:5 nt:1 sin:1 ri:1 θi:17 θc:1 de:1 dσel:3 a0:1 mev:17 v0:5 dω:8 nov:1 eα:1 n2:2 x5:1 a1:1 r0:2 emin:1 sr:4 arxiv:1 dσ:8 tc:2 dedω:1 a2:1 l2:2 deα:4 n1:2 2n:3 jπ:1 deg:2 |
0705.1679.txt |@word neighbors:1 represent:3 now:1 code:1 sci:5 consider:5 chain:1 priori:2 green:1 global:5 people:2 focus:1 ds:1 existing:1 four:7 signatures:1 per:1 edu:1 consists:1 follow:1 remarkably:1 abundant:5 gj:1 gi:2 row:1 excludes:1 ıs:1 cardinality:2 caveats:1 combined:1 similarity:1 centers:2 send:1 res:2 finally:3 monotonically:1 those:4 under:1 nodes:64 division:1 belonging:1 labels:1 g1:2 divisions:1 far:2 choice:1 c47:1 every:1 cellular:1 associated:1 segr:1 matrices:4 encounter:1 partitions:5 northwestern:3 school:3 thiele:1 dij:1 level:76 uncovering:2 natl:5 girvan:1 large:2 small:1 biological:4 markov:1 shows:2 uncovers:1 averaged:1 ten:2 maximization:1 direct:1 bergmann:1 second:15 cost:2 displays:2 go:1 milo:1 rigorous:1 further:1 dynamics:2 ıaz:3 goes:1 even:5 reproduce:1 material:3 nonlinear:1 plays:1 appear:1 organisms:1 sum:2 selected:1 find:16 current:2 keck:1 kashtan:1 above:3 new:5 ever:1 method:27 contrast:3 satisfy:1 detects:2 statistically:1 processing:1 simultaneously:1 degree:5 exchange:3 respectively:2 genes:1 component:1 here:6 understanding:2 reported:1 ansatz:2 groups:15 address:1 alone:1 based:2 along:3 table:2 appears:1 interpret:1 box:7 balance:1 institute:1 study:1 studied:2 shades:1 reason:1 commonly:1 amount:1 throughput:1 social:3 genome:2 hopfield:1 fitting:1 uniquely:1 via:1 useful:2 randomness:1 family:1 africa:1 seven:1 objectively:2 visible:2 addressed:1 duch:2 subjectivity:1 apply:3 total:2 establish:1 asi:2 landscape:4 ziv:1 plot:5 use:6 john:1 hierarchically:9 proceed:1 usa:6 probabilities:2 contains:1 predictions:1 next:1 eleven:1 program:1 call:1 opposed:1 means:1 iteratively:1 validated:1 theoretical:3 andr:1 separated:1 flat:2 leese:1 schematic:1 share:2 watts:1 award:1 virtue:1 particular:3 known:2 cases:3 hold:7 iii:1 must:6 states:1 amaral:10 graphic:1 ma:2 evolution:1 cluster:2 science:8 work:1 theories:1 erd:2 left:2 minimum:1 caveat:1 growing:3 fulfill:2 example:1 decoupled:2 control:1 compare:2 links:4 organized:5 naturally:1 pons:1 high:3 assumptions:1 want:2 exclude:1 vecchi:1 organizes:1 itzkovitz:3 azquez:1 information:21 needs:2 united:1 requirements:2 fortunato:1 s3:1 s2:1 s1:2 holds:2 chemical:1 maps:3 criterion:5 significance:3 optimal:2 axis:1 parameter:2 ensemble:11 classify:1 belongs:1 guimer:9 description:1 mav:4 may:2 max:1 advice:1 earlier:1 lab:1 connectivity:2 membership:16 zuk:1 date:5 representations:1 truly:1 data:6 types:2 sx:1 jiang:1 explicit:1 correspond:5 mjk:1 provide:1 annealing:1 sons:1 algorithms:3 decreasing:1 representation:4 element:2 acknowledges:1 transitivity:1 order:8 g11:2 pardo:4 interpretation:2 closely:3 correlation:2 hierarchy:18 indeed:3 over:3 insight:1 g111:1 murray:1 hartwell:1 including:1 statistical:2 coli:7 existence:2 still:1 ieee:1 its:9 palsson:3 group:18 thank:2 fit:2 how:1 chosen:1 li:2 better:1 attraction:1 absence:1 lu:1 degrees:2 systems:10 orange:1 mail:2 main:4 overcome:1 eur:2 correspondence:1 non:5 affected:1 greater:1 reveal:1 propose:5 cel:1 ye:1 fig:22 introduce:3 landau:1 scaling:1 arnold:1 they:5 half:1 communities:3 bar:2 comprised:11 nor:2 structural:1 guilera:3 minnhagen:1 airports:1 always:3 university:7 classified:8 proteins:1 normally:1 pathway:11 merge:1 improvements:1 2a:1 2b:1 each:34 2l:1 found:2 identifies:5 european:1 side:1 mean:1 homogeneous:3 weighs:2 schemes:2 significantly:1 secondary:1 contiguous:1 principles:1 related:1 challenges:2 used:4 expect:1 measure:9 our:23 beyond:2 extract:4 clauset:2 out:2 maximizes:2 network:65 quantify:3 furthermore:1 since:2 rev:11 research:1 increase:1 assignment:3 surprise:1 collocated:1 squares:3 issue:11 correct:2 red:1 common:1 foundation:2 wiley:1 goto:2 interactions:3 koopmans:1 diagonal:10 pub:1 standard:3 versus:1 completely:1 verify:1 uncover:3 put:1 org:5 detecting:3 barab:2 inevitable:1 definition:1 pairs:2 transistors:2 ministry:1 airport:1 modularity:11 turn:1 edges:1 circuit:5 signature:1 facilitate:1 think:1 first:7 size:3 major:7 already:1 features:1 probability:5 reveals:1 researcher:1 relate:1 bioinformatics:4 powerful:1 number:22 nested:17 restrict:1 randomized:1 smaller:3 biol:1 another:2 spanish:1 comprises:3 4b:1 precisely:1 electronic:8 coauthored:1 illustrate:2 given:6 necessarily:4 likely:1 indicate:2 ordering:7 top:31 system:2 least:2 1a:3 their:9 assumption:1 ordered:2 molecular:1 structures:3 pmax:4 assign:2 fraction:2 academy:2 tool:1 transistor:3 accurately:6 generate:2 oltvai:2 maxima:8 authors:2 on1:1 than:12 center:1 distance:3 scheme:1 princeton:1 uk:1 tree:11 imply:1 submitted:1 matter:2 historical:1 represents:2 india:1 enables:2 solely:1 extracting:4 lowest:1 fashion:2 reproduces:1 intriguingly:1 ann:1 randomly:1 zt:2 mossa:1 width:2 socio:1 manner:3 close:1 need:1 affinities:3 null:2 any:3 relatively:1 mik:1 mij:7 econometrica:1 zero:2 depending:1 efficient:1 convenient:1 responsible:1 able:6 note:9 instance:2 emphasis:1 internal:10 build:3 objective:2 so:6 coincide:1 switching:1 accuracy:5 circles:1 blue:1 inference:1 transactions:1 price:1 measures:3 sequence:1 what:2 most:10 said:1 connected:6 but:6 significant:3 pair:3 america:1 class:1 achievement:1 sub:15 unsupervised:4 gk1:8 average:8 gather:1 memberships:4 graphs:10 proceedings:1 wasserman:1 comprise:1 gratefully:1 dor:1 kx:1 physics:1 section:1 fact:2 quantity:1 drastically:1 show:10 text:3 detection:2 random:15 nonlin:2 ravasz:2 implying:1 colors:2 joshi:1 threshold:2 bacteriol:1 gate:1 parsimony:1 trivial:1 networks:58 principal:1 highest:1 ratio:2 knowledge:1 northern:1 implementation:1 distributed:1 outside:2 topological:4 should:3 cohesiveness:2 only:4 going:1 compiled:1 captures:1 local:9 proximity:1 merged:1 do:11 mixture:2 keeps:1 reconstruction:2 di:2 landscapes:1 simplest:1 overall:2 scalable:1 trees:2 expects:1 words:1 despite:2 report:1 mutual:3 geo:1 emails:1 areas:1 campus:1 following:3 processes:1 metabolite:2 countries:4 numerous:1 arxiv:1 comprising:3 yield:2 investigate:1 roger:1 architecture:1 through:2 implication:1 fixed:1 automatic:1 view:1 coefficient:1 set:10 art:7 iteration:1 national:2 testing:1 module:28 connections:5 culture:1 see:6 num:2 descriptions:1 sea:1 fail:4 transportation:8 splits:1 best:4 subject:1 fails:2 detect:6 draws:1 vertical:1 consistency:2 erez:1 pattern:4 footline:8 nature:3 fulbright:1 soffer:1 boundaries:2 case:1 metabolites:11 score:1 identification:4 correctly:1 between:16 neither:2 approach:2 email:6 wide:2 available:1 realizations:1 recently:1 ability:3 right:4 sampled:2 importance:1 genet:1 however:7 comi:1 efficiency:1 fits:1 densely:1 key:1 probing:1 come:1 problem:1 topology:1 suggested:1 both:2 providing:1 last:2 barkai:1 zeng:2 modular:7 many:3 extracts:1 alon:3 according:2 barrat:1 connection:1 logic:4 marta:1 variance:1 com:1 finds:1 otherwise:2 greedy:1 among:1 presumably:1 relevant:5 co:5 conclude:1 simple:1 quality:1 others:1 kirkpatrick:1 corresponds:5 community:3 except:2 represented:1 exclusively:1 middle:3 affiliated:1 cs:1 moreover:3 sensible:1 described:1 tuning:1 capable:1 union:1 px:3 locally:2 oder:1 three:11 been:3 pute:1 whom:1 much:1 change:1 expected:3 figure:1 ph:1 empty:1 define:4 obtained:6 life:1 enable:2 corresponding:5 deeper:3 reaction:1 moreira:1 sufficient:1 theorem:1 everitt:1 realworld:1 external:1 clusters:3 bayesian:1 spirit:2 present:4 sound:2 k2:6 multi:3 classifications:1 reichardt:1 contexts:1 empirical:3 value:1 air:7 will:11 while:2 aij:4 property:1 interconnected:1 procedure:2 ein:1 identical:4 stop:2 larger:3 elemy:1 refs:1 drawbacks:1 thus:11 them:2 vo:2 ii:6 characterize:1 pressing:1 nishioka:1 il:1 arenas:5 elements:7 capture:1 different:21 verified:1 author:8 make:2 belong:1 administration:1 merging:1 same:15 clearly:2 microarray:1 reconstructed:1 complex:11 split:1 geographical:1 units:4 vespignani:1 hierarchies:4 several:1 composition:2 higher:4 development:1 independent:1 nih:1 literature:2 http:1 raymond:1 again:2 comprehensive:1 bornholdt:1 upon:1 agglomerative:2 hand:1 plos:1 levels:24 validate:3 totally:1 single:5 built:1 break:1 lower:1 mech:2 whose:1 scenario:1 database:3 minimize:1 expression:1 well:2 roughly:1 analysis:7 obtaining:1 directly:1 edge:2 components:1 sets:1 organization:39 model:12 soviet:1 researchers:2 subgroup:1 gates:6 stringent:1 maslov:2 proposed:2 less:1 being:3 when:3 accurate:5 obtain:2 schools:3 shape:1 underlying:2 identify:10 transforms:1 human:1 using:2 regardless:1 alternative:1 previous:3 k3:3 levitt:1 aiming:1 classification:5 sciences:2 point:1 k1:4 evanston:1 color:5 k0:1 affinity:35 lett:3 samples:1 technological:2 newman:4 els:1 remaining:1 match:2 majority:3 real:8 increased:1 depends:1 worlds:1 satorras:1 results:6 dark:1 catalan:2 boxes:8 five:2 know:3 background:1 mcdonnell:1 press:3 world:9 nucleic:1 poses:1 loss:1 necessary:1 sizes:1 follows:3 collective:1 zoom:1 facing:1 steps:2 schwarz:1 output:4 ottino:1 soft:4 interestingly:1 www:5 google:1 methods:12 metabolic:11 some:5 back:1 identified:2 supplementary:9 economic:2 acad:5 unraveling:1 proper:1 wiggins:1 scale:8 dense:5 pnas:10 bottom:5 tools:1 overlap:5 whole:2 does:5 connecting:1 ucsd:6 assuming:1 offices:1 proc:5 refer:1 measuring:1 biology:6 scientific:1 equivalent:3 2c:2 uniform:1 illustration:1 restrictive:1 step:6 although:1 plots:1 post:1 finding:2 inc:1 limitation:1 inter:1 central:2 would:2 sneppen:2 o:1 regular:1 faust:1 obeys:1 importantly:1 constraints:1 os:2 block:5 considerations:1 soc:1 cambridge:2 simulated:1 inclusion:3 previously:1 political:3 into:11 within:7 splitting:1 assess:3 appropriate:1 because:4 determine:5 proportional:2 sports:1 often:1 clustering:12 nunes:1 rows:1 c52:1 extraction:2 support:1 there:9 question:1 specifically:3 sampling:1 occupy:1 anderson:1 quadratic:2 adaptability:1 way:2 danon:2 analyze:4 metabolism:3 therefore:1 function:5 vicente:1 kegg:3 continents:1 pastor:1 overlapping:2 idea:2 volume:5 hierarchical:61 reed:1 schilling:1 domany:1 line:1 trying:1 basin:1 r54:1 he:1 iterates:1 compute:4 input:1 full:2 whether:5 type:1 inside:3 blockdiagonal:1 generating:1 up:1 us:5 until:1 considered:1 below:2 limit:1 distinctly:1 heterogeneous:1 distribution:1 more:13 similar:2 clear:2 ex:1 strongly:2 pij:2 partition:12 constant:1 moore:1 defined:8 certain:1 describe:2 condition:5 sales:4 deep:1 general:3 globally:1 divisive:2 engineering:1 exist:1 departments:1 surveying:1 flight:1 education:1 intra:1 constructed:1 ni:8 nj:3 akaike:2 no:16 dashed:1 whereas:2 eastern:1 cohesive:2 peptides:1 barth:1 application:2 other:9 role:1 details:2 holding:5 department:1 eight:4 theor:2 bmax:1 node:12 stat:5 enyi:2 kinds:1 exp:2 models:1 leibler:1 berman:1 problems:2 includes:1 chance:1 important:2 pathways:7 developed:1 diamonds:1 structure:30 matrix:26 building:1 implies:1 algorithm:8 beckmann:1 assume:2 quantifying:1 acids:1 modules:52 together:2 original:2 gelatt:1 dot:1 time:1 applied:1 validation:1 starting:1 having:2 4a:1 |
0705.1681.txt |@word magnetic:31 comparatively:1 four:2 whose:1 violate:3 tween:1 under:10 shielding:11 rise:1 connects:1 experimentally:1 cause:1 viable:1 vector:11 jhep:1 semileptonic:1 consistent:1 direct:7 approximation:4 likely:1 spontaneously:1 even:18 above:4 new:8 net:3 contributes:2 ˆm:1 coefficient:1 evolving:1 residual:3 here:14 atoms:13 refinement:1 asymmetry:1 obtained:3 elaborate:1 changes:1 cancellation:4 divide:1 total:1 linearly:1 would:14 m1:8 therefore:3 m2:4 type:2 until:1 composite:2 holt:1 berlin:1 hold:1 must:2 me:3 springer:1 mm:1 work:9 cancellations:1 mj:11 example:8 jarlskog:2 defer:2 indicated:2 give:4 relativistic:9 generically:1 involve:6 indicates:3 end:2 provide:4 revisit:1 ordinary:4 classify:1 earlier:6 diagram:1 summarize:1 types:2 photoabsorption:1 effective:10 neglect:1 maintain:2 green:3 correlation:1 observability:1 order:28 origin:5 interpretation:3 over:7 xi:16 satisfies:1 diagonalized:1 difference:5 fiz:2 fig:2 persist:1 them:2 affected:1 combination:4 break:1 penetration:14 effects:28 they:5 represents:1 netherlands:1 each:2 side:3 mean:1 feinberg:2 displacement:5 used:18 laboratory:2 octupole:1 gradient:6 quantify:1 particles:4 laid:1 ra:2 rn:3 rj:2 rk:4 foundation:1 linear:3 barrier:1 free:1 standard:5 created:1 cabibbokobayashi:1 corrections:46 key:2 already:3 features:1 rank:4 quadrupole:8 electronic:48 illustrate:2 cartesian:1 xij:4 needed:3 perturbations:1 observations:2 edms:25 somewhat:1 distance:1 showed:1 ac52:1 approximations:5 second:9 matter:3 classes:1 solely:2 minus:1 mind:1 ginges:2 seen:2 der:1 latter:7 responsible:2 absorbed:1 forces:1 reversed:1 subscripts:3 denominator:2 involving:14 retaining:4 transverse:5 observation:3 principle:3 quantifying:1 sum:7 incomplete:1 signatures:1 probe:1 dependences:1 implying:1 gauge:2 substituting:3 d3:22 alluded:1 implementation:2 sˆ:34 screening:27 adequate:1 axion:2 continuity:1 do:2 dm:2 de:23 da:6 dx:1 dy:1 ˆj:3 bau:4 fields:10 respond:1 reference:3 sensitivity:3 observed:2 depends:4 electrostatic:11 radius:4 result:12 discussions:2 nuc:27 instance:1 tensor:2 symmetric:1 approach:4 terms:52 wa:1 nature:2 weak:2 however:9 wi:1 extent:4 news:1 improve:1 5z:1 logic:2 contribution:9 quinn:1 polynomial:1 proceeded:1 basis:2 simplification:1 three:11 been:13 much:2 interest:2 expected:1 ann:2 suppress:1 worked:1 spin:9 applied:6 originate:1 remaining:1 employ:1 contemp:1 near:2 applies:1 study:2 procedure:6 a20:1 vogel:1 explanation:1 iv:4 ii:7 characterize:7 ij:3 il:1 seattle:1 containing:3 make:3 complex:2 potentially:1 several:7 hermiticity:1 independent:2 numerical:3 differing:2 hand:1 characters:2 potentials:13 xjm:2 quantitative:1 possesses:1 left:1 unified:1 stringent:1 just:2 identify:5 transforms:1 tilde:1 previous:7 adding:2 candidate:1 decomposing:1 had:2 cirigliano:1 hat:1 possible:5 unique:1 characterized:1 apart:1 appearing:3 contradict:1 performing:2 specific:3 arbitrary:1 www:4 acad:1 people:4 separately:1 electromagnetic:5 antimatter:1 comments:1 bra:4 fom:1 rearrangement:2 revtex:1 confrontation:1 properties:10 takes:1 o:78 nonvanishing:2 plus:1 larmor:2 efforts:1 considerations:3 sandars:8 presence:12 obtaining:2 down:1 hermitian:1 sov:1 refined:1 existed:1 rely:1 initial:2 transform:1 way:2 was:5 lowest:2 form:15 attempted:1 differences:3 denoting:1 b5:1 inside:3 complications:1 accelerate:1 adopt:2 computing:1 abstract:1 conserved:1 exist:3 dλ:1 distributions:3 nm:1 nn:4 no:10 na:1 when:13 ne:1 interested:1 role:1 nr:2 picture:1 intend:1 models:1 coulomb:7 together:4 time:8 push:1 nuclei:2 chupp:2 leads:11 computation:3 certainly:1 depend:2 charge:28 division:1 advantage:1 maskawa:1 exact:1 evaded:1 level:8 leave:1 evades:2 round:1 upper:1 mn:2 rλ:1 cˆj:10 appear:2 foregoing:3 current:14 goes:1 eext:6 multipole:31 along:2 change:1 box:1 institute:2 shift:8 studied:1 simultaneous:1 studies:8 diamagnetic:5 spatially:1 extra:2 modifying:1 translational:1 working:1 explicitly:4 scope:1 theoretical:7 apparent:1 validity:1 appendix:5 avoiding:1 yjj:1 modified:1 reviews:1 labeled:1 following:8 making:4 arrive:3 claim:1 figure:2 expanding:1 performed:2 hydrogen:1 occur:2 verlag:1 divided:2 write:4 pure:1 ensure:1 map:1 product:7 b75:1 may:8 produce:2 mag:8 dynamical:2 explicit:4 cosmology:2 so:14 sm:5 definitions:1 typical:5 subsections:1 nucleon:4 bernabeu:2 constituents:11 pointed:3 stability:1 experiments:6 differs:3 derive:6 group:1 thank:1 interesting:2 coordinates:3 forms:1 decades:1 τp:2 non:15 thereby:2 introduce:3 now:4 discuss:5 nor:1 groningen:2 term:33 equality:1 dzuba:1 tials:1 entirely:2 em:1 en:45 ei:8 vanishingly:1 ee:15 eg:12 conventions:1 entering:1 eq:43 adequately:2 ejm:3 jackson:1 space:3 furthermore:1 cancels:2 generation:1 contained:1 dutch:1 formula:1 instituut:1 correct:1 after:2 reformulation:2 theory:6 flambaum:5 california:1 remainder:2 e0:6 derivation:8 dλn:11 transition:2 motion:2 place:1 βi:3 first:23 xj:18 xk:3 simplifies:1 symmetry:3 omitted:1 xe:1 long:2 carry:2 open:1 angular:5 size:18 given:11 necessarily:1 indicate:2 convention:6 exerted:1 speaking:1 gives:6 electroweak:4 x2:4 x3:2 representing:2 than:9 specify:1 third:2 require:2 fm2:1 future:9 were:5 decompose:1 prospect:1 correction:11 argument:1 any:10 isolate:1 note:7 potential:10 take:2 wch:1 hyperfine:3 begin:1 opposite:4 probed:1 molecule:1 probes:1 especially:1 considered:4 later:5 implications:1 typeset:1 feynman:1 typically:1 precise:1 madison:2 show:2 workshops:4 notations:1 spaces:1 ground:12 only:24 going:1 contracts:1 expectation:1 sushkov:2 cannot:1 nearly:1 conjunction:1 closure:4 regarding:1 αj:3 yield:2 06na25396:1 ignored:2 ωxi:1 physically:2 relative:2 biedenharn:1 commutation:2 ways:1 subsequent:3 review:1 definite:2 label:2 between:25 αi:13 justified:2 before:2 screen:1 jm:2 concentrate:2 multiplies:1 jetp:2 suppressed:6 concentrated:1 σi:5 x2i:1 many:4 according:2 multipoles:9 expression:3 among:1 jj:8 characterization:1 pol:5 anti:1 conjugation:1 associated:21 endeavor:1 considering:4 collider:1 harmonics:2 kaon:1 photon:1 observe:5 external:29 careful:2 former:2 those:10 case:8 timmermans:2 invoking:1 cancelled:1 situation:3 coupled:1 unit:3 technology:1 herczeg:1 different:3 same:3 shifts:3 arguments:1 breakdown:2 invariance:1 relies:1 charges:4 ıvely:1 roughly:1 without:5 components:11 coordinate:5 model:1 charged:3 comment:1 being:3 generally:4 resolution:1 rest:1 vanishes:1 hint:12 rose:1 heckel:1 pasadena:1 treatment:2 versa:2 poised:1 heavier:1 momentum:9 around:1 read:1 sums:2 dark:1 using:7 particle:3 identifying:1 reduces:2 either:7 integrals:1 friar:2 jˆ:3 reduced:1 table:2 intact:1 conventionally:2 nonzero:12 decomposition:1 expressing:1 o1:1 refer:4 equivalent:1 broken:1 assemble:1 comparison:1 y2m:1 discussed:3 generated:4 mixes:1 practical:6 2j:9 act:3 perturbed:4 inclusion:2 communication:5 numerically:1 references:3 determine:2 operator:75 theoretically:1 refinements:1 there:5 stark:1 los:2 detectable:1 assumes:1 complete:9 metastable:1 ωx:1 practically:1 organize:1 monopole:1 expect:5 detailed:3 taylor:1 ai:17 certain:1 ak:6 describe:2 general:12 formulation:4 moves:1 again:7 completeness:2 field:23 caltech:1 spatial:2 separate:1 symbol:1 deriving:3 commutator:15 a3:1 important:9 nucleus:38 a4:1 60b:1 included:6 delineate:2 cpl:2 firstorder:1 cpt:1 original:4 cpv:24 sci:2 consider:10 lack:1 splitting:3 scalar:5 commute:6 talks:4 follow:4 expressions:4 caveats:1 schiff:110 fortson:1 program:1 onderzoek:1 th:1 far:1 induce:4 puzzles:1 breit:3 existing:1 condition:1 treating:4 hamiltonian:18 list:1 applicable:1 large:3 interchanging:1 small:8 enhancement:2 further:3 hayes:1 tev:1 y1m:2 what:3 sub:2 section:7 brief:1 acknowledgments:1 contrast:2 full:3 component:2 provides:1 ansatz:2 strong:3 equations:1 transformation:4 search:1 generalizing:1 allows:2 via:3 depart:1 requiring:1 analyzing:1 readily:1 proceed:3 distinct:1 ψs:4 ψp:4 contains:12 comparing:1 nucl:5 taken:5 more:12 rk2:1 operators:56 pisma:1 varying:1 known:1 science:1 equation:2 centrifugal:1 remain:2 compare:3 challenging:1 cosmological:1 neglected:2 states:30 yλ:1 numbers:2 arise:10 rather:3 acts:1 hampered:1 simplicity:1 algebra:1 wiley:1 derived:6 treatments:3 response:2 short:1 departure:1 perhaps:1 negligible:2 specifying:2 help:2 ith:4 soon:2 thermal:1 paper:11 through:3 y1:10 y0:9 y2:22 excitations:3 its:9 jacobs:1 boson:1 resort:2 systems:3 might:4 supersymmetry:1 yj:31 yl:5 framework:2 formulating:1 easily:1 characterizes:3 presented:1 radial:3 found:2 exquisite:1 referred:2 heavy:4 reactions:1 another:3 hadronic:7 energy:17 connect:1 quantum:4 beyond:3 admixtures:5 since:6 denotes:7 acting:9 denoted:1 induced:8 issue:1 wisconsin:1 reformulated:1 rkλ:1 electrostatically:2 generate:1 retained:3 voor:1 relativistically:2 eqs:14 probability:1 number:12 differ:1 perturbation:4 guest:3 introduction:1 leading:21 interact:2 assumption:6 expand:1 calculations:6 imperfect:1 baryon:2 part:6 authors:2 focusing:2 believe:1 18b:1 18c:1 18a:1 18d:2 double:1 pairwise:1 treated:6 outstanding:1 electrodynamics:1 willmann:1 substantiates:1 substantial:1 orders:3 built:1 depending:2 liu:3 internal:15 square:3 unperturbed:7 play:1 added:1 electric:20 rhs:4 reach:1 most:1 comparisons:1 measured:1 clear:1 ext:43 electrons:33 exp:1 velocity:1 physics:6 lying:1 sector:2 particularly:2 muon:1 relation:2 fine:1 find:5 impact:4 parameters:1 condon:1 factor:11 his:1 dominant:1 notation:5 dependent:2 express:2 polarized:2 sˆλ:5 arxiv:1 factorization:7 common:1 set:2 see:15 muonic:1 close:1 vint:11 analog:1 ritz:1 currently:1 dipole:12 engel:2 various:4 eksp:1 subscript:1 conditions:1 complementary:1 vanishing:7 eˆm:1 distinguish:2 both:16 last:3 powers:3 henley:1 sensitive:1 connection:1 context:1 pdf:4 experimental:2 nonrelativistic:4 simple:1 corresponds:1 proton:4 dimensional:1 throughout:2 described:1 transformations:1 pt:4 due:14 hellmann:1 describes:2 collected:2 pi:8 lett:7 generating:1 precision:1 systematic:1 evaluated:3 while:8 evaluating:4 error:1 couplings:4 aa:1 unitary:1 approximate:2 itself:1 vanish:1 currents:8 grant:1 emphasize:2 resulting:3 neutron:2 higher:10 literature:7 pospelov:1 anapole:2 sym:3 moment:42 uses:1 recent:2 lower:2 task:3 cˆ2:1 kellogg:1 analysis:5 cˆ1:2 4th:1 atomic:125 useful:9 letting:5 onebody:1 source:4 location:1 theorem:15 input:1 excited:1 evaluate:5 couple:1 advocate:1 appendices:1 helpful:3 sakharov:2 systematically:1 follows:7 ignore:1 collect:2 yields:4 popular:1 spins:1 pertaining:1 often:2 1st:2 some:3 back:1 b4:1 understood:2 b6:1 b1:4 b2:1 b3:1 scale:2 measurements:1 integration:3 connecting:1 inserting:1 bi:7 bj:4 bk:2 hilbert:1 kozlov:1 sharper:1 ylm:1 consequently:2 conserving:3 into:16 within:2 integral:5 phase:4 appropriate:3 primarily:1 proportional:6 placing:1 specifically:3 hext:5 elsewhere:1 properly:1 atom:12 line:2 considerable:1 up:4 us:6 ur:1 similar:9 called:5 purcell:2 constant:5 defined:7 haxton:4 formalism:5 materie:1 amounts:2 sˆl:4 department:3 elements:16 generates:1 excitation:5 meaning:1 allowing:1 suppression:3 structure:8 ago:1 implies:2 delineation:1 vice:2 requires:4 having:3 partial:1 results:7 edm:45 illustrated:3 edu:4 go:2 contributions:19 issues:1 alamos:2 stable:1 include:8 presently:1 implicitly:2 wave:17 electron:33 mixing:4 matrices:1 severely:1 manifestly:1 noted:3 smaller:2 zh:2 peccei:1 imply:1 zx:2 insertion:1 subtle:2 odd:16 3z:10 expressed:2 henceforth:2 consistently:1 experiment:1 expresses:1 body:12 lee:2 degree:1 exchange:2 respectively:6 gathered:1 ramsey:5 others:1 khriplovich:3 trans:1 technical:1 involved:2 larger:2 leaving:1 products:2 makes:1 involves:1 private:5 apply:1 meson:2 cloud:4 use:9 usa:4 next:2 few:3 jungmann:2 panel:1 formally:2 diagonalize:1 started:1 becomes:2 about:5 carrying:1 iii:7 oj:1 account:3 infinitesimal:1 universe:3 dn:67 calculation:1 purposes:1 effectively:1 assumptions:2 delineating:1 instead:2 underway:1 unnaturally:1 lamoreaux:1 realized:1 computations:4 mjm:2 correspond:4 element:9 allow:1 subsequently:3 discussion:4 unsolved:1 saturated:1 reversal:6 produces:1 including:8 yjm:7 la:1 chosen:1 masses:1 permanent:3 degrees:4 symmetrization:1 violating:1 greater:1 polarizations:1 practice:1 2s1:2 dirac:3 university:3 identified:3 sufficiently:1 magnitude:5 electrically:1 accounts:1 constraints:2 doing:4 frequency:3 static:9 interplay:1 separating:3 our:13 transitions:4 special:1 out:10 respects:2 matrix:28 rev:15 reformulate:1 ref:8 tildes:1 interactions:41 diagonal:5 interaction:40 could:7 times:3 explored:2 derivations:1 assumed:1 hence:1 teor:2 demonstrating:1 powerful:1 jesus:1 publication:1 system:3 their:6 intermediate:1 final:3 shell:1 completed:1 exactly:1 zλ:2 constituent:1 symmetries:2 need:1 clearly:1 studying:1 polarization:14 mix:1 accuracy:1 mjr:2 who:1 rearrange:1 consequences:2 ckm:1 χm:3 superscript:1 fact:4 violation:5 supported:1 purely:2 based:1 should:4 molecules:1 indeed:1 employed:3 local:7 achieve:1 equilibrium:4 means:2 quantified:2 exchanges:3 penetrate:1 precession:1 densities:1 paramagnetic:1 expansions:1 contain:7 deuteron:4 2p3:2 national:2 correlations:1 argued:1 romalis:2 interacting:1 attempting:1 nuclear:124 state:17 neither:1 importance:3 p2i:4 hypervirial:1 ket:4 tensors:1 limits:3 taking:2 equal:1 etc:1 tlf:1 safely:1 ck:5 cj:12 relevant:6 ca:1 respect:2 cp:8 addition:3 hinds:2 define:1 arises:7 corresponding:13 leptonic:1 poten:1 c2:6 c1:4 c0:12 present:8 unlike:1 value:2 will:34 profumo:1 refs:7 thus:12 conserve:2 orbital:2 cjm:4 generic:2 radiation:1 cross:1 parts:5 pauli:1 vext:22 φi:8 φj:1 finite:18 residing:1 http:4 upon:1 effect:14 parametrized:2 phy:1 identity:2 nevertheless:1 variety:1 well:5 bohr:2 displacing:1 sets:1 position:3 arising:2 spherical:10 less:1 moments:25 obtain:10 sources:5 griffith:4 density:10 point:13 reasons:1 adoption:1 diagonalization:4 timereversal:1 increases:1 displaced:1 musolf:4 like:13 qualitative:1 become:1 nucleons:2 therein:3 parity:12 exceed:1 because:6 classical:4 fundamenteel:1 neglecting:1 projection:1 lead:2 demonstrates:2 overlap:1 does:4 assuming:2 intersections:1 enuc:1 expansion:6 although:1 analyses:2 simpler:1 a1:1 stichting:1 a0:5 freedom:4 introduces:1 dependence:3 recognized:1 carries:1 a2:1 introduced:4 goldstone:1 strangeness:1 previously:6 h0:22 washington:5 weighted:1 additional:8 function:11 but:15 neutral:5 hi:5 fg02:2 hg:3 illustrative:1 he:3 lynn:1 made:3 compute:3 wieman:1 below:4 limit:6 dωx:2 problem:2 mechanics:1 int:49 contribute:3 remove:1 denote:1 functions:11 compared:4 ingredients:1 cˆ:2 other:11 details:3 quantities:2 searches:6 coupling:5 starting:1 baker:1 factors:1 expands:1 |
0705.1682.txt |@word logarithms:1 consider:2 chain:1 helstrom:1 varying:1 results:3 leads:1 hannel:1 scalar:2 generalize:2 expressions:1 contributions:2 localized:1 relationships:1 const:1 γp:3 corrections:1 γt:1 finally:4 weyl:2 th:2 under:15 tf:23 exposition:1 awgn:5 xtk:1 division:1 random:3 straightforward:1 orthogonal:3 very:1 assuming:3 choice:1 corollary:1 verd:3 summarized:2 difference:1 matrices:9 laneman:1 condition:2 entire:1 squares:1 ppeak:6 xt1:1 presented:2 evaluation:1 july:4 eve:1 occurs:1 large:4 discrete:1 wss:2 vector:4 excellence:1 dealt:1 small:1 radio:1 referred:2 related:1 upper:17 zk:4 prediction:1 pulse:1 approximation:3 second:5 value:1 linear:1 spectral:4 index:4 stands:4 chicago:1 gk:6 section:4 http:1 zhang:1 access:1 goes:1 sup:11 new:4 method:1 contrast:1 gursoy:1 satisfy:3 evaluating:1 respectively:2 loose:1 spacing:1 equals:2 desired:1 selective:18 based:3 obtained:6 almost:1 dec:1 dividing:2 institute:1 shift:3 vectors:3 subcarrier:1 ignoring:1 bol:1 orthonormality:1 see:2 apr:3 highly:2 austria:1 achievable:3 unit:2 jan:1 use:8 additive:2 asymptotic:2 codewords:1 sake:1 6b:1 next:4 shitz:3 mation:1 bases:1 memory:2 taken:3 compactly:1 flat:3 israel:2 sharing:1 relax:1 aware:1 correspondingly:1 doob:1 normalized:1 impulse:3 particular:1 known:4 cases:1 iv:1 iii:2 hints:1 lowercase:1 vienna:2 ers:1 work:1 det:5 mw:1 assumptions:1 publications:1 sethuraman:2 following:6 trans:10 proof:17 νt:1 multipath:2 process:4 xch:1 states:1 minimum:2 ounds:1 sense:3 hhh:1 αkn:1 normalize:1 information:13 csi:5 invoke:1 rather:2 discussion:2 holds:2 write:3 how:1 ens:1 edard:1 instead:1 profile:3 inputs:1 mar:3 blocks:1 modulation:1 db:1 lag:1 variant:1 containing:1 lab:1 helmut:1 plane:1 snr:5 law:1 data:6 response:3 outline:1 effective:2 whenever:1 spectra:1 explicit:7 ghz:1 element:1 codebook:1 provide:1 fp6:2 used:4 allow:2 correlation:2 order:1 over:9 entries:1 soc:1 interpreted:1 symbols:8 paper:5 netw:1 existence:2 satisfies:2 still:1 ieee:14 its:2 diagonalized:1 perfect:4 derive:2 ime:2 eurasip:1 τf:1 lo:1 fix:1 tse:1 lh:6 forms:2 absence:1 distinguishing:1 fig:2 constitutes:1 olcskei:3 mail:2 main:3 defining:2 setting:1 eventually:1 yk:3 good:1 motivated:1 thereby:1 numerically:1 scaling:1 band:2 optimal:1 diag:3 now:1 nor:1 establishes:1 eigenvalue:2 transmitter:1 dirac:1 products:1 university:1 xt0:1 concave:1 via:1 orthonormal:1 sufficiently:1 inequality:2 transmitted:2 each:2 found:5 side:1 constraints:8 domain:2 schemes:1 eh:1 zurich:2 ee:3 guo:1 energy:2 gaussian:6 ec:1 frequency:23 ex:4 measure:1 our:3 eq:2 es:1 shown:1 superscripts:1 matrix:6 rep:1 since:2 matz:1 time2:1 denotes:4 may:2 reader:1 denoted:2 ro:1 rh:3 integrated:1 shows:1 doppler:3 turning:1 theory:15 divergence:2 diagonal:2 standard:1 admits:2 approaches:1 base:1 surely:1 york:4 hand:2 remainder:2 mimo:1 βp:8 applications:1 argument:1 starts:1 impose:3 int:3 place:1 enough:2 hence:1 first:8 xk:12 xh:2 xi:10 ntroduction:1 channels:23 least:1 preparation:1 ystem:1 size:1 dispersive:1 given:8 jet:1 structured:1 system:3 approximately:2 their:1 assumption:2 show:1 white:2 scheme:8 inner:1 relationship:1 tool:1 continuous:2 bello:1 technique:1 part:2 because:1 signaling:7 eliminated:1 representing:2 than:2 coefficients:1 wide:2 dth:1 j2π:1 double:1 rate:5 project:1 kth:1 kti:1 shlomo:1 matched:1 providing:1 minus:1 hz:1 well:6 eak:2 generalization:4 randomly:1 codebooks:1 conjugate:1 recover:1 fading:33 prohibits:3 generalizes:1 built:1 zero:5 min:1 optimum:1 lin:1 note:2 take:1 transmit:7 so:1 coincide:1 modulus:6 channel:52 heisenberg:2 shall:3 rhs:6 decreasing:1 mimics:2 most:1 satisfying:3 phase:2 class:3 exponent:1 technion:2 wiley:3 consequences:1 mobile:1 average:11 max1:1 coincides:1 kn:3 kp:7 tech:1 kt:12 effect:1 fact:1 multilevel:1 precise:1 phenomenon:1 rayleigh:8 supported:1 discovered:3 relation:7 substituting:1 assumed:1 ratio:3 knowledge:1 parameters:2 eigenspace:2 distributed:1 written:1 penalty:3 being:1 only:8 explicitly:2 burstiness:1 rectangle:2 do:1 gains:1 notation:1 get:1 dependent:1 overall:1 expectation:1 cannot:1 nels:1 αkp:3 differentiating:1 reveal:1 processes:1 dissertation:1 arxiv:1 expansions:1 summary:1 common:1 switzerland:1 www:1 karhunen:1 set:4 above:1 ofdm:5 achieved:4 ary:1 maximum:1 depends:2 sec:1 result:3 wideband:5 uncorrelated:2 techniques:3 αp:2 said:1 capacity:37 eigenfunctions:2 αw:1 propulsion:1 hajek:3 symmetric:2 state:1 closed:5 between:4 neither:1 across:2 schuster:1 available:2 wa:1 restricting:1 transpose:2 however:1 efficiency:1 key:1 lb:10 amer:1 problem:1 shamai:3 both:5 σh:10 reported:1 chelsea:1 taking:1 according:4 contract:1 und:1 context:2 receiver:4 variance:1 eth:1 expression:6 otherwise:1 duty:1 ch:24 cn:4 conclude:1 simple:2 ca:1 corresponds:1 environments:1 dimensional:4 simply:1 conjugation:1 path:1 cs:1 moreover:1 throughout:2 speak:1 qpsk:1 pp:15 described:1 keying:3 pt:3 basis:1 addition:2 px:10 concavity:1 been:3 commission:1 odel:1 noncoherent:5 tering:1 brick:1 prototype:1 ricean:1 define:2 determinant:1 corresponding:1 received:2 going:1 covariance:1 else:1 stochastic:2 constellations:2 apacity:2 general:4 case:5 unlike:1 reliable:1 evaluated:1 will:5 receive:4 while:2 behavior:1 error:4 nonstationary:1 property:3 memoryless:3 metric:1 equal:1 ii:8 characterize:1 focus:1 il:2 supremum:6 seattle:1 technology:3 different:5 ing:1 grant:1 circularly:3 realizing:1 same:3 complex:3 resulting:4 adelaide:1 european:1 independent:1 literature:2 infinity:1 imply:1 mmse:4 ulation:1 numerical:2 functions:1 sym:1 peaky:3 pubs:1 infinite:12 gallager:2 identity:1 cycle:1 lower:20 off:2 maximizing:4 simplicity:1 viterbi:4 analysis:1 without:2 lim:5 swiss:1 stating:1 arbitrarily:1 proposed:2 transmitting:2 accurate:1 identically:1 obtain:4 bandwidth:26 relevant:1 identify:1 alternative:1 scattering:17 previous:1 letting:1 rewriting:1 density:3 characterization:1 eferences:1 exclusively:1 signals:3 spread:2 maintaining:1 theorem:11 diagonalization:1 input:10 mod:1 designate:1 opt:1 psk:1 australia:1 eigenfunction:1 exploiting:1 term:9 increases:1 noncausal:1 grid:1 performance:1 using:4 unique:1 advanced:1 apart:1 multiplexing:1 loss:1 imposed:2 replacing:1 shaped:2 follows:9 signal:9 kennedy:1 translates:1 specific:4 communications:1 yields:1 δk:1 δi:1 output:4 giuseppe:1 stationary:4 reduces:1 sketch:4 right:1 namely:2 uppercase:1 ingly:1 respect:1 duration:1 neglecting:1 δn:1 vol:13 lead:1 ported:1 broad:1 exceeding:1 per:2 prop:2 critical:3 decomposition:2 innovation:1 proc:3 symbol:1 telatar:1 refer:2 inserting:2 noise:6 11a:1 power:15 symp:3 shifting:1 hadamard:1 feb:1 isit:3 takes:1 constraint:34 technologie:1 commun:2 discussed:1 o:4 grenander:1 stand:1 subramanian:1 mean:5 sept:3 other:1 block:5 allowing:2 thermore:1 letters:2 computes:1 communication:4 into:1 within:1 integral:2 bound:28 ppendix:2 retaining:1 appropriate:2 square:4 operator:1 conceptually:1 rely:1 log:18 area:1 transfer:1 approximate:5 specifically:1 start:1 noting:1 low:4 was:1 pasadena:1 toeplitz:11 function:24 hx:2 complete:1 form:5 szeg:4 denoting:1 but:2 idea:1 wireless:1 hk:5 ethz:2 delta:1 haifa:1 ph:1 he:1 made:2 wise:1 bandwidths:3 bounds:11 us:1 ur:1 below:1 limit:7 boldface:2 distribution:4 similar:2 detailed:3 bearing:1 ac:1 constant:6 ub1:5 ub2:3 computing:2 defined:4 recognize:1 abstract:1 sion:1 ergodic:1 denote:2 rvs:1 ap:1 dν:10 laboratory:1 inf:14 tiling:1 distributions:3 regime:4 again:1 mutual:8 no:10 image:1 when:2 detail:1 nf:7 continuoustime:1 ny:4 interested:1 nat:1 poor:1 elements:1 provided:1 sided:3 june:2 rv:2 restoration:1 bounded:4 peak:35 variable:1 narayanan:1 structure:2 network:1 correlated:1 algorithm:1 assume:2 dτ:10 fsk:8 rule:1 appendix:2 time:30 n0:2 appl:1 having:1 |
0705.1683.txt |@word fredenhagen:1 casimirs:4 rev:1 equalities:1 results:1 superfields:1 four:28 eds:1 commute:8 comments:1 grateful:1 σcd:1 go:1 expressions:2 gl:1 gh:1 compact:2 looking:1 inverse:6 depend:2 superspace:3 undetermined:2 finally:5 behave:1 present:1 th:18 under:7 analogous:1 divergent:1 applied:1 deforming:3 straightforward:1 far:2 rise:2 dokl:1 unchen:4 chaichian:3 antipode:1 entries:1 matrices:18 fakult:3 condition:4 leads:1 conjugating:2 presented:2 lorentzinvariant:1 notes:1 list:1 deals:1 vector:8 phase:2 wolfram:1 indices:14 relation:6 superalgebras:5 noted:1 inserting:2 2k1:2 2k2:2 consistent:5 prevents:1 second:6 invention:1 pass:2 zu:1 analogue:1 linear:2 index:1 what:1 plays:1 stands:2 schmidke:2 section:5 3p:4 expressed:1 reminiscent:1 version:1 above:7 new:6 method:1 satisfy:2 deser:1 construct:1 exponentials:1 whose:1 respectively:5 modify:2 here:1 canonically:1 l23:7 l24:5 groups:9 fulfill:3 alone:1 σab:2 sine:1 equations:3 change:2 differential:4 great:2 antisymmetric:7 remarks:1 institute:1 culminate:1 schwarz:1 lledo:1 products:1 nski:3 action:4 hospitality:1 suitable:2 makes:1 anticommutators:3 montreal:1 uniquely:2 formulated:1 useful:2 takeuchi:1 muenchen:2 alg:2 apply:1 neutrino:1 establish:2 planck:2 kobayashi:1 interest:1 use:7 qcp:1 takes:1 working:1 prove:1 remains:3 supergroups:1 give:5 universelle:1 next:4 nucl:5 ust:1 m2:2 means:4 compactly:2 type:1 metric:11 more:11 lowering:1 israel:1 clearly:1 becomes:3 operators:14 supergroup:2 ematiques:1 aware:1 berlin:1 appendix:2 proceed:1 known:2 foundations:1 qλ2:2 hold:1 effort:1 must:1 springer:2 eberhard:1 ma:3 gνν:1 world:1 deformed:108 recall:3 mo:1 work:6 theories:3 obvious:2 achieve:1 following:3 making:3 arrive:1 example:5 plaza:1 qdeformed:5 kosi:3 stated:1 calculation:1 mentum:1 arise:1 confused:1 sake:2 lorentz:18 qq1:3 hyperplane:1 sense:5 rodr:1 verlag:2 compatible:1 end:8 gcd:5 thing:1 provide:1 verify:2 holds:3 theresienstr:1 write:6 how:3 commutative:3 fourth:1 instead:3 ordinary:3 gordon:1 map:1 product:6 continues:1 sommerfeld:1 whereas:1 algebra:83 replacing:1 max:1 invitation:1 applications:1 tries:1 plane:3 physik:5 multiplication:1 representations:7 choice:1 doplicher:1 types:2 goal:1 short:2 attempt:1 effective:1 explicit:6 su:36 rather:2 switch:1 witten:1 so:25 expression:2 qλq:2 representation:3 lν:3 make:2 gµν:7 ogievetsky:1 interpretation:2 help:2 duke:1 hierarchy:2 indeed:1 over:2 eqs:1 satisfied:1 equality:1 mathematicians:1 already:1 through:1 thesis:3 mentioned:7 existence:1 its:16 gausterer:1 nieuwenhuizen:1 ld:4 lb:6 thank:2 la:26 interesting:1 subalgebra:1 solving:2 conjugation:5 li:3 lect:1 λq1:4 whole:1 van:1 mail:2 schmidt:6 defining:2 deformation:6 supersymmetry:25 ideal:1 correspondence:1 non:13 qq2:2 coproducts:2 propose:1 watamura:4 introduce:6 tureanu:1 scaling:3 framework:1 they:9 now:8 yu:5 realize:2 group:7 gbc:1 easily:2 2p:13 2q:18 always:1 university:3 hamiltonian:2 sobczyk:3 factorizable:1 iff:1 fabian:1 l2:20 l3:24 reasonable:1 each:2 found:8 universit:4 superspaces:1 side:1 2k:1 baxter:2 spinor:25 square:3 financial:1 eh:1 formulate:1 doing:1 ed:2 ef:1 idea:1 related:3 conventions:2 extended:1 die:1 quantum:69 our:14 eq:1 special:1 out:5 try:1 shown:2 jimbo:2 matrix:8 space:49 restricted:1 furthermore:5 since:4 vectorial:2 denotes:4 particles:1 geom:2 reader:4 denoted:2 constants:2 ref:28 mθ:1 math:23 1q:5 theory:6 given:7 free:2 standard:1 reason:5 threedimensional:3 span:1 subalgebras:2 wanted:1 generate:1 additional:1 ange:1 watts:1 interaction:1 derivation:1 nishijima:1 geometry:3 wachter:11 could:3 ferrara:2 εabc:7 counterpart:1 turn:3 due:1 gµµ:2 leading:1 assign:1 first:7 note:3 einer:1 symmetry:17 striking:1 klimyk:1 variables:1 koch:1 number:1 rank:1 twisted:1 restrict:1 l34:5 set:4 done:3 relations:55 carry:3 angular:7 udgen:1 counits:2 1p:12 antisymmetrizer:4 introduction:2 unknown:1 adjoint:4 achieved:1 system:3 least:4 their:12 demichev:2 antisymmetrized:3 listed:1 seiberg:1 structures:5 1l:1 ocampo:1 baryon:1 takhtadzhyan:1 62b:1 quan:1 supergauge:1 qli:1 off:1 theorie:2 than:1 coefficients:1 bialgebras:1 kind:3 determines:1 kulish:2 edition:1 sections:1 require:1 imply:1 roberts:1 appealing:1 determined:4 were:2 bauer:1 toward:1 symmetries:3 biedenharn:1 outstanding:1 ann:1 schladming:1 manner:6 conjugate:1 seen:1 saw:1 tells:1 viewed:2 symmetrized:1 lie:13 multiparametric:1 built:1 der:2 dilatation:1 convenient:1 ruegg:1 able:2 ideas:3 pseudogroups:1 k3:11 sciences:1 k1:100 take:7 analogy:3 indexed:1 analogs:5 miyazawa:1 calculus:5 play:2 towards:1 centre:1 3q2:1 3q1:1 sets:1 reach:1 most:2 germany:2 formulae:2 nothing:2 acknowledgements:1 gρσ:1 commutation:22 teilchenphysik:1 preˇsnajder:1 schm:1 especially:1 considered:3 clear:2 sometimes:1 implications:1 looked:1 proceedings:2 yang:2 physics:2 3q:16 fact:2 show:2 violation:1 lµν:16 notations:1 ki:7 spaces:14 gauge:1 solutions:1 counit:1 superalgebra:21 trivial:2 find:5 soq:2 q1:50 q3:2 q2:52 based:2 q4:1 commutators:23 should:15 only:3 explicitly:7 generators:65 specify:3 mechanics:1 local:1 hopf:11 hope:1 his:3 suq:1 notation:9 get:6 de:3 dc:1 extension:1 pions:1 cannot:1 words:1 progress:1 hartmut:2 freedman:1 alexander:1 qq:14 qp:9 volkov:1 qt:1 qv:1 conditions:1 arxiv:1 fixes:1 nowicki:1 qa:1 coproduct:3 wish:1 qm:7 ql:2 view:1 reveals:1 requirement:2 multiplying:1 dobrev:1 reference:1 sep:1 schr:1 grosse:2 differs:1 see:11 computer:1 sec:2 eliminating:1 uller:1 led:1 ur:4 momenta:3 analog:5 subject:5 αq:1 sudbery:2 tensor:16 review:1 definite:2 supergravity:4 symmetric:1 tantamount:1 written:9 identification:2 closed:1 between:18 invariant:2 approach:1 checks:1 choose:1 notice:9 εij:2 terms:4 extend:2 nature:1 neveu:1 attention:2 however:2 comi:1 implementing:1 vanishing:7 maximilians:3 comm:1 tum:1 article:3 jetp:2 come:2 tensors:1 concentrated:1 isoq:1 recherche:1 0q:4 last:8 qft:1 many:2 σa:5 equal:2 contract:1 quantization:1 und:2 casimir:18 uni:2 adapted:1 experimental:1 otherwise:1 uber:1 fields:1 point:3 leipzig:2 cf:3 cd:10 dimensional:51 superstring:1 grouplike:1 respect:3 cp:7 mpi:1 amer:1 described:3 transformations:3 basis:1 addition:1 rewrite:1 three:37 wess:9 int:4 much:4 4q1:1 4q2:1 certain:1 combine:5 ph:6 algebras:19 universal:1 define:2 antipodes:2 enable:2 supersymmetric:5 reasonings:2 commutes:1 concerning:2 noncommutative:4 schupp:1 c2:9 c1:9 gad:1 spin:9 gab:8 those:1 case:3 invariants:1 ina:1 decades:1 slq:1 arnold:1 remaining:2 aim:2 euclidean:50 lukierski:4 σb:1 property:1 conformal:1 majid:6 unitary:2 dieter:1 linked:1 refs:2 thus:5 reads:3 ij:1 dual:2 1k2:1 gervais:1 vanish:1 superconformal:1 currents:1 different:2 identities:1 divergences:1 oeckl:1 cross:4 same:9 poincar:26 princeton:2 arguments:2 pauli:11 castellani:1 finite:1 ludwig:4 higher:1 independent:4 zumino:6 used:2 singapore:1 grassmann:1 assignment:1 superanalysis:1 counterparts:1 1q1:1 1q2:1 changing:1 invariance:2 totally:2 identity:1 lower:3 task:1 supercharges:1 center:1 k22:2 spacetime:1 well:5 analysis:1 without:1 components:26 consistency:3 very:3 undertaken:1 model:1 grounds:3 wohlgenannt:1 stating:1 left:1 λs:1 fand:1 λq:5 λp:6 graded:1 just:1 λt:5 being:2 formula:1 slanka:3 obtain:5 actions:2 gravity:2 via:1 drinfeld:3 summed:1 shorthand:1 alternative:1 λm:3 previous:3 adding:2 preprint:2 generator:4 k2:98 similarities:1 bicovariant:1 relatives:1 lattice:1 add:2 other:5 extends:1 lett:10 eur:6 consideration:1 mod:4 transformation:2 momentum:32 build:1 real:2 stein:1 exploiting:1 read:5 possible:1 spanned:3 know:3 press:3 using:7 sakita:1 helpful:2 reshetikhin:1 appearing:1 like:6 particle:1 alternatively:3 collect:1 yields:2 λk1:1 follows:1 completely:2 become:7 conclusion:1 ıguez:1 heisenberg:2 indications:1 right:2 often:3 deal:1 some:3 gleason:1 suppl:1 moreover:1 δba:1 reconsider:1 soc:1 ourselves:1 kern:1 scale:1 bicrossproduct:1 dimensions:10 l14:10 integration:1 l12:6 l13:6 everything:2 does:2 mutation:1 tends:2 prog:1 akulov:1 scholl:1 refer:5 regain:2 carow:2 faddeev:1 2q2:1 scientific:1 2q1:1 equivalent:1 l1:11 likewise:1 q2q:6 step:1 super:2 properties:5 projector:1 about:2 would:6 concretely:2 likhtman:1 discussed:2 o:2 pν:1 nonvanishing:1 covariant:4 stand:3 woronowicz:2 introduced:2 book:1 considerations:4 discretization:1 cambridge:2 undeformed:3 maxwell:1 into:6 within:2 copies:1 down:5 lies:1 references:1 podle:1 determine:2 sov:4 operator:17 lastly:1 mass:2 leningrad:1 spinors:3 hep:18 classical:9 jhep:3 support:2 there:2 transform:4 equation:4 start:1 pa:25 way:6 was:5 witt:1 complete:1 form:18 epsilon:7 but:6 repeated:1 construction:1 bagger:1 hb:1 observation:2 commun:6 made:1 applying:2 intuitive:1 minkowski:16 mat:1 uq:52 up:1 us:12 theoretical:1 limit:3 internationale:1 ansaetze:4 problem:2 called:4 examples:1 strongly:1 fulfills:1 ab:26 constant:3 defined:5 recognize:2 abstract:1 describe:2 proven:1 general:4 regularisation:1 formulation:1 corresponding:7 commuting:2 check:2 physical:2 qα:47 again:10 qγ:5 qβ:18 completeness:4 no:1 qλ:9 mathematica:2 field:6 zeidler:1 interested:1 role:3 details:2 ambitious:1 uematsu:1 braided:5 mathematics:1 theor:2 regularizing:1 elements:5 denote:4 congress:1 gol:1 models:2 remarked:1 problems:1 odinger:1 manin:2 commutator:2 generated:4 important:1 sweedler:1 structure:5 implies:4 anticommutator:2 assume:1 values:1 together:4 4q:4 lyubashenko:1 arisen:1 time:9 international:1 requires:2 once:1 |
0705.1684.txt |@word positions:1 partial:1 maximum:1 rev:23 magnetic:1 results:3 four:2 computation:12 edu:2 sci:1 primes:1 research:1 factorizing:1 knill:2 deterministic:1 factoring:3 presents:1 finally:1 program:1 present:1 under:1 include:1 resources:1 case:5 digit:1 supported:2 amplitudes:1 outside:1 far:1 wave:2 ultraviolet:1 experimentally:3 matrices:1 condition:2 leads:1 pbs:7 suffices:1 t1:2 large:2 excellence:1 postselection:1 small:1 3b:1 optics:7 proof:2 programme:1 still:1 application:1 squared:1 grateful:1 deutsch:3 d3:1 pulse:1 outcomes:1 second:3 enhancement:1 pass:3 nmr:2 implemented:4 odd:1 theory:1 even:2 what:1 brien:1 giving:2 d2:3 near:1 find:3 ahead:1 experiment:7 above:2 3c:1 new:2 public:2 contrast:1 3d:1 full:2 simultaneously:2 respectively:4 here:5 modular:2 china:3 others:1 path:1 along:1 invented:1 imperfections:1 deduced:2 arrive:1 mef:12 shift:1 larger:1 commonly:1 optimal:1 yield:1 pick:1 resonance:1 implement:7 fourier:2 involves:1 fourfold:3 named:1 via:1 followed:1 griffiths:2 vhv:1 polarizers:2 highly:3 brought:1 singlephoton:1 counts:1 total:1 univ:1 hhv:1 alamitos:1 use:5 takes:3 would:2 prove:1 probabilities:3 positive:1 mexico:1 predictions:1 next:2 simpler:1 type:3 theoretical:1 more:5 linden:1 shamir:1 composite:1 becomes:2 emission:1 visibility:1 aware:1 hein:1 arms:1 particular:1 known:3 further:2 easiest:1 states:5 grant:2 cas:1 science:4 work:4 london:1 zhao:1 grover:1 values:1 indicating:2 dec:1 my:2 example:1 numbers:3 control:1 challenging:1 figure:1 implementations:1 involve:1 performed:2 employs:1 arise:1 tao:1 distinguishable:1 axis:1 information:2 united:1 goal:1 verify:1 browne:4 delay:3 barium:1 nontrivial:2 pair:1 pure:1 gate:4 exponentially:1 yxy:1 description:1 may:2 after:7 confirmed:1 epsrc:1 expectation:2 reflect:1 produce:2 designed:2 date:1 horizontal:1 meaningful:1 parallel:1 efficiently:1 realized:2 undesired:1 outline:1 register:7 lines:1 yielding:1 ghz:5 algorithms:1 allow:1 representation:1 sackett:1 order:2 operations:3 horne:1 pulsed:1 over:2 move:1 mainly:1 soc:2 produced:1 experiments:2 through:5 statistical:1 fidelity:4 multipath:1 ieee:1 its:6 perfect:1 anhui:1 manuscript:1 how:1 chosen:1 polarizing:1 temporal:3 translation:1 complex:1 exhibits:2 better:1 lu:3 choose:2 mail:1 easier:1 eur:1 maximal:1 non:1 good:2 greater:1 splitter:1 superposed:1 polarizations:1 mixtures:3 merton:1 reflected:1 break:1 warranted:1 subtraction:1 they:3 half:1 oxford:3 exploration:1 rotation:3 now:2 counter:1 represents:1 vidal:1 e2πi:1 always:1 university:3 identified:1 labeling:1 transmitted:1 mode:1 each:4 fψ:2 universit:1 quarter:1 modn:5 weighted:1 directly:1 independent:1 ed:1 reduce:1 principles:1 related:1 challenges:1 society:1 owing:1 ey:2 ex:1 measurement:7 multiparticle:3 laboratory:1 happen:1 computationally:1 eq:1 event:1 out:5 shown:3 network:5 quality:1 furthermore:2 since:4 interference:7 denotes:1 daniel:1 induced:1 supports:1 shows:2 foundation:1 log2:2 linear:7 kok:1 standard:2 difficulty:1 complicated:1 org:1 jozsa:2 pairs:2 created:3 dip:1 could:4 times:1 filter:1 bourennane:1 place:2 massive:1 circuit:16 quadratically:1 first:13 xn:1 humboldt:1 probability:7 powerful:1 number:5 xy:5 simplified:6 another:1 foundations:1 fine:1 between:4 compensator:1 passes:1 given:2 smaller:1 data:3 eu:1 system:1 least:2 1a:1 1c:4 1b:2 california:1 observations:1 realization:5 white:1 scheme:2 final:1 pect:1 lot:1 completed:1 rsa:3 rivest:1 barbieri:1 optical:2 simulate:1 x0:1 than:2 detection:4 polarized:1 determines:1 target:2 fuchs:1 double:2 require:1 summary:1 zero:2 submitted:1 appealing:1 future:1 polarizer:1 toward:2 counting:1 pre:1 fashion:1 dan:1 rewrite:1 correction:1 modern:1 correspond:1 raw:2 initialized:1 need:1 seen:1 seem:1 demonstration:6 paths:1 ax0:1 constructions:1 genuine:7 raussendorf:1 efficient:6 ρexp:1 able:1 parks:1 note:4 sciences:1 high:3 concerns:1 finding:1 so:2 accuracy:1 hwps:2 added:1 multiple:1 fundamental:1 transmit:1 denominator:1 prevedel:1 systems:1 eliminates:1 most:3 detect:1 germany:1 letter:1 phase:3 marie:1 measured:4 appear:1 deviations:1 cause:1 observation:1 nonlinearity:1 average:1 400s:1 detectors:2 multiqubit:3 yang:3 principle:5 nuclear:1 physics:2 fact:1 precise:1 incorporate:1 shor:17 selection:1 show:3 vandersypen:4 random:1 anyway:1 registers:5 chuang:2 pbss:4 d4:3 trivial:1 networks:1 d1:1 based:2 knowledge:1 implementation:3 delays:2 entangling:2 ox1:1 should:1 only:8 version:4 judged:1 factor:3 plate:2 intractable:1 mixture:1 degrade:1 pauli:2 simplest:3 scalable:3 mohseni:1 beam:1 cannot:1 despite:1 report:1 during:5 alexander:1 prime:2 arxiv:1 factorization:6 method:4 common:2 pulses:1 fixed:1 flagged:1 wiki:1 bars:1 set:3 ser:1 achieved:3 national:2 correlations:1 distinguishability:1 observed:4 lanyon:1 see:9 computer:5 college:1 result:1 discussions:1 arm:1 best:1 satisfying:1 capacity:1 arguably:1 currently:1 wikipedia:1 state:20 smallest:1 routine:1 propagated:1 approach:3 email:3 emissions:1 triplet:1 terms:2 vertical:1 nature:12 qubits:15 comp:2 however:3 hefei:2 implementing:1 scalability:1 key:2 originates:1 both:1 braunstein:1 improved:2 desired:1 qft:11 many:1 beckman:1 april:1 σy:1 σx:1 dated:1 qubit:12 photons:14 experimental:12 nnsf:1 unitarily:1 hvh:1 cn:2 simple:1 poissonian:1 period:8 coincidence:3 semiclassical:3 exploit:1 polynomial:2 comput:1 ucl:1 kiesel:1 expensive:1 hvv:1 bbo:4 described:1 transformations:1 basis:3 simplification:1 create:1 due:1 been:10 strategy:1 offers:1 expected:1 ph:3 ann:1 fig:16 graphical:1 corresponding:2 fire:1 josza:1 xxx:3 photon:10 borate:1 zeilinger:1 coherent:5 observe:1 coherently:1 general:2 arisen:1 applied:1 curie:1 laser:2 noticeable:1 exponential:3 hoc:1 value:4 transformation:2 aim:1 while:2 proves:1 suppose:1 evaluating:1 error:2 35th:1 walther:1 opt:1 goldwasser:1 coupled:1 von:1 thus:11 them:1 conditioned:2 cluster:7 crystals:2 mod:4 technology:1 binary:1 hong:4 multiphoton:1 fibers:1 thesis:2 submission:1 same:1 shifts:1 became:1 quant:1 widely:1 evaluate:1 filtered:1 several:1 hhh:3 events:3 pan:3 evolve:3 used:6 http:1 peaks:1 trivially:1 vvv:1 upon:2 effect:1 possible:2 steps:2 bouwmeester:1 purpose:2 vvh:1 entanglement:11 angle:1 contribution:1 outputs:1 niu:1 implements:1 11x:1 task:1 modes:2 fully:1 rules:1 substantially:1 well:2 materials:1 solve:1 greatest:1 model:4 left:1 gates:12 popescu:1 being:1 when:2 adjustments:1 photonic:5 siam:1 front:1 underlying:1 integer:2 alternative:1 speed:2 projection:2 feedforward:1 polarization:1 instance:3 wei:2 ideal:3 source:1 lett:15 easy:1 input:1 qwp:1 heidelberg:2 kingdom:1 entangles:1 nielsen:1 demands:2 read:2 replaced:1 decomposed:2 3pu:1 creations:1 increases:1 zukowski:1 entangled:7 performance:2 press:1 using:10 execution:5 prominent:1 factorize:2 necessary:3 helpful:1 semi:1 follows:2 reduces:1 yields:2 either:1 arbitrary:1 output:4 acad:1 classical:7 sequence:1 conditional:3 some:2 sight:1 provided:1 illustrated:2 annu:1 measurements:4 hybrid:1 overlap:4 manipulations:2 seevinck:1 adleman:1 provides:2 greenberger:2 compute:1 proc:3 demonstrated:2 scarani:1 who:1 run:1 disentangle:1 processing:1 immediately:1 step:4 symp:1 although:2 hadamard:2 post:1 prepared:1 2n:9 cnot:6 proceed:1 integers:1 about:1 directed:1 central:1 adopting:1 simplify:1 microscale:1 tracing:1 o:3 kwiat:2 important:1 ensure:1 ou:3 road:1 equally:1 computational:2 significant:1 jian:2 presence:2 xyy:1 into:2 rotations:2 yyx:1 three:11 lies:1 en:1 determine:1 operator:1 quickly:1 nowadays:1 unambiguous:1 statistics:1 institut:1 additional:2 prepare:2 inserted:1 there:2 vedral:1 transform:1 long:1 tame:1 los:1 mandel:3 way:3 resulted:1 was:6 function:2 considerably:1 complete:1 form:1 offer:1 femtosecond:1 simplifications:1 denoting:1 failure:1 encoded:1 line:1 count:1 made:1 applying:1 circuits:2 wish:1 uv:1 probabilistic:1 up:4 us:2 different:2 physikalisches:1 vhh:1 uk:1 suitable:1 demonstrate:4 problem:1 stages:1 called:1 multiplications:2 ac:1 proved:2 ad:1 defined:1 universal:1 measure:1 am:2 chao:2 denote:3 quantum:34 single:6 ar:2 our:10 ax:5 physical:1 codes:1 nm:1 ref:1 no:4 fixing:1 ekert:1 generally:1 successful:1 valid:1 remarks:1 spatial:4 department:3 philosophenweg:1 sufficient:1 ny:1 deviation:1 elements:1 superposition:2 models:1 ustc:2 120s:1 spectrally:1 a2:2 decoherence:1 hwp:3 cryptographic:1 regime:1 algorithm:30 controlled:3 implied:1 parallelism:1 time:3 observables:2 n2:1 n3:1 once:1 |
0705.1685.txt |@word represent:1 code:3 partial:1 gr:40 illustrates:1 green:1 locations:1 results:21 produce:1 integration:4 leads:2 scalar:13 entropy:2 higher:1 consists:1 follow:1 amplified:2 3a0:1 contributions:3 reasoning:1 dα:4 consider:5 compact:1 whose:1 certainly:1 hold:2 depend:1 calculate:1 δρe:5 33a:1 description:1 show:12 29b:1 29c:1 φgr:1 29a:1 supported:2 finally:8 behave:1 weyl:6 present:3 th:31 under:1 rham:1 stochastic:2 33b:1 worth:1 γe:1 placed:2 sound:1 confirmation:1 amplitudes:2 rel:1 straightforward:1 orthogonal:1 very:7 frequencies:2 rise:1 induce:1 wave:14 manipulated:1 mps:1 cardoso:3 difference:3 exact:1 condition:6 common:1 entire:1 school:1 normalize:4 solves:1 presented:2 sundrum:9 solution:5 standards:1 large:9 solved:1 vector:1 phase:1 section:3 small:8 gc:2 shows:1 confidence:1 upper:1 smaller:2 force:7 braneworld:9 dealing:1 consistent:1 sendouda:3 sss:1 direct:1 zb:4 approximation:2 go:1 second:7 enhancement:26 davis:2 3a2:3 dynamics:5 port:3 tev:1 theory:20 blue:1 reproduce:1 what:4 wavenumbers:1 appear:1 rate:1 incompatible:1 d2:5 takashi:1 selected:1 3w:5 uniform:2 current:1 3h:3 causes:1 above:7 3c:1 new:3 change:1 method:10 contrast:6 era:10 satisfy:1 27a:1 27b:1 full:5 simultaneously:1 degree:5 respectively:4 even:1 modify:2 here:10 behaviour:27 growing:14 amplification:3 free:1 groups:1 address:4 xβ:1 based:1 along:2 xα:2 equations:20 implicit:1 z2:3 knowledge:1 obtained:2 ref:6 parameters:2 algebra:1 institute:1 maximum:1 study:1 larger:9 allows:2 leaving:1 amount:1 supercritical:9 poisson:1 domains:1 fourier:1 makes:2 via:6 4a0:1 projection:1 scales:27 problematic:1 namely:2 taruya:2 ψgr:1 sinusoidal:1 decrease:1 1st:1 apply:1 should:6 armed:1 causal:1 9w:1 derivatives:1 use:6 ds25:2 asymptotic:4 would:2 covariant:1 d68:2 tanaka:4 predictions:4 magnification:3 sitter:3 call:1 therefore:2 taken:1 kη:23 themselves:1 panel:4 type:2 metric:10 subcritical:7 more:3 flat:1 seems:4 formally:1 kˆ:1 clearly:1 ua:3 d70:2 hubble:7 curvature:19 tested:1 domination:3 normalized:2 coincident:1 particular:1 known:3 cases:4 given:21 iii:9 must:4 abundance:1 comoving:4 account:1 crosses:1 locked:1 51b:1 tokyo:3 mm:3 science:1 equation:28 work:3 lukas:1 theories:4 reviews:1 values:2 thin:2 freedom:13 following:7 modifies:1 example:1 decoupled:1 initial:43 kyi:2 transition:1 tab:5 cosmological:7 give:5 predict:1 relativistic:1 choice:5 magnitudes:1 neglected:1 parameterize:2 respective:1 high:31 dxj:3 dxi:5 allowed:1 handle:1 simulation:7 conversely:2 ratio:5 dominant:8 needs:6 rays:2 end:1 notation:1 decaying:2 verify:1 discussion:1 get:1 revisit:1 write:1 how:9 pseudo:2 pure:1 familiar:1 ordinary:7 3w2:2 parameter:5 priori:1 gordon:1 profile:1 tension:2 seahra:3 rept:1 δij:4 undergoing:1 singular:1 may:5 after:4 derived:2 dx2:2 expectation:1 hence:8 3c2s:2 superhorizon:14 waves:3 summarize:2 law:2 data:17 parallel:1 constants:1 efficiently:1 stress:14 short:1 attempt:1 dynamical:1 effective:19 wins:1 goal:1 explicit:1 watson:1 parameterized:1 cosmology:14 bunkyo:1 generic:3 spectral:2 algorithms:6 increasing:1 allow:1 enter:5 definitions:1 heuristically:1 order:10 typical:6 wavelengths:1 holds:1 afterwards:1 furnished:1 developed:4 over:6 move:1 constrained:1 satisfied:2 evaluated:2 paper:8 26b:1 denotes:1 hypersurface:4 differs:1 japan:1 satisfies:3 its:2 before:5 perfect:3 regions:1 derive:4 render:1 directional:1 energies:10 interesting:2 zˆ:1 relativity:8 τb:2 expectations:3 coordinates:2 actually:4 late:5 attraction:3 primordial:10 degrees:13 fig:21 van:4 total:1 derivative:2 setting:3 outside:1 yi:3 non:1 good:3 junction:3 greater:4 later:1 matches:1 dxβ:2 introduce:3 number:1 often:1 units:1 bang:1 effects:13 they:12 identically:1 now:5 wands:7 discuss:1 bigger:1 fields:1 represents:2 dht:1 40c:1 40b:1 2r:1 invariants:5 university:2 level:1 identified:1 sin:2 sufficiently:2 magnitude:2 mode:29 reasonable:1 each:9 crossing:9 found:3 residing:3 dxα:3 2eg:1 characterized:2 neglects:1 domain:2 differential:3 24a:1 significantly:1 24c:1 24b:1 series:3 energy:36 positioned:1 idea:1 numeric:9 conventions:1 kℓ:3 kobayashi:4 decays:3 expect:7 entering:2 impossible:1 laboratory:1 beyond:1 eq:5 out:2 arguments:1 ultimately:2 rs:12 51a:1 furthermore:3 since:7 rev:31 day:1 research:1 increase:4 re:2 contained:1 dominated:9 wide:1 rc:4 qe:5 induced:1 issue:3 correct:2 customary:1 kazuya:2 exactly:1 linear:1 written:1 mapped:1 confirms:1 transfer:15 governing:5 standard:9 signal:1 reason:4 kodama:4 formation:2 element:2 randall:9 phd:1 8w:2 49b:1 definition:1 randallsundrum:1 overtake:1 retained:1 r2:2 r3:2 geometry:7 determining:1 alluded:1 ds2b:2 cosmic:4 times:8 motion:6 turn:3 length:1 dφ:2 period:1 including:3 incorporated:1 sanjeev:2 corrections:10 uses:1 undergo:1 onto:2 neglect:1 first:8 separable:1 major:1 already:1 symmetry:1 perturb:1 variables:6 40a:1 comprised:1 restrict:1 done:1 construct:3 directly:1 battye:2 radiate:1 unattainable:1 electronic:4 illustrate:1 differ:1 perturbation:32 ceff:4 simulated:3 introduction:4 leading:2 extrinsic:1 system:6 least:1 yij:3 perturbations:48 master:13 too:1 calculations:1 realization:1 dt2:2 final:7 speaking:1 gives:8 subhorizon:3 excellent:2 a30:2 becomes:2 mostly:1 wavelength:1 acquire:1 realized:1 plane:1 prediction:1 assumption:1 part:1 koyama:12 somewhat:1 authors:2 translation:1 representing:1 than:20 center:1 past:2 kind:1 teff:1 third:3 portugal:1 easther:1 approximations:5 zero:3 limiting:1 regulator:2 hiramatsu:7 future:2 recovered:2 amplitude:22 were:2 rubakov:1 descriptions:1 enforced:1 portsmouth:2 objects:2 outstanding:1 lines:2 correction:3 canceling:1 spectrum:15 regime:10 reassuring:1 tac:1 close:1 δe0:1 seen:4 recover:7 any:4 relatively:1 kˆ2:1 relationship:2 output:1 separate:2 responsible:1 gravity:2 ode:2 note:15 k2:6 potential:2 generalized:1 simplified:1 finding:1 so:4 canonical:1 eff:6 kab:2 πab:3 eab:6 fct:1 electric:1 bruck:4 opposite:2 arguing:1 object:1 reach:1 accurately:1 most:3 bd:1 satisfying:1 propagate:1 ht:4 formulae:5 retaining:1 extremely:2 kc:15 5dimensional:1 deviations:1 cause:1 considered:2 clear:1 kh:1 implications:3 tangible:1 necessary:1 points:1 comprise:1 velocity:2 constrain:1 left:8 notion:1 wavenumber:4 choose:1 sector:1 particularly:1 fα:2 labels:1 dependant:1 soda:2 connect:1 waveforms:7 gauge:20 solutions:4 faster:1 substituting:1 fine:1 find:7 fifth:1 principal:2 postulates:1 henceforth:1 aσ:2 removed:1 layout:1 resceu:2 m53:1 pdes:2 garriga:1 enough:1 negligible:1 peculiar:1 analytic:7 only:5 explicitly:1 black:4 subsection:2 factor:7 employed:1 sato:3 kaluza:2 astronomical:1 do:4 sense:4 klein:2 means:6 intersecting:1 revolutionized:1 maartens:6 de:8 overall:2 fluid:10 steadily:2 da:1 subdominant:5 unimportant:1 dz:2 nearly:1 closely:1 despite:2 combinations:1 during:10 dt:11 conjunction:1 subscript:1 differentiating:1 ichiki:1 evolution:1 technical:1 2kab:1 places:1 approach:3 arxiv:2 expansions:1 yield:1 acknowledgments:1 4πg:1 qc:4 tbc:2 predicted:2 though:1 characteristic:3 through:1 implication:1 fixed:2 view:1 set:6 could:2 lasenby:2 physically:1 sensitivity:1 grey:1 relative:2 collectively:1 see:17 radius:1 result:8 enhanced:1 existence:1 terms:6 dµ:2 tcd:1 subject:1 c2s:6 fails:1 gravitation:1 tensor:10 tackling:1 ways:1 panels:2 d66:4 tend:1 boundaries:1 state:3 classes:1 various:8 closed:2 simplest:1 invariant:13 boundary:10 conditions:18 tried:1 available:1 size:1 notice:1 recently:1 ability:1 right:7 attention:1 jp:1 however:7 interpolate:1 2αy:1 majumdar:1 2σk:1 argument:1 artificially:1 53b:1 σk:1 observable:2 essentially:4 stages:1 last:1 limits:2 always:2 many:3 brax:2 σg:2 equal:2 previously:1 called:1 sensitive:1 hψ:2 hω:1 transcribe:1 dated:1 context:2 retarded:1 quite:1 contribution:1 ub:1 expression:1 finds:1 otherwise:1 tgr:2 ci:16 relevant:3 separation:1 point:2 simple:8 cb:1 av:1 excess:3 harmonic:2 encapsulated:1 dimensional:18 concluding:1 simply:1 boson:1 constant:11 throughout:3 d73:3 considering:2 ps:15 described:5 tuning:1 argued:2 basis:1 addition:1 create:1 odes:2 been:8 ai:3 much:1 treat:1 interest:2 kapner:1 anisotropic:8 living:1 ph:13 extreme:1 define:7 sfrh:1 wish:1 corresponding:1 mci:1 both:4 25b:1 quantities:9 sufficient:1 25a:1 excite:1 cos:5 6n:3 po1:1 bulk:36 maps:1 6r:1 position:1 6w:2 shiromizu:1 prescription:1 evidence:1 dh:1 gab:2 those:3 matter:19 case:14 exception:1 unlike:1 leave:1 straight:1 stars:1 conserved:3 value:14 choices:3 will:16 cast:1 while:8 match:2 nakamura:1 error:1 situation:1 eik:1 conformal:2 studied:2 ve:4 spacelike:1 coupled:5 refs:4 simulations:16 surface:5 iv:7 ii:4 qeff:5 motivated:1 examine:1 different:15 null:2 righthand:2 perform:1 suggest:2 make:5 radiation:20 lett:7 same:6 poincar:1 epoch:13 newtonian:2 virtually:1 magnified:1 modification:3 conventional:2 dimensionless:5 several:6 couple:1 conflict:1 difficult:2 independent:3 used:8 imply:1 maeda:1 again:1 numerical:9 upon:1 effect:2 49a:1 kohri:1 moment:1 compared:1 moving:3 purpose:1 robust:1 anticipated:1 normalization:3 scaling:1 lower:2 suitable:1 off:1 modes:27 scenario:1 spacetime:2 asymptotically:2 seto:1 well:3 roughly:1 analysis:4 antonio:2 observations:1 without:1 solve:5 consistency:3 coordinate:1 entry:1 model:13 grounds:1 leong:2 dimension:2 parametrically:1 usual:4 26c:1 distances:1 26a:1 b578:1 just:2 less:3 formulation:1 generally:3 epochs:1 newton:1 obtain:3 rest:2 detail:1 2hl:2 against:1 select:1 8πga2:1 fact:6 predicts:3 hongo:1 useful:3 alternative:1 sinusoid:1 speed:1 down:1 reduced:1 jcap:7 k3:1 δpe:1 enters:2 ads:3 53a:1 density:27 hℓ:7 hab:6 slices:2 had:1 confirmed:2 wavevector:1 source:1 interested:2 treatment:1 5d:2 solvable:1 excited:1 hav:2 pparc:1 identical:5 brandenberger:1 tests:1 δt0:1 insensitive:2 around:1 differentiation:1 easily:2 d71:2 big:1 breaks:1 possible:1 corresponds:1 early:13 increases:1 inflation:5 know:5 background:8 confined:1 using:3 8πg:1 generated:1 modifications:3 theor:2 imposed:1 like:3 semi:1 follows:7 reduces:3 dunsby:1 δp:2 δq:1 transform:2 yields:4 either:1 δi:2 anti:2 circumstances:1 interestingly:2 qαβ:4 warping:1 another:4 methods:6 deal:2 δei:2 oriented:1 langlois:5 some:9 self:1 understood:1 growth:1 serves:1 specified:1 oscillations:1 30a:2 30b:2 30c:2 ourselves:1 solving:2 scale:15 highlighting:1 dimensions:2 confirm:3 stronger:2 demonstrates:2 measurements:2 extensively:1 microwave:2 ishibashi:1 critical:12 linearly:1 prog:3 three:4 b609:1 demonstrated:2 refer:1 limitations:1 varying:1 power:9 plot:2 nagataki:3 arbitrary:1 agreement:2 expansion:5 unity:1 pressure:1 clancy:3 substituted:1 although:1 become:1 plots:5 cgr:4 between:9 simpler:1 comparison:2 central:1 d74:1 universe:13 eqns:2 discussed:5 factors:9 o:20 ρˆc:1 compatible:1 distinct:1 range:1 important:5 d69:1 d65:3 horizon:18 act:1 monotonically:1 introduced:3 mizuno:1 automatically:1 d62:5 d63:2 perturbed:1 own:1 ηc:1 decreased:1 h2:1 into:9 within:2 numerically:2 attributed:1 due:9 eqs:2 remarks:1 perturbing:2 schemes:2 tiny:1 determine:1 einstein:2 computational:2 infer:1 approximately:1 physical:6 ρh:1 rely:1 hep:32 additional:2 switches:1 confident:1 jhep:1 assumed:1 there:9 approximate:1 challinor:2 u2:1 conservation:4 low:12 way:1 bodies:1 was:2 indeed:1 function:12 bridgman:1 insensitivity:1 complete:1 form:4 quantity:2 brane:52 but:15 2ht:2 astro:12 expected:2 dωb:4 hl:4 hc:3 line:3 ha:13 true:3 amplify:1 2dµ:1 wσ:2 embedded:1 minkowski:1 gravitational:12 up:2 us:6 tell:1 kk:30 below:2 frequency:1 limit:1 today:2 uk:5 malik:1 fαβ:5 fluctuations:7 problem:5 ωb:20 similar:2 calculated:1 regimes:2 detailed:1 bearing:2 ac:9 ab:1 associated:1 computing:1 defined:5 certain:1 describe:5 influence:3 liddle:3 general:10 weff:2 single:1 au:2 our:22 dζ:1 dη:18 formalism:1 dβ:2 check:1 sasaki:4 defines:1 friedmann:5 functions:11 codes:7 fellowship:1 no:4 na:3 nb:2 when:10 vanishes:3 perturbative:2 field:7 other:8 details:1 normal:1 papers:1 test:3 incredibly:1 kv:1 deffayet:1 alternate:1 briefly:1 suppl:2 superposition:2 provided:2 models:2 finite:1 smoothly:1 shown:7 nonstandard:1 a0:3 a3:1 a2:9 mukohyama:1 suppression:1 kz:1 variable:8 gets:1 structure:1 observers:1 implies:7 coupling:1 algorithm:2 assume:4 expands:1 dτ:2 space:4 holes:4 δti:2 governed:2 dρ:1 equivalently:3 investigated:1 principle:1 aspects:1 4k:2 time:16 far:2 applied:1 4a:1 4b:1 original:2 once:2 |
0705.1686.txt |@word sergei:2 aring:2 l17:1 consider:3 limited:1 caused:1 astron:3 activated:1 sirko:2 leads:1 disc:95 stochastically:8 consists:1 disk:1 optical:2 compact:1 whose:1 supposedly:1 feeding:18 const:1 catastrophe:3 zone:2 clarke:1 ott:1 concerned:1 show:5 young:1 containing:1 supported:1 quasi:5 mediated:1 stable:2 stochastic:6 include:1 starbursts:2 sound:1 cuadra:4 g1:1 md:2 very:11 dynamic:1 continues:2 account:1 geometrical:1 hosting:1 putting:1 kiloparsec:2 difference:1 cool:1 coeval:1 clouds:28 unlike:1 presented:1 experiencing:2 shock:1 proposals:1 obscuration:2 fewer:3 large:15 unrelated:1 asp:1 succession:1 small:9 radio:1 midplane:2 noted:1 smaller:5 exposed:1 estimates:2 direct:2 le1:1 rate:15 ionisation:1 design:5 go:1 equal:1 further:6 estimated:1 avoiding:1 even:3 kinetic:1 appear:2 interactions:1 while:1 supplied:1 tremaine:2 current:2 above:2 frank:1 krumholz:2 new:4 claimed:2 contributes:1 apply:1 contrast:1 shocks:2 coefficient:1 wehner:2 led:1 dwarf:3 degree:1 promising:1 component:4 here:6 perpendicular:1 deposition:11 objects:1 operating:1 separation:1 situation:1 active:5 consideration:1 quite:1 appears:1 supplying:1 suggest:1 convert:1 incoming:3 division:1 environment:2 until:1 larger:10 allows:1 reason:1 gravitationally:4 suggests:1 bulges:1 resulting:2 suggestion:1 action:2 formation:16 narrow:1 makes:1 cancellation:6 summarising:1 prints:2 via:2 tvisc:1 classification:1 scales:8 requiring:2 vii:1 highly:1 apj:9 tdyn:2 illumination:2 total:1 sch:1 externally:4 cloud:14 eddington:2 presents:1 fed:15 l33:2 cosmological:1 would:19 brighter:1 blandford:1 generate:1 few:12 lodato:1 call:1 therefore:4 strike:1 themselves:1 type:9 theoretical:2 more:13 flat:8 almost:2 becomes:2 starburst:2 m82:1 warp:2 bodily:2 thompson:4 long:2 circular:1 observations:3 particular:3 known:2 hole:10 aligned:2 iii:1 must:4 rin:5 none:1 sphere:7 decouples:1 torques:3 mn:1 impasse:1 minimum:3 obvious:1 mp:1 princeton:2 arrive:2 springel:1 example:7 address:1 interstellar:1 figure:7 give:1 predict:2 thermally:1 neglected:1 generically:1 high:8 collision:4 way:8 sense:2 times:2 conversely:1 occur:1 simple:1 axis:1 huge:1 needs:1 end:2 provide:3 hydrogen:1 divided:1 regions:1 far:1 hot:3 instead:3 isotropic:1 profile:1 orbital:1 galactic:9 may:12 broad:2 after:1 flattening:1 orbits:6 hence:2 waves:2 law:2 kinney:1 grow:2 diffusion:1 short:2 natural:1 dynamical:5 imply:2 elmegreen:2 onto:1 aretxaga:1 spectra:1 lines:3 rather:1 complexity:1 edited:2 negligible:1 expression:1 fundamental:1 correlation:5 llagn:2 representation:1 first:3 words:1 order:3 typical:4 lsg:3 feedback:14 reservoir:2 produces:1 over:2 move:1 mainly:6 murray:1 years:5 stability:2 coll:1 paper:2 through:6 motions:1 affect:3 argued:1 existence:1 cold:1 still:1 its:1 galaxy:12 observational:4 style:1 le:1 rapidly:3 fit:1 imf:1 warps:1 interesting:1 masses:3 vicinity:3 actually:2 forms:4 previously:1 absence:2 production:2 systems:1 stalled:1 clusters:4 main:1 might:9 overcome:1 misalignment:1 non:1 mardones:1 affected:1 l27:1 propose:2 material:15 innermost:2 collide:5 zooms:1 bulk:1 avoids:1 they:7 acta:1 arriving:1 now:1 yu:2 discuss:1 halo:1 february:2 several:1 always:2 university:2 normally:1 crudely:1 magnitude:2 mode:2 reasonable:1 radial:11 found:3 difficult:1 scattering:1 mean:1 heavy:1 t5:5 directly:2 weight:1 dichotomy:1 energy:7 hard:1 availability:1 principles:1 related:3 line:1 used:1 expect:1 entering:2 year:3 our:14 happen:1 beyond:2 neighbourhood:1 out:7 ultimately:1 mediates:1 100h:2 furthermore:2 since:5 requires:1 diffusive:1 collisions:7 settle:1 dominated:2 performs:1 rh:1 occurs:1 shut:1 trajectories:3 theory:1 fluctuates:3 state:4 change:1 million:2 galaxies:18 little:1 standard:3 difficulty:3 completely:3 advantages:1 put:1 nayakshin:12 estimate:6 combes:4 ate:1 r2:3 r3:1 geometry:1 widths:1 could:4 transition:1 keep:1 disturbed:1 place:2 massive:20 mdisk:1 isc:1 trickle:1 facilitate:1 think:1 mdisc:5 feed:4 major:2 already:2 features:2 feel:1 question:1 viscosity:2 number:1 spiral:1 warped:12 done:1 least:2 another:2 carry:1 impossible:1 thick:3 miss:1 angular:42 size:6 mbulge:3 given:5 necessarily:3 temperature:2 jet:1 their:8 introduction:1 πh:1 collimated:3 unspecified:1 roche:1 needed:3 cooling:4 accretion:51 rates:8 too:8 postulate:1 structures:2 final:1 low:8 stars:9 discussion:1 expelling:2 explanation:1 rsg:17 assumption:1 part:3 astrophysically:1 authors:1 lobe:1 than:28 peaked:1 king:12 fuelled:1 unfortunately:1 fold:1 behaved:1 require:1 martins:1 likely:4 seyfert:1 contrary:1 were:2 ard:1 kunth:1 inflow:6 tacc:7 smbhs:12 suggestions:1 jogee:1 takes:1 deposited:1 fuelling:3 julian:1 turned:1 argument:1 randomly:6 say:2 kepler:1 manner:1 need:2 quasars:5 seem:2 obviously:1 apparently:2 intersecting:1 collapse:1 forced:11 angle:2 zero:1 self:10 propagation:1 able:3 gravity:8 mechanism:2 note:5 mix:1 goodman:12 potential:1 take:3 forces:1 k4:1 collapsed:1 channel:2 infalling:3 lectures:1 continuous:2 unless:1 starved:1 though:1 arguing:1 keeps:1 reach:1 most:6 impacting:1 printed:1 significant:4 pair:1 extremely:1 msg:3 latex:1 especially:1 considered:1 sg:1 clear:3 flow:5 disease:1 km:5 heating:1 principle:2 kt:1 velocity:6 physics:1 incomplete:1 emerging:1 mckee:1 particularly:2 leicester:2 random:11 friction:1 ending:1 relatively:1 radii:2 relation:1 rough:1 find:2 ldisc:1 help:1 larson:1 ratio:2 zahn:1 merger:2 cousins:1 explain:4 distributed:2 outside:2 should:3 liberation:1 only:13 going:1 black:14 factor:1 fuel:5 emitting:1 falgarone:2 local:4 pointed:3 sgr:1 ser:1 do:6 dominant:2 klein:1 get:1 dependent:1 simplest:1 agns:1 cannot:3 nearly:6 lighter:2 altogether:1 during:2 averaged:1 tbd:1 processes:1 increasing:1 krolik:3 luminosity:1 arxiv:3 yield:1 discs:40 schemes:1 common:1 inefficient:2 activity:6 analytical:1 3d:1 inside:3 mergers:9 view:2 inferred:1 bars:5 set:1 aspect:1 swept:1 expel:1 controlled:1 lett:1 maximum:2 observed:5 see:5 radius:15 result:3 100pc:1 fail:1 recently:1 idea:1 rcoll:11 subject:1 nuclear:6 away:2 nature:2 rings:4 modulate:1 case:4 enough:10 difficulties:2 radiated:1 between:8 probably:3 numerous:1 tent:1 arrival:1 comparable:1 bound:1 statistically:1 extend:2 adding:1 importance:1 parameterising:1 supernova:2 deliver:2 however:4 efficiency:3 key:2 quataert:1 jets:1 outer:14 distribution:3 originates:1 faced:1 both:2 last:1 outflows:3 many:1 region:12 compton:2 explore:1 etc:1 connection:1 streams:1 context:2 siemiginowska:2 l25:1 contribution:2 argue:1 whole:1 shots:2 coincides:1 σt:1 σr2:1 presumably:1 relevant:2 extent:1 reprocessed:1 supply:1 reasons:1 excess:1 walk:3 directions:1 rpc:5 regulated:1 cs:1 respect:1 throughout:2 better:1 unusual:1 second:1 addition:1 radiative:1 due:4 tiny:1 quickly:1 pc:18 odel:1 much:15 slowly:1 combined:1 expected:4 pile:1 ph:1 hardly:1 define:1 engine:1 suggested:2 direction:2 contribute:1 corresponding:1 champion:1 elvis:2 transferring:1 gas:39 andrew:1 blackhole:1 else:1 pringle:7 external:2 mail:1 kicks:1 obscuring:3 general:1 spin:5 former:1 present:2 applied:1 supernovae:3 solid:2 fin:1 harder:1 nski:2 value:2 promotes:1 will:11 near:1 suppose:1 viii:1 rbh:1 cancelled:1 radially:1 fluctuating:1 salpeter:2 orientation:5 rix:2 linked:1 vi:1 thus:13 site:1 surface:6 iv:1 ii:4 apjl:5 itself:1 conf:1 illustrates:1 situ:1 parsecs:4 binary:4 different:4 lacking:1 cools:1 perhaps:3 threatens:1 make:2 radiation:7 merging:1 same:4 any:3 shorter:6 epoch:1 parts:2 arguments:3 schematic:1 grand:5 units:1 spirals:1 shakura:3 regime:1 events:2 conflict:1 higher:3 independent:1 calculation:1 extended:1 misaligned:1 numerical:4 flows:2 hand:5 driven:5 constraining:1 v2:1 edges:1 arrived:2 appreciable:1 dust:1 frequently:1 sunyaev:5 recent:1 centred:1 lower:5 off:3 nevertheless:1 changes:1 well:7 analysis:1 without:1 thought:1 paumard:1 edge:3 comes:1 components:3 sets:2 firstly:1 quantitative:1 model:19 nearby:2 arising:1 rout:5 left:2 spherical:3 distances:2 circularisation:2 proposed:3 less:6 beloborodov:2 obtain:2 ideas:2 circling:1 predicts:2 spherically:1 absorbers:1 momenta:1 speed:1 yet:2 oriented:4 secondly:1 density:5 passively:1 seems:4 except:1 source:3 shlosman:4 extends:1 treatment:1 momentum:42 build:1 real:1 explained:1 around:1 depends:1 loss:1 observationally:1 unlimited:1 possible:2 l89:1 early:2 possibly:1 spheroidals:2 kpc:1 unification:2 mon:1 background:1 press:1 immediately:1 height:2 usually:1 advanced:1 vertically:2 like:1 bulge:14 alternatively:1 schmitt:2 zoom:1 shrink:2 specific:2 flux:1 continue:1 unstable:4 either:3 become:4 soviet:1 genzel:2 opacity:1 because:3 schematics:1 begelman:5 affects:1 deposit:1 some:2 overheated:1 masing:2 growth:7 flatten:2 sight:1 escape:1 infall:3 transport:1 harris:2 separately:1 scale:21 encouraging:1 πr2:2 avoid:2 centre:2 per:1 does:5 unit:1 conclusions:1 assuming:2 closely:1 demonstrated:1 core:1 paczy:2 power:2 diminishing:1 each:2 ensures:1 illustration:2 stellar:11 pressure:2 host:1 instability:2 escala:2 obscured:1 super:2 panel:2 acc:1 about:2 central:11 column:4 universe:2 dependence:3 7rh:1 range:2 stand:1 insufficient:1 hatched:1 l9:1 soc:1 mbh:10 smbh:46 presence:3 h2:1 into:9 within:2 implications:4 latter:4 down:1 right:2 references:1 been:1 physical:1 significantly:1 explaining:1 additional:1 area:2 transfer:4 support:1 there:8 convincing:1 catalysts:1 equation:4 dispersion:1 spread:1 accordingly:1 outflow:1 inner:27 fraction:6 astrophysics:2 m1:5 formed:1 viscous:12 was:3 cancel:1 function:7 medium:2 gaseous:18 complete:1 form:9 forming:5 becoming:1 agrees:1 but:5 sophisticated:1 astro:2 hydrostatically:1 heat:2 link:1 solar:1 mnras:5 overflow:1 promote:1 longer:1 directed:3 fragmentation:2 made:4 gravitating:1 whether:2 levin:2 gravitational:9 uv:1 smooth:1 up:10 us:2 m8:6 rees:1 below:1 limit:3 uk:2 approaches:1 problem:3 radiatively:1 average:2 ex:1 strongly:6 bearing:1 ac:1 attained:1 located:1 defined:1 steady:4 abstract:1 redshifts:1 influence:1 evidence:1 consumed:1 fringes:1 coppi:1 file:1 simulations:4 orders:1 lifetime:1 parsec:12 work:2 steeper:1 again:2 compared:2 no:6 amounts:1 collin:2 whereas:2 when:4 field:2 other:10 department:1 thousand:2 weak:1 conclusion:1 optically:1 picture:7 draw:1 m85:1 star:24 provided:1 models:6 uniformly:1 shown:2 helping:1 important:3 nucleus:2 allowing:1 additionally:1 astronomy:1 sides:1 structure:3 feasible:1 ago:1 agn:39 isotropically:1 implies:1 faster:5 assume:3 typically:1 required:7 holes:4 orbit:3 them:1 depth:5 mass:25 presenting:1 time:22 nuclei:4 protostar:1 joins:1 original:1 |
0705.1687.txt |@word dist:4 consider:3 funct:1 global:1 alternatives:3 results:5 fluids:1 four:3 proposition:28 pℓ:3 gb:7 gs:1 research:1 gj:1 gi:6 compact:4 whose:1 depend:1 analytic:2 paris:2 concerned:1 prin:1 tn:3 tl:5 does:1 tj:3 tk:1 elliptic:7 under:5 sens:1 norm:2 plasma:2 belonging:1 jensen:2 straightforward:1 orthogonal:1 very:1 tends:1 choice:2 corollary:3 every:16 stays:1 noncontractible:2 gℓ:1 bubbles:2 subsets:1 evn:3 level:1 notes:2 solution:4 t0:8 large:17 smale:6 2l2:1 fourier:1 small:7 eigenvalues:1 anal:5 concluded:1 sℓ:1 lecture:1 bubbling:1 estimates:5 direct:2 zero:2 harnack:1 pass:3 chen:7 further:1 reine:1 mj:1 even:1 employ:1 what:1 nonlinear:6 stands:2 d2:2 section:4 interactions:1 find:3 3k:1 version:1 above:5 sup:8 increasing:1 method:2 satisfy:2 egb:4 degree:2 b2r:2 boll:1 ranges:1 following:25 arch:1 standard:5 equations:13 z2:1 tρ1:2 obtained:1 remark:2 sobolev:4 tρ2:10 study:3 contradiction:2 amount:1 action:1 suitable:1 sci:2 boundedness:1 palais:6 via:3 useful:1 addresses:1 classification:2 mech:1 logarithmic:1 texts:1 condensates:2 apply:5 total:1 univ:1 use:3 homotopic:2 would:2 prove:9 recalling:3 positive:14 negative:11 next:13 choosen:1 vol:2 m1:2 therefore:3 m2:2 indiana:1 stage:1 type:7 more:2 introducing:2 solitons:1 ti:17 ital:1 curvature:4 merle:2 bpi:2 berlin:2 everywhere:1 vn:8 known:3 cases:1 hold:3 marchioro:2 springer:2 onsager:1 henri:1 ρi:9 recall:5 equation:17 saddle:1 mi:4 modified:1 radon:1 values:4 sharp:2 lipschitz:1 struwe:6 making:1 endow:1 example:4 proof:26 claim:8 ration:1 wang:7 give:4 purposes:1 states:1 assumptions:2 numbers:4 want:1 allowed:2 dj:3 brezis:3 occur:2 verlag:2 normalize:1 e2u:1 notation:1 s2:8 s1:10 get:17 write:1 trieste:1 criterion:2 pure:5 answer:1 acta:1 g12:1 parameter:2 belongs:1 profile:1 map:10 pρ2:1 description:4 singular:2 may:1 max:6 after:1 variant:1 br:4 consequence:3 produce:1 inst:1 coming:1 data:2 constants:3 goal:1 stress:1 natural:1 barycenters:6 third:2 higgs:1 chern:5 lines:1 su:2 element:1 lundgren:2 si:16 so:15 asserts:1 sl:1 representation:2 order:7 typical:1 holds:11 subsections:1 indeed:3 over:2 vary:2 shafrir:3 paper:2 london:1 statistical:6 existence:17 satisfies:3 still:1 its:2 before:3 eul:1 eun:7 monotonicity:2 maps:1 ln:2 fix:2 uniformization:1 li:11 onb:1 choose:3 lp:2 mail:1 main:2 decades:1 setting:1 maximal:1 non:14 fourth:2 combination:1 introduce:2 refines:1 mention:1 now:16 bigger:2 riemann:4 eigenvalue:1 dirac:2 exits:1 always:1 hamiltonian:1 infer:2 sufficiently:2 l4:2 inequality:19 l2:13 mode:1 l0:2 l1:8 2l:1 found:2 repeating:1 mean:17 domain:1 arxiv:2 tuples:1 idea:1 related:3 toda:6 sj:5 combining:1 eu:57 our:5 differ:1 nonlinearities:1 partial:2 special:2 mat:2 deals:2 precisely:1 container:1 part:1 gradient:1 res:1 furthermore:1 since:11 diam:3 denotes:2 particles:1 prescribing:1 geom:2 denoted:1 formula:4 supports:1 ri:5 math:17 pun:3 folowing:1 theory:9 loc:1 easily:3 singularities:1 given:16 free:1 quite:1 admits:1 proportionality:1 van:1 estimate:1 additional:1 definition:7 dunne:1 derivation:1 r2:1 applications:2 geometry:1 bxi:7 2p:1 used:1 int:1 panorama:1 hence:21 onto:2 first:5 ding:4 there:29 xn:4 ℓs:1 number:3 ℓi:1 done:3 construct:1 impossible:1 g1:9 open:1 little:1 temperature:1 similarly:1 introduction:3 πk:3 system:4 relations:1 their:1 appl:5 identity:3 calculations:1 scheme:8 cite:1 gives:3 discussion:1 completed:1 continuous:7 proving:2 tarantello:5 weakly:1 l2δ:1 sublevels:7 than:1 distance:6 variational:6 namely:5 1l:2 subsequence:2 yang:1 stratified:1 rǫ:2 decompose:1 projections:2 generality:2 well:3 ann:1 concludes:1 measure:1 argument:9 ohtsuka:5 extremals:1 angew:1 close:1 disjoint:2 seen:1 concentration:6 any:6 mountain:3 eq:1 min:7 latter:1 ideas:1 montgomery:2 k2:3 k1:7 maxi:1 take:1 εk:5 xi:11 green:4 beirut:1 formulas:2 centre:1 twodimensional:1 measures:1 sequence:7 systems:3 metrics:2 most:1 said:1 pulvirenti:2 preliminary:1 remarks:1 acknowledgements:1 class:3 eigenfunctions:1 4l2:3 caglioti:2 ke:1 kk:1 ki:1 later:2 curvatures:1 dimension:3 points:10 principle:1 exp:1 m36:1 blowup:1 physics:3 naively:1 fact:8 precise:2 show:4 supported:1 notations:1 theories:1 gauge:1 solutions:23 multivortex:1 uniform:1 trivial:5 translation:1 δx0:1 homology:2 finally:1 based:1 knowledge:1 parameters:5 topological:7 lemma:12 only:8 going:1 gb2:2 subsection:5 factor:1 moser:7 local:1 preliminaries:1 continuity:1 do:3 triangle:1 δxi:2 means:1 obtain:7 ϕl:5 words:1 dv:6 differential:4 derive:1 underlying:1 fixed:2 riemannian:4 set:12 exists:19 sez:1 edition:1 see:22 result:11 deduce:2 terms:2 best:1 subject:1 surfaces:7 appear:2 satisfying:5 unione:1 inequalities:1 liouville:1 boundaries:1 kiessling:1 state:1 µi:7 closed:5 between:3 invariant:1 geometric:1 previous:1 conditions:2 checks:1 available:1 αt:1 notice:3 recently:2 wn:9 guiding:1 attention:1 weak:3 however:1 wi:2 wj:5 concentrate:1 dmin:5 key:1 supσ:1 differentiability:2 topology:6 σk:36 received:1 last:4 desired:1 many:1 taking:1 σe:5 called:4 etc:1 densely:1 embedding:2 comm:7 pde:2 malchiodi:6 adapted:2 comes:2 ck:10 among:1 relevant:1 point:4 dimensional:7 adaptation:2 sequences:8 proved:3 writing:1 diff:1 contractibility:1 longman:1 pp:1 pv:2 second:1 e4u:2 union:1 due:4 been:2 springerverlag:1 much:1 asymptotics:1 pj:1 pk:3 improve:1 empty:1 define:5 arises:1 corresponding:4 both:2 sufficient:4 subscripts:2 understand:1 improved:1 c1:2 general:3 manifolds:3 case:2 multi:1 p1:5 exponential:2 laplace:2 defining:1 value:2 will:8 fubini:1 near:1 ar:6 suppose:5 compactness:8 behavior:2 applies:5 di:3 property:2 conformal:1 characterizing:1 exponent:1 attains:1 simons:5 almost:1 h3k:1 metric:2 vk:1 thus:8 surface:5 ii:10 tφ:1 regularity:4 cone:2 dual:1 argue:1 conical:1 ric:1 different:3 italy:1 coron:1 author:1 perform:2 belong:2 same:3 poincar:1 verifies:1 arguments:2 φl:5 couple:1 interpolation:1 independent:2 literature:2 infinity:1 imply:1 trivially:1 effect:1 flows:3 hand:5 running:1 moving:1 purpose:1 composition:1 uˆ:1 normalization:1 relies:1 53c21:1 genus:4 depending:9 x0:17 analysis:5 without:2 trudinger:7 sets:3 arising:2 lin:6 vε:5 spherical:1 deltas:1 manifold:1 just:1 orientable:2 resp:2 solvability:1 formulated:1 thanks:1 integer:7 facts:1 converges:1 toland:1 projection:2 letting:2 preprint:6 family:2 application:1 8πg:1 cl:2 except:1 δpi:1 improvement:3 jost:7 add:1 other:7 corollaries:1 theorem:24 pitman:1 solvable:3 remaining:1 euler:4 divided:1 real:7 aspects:2 depends:1 loss:2 showing:2 sums:1 possible:1 bredon:1 8πk:1 finding:1 8πi:1 know:1 turbulence:8 ams:1 moreover:9 advanced:1 formal:6 dµi:1 necessary:1 δx:1 sublevel:1 exploiting:1 sissa:2 performing:1 collect:1 vortex:3 yields:3 possibles:1 arbitrary:3 pointwise:1 stationary:2 beltrami:2 therein:1 satisfactory:1 acad:2 methods:3 classical:4 olg:1 some:13 self:1 e4π:1 choosing:1 convex:1 provided:2 dense:1 dimensions:2 cσ:4 minimax:3 bps:1 critical:6 assuming:2 refer:1 inserting:2 core:1 bf:1 minimization:1 uniformly:8 equivalent:1 each:2 bi:3 immediately:1 although:1 putting:1 anticipated:1 properties:3 cε:6 cδ:3 about:2 ol:5 constraint:2 triviality:1 hatcher:1 dependence:1 o:6 distinct:1 involving:2 introduced:2 automatically:1 considerations:1 follows:7 unbounded:1 into:7 within:2 integral:1 functional:10 three:1 schemes:1 references:2 laplacian:1 joyce:2 elementary:1 heu:2 span:1 log:71 homotopy:2 removing:1 vortices:2 question:1 start:2 describes:1 lions:2 low:3 way:2 blow:3 analyze:1 sections:1 suzuki:5 function:11 complete:2 form:2 but:1 gaussian:1 volume:4 construction:3 delta:1 convergence:1 true:1 commun:5 pi:4 gi2:1 consist:1 supp:3 cells:1 smooth:1 up:5 us:1 ul:4 below:9 un:30 limit:2 planes:1 problem:7 similar:1 average:1 eg1:4 mechanics:6 constant:13 iit:1 defined:3 wich:1 abstract:1 describe:2 denote:6 ap:2 proves:1 exist:6 inf:6 dε:3 distributions:1 check:1 fill:1 functions:1 differentiable:2 no:3 fixing:1 when:4 bartolucci:2 graduate:1 d2i:6 field:16 ricciardi:3 branch:1 papers:1 mathematics:2 homotopically:1 2di:1 conclusion:1 conclude:1 models:1 sided:2 problems:3 lucia:1 bounded:16 structure:2 algebraic:1 bahri:2 using:17 dvj:1 assume:4 dvg:138 interval:2 together:1 jeanjean:1 |
0705.1688.txt |@word ibid:2 secondly:1 concept:2 gr:3 represent:1 interference:5 forbidden:1 stems:1 results:9 existing:1 leads:3 discreteness:2 scalar:11 entropy:1 comments:1 broader:1 op:1 consists:2 follow:2 expressions:1 loll:1 cases:1 causes:1 consider:2 inverse:3 depend:2 calculate:2 sahni:1 caldwell:2 simplify:1 send:1 removal:1 critical:1 under:5 popularity:1 kκ:4 analogous:1 cm3:2 divergent:1 string:1 advantage:1 orthogonal:1 far:3 bm:1 indication:1 springer:1 wave:51 normalizability:2 electron:1 lrr:1 additional:1 fall:2 inequivalent:1 inherited:1 difference:10 exact:6 prevents:1 categories:1 entire:2 differentiated:1 obvious:1 hamiltonian:10 diverging:1 suffices:2 nucl:1 solution:32 t0:11 prototypes:1 large:13 solved:5 zeh:2 fabris:1 mariusz:1 science:1 small:9 eigenvalues:4 shows:2 barbara:1 lapse:1 mon:1 strongly:1 approximately:1 occurrence:3 2k2:3 lessen:1 consistent:4 plot:2 direct:1 literature:1 sign:1 approximation:18 gaussians:2 zero:10 d69:1 evaluated:3 go:1 substituting:1 zu:1 dynamics:2 primes:1 spreading:1 canonical:4 even:3 index:2 what:3 stood:1 stands:1 geometrodynamical:6 trivial:2 section:1 selected:1 area:8 analogously:1 expressed:1 current:2 wiggles:1 version:3 fifth:1 goes:4 boundary:6 new:1 change:1 connected:3 method:1 filled:2 bertolami:1 crunch:1 full:12 simultaneously:1 degree:1 respectively:2 concepts:2 component:1 interested:3 here:14 behaviour:6 grav:6 free:1 sinh:4 z4:1 consideration:1 along:1 standard:1 equations:6 z1:3 interpret:1 obtained:7 moschella:3 suitably:1 institute:3 study:4 studied:7 allows:1 later:1 1v:3 resulting:3 loop:17 usually:1 triad:2 implement:1 suitable:2 spacetime:4 livingreviews:1 plays:1 uniquely:1 boundedness:3 showing:2 via:4 useful:2 4a1:1 figure:7 scales:4 information:1 requiring:1 namely:2 conclude:1 ebert:1 expect:1 coinciding:1 decrease:1 summation:1 orderings:2 total:3 causal:1 linearly:1 derivatives:7 conventional:2 asymptotic:1 would:7 remains:2 positive:1 contains:3 negative:1 classically:4 depicted:2 therefore:7 criteria:2 taken:2 candidates:1 astr:1 type:3 theoretical:2 more:7 flat:2 exhibiting:1 becomes:5 naive:1 claus:1 x12:2 odinger:4 curvature:6 vandersloot:1 appendix:3 basically:1 particular:2 known:2 hole:1 iii:4 sepangi:1 hints:1 ii:2 account:1 tachyonic:1 quantized:2 integrating:1 recall:2 equation:61 work:2 modified:1 theories:2 sudden:1 values:5 publications:1 evolved:1 freedom:3 following:5 making:2 root:1 example:5 proof:1 6aa:1 l101:1 cosmological:18 mirrors:1 process:1 stiftung:1 cited:1 sense:5 organized:1 near:2 weinberg:1 states:2 caused:1 numbers:1 want:3 arise:3 dxe:1 keep:1 hydrogen:3 occur:4 calculated:1 dk:2 motion:3 respective:1 end:7 instant:1 z20:1 provide:1 discussion:5 means:2 berlin:1 feature:4 orthogonality:1 tupper:1 regions:3 located:1 lam:1 simplifies:2 instead:3 ordinary:2 parameter:6 belongs:1 simplicity:1 product:3 d74:1 description:1 undergoing:1 minus:2 replacing:1 stop:1 after:1 singularities:14 lengthy:1 fluid:7 lan:1 consequence:2 plane:5 deviates:1 physik:1 winkler:1 φt:1 s0k:7 choice:8 constants:1 recovery:1 short:1 branches:1 dynamical:1 third:1 counter:1 explicit:1 yielding:1 introducing:2 cosmology:17 lengths:1 cannot:1 so:17 fundamental:1 april:1 representation:5 heuristically:1 order:8 integrated:1 s0:4 interpretation:3 ϕk:25 john:1 over:5 goncalves:1 choose:4 interpreted:1 stability:1 course:7 paper:4 through:6 da2:1 hypersurface:1 differs:1 existence:3 satisfies:1 still:2 its:17 before:2 perfect:2 write:2 derive:2 rapidly:1 probability:6 tipler:1 how:1 chosen:6 fractal:1 fix:1 relativity:3 vicinity:11 coordinates:2 gen:1 h2:1 comment:1 degrees:2 encounter:1 constitutes:1 persist:2 jacobi:3 derivative:7 main:1 might:1 setting:1 correspondence:1 non:5 good:1 return:1 halt:1 than:1 carter:1 press:2 integral:5 best:1 regarding:1 investigated:2 landau:1 break:1 framework:6 bang:16 4dimensional:1 hamilton:3 effects:1 they:4 hands:1 front:1 souza:1 singularity:69 now:2 yu:1 discuss:2 bigger:1 heaviside:1 easily:1 2v:1 several:1 dirac:5 name:1 spacetimes:2 galloway:1 invariants:1 university:3 level:2 2x:1 sufficiently:1 x21:2 2a:1 reasonable:1 each:3 found:7 universit:1 quarter:1 side:3 constraints:1 homogeneous:2 differential:1 financial:1 http:1 formulate:1 independent:4 series:1 energy:15 reduce:1 gaussian:5 related:2 deterministically:1 2z0:2 extended:1 ex:2 measurement:2 quantum:55 our:5 happen:1 avoided:4 eq:1 refined:1 special:3 out:13 living:1 shown:3 space:8 conjugate:1 furthermore:1 dewitt:21 squared:2 investigate:2 cancels:1 denotes:2 may:5 handles:1 safety:1 socalled:1 rel:1 formula:1 get:2 induced:1 evaluation:1 occurs:2 math:2 unifying:1 refining:1 foundation:1 trajectories:6 turning:3 theory:19 reformulated:1 derived:2 mapped:2 divergence:3 fisica:1 possibility:2 quite:1 approaches:4 complicated:1 term:2 org:1 ofer:2 led:1 knit:1 finite:4 occuring:3 basi:1 v0:11 hubble:4 derivation:2 created:1 geometry:1 starts:2 could:1 transition:1 cosmic:4 v2:2 used:1 feasible:1 creates:1 ordering:14 length:7 isotropic:4 arccos:2 hence:1 neglected:1 l1m:4 onto:1 first:10 origin:2 xk:15 v1:2 initial:8 xn:4 features:1 symmetry:2 laguerre:2 relegated:1 variables:2 superpose:1 number:2 system:1 restrict:2 done:4 2a3:1 another:1 robust:1 carry:2 reached:1 ulpicher:1 u2:1 quality:1 tively:1 spread:4 given:17 πa:2 geodesic:1 publication:1 table:1 start:1 introduction:3 bologna:1 dipartimento:1 theoretische:1 least:2 their:4 intermediate:1 too:2 justified:2 dt2:1 dfg:1 recent:1 recovered:3 subsection:1 ashtekar:6 sociated:1 cope:1 centered:5 academy:1 moscow:1 continuous:2 zeroth:1 jurkiewicz:1 pawlowski:4 employ:1 mn:1 part:10 deceleration:1 somewhat:1 x2:3 off:1 eliminated:1 cosh:2 peculiar:1 coefficients:1 peaked:4 cologne:1 kind:3 analyze:1 sections:1 require:7 second:11 viollier:1 hypersurfaces:1 matter:5 units:1 future:4 validity:3 str:1 were:2 sec:10 negatively:1 gives:1 russia:1 lowest:1 enforced:1 lewandowski:1 san:1 pasquier:2 anm:4 measure:2 spectrum:2 regime:2 compactification:1 husain:1 width:2 z0:4 analysis:3 vilenkin:1 further:1 need:1 constrained:1 give:1 any:2 gathering:1 she:1 acceleration:2 decomposing:1 issue:1 realm:1 holonomies:2 rotations:1 depending:1 latter:1 ryzhik:2 able:2 gravity:9 abrowski:3 note:9 sciences:1 potential:18 square:1 substitute:1 analogy:2 obviously:1 negligible:1 singh:4 shtanov:1 added:2 altered:1 investigations:1 probed:1 quote:1 birkh:1 most:2 involving:1 germany:1 ensure:1 gradshteyn:2 phase:5 accepting:1 ensuing:1 acknowledgements:1 class:8 imposition:1 ka:2 constructed:6 especially:1 considered:3 clear:5 clock:1 coincides:1 vertices:4 possesses:2 bohr:1 reuter:1 principle:5 exp:6 mechanical:1 corroborate:1 physics:3 notion:2 incomplete:1 12a:1 emerging:1 tolksdorf:1 show:2 german:1 labels:1 merit:1 justifies:1 obtains:5 purely:1 xl:1 xa:1 relation:2 solutions:14 subtle:1 determined:1 d2:2 find:6 chaplygin:4 ground:1 completion:1 x1:3 criterium:1 implementation:3 edited:1 basel:1 state:12 should:7 xm:5 only:20 3h:2 black:1 geodesics:1 ambiguity:1 factor:43 parabolic:1 employed:8 oct:1 impose:1 continuity:1 do:2 dm:1 above:5 notation:1 di:1 dependent:2 kamionkowski:1 de:1 overall:1 expectation:7 da:1 ϕm:1 ϕl:2 community:1 ϕn:2 dz:1 uℓ:1 kiefer:7 supplies:1 dv:1 dt:5 ds:1 differentiating:1 alexander:1 normalizable:7 evolution:13 resolve:1 continuum:7 settings:1 approach:7 arxiv:4 alteration:1 yield:1 oppenheimer:7 imposed:3 qc:4 predicted:1 contain:1 including:1 barrow:4 fixed:2 approaching:1 requirement:2 set:3 redundant:1 exists:3 achieved:1 acquired:1 carrying:2 signs:1 respect:8 emergent:1 packet:29 observed:2 edition:2 see:3 radius:5 result:6 discussions:1 terms:9 limiting:2 lna:2 quantizing:1 satisfying:1 eigenfunctions:1 ways:1 regularity:1 cosmologies:1 label:1 outside:1 smallest:2 various:1 turn:1 closed:1 between:1 neither:1 avoidance:16 conditions:10 across:2 x23:2 x22:2 basis:1 ends:2 x13:2 recently:1 ability:1 right:1 khanna:1 implementing:2 vanishing:2 l79:1 fauser:1 configuration:6 come:1 distribution:1 irnerio:1 both:11 cos:1 last:1 dunkl:1 region:10 density:5 according:2 is0:1 quantization:9 fulfilled:2 etc:1 connection:1 vℓ:1 context:4 dka:1 beyond:1 contribution:1 argue:1 expression:3 finds:7 comes:2 ansatz:9 arbitrarily:1 mechanics:2 unclear:1 fields:1 point:7 simple:4 limx:1 recollapsing:2 corresponds:5 whatever:2 coincidence:1 semiclassical:1 taylor:1 anti:3 starobinsky:1 bento:1 nent:1 wider:1 moreover:4 throughout:2 grateful:1 speak:1 sensible:1 pp:1 strong:1 described:1 persists:1 addition:2 trajectory:14 minisuperspace:3 due:6 been:13 lauscher:1 describes:1 z2:5 interest:2 basic:1 expected:2 utilizing:1 fig:7 dots:1 direction:1 arises:2 corresponding:3 observable:3 arcsin:2 mind:1 sufficient:2 wheeler:21 subspace:1 requires:1 imaginable:1 wish:1 versions:1 6v:3 demand:1 c2:4 c1:12 denote:5 present:1 case:8 k2:5 intriguing:1 exponential:2 pacs:1 defining:1 mimicked:1 value:13 will:1 technical:1 while:4 elimination:2 applies:1 situation:1 property:1 taking:3 procedure:4 enforces:1 polymer:4 cylinder:1 changed:1 gorini:2 vα2:1 vi:2 wkb:3 thus:23 them:1 rip:3 iv:3 obeying:3 φk:1 reads:3 itself:5 brake:24 vanish:9 k0:5 different:8 italy:1 since:3 maki:1 grant:1 generic:1 make:1 cross:1 same:6 complex:1 diego:1 emphasize:1 evaluate:1 avoids:1 products:1 dimensionless:1 defines:1 grows:1 higher:3 restrained:1 evolve:3 calculation:2 arrives:3 infinity:3 imply:1 thank:1 again:2 i0:2 numerical:1 upon:5 differing:2 hand:4 triangulation:1 action:5 moment:2 edges:1 uses:2 introduce:1 potentials:1 infinite:2 changing:1 kamenshchik:4 spreads:1 stack:1 normalization:5 e1:1 amplitude:2 schr:4 center:1 scenario:2 pennsylvania:1 makes:1 preceeding:1 well:10 wiggly:1 without:2 academic:1 approached:3 edge:3 solve:1 coordinate:1 equidistant:2 model:27 dimension:3 polynomial:1 left:2 λa3:1 ck:18 construct:2 cosh2:1 just:6 sentence:1 being:2 generally:1 λx:1 4a6:1 actions:3 vanishes:5 oxford:2 underlying:1 thanks:2 predicts:1 world:1 differentiation:1 momenta:1 friedrich:1 speed:1 compared:2 previous:2 adv:1 2v02:1 candidate:2 hint:1 z00:2 auser:1 cl:1 seems:3 except:1 macdonald:1 lattice:2 other:6 treatment:1 relevance:1 role:1 iσ:1 apart:2 gave:1 real:1 ambjørn:1 aspects:1 around:8 depends:1 read:1 big:42 breaks:1 implications:1 possible:1 cf:10 dark:5 vα:12 know:1 shrinking:1 elapses:1 using:9 8πg:1 sk0:10 meaning:1 separation:1 forcing:1 necessary:3 particle:1 semi:8 follows:4 reduces:1 lett:9 tsagas:1 manifest:1 specific:1 similarly:1 z0k:2 yields:6 either:2 integrals:1 fully:1 become:1 works:1 soft:2 reduced:4 beltrami:2 mathematical:1 www:1 because:6 classical:50 discrete:1 creation:1 some:13 oln:2 born:7 ku:4 choosing:2 specified:2 sen:2 soc:1 neglecting:1 matching:3 kφ:2 a10:1 3m:1 formulation:1 scale:29 describing:2 mology:1 demonstrates:1 d73:1 though:3 integration:2 stops:2 whole:1 does:9 connecting:1 provides:1 tends:3 steps:1 bessel:1 survive:1 minimal:8 densitized:1 inserting:2 obey:1 power:1 reaching:1 performed:1 sixth:1 equivalent:1 radial:1 aj:1 use:3 expansion:2 constructive:5 bojowald:7 pressure:2 viewpoints:1 although:1 x11:2 bilic:1 rus:1 post:1 refers:1 bx:1 hilbert:2 takes:2 comparison:1 kinematical:3 actual:1 carried:7 constraint:11 universe:13 theorems:2 discussed:5 dependence:1 o:5 langer:1 covariant:2 l1n:3 plus:1 obeys:1 pression:1 l1k:5 importantly:1 2k:4 consequently:2 plan:1 outlook:3 rev:16 firstly:1 presence:1 previously:1 into:6 numerically:1 bound:2 three:1 down:2 lies:3 hermitian:1 holonomy:1 einstein:3 operator:9 strasse:1 prefactors:1 geometrodynamics:1 theor:1 arrow:1 institut:1 ek:4 definiteness:1 jhep:1 support:2 there:12 question:5 approximate:8 noticed:1 strict:2 much:1 inner:3 way:7 artanh:2 decisive:1 pragmatically:1 was:12 naturally:2 function:19 hospitality:2 complete:3 form:9 unsettled:1 δkl:1 denoting:3 but:11 volume:5 anisotropic:1 construction:4 quiescent:1 bounce:4 atom:3 russian:1 line:1 removed:1 ph:1 infinitely:1 fades:1 infn:1 made:2 applying:1 cosmol:1 understood:1 whether:7 laplace:2 gravitational:3 robustness:1 up:2 ur:1 url:1 below:1 coule:1 limit:13 verification:1 cit:1 problem:2 similar:4 called:4 regimes:4 aa:2 µx:1 diverges:1 constant:7 ln:1 defined:7 packets:12 ak:4 describe:1 condition:15 thiemann:1 general:8 conserved:1 pˆ:1 rule:1 relates:1 ay:1 lifetime:2 exist:3 ing:1 internal:2 physical:6 phantom:1 friedmann:6 functions:3 nk:6 completeness:1 nm:3 no:6 whereas:2 when:9 detail:2 arctan:2 field:12 zeidler:1 valid:2 remarks:1 details:2 branch:1 massless:1 operators:1 deviation:1 picture:2 briefly:1 transferring:1 conventionally:1 calculating:1 models:14 gas:2 preceding:1 remarked:1 polynomials:1 a1:8 a0:1 a3:7 a2:1 bounded:2 a4:1 a6:8 variable:4 lemaˆıtre:2 gets:4 structure:1 implies:3 longer:1 coulomb:3 dφ:8 starting:4 age:1 martin:1 cally:1 contemp:1 together:1 original:1 implied:2 mass:2 fact:8 time:24 recognize:2 observables:2 n2:2 resolution:1 strings:2 |
0705.1689.txt |@word |
0705.1690.txt |@word precise:1 sci:1 consider:6 results:2 laura:1 proposition:9 generalize:1 gl:1 whose:2 preserves:1 c0:2 depend:3 graph:3 editors:1 finally:3 tj:6 th:1 under:5 include:2 xtj:3 norm:1 very:1 choice:7 putting:1 anα:1 difference:3 continued:25 cavalieri:2 condition:6 turns:1 notes:1 t2:1 t3:1 t1:3 involution:1 science:1 small:8 entropy:1 linearizing:1 smaller:1 periodicity:1 measurable:1 approximation:3 second:3 yoccoz:7 luzzi:3 theory:3 even:4 aim:1 what:1 iterating:2 ast:1 while:2 version:1 above:2 sup:3 equivalent:2 satisfy:1 notions:1 vall:1 respectively:1 nakada:5 here:1 behaviour:1 modular:3 objects:1 q2n:3 excess:8 xα:106 observing:2 interpret:1 obtained:5 remark:9 technical:1 study:2 allows:1 periodic:1 action:3 golden:1 diffeomorphisms:3 prefer:1 natural:1 julia:1 replace:2 sgn:4 use:1 would:2 prove:7 positive:6 kα:12 m4:2 m1:5 therefore:1 m3:2 m2:3 associated:4 more:1 fractions:7 said:2 becomes:1 diophantine:4 particular:3 known:5 cases:2 hold:1 women:1 logarithm:2 springer:1 tokyo:2 recall:3 equation:6 work:1 det:2 ρn:1 dei:2 cocycle:1 values:1 following:8 example:4 proof:11 nearest:2 compare:1 metrical:1 figure:4 expanding:1 way:1 numbers:19 want:2 indifferent:1 verlag:1 lemma:10 verify:1 s1:1 holds:6 algorithms:2 write:1 maps:6 convergents:8 optimal:3 cartier:1 map:11 de:2 irrational:15 replacing:3 max:5 after:1 stefano:1 consequence:1 fc:1 sns:2 verified:2 constants:2 keio:2 dynamical:2 third:1 whenever:2 st:2 so:9 decreasing:1 omes:1 definitions:2 order:1 ito:1 indeed:1 moussa:5 paper:1 including:1 omitting:1 japan:3 satisfies:4 its:4 dynam:1 group:3 x1n:1 how:1 matrices:1 fix:1 finiteness:2 actually:3 choose:1 lp:6 mail:4 might:1 good:2 focus:1 frontiers:1 bound:1 they:1 instead:2 rotation:1 now:2 nor:1 possess:1 easily:2 term:2 equality:1 always:1 university:2 sufficiently:2 2g:1 each:2 found:1 side:2 characterized:1 2k:1 domain:1 erisque:1 simplicity:1 ee:1 series:6 stronger:2 related:1 measure:2 our:1 special:1 really:1 factors:1 since:9 denotes:3 may:2 mα:5 rational:2 lecture:1 math:8 linear:1 dictionary:1 associate:1 divergence:2 standard:7 admits:1 indices:1 superiore:2 put:2 estimate:4 definition:6 geometry:1 plane:1 hence:1 quadratiques:1 βn:37 onto:1 first:3 origin:2 already:1 xn:38 2kα:1 probability:1 xm:21 xb:1 xf:1 primary:1 another:2 xu:2 given:3 checked:1 similarly:2 introduction:1 1x:1 relations:1 their:5 assumption:5 1l:2 denominators:1 holomorphic:1 eor:1 terminates:1 continuous:3 japanese:1 part:4 extensions:1 authors:1 x2:2 number:24 x0:14 x1:41 below:3 coefficients:3 approximations:3 iteration:1 imply:2 were:2 comput:1 generality:1 bourdon:1 say:1 seen:1 any:12 zero:1 depending:3 lim:3 note:1 generalized:5 negligible:1 btj:12 rationals:2 spectral:1 begin:1 index:1 who:1 systems:2 most:2 regular:1 an0:1 but:2 class:1 invertible:1 coincides:2 tα:7 graphs:1 ku:2 left:1 physics:1 notion:2 fact:1 2m2:1 2m3:3 show:4 3x1:1 relation:2 keywords:1 analogue:1 trivial:1 find:1 q1:26 q0:1 q2:2 ratio:1 scuola:2 dividing:1 assertion:1 than:1 analytic:4 only:5 explicitly:1 black:1 germs:1 circle:2 do:1 his:1 legendre:4 notation:1 get:6 dependent:1 there:10 fractional:1 aα:29 dx:2 consecutive:1 ds:1 secondary:1 eme:1 exhibiting:1 qt:16 arxiv:2 expansions:3 method:1 investigate:1 fixed:4 qm:1 qn:95 available:2 set:12 exists:8 respect:1 grey:1 see:13 computer:2 radius:1 result:3 close:1 qtj:3 btk:1 subject:1 satisfying:1 exponent:2 away:2 marmi:7 uα:6 pisa:2 diverge:1 enough:1 between:7 invariant:4 neither:1 conditions:3 knowing:1 extend:6 importance:1 jp:2 however:3 hitoshi:1 amer:1 both:1 prospects:1 last:1 infinitely:1 space:2 admit:2 whole:2 comes:1 point:2 brjuno:52 corresponds:1 dimensional:1 bα:21 lagrange:1 proved:2 pq:1 transformations:2 pt:1 equations:1 due:1 been:3 belongs:1 change:1 basic:2 pn:1 define:8 ergodic:1 corresponding:1 2qα:1 bmo:2 observe:3 c2:2 c1:2 denote:1 case:16 p0:1 p1:2 means:1 value:1 will:7 euclidean:1 near:1 suppose:8 2xα:1 almost:1 endowed:1 thus:3 regularity:4 itself:1 rie:1 different:1 italy:2 suggest:1 same:4 clearly:2 complex:3 split:2 dµα:2 finite:4 independent:1 investigated:1 again:1 numerical:1 upon:1 siegel:1 hand:4 infinite:2 a2j:4 a2n:3 normale:2 piazza:2 older:1 expression:1 min:4 well:1 analysis:1 without:1 hiyoshi:1 thoroughly:1 usual:1 world:1 obtain:3 integer:3 singularity:2 previous:1 adding:1 xs1:1 preprint:2 classification:1 density:4 other:3 easy:4 theorem:10 dµ0:1 guarantees:1 transformation:2 real:8 depends:1 iα:6 showing:2 possible:3 possibly:1 using:2 unique:2 loss:1 necessary:1 semi:9 follows:5 bn1:10 arbitrary:1 xsj:2 vanhove:1 mathematical:1 parity:1 2qt:1 because:3 often:1 classical:1 truncated:1 absolutely:2 sequences:1 some:13 remarking:1 growth:1 b0:27 b1:12 b2:3 moreover:6 2qn:2 happens:1 provided:3 nonempty:1 normal:1 does:6 assuming:1 uniformly:3 bn:28 expansion:13 cα:5 properties:5 publishing:1 pα:25 extension:2 commun:1 o:1 simulation:2 a2:2 ensure:1 2j:1 2x1:2 introduced:3 soc:1 functional:3 polynˆ:1 included:1 right:1 references:1 log:80 sequence:7 long:1 appl:1 fraction:18 nombres:1 call:2 opposed:1 function:21 form:1 sequel:1 gauss:3 convergence:2 line:2 true:1 divisors:2 iterates:1 liouville:1 problem:1 similar:5 called:1 ac:2 constant:13 defined:3 certain:1 abstract:1 b3:2 general:3 exist:1 yokohama:1 simulations:1 check:1 qα:93 ni:3 functions:16 no:1 q2j:4 when:13 xb0:1 setting:1 details:1 department:2 mathematics:2 out:1 conclusion:1 elements:1 completes:1 sided:1 problems:1 includes:1 a1:3 a0:6 a3:2 important:1 bounded:12 a4:1 linearization:3 function2:1 implies:7 assume:1 interval:2 equivalently:1 remarked:1 n1:3 n2:10 n3:4 |
0705.1691.txt |@word ibid:1 limited:2 monte:1 quarks:3 partial:1 angles:3 similarity:1 gupta:2 rev:11 magnetic:4 global:69 results:26 fapesp:1 although:2 roy:1 code:1 ga:1 follow:2 alt:1 mesons:1 contributions:3 reˇ:1 consider:1 increase:1 prindle:1 depend:2 system:25 aug:1 jaipur:1 shanghai:2 corrections:3 dφh:5 created:2 presents:3 charge:1 according:2 providing:1 those:5 elliptic:2 under:1 dominated:1 summarizes:1 case:6 supported:1 string:1 zhang:5 far:1 assuming:2 hughes:1 trigonometric:1 orientations:1 fom:1 span:1 moura:1 spanned:1 smd:5 level:1 sucher:1 integrating:1 laue:1 large:5 solid:3 vector:8 mλ:2 yale:1 small:5 lisa:1 nine:1 shows:2 equation:9 zdc:5 upper:4 heinz:2 kowalik:1 miller:1 consistent:4 htl:2 ritter:1 morozov:1 pawlak:1 sign:4 tokarev:1 zero:10 doe:1 may:3 chen:3 invariant:5 estimated:12 carlo:1 haag:1 linear:2 even:2 established:1 errors:6 preferences:2 chicago:2 sun:2 section:6 interactions:2 sakuma:1 zhao:1 uniform:5 b592:1 indian:1 cheng:1 new:5 falling:1 method:3 filled:12 leeuwen:1 impact:2 full:1 integrated:1 lee:1 degree:1 indicates:1 underwood:1 here:1 lednicky:1 wuhan:1 asymmetry:2 simon:1 china:7 lindenbaum:1 berkeley:3 mahapatra:1 re:2 along:5 quite:1 respect:4 change:1 bhubaneswar:1 obtained:5 daughter:5 institute:10 shift:1 study:1 larger:1 allows:1 typically:1 coffin:1 cervantes:1 suppress:1 resulting:1 procedure:2 dinh:1 harmonics:2 formation:1 ization:1 relation:1 via:5 love:1 projection:1 panjab:1 sample:1 subatech:1 neutrons:2 tio:1 gluon:2 protvino:1 frame:9 summation:1 counts:1 total:7 planck:1 predicted:3 plot:1 use:4 takes:1 would:2 levine:1 positive:5 stated:1 tends:1 france:3 few:3 nucl:21 derivation:1 hirsch:1 taken:2 indiana:4 associated:2 main:2 theoretical:1 reflects:1 more:5 hoffmann:1 mellon:1 th:4 india:7 hoffman:1 corrected:2 ψrp:22 connecticut:1 subba:1 normalized:1 vasiliev:1 known:2 qgp:2 hjort:1 iv:1 iii:1 insights:1 kumar:1 account:7 recombination:1 ma:4 bouchet:1 science:3 der:1 sahoo:1 protons:7 judd:1 pruneau:1 cai:2 nebraska:1 values:11 henry:1 following:2 arrive:1 timoshenko:1 numbers:1 beijing:1 compare:1 ach:1 wang:7 figure:5 give:1 relativistic:4 arise:1 valparaiso:2 smirnov:1 high:4 collision:3 minimum:2 performed:4 mohanty:1 occur:1 mcshane:1 absolute:1 reversal:1 information:1 united:2 decaying:2 eng:1 provide:1 clarke:1 di:2 erratum:1 hofman:1 write:2 varies:1 instrum:4 consist:1 opposite:2 kolkata:1 parameter:5 ensemble:1 stock:1 φp:3 2µh:1 proc:1 contribute:1 fu:1 snn:14 max:1 after:1 losses:5 epsrc:1 diagram:1 hence:2 argonne:2 humanic:1 physik:1 coming:2 fits:1 data:15 practical:1 unity:4 short:2 liang:3 momen:1 effective:1 austin:1 spectra:1 lines:1 blyth:1 rather:1 balewski:1 sn:17 correlation:1 taking:3 subsequently:1 fireball:1 discussion:3 bins:1 figs:2 operations:1 houston:1 ener:1 dx:1 office:1 topol:1 over:12 mainly:1 indistinguishable:1 hallman:1 thermal:4 caines:1 including:1 same:6 statistical:10 ity:2 argued:1 its:3 sizable:1 perfect:3 chemical:1 jacobs:2 group:2 thank:1 voloshin:5 la:1 energies:2 preferentially:1 christie:1 interfere:1 filip:1 zubarev:1 window:2 lu:1 fig:19 secondary:2 texas:5 dae:1 non:12 affected:4 squares:12 than:9 zagreb:2 integral:2 polarizations:2 krueger:1 baumgart:1 example:2 tsinghua:1 das:1 tance:1 eidelman:1 inelastic:2 yu:2 reconstruction:5 bhardwaj:1 february:1 netherlands:2 purdue:1 lbnl:1 university:31 presented:2 requires:1 detroit:1 sin:25 possibilities:1 hollis:1 magnitude:4 component:1 each:2 found:1 organized:1 characterized:1 betts:1 heavy:1 en:1 dong:1 chung:1 hadronic:5 kang:1 energy:4 hard:2 reduce:1 gaussian:1 used:13 manifests:1 burton:1 decays:2 ex:13 measurement:19 laboratory:6 happen:1 summary:1 eq:16 event:19 shown:6 3rd:1 assignments:1 restricted:1 rep:4 since:4 interference:1 angular:10 particles:7 collisions:38 multiply:1 ra:2 kent:2 fit:6 rea:1 correct:1 gos:1 nayak:1 foundation:1 downs:4 theory:1 lawrence:1 na49:1 quark:6 centralities:1 calder:1 california:9 york:4 van:4 estimate:4 dubna:2 beginning:1 definition:3 chose:1 hamed:1 conceivably:1 c73:1 anchez:1 recon:1 determining:1 could:6 similarly:2 so:1 times:1 caption:1 plane:38 incorporated:1 transfer:1 davis:1 yue:1 first:9 origin:1 tpcs:6 there:5 symmetry:1 variables:1 primary:6 perkins:1 dilute:2 adopted:2 bonner:1 bland:1 ons:1 open:12 kisiel:1 xu:3 city:2 given:4 smaller:2 temperature:1 strasbourg:1 los:1 introduction:1 top:2 anderson:2 least:2 gies:1 their:4 station:1 calculations:3 convention:2 show:10 kulikov:1 prague:1 dutta:1 correlations:5 imperfect:1 fraction:3 draper:1 pittsburgh:1 baryon:7 moscow:2 park:1 lamont:1 transverse:14 technique:4 assumption:1 tracking:1 b21:1 tive:1 solenoidal:1 haven:1 positively:1 e877:1 relative:7 polarized:3 unfortunately:1 sections:2 in2p3:1 surrow:1 second:2 final:2 roberts:1 c66:1 determined:5 sured:1 regions:1 tsai:1 bellwied:1 college:2 tion:1 gives:3 russia:4 bet:1 function:27 sao:2 rewrite:1 correction:4 modern:1 pri:1 dash:1 further:1 events:3 constrained:1 any:1 ray:1 angle:19 gagliardi:1 check:1 landgraf:1 lin:2 c72:1 proportional:1 mechanism:1 c76:1 polarization:75 liu:4 fitting:1 take:1 offices:1 kaplan:1 negligible:2 detector:23 primarily:1 circles:12 2n:2 cnrs:1 dunlop:1 spectator:2 centre:1 track:1 collaboration:2 rcf:1 dθp:1 most:4 seyboth:1 germany:3 but:4 significant:1 nnsfc:1 phase:2 µn:2 measured:14 appear:1 tpc:14 omaha:1 consequences:1 qual:1 calculated:2 later:1 flow:23 vertices:1 gest:1 order:12 pseudorapidity:12 points:7 ackermann:1 aip:1 conservatively:1 brookhaven:1 charged:7 physics:8 sum:3 fact:1 ftpc:1 thomas:1 axes:1 lebedev:1 phenomenon:1 exclusive:1 text:1 agreed:1 random:2 notations:3 determine:4 gorbunov:1 fine:1 indicate:5 partonic:1 near:2 feng:1 affects:2 based:5 knowledge:1 mumbai:1 much:2 reliable:1 less:5 written:1 b668:1 lansing:1 only:7 wayne:1 candidates:7 subsection:2 factor:2 admixture:2 rice:1 equilibrium:1 dn:1 do:1 gev:47 klein:1 jammu:2 dependent:1 michigan:3 de:6 overall:3 yielded:1 pions:3 beam:7 v1h:1 rest:7 words:1 αh:5 report:2 during:1 respectively:1 du:1 salur:1 takahashi:2 produced:5 evolution:2 precession:4 ks0:2 settings:1 hits:1 suarez:1 arxiv:2 nucleusnucleus:1 acknowledgments:1 garcia:1 paper:4 croatia:1 longacre:1 multiplicity:3 ohio:3 fixed:1 subatomiques:1 hadronization:1 bai:1 magneton:1 bars:1 set:1 ψep:2 committee:1 laurikainen:1 acquired:1 national:4 cuts:1 determination:2 exists:1 observed:2 see:9 csir:1 margetis:1 result:1 cyclotron:1 terms:5 techniques:1 brazil:2 shower:1 table:3 interacting:1 ωh:1 irp:1 nuclear:2 struction:1 bias:2 below:2 didenko:1 state:6 classes:1 various:1 µh:1 toledo:1 tens:1 limit:4 approach:1 wide:1 mul:1 korea:2 recently:2 parent:1 online:9 lange:1 were:7 weak:2 ld:1 jr:1 poorer:1 prediction:1 efficiency:2 wu:2 hefei:1 huang:1 contamination:2 jets:1 estienne:1 come:1 negatively:1 observable:3 cos:12 cor:1 τh:1 odyniec:1 many:1 ganti:1 decay:14 nikhef:1 called:1 sazhin:1 figures:1 dated:1 vander:1 contribution:10 col:2 experimental:3 tum:2 sci:1 detailed:1 relevant:1 cm:5 point:1 color:9 overview:1 corresponds:1 proton:3 imperfection:1 directions:1 anti:4 deflected:1 polynomial:1 cosentino:1 ogawa:1 li:3 suppressing:1 rpl:1 ct:1 ps:1 pp:2 pq:2 collider:1 hadrons:2 kinematic:1 buren:2 west:2 acceptance:24 romero:1 due:12 been:7 varma:1 c68:1 production:2 combined:1 olson:1 anisotropic:8 ph:70 crawford:1 pl:1 define:1 lanzhou:1 chandigarh:1 direction:16 lived:1 corresponding:4 reaction:21 sorensen:1 formed:1 gas:1 precision:1 potekhin:1 finds:1 equations:1 systematic:16 elastic:1 c2:2 θp:19 spin:13 present:5 barrette:1 applied:2 extracted:4 srivastava:1 novel:1 guimaraes:1 pacs:1 tang:1 snellings:1 single:1 value:8 ministry:2 will:3 while:2 lead:2 error:3 exist:1 mitchell:1 region:28 loop:2 solis:1 uncertainty:10 orientation:2 almost:1 averaging:1 borghini:1 simulations:1 thus:3 saturation:1 chattopadhyay:1 equal:1 ii:11 itself:2 io:1 westfall:1 seattle:1 technology:6 feed:6 orbital:13 ccnu:1 different:8 education:1 combination:2 conservation:2 suggest:1 reconstructed:4 cross:3 start:1 sions:2 paulo:2 poskanzer:3 strange:3 factors:1 φh:15 products:1 warsaw:2 pal:1 shao:1 higher:7 literature:1 rescattering:1 closest:1 keys:3 lapointe:1 numerical:1 effect:6 possible:6 ion:1 moment:1 harris:1 introduce:3 necessity:1 hep:5 changing:1 both:3 expand:1 nantes:1 fourier:1 center:3 scenario:3 pennsylvania:3 poland:1 depending:2 well:3 analysis:13 evolves:1 directly:2 utrecht:1 comes:1 components:1 c70:1 swiss:1 model:3 possesses:2 left:1 lauret:1 sec:1 term:1 among:1 when:3 rajasthan:1 lorentz:1 resolution:8 valuable:1 ctio:1 disfavoring:1 birmingham:2 botje:1 polish:1 scattering:1 brackets:1 note:2 becattini:1 candidate:1 upton:1 rose:1 photons:1 fatemi:1 hyperons:20 source:1 ruan:1 other:3 transformed:1 lett:6 bnl:1 role:1 east:2 plasma:1 transformation:2 momentum:43 divided:1 kingdom:2 cramer:1 around:2 government:1 showing:1 mazumdar:1 nersc:1 tribble:1 munich:1 harmonic:4 np:1 increases:1 poljak:1 gaillard:1 tracks:4 background:3 nandi:1 using:6 part:1 calculate:1 rhic:6 adams:4 g31:3 loss:1 whitten:1 schmitz:1 particle:11 follows:4 efimov:1 analyzing:1 vernet:1 specific:1 chamber:1 indication:1 either:1 martin:1 become:2 conclusion:1 ptλ:1 reduces:1 creighton:1 deconfined:1 webb:1 tending:1 right:1 czech:2 resonances:3 phenomena:1 back:1 self:1 qep:1 pπ:1 sug:1 cr:1 closer:1 kolk:1 rapidity:2 calorimeter:1 dominate:1 meson:1 sharma:1 calculating:3 stringfellow:1 realistic:2 markert:1 measurements:8 recorded:2 integration:1 chaloupka:1 contrast:1 tracker:1 pei:1 provides:1 yepes:1 yields:3 closely:1 emn:1 columbus:1 run:1 scientific:1 indicated:1 cha:1 perpendicular:1 expansion:2 dca:2 ollitrault:1 lisions:2 leptons:1 substitution:1 described:1 falls:1 jn:1 between:4 hadron:3 stage:1 sub:1 about:2 central:5 pt:8 meth:4 a0:13 pλ:29 basis:2 discussed:7 dependence:9 o:5 ndf:10 angeles:1 range:4 a2:10 aλ:4 evident:1 multistrange:2 mixed:2 subevents:1 mean:2 aggarwal:1 cambridge:1 kuznetsov:1 into:11 within:19 washington:2 coefficient:1 nsf:2 negative:1 down:2 included:1 parton:2 cormier:1 amsterdam:1 centrality:29 wada:1 a499:3 significantly:1 uncertainties:16 c55:1 statistics:2 institut:2 barca:1 comparing:2 assumed:1 support:1 szanto:1 edges:1 c58:1 shen:1 kravtsov:2 trigger:1 slovakia:1 low:1 strong:3 jinr:2 forward:10 bloomington:1 rela:1 was:12 propagator:1 assumes:1 etc:2 witt:1 azimuthal:9 form:2 effects:12 hr:1 some:1 hydrodynamic:1 direct:1 expected:3 neutral:1 eppley:1 ullrich:1 related:1 russian:1 unreliable:1 line:7 conventions:1 adler:2 hyperon:55 he:1 directed:9 lynn:1 fragmentation:1 responding:1 input:1 naming:1 conf:1 wieman:1 maximum:1 us:1 ur:1 paired:1 trainor:1 frequency:1 pusan:2 time:1 kuhn:1 horner:1 distribution:8 stages:1 similar:8 average:6 mioduszewski:1 distance:1 strongly:2 required:2 constant:7 bmbf:1 defined:12 year:1 am:1 abelev:1 denote:1 globally:1 engineering:1 au:67 research:1 our:4 lifetime:1 work:4 distributions:1 universidade:1 defines:2 yoo:1 again:1 functions:3 compared:4 no:3 zhong:1 edwards:1 percent:2 colli:1 illinois:3 field:3 pasadena:1 republic:3 details:3 normal:1 finch:1 igo:1 mass:6 midrapidity:1 particular:3 deviation:5 polar:1 star:26 zhou:1 symbol:3 zhan:1 vertex:5 bottom:2 carnegie:1 stay:1 firstorder:1 scale:3 nucleus:4 massachusetts:1 averaged:2 vectors:5 variable:1 jones:1 correlated:2 implies:2 coupling:2 pion:3 dω:6 dφ:1 ghosh:1 space:2 pseudo:1 orbit:3 them:1 observe:1 lafayette:1 nelson:1 phatak:1 recherches:1 observables:2 keane:1 frankfurt:2 dst:1 |
0705.1692.txt |@word represent:1 monte:2 concept:1 mcmahan:2 magnetic:2 global:1 results:6 dynasty:1 leads:1 entropy:1 computation:3 mattheiss:1 contributions:1 hole:1 localized:1 parcollet:1 zone:3 fellowship:1 groundstate:2 tn:1 charge:7 under:1 aligia:1 include:1 spec:1 division:1 supported:1 straightforward:1 zhang:6 far:1 frequencies:1 oxides:2 figs:1 experimentally:2 solver:1 exact:1 severely:1 leonov:2 mo:1 incoherent:1 solves:1 upi:1 list:1 solution:2 solved:1 small:1 equation:2 upper:6 employing:2 metzner:1 broader:1 periodicity:1 consistent:1 approximation:2 zero:1 further:1 qmc:2 theories:2 carlo:2 canonical:1 spectral:12 appear:1 minami:1 near:2 t2g:5 access:1 consistently:1 experiment:4 method:3 body:1 condensed:1 full:3 simultaneously:1 respectively:1 suga:1 orbitals:7 pruschke:2 magnetism:1 smearing:1 separation:1 address:1 represented:1 along:5 strong:5 equations:2 obtained:4 institute:3 study:2 studied:1 allows:1 reports:1 resulting:1 usually:2 spicer:1 studies:1 plotted:1 adjustable:3 followed:1 projection:2 scales:1 app:1 marked:2 first:2 total:1 dmft:11 standing:3 plot:2 use:2 handled:1 next:1 depicted:1 therefore:1 hirsch:1 iteratively:1 theoretical:5 today:1 more:4 separated:1 introducing:1 formally:1 initiated:1 successful:1 emission:1 excellent:2 known:1 ural:2 aligned:1 iii:3 high:1 crosses:1 integrating:1 challenge:1 work:3 ferro:1 affected:1 sekiyama:1 cond:1 example:1 compare:2 calculation:2 preserving:1 states:3 numbers:1 sharp:2 axis:1 afm:1 andersen:1 rather:2 discussion:1 chemical:1 located:3 numerous:1 field:4 constraints:1 lindberg:1 description:4 may:1 demonstrates:1 earlier:1 vollhardt:7 produce:1 physik:1 effects:1 data:6 forschungsgemeinschaft:1 attempt:1 dynamical:6 spectra:3 lines:5 deutsche:1 element:1 provide:2 complexity:1 so:1 automatically:1 enter:1 acknowledges:1 order:4 restricted:1 kollar:1 interpreted:1 symbols:1 held:2 including:2 humboldt:1 find:4 decay:1 inclusion:2 05ev:1 late:2 window:1 fig:12 insulator:5 clusters:1 gubernatis:1 non:2 good:5 combination:2 entire:1 qualitatively:1 material:2 sol:1 band:15 they:1 half:1 configurations:1 possess:1 term:1 oxygen:1 university:2 hamiltonian:6 2d:1 found:5 mean:4 el:1 en:1 weight:7 krauth:1 energy:15 difficult:1 principles:1 investigated:1 static:2 quantum:2 our:3 avoided:1 adequately:1 es:1 mat:1 shown:3 impurity:2 space:1 quality:1 since:2 rev:21 cuprate:2 research:2 jarrell:1 re:1 ren:2 orbitally:2 ref:8 integrated:1 eskes:1 foundation:4 theory:10 midpoint:1 diagonal:2 standard:1 completely:1 complicated:1 interaction:1 transition:4 insulating:1 turn:1 mesh:1 consequence:1 onto:3 copper:1 sugano:1 already:1 features:1 symmetry:5 effective:3 reciprocally:1 fujimori:2 relations:1 directly:1 electronic:6 size:1 dispersive:1 temperature:2 start:2 top:3 system:1 approximately:1 their:1 dessau:1 observations:1 calculations:1 scheme:3 williams:1 tmos:4 recognizable:1 academy:2 augsburg:3 unoccupied:1 plane:1 part:3 eyert:2 oguchi:1 marianetti:1 project:1 matter:1 determined:2 str:1 were:2 russia:2 exhibit:1 lowest:1 ubler:1 explicit:1 conventional:1 spectrum:2 substantial:1 enforces:1 wannier:5 allen:4 reflects:1 occupied:1 any:2 relatively:1 arko:1 angle:2 kozhevnikov:1 self:5 sciences:2 edge:1 initio:1 generalized:2 online:3 converged:2 green:2 subject:2 explanation:1 channel:1 sect:1 scalettar:2 normal:1 price:1 correlation:1 wells:1 singlet:1 most:1 germany:1 letter:1 phase:1 measured:1 why:1 deviations:1 hk:2 photoemission:3 satisfied:1 broadened:1 metal:5 construction:3 electrons:2 principle:1 physics:6 width:1 lying:1 insulators:1 show:4 doped:1 flat:1 visualized:1 girard:1 jepsen:2 manifold:2 trivial:1 agrees:1 based:1 parameters:4 original:1 jan:1 analytic:1 only:5 explicitly:1 uppermost:5 rice:6 local:8 do:1 ferred:1 dependent:6 dd:2 de:1 overall:1 brillouin:3 despite:2 alexander:1 reveal:1 oudovenko:1 paramagnetic:1 arxiv:1 investigate:1 contain:1 london:1 doublet:1 computed:1 lifetimes:1 correlations:5 observed:4 see:2 projections:1 uncorrelated:1 contour:4 prototypical:2 points:1 hilbert:1 nekrasov:4 opening:1 dipole:1 symmetric:1 case:3 state:4 between:8 without:1 limit:1 approach:1 across:1 effect:1 comparable:1 infinite:1 terms:1 missing:2 notion:1 weak:1 however:2 gratefully:1 vanishing:2 here:3 key:1 problem:3 suggested:1 both:5 haule:1 panels:3 many:1 asymmetry:1 connection:1 dated:1 context:1 uni:2 contribution:4 experimental:5 otherwise:1 solving:1 huang:1 point:5 simple:2 continuation:1 corresponds:1 sampling:1 grants:1 anti:1 framework:1 moreover:1 considering:1 broadening:2 puts:1 addition:2 savrasov:2 due:6 been:2 mark:1 much:1 combined:1 basic:2 expected:1 hardly:1 systems:3 ergodic:1 corresponding:2 kronig:1 bandstructure:13 quantities:1 formed:1 gap:3 kramers:1 systematic:1 general:2 spin:3 present:4 applied:2 multi:1 unlike:1 pacs:1 solid:2 terakura:1 technical:1 while:4 procedure:1 real:2 chargetransfer:1 almost:1 von:1 keller:4 thus:3 site:1 iv:1 ii:2 middle:1 mott:2 seen:1 fermion:2 orbital:4 capture:2 hubbard:9 slab:1 lindau:2 lett:7 same:1 clearly:1 avoids:1 proved:1 several:2 composition:2 development:1 independent:1 extended:1 nio:12 upon:1 mutual:1 bala:4 possible:2 moment:2 kim:1 gsp:1 lower:8 task:1 center:1 significant:1 changes:1 well:5 justified:1 materials:4 solve:1 very:2 quantitative:2 model:8 arising:1 latter:1 left:2 lda:13 routinely:1 less:1 rozenberg:1 superconductors:2 obtain:2 shape:1 formulated:1 gdd:2 zaanen:5 density:3 character:3 improvement:2 lattice:3 add:2 potential:1 georges:1 location:1 diagonalization:1 mod:2 transformation:1 sawatzky:3 hybridization:8 resolved:3 psi:1 insensitive:1 around:3 fye:1 bands:27 decomposed:1 february:1 early:2 using:3 unified:1 color:3 like:1 necessary:1 particle:2 success:1 qualitative:1 separately:1 eel:1 steps:1 either:1 valence:10 spins:1 right:3 methods:2 picture:2 czech:2 competition:1 rffi:2 finite:1 newsletter:1 pronounced:1 bottom:2 broad:1 investigations:1 sfb:1 umer:2 specific:2 does:2 decomposition:1 provides:2 capability:2 proc:1 presented:1 particular:2 who:2 bl:2 agreement:5 notably:1 anisimov:7 properties:1 panel:6 comparison:2 about:1 ferromagnetic:1 column:2 discussed:2 dependence:2 o:16 range:1 ensure:1 mixed:1 introduced:3 block:1 peak:1 soc:1 computational:2 presence:1 previously:1 into:3 within:2 bound:2 karlsson:1 rendering:1 appropriate:1 because:1 formidable:1 ole:2 additional:2 featureless:1 transfer:7 long:4 dispersion:1 shen:4 low:6 was:9 eg:9 opens:1 treat:1 function:5 underestimated:1 metcalf:1 failure:1 properly:1 trum:1 russian:2 line:2 considerable:1 coupling:1 made:2 places:1 antiferromagnetic:1 maximum:1 crystal:1 below:1 off:1 spectroscopy:2 demonstrate:1 distribution:1 matsubara:2 agree:1 batista:1 strongly:3 shih:2 ab:1 constant:1 describe:1 direction:1 proven:1 evidence:1 parmigiani:1 single:4 praha:1 moves:1 proceeds:1 constructed:1 ni:10 functions:3 ev:8 dotted:1 no:1 amounts:1 detail:2 application:2 other:1 republic:2 special:1 out:3 conclusion:1 explaining:1 stat:1 elements:2 models:2 kotliar:4 includes:1 allowing:1 included:3 structure:4 matrix:3 ago:1 correlated:4 auxiliary:1 coulomb:1 typically:1 holes:3 kuneˇs:2 arpes:6 time:1 inaccuracy:1 having:1 |
0705.1695.txt |@word squared:7 four:5 parameterization:1 consists:2 aug:1 quarkonium:5 under:1 γa:5 worth:3 rise:2 every:1 summarized:1 bringing:1 supports:1 solution:3 integrated:1 solid:3 originate:1 consistent:6 estimates:1 approximation:6 second:14 correlator:2 qualitatively:1 implemented:1 even:6 established:2 errors:11 selected:1 above:6 told:1 pictorially:1 never:1 here:10 hundreds:3 reported:2 mev:49 q10:9 represented:3 path:1 quite:4 logarithmic:2 obtained:12 study:1 approaches:3 fourier:1 appropriately:1 elaborated:1 explained:1 would:4 negative:1 m4:1 noting:3 m1:4 m0:5 m3:2 m2:15 type:5 separated:1 bakker:1 skullerud:1 md:1 mf:2 ma:4 mc:2 mb:3 fµν:1 mk:1 mu:1 mq:1 ms:2 exceptions:2 example:3 renormalization:8 give:5 relativistic:4 cited:2 involve:1 celoria:1 end:2 logunov:1 feature:1 how:1 ordinary:1 description:1 replacing:2 ladder:1 after:3 confirmed:1 diagram:1 phenomenological:3 italy:1 summarize:1 constants:1 attempt:1 effective:15 acknowledged:1 things:1 order:25 over:5 satisfies:1 before:1 fit:3 fiz:6 better:2 fig:14 schmidt:3 maximal:1 eventually:1 them:1 combination:1 lambert:1 effects:8 they:4 eigenvalue:9 gev2:2 reasonably:4 reasonable:3 each:8 series:3 valenzuela:2 principles:1 webber:1 marchesini:1 combining:1 laboratory:1 extract:4 re:2 rg:8 mπ:2 1s:5 free:3 estimate:6 chiral:1 r2:1 ds2:1 ds1:1 incorporated:1 corrections:5 already:3 smekal:1 channels:6 nonperturbative:3 sazdjian:2 rewritten:1 similarly:3 eqs:6 confirming:1 listed:1 somewhat:3 distance:1 last:3 approximations:1 tree:1 enables:1 powers:2 extracting:2 bs0:1 spectrum:13 seen:2 relatively:1 strength:1 convenient:1 latter:6 thorough:3 fitting:1 forces:1 circles:4 shall:1 optimized:1 involving:2 bsj:1 acknowledgements:1 professor:1 vertices:3 points:6 sum:5 incomplete:3 rayleigh:1 infrared:5 gauge:2 diminish:1 subtle:1 d4:3 d2:12 d3:8 d1:5 layout:1 proposed:2 specify:1 integrate:1 constant:6 dn:4 αkj:1 mixture:1 dj:4 dk:2 di:3 da:1 congruent:1 dz:12 report:1 reconstruct:1 ds:5 fields:1 λp0:1 twice:1 4πi:2 reference:1 sensitivity:1 asterisks:1 observed:1 result:3 w1:20 discussions:1 dµ:4 roberts:2 drawn:2 approach:10 triplet:3 terms:12 positron:1 restricting:1 however:13 improve:1 essentially:3 irregular:1 uncertainty:3 against:2 contribution:7 σjk:3 basis:1 three:15 been:18 much:3 basic:2 expected:5 bethke:3 quantities:1 concerning:1 confinement:12 spin:5 applied:2 exception:2 resummation:1 aip:2 remaining:1 euclidean:3 near:1 property:2 procedure:3 spacelike:3 iq:3 ir:14 iv:2 ii:3 im:1 conf:2 qj0:1 containing:1 suggest:1 dµν:3 evaluate:3 avoids:1 independent:2 numerical:6 hand:4 normalization:1 quantitative:1 possesses:3 left:1 just:1 assigned:1 identify:1 instance:1 cornell:1 easy:1 apart:1 bands:1 iγ:2 iε:1 possible:3 possibly:2 outcoming:1 occurring:1 specific:1 remind:1 sezione:1 papavassiliou:1 quarks:7 comments:1 rfbr:1 dµµ:1 properties:3 limitation:2 igaµ:1 nonvanishing:1 plus:1 considerations:1 presence:1 maxwell:3 dyson:3 bound:3 down:6 sov:1 grunberg:1 support:1 transform:1 width:4 way:5 kinematics:1 was:9 synthesis:1 form:6 attempted:1 denoting:1 encoded:1 4m2π:2 maximum:1 mth:7 dξ:1 dν:1 exist:2 dλ:2 simulations:3 physical:4 nl:1 no:2 whereas:1 generally:1 nf:4 schwinger:5 role:5 papers:1 ns:1 a15:1 a14:1 a11:1 a10:2 a13:1 a12:1 models:3 variable:1 strips:1 pion:2 assume:1 dσ:4 together:2 time:2 observables:3 focus:1 leads:3 computation:1 remarkably:1 devoted:1 depend:1 graph:2 charge:2 string:2 advantage:4 choice:8 stays:1 exact:1 presented:2 turns:5 proposals:1 solved:3 λnf:25 dip:1 work:6 occurrence:1 spectral:5 g22:1 appear:1 g21:1 foregoing:1 current:5 satisfy:2 understanding:2 along:2 appears:1 change:2 box:2 institute:1 shift:1 usually:3 adjustable:1 useful:3 problematic:1 compare:3 gluon:5 covariant:2 suppl:4 encode:2 theoretical:31 diagrams:1 sponds:1 apparent:2 validity:1 appendix:3 cases:1 originally:1 oscillator:1 modified:1 values:14 following:1 arrive:1 claim:1 figure:2 sense:2 sample:2 performed:2 unphysical:6 simulation:1 occur:1 discussion:3 s0:16 freezes:1 write:1 fourth:2 optimal:1 parameter:1 rept:1 mat:4 needs:2 applications:2 improving:1 data:20 stress:3 sectors:1 ss:10 explicit:2 so:8 representation:7 typical:2 indeed:1 thresholds:3 displayed:5 years:2 stability:2 differs:1 tendency:3 group:3 thank:1 interesting:1 constitutes:1 main:2 dosch:2 non:3 matches:1 kuzmenko:1 qs:1 introduce:1 scaling:3 half:3 bogoliubov:2 now:2 discuss:1 term:13 prosperi:9 αexp:33 domain:3 square:1 significantly:1 inhomogeneous:1 ex:1 approximated:1 eq:20 shown:2 furthermore:3 lagrangian:1 contained:2 formula:1 squares:4 correct:2 hcm:3 complicates:1 theory:10 derived:3 fisica:1 brooks:1 quark:26 complicated:1 besides:4 derivation:1 widths:1 impose:1 turn:4 massive:11 rewrites:1 βj:1 first:12 symmetry:1 kernel:4 approximate:1 horizontal:1 size:1 1p:9 given:22 checked:2 iab:2 williams:1 gives:4 continuous:2 artifact:1 x2:5 eliminated:1 x1:5 representing:1 than:13 coefficients:2 milton:1 hepph:1 third:1 φaµ:2 were:5 russia:1 argument:3 generalization:2 any:4 note:6 potential:14 take:3 timelike:1 coincide:1 hyperfine:6 algebraic:1 successive:1 remarks:1 picture:1 considered:1 average:10 feynman:2 typically:2 quantity:2 2m2:1 threshold:4 nlo:14 ground:3 ratio:1 state:16 analytic:43 only:13 explicitly:5 gev:25 between:10 freezing:5 summary:1 discussing:1 ignored:1 concert:2 relative:4 namely:2 corre:1 αs:41 review:3 definite:1 αa:1 αe:37 diamonds:3 across:2 notice:3 comm:1 jetp:1 many:1 region:14 according:10 called:4 mourad:1 σr:2 expression:15 comes:1 among:3 color:1 overview:2 exploit:3 grants:1 spans:1 curr:2 considering:1 sensible:1 combined:3 anomalously:1 arcsin:2 fortschr:1 external:2 former:3 those:2 case:8 embodying:1 irrespective:1 conformal:1 taking:1 versus:1 discrepancy:2 caprini:1 different:7 hecht:2 same:13 investigated:1 σs:1 running:21 charges:1 roughly:2 pertur:1 solve:1 model:7 justify:1 being:11 when:9 aspect:1 multiplet:1 hint:3 seems:2 param:1 lett:9 extensive:1 momentum:12 real:1 chromodynamics:1 around:1 multiplets:6 vacuum:2 world:7 moreover:1 mod:3 particle:1 reduces:1 pole:4 latters:1 serious:1 either:2 reduced:2 satisfactory:2 bakulev:1 exposed:1 respect:5 matching:3 extensively:2 mesons:2 provides:1 badalian:2 refer:8 montaldi:1 process:1 scientific:1 power:4 retains:1 equivalent:2 found:2 refers:1 hadron:1 comparison:9 oc:1 practical:4 stand:1 jν:1 ηc:2 inclusion:1 references:5 operator:7 theoretically:2 hep:22 area:4 assumed:2 there:5 dispersion:3 extremizing:1 low:11 stars:1 fish:2 assumes:1 complete:6 alekseev:2 sophisticated:1 aµ:2 adler:4 improved:1 quantitatively:1 3t2:1 obtains:1 detailed:1 ab:1 certain:3 deep:3 general:5 reliability:1 controlled:1 again:2 field:4 massless:3 deviation:1 briefly:1 vertex:1 deriving:1 a3:1 a2:2 a5:3 a4:2 a7:3 a6:3 a9:3 a8:4 conclusive:1 curve:9 mass:43 resolution:1 original:4 represent:1 consider:1 splitting:6 scalar:1 mnl:2 follow:1 expressions:5 research:1 referring:1 c5:1 th:3 dressing:1 stochastic:1 eiq:1 straightforward:1 very:5 fall:3 difference:4 hamiltonian:3 evaluation:2 t2:3 large:5 small:3 ten:1 solovtsov:5 zero:1 displays:3 further:2 linear:2 what:4 9m2:1 section:1 brief:1 version:1 fractional:1 method:12 full:1 component:2 behaviour:8 ansatz:11 situation:2 strong:10 equations:1 search:1 dokshitzer:1 allows:1 experience:1 via:3 faustov:1 annihilations:1 vii:3 analyzing:1 conventional:1 rises:1 takes:4 finally:8 comparing:1 nucl:10 qcd:29 taken:11 minor:1 more:10 flat:1 corrected:1 2w1:2 particular:5 known:1 erratum:1 recall:1 equation:26 det:1 evolved:1 f0:1 f1:1 f2:7 f3:2 f4:2 neglected:4 states:29 contradicts:1 numbers:2 arise:1 information:1 respective:1 rather:13 orbital:2 ζe:1 algebra:1 singularities:11 mapping:1 plane:1 fj:3 negligible:1 developed:2 paper:9 through:3 signs:1 y1:5 existence:2 y2:5 excitations:2 its:8 meff:2 energies:3 solving:2 boson:5 actually:2 absence:2 systems:2 might:1 good:5 motivated:1 severely:1 framework:10 yu:3 2t:1 2p:4 2s:3 level:8 infer:1 radial:1 inherent:1 universit:1 2i:1 heavy:15 mikhailov:1 hadronic:1 energy:12 extended:2 expect:2 undertake:1 quantum:5 since:8 testify:1 denotes:3 dominated:1 denoted:1 issue:3 π2j:1 inapplicable:1 brambilla:2 difficulty:1 reason:1 dubna:2 generate:1 definition:1 alkofer:1 consequence:4 hadrons:2 assign:1 fischer:3 number:3 antiquark:6 done:2 equating:1 differ:1 perturbation:10 γjk:1 introduction:1 leading:5 least:1 semiaxis:1 assumption:3 calculations:8 scheme:7 too:2 baryon:1 sizable:1 part:11 kind:1 γj0:1 annihilation:1 determined:2 contrary:1 supposed:1 treated:1 electrodynamics:1 cumbersome:1 confirms:1 wilson:6 self:2 efremov:1 k3:2 k2:11 k1:2 k0:4 useless:1 analogy:2 k4:1 eff:8 unperturbed:6 play:1 added:1 singlet:3 most:2 measured:1 exp:11 physics:1 lying:1 sector:3 particularly:3 relation:6 fine:2 find:1 causality:1 parameters:4 ebert:1 columns:1 dominant:1 shirkov:10 dependent:2 transversal:2 arxiv:23 common:2 doublet:1 bars:2 set:7 overwhelm:1 iteration:1 plausible:1 stefanis:1 see:26 sec:15 close:2 practice:1 ritz:1 various:3 eksp:1 conditions:1 recently:1 missing:1 premises:1 vanishing:3 raczka:1 both:16 prescription:5 reverse:1 context:2 pdg:1 perturbative:27 whole:3 finds:1 experimental:27 l27:1 point:10 simple:1 dimensional:7 simply:1 throughout:2 kernels:1 described:1 pt:3 due:6 strategy:1 reduction:5 4q2:2 pj:4 ph:19 pl:1 treatment:1 tg2:1 tg1:1 determination:2 p2:8 p0:12 p1:17 uncertain:1 look:1 frozen:3 reliable:2 expanded:2 evaluated:2 while:1 replaced:6 error:19 couplings:1 loop:53 galkin:1 unitary:1 von:1 confining:1 eigenfunction:2 2g2:1 twofold:1 belong:1 modification:4 higher:5 used:15 levels:2 uses:2 recent:5 lower:3 pµ:1 analysis:6 obviously:2 howe:1 using:7 tables:7 cut:6 extracted:3 relevance:1 input:3 ruled:1 excited:2 generalized:2 phenomenology:1 appendices:1 zachariasen:2 follows:4 mexp:11 yields:2 stevenson:2 mathematical:1 pertaining:2 methods:1 some:8 understood:5 b0:1 b1:3 b2:1 scale:12 eliminate:1 prog:2 proc:6 bb:1 agreement:5 bj:1 step:3 bs:26 dictated:1 pα:2 pν:1 range:2 into:10 within:12 integral:2 appropriate:6 proportional:3 reabsorbed:1 extremely:1 u0:1 specifically:4 propagator:3 considerably:1 atom:1 line:8 infn:1 characteristic:1 up:1 us:3 marginally:1 similar:6 calculated:2 associated:1 worthwhile:3 defined:11 single:3 formalism:13 fizika:1 rainbow:1 amounts:2 dashed:5 application:1 b12:2 problems:1 develops:1 graphically:1 structure:1 ago:1 independently:1 correlated:2 algorithm:1 practically:1 orbit:1 implied:1 dot:3 retardation:1 fresh:1 requires:1 having:1 once:1 partial:1 results:34 eds:2 manipulations:1 contributions:1 excludes:1 excluded:1 stable:2 include:2 g2:3 g1:3 implicitly:1 wave:2 electron:1 putting:1 matrices:2 entire:1 positions:1 try:1 noted:3 smaller:3 zh:1 iˆ0:2 dynamics:1 plays:2 3s:2 synthetically:1 consistently:3 concisely:1 body:2 analytization:2 ibid:3 exchange:4 respectively:7 separation:2 others:1 drell:1 extreme:1 technical:2 involved:7 larger:2 suggests:1 resulting:7 definitively:2 implement:1 makes:2 scales:4 app:14 apt:25 summation:1 meson:13 m2π:2 use:3 remains:1 next:4 few:7 estimated:3 bethe:6 formally:2 becomes:2 normalized:7 iii:3 account:7 crosses:1 ρn:3 reproduce:1 do:4 calculation:7 discussed:3 purposes:2 high:13 irreducible:1 spurious:4 instead:1 tension:2 singular:3 inst:4 fits:2 renormalizability:1 light:21 lines:3 s1:26 produces:2 insight:1 interpreted:3 including:1 mentioned:3 decay:1 ln:11 masses:19 derivative:1 eur:1 outlined:1 material:1 landau:1 mention:2 subtraction:1 dirac:2 simonov:2 identified:5 l0:2 crossing:3 constraints:1 homogeneous:1 related:5 static:3 our:19 out:11 matrix:1 m2u:1 rev:20 m2d:1 ref:16 m2a:2 math:7 discontinuity:2 completely:1 interaction:3 could:6 m21:1 m22:1 counterpart:1 teor:5 eters:1 hurdle:1 adopted:2 their:3 final:1 reversed:1 exactly:2 regards:1 mattingly:1 oge:5 constituent:9 limiting:1 inversely:1 reproduction:2 providing:1 w2:22 exhibit:1 curves:4 clearly:1 gravity:2 polarization:1 gφ:1 concerns:1 accuracy:2 gγ:1 preliminary:1 formalisms:1 milano:3 graphs:3 fact:2 selection:1 bring:1 rough:1 o:18 q2:98 based:2 should:7 employed:1 local:2 handle:2 means:3 syst:2 overall:1 joint:1 ones:2 qq:2 processes:3 dpt:1 differential:1 qa:7 fixed:8 view:2 requirement:1 omission:1 frame:3 cvetic:2 merits:1 p20:2 enhanced:2 exploited:1 qµ:2 extend:1 nuclear:1 written:4 correctly:1 crude:1 invariant:2 reproduced:3 tensorial:1 importance:1 wj:2 p2t:1 reproduces:5 hypothesis:1 key:2 observable:3 qft:3 salpeter:6 equal:1 chosen:3 otherwise:1 comment:1 strongly:2 adjusted:3 relevant:10 cc:1 harmonic:1 table:7 kinematic:1 addition:1 yao:1 treat:2 yad:1 define:1 corresponding:6 sufficient:1 χc1:1 χc0:1 χc2:2 c3:1 c2:1 c1:1 c7:1 c6:1 present:2 c4:1 value:27 barbashov:1 will:2 mz2:2 vi:2 refs:5 thus:5 suganuma:1 dual:1 φp:3 indistinguishable:1 φa:28 strange:5 arbuzov:1 pauli:1 finite:4 privileged:1 difficult:1 ball:2 αth:9 off:1 center:5 nonetheless:1 well:9 sets:2 position:2 arising:1 usual:7 less:1 obtain:2 sources:3 4m2:6 rapid:1 density:2 lattice:5 extends:1 match:1 devised:1 nesterenko:5 necessary:2 like:5 success:1 alternatively:1 efimov:1 become:1 works:1 replacement:1 therein:5 exceed:1 qed:2 phenomena:3 q20:9 proper:2 neglecting:2 diagonalizing:1 β0j:1 instantaneous:2 assuming:1 q2a:2 2q2:2 slight:1 expansion:4 simpler:1 a1:6 about:2 column:3 dependence:3 important:1 h2:5 h1:1 h4:3 included:3 weighted:2 additional:4 transfer:5 jinr:2 function:19 redmond:2 triangular:2 but:3 boucaud:1 construction:1 m02:3 gain:1 hc:2 made:3 below:11 limit:8 iterated:1 problem:5 display:2 int:1 recognize:1 universal:3 denote:2 χb2:2 χb0:2 χb1:2 functions:5 compared:4 variety:1 qν:2 arctan:1 other:13 details:9 theor:5 stay:2 qρ:2 qσ:2 ghost:2 coupling:75 baker:2 4s:1 rule:2 |
0705.1696.txt |@word replacing:1 represent:1 homomorphism:1 consider:18 gp:11 results:14 leads:1 obstruction:2 proposition:13 edu:1 consists:4 customary:1 chair:1 research:1 contributions:1 gr:3 compact:13 subscripted:3 depend:1 providence:2 graph:12 γq:6 technique:1 contained:1 nonlocal:1 finally:1 does:3 those:5 elliptic:9 under:3 analogous:1 include:1 norm:6 reo:3 alternating:1 ρa:4 belonging:2 supported:1 stanton:1 provides:1 orthogonal:9 very:4 choice:3 corollary:7 putting:2 formula:19 pression:1 exact:10 condition:50 dim:31 induced:1 obvious:1 riemann:2 immediately:4 presented:1 bn:6 proc:1 solution:1 herbert:1 large:1 admissible:1 vector:12 epstein:2 indices:4 noted:5 lefschetz:1 nullspace:12 estimates:18 direct:2 approximation:1 zero:6 perspective:1 follow:2 odd:4 quite:1 canonical:2 even:6 index:14 material:1 lemmas:5 appear:1 annali:1 section:34 selected:1 while:3 expressed:2 pseudoconvex:31 henceforth:1 version:1 above:14 boundary:113 replaced:3 method:1 satisfy:6 degree:5 deduces:1 respectively:4 applies:2 modify:2 equals:1 here:11 canonically:2 objects:5 groups:7 others:1 consideration:1 along:7 strong:2 observing:3 change:1 differential:2 obtained:4 remark:11 study:1 larger:1 allows:1 later:1 p2:11 vacuous:1 usually:4 fourier:1 changes:1 hbp:16 quotient:2 composed:2 via:1 useful:3 projection:8 f1:3 aps:1 convexity:1 f2:3 modifying:1 reiner:1 inverses:2 apply:4 establish:2 use:22 refers:2 projector:30 would:4 prove:9 remains:3 positive:5 agranovich:7 bundles:9 negative:1 next:3 vol:6 call:2 therefore:16 means:2 type:3 more:3 formally:2 duality:4 thus:9 operators:40 adapt:1 carrying:1 stick:1 employed:1 known:3 cases:9 hold:4 must:1 me:1 springer:1 isomorphism:7 recall:7 equation:2 work:3 actly:1 modified:5 labeled:2 values:5 containment:1 following:16 ingredient:1 my:1 example:4 proof:32 cokernels:1 dedicated:1 omit:1 give:1 process:1 beals:1 purposes:1 pieces:1 indicates:1 assumptions:1 sense:5 distributions:3 µj:2 regularization:1 end:2 lemma:19 ahler:11 rather:1 conversely:1 divided:1 acts:3 evidently:2 write:4 far:2 nontrivial:1 fourth:1 instead:4 belongs:7 map:5 product:3 express:1 intended:1 includes:2 algebra:1 may:3 earlier:2 applications:2 levi:1 produce:1 duistermaat:1 subelliptic:20 types:2 goal:1 plies:1 realized:1 ide:1 gluing:5 generalizations:1 twisting:1 explicit:1 sv:4 element:6 hypotheses:6 so:18 sn:5 gid:1 definitions:2 order:8 se:5 restriction:6 holds:11 lewy:1 indeed:1 over:2 satisfied:2 interpreted:1 equality:3 course:3 paper:5 through:2 hypersurface:4 existence:1 satisfies:14 its:1 before:3 group:3 thank:1 maps:2 appropriate:3 cle:1 fix:1 inclusion:1 conjugation:1 forms:29 parts:1 degrees:7 choose:1 relate:1 mail:1 defining:4 formulæ:7 arguments:1 prime:1 return:1 pure:1 thereby:1 greiner:1 introduce:2 isomorphic:2 often:3 they:2 focus:1 now:18 nor:2 easily:4 term:2 several:1 dirac:26 2q:6 lies:1 always:3 university:3 concave:1 identified:2 establishing:1 sufficiently:1 l2:25 each:7 entirely:1 difficult:1 side:6 2j:2 spinor:2 domain:9 square:3 directly:3 series:2 revised:1 reduce:1 related:1 equivalence:1 extended:1 ex:2 combining:2 separating:2 our:6 really:1 leave:2 shown:3 precisely:3 matrix:4 space:16 restricted:1 since:3 induces:2 denotes:10 re:19 acting:40 hill:4 rb:1 reader:3 denoted:11 dolbeault:2 ro:2 suffices:4 ri:2 math:9 shows:12 theory:4 standard:3 york:1 estimate:4 remainder:1 e0:2 definition:2 pairs:3 cycles:2 chiral:2 geometry:2 could:1 impose:1 turn:3 ish:1 iso:1 incorporated:1 consequence:5 βn:2 onto:8 first:13 omitted:1 hilbert:1 βe0:1 hans:1 calderon:2 clarity:2 tanton:1 given:16 similarly:1 introduction:2 adjoint:14 twisted:4 relations:2 their:3 assumption:1 zeros:2 constants:1 statement:1 scription:1 john:1 final:1 gives:4 holomorphic:28 commutativity:1 pseudoconcave:19 exactly:4 proving:1 immediate:1 part:5 somewhat:1 natural:3 tive:1 than:1 specify:2 λpq:1 pointers:1 imply:10 matter:2 elementary:1 classes:2 letters:1 were:3 treated:1 distinguished:2 tangential:1 sp:69 durham:1 boston:2 ann:1 argument:6 generalization:1 say:1 conjugate:6 need:15 seem:1 null:11 any:5 studying:1 self:5 able:1 note:5 instance:1 ideal:1 without:1 generalized:17 interior:1 mayer:1 calculus:4 begin:4 unless:1 though:2 measures:1 what:1 compare:1 birkh:2 metrics:1 most:1 regular:1 connected:6 pair:6 class:5 singer:1 observation:3 dom:15 considered:5 upenn:1 clear:8 sometimes:2 stronger:1 traditional:1 points:1 sorts:1 χo:1 occasion:1 left:3 notion:1 fact:8 applied:1 show:26 charles:1 contemporary:1 sup:2 notations:1 spaces:2 relation:1 decompositions:5 keywords:1 unconnected:1 analogue:4 trivial:1 indicate:2 principal:3 homology:4 trying:1 scuola:1 much:1 topological:3 jection:1 analytic:3 only:12 explicitly:2 coefficients:2 ambiguity:1 geometric:1 integrable:4 constant:7 local:2 γn:6 do:5 roe:1 establishes:1 notation:10 get:2 de:5 hid:24 closely:1 new:1 dv:2 andreotti:4 geo:1 subscript:2 closure:10 qp:3 consisting:1 arxiv:1 remove:1 acknowledgments:1 predicted:2 fixed:2 view:1 kernel:1 requirement:3 set:1 exists:1 frame:1 closures:3 relative:5 see:18 individual:4 projections:3 αq:2 fails:1 satisfying:11 αx:1 review:1 definite:1 pisa:1 state:4 αb:10 various:3 closed:10 between:2 neither:1 conditions:46 αn:21 preserve:1 terms:5 extend:3 nature:1 restricting:1 analogues:1 p3:2 comm:1 extent:2 analyzed:1 βq:2 amer:2 ker:17 suggested:1 both:3 essentially:2 0q:2 last:7 friedrichs:3 σb:17 ill:1 equal:2 vietoris:1 etc:1 connection:2 present:1 distinction:2 pde:1 expression:2 among:2 conclude:1 simple:3 cohomology:4 harmonic:3 dimensional:15 skips:1 grants:1 sequences:5 cs:10 cr:4 diff:1 cv:1 kernels:2 pp:8 pq:74 second:4 basis:1 equations:2 lempert:1 locally:1 due:1 been:2 pb:1 cauchy:2 treat:2 interest:1 basic:11 algebras:1 pn:14 exactness:8 partial:2 define:18 surjective:2 describe:1 easy:2 θb:2 baum:1 degenerates:1 subspace:3 observe:2 representative:6 univ:1 general:4 spin:3 manifolds:7 case:21 grassmanian:1 p0:17 p1:23 might:1 value:15 employ:1 near:2 suppose:19 many:1 property:1 identical:1 layer:3 almost:3 characteristics:2 metric:12 kohn:4 ii:2 cocycle:1 im:37 dual:13 vanish:3 id:59 result:3 different:2 qpq:2 perhaps:1 things:3 make:1 belong:3 atiyah:1 same:7 clearly:2 princeton:4 complex:27 split:3 established:1 modification:3 proved:5 finite:9 higher:2 used:5 folland:1 dimh:1 effect:1 hand:7 domains:6 uses:2 purpose:1 infinite:9 interested:1 identity:3 subspaces:2 eigenvectors:1 normale:1 annals:3 largely:2 pennsylvania:1 studies:2 variety:1 well:11 analysis:4 contact:2 components:2 lim:1 jean:1 dimension:2 usual:3 λp:68 manifold:37 vent:1 when:6 resp:2 obtain:14 detail:1 λb:8 underlying:1 identify:7 λe:3 integer:1 facts:3 shorthand:1 λo:3 λn:3 previous:3 adding:1 intersection:1 preprint:1 sciences:1 auser:2 point:1 seems:1 except:1 e0p:14 bp1:1 other:9 parents:1 versa:2 theorem:24 mod:1 euler:8 take:1 real:1 stein:3 isomorphisms:4 morphic:1 sums:1 possible:1 background:1 vacuum:1 press:3 using:12 unique:2 moreover:1 formal:6 modifications:2 necessary:5 like:4 follows:19 bavnbek:1 spinc:17 separately:2 remind:1 imposes:1 either:2 invariants:1 pointwise:1 grouping:1 mathematical:2 heisenberg:8 because:6 neumann:28 classical:23 sequence:10 sympos:1 some:6 play:1 ify:1 regularized:2 deduce:6 repeat:1 e00:1 specified:4 proofs:3 absent:2 provided:7 dimensions:1 res:1 opposite:1 hodge:13 injects:1 injectivity:2 prop:1 everything:1 continue:1 decomposition:4 expressing:2 assuming:1 adjoints:4 equivalent:1 pose:1 βb:3 patodi:1 bp:1 bs:1 assemble:1 francis:1 bx:67 2n:1 injective:4 proceed:1 chapter:1 about:2 works:1 carried:1 extension:14 extending:2 oe:5 introduces:1 dependence:2 o:46 compatible:2 range:7 extensions:1 fredholm:14 act:1 introduced:4 slightly:1 projectors:16 block:2 hence:13 converging:2 considerations:1 soc:2 distributional:2 statements:3 ηb:5 parity:2 h2:8 unbounded:2 into:8 h1:8 integral:1 eo:27 nsf:1 carey:1 remarks:1 hermitian:4 references:1 operator:66 rossi:2 methods:1 descriptions:1 spinors:5 additional:1 completing:1 strictly:38 there:28 question:2 long:4 quadratic:2 inner:3 resolvent:1 sections:41 m0:2 function:2 complete:4 form:42 szeg:32 hr:85 hs:8 hp:3 converse:1 but:6 volume:1 failure:1 heat:2 link:1 hb:1 removed:1 true:5 partially:1 inverse:1 applying:3 embedded:1 versions:1 whether:1 characteristic:6 h0p:1 smooth:29 up:1 us:1 frechet:1 below:2 represents:2 sum:3 problem:12 similar:5 called:2 expect:1 bearing:1 taylor:3 associated:4 defined:53 coincides:3 abstract:1 pseudodifferential:8 denote:30 ind:49 laszlo:1 identities:10 defines:9 nh:1 again:7 functions:5 no:9 fixing:1 generally:2 vanishes:9 field:4 finish:2 setting:2 role:1 properties:1 papers:1 department:1 mathematics:3 orthocomplement:1 elements:2 star:6 completes:1 symbol:3 problems:15 bundle:13 helpful:1 replace:1 important:3 suited:1 ξb:5 needed:3 structure:12 implies:12 partitioned:3 vice:2 assume:1 requires:1 dvg:1 pseudo:1 together:4 tandem:1 time:1 starting:1 having:1 once:2 |
0705.1697.txt |@word limited:1 abundances:2 consider:1 gq:2 rev:34 excellent:1 results:10 four:36 scalar:1 gd:2 per:2 edu:2 obtaining:1 expressions:1 m2s:3 contributions:2 lk:1 particles:11 inverse:2 depend:1 calculate:1 re:1 shanghai:3 shall:2 deng:1 finally:2 program:3 present:5 th:8 under:5 tf:3 include:1 tc:8 case:4 kπ:5 amplitudes:5 expressing:1 orthogonal:1 very:1 m2k:5 mg:1 wave:9 bjorken:4 denoted:1 sensitivity:1 affect:1 ln:2 difference:3 rapidities:1 treating:1 leads:3 cmk:1 exponential:1 presented:1 rh:1 t2:2 b541:1 laue:1 large:5 vector:7 m2b:1 sjtu:1 small:9 zhu:2 nos:1 evai:5 degeneracy:1 prevent:1 α2b:1 mn:3 ten:1 jacobians:1 matheus:1 meansquare:1 consistent:1 prediction:1 cosh:1 approximation:2 rate:3 bracco:3 evaluated:7 reinders:1 equal:2 chen:5 further:1 dynamics:4 estimated:1 carlo:2 yang:1 what:1 giving:3 gk:2 sum:14 rum:1 near:3 expressed:2 d3:11 bass:1 experiment:2 poles:1 goes:2 3c:1 mq:15 3a:1 rd:4 boost:1 method:2 filled:1 outgoing:1 full:1 lee:2 ibid:7 whose:1 respectively:17 presence:1 equals:1 here:1 understanding:1 lu:1 mev:14 china:4 consideration:2 along:1 standard:2 z0:2 change:4 obtained:15 instituto:1 incoming:1 weinstein:1 institute:2 study:7 larger:11 resulting:1 wl:1 resonance:1 narrow:2 changes:1 m3b:1 m3a:1 eichten:1 via:10 useful:1 br:1 gluons:3 extrapolations:1 kinematically:1 quarkgluon:3 extracting:1 j5µ:4 f2:1 p3:6 vc:5 gluon:33 karsch:1 org:1 welch:1 resolutions:1 meson:114 linearly:2 d73:1 use:14 takes:3 would:1 remains:3 nine:2 charge:3 next:1 m5:1 few:3 nucl:10 m6:1 m1:2 m3:1 qcd:15 taken:9 survive:1 means:1 dσµ:1 type:2 theoretical:2 diagrams:3 more:2 almost:1 rapp:3 elliptic:1 fourquark:3 thus:8 virtualities:1 mismatch:2 grandchamp:1 γc:4 appendix:7 normalized:1 monte:2 known:1 srf:1 iii:2 abundance:14 md:4 account:9 ma:1 ρd:5 mc:43 mb:6 ρi:2 science:1 equation:4 averaged:9 oscillator:6 modified:2 mk:3 mu:1 mt:3 values:7 ms:40 widths:1 following:12 drops:1 root:3 f1:1 compare:1 wang:4 indicated:1 give:1 process:1 expanding:3 umin:2 organized:1 respective:1 states:7 collision:4 lorentz:1 chin:1 numbers:12 allowed:1 made:2 calculated:1 dk:39 krokovny:1 information:3 needs:1 end:4 goal:1 rather:1 s2:2 s1:1 kτ:2 range:1 chemical:9 molnar:1 varies:1 pair:1 smilga:1 doublet:3 b5:1 instead:3 parameter:7 dominance:1 rapidity:6 fq:5 product:5 express:1 description:2 may:1 max:1 after:1 different:2 reflect:1 fa:2 independent:1 plane:2 fd:10 fe:1 waves:1 hayashigaki:1 fi:4 fk:6 data:1 fm:16 constants:4 short:1 natural:1 dσi:2 ss:1 light:2 sq:1 spectra:1 lines:2 summing:1 parameterized:1 element:4 sj:39 accelerated:1 extrapolation:1 b7:1 sn:4 torrieri:1 correlation:2 definitions:2 silva:1 order:10 eµs:1 isospins:2 s0:5 wigner:9 ature:1 nucleon:5 beveren:1 over:3 vary:1 produced:32 thermal:4 paper:3 through:5 statistical:9 hypersurface:2 y1:1 converting:2 kinetic:7 y2:4 excitations:1 its:31 write:2 ld:1 lb:1 symmetry:1 τh:6 decay:6 chosen:1 matrices:1 masses:2 solving:1 τc:7 decreases:3 qgp:1 destroyed:1 window:1 production:26 degrees:1 fig:20 van:1 texas:2 eur:1 yi:5 non:1 good:2 pauli:1 combination:1 numerically:2 b232:1 yazaki:1 introduce:1 adams:1 heinz:2 effects:4 they:5 front:1 now:1 discuss:1 2s2:1 above:14 2u:1 term:1 b11:3 gev2:7 gev3:1 tral:1 university:2 level:2 rocs:1 magnitude:3 reasonable:3 radial:2 found:4 decreasing:1 side:4 mean:5 heavy:25 reactions:11 square:4 ei:4 significantly:3 simplicity:1 hadronic:34 ed:1 energy:9 hard:2 ea:1 related:4 eb:1 operator:3 decays:3 isospin:13 expect:1 combining:1 our:3 approximated:1 beyond:1 eq:21 out:6 shown:17 kokoski:1 matrix:3 factors:7 although:3 rep:1 since:9 squared:5 2m2c:1 denotes:3 increase:1 collisions:35 rodrigues:1 dsj:148 rc:2 m2d:10 formula:1 get:3 squares:2 ref:12 m2a:1 2m2s:2 m2c:17 foundation:2 3u:2 i2:1 linear:1 interactions:1 m2:4 discontinuity:1 ısica:1 m4:2 possibility:4 quark:137 ex:1 threedimensional:1 formation:1 mi:3 antiquark:1 igd:1 bigger:1 godfrey:2 diagram:1 unique:1 interaction:3 derivation:1 created:1 starts:1 transition:2 fb:2 diquark:2 times:1 phenix:4 massive:1 transfer:1 hadrons:11 neglect:1 first:4 exotic:2 b8:1 xi:4 xn:1 probability:4 variables:2 number:39 transform:2 channels:1 smaller:2 nonperturbative:1 representations:1 carry:1 shifman:1 size:2 equating:2 given:20 temperature:11 πd:10 their:7 introduction:1 twenty:1 eqs:1 system:2 approximately:2 needed:3 station:1 calculations:4 schnedermann:1 show:4 final:18 eip:2 gives:4 parameterizations:1 shell:10 way:2 ratio:7 baryon:4 braun:1 transverse:17 assumption:1 ncn:3 x2:6 constituent:2 45c:1 than:15 coefficients:2 relative:15 ahmed:1 hyperbolic:2 65c:1 anyi:3 was:4 approximations:1 largely:1 tree:2 likely:2 correlators:2 annihilation:2 matter:17 determined:7 contrary:2 amplitude:2 were:1 radius:5 tion:1 providing:1 powers:1 factorable:1 lowest:1 sp:1 unchanged:2 correlator:2 spectrum:1 lin:7 dash:1 discussions:1 su:1 b489:1 seen:4 st:1 isgur:2 any:1 viewed:1 hydrodynamic:1 acceleration:1 wilson:3 forthcoming:1 2st:1 depending:3 studying:7 latter:5 mid:1 mechanism:5 note:3 extracted:2 fitting:1 potential:7 absorbed:1 take:7 ope:1 online:3 finding:1 b10:1 channel:4 s27:1 circles:2 closer:1 differences:1 2su:1 normal:3 collaboration:10 denominator:1 molecule:1 mains:1 2tu:1 most:1 boltzmann:1 involving:3 charm:14 rho:5 phase:12 baryons:5 analytically:1 measured:4 thermally:8 surprising:1 kd:22 considered:2 ki:7 flow:9 vertices:4 reaction:10 electrons:1 principle:1 exp:5 subsequent:3 velocity:6 left:1 physics:3 section:12 fact:1 quantity:1 q2:23 somewhat:1 τf:2 violation:1 supported:2 longitudinal:3 cnpq:1 ioffe:1 relation:5 artificial:1 x3:2 threshold:3 d4:4 uniform:1 find:5 partonic:2 x1:7 based:8 parameters:3 distributed:1 written:1 only:7 explicitly:2 x4:1 factor:21 employed:1 thresholds:3 achieve:1 equilibrium:6 ip:1 do:2 2mq:3 dominant:1 gev:27 distance:2 dependent:2 there:1 de:2 lhc:1 da:1 pions:5 2mc:3 unimportant:1 ones:1 dz:1 3b:1 during:12 du:2 ds:13 jaffe:1 qq:2 stability:1 evolution:14 increasing:1 densities:2 fields:2 coalescence:24 arxiv:2 yield:8 summary:2 bag:1 experiments:2 li:5 predicted:5 double:3 analytical:2 including:4 peak:2 fixed:2 hadronization:6 fugacity:2 2p3:1 2p2:2 2p4:1 undergoes:1 violated:2 cuts:1 lett:22 freeze:5 observed:4 differs:1 depends:6 college:1 result:6 holding:1 cyclotron:1 terms:6 sem:1 endothermic:1 momenta:8 brazil:1 pµ:2 still:1 interacting:2 consistency:1 nuclear:1 frye:1 µq:3 navarra:5 µs:5 αa:4 state:17 αb:4 µi:1 αd:1 between:5 tens:2 invariant:6 babar:2 approach:7 µb:3 comparable:3 triplet:2 recently:1 statistically:2 initially:1 comp:2 yi2:1 p2i:1 however:4 huang:1 jd:6 kev:3 suppressed:1 valid:1 thank:1 suggested:1 both:8 σi:2 σh:1 last:1 fit:6 σc:2 many:1 taking:3 according:3 sensitive:2 contribution:3 boltzmannian:1 expression:3 scope:1 experimental:2 otherwise:1 detailed:1 ch:1 cn:1 tong:1 nonrelativistic:1 color:7 lagrangians:1 2i2:1 corresponds:2 proton:1 2i1:1 dimensional:2 offshell:1 simply:4 coordinates:7 σab:3 cs:3 associated:1 writing:1 pseudoscalar:2 considering:1 ensures:1 described:4 transformations:2 pt:3 basis:2 pz:1 pierro:1 due:4 been:10 rupp:1 pb:5 reduction:1 much:4 pf:2 agreements:1 interest:1 expected:2 ph:3 pi:10 pn:1 ann:1 choose:1 6a:1 direction:3 relations:1 corresponding:2 kaon:9 fire:9 suppress:1 formed:1 magestro:1 essentially:2 gao:1 offers:1 determination:2 c2:2 mandelstam:1 rubinstein:1 spin:6 former:1 those:10 σn:1 p2:19 k2:7 p0:1 p1:9 uncertain:1 p4:8 pacs:1 solid:3 empirical:1 value:14 will:2 schat:1 while:5 greco:3 evaluating:3 b634:1 di:1 balance:1 region:1 procedure:1 interpolating:1 cylinder:9 studied:6 a4:1 coupled:2 phenomenological:4 vi:2 refs:2 tions:1 them:2 redlich:1 iv:2 ii:2 phen:1 umax:2 rafelski:1 zhang:7 csizmadia:1 increased:2 cleo:1 binary:1 confirmed:1 grant:4 perform:1 belle:2 cross:24 same:9 check:1 paulo:2 strange:4 schematic:2 cen:1 units:2 finite:1 pal:2 composition:1 higher:4 evolve:1 calculation:3 used:9 see:1 ni:1 i1:1 i0:2 numerical:1 uncertainties:1 effect:4 flows:1 hand:1 ion:25 phy:1 appreciable:2 kim:1 potentials:2 vainshtein:1 qcdsr:1 expand:2 weakly:1 off:13 center:4 scenario:1 penta:1 hwang:1 ncet:1 modeled:1 well:8 except:2 coal:3 b147:1 involves:1 na:1 coordinate:6 model:41 nnsf:1 dimension:1 usual:3 nonrelativistically:1 less:3 being:2 nd:9 accurate:1 obtain:8 aside:1 cutkosky:1 uller:1 flavor:3 scattering:1 previous:1 k3:1 cut:3 candidate:1 liu:5 zakharov:1 absorption:17 wei:1 point:4 k1:3 2s1:1 interested:1 moe:1 requiring:1 stable:1 unitarity:1 plasma:33 terasaki:1 momentum:19 b13:1 evaluation:1 nielsen:8 αc:1 rules:9 evaluate:5 jacobian:1 possible:3 harmonic:2 qγ5:1 matters:2 increases:2 know:1 swanson:1 using:20 cd:4 bir:2 rhic:11 helpful:1 ns:5 imposed:1 like:1 particle:1 sizes:1 follows:1 reduces:1 performing:1 agreement:1 cooper:1 yields:2 either:3 integrals:1 anti:15 nucleons:3 vdm:1 reasonably:1 spins:2 empirically:1 parity:1 right:1 zim:3 predictions:1 polar:1 affects:2 successfully:1 b4:1 σi2:2 b6:1 growth:1 b1:3 b2:3 b3:1 proper:7 star:5 extended:2 neglecting:3 b9:1 transport:3 nonzero:1 total:10 describing:1 lead:2 resonances:5 avoid:1 quarks:30 fapesp:1 overlap:1 mesons:47 critical:2 unit:2 provides:3 assuming:3 borel:6 bessel:2 b15:3 parametrization:1 averaging:1 2µi:2 bc:1 uniformly:1 each:1 conventional:2 expansion:6 pressure:1 ratios:2 2m:1 collider:1 stage:4 deriving:1 about:20 seibert:1 central:9 munzinger:1 oh:2 freedom:1 discussed:1 dependence:4 o:3 reduced:4 covariant:1 antiproton:1 a2:1 nj:1 mixed:6 nds:1 αi:1 slightly:2 sensitively:2 kaons:10 cutoff:1 strangeness:4 jiao:1 previously:1 into:12 integral:6 bound:1 three:10 neutrality:1 appropriate:1 because:2 rising:1 mikami:1 determine:1 balanced:1 proportional:1 binding:1 fixing:2 theoretically:1 aubert:1 relativistic:12 wan:2 fast:1 hep:3 fm3:1 vab:3 assumed:2 adare:1 initial:18 approximate:2 specifically:3 u2:1 dispersion:2 width:10 pa:5 low:1 fraction:2 series:1 sections:18 tamu:2 function:24 project:1 form:18 reduce:1 usp:1 denoting:3 but:7 volume:3 anisotropic:1 neutral:1 atom:1 convergence:1 line:5 adler:1 charmed:7 2m2q:1 compute:1 improved:1 born:3 whether:4 fries:1 k2i:1 us:1 until:1 work:2 below:3 frequency:4 dmt:1 y3:1 distribution:15 monopole:1 similar:8 temper:1 continuum:4 strongly:2 ab:1 constant:7 inclusive:1 defined:2 ko:19 universal:1 describe:1 influence:1 6b:1 ao:2 denote:2 aq:1 dashed:3 conserved:1 au:17 dπ:5 lifetime:1 ing:1 distributions:2 universidade:1 condensates:2 again:2 functions:11 compared:1 dotted:2 no:3 vh:3 nc:11 when:5 ne:1 perturbative:1 acknowledgments:1 b14:1 other:5 b12:1 details:1 u0:5 spatial:2 department:1 midrapidity:3 igk:1 nu:3 nonaka:1 picture:1 stat:3 elements:1 snn:2 calculating:1 models:3 exothermic:1 stachel:1 vertex:6 hwa:1 a1:1 a3:3 important:1 a5:1 pythia:2 included:1 proceeding:1 structure:10 national:1 coupling:10 pion:4 dω:1 assume:2 requires:3 dτ:3 space:7 curve:1 dσ:2 rule:7 m2t:1 mass:13 time:23 understand:2 5gev:1 dover:1 expands:1 4c:1 |
0705.1698.txt |@word homomorphism:1 consider:11 chain:1 hi1:2 datum:13 results:1 andre:1 ginzburg:2 proposition:8 minors:2 gk:2 gr:22 whose:3 preserves:3 cardinality:1 clarification:1 aug:1 fellowship:2 equivalence:4 tr:1 young:1 recurrence:7 finally:5 electron:1 tk:2 under:6 analogous:1 applied:1 conjecture:5 zelevinsky:1 g3:3 g2:7 g1:9 very:2 dokl:2 corollary:2 every:1 interpreting:1 difference:5 matrices:1 condition:7 dim:1 mw0:1 immediately:1 presented:1 wsi:4 irreducible:2 joel:6 wsj:1 hive:16 vector:10 recall:2 relation:3 equation:2 degeneracy:1 application:2 zn:2 literature:1 horn:1 speyer:4 second:4 fibres:11 wijk:6 even:1 aim:1 intersection:1 filtration:2 appear:2 nei:2 sum:3 current:1 version:1 above:9 obvious:1 increasing:2 coefficient:1 supporting:1 λij:1 mem:1 applies:1 component:9 equals:7 here:4 strata:1 desired:3 objects:3 groups:2 berkeley:3 ucker:6 along:3 appears:2 change:2 obtained:1 gln:20 involved:1 inspired:1 studied:2 rhombus:7 resulting:2 loop:1 suggestion:1 pick:1 action:2 hospitality:1 uller:1 involves:1 quotient:1 being:1 via:2 useful:1 convolution:12 apply:3 unit:2 use:5 takes:1 would:6 prove:3 positive:4 contains:1 ej:3 next:1 call:1 injective:1 reductive:2 associated:1 vilonen:4 more:3 duality:2 clearly:1 vl:3 local:1 kn:5 labelled:3 particular:7 known:3 aligned:1 iii:2 word:2 gh:2 klm:2 setup:1 work:3 det:1 mw:6 mv:32 values:8 mδ:5 following:10 example:2 proof:13 f0:5 compare:1 curves:1 give:4 purposes:1 minimum:1 arise:1 dominant:2 tao:3 νi:3 νk:6 information:1 νn:5 goal:1 describes:1 discussion:1 acts:4 write:3 kapovich:3 fourth:2 instead:1 bit:3 polytopes:8 map:11 product:11 description:2 fv:6 algebra:1 may:6 singularities:1 orbits:4 collection:6 consequence:1 plane:1 ξijk:5 fg:3 date:1 fi:30 data:2 fn:3 times:1 short:1 third:4 sw:5 correspond:1 element:9 generic:11 si:1 so:14 sn:1 fundamental:3 decreasing:1 representation:9 unipotent:1 order:2 satake:3 restriction:2 gaitsgory:2 holds:4 words:1 ith:1 duke:3 developed:2 over:5 ξi1:2 postnikov:2 interpreted:1 course:1 paper:4 dw:2 mentioned:1 existence:1 satisfies:9 its:7 roots:1 before:3 horizontally:1 group:8 thank:3 chosen:1 interesting:3 sheaf:2 affine:7 lk:4 coordinates:1 actually:2 lt:1 continue:1 choose:2 mail:1 main:7 sheaves:2 semisimple:1 correspondence:3 constructible:5 greater:1 conversations:2 introduce:1 geodesic:2 mention:3 they:2 now:14 eigenvalue:1 february:1 name:1 goncharov:2 invariants:1 level:1 identified:2 inequality:5 l2:16 l3:5 l0:15 l1:18 higher:1 side:3 subset:1 domain:1 grν:1 ei:4 weight:4 independent:1 series:3 idea:1 related:4 sj:1 millson:2 combining:2 our:10 special:3 out:3 category:3 ihes:1 shown:3 part:1 space:2 since:9 denotes:3 looking:2 combinatorial:5 mα:4 mγ:9 math:21 shows:4 reformulation:1 theory:5 ast:1 hull:1 diagonal:4 mikhail:1 applications:1 base:2 put:1 org:1 publ:1 combin:1 xg1:1 definition:2 backwards:1 ggms:5 v1:5 rule:1 david:1 kamnitzer:9 produce:1 due:4 tempting:1 hence:21 imrn:1 think:1 first:13 xi:2 bijection:12 radical:1 number:8 tableaux:1 sssr:1 restrict:1 multiplication:3 construct:1 another:1 representations:4 ring:1 precisely:1 open:1 fijk:1 size:3 vλi:7 vλj:1 vλk:2 similarly:2 introduction:2 top:2 twisted:1 relations:5 their:3 constants:1 statement:3 bijections:2 scheme:1 gives:6 haines:3 tool:1 akad:1 dylan:1 translation:1 copy:1 than:1 clarifying:1 showed:1 cyclic:1 ktw:6 stratified:1 were:1 arun:1 vλ1:2 vλ2:1 similar:3 coweights:3 conjectural:2 strengthen:1 explicit:1 ann:1 ram:1 argument:2 generalization:3 descends:1 buildings:1 say:5 manner:2 need:1 allen:1 any:12 lie:1 mirkovi:4 min:6 studying:1 ideas:1 note:8 k2:3 k1:10 take:2 lhs:1 mit:1 realizes:1 calculus:1 formulas:1 begin:2 differences:3 unless:1 allow:1 though:3 rhs:1 object:1 systems:1 algebraic:2 involving:3 connected:1 successive:2 remarks:1 acknowledgements:1 class:2 inequalities:11 tν:11 laurent:1 tλ:2 consequences:1 considered:2 vertices:3 points:4 usual:1 section:4 fact:3 saying:1 show:2 rings:2 supported:1 multiplicities:5 postdoctoral:1 careful:1 enjoyed:1 fibre:2 explain:1 written:1 should:1 lemma:10 only:3 berenstein:1 achieve:1 his:1 triangle:2 notation:3 get:3 joint:1 grµ:6 longest:1 closely:1 dv:9 during:1 reprove:1 boundary:13 alexander:2 closure:2 henriques:3 arxiv:2 grλ:12 qa:1 nauk:1 schemes:1 cycles:14 inside:1 combinatorially:1 view:1 satisfy:1 moduli:1 set:20 exists:1 closures:4 trick:1 see:19 individual:2 result:12 w0:4 recently:1 analog:1 satisfying:1 tensor:9 crystal:1 pattern:2 µw:3 convex:2 symmetric:3 enough:1 µi:3 between:6 µe:1 invariant:7 geometric:5 reading:1 conditions:3 across:2 terms:1 hecke:1 vertical:1 wn:1 inclusions:1 hypothesis:1 subgroup:3 distinguish:1 suggested:1 both:3 fock:1 polytope:10 many:1 taking:1 parts:1 nserc:1 personal:2 admit:1 lusztig:4 faces:2 expression:2 fix:3 comes:2 relevant:1 co:2 cn:1 point:1 simple:2 character:1 ca:1 address:1 corresponds:3 dimensional:3 simply:1 sequences:1 moreover:5 hijk:7 commutative:1 basis:2 associativity:1 skew:1 three:1 been:2 tropical:8 extraction:1 much:1 empty:2 define:11 determinant:2 referee:1 corresponding:4 eigenvector:2 0s:1 given:2 puiseux:1 stratum:3 vinnikov:1 vµ:3 last:1 denote:9 kashiwara:2 present:1 case:13 look:2 subsets:3 knutson:5 defining:1 means:1 tetrahedron:1 appearance:1 value:15 will:17 while:1 dense:1 suppose:2 coweight:13 aij:2 situation:2 study:2 procedure:1 wki:1 tµ:2 conv:10 gel:1 vk:2 thus:1 non:4 ii:3 characterize:1 ik:8 experts:1 cone:1 dual:3 turns:2 ic:2 spaces:2 different:2 author:3 lengths:2 same:3 check:3 complex:2 involutions:1 finite:2 composition:2 evidence:1 difficult:1 fairly:1 used:1 i1:3 hand:2 subvariety:2 octahedron:8 moment:1 edges:1 purpose:1 infinite:2 identity:2 cycle:7 relies:1 lower:2 weakly:1 records:1 no:10 well:7 edge:6 components:25 sets:1 position:1 model:1 soviet:1 dimension:8 left:4 fand:1 gelfand:2 just:1 less:1 monomial:1 woodward:3 thanks:1 using:5 λk:14 λj:4 λi:28 λo:2 λn:6 previous:2 adv:2 adding:1 unique:1 vχ:1 seems:1 except:2 improvement:1 lattice:1 erisque:1 braverman:2 easy:2 theorem:16 generalized:1 thurston:1 read:1 replaced:1 possible:1 vα:2 vβ:2 vγ:6 know:2 background:1 integer:3 variants:1 vλ:4 vν:1 helpful:1 like:3 semi:2 follows:2 specific:1 chamber:2 langlands:4 either:1 alternatively:1 reduced:2 copies:1 right:4 classical:1 sequence:2 some:6 b1:4 respect:3 proper:1 ams:1 perverse:2 lead:1 nonpositive:1 extensively:1 prop:1 everything:1 does:2 linearly:1 plucker:1 straightforward:1 refer:1 bg:2 hold:1 power:1 retains:1 equivalent:4 each:10 rhombi:2 br:3 bruhat:2 rt:3 bz:13 integers:3 about:1 extension:1 constraint:1 theorems:2 o:26 convenient:1 carries:1 comp:2 observation:1 morphism:12 considerations:1 communication:2 boundaries:1 stratification:1 isomorphic:1 locus:1 down:1 pair:1 weyl:1 references:1 val:16 there:5 long:1 why:1 anderson:4 borel:1 way:3 labelling:1 forward:1 analyze:1 was:3 function:20 elsewhere:1 form:4 regard:1 triangular:1 but:4 hk:3 construction:3 grassmannian:6 teichm:1 russian:1 highest:2 valuation:5 tsetlin:3 mλi:1 tropicalization:1 count:2 inverse:1 coset:2 surprising:1 proceeds:1 multiplicity:3 cells:2 us:3 record:2 represents:1 pl:6 problem:3 subrepresentation:2 called:6 uc:2 mλµ:3 constant:5 ad:1 ag:7 defined:7 certain:1 abstract:1 describe:2 general:6 littlewood:1 hoc:1 ar:3 departments:1 gons:4 ind:1 crystals:3 dγ:6 triangles:4 functions:7 nk:2 variety:11 aji:2 when:2 graduate:1 field:2 other:4 leeb:2 es:3 tits:2 gra:2 department:1 mathematics:2 er:3 grk:2 nw:3 sijk:2 draw:1 elements:2 vertex:2 a1:6 a0:2 describing:1 structure:3 inspiration:1 building:2 implies:1 gr3:3 assume:3 modules:1 orbit:1 together:1 vλµ:2 weights:1 push:1 richardson:1 having:1 |
0705.1699.txt |@word homomorphism:2 consists:1 wj2:3 localized:3 relationships:1 whose:1 under:3 stanton:4 every:2 formula:15 affect:1 encounter:2 differentiated:1 prize:1 solution:17 vector:19 enclosing:2 indices:3 nullspace:2 estimates:20 direct:1 second:7 tangential:2 seeley:4 even:30 established:2 coframe:2 sj0:3 above:19 new:6 increasing:2 consisting:1 behavior:1 mem:1 aij:1 equals:1 here:21 represented:2 obtained:4 study:3 changes:2 cancellation:1 appropriately:1 projection:16 a21:2 a22:2 tp:5 unit:5 would:6 e1:4 bundles:5 negative:12 call:3 m0:2 m2:1 type:2 composite:1 brings:1 berlin:2 must:1 me:1 springer:4 mc:4 work:5 mj:1 containment:1 example:2 impose:1 indicated:4 give:4 indicates:1 keep:2 end:4 provide:1 verify:2 hom:1 how:2 nontrivial:1 arcs:1 oscillators:2 earlier:2 lax:1 summarize:1 subelliptic:16 constants:1 hypotheses:1 decreasing:1 order:88 restriction:2 interpretation:1 over:10 satisfied:1 satisfies:9 before:9 heretofore:1 fix:2 writing:2 better:1 condition:5 eventually:1 them:3 greiner:5 they:6 component:3 each:9 side:12 associative:1 mean:2 lifted:3 series:3 used:8 combining:4 rr:10 restricted:1 crucial:1 content:1 re:14 laid:1 reader:5 rn:14 rh:4 linear:9 given:40 standard:11 mϕ:5 estimate:3 chiral:3 r2:6 onto:11 adjoint:14 rank:10 πl:1 another:2 clarity:4 twisted:3 needed:5 too:1 john:2 centered:2 tool:1 somewhat:1 xj:1 finitely:1 last:4 princeton:4 ators:2 matter:3 classes:9 tion:2 contrasted:1 powers:1 rewrite:3 boston:2 ram:1 esti:1 ible:2 seen:1 relatively:2 genuine:1 oriented:4 do1:5 though:2 denominator:2 wells:1 dθp:1 simplify:4 involving:2 singer:1 observation:4 dom:13 upenn:1 doe:2 points:4 principle:1 sum:5 solutions:3 keywords:1 d0:4 d1:28 integrate:1 adequate:1 continuity:1 do:14 dj:1 de:5 dy:1 dt:5 contributes:1 riemannian:1 δjk:1 depends:4 result:23 w1:1 tensor:2 away:7 µq:2 symmetric:2 µn:1 µj:2 approach:1 terms:52 extend:1 wn:1 weak:2 however:2 stants:1 topology:2 suggested:1 essentially:4 providing:1 0t:1 faces:6 contribution:3 adapted:5 16d:1 2nd:2 nomizu:1 polynomial:11 observing:1 three:6 been:2 much:2 basic:4 expected:1 nally:1 cotangent:6 suppress:4 rockland:1 lift:8 θp:1 spin:3 manifolds:4 applied:3 euclidean:1 near:12 suppose:7 applies:3 property:2 leaves:1 ix:1 cylinder:1 iq:1 kohn:1 ii:1 characterize:2 ik:6 ij:1 im:3 bij:1 id:114 suggest:1 make:2 isomorphisms:2 atiyah:1 complex:43 split:5 λoe:1 independent:5 con2:1 i1:1 i2:1 hand:7 auser:2 weakly:1 contact:43 left:9 graded:9 just:4 solvability:1 facts:1 previous:3 adding:1 regarded:1 belongs:11 homogeneities:1 gave:1 possible:1 spanned:5 unique:5 appearing:1 performing:1 specific:1 remind:1 arbitrary:1 heisenberg:104 right:11 grading:1 arguing:1 exposition:1 kobayashi:1 compactifications:2 properties:5 chapter:1 o:102 nonvanishing:1 slightly:2 soc:1 statements:1 remarks:1 hermitian:5 abel:1 often:3 rely:1 support:2 initial:1 tame:1 way:3 m1:1 was:1 therefore:26 form:35 simplifications:2 becoming:1 differences:1 heat:2 trivialized:1 true:1 absent:1 versions:1 compactification:10 proved:4 computing:5 abstract:1 dξ:1 proves:5 exist:1 dθ:7 dη:1 distributions:6 check:1 constructed:4 k1µ:7 no:7 whereas:4 generally:4 vanishes:18 interested:2 intend:1 a12:2 ξt:2 ξj:5 ξk:3 ξn:77 variable:1 ξc:6 dφ:3 pseudo:1 dσ:2 dρ:7 time:1 customary:1 global:1 roe:1 leads:2 computation:7 chair:1 inverse:9 depend:6 graph:7 finally:1 elliptic:14 mutandis:1 analogous:7 charles:1 advantage:1 orthogonal:2 choice:8 exact:2 leave:3 solved:1 upper:9 lefschetz:1 sign:4 substitute:1 appear:4 annals:2 booss:1 satisfy:9 along:45 appears:1 change:7 sobolev:1 vectors:2 ξ2j:1 ξ2n:4 poisson:4 usually:4 studies:1 useful:8 hermite:6 compare:1 modifying:1 inverses:8 projector:34 working:1 prove:11 positive:28 ib1:1 dudv:1 tandem:1 everywhere:1 cases:14 effort:2 valued:1 tokyo:1 oscillator:2 modified:1 printing:1 values:3 following:19 claim:1 dedicated:1 arise:2 dxn:2 dxj:5 spanning:3 occur:1 verlag:4 normalize:2 darboux:5 discussion:4 write:1 v0j:2 parameter:1 r2n:2 product:9 may:3 dx2:1 dx1:1 applications:4 representations:4 data:1 lifting:2 natural:2 outline:2 succeeded:1 sr:4 explicit:6 switch:1 sh:2 so:20 block:23 definitions:2 blowup:3 se:2 schwartz:6 indeed:6 thank:1 coordinates:34 forms:9 mail:1 main:4 formulæ:8 non:4 thereby:2 dxα:1 scaling:1 half:14 nov:1 now:17 term:33 corners:1 orthonormal:1 el:1 eo:162 ei:2 eh:81 ek:5 ej:28 revised:1 conventions:1 er:1 shown:8 space:28 v02:3 contained:1 dolbeault:1 correct:2 shows:16 after:3 theory:4 quite:1 complicated:1 remainder:2 e0:2 e2:3 transition:1 turn:5 place:1 think:1 first:18 oper:1 xk:2 simplifies:2 xn:2 omitted:1 variables:8 symbolic:12 little:5 necessarily:1 indicate:1 types:2 convention:4 structures:6 gives:14 pseudoconcave:33 continuous:2 proving:1 j2:3 x2:1 x1:2 than:3 coefficients:2 require:1 hypersurfaces:1 hessians:1 were:2 generality:2 pro:1 argument:8 say:2 mates:1 any:10 converges:4 note:14 sciences:1 ideal:6 take:4 interior:3 begin:5 multiple:2 trace:2 normal:2 track:1 pair:1 inserted:1 phic:1 considered:3 later:1 parabolically:9 diagonals:1 quantity:1 precise:4 show:27 dy0:2 dy2:1 spaces:4 corner:1 ground:1 homology:1 ratio:1 aφ:2 analytic:1 only:21 explicitly:1 parabolic:12 normalizations:1 get:6 cannot:2 nearly:1 dyj:2 differentiating:2 closure:6 dx2n:2 kernel:9 j1:3 closures:7 relative:1 existence:1 satisfying:5 commutation:2 subsequent:1 review:1 definite:2 enough:2 between:4 notice:1 jx:2 jy:1 jr:1 densely:4 comm:1 jj:2 suppressed:3 σj:1 x2n:2 σn:3 σm:13 tractable:1 many:1 according:3 called:6 deduction:1 embedding:2 cle:1 expression:1 comes:1 σt:3 among:3 continuation:1 grants:1 cancel:1 considering:1 come:2 skew:2 carey:1 direction:18 duces:1 observe:4 former:1 those:9 case:44 x2j:2 k2µ:2 situation:1 metric:22 middle:1 regularity:3 different:7 same:8 arguments:2 extended:29 changing:1 invariance:2 totally:1 pennsylvania:1 solve:1 components:2 coordinate:9 model:39 dimension:6 manifold:23 when:7 multiples:1 except:2 setting:3 versa:1 π0j:2 extensive:1 eigenstate:1 real:7 sums:3 vacuum:4 using:33 ams:1 iξn:10 iξj:2 reduces:1 either:11 integrals:5 deduce:5 2ξn:1 specified:2 a11:2 nonzero:3 provides:1 o2:1 o1:4 o0:3 σmc:1 equivalent:1 2m:4 refers:4 ηj2:2 comparison:1 trivialization:2 ok:1 oh:7 dzk:1 dzj:1 oc:1 ejk:2 whence:1 act:3 invert:1 vi:1 ξ1k:1 image:2 ηj:9 references:1 elementary:1 spinors:4 parities:1 distinctions:1 strictly:30 there:23 start:3 resolvent:1 assumes:1 complete:11 szeg:26 implies:22 applying:3 annihilate:1 ωi:2 assume:9 ωj:3 agree:1 ωg:2 ab:1 certain:2 describe:5 am:4 general:4 ap:1 examine:2 invertibility:5 again:4 embeddable:1 graduate:1 field:7 mathematics:3 polar:1 briefly:1 symbol:107 a0:8 important:4 bounded:5 included:2 noncommutative:1 starting:1 represent:2 consider:9 splitting:7 follow:5 expressions:7 denotes:6 mutatis:1 tr:4 nonlocal:1 preserved:1 te:4 presentation:1 norm:7 belonging:1 worse:1 straightforward:1 very:4 rc:2 corollary:9 sons:1 worst:1 nijenhuis:1 small:2 neighborhood:5 kato:1 b22:3 b21:2 zero:10 further:2 canonical:1 residue:4 what:4 brackets:1 section:29 pseudoconvex:30 version:1 subspaces:1 acknowledgments:1 modify:1 answers:1 ranges:2 directions:2 november:1 equations:5 allows:2 action:6 uniquely:2 texts:1 establish:1 ψr:2 de1:6 contains:1 comparing:1 ψh:2 ψm:6 taken:2 entails:2 minor:1 more:3 flat:2 operators:107 corrected:1 particular:2 known:1 foundations:1 quantized:1 recall:8 equation:16 deo:1 canonically:1 f0:2 f1:6 f2:6 multiindex:1 stated:2 beals:5 states:2 minimum:1 numbers:1 hyperplane:1 sense:17 sharp:1 axis:1 respective:1 acts:3 maps:3 v01:2 algebra:10 wiley:1 mapping:2 plane:4 coming:5 fi:5 fj:1 fundamental:4 cs1:2 cs2:2 paper:14 through:1 y1:1 y0:1 y2:1 its:15 rapidly:1 actually:4 deformation:2 yj:2 geodesic:1 easily:11 2q:2 always:1 radial:4 2l:1 found:2 2n:7 2i:1 2j:11 2k:13 finish:1 operation:2 really:2 since:9 induces:1 research:1 acting:15 denoted:4 induced:3 evaluation:2 fiber:13 difficulty:1 reason:1 definition:5 pairs:2 nonnegative:2 consequence:8 integrand:2 number:2 done:3 differ:1 perturbation:1 introduction:1 leading:6 construct:3 assumption:1 calculations:4 dt1:2 observations:1 holomorphic:5 statement:9 recursively:1 helpful:1 immediate:5 part:6 determines:1 double:1 annihilation:1 determined:7 conjugate:12 null:16 orders:22 lie:2 dη0:5 jour:1 built:1 lim:2 ation:1 hyperplanes:2 eucl:2 k2:7 k1:7 lifts:10 generalized:15 finding:1 yǫ:1 most:14 significant:1 compu:1 kc:1 ke:2 clear:8 sometimes:3 cover:1 h2m:2 exp:2 h2j:5 relation:4 carefully:2 find:9 assertion:2 positively:1 factor:3 integrable:10 tations:1 his:1 notation:15 express:6 methods:1 ϕn:1 arxiv:1 common:1 approaching:1 set:4 see:32 arc:2 close:3 contour:11 seh:4 various:7 subscript:3 conditions:21 initially:1 complement:9 vanishing:3 condi:1 both:3 prescription:2 quantization:8 connection:1 symplectic:2 pde:1 point:12 simple:5 corresponds:1 dimensional:12 bξ:9 throughout:1 suppressing:1 kernels:3 pp:3 pq:1 described:1 lempert:1 due:1 laplacian:1 calculi:1 pe:4 anisotropic:2 po:2 surjective:4 spectrum:1 understand:1 representative:1 idρ:2 p0:3 ǫk:5 ǫj:24 iξ1:16 while:5 replaced:1 evaluating:3 error:5 vol:8 vanish:8 fibers:4 belong:1 emphasize:1 ray:2 composition:9 higher:6 literature:1 domains:2 moment:2 purpose:1 lower:16 parametrix:11 analysis:10 entry:1 self:6 things:1 λe:1 λo:2 letting:1 theorem:28 heidelberg:2 hj1:1 stein:4 hj2:1 evaluate:4 showing:3 integer:1 formal:6 modifications:2 follows:23 disks:1 bavnbek:1 spinc:17 continue:1 spinor:3 pointwise:2 mathematical:3 neumann:11 creation:1 some:3 understood:2 b0:5 b1:3 shall:3 integration:1 peo:3 eliminate:1 tends:1 adjoints:7 ba:1 bl:3 bm:3 patodi:1 step:2 br:4 birkh:2 bx:149 hilbert:1 bz:2 pα:2 anything:2 extending:1 idt:6 range:10 fredholm:16 2iω:1 idf:1 ide:17 cr:7 into:12 within:3 integral:5 nsf:1 appropriate:18 next:5 ixj:1 smoothly:2 u1:50 u0:15 analyze:3 sections:34 properly:1 repeatedly:1 line:17 up:7 us:4 un:9 verification:1 uj:2 continuously:1 similar:8 laplace:1 constant:10 defined:65 pseudodifferential:13 globally:5 single:4 numerators:1 laszlo:1 defines:11 proofs:2 amounts:1 composing:2 rewriting:2 priori:1 b12:2 b11:2 department:1 elements:10 ku:1 problems:14 polynomials:1 prepared:1 structure:43 2d1:6 vice:1 dvg:1 required:2 orbit:2 far:1 requires:2 having:2 once:2 partial:4 results:16 proposition:49 edu:1 gi:2 compact:4 uniqueness:1 expressing:1 implicitly:2 putting:1 microlocal:1 matrices:3 arrange:1 notes:1 epstein:3 refer:3 noted:7 zn:1 zj:7 zk:2 imply:9 odd:29 index:6 invertible:15 analogously:1 expressed:3 poles:3 codimension:3 degree:22 respectively:5 desired:4 objects:1 z0:17 z1:5 deduced:2 remark:15 technical:2 larger:1 products:1 involves:2 composed:3 aps:1 apply:5 cα:2 use:28 francis:1 asymptotic:1 recalling:2 germ:2 classically:3 zik:1 formally:3 carrying:1 normalized:2 account:1 isomorphism:1 zi1:1 splittings:2 oe:45 proof:46 cokernels:1 theorems:1 calculation:2 purposes:5 high:1 tions:1 holds:1 evidently:1 instead:3 blocks:12 singular:3 collection:1 michelsohn:1 duistermaat:2 conormal:1 computations:28 light:1 element:5 diffeomorphism:1 allow:3 produces:1 symbols:65 hypersurface:5 hloc:1 chosen:3 lk:4 degrees:4 choose:1 lp:1 ηn:4 derivative:1 defining:17 greater:1 dirac:21 verifying:1 university:4 identified:1 sufficiently:1 l2:25 truth:1 parametrices:13 homogeneous:21 weyl:1 map:7 doing:1 related:2 operator:80 interplay:1 our:22 special:1 out:4 matrix:14 reh:9 suffices:17 math:5 diagonal:6 8d:1 approaches:2 york:4 compositions:1 geometry:9 could:1 times:2 ahler:15 length:5 isotropic:20 assumed:4 hence:16 quadratically:1 multiplication:3 calderon:24 precisely:1 πh:4 πi:1 πn:3 system:9 relations:8 their:5 πq:3 πt:2 final:3 denominators:1 completed:1 completes:9 pointers:1 limiting:1 subsequence:1 individual:1 lemmas:3 negatively:1 rate:1 projections:8 need:24 clearly:3 hessian:1 studying:1 able:1 instance:1 calculus:20 unless:1 class:6 fjk:2 consequences:1 face:11 occasion:1 fact:14 ho:1 supported:2 terminate:1 purely:3 agrees:3 principal:47 q0:1 b111:16 should:5 lemma:35 bases:1 partially:1 local:5 preliminaries:2 meant:1 means:2 determinants:2 differential:5 expansions:2 2b1:1 qe:10 fixed:7 dξα:1 exists:2 notational:1 frame:2 p21:4 quantizing:1 qµ:4 state:4 difficulties:1 melrose:1 closed:6 boundary:78 meromorphic:1 importance:1 wj:9 hypothesis:1 amer:2 ker:2 restrictions:2 taking:3 etc:2 ck:7 cj:44 relevant:1 co:1 cn:2 conclude:4 harmonic:4 taylor:7 quantizations:1 cs:14 respect:11 distributional:1 treat:3 define:22 determinant:1 arises:1 corresponding:2 sufficient:1 subspace:2 covered:1 c3:4 c2:7 c1:6 c0:2 multi:4 splits:1 value:13 choices:1 layer:2 almost:19 iηn:4 vj:2 thus:7 iηj:2 quantize:1 dual:4 compactified:2 φx:2 parts:9 units:1 finite:14 difficult:1 infinity:3 effect:1 v0:3 introduce:1 infinite:12 identity:6 off:3 nonetheless:1 well:13 sets:2 arising:2 usual:11 invariantly:1 less:3 obtain:13 underlying:1 preprint:1 add:1 extends:2 propositions:1 usage:2 identical:7 2δjk:1 boundedly:2 crux:1 ψ0h:1 know:1 press:3 loss:1 necessary:7 like:1 diffeomorphic:1 z0t:1 lawson:1 become:2 works:1 parity:5 because:11 classical:45 sequence:2 ideals:1 convex:1 proper:1 peter:1 happens:1 lead:1 does:7 assuming:1 blowing:1 expansion:7 imaginary:2 injective:6 simpler:1 about:4 carried:1 extension:2 column:1 dependence:6 compatible:21 carries:1 introduced:5 projectors:18 converging:1 outset:1 dξ1:6 subbundle:1 h2:1 h1:2 domain:6 utility:1 additional:2 smoothing:6 quadratic:2 inner:5 function:24 hs:6 hp:1 sequel:1 triangular:1 but:2 hj:6 construction:3 gain:1 hl:5 highest:4 hd:2 dξj:2 made:1 compute:24 whether:1 smooth:28 below:3 limit:3 problem:6 bearing:1 contribute:10 correction:1 denote:44 identities:4 functions:12 variety:1 detail:3 other:6 details:3 conclusion:1 repeat:1 radially:3 bundle:30 factors:1 rule:6 4k:1 |
0705.1700.txt |@word 1st:1 represent:4 concept:1 partial:1 systematic:1 springer:1 pairing:1 green:1 dios:1 alternatives:1 focus:1 month:1 leads:2 eds:1 scalar:1 disappears:1 overlap:1 computation:1 ǫm:1 follow:3 colon:1 disk:1 mercer:1 assembled:1 optical:1 feeding:1 depend:2 technique:3 corrections:1 removal:1 outside:4 rightmost:1 compensate:1 those:1 th:3 under:2 stochastic:6 alternatively:1 must:1 ingredient:1 summarizes:1 applied:2 g4:3 amplitudes:4 g2:9 g1:6 orthogonal:5 dynamic:1 a18:1 keeping:1 angulaire:1 gz:1 rotational:1 refractive:2 inherited:1 difference:1 appropriately:1 condition:1 rn0:1 founded:1 randomness:3 percent:1 obvious:1 solves:1 harri:1 bn:1 positions:1 eigenmodes:4 list:3 eve:2 correct:1 large:4 solved:1 watkins:1 vector:16 math:6 small:3 eigenvalues:8 markov:1 optics:3 lines:2 inconsistent:1 upper:2 mn:2 zj:1 spatiale:1 const:1 consistent:4 square:3 ornstein:2 sign:4 approximation:1 threshold:1 βm:1 traveling:1 insertion:3 multipliers:1 7th:1 further:1 odd:1 substitute:3 linear:8 even:1 established:2 stegun:1 nwo:1 centering:1 sub:1 speckle:2 fine:1 section:9 axes:1 while:1 consistently:1 complexvalued:1 version:2 en:1 above:1 method:1 judicious:1 new:7 principal:1 acknowledgments:1 coefficient:2 edited:1 full:3 chose:1 hufnagel:1 exchange:1 d1:1 respectively:1 component:8 residual:1 here:12 ǫs:10 tangent:1 ansatz:3 separation:4 kilometers:1 represented:2 path:2 along:6 sine:3 equations:3 auxiliary:1 change:1 ıguez:1 box:1 undulation:1 chaotic:1 divisor:1 division:1 splitting:1 shift:1 larger:5 allows:2 philosophies:1 amount:1 periodic:1 simply:2 stiffness:1 decouple:1 implement:1 fourier:12 changes:2 explain:1 york:1 diameter:4 deterministic:3 term:10 projection:2 clark:1 scales:8 hermite:1 app:2 substitution:2 marked:1 replace:1 screens:9 markey:2 translational:1 rousset:1 δn:12 mckenna:1 des:1 comma:1 post:1 linearly:1 a25:2 use:4 stream:1 would:7 may:1 remains:2 positive:1 fem:1 single:2 negative:1 guideline:1 erence:1 few:3 a20:1 bases:1 jj:1 therefore:1 keen:1 memory:1 aperture:3 themselves:1 2πiv:1 type:4 more:3 separated:2 entrance:1 applicable:1 weight:1 name:1 composite:1 becomes:4 stable:1 gendron:1 odinger:1 vici:1 iid:1 bold:1 appendix:9 normalized:4 particular:2 known:5 benefits:1 iii:5 dot:1 r1:5 fly:1 account:1 valued:3 thun:1 mm:7 equation:25 work:4 mk:2 reviews:1 movies:2 labeled:1 infinitesimal:1 mq:8 publications:1 ms:1 byers:1 akin:1 merely:1 trans:1 my:1 ollivier:1 dither:1 proof:1 grained:1 haute:1 wang:2 indicated:1 dxx:1 process:1 expanding:1 choice:1 τn:14 states:1 weighting:1 pulling:1 numbers:5 oscillating:1 sense:1 g3:2 times:2 dσσ:3 axis:1 motion:7 needs:3 rodr:1 tune:1 pure:1 tilt:2 purpose:1 means:3 berlin:1 feature:1 orthogonality:2 recovers:1 write:2 how:4 magnus:1 fourth:1 frequencies:2 opt:37 instead:1 bit:1 warner:1 parameter:4 sin:39 circular:5 oscillatory:1 wave:6 product:5 proc:1 description:1 benner:1 algebra:2 easily:1 demonstrates:1 jk:1 after:8 derived:1 orbits:1 echelle:1 mixed:2 plane:6 physik:1 waves:4 multiplication:5 fi:1 fj:5 law:3 fl:1 response:1 fn:2 short:4 dα:5 overtaken:1 northcott:1 light:1 sq:9 eng:1 strw:2 element:2 their:1 negligible:1 inhomogeneity:1 2u:4 representation:9 λ2p:16 βk:5 order:7 wind:6 martin:2 quirrenbach:1 theme:1 a27:1 eigen:2 schwartz:1 rand:1 tavis:1 over:14 move:3 vary:1 interpreted:4 stability:1 i00:1 paper:1 through:5 looks:1 thesis:1 during:1 hybridization:1 still:1 its:5 before:2 ωks:1 respect:1 mod2:3 du:5 outer:1 render:1 chosen:2 lo:2 temporal:2 37b:1 comastri:1 coordinates:9 fruitful:1 dβk:2 tyler:1 degrees:2 systems:1 jacobi:1 derivative:3 main:1 might:1 image:1 τp:5 split:1 a29:1 non:1 mathematischen:2 contributions:1 matches:2 36c:1 fig:3 introduce:1 scaling:4 modification:1 vorontsov:2 equidistant:1 whiteley:1 they:3 identically:1 front:5 mathar:5 rotation:2 now:1 πd2:7 maintaining:2 eigenvalue:5 2v:4 netherlands:1 2q:6 randomized:1 university:2 arrows:1 radians:2 2z:1 orthonormal:1 sufficiently:1 fassbender:1 mode:3 each:12 accompanied:1 2n:1 quarter:1 errata:1 typographic:2 mean:1 homogeneous:1 domain:3 differential:11 telescope:5 formulate:1 masiero:1 generation:1 series:3 hypergeometric:3 reduce:1 gaussian:6 snapshots:2 solution:2 inhomogeneous:1 literature:2 static:2 yield:1 accumulated:1 quantum:2 wavelength:2 avoided:1 wander:1 special:2 out:3 principles:1 shown:1 divide:3 matrix:23 part:1 factors:2 gradient:15 since:4 induces:2 leidenuniv:2 cancels:2 synthesizing:1 increase:2 re:4 nominal:1 multiply:3 ra:1 anal:1 wilson:1 adaptive:4 induced:2 suffices:1 integrated:1 independence:1 shows:1 ass:1 fiber:1 theory:1 kpq:2 abramowitz:1 column:2 diagonal:1 standard:1 rows:2 complicated:1 imaging:1 nice:1 generate:1 holland:1 definition:3 pairs:2 r0:8 πd:1 r2:3 applications:1 just:1 insert:3 so:3 used:1 keep:2 filter:1 turn:1 length:1 produce:1 isotropic:1 resumes:1 βl:3 retain:1 βn:6 onto:1 βi:1 βj:14 first:10 xj:1 externe:1 major:1 xi:1 isbn:2 symmetry:6 ignored:1 omitted:1 variables:10 number:10 xd:1 instances:2 xx:9 smaller:2 done:1 another:1 solvers:1 carry:1 apparent:1 precisely:1 electronic:1 angular:1 mix:1 size:7 given:4 cartesian:1 ten:2 requirement:2 simulated:1 unknown:2 top:1 deutsch:1 amsterdam:1 system:3 relations:1 compatibility:2 γjj:1 needed:2 assumption:4 ballistic:1 observations:2 oberhettinger:1 siam:1 scheme:1 quadratic:3 listed:1 shifted:3 a31:1 a30:1 option:1 ratio:1 predictably:1 reintroduced:1 wolf:2 eliminates:1 immediate:1 γ1k:1 employ:1 λ2i:1 because:2 x2:5 shortly:1 x1:1 than:1 coefficients:27 center:3 legendre:1 distance:3 observatory:1 third:1 winzer:1 isolation:1 second:3 aims:3 project:1 computer:2 contrary:1 supposed:1 amplitude:3 buscher:1 iωl:3 synthesis:3 minus:2 symmetries:1 explicit:2 correction:1 argument:3 elem:1 randomly:2 say:1 conjugate:1 north:1 ribak:1 any:4 elisation:1 symmetrized:1 forced:1 conversion:1 strength:2 angle:1 der:2 depending:2 efficient:1 astronomie:1 latter:1 udu:3 isolate:1 om:1 instance:1 k1:1 k0:3 absorbed:1 build:3 jacobian:1 fj2:1 a28:1 switching:1 evaluated:1 circles:3 clarifications:1 b3:1 added:2 fundamental:1 trace:1 index:5 track:1 sets:1 reach:1 compl:1 boiling:1 artifact:1 g0:1 phase:36 analytically:1 measured:2 why:1 dai:4 appear:1 annulus:1 roy:1 richard:1 url:1 kj:15 calculated:2 steady:1 kl:29 erez:1 points:1 snapshot:1 principle:1 exp:10 movie:4 velocity:6 effect:1 physics:1 specification:1 fact:2 dover:1 incorporate:1 atmosphere:2 selection:1 wallner:1 show:1 random:12 grundlehren:1 anisoplanatism:1 esolution:1 purely:1 radii:1 solutions:1 keywords:1 conclusion:1 d2:5 ground:1 impact:1 astron:1 root:1 based:1 dice:1 parameters:3 implementation:2 delays:1 distributed:1 pickup:1 supported:1 should:1 analytic:1 only:6 unable:1 notes:1 factor:13 integrate:1 employed:1 oct:1 columns:2 thompson:1 do:2 his:1 dominant:2 dk:4 notation:4 wide:1 dependent:10 mainly:1 dd:1 de:4 expectation:1 aim:1 made:1 a10:1 dx:20 piston:2 speckles:3 ϕd:5 dt:9 conjunction:1 comply:1 xdx:1 symbols:1 qr:1 initial:5 die:2 transposition:1 arxiv:2 wiener:1 remove:1 summary:3 nθ:4 contain:1 including:1 nβ:1 fixed:1 silently:1 view:2 kernel:7 karhunen:3 set:13 emat:1 achieved:2 throwing:1 attached:1 oscillations:1 kolmogorov:4 deconvolution:1 ωt:1 relative:1 edition:4 namely:1 individual:2 radius:2 existence:1 suffers:1 uncorrelated:1 βˆl:6 ergodicity:1 phases:1 rigidly:2 eigenfunctions:9 r00:3 subsequent:1 review:1 extrasolar:1 dipole:1 loeve:1 symmetric:5 written:1 determined:4 cambridge:2 between:6 conductive:1 drawn:2 αk:8 diagonalized:2 conditions:1 across:3 side:10 hence:1 multiplied:5 terms:6 statistically:3 missing:7 numer:1 comp:1 screen:19 back:3 however:1 jq:19 efficiency:1 jn:8 vσ:1 hypothesis:3 key:2 fluctuations:3 τj:1 generates:1 diverges:1 distribution:1 uσ:1 τk:1 both:4 essentially:3 parentheses:1 last:1 universit:1 limits:2 triggers:1 taking:1 infinitely:1 36b:1 nomenclature:3 incomplete:1 36a:1 enabling:1 37a:1 connection:2 figures:1 dated:1 embedding:4 variance:1 contribution:1 expression:1 lateral:2 otherwise:1 regulates:1 hydrogenic:1 timescale:1 point:3 simple:3 overview:1 address:1 period:2 whatever:1 sampling:2 dimensional:4 na:1 γ0k:1 differ:1 conjugation:1 cancel:1 associated:3 writing:2 exponent:1 ensures:1 transformations:1 puts:2 basis:32 observing:1 skew:4 9th:1 three:1 been:8 implicit:1 stanley:1 reduction:1 much:4 interest:2 electr:1 expected:1 ph:2 define:3 followup:1 obtained:2 direction:10 corresponding:1 baum:1 coherence:1 covariance:12 eigenfrequencies:1 external:1 angles:1 coherency:1 conan:5 general:1 present:2 case:4 atmospheric:1 pacs:1 frozen:3 variances:1 expanded:3 ǫn:9 value:6 choices:1 will:5 information:2 ǫq:2 momentum:1 determinism:1 pictures:2 5b:1 region:3 spawn:1 a21:2 a22:1 a23:2 a24:1 planets:1 a26:1 coupled:1 almost:1 endowed:1 binding:1 them:1 surface:1 iv:4 ii:3 middle:1 unit:4 vt:6 turns:2 mennesson:1 discarded:2 c0:1 vanish:2 ie:1 eigenfunction:1 summarize:1 wissenschaften:1 different:1 baseline:1 grant:1 generic:1 recursion:1 make:1 lett:2 same:4 read:11 unity:2 complex:3 arguments:2 largest:2 units:5 und:2 finite:5 higher:3 independent:8 tighten:1 decomposed:1 http:1 slightly:1 welsh:1 jakobsson:1 numerical:8 nj:1 hand:10 squared:3 mq2:1 moving:3 stripe:1 coh:1 normalization:2 eigenvectors:3 noll:9 lower:2 off:3 modes:10 largely:1 studies:1 page:1 well:3 increases:1 analysis:4 patterns:1 without:1 components:7 qθ:5 coordinate:2 quantitative:1 model:5 macintosh:1 left:5 spherical:1 distances:2 bottom:1 atze:1 proposed:2 less:2 increasingly:1 generally:1 accurate:1 kinks:1 shape:1 intervals:2 transforms:1 actually:2 tilde:1 λk:10 λj:11 alternative:1 arctan:1 speed:1 rnq:6 alignment:1 λl:6 adding:1 cut:1 num:2 generator:1 density:1 seems:1 theorem:1 sky:2 parametrization:1 reasons:1 lets:1 other:1 transformed:3 treatment:1 samples:2 δpp:3 diagonalization:2 shaklan:1 practise:1 transformation:10 ought:12 generalized:1 real:5 iθ:2 fluctuating:1 aspects:1 around:1 format:1 rules:1 spatial:9 integrals:6 possibly:2 working:4 performance:1 press:1 turbulence:2 variants:1 2nd:1 disadvantage:1 scaled:1 imposed:1 like:1 2r0:1 follows:1 reduces:1 velocities:1 isotropy:1 translates:1 specific:1 benefit:1 history:1 steps:1 either:1 sparse:1 arbitrary:1 bunch:1 become:2 works:1 reduced:2 replacement:1 mathematical:3 parity:1 www:1 right:7 neumann:1 lundstr:1 discrete:1 creation:1 some:18 searching:1 library:1 δs:2 b4:1 employing:1 b6:1 a16:1 meters:1 b1:1 b2:1 table:5 duration:2 a11:2 diagonalizing:2 electric:1 provided:2 born:1 scale:2 there:2 realistic:1 electromagnetic:2 onde:1 shall:1 paardekooper:1 integration:11 comments:1 2xx:7 does:2 decomposition:4 periphery:1 assuming:2 prog:2 yields:3 bessel:2 cϕ:19 refer:1 denominator:2 a15:2 obey:2 power:5 dropped:1 a19:1 equivalent:7 radial:9 carried:1 pp:1 expansion:20 interval:1 schr:1 host:1 f1:10 polynomials:4 found:2 imaginary:1 refers:2 super:2 11x:54 a14:3 actual:2 decoupling:2 27c:1 barenblatt:1 row:1 freedom:2 commun:2 discussed:2 dependence:6 o:3 simulation:4 compatible:1 mutually:1 range:1 a2:1 ensure:3 obeys:1 modal:2 uhlenbeck:2 fˆl:1 brummelaar:2 introduced:5 consequently:1 block:1 cutoff:1 soc:25 contains:5 a7:1 followed:1 into:24 within:5 integral:14 bound:1 down:2 pair:2 exploiting:1 selected:1 paramonov:1 operator:5 proportional:3 next:1 physical:1 a3:2 diameters:1 27e:1 statistics:8 additional:4 synthesized:1 u4:4 support:1 twodimensional:2 available:1 transform:4 long:2 u2:5 graves:1 width:1 cosine:3 handbook:1 inner:1 mod:1 chorin:1 2m:1 valley:1 was:1 assumes:1 interferometry:2 function:13 media:3 gibb:1 azimuthal:8 form:4 covariances:2 a9:1 leiden:3 but:5 displacement:1 astro:1 strictly:1 atom:1 sustained:1 line:9 editing:1 a5:2 partially:1 volume:2 leeb:1 eran:1 october:1 calls:1 places:1 b5:1 2πi:1 inside:1 smooth:3 up:4 ur:1 kk:9 converted:1 2πiq:2 ωl:2 sum:1 observation:1 2πx:3 problem:3 fried:11 similar:1 produkt:1 eigenvector:1 excess:1 taylor:15 constant:3 heidelberg:1 defined:2 roddier:6 universal:1 aj:8 am:25 evidence:1 resumption:1 dashed:1 inn:4 exist:1 effets:1 dθ:9 our:2 prasad:1 perez:1 dragging:1 σm1:1 constructed:3 functions:33 compared:1 nl:2 no:3 cos:52 whereas:2 tip:2 vanishes:1 virtual:2 zernike:10 field:3 kp:21 remarks:1 pour:1 papers:2 mathematics:1 xkp:8 funktionen:1 outsourced:1 conclude:1 polar:4 a17:3 elements:3 star:1 superposition:5 a13:3 a12:1 azimuth:1 radially:1 virtually:1 variation:1 herrmann:1 a1:3 generated:4 important:1 intent:1 a4:2 ridges:1 a6:1 variable:4 a8:1 formal:1 astronomy:1 sides:3 structure:7 rq:5 lane:1 calculation:1 implies:2 coupling:3 using:2 u1:2 assume:3 values:4 apertures:1 space:7 changed:1 dσ:7 eom:5 gridded:1 factorizes:1 implied:1 weights:1 pupil:31 introduces:2 time:34 appl:3 once:4 starting:1 original:1 basically:1 |
0705.1701.txt |@word similarity:1 four:3 whose:2 γn:103 under:5 replication:1 p1:23 called:10 solution:1 math:15 indices:1 glued:2 estimates:4 second:12 chen:1 estimated:1 even:20 established:6 ˆe:2 above:28 new:1 ǫsn:1 simultaneously:1 never:2 equals:1 here:23 refinement:4 path:74 marchenko:6 obtained:10 study:9 sbornik:1 pastur:7 fourier:1 divide:1 explained:1 replace:1 9p:1 total:2 plot:1 plos:1 chooses:3 call:7 therefore:1 m2:9 type:50 until:4 matlab:2 brings:1 hold:2 brasil:1 mc:1 mo:8 mn:20 mp:10 determining:1 example:1 unmarked:7 indicated:1 give:15 organized:1 degenerate:1 absolute:1 end:5 revisit:1 how:1 blanks:5 after:1 law:5 constants:19 summing:1 hypotheses:1 decreasing:1 order:19 restriction:3 over:1 vary:1 satisfied:2 before:6 xl:1 fit:1 fix:4 expectations:1 fig:4 clt:2 versus:1 pfaffians:1 they:7 mimicking:1 eigenvalue:20 filling:2 reasonable:2 each:18 mean:1 successively:1 t2:4 journ:2 literature:1 combining:1 goe:6 crucial:1 re:1 adapt:1 reader:4 ri:1 numerical:1 associate:4 standard:2 estimate:15 r1:10 r2:12 mvw:1 isn:2 probab:2 already:6 rank:3 restrict:1 enumerate:1 electronic:1 illustrate:3 similarly:4 top:21 xio:4 needed:6 rates:1 airy:2 ordered:2 centered:1 guhr:1 1m:1 painlev:1 xi1:2 classes:1 kth:1 tion:1 powers:9 spectrum:3 7th:1 seen:3 latter:2 maxt:3 oriented:14 maxk:1 shall:14 object:3 phase:1 doi:1 vertices:65 fluctuations:3 yang:1 sum:3 channels:1 random:39 ending:2 d4:3 d5:1 d2:2 d3:3 d1:15 latent:1 explain:1 subpaths:1 do:6 mixture:12 di:1 dd:13 dx:2 dy:19 reconstruct:1 dt:2 du:10 fields:1 acknowledgments:1 twice:13 analytical:1 psych:1 bai:2 testing:2 observed:2 depends:5 result:22 λi:2 best:2 techniques:2 said:4 capacity:1 symmetric:5 µo:5 µn:2 µi:5 drawn:1 approach:2 shields:1 petz:1 terms:3 extend:2 wn:3 weak:1 stants:1 modeling:1 improve:1 essentially:10 c21:1 met:1 xv2:1 against:1 variance:7 contribution:35 con:1 2no:1 wider:1 telecommunications:1 xe:1 union:1 three:4 been:15 much:3 interest:5 basic:2 expected:2 deeper:1 johansson:2 aim:4 endpoints:2 procedure:2 cont:1 iv:4 ii:3 characterize:1 ik:1 ij:7 io:6 id:6 descent:1 make:3 cumulative:4 linked:2 complex:15 split:1 mixtures:3 european:1 independent:36 i1:3 trajectories:12 counterparts:1 hand:2 suitable:3 claims:1 left:5 homogeneity:1 identify:1 thanks:5 yet:4 previous:1 hotelling:1 belongs:2 easy:10 polon:1 rescaled:9 iν:16 advances:1 possible:5 possibly:1 boxes:1 grenoble:1 advanced:1 apart:2 cizeau:1 steps:67 arbitrary:1 www:1 right:4 deal:1 intern:1 bottom:22 comments:1 telatar:1 core:1 rescale:1 properties:2 would:1 deduced:1 probabilities:2 ensure:5 soc:1 bound:4 down:10 remarks:1 ussr:1 refined:2 combinatorics:3 support:1 approximate:1 class:5 way:9 m1:7 was:9 form:2 quantity:1 denoting:1 wireless:1 so2:3 true:1 timated:1 inside:5 maximum:5 examples:1 proved:15 ln:12 abstract:1 proves:1 exist:9 simulations:4 distributions:6 check:3 kˆ:5 ni:37 no:36 when:9 setting:5 role:1 papers:1 test:2 picture:1 models:3 preceding:6 uniformly:2 faster:2 assume:25 interval:18 time:11 n0:1 n1:11 n2:13 n3:3 switched:1 focus:5 leads:1 computation:2 dimensionality:1 depend:3 finally:5 soshnikov:9 orthogonal:2 choice:8 entries:21 gue:6 level:28 turns:1 sulanke:3 discrete:1 pgen:1 upper:3 work:2 occurrence:1 discover:2 preimages:1 spectral:7 appear:3 heres:1 uniform:6 current:1 goes:5 international:1 falling:3 filled:1 genet:1 understanding:1 lu:4 address:2 along:3 appears:2 change:3 vectors:2 bol:1 usually:1 conveniently:1 studies:1 regardless:1 extra:1 problematic:1 ipi:5 f2:2 marked:45 prove:17 positive:15 france:1 scope:2 theoretical:1 sharing:1 acceptable:1 apparent:1 appendix:1 cases:4 amaral:1 values:1 following:20 figure:4 sample:33 refine:2 rescaling:1 occur:5 s3:1 s2:45 divided:2 write:1 fourth:1 optimal:3 parameter:2 product:1 mat:1 information:1 may:9 max:29 applications:4 data:5 grow:2 maybe:1 yielding:2 st:1 sk:2 switch:3 so:21 sn:301 definitions:2 typical:22 subsections:2 indeed:13 statistical:11 differs:1 still:4 no3:1 thank:1 interesting:1 decreases:1 mail:1 main:6 non:22 tjb:11 finance:3 introduce:3 scaling:1 tails:4 identically:1 now:30 widom:13 term:8 equality:1 james:1 instabilities:1 el:4 weighted:1 ei:2 ek:13 gaussian:25 shown:2 factors:1 furthermore:2 increase:1 investigation:2 u2s:2 formula:13 squares:1 shows:2 theory:2 quite:2 california:1 org:1 e2:1 derivation:1 transition:1 turn:3 first:41 origin:18 xk:45 xi:9 xn:1 xo:20 symmetry:3 variables:7 xij:5 xg:7 transform:2 xx:13 specifically:1 directly:1 xq:1 xv:1 size:8 1p:2 given:30 necessarily:4 checked:1 yin:1 indicate:1 returns:18 types:1 white:1 structures:1 1l:1 gives:3 x2:1 copy:2 than:30 population:4 hoyle:1 were:3 johnstone:3 generality:1 ann:5 say:1 any:39 ideas:1 converges:5 note:12 take:1 formulas:1 multiple:1 selfintersections:1 normal:1 price:1 correlation:2 fails:1 algebraic:1 successive:1 pair:1 tracy:15 pages:1 especially:1 fills:1 considered:7 later:4 implications:1 replications:3 typically:1 laws:2 precise:1 show:23 notations:1 ns2:1 ratio:5 ensembles:14 proportion:2 only:25 going:2 get:1 expectation:13 cannot:2 symmetrically:1 2mo:1 secondary:1 regarding:1 yield:2 kernel:2 rmt:1 sear:1 j1:2 bounds:1 relative:1 lnl:5 namely:3 stanley:3 αs:1 satisfying:8 ways:11 subsequent:3 review:3 enough:27 percentiles:1 between:9 reading:2 αn:6 multiplied:1 notice:1 ju:2 jo:8 comm:3 ud:2 come:5 jb:3 gaussianity:1 according:2 laplace:2 comes:7 among:2 jk:1 learning:1 constant:25 technicalities:1 considering:8 mark:2 combined:1 direction:4 formed:1 observe:1 those:6 case:49 developing:1 dρm:2 intimately:1 maximal:7 orientation:1 characteristics:2 eral:1 αsn:13 discrepancy:1 cluster:1 good:1 different:3 develop:2 k2p:3 same:25 arguments:11 regime:2 investigated:1 companion:2 edges:21 relies:1 roughly:3 without:2 components:2 very:1 ujf:1 dimension:3 being:4 resp:49 identit:2 seems:1 except:3 improvement:2 lett:1 samples:7 real:16 psn:2 around:2 read:25 admitting:3 coexistence:1 np:2 mpm:5 quantiles:3 using:28 acquainted:1 collective:1 either:4 conditional:1 deduce:21 erase:1 respect:7 provided:9 variates:1 genetics:2 dimensions:2 refer:4 power:2 ratios:1 2m:2 refers:1 central:5 package:1 theorems:2 discussed:1 practical:2 cambridge:3 ηn:18 references:1 determine:3 financial:2 loe:3 removing:1 strictly:1 there:71 start:1 cauchy:1 series:1 ωmax:6 complete:3 jun:1 amongst:4 implies:1 arranged:1 multiplicity:2 robustness:1 regimes:1 ai:2 certain:2 describe:1 ao:6 general:5 ar:2 fill:2 again:1 antenna:1 mathematica:1 mathematics:2 pi:36 congress:1 vertex:41 a1:24 a3:2 a2:28 bounded:4 a4:1 suited:2 studied:2 semicircle:1 insertions:1 passed:5 starting:10 sci:1 consider:37 lack:1 4e2:1 combinatorial:7 tr:14 tn:8 c5:3 ti:11 te:27 norm:1 straightforward:2 far:2 conjectured:1 fat:1 corollary:1 fall:1 condition:2 laloux:1 list:1 t3:2 t1:5 large:28 small:9 anal:4 neighborhood:1 rate:2 silverstein:1 further:3 sub:16 section:17 version:1 method:1 component:3 relaxation:1 strong:2 mult:2 δλi:1 allows:1 amount:1 published:1 establish:3 readily:6 proceed:3 distinct:4 asn:2 microarrays:1 taken:3 minor:3 more:23 knows:2 tested:1 basically:2 particular:15 known:7 foundations:1 none:2 endpoint:6 recall:4 equation:1 des:1 semadeni:1 paragraph:1 f1:7 compare:1 stated:4 states:1 numbers:11 νo:1 νn:82 huge:1 respective:2 csn:2 csk:3 reject:1 acta:2 ensemble:12 fr:1 derived:3 coming:5 horizontal:2 short:1 spectra:1 negligible:17 fundamental:3 help:1 developed:3 paper:14 y1:2 its:6 roots:1 actually:9 systems:1 pca:2 might:1 deformation:2 yi:5 yk:1 skipped:2 return:1 yl:6 yo:14 universality:13 yp:2 easily:2 2p:2 2q:3 2s:2 2a:2 2l:14 found:3 2n:6 2k:7 hard:1 idea:4 event:5 since:7 denotes:4 denoted:1 induced:5 issue:2 occurs:4 motzkin:1 reason:2 maths:1 generate:2 definition:8 pairs:4 wachter:1 consequence:1 assign:1 major:1 probability:6 laguerre:2 number:69 done:3 construct:1 introduction:1 leading:5 least:3 assumption:5 statement:2 saint:1 part:3 pairwise:2 null:1 paths:98 jour:1 zero:4 depending:2 lim:8 self:18 k3:3 k2:5 empirically:1 wishart:19 build:1 towards:1 patterson:2 jsn:7 most:25 significant:1 model:2 stands:2 sornette:1 clear:2 ko:33 physica:1 traditional:1 kp:1 exp:44 physics:1 phenomenon:1 impact:2 parameters:8 distributed:2 subsection:14 factor:3 distributes:1 columns:1 occuring:17 during:4 restart:1 arxiv:5 stirling:2 investigate:3 spiked:2 statist:4 dyck:33 set:27 emax:4 see:20 close:5 visiting:1 various:4 consecutive:2 conditions:3 knowing:2 missing:1 sole:3 distinguish:2 selfintersection:1 both:9 last:3 reverse:1 connection:1 symplectic:1 context:1 pdf:1 whole:6 arbitrarily:2 point:5 simple:2 corresponds:3 whatever:1 dimensional:4 instants:38 simply:2 pr:2 ps:2 ensures:9 pv:3 discriminant:1 due:10 strategy:5 pc:4 reduction:1 asymptotics:6 pe:18 pk:39 extreme:3 po:2 pl:3 covariance:33 determination:1 educ:1 p2:39 p3:1 replaces:2 fur:1 look:1 exponential:3 ǫs:1 while:4 replaced:3 behavior:8 unitary:1 vol:1 encountered:4 reads:1 karoui:4 lengths:1 belong:1 copying:1 grand:1 higher:5 used:15 temporary:1 moment:7 recent:3 lower:1 task:2 qa2:2 analysis:8 edge:44 machinery:2 stating:1 shape:1 intervals:2 λg:3 inference:1 alternative:1 λn:4 cut:1 k1:27 theorem:32 contrary:1 remaining:3 catalan:3 integer:10 formal:1 modifications:5 imposed:1 follows:21 translates:1 separately:1 continue:1 yields:13 terminology:1 mathematical:3 sketch:2 often:1 some:64 back:8 b4:4 understood:2 b1:4 b2:2 b3:2 scale:3 transactions:1 behave:1 proc:1 prob:2 inserting:3 performed:3 processing:1 bi:1 rue:1 step:29 bp:1 integers:1 constraint:3 simulation:1 remains:1 range:1 nsn:2 into:12 appropriate:1 adequacy:1 statistics:3 institut:1 long:3 xpq:1 translate:1 sections:2 sinai:2 jonsson:2 great:2 relaxed:2 line:28 uu:5 characteristic:1 up:33 us:12 2πx:1 similar:6 ki:3 uc:7 associated:15 defined:10 inferred:1 associates:1 defines:1 amounts:1 fixing:1 rewriting:3 application:1 department:1 draw:3 elements:2 problems:3 polynomials:1 generated:2 structure:3 independently:2 correlated:7 methodologies:1 potters:1 required:1 notion:1 requires:2 having:3 once:9 code:1 funct:1 results:15 proposition:42 broader:1 go:5 adjustment:1 compact:4 include:1 electron:1 matrices:49 trm:7 gopikrishnan:1 deals:1 reich:1 eigenvalues:32 smaller:3 odd:43 aγn:2 baik:1 plays:1 giving:2 expressed:1 multivariate:1 deduces:1 respectively:1 spacing:1 objects:3 z4:4 z1:10 z2:5 z3:9 remark:18 technical:7 involved:1 makes:1 formulated:1 scales:2 limn:11 summation:2 apply:1 tools:5 narayana:12 use:6 asymptotic:7 usa:1 commun:2 recalling:1 next:3 few:3 becomes:2 occurred:1 iid:1 iii:2 account:4 ρm:2 obvious:1 publications:1 meet:1 closing:4 proof:47 control:2 weaker:1 purposes:1 high:6 assumptions:6 counting:7 holds:12 instead:1 nips:1 sin:2 cuesta:1 computations:3 lines:5 correspond:3 lβ:2 s1:53 erasing:1 2sn:95 wigner:8 insight:1 mathematicians:1 including:1 ld:4 le:1 lc:1 decay:2 chosen:12 lo:10 li:3 permanent:1 degrees:6 choose:6 communication:1 greater:6 february:1 university:2 l2:3 l1:2 traces:11 related:2 measure:2 separating:1 our:8 special:1 out:2 matrix:24 rev:2 snn:1 socalled:1 announced:2 common:1 diagonal:2 ech:2 approaches:2 bouchaud:1 sinica:1 could:1 times:25 counterpart:5 length:20 assumed:2 davis:3 occurrences:3 reached:3 behaves:1 their:9 final:1 completed:1 exactly:5 completes:1 contribu:1 limiting:16 lemmas:5 visited:4 providing:1 distinguished:2 occurences:2 exhibit:1 need:5 clearly:1 mij:1 min:1 instance:5 combin:1 but:7 preliminary:1 why:1 proceedings:1 fact:13 eigenspectrum:1 bring:1 principal:4 q1:13 o:57 q2:13 based:1 should:3 lemma:36 ambiguity:1 handle:1 means:1 geman:2 joint:14 ones:2 probably:1 determinants:1 qt:9 differential:1 qi:1 fixed:16 view:2 available:2 computed:2 exists:34 correlations:2 closes:1 tend:1 state:3 lue:3 closed:13 progress:2 boundary:1 importance:1 hypothesis:2 distribution:70 instant:34 limits:1 equal:3 2e2:1 admit:1 otherwise:1 ck:4 ci:5 ch:1 co:16 cm:2 cl:3 ca:1 cf:1 walk:1 sequences:4 table:5 erased:1 trajectory:35 genetic:1 yan:1 copied:1 outliers:1 define:5 corresponding:9 finishes:5 c20:2 c9:5 c8:5 c3:7 c2:7 c1:10 repetition:2 c7:3 c6:4 present:1 c4:9 appearance:1 value:9 choices:9 will:9 almost:2 thus:23 vs:1 ave:1 s2n:14 cross:1 largest:39 finite:3 infinity:8 nγn:1 v1:2 v2:1 student:8 distinction:2 identity:2 neural:1 nevertheless:1 well:10 sets:1 usual:2 less:3 moments:24 proximity:2 half:1 numbering:1 obtain:6 underlying:1 paul:1 glue:1 density:1 lattice:2 c18:2 propositions:1 c13:4 c12:5 c11:2 c10:2 c16:2 c15:2 c14:2 sandrine:2 increases:3 press:1 intersection:7 insert:4 sizes:1 δn:5 martin:1 become:1 works:1 xsn:7 therein:4 parity:6 because:2 classical:2 sequence:6 rosenow:1 polynomial:3 choosing:2 lead:5 cσ:2 cτ:2 does:3 assuming:3 intersections:11 conference:1 noise:1 journal:1 expansion:3 cν:3 cγ:2 described:2 noisy:1 about:5 column:2 freedom:7 important:4 tailed:1 introduced:2 thermore:1 enumerative:1 appl:2 var:4 function:4 sequel:2 2ηn:1 repeated:2 construction:3 ho:5 convergence:4 ha:2 truncation:1 count:4 made:7 compute:4 whether:1 below:12 limit:13 problem:1 mechanics:1 universal:1 denote:38 ini:7 inf:1 ing:1 identities:1 functions:3 detail:7 disjoint:1 other:9 details:1 theor:1 stat:1 repeat:1 kinds:1 rule:4 4k:2 4i:1 |
0705.1702.txt |@word proposition:18 σt0:2 consider:9 pointing:1 results:23 gy:4 gx:2 leads:3 p01:13 p00:11 edu:1 consists:7 follow:2 chair:1 research:1 restrictions:1 compact:19 whose:2 c0:3 depend:4 tx:5 bx1:1 graph:2 mutatis:1 tr:4 contained:1 p1t:1 finally:4 tj:4 manifolds:21 elliptic:16 under:13 mutandis:1 x01:28 circumstances:1 tb:1 norm:1 applied:4 conjecture:1 supported:2 deforming:1 expressing:1 orthogonal:7 far:1 could:1 implicitly:2 assuming:1 recursively:1 focus:2 rl:1 corollary:14 every:1 microlocal:3 bounding:1 difference:5 exact:1 deformations:2 condition:26 treating:1 dim:5 ro:11 riemann:3 hamiltonian:1 did:1 solution:12 ri:2 try:1 vector:3 epstein:4 brevity:1 indices:23 bxc:4 rk:2 glued:3 noted:1 rubric:1 neighborhood:19 findings:1 renormalized:1 sloppy:1 estimates:3 direct:1 jump:1 zero:7 pkk:2 further:1 mj:2 odd:6 addition:1 even:7 index:35 what:1 sub:12 invertible:19 diag:1 section:14 while:1 expressed:2 pseudoconvex:47 version:1 above:8 replaced:2 subtracting:1 3g:2 consisting:1 3d:1 satisfy:10 full:1 evaluating:1 degree:7 newyork:1 respectively:8 component:13 equals:1 here:8 understanding:1 following:15 identifications:2 reasonably:1 address:1 path:1 along:10 standard:2 equations:2 appears:2 change:5 obtained:4 interscience:1 remark:9 sobolev:1 study:4 larger:1 allows:1 p2:1 bx0:2 domains:1 proof:23 makes:1 tt:4 65th:1 useful:2 homotopic:1 family:5 unconnected:1 requiring:3 cobordism:4 x02:1 modifying:1 analogous:1 apply:9 establish:2 select:1 clifford:8 embeddability:1 plurisubharmonic:5 use:8 refers:1 projector:71 working:2 prove:8 remains:3 positive:12 h0:4 contains:3 bundles:5 negative:1 their:2 qcc:1 classically:1 assuring:1 m1:1 therefore:10 m2:1 taken:1 type:1 beals:1 minor:1 more:6 introducing:2 formally:1 duality:1 orem:1 becomes:3 operators:24 curvature:2 appendix:1 integrable:6 cases:1 hold:3 iii:1 circle:4 must:4 isomorphism:1 deformed:8 science:2 equation:4 work:3 modified:17 acts:2 huge:1 cocycle:4 values:12 canonically:2 making:2 example:4 deg:7 wojciechowski:1 dedicated:1 degenerate:1 give:2 process:1 choice:1 generically:1 pieces:1 assumptions:3 enquire:1 hyperplane:3 sense:1 phrase:1 fillability:2 evidently:1 taj:1 information:1 scalar:1 end:1 lemma:1 s2:7 s1:31 get:1 american:1 write:2 how:2 sig:2 stipsicz:4 parameter:4 map:1 product:3 de:1 nonseparating:1 algebra:3 may:3 earlier:11 collection:2 reflect:1 consequence:1 levi:5 birthday:1 inst:1 studies:2 coming:1 multiplication:1 subelliptic:4 data:2 cokernel:1 realized:1 gluing:17 imply:5 light:1 author:2 element:4 hypotheses:3 sj:4 si:1 so:18 fundamental:16 jussieu:1 pulled:1 order:5 operations:1 restriction:4 s0:23 deform:4 monvel:1 developed:2 over:8 satisfied:1 p1n:1 symbols:1 paper:9 including:2 k2t:3 hypersurface:9 y1:27 y0:22 satisfies:10 y2:2 its:12 before:2 culmination:1 symmetric:1 ginzburg:1 group:3 fit:1 maps:1 cle:1 fix:1 lj:3 lk:1 forms:2 complex:43 degrees:1 convexity:2 mail:1 main:2 defining:9 deformation:3 formulæ:4 ly:6 non:7 yj:7 greater:1 pjk:1 views:1 integral:2 yc:3 material:2 dai:1 isomorphic:9 often:2 framework:1 p12:1 they:6 instead:1 multidimensional:1 now:7 inducing:3 realize:1 wiley:1 rj:3 represents:2 term:4 dirac:27 2r:1 lies:1 always:1 university:3 sufficiently:4 2g:4 l2:9 each:18 modi:1 2n:2 difficult:1 traces:3 side:4 carlos:1 mean:2 subset:3 spinor:1 domain:5 differential:3 directly:2 simplicity:1 idea:1 related:1 society:1 extended:3 ey:2 ex:1 begun:1 combining:2 separating:6 our:20 operation:1 differ:1 tubular:5 partial:1 special:1 might:4 large:1 shown:3 rp:2 matrix:5 space:17 restricted:1 since:3 induces:2 denotes:5 re:24 acting:9 reo:28 reader:1 denoted:1 formula:15 rn:1 induced:6 correct:1 math:18 shows:12 foundation:2 gromov:4 after:2 theory:1 circumstance:2 routine:1 diagonal:16 quite:1 small:8 reason:2 perturbation:3 doubles:1 earliest:1 monographs:1 rewritten:1 hc2:10 definition:7 pairs:10 r0:28 r1:32 r2:3 applications:1 geometry:1 re0:15 re1:5 turn:2 length:2 choices:1 signature:3 hence:4 agranovich:1 onto:3 first:5 origin:1 xk:2 pn1:1 xc:25 gradg:2 pn2:1 number:2 least:1 calderon:43 yk:1 tame:6 open:3 size:1 given:6 necessarily:1 embeddings:2 nullspace:4 likely:1 indicate:1 introduction:1 adjoint:7 was:1 construct:3 needed:3 assumption:4 draft:1 statement:4 dt2:1 structures:12 conse:1 discussion:2 attach:1 holomorphic:7 grant:1 relationship:1 pseudoconcave:30 reversed:3 immediate:1 part:7 bounded:4 pnn:1 x2:1 natural:1 x0:25 x1:20 than:1 xj:4 finitely:1 td:4 showed:3 princeton:2 holds:2 double:13 require:1 parametrix:6 see:16 hypersurfaces:1 determined:1 letters:1 gives:1 declare:1 decompose:1 projections:1 seminal:1 quence:1 boston:1 ann:2 p22:1 argument:5 generalization:3 compactification:1 endomorphism:1 say:2 adding:1 unlikely:1 need:1 seen:1 ihes:1 null:10 any:9 relatively:1 generalizes:1 constructions:1 jour:1 depending:1 studying:3 self:5 oriented:3 k2:4 k1:4 build:1 analogy:1 griffiths:1 interior:1 canonical:1 tool:2 heisenberg:5 spectral:1 added:1 multiple:1 trace:1 though:3 birkh:1 coordinate:1 attempt:1 regular:1 importantly:1 amongst:2 pair:6 device:1 why:1 appear:4 declaring:1 bound:1 isotopic:3 incisive:1 considered:1 upenn:1 clear:2 stronger:2 chiral:3 occasion:1 left:2 fied:1 notion:2 fact:6 joining:1 pd:11 show:9 tb0:6 charles:1 fillable:1 relation:4 solutions:4 keywords:1 excessive:1 boutet:1 trivial:1 principal:7 q1:4 q0:2 based:1 situations:2 assertion:2 topological:1 should:1 analytic:10 only:7 annals:5 coefficients:2 indeed:4 identification:8 constant:5 preliminaries:2 perturbations:2 do:4 his:1 notation:4 means:1 df:1 michigan:1 express:1 tbj:1 covered:1 actions:1 closely:1 invariant:4 dv:2 applying:3 dt:15 dr:5 geometric:3 closure:2 stability:1 regarding:1 booss:1 covering:1 conditions:14 arxiv:1 calling:1 twice:1 recommendations:1 through:5 arises:2 riemannian:1 kernel:5 requirement:3 set:5 computed:6 attached:1 national:2 banach:1 module:1 bounds:2 relative:26 computes:2 guillemin:2 p21:1 result:23 existence:2 terms:4 outward:1 philosophy:1 surfaces:2 knowing:1 satisfying:4 x12:1 review:1 definite:8 pd2:1 label:1 boundaries:7 mem:1 state:1 kj1:2 various:3 closed:7 between:7 import:1 boundary:133 approach:3 across:1 choose:3 ends:1 jx:1 jy:1 extend:9 complementary:1 modify:2 complement:3 p2n:1 roe:1 however:1 vanishing:2 subbundles:2 hypothesis:4 jj:1 analyzed:1 geography:1 amer:2 ker:3 topology:6 suggested:3 both:4 essentially:5 last:1 repeating:1 limits:1 desired:1 many:3 taking:1 equal:1 constructed:1 homotopy:2 etc:1 connection:1 improves:1 embedding:2 comm:1 genus:5 com:1 otherwise:1 strongly:2 unclear:1 co:4 rpt:1 point:3 simple:3 had:1 kj2:2 cohomology:1 harmonic:7 dimensional:9 distinguish:1 cx:4 simply:2 rpd:1 right:3 sequences:1 cs:2 cr:9 pod:2 ct:1 gratitude:1 pp:13 described:2 second:4 agree:1 would:3 lempert:4 distributional:1 carey:1 noncommutative:1 attaching:1 cauchy:1 combined:2 interest:2 basic:4 pj:3 collections:1 ak:1 empty:1 define:19 describe:1 corresponding:1 embeddable:7 sufficient:1 propositions:1 pact:1 generalizing:1 understand:1 ao:1 derivative:1 c2:2 worked:1 general:5 spin:8 those:2 σn:6 case:27 p0:19 p1:15 splits:1 subsets:2 karshon:1 ǫj:1 pjj:5 value:15 act:2 will:2 contemp:1 near:2 suppose:23 behavior:2 applies:7 property:1 identical:2 unitary:1 orientation:5 coupled:1 almost:28 metric:8 grauert:1 thus:4 them:1 surface:4 ii:2 disjoint:1 itself:4 dual:1 zhang:1 vanish:2 id:98 yl:5 different:1 formalism:1 thereby:1 fibers:3 generic:1 arguments:1 make:2 yn:6 same:2 clearly:5 another:2 parts:4 split:2 runge:1 modification:2 several:13 higher:1 dimc:1 calculation:1 used:5 infinity:1 sequel:2 upon:3 hand:4 action:6 moment:1 harris:1 uses:1 auser:1 infinite:1 recall:1 greiner:1 collar:3 identity:3 relies:2 p10:9 fourier:4 off:2 p11:13 pennsylvania:1 changes:1 variety:1 well:3 analysis:8 thought:1 contact:25 tq1:1 components:33 easily:6 very:1 σt:6 latter:1 usual:2 opinions:1 surveys:1 λp:6 manifold:78 just:1 less:1 moments:1 when:5 resp:1 obtain:8 rest:1 immediately:3 glue:2 yet:1 previous:1 note:3 intersection:2 collars:3 integer:1 conclusions:1 practice:1 conclude:6 seems:2 cc:2 add:1 belongs:4 extends:2 easy:1 theorem:50 usage:1 input:1 extensive:1 remaining:1 euler:2 generalized:22 real:1 acta:2 explained:1 stein:7 isomorphisms:2 showing:1 possible:1 smallness:2 ψ0h:4 know:1 press:2 using:18 bit:1 unique:1 moreover:1 usually:5 formal:2 modifications:2 necessary:1 identifying:1 obvious:2 diffeomorphic:4 spinc:90 cobordant:1 specific:1 lawson:4 either:8 follows:11 expresses:1 reduced:1 mathematical:2 calculus:2 because:5 neumann:21 classical:14 smoothly:4 bavnbek:1 some:6 back:1 certain:1 understood:1 deduce:1 henkin:2 flatten:2 respect:11 pω:2 ourselves:1 ams:1 provided:3 vol:5 avoid:1 opposite:1 providence:2 does:6 decomposition:1 unit:4 provides:2 tends:1 compute:1 adjoints:2 tk:1 bd:1 uniformly:1 equivalent:1 aj:2 bj:2 bk:1 convex:1 melrose:1 relating:1 francis:1 bx:74 properties:11 takes:4 chapter:2 comparison:1 about:3 fillings:5 pt:9 extension:3 algebraic:1 oe:5 theorems:1 o:39 compatible:3 sake:1 range:12 extensions:2 fredholm:16 oy:1 ox:1 publ:1 connected:4 introduced:2 projectors:35 block:8 soc:2 statements:1 subbundle:2 p1e:8 into:12 h1:4 splitting:9 eo:76 three:1 remarks:1 hermitian:2 adjointness:1 references:1 operator:56 ηx:2 spinors:9 assumed:4 strictly:48 there:21 u1:1 long:2 smoothing:13 analyze:1 sections:12 assumes:2 toeplitz:1 function:11 complexified:1 hy:1 complete:5 form:17 szeg:35 regard:1 but:4 principles:1 volume:1 reeb:1 construction:11 ho:1 andreotti:1 pk:1 line:3 true:3 considerable:2 excision:3 admiration:1 made:1 cylinders:2 neighborhoods:2 embedded:1 k1t:3 whether:3 characteristic:2 smooth:12 up:1 us:1 ul:2 below:2 un:1 limit:4 exhaustion:5 uj:3 problem:5 similar:1 called:3 expect:1 detailed:1 taylor:1 proved:6 defined:70 pseudo:1 abstract:1 pseudodifferential:6 ormander:1 denote:35 ap:1 proves:2 exist:1 dθ:2 ind:109 families:1 cbx:2 laszlo:1 defines:15 again:2 functions:5 entirely:2 no:5 amounts:1 generally:3 vanishes:4 field:4 other:3 details:1 normal:1 papers:7 department:1 mathematics:2 genericity:1 belong:1 briefly:2 elements:2 completes:2 multiplicity:1 symbol:6 problems:12 bundle:16 includes:1 replace:1 important:3 augmentation:1 allowing:1 structure:68 implies:10 assume:12 established:2 curve:2 dρ:1 adequate:1 res:1 4g:1 cobordisms:1 original:2 once:1 |
0705.1705.txt |@word limited:1 code:1 schlegel:1 referee:1 represent:2 magnetised:1 results:2 esz:1 four:1 known:1 selection:1 into:1 cameron:2 wynn:1 remarkably:1 disk:1 spike:2 poorly:2 al10:1 whose:1 moshir:4 pj:1 terms:2 ergs:6 acknowledges:1 andalucia:1 canonical:1 young:1 trivial:1 environment:2 finally:1 does:2 present:3 environments:1 under:2 ajl:1 pedersen:3 vej:1 2mass:3 overlaps:3 activities:1 lack:1 mpc:7 zhang:1 very:12 ugarte:3 non:2 every:1 specific:1 infrared:6 nor:1 vlt:5 entire:1 induced:1 cresci:1 presented:1 soderberg:3 positions:4 large:9 solid:1 delivered:1 softer:1 l17:1 fruchter:2 asp:2 science:3 small:2 relation:1 c03:1 inspection:4 noted:1 programme:1 foley:1 revolution:1 faintest:1 foreground:1 trend:1 consistent:2 estimates:1 todd:1 literature:1 hosts:1 past:1 le1:1 postigo:3 ofek:2 concludes:1 currie:1 further:5 copenhagen:2 repeaters:1 λcdm:1 even:6 what:1 software:2 sub:1 rate:11 l15:1 comparable:4 anton:1 section:1 selected:1 mw:2 afterglows:6 uniform:1 current:2 arcminutes:2 experiment:1 above:3 new:1 l1:2 consisting:1 body:1 compact:3 statistically:1 full:3 led:1 lee:2 valle:1 light:1 interplanetary:1 angelini:1 iraf:2 residual:4 here:1 localisation:5 reported:2 m81:2 objects:1 them:4 separation:1 berkeley:1 active:1 iras:6 along:2 strong:3 appears:2 obtained:8 instituto:1 over:1 suitably:1 institute:1 larger:4 funded:1 commonly:1 example:1 peaking:1 private:1 resulting:3 aic:1 suggestion:1 milky:3 prochaska:2 weakens:1 makes:2 dnrf:1 plotted:2 examining:1 prints:6 via:9 useful:2 ratios:1 extrapolations:1 explained:2 ipn:5 marked:3 highly:3 expect:2 put:1 o:1 morphology:1 total:4 select:1 predicted:2 pscz:3 iglesias:2 confidence:3 cosmological:1 would:22 brighter:3 remains:2 likelihood:2 jenness:1 faint:9 arms:1 intense:1 few:3 camera:1 therefore:5 luminosity:5 butler:2 material:1 type:1 until:1 postdoctoral:1 more:10 israel:2 formally:2 elliptical:1 populations:4 conclusions:1 starburst:1 m82:3 emission:10 surprisingly:1 batse:6 visual:1 transient:1 particular:4 localised:5 kulkarni:3 cases:1 must:1 falls:1 high:9 none:2 terada:1 mb:1 seeded:2 tb:1 challenge:1 mn:5 eclipse:1 tanvir:8 reviews:2 levan:22 remain:2 mv:2 mannucci:2 ms:3 following:4 about:4 dec:5 route:1 numbers:1 demers:1 prompt:3 figure:10 give:1 calculation:1 attribute:1 cited:1 near:1 sample:2 renewed:1 way:3 performed:3 distant:4 magnitudes:5 kosugi:2 occur:4 weaken:1 filter:3 united:1 unexpected:1 sphere:1 extinction:1 rather:3 comparing:1 discussion:1 european:2 globular:1 concentration:2 overlayed:2 regions:5 located:3 hjorth:12 cline:1 fourth:1 significance:1 flares:9 absolute:1 isotropic:3 sne:1 galactic:4 information:1 may:18 after:5 derived:1 containing:3 reflect:1 hence:3 catalog:1 produce:3 lay:1 catalogues:1 date:4 truly:1 bloom:7 types:2 mazets:1 short:32 occurence:1 overplot:2 imagers:1 localisations:1 greatest:1 lines:1 xii:1 ghz:1 cosmology:3 emphasise:1 sj:1 extrapolation:2 davies:5 gamma:6 correlation:1 sc:2 subsequently:3 fireball:1 order:4 coziol:3 9ab:1 operations:2 2002ap:2 september:1 indeed:5 astronomical:3 spectral:2 equally:1 produced:1 overdensity:3 paper:1 including:5 statistical:1 existence:1 still:2 kpc:1 its:12 galaxy:38 fir:1 arcminute:1 style:1 difference:1 group:1 thank:2 fit:1 la:4 dr:1 fenimore:1 mulchaey:1 exhibits:1 writing:1 late:2 estimating:1 detected:11 production:1 systems:4 pena:1 isaac:5 main:1 roming:3 image:3 archival:1 associate:1 gmos:2 good:2 greater:3 matches:1 safe:1 enrico:1 13s:1 band:6 course:3 subtraction:1 they:9 rosswog:5 oxford:3 yr:4 hertfordshire:2 discuss:1 association:5 matched:1 tagliaferri:1 february:1 several:5 notable:1 name:1 2s:1 january:1 university:7 identified:3 infer:1 kruislaan:1 bursts:31 manuscript:1 mode:1 reasonable:3 barthelmy:3 found:4 photometry:2 elements:1 typical:1 constraints:2 heavy:1 significantly:6 doing:1 there:6 eg:7 hard:1 idea:1 moretti:1 grbs:19 used:1 2006b:3 year:3 sgrbs:2 laboratory:1 beyond:3 event:8 out:8 leave:1 ultimately:1 patel:1 network:11 space:3 3rh:1 since:7 aptekar:1 research:2 similarly:1 posteriori:1 dominated:1 ra:5 wide:2 rc:1 wainwright:2 instituut:1 krimm:3 issue:1 viable:3 red:1 shows:3 catalogue:3 clustering:1 creating:1 provide:3 theory:1 offsets:1 magnetars:1 kennicutt:2 galaxies:31 surveys:1 possibility:1 standard:4 cut:1 approaches:1 california:1 imaging:2 wfcam:7 uncover:1 ask:1 8s:1 estimate:5 beginning:2 telescopes:2 m51:4 perform:1 subtractions:4 created:1 flare:10 could:4 area:1 days:4 furthermore:2 times:1 counterpart:2 paramo:1 disturbed:1 place:4 massive:5 leading:2 kingdom:1 locating:1 2005a:5 south:2 first:4 origin:3 already:3 features:1 probability:8 feel:1 sn:7 number:8 linking:1 l36:1 clear:1 enlarged:1 smaller:1 approximately:1 another:1 spanish:1 jeltema:1 fluxes:2 angular:1 size:1 2005b:2 given:5 necessarily:1 indicate:1 introduction:1 revealed:2 top:1 moderately:4 system:2 least:5 their:5 distinctly:1 accretion:1 rates:1 observations:30 show:2 ryder:1 white:2 scheme:1 southern:1 l13:1 recovered:1 gives:1 mini:2 stars:6 relative:1 uvot:1 took:1 plane:4 optical:21 dozen:1 somewhat:4 l9:1 occurring:2 progenitors:2 17s:1 than:11 intrinsically:1 population:2 tonoise:1 king:3 observatory:1 prep:3 behaviour:2 petrosian:1 enabled:1 likely:7 limiting:4 actively:2 were:12 radius:3 maiolino:1 exhibit:2 function:2 fashion:2 false:1 diameter:2 appreciate:1 radial:1 mind:1 locations:3 curves:1 chapman:2 randomly:1 say:1 variable:4 ras:8 close:4 need:1 north:1 seem:1 null:1 apparently:2 any:16 novae:1 collapse:3 lie:9 adelberger:1 responsible:1 mechanism:1 oriented:1 sciences:1 2006a:4 pparc:1 forming:3 finding:2 so:7 many:6 explanation:1 channel:1 accuracy:1 circles:1 blue:1 added:1 relatively:11 trace:2 centre:6 object:1 reach:4 chart:1 accurately:1 did:2 most:4 printed:1 significant:3 scripts:1 buried:1 acknowledgements:1 class:1 appear:2 latex:1 7al:1 radioactive:1 gorosabel:2 surprising:1 average:4 hurley:11 implications:2 inferred:4 km:1 ramirez:7 curie:1 positional:3 formation:14 principle:1 clean:1 parenthesis:1 senior:1 left:1 typically:3 lying:1 precise:1 signatures:2 set:1 eiso:4 leicester:2 text:1 detection:1 random:1 osborne:1 juliane:1 discovered:3 fors:2 bright:16 radio:2 m31:2 campana:4 especially:2 epochs:3 find:2 nominally:1 µm:4 giant:16 specifically:1 based:3 knowledge:1 parameters:1 merger:5 proportion:3 ox1:1 negligible:1 should:8 conselice:2 failed:2 only:12 usov:2 black:1 condon:1 rich:2 various:1 circle:27 local:9 pointed:1 ruiz:7 contenders:1 lived:1 do:3 predict:2 explosion:1 dk:1 means:2 hete:3 remedied:1 de:5 sf:1 bear:1 yielded:2 community:1 cannot:1 words:1 probably:1 during:3 t90:3 reveal:1 bat:16 exhibiting:1 covering:1 denmark:1 arxiv:13 ministry:1 investigate:1 processed:2 though:1 contain:1 release:3 through:2 previous:2 mjy:1 mergers:7 view:1 reveals:2 uv:1 nir:1 ser:2 observer:1 burst:26 acquired:1 lifetimes:1 frame:3 box:5 hδ:1 maximum:2 plausible:7 ara:1 see:7 individual:3 college:1 result:2 converting:1 fail:1 contains:4 luminous:3 jy:8 closer:1 instance:1 aros:1 supported:1 ways:1 subsequent:1 review:2 artificial:1 colours:3 outside:3 determined:1 identification:1 between:4 progress:2 avoidance:1 template:3 email:1 discovery:2 variability:1 03h:5 wd:3 recently:1 spectroscopy:1 parent:1 nature:16 originated:2 supernova:6 however:12 jr:1 spectroscopic:1 lightcurve:1 ukirt:3 hypothesis:1 key:1 awards:1 kev:3 vri:1 jg:1 swift:18 originates:2 paranal:1 received:1 last:1 limits:9 spectra:6 minutes:1 region:3 uncertainty:1 hours:4 against:1 april:1 merging:2 figures:1 ajc:1 halo:1 quite:2 estimation:1 whole:1 nearby:5 originating:2 31m:5 cm:1 point:4 sky:1 ca:2 each:6 cf:1 harbour:1 coincidence:2 chincarini:1 sxc:2 simply:1 coordinates:10 framework:1 table:6 li:2 consider:1 ct:1 fors1:4 unusual:3 fors2:16 described:3 µjy:1 second:1 instrument:3 addition:3 west:1 cv4:1 due:9 been:21 yam:5 much:2 progenitor:4 expected:6 ph:6 outliers:1 board:1 lupton:2 field:6 certainly:1 partly:1 frontera:1 both:6 della:1 formed:2 search:2 studentship:1 spectrum:1 extrapolating:1 gal:5 l125:1 dearth:1 data:2 astron:1 kicks:1 general:1 djorgovski:1 former:1 spain:1 nrt:1 case:6 uncertain:2 look:1 romano:1 coventry:1 might:4 nakar:3 originate:5 nski:1 castro:3 sgrs:10 will:1 dusty:1 while:6 gemini:1 ongoing:1 kick:2 error:37 fainter:3 sgrb:1 unlikely:3 real:1 penprase:1 credence:1 almost:1 ir:8 thus:10 hatfield:1 apjs:1 ii:2 cluster:16 itself:2 extrapolated:2 contract:1 conf:2 seen:5 limit:5 ic:50 id:1 bepposax:1 comments:1 binary:2 different:5 education:1 perhaps:2 l59:1 radiation:1 same:3 clearly:2 shorter:1 epoch:2 parts:1 potentially:1 positively:1 survey:1 l83:1 ray:13 events:4 neutron:2 higher:6 shortlived:1 fairly:1 satellite:1 extended:1 turatto:1 jakobsson:2 economou:1 companion:1 constraining:1 v2:1 dust:2 fellowship:2 recent:2 costa:1 lower:5 kouveliotou:1 sed:1 scenario:1 older:2 macro:1 colour:1 nonetheless:1 well:5 roughly:3 analysis:4 bohr:1 thought:3 directly:1 edge:3 residuals:3 simulated:1 firstly:1 position:5 model:2 preference:1 distances:2 priddey:2 just:1 less:4 being:4 observed:11 obtain:1 sources:6 identify:1 thanks:1 using:9 ωm:1 alternative:4 reality:1 alignment:2 1800s:1 note:1 impetus:1 rapid:1 timescale:1 candidate:5 density:3 absorption:1 regarded:1 tirado:2 had:4 exclusively:1 day:2 source:7 location:9 grating:1 compares:1 east:1 expelled:1 momentum:1 majority:1 associations:1 sgr:20 march:2 depends:1 bands:2 frail:3 psf:1 possible:4 period:1 dark:2 possibly:3 boxes:1 natal:2 indicative:1 mon:1 background:1 xrt:4 press:1 immediately:1 part:1 accepted:1 projects:1 ruled:2 apj:14 aramo:1 approach:1 like:5 sizes:1 meif:1 signal:1 brightness:1 niels:1 separately:1 flux:5 keble:1 yields:3 either:5 malesani:1 night:1 rarely:1 28s:1 soft:4 reduced:2 gauge:1 sign:1 because:1 old:1 often:1 hirst:1 some:6 dwarfs:1 steidel:1 understood:2 towards:1 b0:1 meszaros:2 sight:1 redshifts:3 duration:17 little:2 undetected:1 provided:2 scale:2 pagani:3 nuclear:1 paczynski:1 broad:1 lend:1 fox:8 integration:1 per:1 conservative:2 mineo:2 magnitude:6 provides:2 assuming:3 eso:2 indication:2 moderate:1 alard:2 locate:3 core:1 paczy:1 frederiks:1 slight:1 selecting:1 equivalent:1 palmer:4 bh:4 use:1 constructive:1 stellar:5 host:10 although:25 offset:3 occured:1 post:1 obscured:2 properties:6 intersects:1 cappellaro:1 comparison:3 pipeline:1 golenetskii:3 rare:2 face:1 universe:5 discussed:2 arcmin:2 7rh:1 page:2 range:3 transients:2 nucleus:1 apjl:6 mean:1 sept:15 road:1 peak:4 panagia:1 berger:9 soc:1 own:1 letters:1 redshift:13 previously:2 communication:1 h0:1 within:26 three:1 accommodate:1 lies:5 appropriate:1 gehrels:7 references:2 amsterdam:1 refined:6 outskirts:1 22s:1 telescope:5 unambiguous:1 pannekoek:1 marie:1 span:1 log:1 examples:1 metzger:2 normalised:1 support:3 initial:2 question:1 spiral:1 long:7 start:1 l117:1 low:7 fraction:9 astrophysics:7 was:21 energy:7 wijers:1 naturally:1 hz:1 repeater:2 complete:2 form:2 enough:1 gammaray:1 warwick:2 but:7 astro:6 taken:1 repeated:1 100mpc:1 rays:1 mnras:12 line:3 true:1 considerable:1 subtracted:2 volume:2 made:2 ut:2 gravitational:1 burrows:8 up:1 maries:1 placed:2 below:3 those:12 uk:5 corrected:1 distribution:5 similar:8 called:2 distance:8 detailed:1 fluence:1 ac:1 later:1 associated:13 050509b:3 abstract:1 aj:2 deep:8 evidence:4 images:8 single:2 diverse:1 rule:2 file:1 our:15 lifetime:1 work:3 intra:1 physical:1 functions:1 6th:1 nl:1 granada:1 dotted:1 no:7 dashed:1 ejected:1 when:1 slew:1 tight:1 other:7 grb:74 details:1 appearing:1 program:1 department:3 shin:1 ns:21 test:1 ogasawara:1 optically:1 apparent:1 star:17 exp:1 separate:1 models:3 astrofisica:1 durations:1 searched:2 convincing:1 shown:10 includes:1 grupe:3 chance:6 important:2 afterglow:8 allowing:2 additionally:1 dissipation:1 devillard:2 astronomy:2 structure:2 exposure:1 lane:1 implies:2 l60:1 physics:4 factors:1 holes:1 parsons:2 waveband:1 having:1 reports:1 mass:6 fact:1 time:6 cores:1 nuclei:1 parola:4 original:1 once:1 |
0705.1706.txt |@word gt:2 sci:1 gr:4 alg:1 global:1 abramovich:1 dumas:2 gf:4 proposition:3 generalize:1 edu:2 disk:1 centers:5 consider:1 compact:6 whose:4 equivalence:1 unanswered:1 γn:5 under:2 atlas:1 maryland:1 worth:1 norm:1 brown:3 conjecture:1 stud:2 corollary:1 every:1 invent:2 riemann:8 irreducible:9 notes:1 michael:3 nostrand:2 discrete:3 epstein:1 fl:1 shiga:1 says:2 variables:1 zero:2 irreducibility:1 dynamics:1 bass:1 richard:2 section:1 schwarzian:3 version:1 suspect:1 above:1 blur:1 replaced:1 construction:1 increasing:1 acknowledgments:1 splittings:1 full:1 aten:1 never:1 component:5 here:2 desired:1 groups:10 along:4 principle:1 equations:1 obtained:1 sending:1 leaving:1 prior:1 simultaneous:3 bol:1 adv:1 fourier:1 studies:1 quotient:1 via:1 projection:1 marked:5 texts:1 durham:1 noncompact:1 apply:1 univ:4 unit:1 clifford:1 use:2 haken:3 would:2 prove:1 remains:2 contains:6 negative:1 their:1 noting:1 associated:1 more:4 flat:1 kinokuniya:1 becomes:2 warn:2 berlin:3 surface:3 particular:1 known:3 projective:26 iii:3 annuli:2 must:1 md:1 springer:4 isomorphism:1 ma:3 tokyo:1 ml:1 work:1 mi:2 kamishima:1 dei:1 vs:9 values:1 codimension:1 morgan:3 following:6 trans:1 example:1 proof:9 figure:2 pleated:1 states:1 hassler:1 performed:1 sense:1 tan:1 dennis:2 guarantee:1 acylindrical:2 s1:5 holds:2 write:1 maps:4 nontrivial:1 low:1 pure:2 instead:1 verlag:3 obius:1 teichm:9 map:22 product:2 mar:1 mat:1 singular:1 may:5 collection:1 diagram:3 xc0:5 inst:1 representations:8 data:1 types:1 realized:1 dσm:1 natural:2 varieties:5 whenever:1 irwin:2 su:1 element:2 hypotheses:2 si:2 so:5 sn:6 fundamental:1 representation:3 hol:23 sd:1 hom:7 holomorphicity:2 produces:1 over:1 interpreted:1 stability:1 cambridge:3 london:2 mentioned:1 satisfies:2 still:1 its:5 tending:1 group:4 thank:1 kapovich:4 affine:4 tori:2 uniformization:5 forms:1 derivative:2 defining:1 image:8 versus:1 cusp:1 lipman:2 curtis:2 hyperbolization:1 dan:1 number:1 slicing:2 cutting:1 hyperbolicity:1 identically:1 now:2 s0:1 structural:1 several:1 porti:1 always:2 university:1 drop:1 properness:2 gallo:3 each:4 found:1 characterized:1 constraints:1 subset:1 domain:1 differential:4 completions:1 ee:2 related:1 elementary:1 our:2 geodesically:1 special:2 out:2 reid:2 shown:3 space:20 parabolics:4 since:8 induces:3 denotes:1 content:1 contained:3 daniel:1 geom:2 kent:2 reader:4 lecture:1 induced:2 suffices:2 ri:1 math:26 shows:2 uber:1 theory:3 divergence:1 given:4 admits:5 homeomorphism:1 demanding:1 ask:1 geometry:6 transition:1 david:3 length:2 hence:1 think:1 first:2 appeals:1 xn:9 manuscript:1 xc:33 quasiconformal:2 geodesic:2 hans:1 enumerate:1 xr:7 neighborhood:1 precisely:1 open:4 ont:1 little:1 cartesian:1 moduli:1 hyperbolic:15 introduction:1 unknown:1 xik:1 indicate:1 appl:1 zeros:1 john:2 structures:18 gives:1 attach:1 holomorphic:7 incompressible:3 park:1 part:3 authors:2 x1:1 than:1 center:2 begins:1 finitely:1 nathan:1 holland:1 princeton:2 iteration:1 namely:1 xi1:1 xi2:1 contrary:2 punctured:1 college:1 igor:2 boston:3 ann:9 argument:2 generalization:2 say:1 parameterized:3 iw1:1 need:3 any:7 karl:1 diffeomorphism:1 issue:1 minimally:1 depending:1 aside:1 note:5 instance:1 lifts:1 square:1 take:1 interior:7 new:4 maskit:2 trace:1 though:3 goldman:7 birkh:1 algebraic:12 regular:3 connected:6 parameterizes:1 nothing:1 measured:4 pages:7 ebrique:1 considered:1 torus:1 stronger:1 fritzsche:1 countable:1 proceedings:1 points:5 absurd:1 assistance:1 fact:4 show:1 albert:3 supported:1 multicurves:1 implying:1 spaces:4 postdoctoral:1 mengen:1 grafted:1 fenn:1 topological:4 analytic:10 only:4 marden:7 black:1 equipped:1 parabolic:4 local:1 toronto:1 his:1 means:1 embeds:1 shalen:4 trees:1 ones:1 drawn:1 tanigawa:8 lamination:1 boundary:5 closure:1 gray:1 arxiv:2 grλ:9 consisting:1 aspects:2 miles:2 schemes:1 common:1 qf:8 analytical:1 homeomorphic:1 nγ:2 requirement:1 set:19 ser:3 fellowships:1 peripheral:1 differentials:3 closures:1 edition:4 see:19 geometrically:1 descriptions:1 w1:1 discussions:2 progress:1 polymorphic:1 hejhal:1 wonder:1 surfaces:8 birational:1 bernard:1 attempting:1 boundaries:1 state:1 gaga:1 closed:7 between:1 invariant:2 geometric:5 contradicting:2 terms:1 vertical:1 wn:2 were:2 jr:1 york:4 hypothesis:1 key:1 amer:5 topology:4 both:3 σn:2 σm:11 many:4 taking:1 infinitely:3 equal:1 analytique:1 poincar:1 context:1 distinction:1 passing:1 orientable:2 co:1 cn:1 point:3 sullivan:4 brook:2 harmonic:1 dimensional:2 simply:1 ahlfors:2 proved:1 throughout:1 smith:1 conference:1 transformations:1 second:2 marc:1 union:4 create:1 locally:3 due:2 sl2:13 int:1 much:1 basic:2 topics:1 generating:1 arises:1 corresponding:1 valuations:1 restrictions:1 concerning:1 lift:1 representative:2 nonconstant:1 bull:1 reinhold:1 general:1 duke:2 manifolds:9 case:1 klaus:1 disconnected:3 subsets:1 developing:1 coventry:1 deformation:1 will:4 suppose:4 monodromy:2 behavior:1 conformal:4 procedure:2 serre:2 cylinder:1 orientation:1 vol:1 metric:3 grauert:1 thus:1 iw:2 iv:2 ii:2 disjoint:1 ik:1 obstacle:1 conf:1 quasifuchsian:3 sits:1 id:1 containing:2 inc:2 author:1 lengths:1 geometrization:2 same:2 tells:1 complex:15 arguments:1 finite:5 infinity:1 embedding:1 lie:1 i1:1 i2:1 functions:5 culler:1 subvariety:7 hulls:1 auser:1 characters:5 mexicana:1 infinite:1 identity:1 subgroups:2 kleinian:5 no:2 well:1 academic:1 gunning:1 without:3 extremal:1 components:8 sets:6 jean:2 dimension:7 left:1 bending:1 surveys:1 manifold:8 less:1 generally:1 obtain:2 underlying:1 thanks:1 uller:9 λn:2 letting:1 oriented:4 cut:2 preprint:1 fuchsian:9 wei:1 conclude:1 character:10 simple:1 setting:1 treatment:1 otal:1 theorem:43 psl2:3 earthquakes:1 euler:1 real:4 acta:2 remmert:2 march:1 stein:2 thurston:7 earle:1 mathematics:3 press:4 intersection:1 grenoble:1 helpful:1 follows:6 orlando:1 homeomorphisms:1 eee:1 essential:2 specifies:1 right:1 classical:2 sequence:2 some:3 pierre:2 acad:1 respect:1 proper:4 peter:3 zariski:3 ourselves:1 lars:1 slice:4 dense:2 nonempty:1 demonstrates:1 providence:1 singularit:1 linearly:1 provides:1 iwn:1 three:1 proc:2 forgets:1 grafting:6 refer:2 inserting:1 translated:2 permitted:1 injective:1 submanifold:1 chapter:3 about:1 shafarevich:2 discussed:1 o:1 page:1 compatible:1 range:1 chow:3 laminations:2 kra:2 stony:2 mathematical:1 soc:6 mcmullen:4 inclusion:4 unbounded:1 into:4 nsf:1 locus:2 lies:2 holonomy:7 references:1 operator:1 amsterdam:1 atoroidal:2 van:2 strictly:1 there:7 question:3 class:1 quadratic:4 handbook:1 charts:1 liang:1 mappings:1 was:1 naturally:1 function:5 north:1 complete:4 bers:8 analyse:1 but:1 volume:8 properly:4 russian:2 lectures:1 etrie:2 embedded:3 characteristic:1 smooth:5 up:1 us:2 2πn:3 called:2 detailed:2 constant:3 defined:3 ah:3 convex:1 denote:5 eom:2 proceeds:1 constructed:1 nj:1 faithful:1 variety:16 joan:1 commutes:1 when:3 detail:1 graduate:1 application:1 dunfield:1 department:1 cp1:2 conclusion:1 picture:1 accidental:4 degenerations:1 prepared:1 william:2 generated:1 bounded:3 needed:1 structure:12 implies:4 cpn:1 assume:1 factors:1 curve:1 together:1 weights:2 robert:1 whitney:2 |
0705.1707.txt |@word partial:1 consider:4 funct:1 magnetic:1 global:1 edu:1 consists:1 perturbations:2 contributions:1 gj:6 compact:2 whose:1 simon:2 deterministic:3 interactions:1 γj:18 rightmost:1 under:3 straightforward:1 very:1 rise:1 translations:1 account:1 seemingly:1 corollary:1 every:4 difference:3 condition:3 entire:2 school:1 presented:1 wegner:14 limℓ:1 ri:2 large:4 discrete:3 small:7 eigenvalues:2 anal:1 originally:1 upper:4 smaller:1 disordered:1 zd:11 estimates:2 approximation:1 go:2 zero:2 further:1 spectral:5 lokale:1 appear:2 contemp:1 leschke:2 celebrated:1 expressed:2 above:2 sup:1 obvious:1 learned:1 increasing:1 realizations:1 spacing:1 here:3 fairly:1 address:2 along:4 strong:1 equations:1 change:2 extreme:1 remark:4 suitably:1 studied:1 allows:2 pastur:1 periodic:1 poisson:1 pick:1 domains:1 hospitality:1 der:1 65th:1 formulated:1 spatially:1 family:1 tools:1 use:1 proceed:1 would:1 prove:3 positive:10 chk:2 finally:1 muller:4 metzger:1 therefore:1 length:2 associated:2 type:1 introducing:1 binding:1 operators:17 odinger:22 validity:1 berlin:1 everywhere:1 particular:1 known:3 hold:2 none:1 valued:1 recall:1 equation:1 work:1 reviews:1 remain:1 cergy:1 values:1 ms:1 lipschitz:2 following:2 arrive:2 example:1 proof:7 dn:1 dedicated:1 give:2 expanding:2 states:33 lϕ:2 taking:1 sense:1 counting:1 absolute:1 needs:1 end:1 klein:1 holds:3 range:1 georg:1 write:2 nontrivial:1 pure:1 answer:1 instead:1 obeys:1 mueller:1 ρmin:3 fu:1 fran:1 after:1 consequence:1 birthday:2 physik:2 constants:3 whenever:1 spectra:1 hypotheses:2 switch:1 so:1 decreasing:2 alloy:1 lλ:3 michel:1 restriction:2 aforementioned:1 indeed:1 over:3 years:1 stability:1 paper:1 through:1 thesis:2 hypersurface:1 existence:3 satisfies:2 still:1 its:5 ld:4 thank:2 energies:2 fix:3 systems:1 derivative:3 into:4 versus:1 non:1 pontoise:1 introduce:1 mention:1 tails:1 identically:2 multidimensional:1 now:2 nor:1 continuum:6 eigenvalue:2 term:5 several:1 university:1 level:3 2d:21 universita:1 l2:1 each:2 universit:2 side:2 bond:1 domain:1 ej:5 energy:6 idea:1 kℓ:7 society:1 veseli:2 dωy:1 measure:6 special:1 acknowledgment:1 space:2 goe:1 furthermore:2 since:3 denotes:1 rd:2 contained:1 print:1 ℓd:10 issue:1 integrated:14 math:14 theory:6 localization:5 frank:1 differ:3 free:1 completely:1 surely:1 estimate:7 hand:1 e1:15 combes:3 e2:15 definition:2 dirichlet:7 derivation:1 american:1 abuse:1 hence:2 strictly:6 first:2 xj:5 fischer:1 probability:4 ignored:1 variables:4 number:1 rank:4 done:1 another:1 size:1 given:4 perturbation:4 uky:1 adjoint:2 theoretische:1 least:1 assumption:1 types:1 behaved:1 insightful:1 e0:23 bochum:1 centered:1 completed:1 continuous:8 part:1 authors:1 translation:1 operatoren:1 finitely:1 kind:1 require:1 depends:2 elementary:1 gives:1 germinet:1 remained:1 boston:1 lλ2:1 argument:5 lλ1:2 say:2 manner:1 null:1 any:1 min:3 lim:5 latter:1 converges:1 note:4 k2:2 trλ:2 potential:1 take:4 εj:2 interior:3 ρmax:2 unperturbed:2 cube:3 trace:1 birkh:1 germany:2 jean:1 average:1 partition:3 cover:1 graphs:1 proceedings:1 points:1 χb:1 occasion:1 physics:1 away:3 quantity:1 incorporate:1 festschrift:1 german:1 random:20 purely:1 fε:23 indicator:1 hλl:6 distributed:2 written:1 only:5 going:1 local:3 oct:1 continuity:5 do:2 his:4 notation:1 get:2 fractional:1 expectation:1 next:2 dx:1 positivit:1 platz:1 densities:1 covering:1 arxiv:2 fixes:1 lexington:1 whether:1 fixed:2 view:1 hλ:2 set:5 exists:4 unpublished:1 see:5 result:2 uller:3 discussions:1 ergodicity:1 error:2 positivity:2 klopp:1 monotone:3 vol:2 enough:2 closed:1 invariant:1 boundary:4 conditions:3 terms:2 august:1 optimal:1 figotin:1 complement:1 restricting:2 however:3 hypothesis:1 key:1 article:1 amer:3 problem:1 concentrated:1 essentially:5 cubes:5 many:2 region:1 according:1 chosen:1 uni:1 kirsch:5 aizenman:2 cl:2 poissonian:1 dimensional:6 werner:1 respect:5 second:1 ensures:1 decoupling:2 addition:1 barry:1 laplacian:5 strategy:1 pf:2 fluctuation:1 ph:2 define:1 ergodic:1 arises:2 molchanov:3 subspace:1 spectrum:6 observe:2 mail:2 affirmative:1 those:2 case:8 multi:2 straight:1 kentucky:2 will:3 minami:4 ruhr:1 suppose:1 hislop:7 couplings:1 k1:2 almost:9 averaging:1 thus:3 site:3 canceled:1 ij:1 properties:1 different:3 perform:1 same:2 arguments:1 finite:11 independent:3 used:1 cubic:1 phd:2 moment:1 delicate:1 kim:2 potentials:5 infinite:1 recent:1 lower:15 schr:22 well:3 honor:1 de:3 model:13 quotient:1 self:2 latest:1 obtain:3 intervals:2 λj:1 alternative:1 macroscopic:3 λl:6 lebesgue:14 density:37 auser:1 point:4 seems:1 except:2 lattice:5 add:1 other:2 extends:1 developments:1 theorem:9 generalized:1 real:1 rescaled:1 warzel:1 big:1 jacobian:1 possible:1 know:1 mol:2 using:1 vλ:2 modifications:1 dµl:1 follows:2 lacroix:1 arbitrary:1 ivan:1 hund:1 disorder:2 essential:2 replacement:1 mathematical:3 because:2 methods:1 sequence:2 absolutely:6 some:6 springer:1 strongest:1 moreover:1 peter:3 happens:1 carmona:1 dense:2 cois:1 lead:1 integration:2 providence:2 does:1 provides:1 proc:2 inserting:1 slight:1 symp:1 although:1 hilbert:1 cδ:5 about:1 usa:1 commun:5 60th:1 o:1 informing:1 whence:1 supervised:1 stand:1 act:1 efforts:1 consequently:2 duke:1 soc:3 unnoticed:1 unbounded:2 h0:2 integral:1 bound:17 negative:1 lies:1 right:3 references:1 been:1 operator:8 proportional:1 abel:1 imposed:1 ηy:3 statistics:2 additional:3 area:1 support:5 there:4 question:2 specifically:1 why:1 width:1 anderson:11 was:2 assumes:1 naturally:1 function:6 tight:1 complete:2 form:1 differences:2 but:4 gaussian:2 volume:6 russian:1 he:2 ωy:1 ωx:7 partitioning:1 supp:2 inside:1 smooth:1 bounds:2 us:3 below:2 limit:6 distribution:3 similar:3 called:1 obtains:1 uber:1 required:1 constant:4 percolation:1 defined:2 certain:2 abstract:1 specified:1 am:2 general:1 ch:2 single:3 proves:2 dλ:2 inf:1 hamiltonian:2 proceeds:1 regime:1 functions:1 proofs:1 vanishes:1 application:1 valid:1 department:1 mathematics:1 conclude:1 nonzero:1 stat:1 denote:1 models:2 αej:2 uniformly:1 important:1 bounded:9 ess:2 lifschitz:1 structure:1 dimensions:1 independently:1 implies:2 coupling:2 assume:3 interval:5 volumes:1 original:1 |
0705.1709.txt |@word ui:4 homomorphism:8 consider:4 pointing:1 global:6 results:6 invent:1 gx:1 proposition:1 computation:1 consists:2 partial:2 expressions:1 toric:33 soc:1 whose:9 depend:1 re:1 equivalence:2 contained:1 tn:7 finally:5 tk:3 th:7 under:4 td:3 include:1 aut:1 p2:1 rtn:1 very:1 induce:1 choice:1 corollary:3 fan:22 rueda:3 exact:7 condition:1 annihilated:2 immediately:1 level:1 irreducible:6 involution:5 vector:16 zdi:4 recall:7 anal:1 cox:1 ups:2 programme:1 upper:1 zn:11 zi:15 zj:1 zd:6 direct:2 sign:2 second:1 zx:1 irreducibility:1 concludes:1 further:1 carlo:7 zr:7 even:1 diag:4 section:6 while:2 version:1 above:7 consisting:2 give:1 degree:11 respectively:1 qλ1:1 component:1 jens:1 here:3 groups:6 address:1 represented:2 respect:1 z1:3 change:3 obtained:5 sending:3 remark:5 divisor:17 algebra:16 suitably:1 shift:1 study:2 studied:2 permutation:1 action:7 fourier:10 changes:2 quotient:7 composed:1 via:4 family:2 multiindex:1 equivariant:1 annihilator:1 apply:1 resolutions:2 linearly:1 berest:2 use:2 would:1 prove:1 remains:2 positive:1 contains:2 bundles:6 negative:1 next:2 depicted:1 going:1 therefore:2 taken:1 means:4 more:3 giovanni:7 operators:30 berlin:1 particular:4 known:1 projective:11 cases:2 stafford:2 me:11 obeying:2 springer:1 isomorphism:18 νr:2 science:2 der:1 work:2 mi:10 labeled:2 infinitesimal:2 values:9 codimension:5 mr:10 following:2 nonsingular:1 trans:1 example:3 fulton:1 proof:12 lχ:4 omit:1 want:1 figure:1 abelian:1 discussed:1 permutations:1 assumptions:4 cartan:3 hyperplane:1 dominant:1 spanning:1 νn:1 νi:22 occur:1 verlag:2 rays:2 end:1 rather:1 s2:2 s1:2 acts:10 maps:5 pure:1 parameter:1 obeys:1 map:13 description:6 singular:4 replacing:1 algebro:1 cohomologies:2 act:1 singularities:4 mapping:1 collection:1 studies:1 multiplication:1 fi:17 natural:1 varieties:34 whenever:1 sr:2 author:1 descends:1 element:3 si:13 fp6:1 so:6 sn:2 fundamental:4 discussion:1 representation:1 order:3 restriction:4 hom:4 numbers:1 over:10 satisfied:1 already:1 through:2 satisfies:1 its:2 roots:1 group:11 thank:1 τi:4 matrices:6 sheaf:3 affine:12 tori:1 coordinates:14 roever:1 fig:2 mail:1 image:5 ideal:3 maximal:3 them:2 university:1 introduce:1 framework:1 a0i:2 they:6 singularity:1 now:6 discuss:2 nor:1 verify:1 several:1 picard:1 goncharov:1 invariants:1 λqi:1 annals:1 identified:1 realise:1 each:13 monomials:9 higher:2 homogeneous:8 differential:31 ei:9 weight:22 zurich:2 ergebnisse:1 related:14 our:5 happen:1 special:3 out:1 space:16 electronic:1 since:7 induces:3 denotes:1 rd:2 may:1 acting:3 geom:1 rational:3 formula:2 get:2 induced:1 ri:1 math:6 foundation:2 linear:1 written:1 contain:1 diagonal:1 free:1 standard:2 admits:1 switzerland:1 reason:1 yuri:1 org:1 md0:16 definition:2 unique:1 geometry:1 qm:5 transition:4 david:1 counterpart:1 omin:1 iλ0:3 δij:1 hence:1 first:6 origin:4 xi:10 xn:4 computations:3 variables:1 number:3 rank:5 transform:7 multiplying:1 relations:3 representations:2 ring:9 open:8 george:1 xt:1 given:3 ian:2 rewritten:2 similarly:2 introduction:4 adjoint:1 twisted:9 least:5 their:3 assumption:4 statement:1 exponents:2 gives:4 shifted:1 mostly:2 exactly:1 part:3 module:17 authors:1 x1:6 representing:1 summarizing:1 coefficients:2 ential:1 kind:2 princeton:2 holds:4 was:1 see:10 matter:1 classes:3 monomorphism:1 were:1 powers:1 qµ1:3 abs:1 correspond:2 say:2 need:2 take:2 recover:1 admitting:1 any:12 viewed:3 brylinski:2 lie:4 wilson:1 constructions:1 min:1 studying:1 subdivisions:1 note:1 k1:8 lifts:2 2006a:1 generalized:1 lectures:1 multiple:1 normal:1 denoting:2 birkh:1 algebraic:3 regular:16 automorphism:6 nothing:1 marie:1 class:4 zki:1 laurent:1 observation:1 kd:6 considered:4 kj:1 ki:23 kn:2 face:2 curie:1 reflections:4 subgroup:2 sum:1 fact:2 enigma:1 show:4 german:1 supported:1 notations:1 spaces:7 solutions:1 decompositions:1 trivial:7 find:1 d0:25 d1:1 q1:6 q2:2 basel:1 assertion:1 lemma:9 only:14 explicitly:2 generators:12 subsection:3 rich:1 parabolic:1 joseph:1 local:2 dn:2 do:26 his:1 dj:3 subspaces:1 di:24 subtorus:1 dd:1 between:1 cochain:1 progress:1 neither:1 areas:1 closure:3 runs:2 qr:13 covering:2 fields:3 transposition:1 arxiv:2 yield:1 underlying:1 cr:1 mapped:1 qi:40 qk:2 qj:1 explanations:1 traceless:1 qn:6 kernel:11 set:7 modulo:4 computed:1 national:1 closures:1 facts:1 namely:8 actively:1 result:3 w1:1 discussions:1 polyhedral:1 qµ:2 exponent:2 coboundaries:2 subsequent:1 review:1 rings:3 representatives:2 symmetric:1 fans:9 luc:1 µi:9 closed:1 simplest:2 αi:1 invariant:9 geometric:2 conditions:3 knowing:1 multiplied:1 notice:4 terms:3 extend:1 wn:1 complement:6 however:1 wi:1 jm:2 vanishing:1 inclusions:1 comm:1 french:1 amer:1 valid:1 uσ:5 topology:1 concentrated:2 both:4 σi:10 last:1 always:3 annihilators:1 many:1 mrtn:1 equal:1 contract:1 called:1 und:1 symplectic:1 interesting:1 eth:1 algebren:2 otherwise:5 ci:2 ch:2 cn:4 cm:1 point:1 simple:3 smith:2 cohomology:18 corresponds:4 cd:1 dimensional:16 simply:1 polynomial:2 proved:1 ct:1 pr:11 described:1 stating:1 basis:9 union:3 been:1 ai:23 belongs:2 treat:1 algebras:10 pn:20 empty:1 define:1 surjective:5 generating:9 pic:3 families:1 formed:1 representative:3 chevalley:5 denote:3 manifolds:1 case:12 p1:1 unify:1 subsets:4 uip:1 contexts:1 ǫi:18 ǫn:6 will:1 ǫr:4 sln:25 proves:1 suppose:3 mono:1 situation:2 serre:4 vectors:19 vol:3 ip:7 thus:20 non:6 carsten:1 ii:6 itself:1 im:2 cone:7 dual:2 turns:1 different:1 grant:1 make:1 same:6 jℓ:2 shifts:1 complex:1 φi:11 finite:5 subalgebra:3 φm:2 european:2 independent:1 used:1 http:1 closest:1 cocycles:1 i0:4 faces:1 nj:1 hand:1 funktsional:1 uses:1 purpose:2 infinite:1 changing:2 felder:8 recent:1 lower:1 reflection:6 onedimensional:1 no:8 well:2 coboundary:3 components:1 sets:3 swiss:1 entry:1 audin:1 ihrer:1 arising:1 dimension:1 left:3 λr:5 just:1 monomial:8 generally:1 resp:2 numbering:1 obtain:2 actions:2 vanishes:1 borho:2 identify:2 transforms:3 integer:3 ad:8 λi:5 multiindices:1 cocycle:2 previous:2 blow:7 adding:1 vσ:6 generator:2 nilpotent:1 auser:1 qν:15 character:5 except:1 ele:1 lattice:7 book:1 extends:2 prilozhen:1 easy:1 theorem:39 remaining:3 euler:1 gave:1 sonia:1 isomorphisms:2 possible:1 spanned:10 erated:1 press:1 using:5 intersection:2 moreover:2 appearing:2 follows:6 performing:1 isotropy:1 automorphisms:2 mial:1 yields:1 either:1 arbitrary:1 translated:1 page:1 therein:1 jean:1 right:1 cones:15 sequence:7 sends:2 some:7 algebraically:1 deduce:2 examples:2 convex:1 proper:3 nonzero:3 provided:1 dense:1 affects:1 when:5 decomposition:2 84b:1 readily:1 levasseur:2 minimal:5 refer:1 equivalent:3 expansion:2 submodule:1 weil:8 trivialize:1 refers:1 injective:2 william:2 about:1 trivialization:1 extension:1 compatibly:1 o:53 distinct:1 whence:1 cartier:6 oy:3 ox:1 cech:6 automatically:1 subset:3 primitive:11 inclusion:1 into:1 isomorphic:6 88k:1 weyl:9 references:2 operator:5 wλ:1 rossi:7 acknowledgements:1 span:2 there:18 available:1 u0:3 restricts:2 subrings:1 way:2 exceptional:2 jantzen:1 sections:12 grenzgebiete:1 function:2 elsewhere:1 form:8 simplifications:1 jun:1 triangular:2 construction:3 ethz:2 mich:1 russian:1 musson:15 line:17 highest:10 true:1 divisors:10 partially:1 pi:27 compute:4 embedded:1 characteristic:1 ωr:1 verma:4 up:6 us:6 simplifying:1 uj:1 problem:1 walter:1 torus:5 strongly:1 associated:10 coordinate:5 ag:1 defined:4 certain:1 abstract:1 describe:3 general:4 images:1 dν:2 corresponding:16 check:1 defines:1 again:2 functions:8 nn:4 variety:19 mathematik:1 qλ:3 nd:1 detail:1 field:3 other:7 department:1 mathematics:4 nr:2 elements:2 thereafter:1 setting:1 bundle:18 includes:1 a1:1 ui0:2 generated:20 a2:1 ξm:4 additionally:1 structure:4 implies:2 assume:1 factors:1 modules:7 orbit:8 equivalently:1 weights:4 appl:1 resolution:3 |
0705.1710.txt |@word externally:1 partial:1 consider:3 magnetic:16 suggests:1 focus:1 tripartite:3 generalize:1 higher:4 computation:3 gs:2 research:1 virmani:1 calculate:1 tx:1 equivalence:1 tr:1 finally:1 ajk:2 outwards:1 under:1 decomposition:1 tr3:1 tr2:2 case:9 very:3 quadruplet:1 results:5 electron:1 every:2 mixing:3 experimentally:1 parameter:1 exact:5 condition:1 tri:1 hamiltonian:4 evaluation:1 anisotropy:2 applicable:1 magnet:1 small:2 eigenvalues:1 shows:1 originally:3 nccr:1 configurations:4 upper:1 smaller:2 stepanenko:1 sin3:1 approximation:1 zero:5 cost:1 value:3 greenberger:2 estimated:1 eigenspaces:1 canonical:2 even:2 power:1 advantageous:1 ere:1 sum:3 uniform:1 witnesses:1 goes:1 new:3 contributes:1 method:3 simultaneously:1 exchange:7 respectively:3 residual:1 here:3 perpendicular:2 desired:3 mev:1 operating:1 directions:3 path:1 along:2 legend:1 obtained:5 remark:3 generalizing:1 study:6 studied:3 typically:1 implementation:3 amount:3 stabilizing:1 suitable:3 makes:1 involves:1 appropriately:1 via:3 spatially:1 ratios:2 discontinuous:1 search:4 merely:1 highly:6 scaled:2 achievable:3 apply:1 gaas:1 derivatives:1 use:1 feb:1 takes:1 kundu:1 probabilities:2 positive:1 negative:2 next:1 comparing:1 ψi:9 therefore:3 taken:1 type:1 theoretical:1 more:4 eisert:1 tions:1 stable:1 tested:1 tangles:2 particular:1 known:3 cardinality:2 must:2 high:4 equilateral:1 rotational:1 tunnel:3 setup:1 mn:1 det:1 modified:1 roof:3 ρp:4 values:7 temperatures:9 following:1 bipartite:1 performed:2 calculation:1 expanding:2 bennett:1 implementations:2 sample:1 indicates:1 numbers:1 degenerate:4 r27:1 subsystem:1 keep:1 conversely:1 axis:1 information:1 needs:1 end:1 goal:1 rather:3 siz:1 s1:1 six:2 feature:1 s4:1 located:1 pure:6 dotted:3 opt:6 optimal:5 absolute:1 config:1 sin:1 goldbart:1 may:1 bulaev:1 plane:6 deviates:1 dominantly:1 grangier:1 parallel:1 constants:1 efficiently:1 realized:2 physical:2 effective:1 dot:2 acknowledged:1 yielding:3 ghz:25 st:3 provide:1 si:6 so:2 mk:1 allow:1 inplane:2 siy:1 typical:1 horne:2 cutoff:1 developed:2 over:5 displayed:1 burkard:1 trade:1 through:1 still:2 its:1 depending:1 diagonalized:1 difference:1 thank:1 chosen:1 interesting:2 inas:2 exhibits:1 parts:1 systems:4 h3:1 main:1 τp:6 maximal:4 them:2 good:2 return:2 greater:1 thereby:1 numerically:4 audenaert:2 fig:9 geodesic:1 effects:3 they:1 bar:1 now:2 realize:1 possess:1 represents:1 february:1 vidal:1 corners:1 university:2 presented:1 identified:2 orthonormal:1 sufficiently:2 each:2 found:3 difficult:1 mean:1 em:5 weighted:1 financial:1 independent:1 energy:10 einstein:1 reduce:1 ec:2 decays:1 measure:2 quantum:12 our:13 eq:4 out:2 large:1 shown:1 tangle:13 matrix:6 space:1 gradient:6 furthermore:1 since:2 rev:18 denotes:3 re:5 contained:1 daniel:1 socalled:1 formula:1 issue:1 red:1 matrices:3 inevitably:1 theory:1 barrier:3 8b:1 monotone:3 discontinuity:2 differ:1 possibility:1 analytical:2 formation:2 york:1 org:1 jozsa:1 e0:4 wall:1 rewritten:1 definition:1 interaction:2 geometry:3 iterative:1 feasible:1 turn:1 terhal:1 isotropic:7 monotones:1 top:2 first:8 placing:1 features:1 symmetry:3 possessing:1 primary:1 reaches:1 xy:3 frequently:1 ring:2 precisely:1 open:1 given:10 1r:2 temperature:9 leading:1 eu:2 system:18 approximately:1 verstraete:1 their:1 cooling:1 calculations:1 hughston:1 scheme:2 exponents:1 gives:1 kirkpatrick:1 exactly:2 rajagopal:1 coffman:1 reflecting:1 favorable:1 representing:1 than:4 kind:1 wootters:3 iteration:1 second:3 bez:1 states:25 classes:1 identical:1 lowest:1 generalization:2 dash:2 parameterized:1 conjugate:4 confirms:1 seek:1 any:4 multipartite:1 paths:1 strength:4 angle:1 min:1 jxy:19 pursued:1 latter:1 able:1 converges:1 note:4 uration:1 generalized:1 forces:1 online:2 strengths:1 accuracy:1 heisenberg:3 trace:1 investigations:1 techniques:1 most:1 optimized:1 letter:1 successive:1 homogeneous:2 extremely:1 kb:15 deviations:1 considered:1 calculated:1 stronger:1 order:9 bopt:4 exp:3 azimuth:1 quantifying:1 χj:1 lying:1 laws:1 particularly:1 show:1 rtn:1 representatives:2 minimizing:1 chuang:1 decompositions:3 find:7 ground:11 current:1 knowledge:1 favor:1 eigenspace:1 rendell:1 less:1 basel:2 increasingly:1 only:8 explicitly:1 indeed:1 local:1 concurrence:1 columns:1 equilibrium:1 mixture:1 triangle:1 above:4 beat:1 nanowires:1 lehmann:1 de:1 2jz:2 arranged:1 vollbrecht:1 resource:1 podolsky:1 converge:1 fields:5 arxiv:1 assuming:2 yield:1 investigate:2 roger:1 switzerland:1 fixed:2 discussing:1 doublet:2 set:5 achieved:3 correlations:1 observed:2 see:6 quantitatively:1 λj:1 discussions:1 recently:1 ur:1 best:1 subject:2 satisfying:1 mintert:1 sites:1 qubits:9 state:35 future:1 various:2 between:4 before:2 numerous:1 publishers:1 terms:3 ability:1 jz:28 importance:1 comp:1 however:5 vanishing:2 ud:1 carbon:1 configuration:1 come:1 both:1 cos:1 reported:1 uhlmann:1 zeeman:4 flipped:1 plenio:1 dated:1 context:1 qubit:4 expression:3 experimental:1 otherwise:1 minima:2 ch:1 point:2 color:2 cf:1 height:2 semiclassical:2 werner:2 simply:1 decreases:1 maximize:1 bose:1 respect:4 throughout:1 broadening:1 ensures:1 described:3 transformations:1 skew:1 due:3 been:5 quickly:1 slowly:1 anisotropic:5 applying:1 ph:1 pi:10 bex:1 choose:1 dots:2 direction:2 corresponding:4 going:1 sufficient:1 precision:1 zeilinger:2 observe:1 curves:2 angles:1 maximally:4 spin:5 present:1 applied:1 pacs:1 solid:2 engineering:1 evaluated:2 excited:6 will:5 while:1 optimization:2 behavior:1 error:1 situation:1 tunneling:1 couplings:2 procedure:1 finitetemperature:1 generate:1 unitary:3 orientation:1 zenith:1 coupled:2 thus:7 non:2 encountered:1 cluster:1 reads:1 itself:1 im:5 against:2 around:1 different:2 twofold:1 akj:1 generic:1 same:1 complex:1 quant:2 split:1 noe:1 finite:8 meaningfully:1 eopt:4 used:3 fluctuations:2 numerical:4 effect:2 hand:1 doublets:1 purpose:3 entanglement:25 computationally:1 eigenvectors:1 lower:2 task:1 off:3 center:1 minimize:1 raussendorf:1 well:2 academic:1 solve:1 swiss:1 model:3 arising:1 left:1 spherical:1 gates:2 manifold:3 fourfold:1 being:2 rosen:1 accurate:1 obtain:4 identify:2 aspect:1 using:8 useful:1 λi:1 eigenstates:1 previous:1 grinstein:1 rapid:1 kluwer:1 density:2 21j:1 wei:1 bell:2 parametrization:1 simple:1 interested:1 lett:9 theorem:1 apart:1 eigenstate:1 skj:1 real:2 increased:1 evaluate:4 sjk:2 possible:4 spanned:1 entangled:9 press:1 immediately:1 nanotechnology:1 depicts:1 moreover:1 mod:2 loss:2 splitting:5 nanoscience:1 separately:1 yields:3 either:1 arbitrary:1 reduced:2 spins:3 function:7 drop:1 classical:2 stiefel:2 creation:1 searching:1 strongest:1 include:1 choosing:1 convex:3 anisotropies:1 bottom:1 broad:1 avoid:1 integration:1 overlap:1 moor:1 connecting:1 provides:1 tends:1 τmax:8 minimal:1 gjk:2 rank:1 minimization:2 rep:1 problems:1 equivalent:3 radial:4 bi:10 11j:1 notably:1 step:2 powerlaw:1 although:4 imaginary:1 properties:1 panel:2 actual:1 ferromagnetic:3 constraint:2 column:1 universe:1 dependence:1 o:1 briegel:1 mixed:7 introduced:1 considerations:1 cambridge:1 suited:1 h2:1 communication:1 h1:1 obtaining:1 bound:3 nsf:1 three:9 down:1 polak:1 hermitian:1 browne:1 formidable:1 factor:1 reducing:1 per:1 robust:1 support:1 there:1 approximate:5 specifically:1 genuine:2 accordingly:1 low:4 way:1 nielsen:1 was:3 naturally:1 hz:2 tight:2 complete:1 form:3 brand:1 differences:1 but:5 back:1 related:1 nanotubes:1 larger:1 ref:2 line:7 highest:1 proposal:1 coupling:10 compute:1 builds:1 antiferromagnetic:1 maximum:2 us:1 2πn:1 below:3 limit:1 demonstrate:2 problem:2 similar:2 called:3 cirac:1 associated:1 defined:2 uik:7 uij:5 influence:1 χi:1 ao:1 general:4 separating:1 single:2 inf:3 regime:2 compared:2 outof:1 dashed:1 coish:1 when:1 detail:1 field:17 conceptions:1 other:3 department:1 deviate:1 uhne:1 elements:1 denote:1 calculating:1 divincenzo:1 models:1 radially:1 update:1 ising:1 additionally:1 vectors:2 tackle:1 hanson:1 algebraic:1 philipp:1 implies:2 eof:3 algorithm:5 assume:2 physics:2 required:2 klingelbergstrasse:1 together:1 inset:2 fact:1 time:2 far:1 4b:2 having:2 |
0705.1711.txt |@word angles:1 gp:2 caused:2 magnetic:12 excellent:2 results:6 illustrated:1 known:2 ga:1 consists:1 contributions:3 increase:1 bremsstrahlung:4 calculate:1 re:1 kγ:1 0gev:1 helps:1 elliptic:3 ti:1 supported:1 very:2 agakichiev:1 electron:1 figs:4 stays:1 difference:1 michael:1 large:2 kolhinen:1 dir:2 concluded:1 jhep:1 trend:1 consistent:1 direct:33 modified:1 dynamics:2 blue:3 errors:2 plays:1 stands:1 section:2 thickness:1 current:1 experiment:4 above:1 priv:2 mee:2 respectively:1 here:1 ranges:1 mev:7 excess:1 ratio:8 drell:2 dileptons:11 involved:1 larger:2 suggests:1 published:2 usually:1 shaded:1 plotted:2 via:2 leptons:1 gluons:1 scales:1 explained:2 neutrons:2 gluon:1 pdfs:1 total:1 200gev:10 usa:1 positive:2 give:1 charge:1 centrality:6 comparing:1 nucl:4 therefore:3 themselves:1 partons:4 conclusions:1 emission:2 separates:1 calorimeter:1 high:11 c41:1 protons:2 mh:1 eskola:1 drops:1 arleo:1 prompt:1 stated:1 process:4 attribute:1 rapp:1 ratios:2 weighting:1 minimum:4 reviewing:1 sense:1 simple:1 information:1 winter:2 decaying:1 describes:1 discussion:2 means:1 regions:1 hot:1 instead:1 frag:1 cocktail:1 may:3 after:1 explored:1 coming:1 law:1 data:11 spectra:2 sn:6 decreasing:1 cherenkov:1 order:2 typical:1 ceres:1 over:3 mainly:2 interpreted:1 produced:5 thermal:5 experiments:1 through:2 kinetic:3 fit:1 decay:5 energies:3 decreases:1 qgp:5 imr:1 takao:1 main:1 eur:2 qq:1 fragment:3 ye:2 yd:2 they:1 now:2 represents:1 february:1 electro:12 drop:3 2z:1 d48:1 found:2 heavy:4 primarily:1 hadronic:2 energy:8 hard:8 idea:1 related:1 decays:1 isospin:6 ex:2 measurement:4 laboratory:1 out:2 shown:9 opened:3 quantify:1 since:2 rev:6 looking:3 collisions:24 participants:2 dominated:2 induced:2 occurs:1 red:3 shows:5 theory:2 possibility:2 quark:2 approaches:1 ααs:1 pairs:2 interaction:3 starts:1 could:2 v2:15 phenix:30 plane:4 gordon:1 leading:2 consequence:1 interact:1 major:1 initial:4 probability:1 sakaguchi:5 4gev:2 production:2 tannenbaum:1 xt:10 given:3 cteq:1 jet:8 introduction:1 πk:1 top:1 system:1 their:1 intermediate:3 peripheral:2 gives:2 prediction:2 sections:1 final:1 annihilation:1 matter:2 coll:6 future:1 were:1 extracting:1 counter:1 raa:17 minb:2 gale:3 seen:3 clearly:1 contents:1 conversion:4 angle:1 min:2 c72:1 npart:1 mid:2 note:1 internal:1 spectral:1 gγ:1 track:1 collaboration:1 reach:1 most:2 montana:1 charm:2 significant:1 preliminary:12 measured:8 don:1 observation:1 calculated:4 implications:1 points:1 electrons:9 pattern:1 brookhaven:1 latest:2 quantifying:1 naively:1 fact:2 gold:1 show:2 pbsc:1 probe:1 scattered:3 keywords:1 d2:1 nlo:4 subtracting:2 partonic:1 q2:2 based:2 just:1 written:1 factor:3 dn:3 dm:1 gev:56 di:2 negative:2 radiations:1 dy:3 dyd:1 dp:1 secondary:1 disentangling:1 processes:2 dpt:2 arxiv:1 alteration:1 yield:12 investigate:1 paper:1 qg:4 ql:1 traverse:1 turbide:3 reference:3 national:1 campbell:1 result:6 nuclear:5 review:2 tend:1 state:2 various:4 between:2 invariant:1 2pt:2 opening:1 originated:1 emitted:1 flow:4 interpolate:1 chatterjee:1 comm:2 jets:3 suppressed:1 reaction:2 f2a:1 successes:1 many:1 region:8 compton:3 etc:1 f2p:2 pdf:3 contribution:6 comes:1 aa:1 cc:2 seems:1 corresponds:2 anti:1 σaa:2 pqcd:5 pp:1 described:3 kinematic:1 come:1 acceptance:1 due:1 been:1 pb:1 reduction:1 workshop:2 interest:1 expected:4 ph:1 fig:17 dilepton:3 both:1 leptonic:1 formed:1 photon:22 6m:1 binning:1 c9:1 understand:1 systematic:3 c2:9 those:3 applied:1 p0:1 pacs:1 will:5 ongoing:2 error:2 au:55 would:1 thus:2 bias:6 different:2 make:1 radiation:15 cross:3 unity:1 bands:1 modification:3 several:3 incl:1 events:1 independent:1 calculation:7 used:1 effect:12 ion:4 sults:1 recent:2 lower:1 literatures:1 c69:1 depending:1 well:5 analysis:2 left:4 proposed:1 able:1 sources:2 predicts:1 σnn:1 scattering:8 cut:1 upton:1 photons:36 sky:1 source:1 combine:1 lett:3 momentum:1 divided:2 real:1 ield:1 increased:1 big:2 meas:1 increases:3 background:1 using:1 rhic:3 loss:5 semi:1 follows:4 signal:4 chamber:1 yields:5 isobe:1 bremss:2 decrease:1 collective:1 right:5 back:2 rapidity:1 dense:1 tracked:1 bottom:2 broad:1 quarks:7 mesons:1 23rd:2 proc:3 refer:1 bkgd:2 power:2 disentangle:2 expansion:1 although:2 salgado:1 hadron:8 central:7 pt:35 range:3 dmee:1 functions:1 into:3 within:2 disentangled:1 predictions:3 down:1 because:2 references:1 parton:4 proportional:1 next:1 statistics:2 hep:1 intrinsic:1 unmodified:1 there:5 rcp:3 3gev:1 ee:11 yan:2 low:5 way:1 was:3 opposed:1 function:7 medium:9 σpn:1 but:2 σpp:2 line:1 adler:1 rejection:1 vogelsang:2 fries:1 up:6 converted:1 distribution:4 stages:1 similar:1 strongly:2 constant:1 inclusive:1 defined:1 certain:1 abstract:1 year:2 single:5 exist:1 qγ:4 compared:3 thermodynamical:1 no:3 detail:2 virtual:2 ny:1 role:1 d2n:1 department:1 nq:1 predominant:1 conclusion:1 snn:12 models:1 gas:4 drift:1 miki:1 suppression:5 ncoll:4 structure:2 assume:1 physics:1 mass:12 fitted:1 electromagnetic:1 agp:1 resolution:1 once:1 |
0705.1712.txt |@word quarks:4 partial:2 consider:2 global:3 results:11 leads:2 sci:1 contributions:1 particles:1 re:1 program:1 elliptic:1 under:1 suffered:1 electrons:2 indicating:1 division:1 lack:1 mpc:2 zhang:1 very:2 tends:2 peripheral:2 categories:1 entire:2 level:3 c43:1 large:7 noted:2 smaller:2 compensated:1 findings:1 c48:1 consistent:2 direct:1 threshold:1 second:3 enhancement:1 further:1 dynamics:2 even:4 index:3 errors:2 appear:1 opaque:1 heaviness:6 section:1 while:1 consistently:1 experiment:8 above:2 new:3 acknowledgments:1 filled:1 3d:2 dissociate:1 full:5 led:1 respectively:1 inviscid:1 modify:1 understanding:2 ranges:1 separation:1 path:1 photonic:2 strong:2 z2:1 great:1 incoming:1 rigorously:1 cern:6 shift:3 study:1 larger:10 contradiction:1 dissolve:1 preferentially:1 simultaneous:1 studies:1 cancellation:2 involves:2 via:4 gluons:1 suddenly:1 gluon:2 karsch:1 apply:2 total:1 linearly:1 derivatives:1 use:1 impacts:1 usa:2 prove:1 breakup:3 predictions:3 centrality:2 scenarios:1 predict:1 nucl:11 qcd:3 paraphrased:1 theoretical:5 more:4 separated:1 rapp:1 partons:2 th:3 thus:7 emission:1 tested:3 excellent:2 must:1 evolves:1 account:1 mb:2 originally:1 det:1 cancellations:1 labeled:1 values:1 caveat:1 making:1 example:5 figure:5 calculation:2 relativistic:1 sps:6 states:6 collision:2 arise:1 simple:5 information:1 needs:3 winter:2 turn:1 rather:1 discussion:1 six:1 feature:3 steepening:1 molnar:3 hot:5 syst:3 answer:1 parameter:1 granier:1 de:2 may:11 after:1 produce:1 date:1 data:19 fm:5 lhc:2 effective:1 recombination:6 spectra:1 parameterized:1 lengths:1 sn:4 correlation:1 order:2 alessandro:2 over:2 competing:1 vary:1 years:2 produced:2 course:1 through:3 statistical:2 cold:13 y2:1 its:1 before:2 perfect:2 rapidly:1 thank:1 termed:1 energies:5 methodology:1 coordinates:2 actually:1 late:1 attraction:1 quarkonia:16 production:3 fig:5 might:7 eur:3 versus:5 non:3 greater:1 auto:1 outlined:1 cascade:1 break:1 abreu:1 effects:3 they:3 adcox:1 now:2 discuss:1 easily:1 february:1 kharzeev:1 undertaking:1 university:1 drop:1 2d:1 magnitude:1 each:1 crossing:1 out:1 side:1 characterized:1 heavy:17 reactions:8 determine:1 series:1 energy:5 hard:1 gaussian:1 related:1 static:1 ex:4 our:1 event:1 really:1 category:1 shown:13 funding:1 shadowing:1 factors:2 since:1 rev:4 increase:2 collisions:6 participants:1 c39:1 fluct:2 correct:1 shows:1 interactions:3 possibility:1 quark:4 completely:1 formation:3 intermediate:1 muller:1 definition:1 pairs:2 interaction:1 created:4 utilization:1 phenix:17 plane:2 first:1 feed:1 copper:2 major:2 initial:5 number:3 another:4 precisely:1 open:3 razor:1 given:1 temperature:1 likely:1 their:5 introduction:1 indicate:1 assumption:1 fortuitous:2 observations:2 passed:1 final:1 gives:1 calculations:1 mostly:1 explanation:6 exactly:1 transverse:1 part:1 authors:1 x2:1 than:4 distance:1 target:1 approximations:2 rate:1 matter:13 future:3 were:2 posit:1 insightful:1 pre:2 raa:9 fluctuation:1 ann:1 curves:2 substantial:3 categorized:1 need:1 seen:1 constrained:1 any:5 jour:1 depending:1 npart:4 mid:9 mechanism:1 predominantly:1 note:2 high:4 extrapolating:1 rebinned:1 circles:1 play:1 multiple:4 though:2 collaboration:8 most:2 montana:1 charm:6 significant:3 pair:4 measured:2 probes:2 b410:1 surprising:1 implications:1 proceedings:2 points:1 χc:3 principle:1 pattern:3 effect:5 physics:6 pvalue:2 atmosphere:1 simultaneously:1 gold:2 probe:2 scattered:1 discovered:1 solutions:1 keywords:1 impact:3 ratio:1 enough:1 should:5 only:2 abs:1 screening:1 factor:3 local:2 thresholds:1 boulder:1 gev:10 compiled:1 simplest:1 overall:1 nearly:1 dy:2 penetrate:1 evolution:2 gauged:1 fields:1 coalescence:1 arxiv:1 assuming:1 summary:1 common:2 including:1 fixed:1 explanations:2 deuteron:2 set:2 sensitivity:1 correlations:1 relative:3 naturalness:3 see:3 individual:1 result:2 discussions:1 close:1 outward:1 best:1 nuclear:20 favor:1 state:2 various:1 closed:1 between:5 import:2 available:1 screen:1 however:5 prediction:3 key:1 probing:1 group:1 suppressed:1 both:5 essentially:1 providing:1 na50:5 many:3 taking:1 decay:3 equal:1 participating:2 sensitive:1 experimental:3 relevant:1 co:1 cc:10 seems:1 proton:3 walk:1 factorize:1 spans:1 suppressing:1 conference:1 collider:1 pt:9 lattice:1 addition:2 due:4 been:3 reduction:1 much:7 change:1 expected:1 utilizing:1 lett:7 contribute:1 formed:2 coherent:2 systematic:2 careful:1 case:4 novel:1 pacs:1 solid:1 value:4 cursor:2 anticharm:1 near:1 match:1 error:1 eπ0:1 identical:1 almost:1 binding:1 surprisingly:1 surface:3 ii:1 bias:3 different:6 grant:1 perhaps:5 things:1 cross:1 same:1 modification:5 events:2 higher:4 monotonic:1 ion:4 v2:1 moving:2 dielectron:1 b557:1 recent:1 lower:4 scenario:2 charges:1 acknowledge:1 random:1 directional:1 thought:1 patterns:2 without:1 sets:1 model:1 just:1 being:1 able:1 rest:1 ideas:1 flavor:4 scattering:4 yet:1 speculate:1 density:4 alternate:1 sky:1 color:5 attractive:1 plasma:1 transformation:1 momentum:3 real:1 g31:1 saturation:1 increased:1 depends:1 checking:2 big:1 couple:1 possible:3 department:1 increases:1 background:1 vacuum:1 correcting:1 rhic:19 adams:1 desire:1 melting:1 thews:1 like:1 particle:1 workshop:3 signal:1 separately:1 indication:1 either:1 decrease:1 inter:1 deal:1 some:2 back:1 statistic:1 matching:1 rapidity:21 testable:1 measurements:4 overlap:1 does:1 masked:1 23rd:2 yields:2 propagating:2 proc:1 dnch:1 bb:1 liquid:3 notable:3 exciting:1 properties:2 panel:2 about:1 nucleons:2 central:5 would:2 dimuon:1 simulation:1 compatible:1 range:2 slightly:1 organizers:1 colorado:1 glenn:1 previously:1 within:3 down:1 phase:1 references:1 parton:7 next:1 significantly:3 cassagnac:1 statistics:4 hep:4 additional:4 assumed:1 adare:2 there:8 yao:1 accordingly:1 influencing:1 low:3 forward:11 assumes:2 function:2 medium:17 complete:1 form:3 relaxed:1 but:6 fg02:1 ph:3 adler:1 type:1 inside:1 smooth:1 up:2 quantitatively:1 un:1 critical:1 fluctuations:1 distribution:2 similar:2 aa:1 constant:3 flow:1 abstract:1 describe:2 influence:1 evidence:1 single:1 au:19 qiu:1 accounting:1 distributions:1 check:2 arsene:1 compared:3 discriminate:1 dotted:2 no:7 dashed:2 when:1 detail:1 narrowing:2 other:2 role:1 spatial:3 test:1 nq:1 nagle:6 midrapidity:3 conclusion:1 opacity:4 picture:1 coherence:1 accidental:1 separate:1 models:2 generated:1 nucleus:2 suppression:31 included:1 needed:2 assume:1 typically:1 space:2 curve:4 original:1 time:3 international:1 nuclei:3 requires:1 having:1 satz:1 |
0705.1713.txt |@word proposition:1 represent:1 partial:1 consider:6 chain:1 saying:1 lagrangian:1 magnetic:4 b175:1 limited:1 produce:1 existing:1 leads:3 gf:19 commute:2 subtle:1 gb:2 ga:3 edu:2 obtaining:1 follow:1 vega:1 contributions:1 gj:4 devoted:2 looking:1 inverse:1 depend:3 calculate:6 doe:2 iii:3 equal:1 simplify:1 tr:1 rf:8 charge:50 program:2 indicate:4 those:4 th:4 under:3 analogous:1 include:2 eikonal:6 carried:1 supported:2 amplitudes:2 g2:1 straightforward:4 returning:1 far:4 cck:4 collision:1 conditions:2 polarization:2 wave:56 88er40388:1 corollary:1 every:3 cdj:1 application:1 jim:3 bubbles:1 little:1 exact:2 appropriately:1 condition:5 bondarenko:1 identity:4 annihilated:1 dominate:3 obvious:1 ryskin:1 solves:1 hamiltonian:44 did:1 turns:2 nucl:30 michael:1 solution:14 large:12 discrete:1 convenience:1 vector:5 abµ:1 avoiding:1 small:13 gauge:13 drop:1 inspection:1 noted:3 degeneracy:2 jhep:5 dilute:8 slower:1 ten:1 construed:1 2gf:1 consistent:1 direct:2 literature:1 approximation:5 shoshi:3 zero:6 interval:1 correlator:1 further:3 dynamics:1 substitute:3 canonical:21 even:9 aim:5 what:4 abc:26 stands:2 rate:2 d2:17 section:17 diab:3 expressed:3 derrida:1 consistently:1 version:2 goes:1 new:3 contributes:2 boost:4 χab:4 b504:1 mp:7 satisfy:5 completion:1 wiedemann:3 altogether:1 ibid:2 whose:1 eksp:2 szymanowski:1 component:3 residual:3 here:13 growing:2 ei:3 objects:4 free:6 address:2 represented:1 quite:2 equations:20 change:4 obtained:1 separating:1 d71:1 2gi:1 deriving:1 cern:3 shift:4 sequential:1 larger:1 approaches:2 scatter:3 adding:1 simultaneous:3 resulting:3 procedure:3 situations:1 action:22 hospitality:2 conveniently:1 fourier:1 makes:1 involves:4 genuinely:1 vib:2 emerge:1 via:5 addresses:1 gluons:25 extra:6 explained:3 scaled:1 addressed:1 gluon:31 summation:1 support:2 total:3 florence:1 approximating:1 unit:1 d72:1 derivatives:2 use:9 done:5 takes:3 usa:2 covariant:3 positive:6 give:6 finally:5 next:3 process:3 linear:4 therefore:12 qcd:10 taken:7 scope:1 themselves:1 type:4 theoretical:1 possible:2 more:11 zh:2 formally:1 duality:1 kozlov:2 clearly:2 becomes:6 operators:29 pisma:1 emission:6 validity:1 levin:5 connecticut:1 interaction:1 normalized:2 lipatov:9 particular:4 known:5 effort:1 bialas:1 must:2 states:2 account:14 rotational:1 defines:1 quantized:1 integrating:1 recall:4 equation:32 work:7 reproduce:4 cai:27 fock:4 values:4 kovner:17 evolved:2 following:17 arxive:1 hatta:1 averages:1 could:1 lhs:1 sub:5 rigidly:1 solved:3 calculation:16 expanding:3 ak:2 allowed:1 neglected:6 stressing:1 pieces:1 high:17 ut:1 lorentz:1 performed:1 tab:1 sense:1 dominant:5 counting:2 completes:1 matrices:1 scales:1 ewerz:1 information:2 ib:1 end:2 opposed:1 discontinuity:1 thing:1 rather:5 discussion:8 γib:6 wusthoff:1 grows:3 write:6 how:1 nontrivial:1 pure:1 answer:1 plus:1 fadin:1 parameter:2 du:1 mueller:9 product:2 de:4 magnitudes:1 jalilian:2 algebra:3 may:3 unitarize:2 after:5 cbi:6 lengthy:1 lab:2 vpi:1 explored:1 waves:2 multiplication:1 excited:1 types:1 collecting:1 short:8 dynamical:4 effective:1 light:13 grant:1 explicit:5 correspond:1 su:1 neglect:2 interpolates:1 secs:1 so:15 road:1 allow:2 keeps:3 representation:2 subsequently:1 manashov:1 stasto:1 order:46 exclusive:1 brodsky:1 saturated:2 dx:13 enter:2 diagonalizes:2 indeed:9 over:9 top:1 years:2 produced:7 course:1 jetp:3 paper:9 through:5 looks:1 statistical:1 signs:1 mentioned:1 y0:11 satisfies:2 still:5 avenue:1 its:11 exchange:3 diagonalized:1 expansion:9 style:1 derive:12 longitudinal:13 treat:1 burkardt:1 fiz:3 interesting:8 fix:1 solving:3 encompasses:1 lk:3 finiteness:5 forms:1 window:1 according:1 degrees:11 systems:2 mail:1 main:3 might:1 easier:1 arguments:1 yi:2 treating:1 non:6 good:1 affected:2 greater:1 than:13 ya:2 rotations:1 polarizations:1 noticing:1 navelet:2 framework:3 example:1 effects:15 they:7 thanks:1 abi:2 bogoliubov:19 now:12 discuss:2 developments:1 above:3 easily:2 term:23 finite:1 alex:1 b483:1 hω:1 characterizes:2 university:4 presented:1 appropriate:1 accompanies:1 events:1 d61:1 2f:1 magnitude:4 mode:4 pij:1 each:4 found:9 entirely:1 difficult:1 side:4 preserve:1 constraints:5 heavy:1 transforming:1 another:2 formulate:1 independent:4 hadronic:15 energy:17 hard:1 mclerran:4 approximates:1 related:6 used:4 expect:1 entering:1 measure:1 loops:4 our:25 beyond:4 eq:74 ep:1 out:2 leave:1 shown:2 matrix:26 space:11 rep:1 since:22 crucial:2 kirschner:1 increase:1 combinatorial:1 misses:2 transposing:1 dominated:1 ra:4 emerged:1 print:1 get:3 induced:1 issue:1 correct:5 element:1 restoring:1 commutation:13 reformulation:1 theory:11 nonlinearities:1 b36:1 contain:2 divergence:1 diagonal:1 possibility:1 standard:3 completely:2 necessarily:1 york:1 imagine:1 put:1 estimate:1 achim:1 iancu:6 rewritten:2 resumed:1 definition:2 aej:1 βp:6 derivation:13 language:1 created:1 starts:1 2p:17 omit:1 days:1 keep:7 motion:9 ordering:1 plane:3 exponentially:3 δij:3 projectile:8 corrections:20 teor:2 bai:19 onto:1 balitsky:4 first:21 there:6 xn:4 probability:7 ebe:1 third:3 variables:5 number:5 reaches:1 motyka:1 xz:1 clear:3 overestimated:1 smaller:4 simplified:2 neglects:1 directly:3 reached:1 conjunction:1 precisely:6 size:2 given:22 πa:1 bracket:1 asymptotic:1 their:2 introduction:3 leading:18 adjoint:1 structured:1 system:3 relations:12 needed:2 perturbations:1 observations:1 statement:1 realization:1 dwell:1 consistency:1 perfectly:1 eur:2 speaking:1 gives:4 assign:1 geneva:1 exactly:4 zeroth:1 braun:2 always:6 transverse:7 part:16 differentiate:1 uconn:2 x2:2 imposing:1 x1:4 sˆ:2 coefficients:1 remember:3 wide:1 bei:1 determines:1 target:25 suppressed:1 fundamental:2 approximations:1 aai:13 second:17 rescatter:1 correlators:6 annihilation:9 matter:1 future:2 amplitude:26 powers:6 perturbative:9 pre:1 motivation:1 close:1 rewrite:1 lines:1 correction:4 argument:1 generalization:1 acd:3 already:4 say:2 vpj:2 brunet:1 unlikely:1 collects:1 need:9 seen:1 seem:2 regulate:1 occupied:1 any:21 contents:1 accounted:2 wilson:5 mij:3 triggered:1 depending:1 efficient:1 lim:3 responsible:2 able:2 sof:1 lij:2 indexes:5 aaµ:1 archive:1 potential:5 take:5 finding:1 cci:5 scatterings:9 accuracy:2 milhano:2 continuous:4 multiple:26 electric:4 munier:3 opposite:1 track:2 rhs:3 correlation:4 fails:3 most:2 regular:1 significant:1 formulae:1 phase:4 colliding:1 probabilistic:1 cc:1 αt:23 γi:2 unequal:1 observation:1 failure:1 considered:2 calculated:2 saturate:2 coincides:2 typeset:1 points:1 rev:22 principle:3 exp:17 urs:2 ggi:1 ky:1 usual:2 physics:5 abj:8 fact:10 2πp:1 sector:2 cde:3 hyper:1 simultaneously:3 somewhat:2 index:5 show:7 b437:1 emphasize:1 random:1 dependences:2 concentrate:1 notations:1 purely:1 iǫ:15 relation:4 solutions:7 b94:1 keywords:1 substituting:1 lublinsky:12 find:17 fifth:1 ground:1 partonic:2 αa:2 fg02:2 based:1 knowledge:5 parameters:1 aω:1 commutators:6 explain:1 furnished:1 distributed:1 written:5 should:10 hierarchy:1 only:25 explicitly:14 generators:1 subsection:2 factor:11 interested:2 marian:2 ip:3 do:11 2mp:1 dj:24 dk:6 notation:1 di:28 property:1 familiar:1 express:3 db:2 dc:1 yielded:1 rapidities:4 ones:2 dyi:4 words:2 dy:16 during:1 interpreted:1 aν:1 boundary:1 dp:6 dq:1 furnishes:1 evolution:83 b634:1 multiplying:1 4πp:1 equality:2 fields:19 arxiv:13 think:1 acknowledgments:1 sum:2 vacca:2 aed:1 gribov:3 including:4 fixed:2 baj:1 require:2 rj:1 view:2 financial:1 kernel:12 requirement:1 set:7 resummed:1 reference:1 achieved:2 physically:7 undergoes:1 δm:6 respect:3 reiterate:1 relative:3 collectively:1 namely:4 full:1 sec:6 result:7 existence:1 discussions:1 terms:28 limiting:1 momenta:3 subject:2 preparation:1 αs:2 said:1 eigenfunctions:2 kl:1 nuclear:1 away:1 missing:1 definite:1 dipole:8 symmetric:2 d59:2 state:11 determined:6 identification:2 between:5 justified:2 before:1 approach:8 across:1 d57:1 available:1 ends:1 attention:1 recently:2 reproduced:1 nature:1 initially:1 modify:1 emitted:3 weak:5 however:15 jr:1 jl:1 reproduces:1 wt:1 would:4 key:1 jk:6 group:1 configuration:2 come:2 distribution:5 thank:1 both:8 vp:10 stages:1 last:9 repeating:1 limits:3 tractable:1 energetic:1 treated:2 taking:1 pauli:1 vanishing:5 comment:1 quantization:1 γic:3 storrs:1 γia:18 0a:2 context:3 logic:1 expand:3 contribution:5 kovchegov:2 expression:11 comes:1 ji:1 ck:2 cj:6 ci:11 ch:2 very:3 cm:1 point:9 color:32 brook:1 ca:2 wp:2 unitarization:1 corresponds:3 cd:4 dimensional:1 galileo:1 grants:1 simply:3 coordinates:2 constant:5 throughout:1 ct:1 considering:1 verlinde:2 strong:1 described:3 bbj:2 bbi:2 basis:4 analogies:1 bfkl:3 induces:4 due:10 been:10 strategy:2 defined:11 much:4 asymptotics:1 basic:2 mean:1 yad:1 ph:16 unchanged:2 acν:1 define:2 reggeon:3 describe:1 observable:3 suppress:1 informative:1 coherent:10 observe:1 dirac:1 derivative:3 antisymmetric:2 acta:2 denote:3 irrelevant:1 spirit:1 present:5 case:13 exponential:2 ap:1 means:1 resummation:2 appearance:1 introduced:1 value:7 choices:1 will:22 institute:2 while:13 suppose:1 behavior:2 involved:2 situation:7 eik:1 2k:1 loop:5 remembering:1 exponent:2 stop:2 unitary:6 coupled:1 vi:4 vj:3 vk:1 thus:40 xiao:1 iv:2 ii:1 vq:1 ik:1 ij:32 properties:2 cone:13 dual:5 return:1 vanish:2 ig:1 participating:1 different:11 dab:3 anymore:1 sensitive:1 generic:2 identities:1 gluonic:1 cross:1 same:15 orders:2 pomeron:6 φb:2 parts:1 interact:1 viewed:3 diagonalize:4 soyez:1 proved:1 regime:8 start:2 higher:3 evolve:2 investigated:1 infinity:2 see:10 boosted:2 foam:1 effect:3 hand:9 purpose:1 d66:1 invariance:1 eij:2 kuraev:1 normalization:9 b335:1 recognized:1 σp:2 off:3 modes:17 fully:1 charges:4 safely:1 ingredients:1 well:7 analysis:1 obviously:2 solve:3 components:1 convenient:2 coordinate:7 position:1 model:1 kwiecinski:1 parametric:3 parametrically:3 left:4 ny:1 spurred:1 permissible:1 just:3 examining:1 being:4 generally:2 rotated:1 obtain:8 vanishes:1 assigned:2 relevant:2 transforms:2 aspect:1 patel:1 alternative:1 scattering:56 singularity:2 down:2 previous:5 adv:1 note:11 preprint:1 jra:2 generator:2 density:73 korchemsky:3 conclude:3 guaranteed:1 except:1 handy:1 simple:2 valid:15 transformed:5 lett:12 easy:4 cb:2 diagonalization:6 input:1 transformation:24 momentum:10 polon:2 real:2 igf:3 saturation:2 jrl:1 increased:1 depends:1 alternatively:1 read:2 couple:1 combination:1 iδ:1 galilei:1 increases:1 know:8 background:1 vacuum:22 step:5 using:13 bit:1 walk:1 praszalowicz:1 weigert:6 multiply:1 necessary:4 like:1 semi:1 follows:5 reduces:1 δu:6 venugopalan:1 translates:1 collect:1 imposes:1 δj:36 either:1 arbitrary:5 anti:1 valence:30 soft:48 interestingly:1 δa:1 right:4 old:1 classical:15 understand:2 δba:1 creation:8 some:18 back:2 δbi:1 understood:5 added:1 jla:2 scatters:5 specified:3 proper:1 d60:1 neglecting:1 diagonalizing:5 rapidity:16 generates:1 nonzero:1 provided:1 scale:1 dense:7 lead:2 fourth:1 avoid:2 though:6 d49:2 jimwlk:52 whole:2 does:13 dipoles:2 expressing:1 steps:1 leonidov:3 minimal:2 refer:2 faddeev:1 dimensionally:1 ba:1 power:5 bc:5 equivalent:6 reflection:1 aj:3 bi:3 bj:9 bk:2 task:2 wong:1 shifting:1 although:6 substitution:2 bcd:1 imaginary:1 hilbert:7 hadron:6 proceed:1 acb:1 works:1 working:3 constraint:7 freedom:12 aci:5 dependence:4 o:49 2i:7 addition:1 range:17 involving:1 ensure:1 stand:1 cbj:14 act:1 d64:1 reproducing:2 participants:1 projectors:1 stony:1 d62:1 cutoff:2 equally:1 contains:1 washington:1 presence:4 jδ:1 into:19 within:2 integral:5 functional:8 triantafyllopoulos:3 negative:3 eqs:10 pair:1 hermitian:4 references:1 determine:5 sov:4 operator:51 proportional:2 approximately:1 particularly:1 descriptions:1 fast:1 hep:18 additional:5 b507:1 assumed:2 strictly:3 initial:5 question:3 transform:2 long:9 doing:2 rept:2 quadratic:3 flawed:1 low:4 way:7 forward:2 was:6 a703:1 ensured:1 function:62 commutes:2 complete:6 form:15 enough:1 precise:2 eab:1 denoting:1 but:16 volume:1 gaij:2 properly:3 discreteness:2 c60:1 line:6 level:1 true:3 bci:1 xi:2 rotation:1 characteristic:1 peschanski:3 up:1 us:4 assume:1 below:5 growth:4 limit:23 acting:7 fluctuations:2 problem:3 piece:3 similar:1 called:3 ac:5 ab:50 associated:1 inclusive:1 ai:18 certain:1 abstract:1 contribute:4 expands:1 general:4 quantum:5 single:4 together:1 contour:1 operatorial:1 qiu:1 b463:1 formalism:1 commuting:2 check:5 physical:3 again:5 functions:10 completeness:2 want:2 no:8 amounts:1 fixing:4 whereas:1 nc:1 when:17 detail:4 bartels:6 matching:2 field:39 other:10 make:1 tij:1 brings:1 department:4 2di:3 vastly:1 happens:1 briefly:2 elements:3 superposition:2 calculating:5 produces:1 preceding:2 time:2 uniformly:1 pinsky:1 ferreiro:1 includes:3 a1:2 commutator:11 meaning:1 important:8 nucleus:1 included:2 describing:1 reason:6 structure:4 lm:1 tailored:1 individual:2 coupling:6 bcj:1 bck:3 perturbatively:4 requires:1 factors:3 curve:1 oel:1 having:1 equivalently:5 itself:6 b409:1 simplicity:3 observables:2 starting:4 original:4 once:1 |
0705.1714.txt |@word partial:1 consider:2 similarity:5 results:2 leads:1 roy:1 consists:1 expressions:2 compact:1 γz:1 equivalence:11 spain:2 excluded:1 under:1 include:1 eikonal:1 updated:1 straightforward:1 very:2 springer:1 geometrical:1 every:1 difference:1 condition:2 solves:1 level:1 turns:1 solution:9 large:1 anal:1 mo:1 application:1 mn:1 estimates:1 sign:1 approximation:1 pme:20 imply:1 further:2 ode:5 linear:5 putting:1 nonlinear:6 plays:1 appear:2 fact:2 section:2 version:2 above:1 new:5 amounting:1 satisfy:2 relationships:1 whose:1 respectively:1 here:1 ranges:1 desired:2 possibility:1 address:2 luis:4 strong:2 equations:15 change:4 obtained:1 remark:1 study:2 studied:3 allows:2 step:1 resulting:1 usually:1 suitable:1 changes:2 options:1 involves:1 technique:1 selfsimilarity:5 classification:1 replace:1 sgn:6 establish:1 use:1 asymptotic:2 intensively:1 ariel:5 positive:4 next:1 few:1 call:1 themselves:1 compactly:1 type:18 minor:1 more:1 introducing:1 formally:1 becomes:1 apparent:1 appendix:1 particular:1 known:6 cases:7 iii:5 must:2 account:1 mc:13 recall:1 equation:29 barenblatt:3 values:9 ms:7 following:1 trans:1 mx:1 compare:1 degenerate:2 give:1 process:2 sense:1 indicates:4 uam:1 want:2 allowed:1 rodr:1 verlag:1 azquez:4 provide:1 means:1 regions:1 maps:1 pair:1 get:4 significance:1 ordinary:1 parameter:1 profile:5 map:3 de:3 description:2 singular:1 replacing:1 after:2 applications:4 plane:8 inst:1 dibenedetto:1 data:1 constants:3 branches:2 explicit:4 summing:1 so:11 definitions:1 juan:5 eron:1 considerations:1 over:4 mainly:1 soon:1 paper:1 london:1 existence:1 satisfies:1 still:2 its:3 before:2 write:1 derive:1 decay:1 interesting:1 solving:1 decreases:1 actually:1 forms:2 offers:2 systems:1 jacobi:1 derivative:1 main:2 decades:1 correspondence:1 non:2 bernoulli:1 undoing:1 introduce:4 scaling:1 mention:2 hamilton:1 they:3 oxford:4 now:6 term:2 2p:1 4n3:1 auto:1 publication:1 university:1 identified:1 radial:3 disregard:1 2m:9 2n:10 side:1 carlos:1 departamento:2 differential:1 series:2 reduce:1 applicable:1 literature:1 separating:1 our:5 special:2 out:2 shown:2 rey:1 space:3 since:7 denotes:1 may:3 lecture:1 rn:1 math:1 shows:1 maz:1 theory:7 free:5 standard:1 york:2 besides:2 intermediate:2 monographs:1 nirenberg:2 r1:4 anchez:1 geometry:1 βx:2 βy:1 times:1 turn:1 produce:1 place:1 universidad:2 consequence:1 first:5 sanchez:5 there:6 symmetry:1 striking:1 variables:7 number:5 xz:1 precisely:1 given:6 noma:1 exists:1 introduction:1 eqs:1 system:12 relations:1 their:1 assumption:1 exponents:2 gives:5 option:1 relationship:1 exactly:2 translation:1 representing:1 diffusion:7 king:2 double:2 second:3 final:1 preparation:1 classes:1 loewner:2 lines:1 ann:1 mind:1 lin:1 any:3 generalizes:1 latter:1 note:5 instance:1 k1:2 objective:1 extrapolating:1 coincide:2 formulas:1 birkh:1 most:1 phase:8 es:2 tpe:1 clear:2 phil:1 flow:3 heat:6 order:2 left:1 dot:4 precise:1 selection:1 show:1 supported:1 functionals:1 minimizing:1 relation:3 solutions:25 find:2 symmetric:1 based:1 ıguez:1 parameters:7 basel:1 only:3 parabolic:4 bureau:1 interested:1 do:1 exceptional:1 aiii:1 between:5 diffusivity:1 ones:1 expresses:2 differentiating:1 prime:1 evolution:2 arxiv:1 fixed:1 view:1 coefficient:1 set:4 reference:1 aplicada:1 reinforce:1 result:1 recently:1 phases:1 exponent:1 αy:3 αz:1 definite:1 dipole:1 boundaries:1 written:1 identification:3 αf:2 progress:1 boundary:1 conditions:1 yamabe:2 preserve:1 terms:2 parallels:1 importance:2 comm:1 key:1 interface:1 problem:2 c22:1 both:10 last:1 many:1 taking:1 laplace:1 propagation:2 connection:1 poincar:1 behaviour:1 contribution:1 whole:1 matema:2 detailed:1 point:1 cf:6 dimensional:2 assertions:1 caselles:1 respect:5 eβt:1 ps:6 combines:1 described:1 transformations:2 equivalent:1 laplacian:10 pc:12 cauchy:1 asymptotics:2 interest:1 basic:1 empty:1 direction:1 corresponding:4 mail:2 c3:9 c2:13 c1:14 careful:1 universitext:1 those:1 case:19 k2:3 straight:1 profiles:3 will:6 while:1 replaced:2 behavior:1 situation:1 property:4 played:1 almost:1 thus:1 them:1 iv:1 ii:9 reads:1 different:7 perform:1 make:1 same:4 clearly:1 ticas:1 finite:2 independent:1 used:2 see:1 trajectories:3 flows:3 hand:1 auser:1 changing:1 identity:1 recent:1 lower:1 shortly:2 proceed:1 disappears:2 well:3 analysis:5 obviously:1 sets:1 vazquez:6 dimension:5 usual:1 just:1 cantoblanco:1 resp:1 obtain:3 differentiation:5 speed:2 eaire:1 cut:1 conclusions:1 except:1 selfsimilar:10 belongs:1 versa:1 theorem:1 extensive:1 transformation:4 real:3 posed:1 possible:4 corresponds:3 tica:1 increases:1 press:3 using:1 bit:1 insert:1 identifying:3 follows:2 qualitative:1 performing:1 porous:11 either:1 arbitrary:1 popular:2 become:2 reduced:1 mathematical:2 because:1 madrid:3 some:6 pacific:1 self:14 calculated:1 growth:1 choosing:1 diff:1 dimensions:2 univ:2 critical:2 novelties:1 bn:1 each:1 ple:17 found:1 analyses:1 properties:2 takes:2 pβ:3 algebraic:1 quasilinear:1 discussed:1 practical:1 range:1 converging:1 ηf:1 soc:1 cambridge:2 into:5 obtaining:1 lies:1 right:1 references:2 been:4 log:2 support:1 initial:1 fast:5 smoothing:1 quadratic:5 way:1 analyze:1 was:1 assumes:1 function:1 medium:11 complete:2 form:6 sequel:1 but:4 repeated:1 pdes:1 made:1 improved:1 consultants:1 ut:3 up:2 us:2 um:1 dφ:2 below:1 limit:2 planes:1 demonstrate:1 autonomous:3 similar:12 called:2 mechanics:1 associated:1 aronson:1 abstract:1 describe:1 general:3 ap:1 exist:1 journal:1 ax:1 esteban:1 check:1 functions:2 nm:1 no:1 when:4 detail:1 ny:1 other:6 role:2 details:2 branch:4 mathematics:2 separate:2 models:2 radially:1 a1:2 a2:2 variable:5 implies:5 dψ:2 vice:1 assume:6 interval:2 curve:1 eαt:1 rule:2 4n:1 parallelism:1 remarked:2 n1:2 n2:3 precedent:1 |
0705.1715.txt |@word proposition:1 restriction:2 probl:2 manifold:5 consider:2 proposed:1 alg:1 loeb:2 obtain:1 spaces:4 andreotti:1 still:1 trivial:1 ohsawa:1 compact:2 erents:1 le:2 group:2 holomorphe:3 kyoto:1 infinitely:1 sheaf:2 aume:1 examples:1 analytic:4 other:2 manifolds:1 th:2 theorem:6 aux:1 analogous:1 main:1 local:3 variables:2 serre:4 colloque:1 conjecture:1 yj:17 relatifs:1 stein:42 means:1 de:15 disque:1 certains:1 corollary:1 completeness:1 every:6 eminaire:2 words:1 lecture:2 ayant:1 using:1 now:3 exact:4 eme:1 dim:2 february:1 mayer:1 subsets:1 exits:1 covering:3 komplexer:1 follows:4 notes:2 arxiv:1 summary:1 solved:1 vector:1 globaux:1 reduced:1 subset:1 annalen:1 domain:1 set:1 neighborhood:3 exists:5 sequence:7 mathematicae:3 espaces:1 see:3 num:2 result:2 diff:1 elliptic:1 es:4 spectral:1 provided:1 said:1 dense:1 space:4 giving:1 demailly:4 since:8 cohomologie:2 holomorph:1 contained:1 annals:1 exit:1 sur:2 above:1 between:1 new:1 increasing:2 induction:1 math:5 shows:2 counterexample:3 fiber:4 localement:1 fibre:3 deduces:1 morphisme:1 journal:1 homologique:1 however:1 refinement:1 hsp:13 base:8 key:1 article:2 along:1 publ:1 equations:1 complexes:1 similarly:1 o:12 vietoris:1 union:1 les:1 ox:47 consequence:1 bounded:1 ou:1 proof:7 generalizations:1 support:2 morphism:5 xj:42 mathematical:1 soc:1 there:8 groups:1 classification:1 point:4 skoda:4 image:1 cohomology:9 cf:1 proves:2 system:2 dimensional:3 bruxelles:1 stehl:1 references:1 exemple:1 moreover:2 fibr:5 open:6 cv:1 plurisubharmonic:1 necessarily:1 raise:1 prove:2 introduction:1 positive:1 strictly:3 locally:3 question:1 negative:1 long:1 france:1 ψk:5 therefore:1 plusieurs:1 fonctions:2 inventiones:3 associated:1 holomorphes:2 surjective:2 holomorphic:4 grauert:1 finitude:1 complete:5 continuous:3 vari:1 vollst:1 oπ:3 ix:1 coherent:1 analytiques:1 univ:1 bull:1 implies:3 youssef:1 coefficients:1 isomorphism:2 showed:1 eor:1 whether:1 la:1 des:1 un:2 pour:1 assumptions:1 ui:8 grothendieck:1 ms:1 uj:3 following:1 under:1 problem:5 ero:2 similar:1 fornaess:2 function:2 quelques:2 constant:1 conv:1 give:1 vol:1 vi:3 ann:1 vk:7 thus:1 psh:2 itself:1 numbers:1 counterexamples:1 vanish:1 lelong:2 any:1 emes:2 functions:2 e2p:1 lemma:5 groupes:1 fibers:4 when:1 same:1 note:2 k1:1 complex:9 ebre:1 runge:2 answer:2 mathematics:1 φj:10 finite:1 map:4 exactly:1 may:1 suppose:2 sets:4 bundle:2 hand:1 hence:1 levi:2 connected:2 plan:1 end:1 arch:1 natural:1 neighborhoods:2 assume:1 clear:1 no:1 non:3 sk:2 sj:3 mathematische:1 points:1 so:1 fundamental:2 time:1 hyperconvex:3 dimension:4 fact:1 |
0705.1717.txt |@word represent:16 sci:1 consider:10 chain:1 secondly:1 rev:20 alternatives:1 results:7 leads:9 gf:17 mild:2 consists:2 contributions:2 localized:1 poorly:1 whose:2 inverse:1 referring:1 zone:1 χg:10 similarity:1 nonlocal:8 answered:1 uniqueness:1 critical:2 tk:1 excluded:1 stable:2 aux:34 analogous:2 dramatically:2 straightforward:2 outside:1 very:3 bm:5 rise:1 seemingly:2 wave:17 electron:18 balancing:2 repulsion:2 affect:1 difference:1 exact:15 condition:1 gg:7 presented:2 bn:4 cause:1 solution:3 correct:8 large:13 vector:3 independence:1 indices:1 eigenvalues:8 refer:1 upper:4 smaller:3 findings:3 equated:1 sign:1 past:1 hirata:2 second:1 enclosed:1 baerends:1 further:2 chem:10 addition:1 even:8 index:3 what:5 fℓ:2 appear:1 sum:5 expressed:1 uniform:1 cell:6 version:1 above:10 elucidate:1 new:3 appeal:1 method:14 themselves:3 paradoxical:3 oep:3 simultaneously:1 chose:3 exchange:118 perdew:2 respectively:9 equals:22 orbitals:66 diagonal:6 met:1 them:2 bj:2 irrespective:1 represented:9 slater:5 along:4 quite:1 equations:1 change:2 obtained:14 great:1 sahni:1 vogl:2 involved:1 vectors:10 completely:2 contradiction:5 periodic:3 products:48 usually:3 della:1 changes:2 uniquely:1 limx:1 via:4 merely:1 magnitude:3 highly:2 decrease:2 achievable:1 translational:1 summation:5 apply:1 total:8 linearly:42 denominator:1 derivatives:1 use:4 andreas:2 additive:1 usa:2 remains:3 contains:7 finally:1 induction:1 next:5 few:3 doubt:1 therefore:21 vi:1 taken:6 means:4 type:2 more:13 kohn:9 operators:7 under:1 odinger:1 purposes:1 appendix:2 superindex:1 far:1 particular:1 known:1 cases:9 hold:1 iii:3 nodes:2 must:7 high:5 account:5 valued:11 aµν:7 equation:25 work:4 remain:2 fock:5 values:5 following:5 nonsingular:1 ernzerhof:1 arrive:1 example:3 stimulating:1 proof:1 corrupted:3 stated:1 calculation:2 choice:1 arise:1 table:4 rc:3 states:1 sphere:1 hhf:1 degenerate:1 sense:5 unphysical:12 sharp:1 mel:1 tions:1 occur:1 axis:3 nonvanishing:1 respective:1 end:2 provide:1 discussion:1 holds:3 occuring:7 carrier:1 instead:2 lehrstuhl:1 oscillatory:3 simplicity:3 product:9 magnitudes:2 may:12 derived:3 mapping:1 δvs:4 applications:2 wrong:2 plane:28 shadwick:1 rinke:1 waves:12 representations:8 minimizes:2 fk:20 response:27 types:1 introduced:2 physical:3 remember:1 effective:16 resemble:1 slightly:3 correspond:4 element:2 si:3 ones:1 so:1 keeps:2 representation:18 subsequently:4 order:9 brillouin:1 interpretation:1 help:1 correlation:1 numbers:1 indeed:4 over:5 displayed:3 choose:1 interpreted:2 funtions:1 course:4 paper:1 including:1 differs:1 kinetic:4 still:3 its:3 before:2 rapidly:8 how:6 energies:13 matrices:9 solving:1 vicinity:1 exhibits:3 actually:2 systems:2 densityfunctional:1 derivative:5 main:1 might:2 setting:1 maximal:1 eventually:1 non:2 greater:1 combination:10 integral:3 practice:2 fig:5 introduce:1 framework:3 they:9 φi:28 singularity:1 now:8 discuss:2 refering:1 represents:8 february:1 φk:14 equality:2 name:1 dreizler:1 goldstein:1 always:9 university:1 hamiltonian:18 orthonormal:1 sufficiently:6 inequality:2 reasonable:1 each:9 found:1 universit:1 higher:8 side:10 characterized:3 bond:3 homogeneous:1 int:1 schemes:9 ei:1 engel:2 generation:1 δφa:2 energy:61 gaussian:4 related:3 applicable:1 constitute:1 balanced:7 ex:1 combining:1 tˆ:5 our:4 differ:5 eq:34 special:5 really:2 minimizations:1 shown:5 accomplish:1 matrix:63 space:24 restricted:2 furthermore:2 since:2 crucial:3 denotes:4 increase:1 orthonormalized:1 reader:1 denoted:2 size:1 ref:10 occurs:2 burke:1 shows:7 8n:2 linear:26 written:2 easily:1 given:32 contrast:1 small:8 reason:5 term:1 full:1 rises:1 generate:1 definition:1 pairs:2 derivation:2 determining:2 could:1 hamel:1 times:4 silicon:7 turn:2 length:3 mesh:1 derivations:1 st:2 dft:1 consequence:2 first:11 note:2 features:1 symmetry:2 variables:1 fg:5 number:20 rank:1 theoretische:1 idempotency:1 bartlett:2 multiplying:1 least:5 another:1 changing:1 carry:2 xs:22 precisely:2 angular:1 illustrate:3 equating:1 little:2 vxn:10 introduction:1 leading:5 eqs:3 system:9 construct:2 their:9 too:13 calculations:10 scheme:22 gives:1 figures:1 shell:1 statement:1 square:1 explanation:1 unoccupied:44 contribute:1 immediate:1 authors:1 representing:5 than:13 coefficients:13 approximation:1 level:1 determines:4 φg:9 showed:1 fuchs:1 lying:1 quantum:1 summary:1 zero:18 submitted:1 matter:3 determined:1 yang:2 were:3 tion:1 distinguished:1 result:2 exhibit:2 function:36 idempotent:1 ev:4 a32:1 unchanged:1 argument:3 summing:1 already:1 adele:2 tables:1 close:1 disjoint:1 seen:1 seem:1 constrained:6 occupied:34 any:16 relatively:2 lie:2 eig:1 depending:1 latter:5 able:1 εs:1 converges:1 onset:1 potential:88 equaled:1 take:1 converged:2 summations:1 εa:9 davidson:10 criteria:1 exactly:6 shall:6 φhf:3 reach:1 δex:5 most:2 optimized:12 germany:1 lists:2 subset:3 why:1 stands:1 volume:1 give:1 consequences:1 considered:11 sala:1 later:1 implications:1 dent:1 ks:87 unbalanced:4 construction:4 electrons:1 oscillates:1 physics:2 section:1 exx:25 optimal:1 emerging:2 show:8 violation:1 converge:2 levy:7 radii:1 relation:6 solutions:3 hohenberg:4 analogue:1 longer:4 schmid:1 ground:39 ock:2 knowledge:1 situations:1 occ:9 state:41 only:42 going:1 minimize:4 constituents:1 employed:2 local:13 carolina:2 dn:2 do:6 dm:5 dj:2 get:3 dependent:21 ivanov:3 de:1 expectation:3 cannot:2 negative:1 closely:1 despite:4 combinations:5 magyar:1 designates:1 procedures:1 boundary:2 increasing:4 determinants:3 densities:6 covering:1 conditions:4 arxiv:1 fixes:1 yield:15 nant:1 twice:1 li:1 common:7 contain:2 through:1 valid:1 integrable:2 view:1 kernel:2 requirement:1 set:143 exists:5 achieved:1 physically:2 lett:5 observed:1 see:2 electrostatic:1 radius:3 usefulness:3 talman:2 collects:1 momenta:1 illustrated:1 points:1 cutoffs:9 ways:3 functionals:3 continually:1 symmetric:6 tantamount:1 enough:2 boeck:1 various:3 closed:1 between:3 fermi:1 neither:1 approach:6 chemie:1 hence:1 terms:2 sections:1 weak:2 deliver:3 however:25 wu:1 concentrate:1 comm:1 here:9 extent:2 article:1 come:1 wx:2 both:5 many:4 taking:1 conclusions:1 according:10 against:1 chosen:16 iv:1 dated:1 context:1 distinction:1 contribution:2 hφ:1 experimental:1 otherwise:5 arbitrarily:2 among:3 relevant:1 key:1 point:11 simple:2 φpi:1 corresponds:1 exploit:1 simply:2 respect:4 throughout:1 described:1 transformations:1 basis:221 would:3 ou:1 due:4 ai:1 much:3 combined:1 basic:1 ph:1 pi:1 define:1 box:5 determinant:18 arises:2 corresponding:25 tµν:1 present:1 quantities:4 sufficient:3 natl:1 gas:1 search:7 spectrum:1 bulk:3 observe:1 determination:1 external:4 func:1 input:1 general:13 those:4 case:34 semidefinite:1 ρhf:2 reciprocal:4 expanded:2 appearance:1 value:5 will:3 while:6 behavior:2 applies:2 situation:4 property:1 neugebauer:2 identical:11 unitary:3 orling:9 vh:12 gritsenko:1 refs:2 thus:19 surprisingly:1 surface:1 equal:13 ii:6 vs:12 auxilliary:2 turns:3 vx:41 orbital:91 different:24 erroneously:5 anymore:1 pseudopotential:2 lengths:1 majewski:2 eigenvalue:1 indistinguishable:1 same:12 clearly:2 φa:31 complex:4 grabowski:1 arguments:11 vext:12 units:2 resulting:24 φj:3 finite:36 horton:1 φm:7 φn:11 sham:5 independent:24 used:6 countable:1 somewhere:1 comprehensive:2 hand:13 a1133:1 potentials:22 infinite:10 paradox:1 hartree:10 expand:3 recent:2 eigenvectors:3 lower:3 schr:1 nevertheless:1 expression:1 nonetheless:1 well:8 roughly:2 analysis:2 obviously:1 solids:1 without:2 solve:2 components:1 sets:29 firstly:3 iafrate:1 arising:3 dimension:3 figs:1 vˆn:1 facto:1 just:2 decreasing:1 true:2 generally:1 accurate:1 obtain:4 atomic:2 integer:1 alternative:1 eigenstates:2 previous:1 adding:2 cut:15 density:30 insufficient:1 seems:1 smoothness:1 lattice:6 staroverov:18 nor:1 theorem:4 εi:8 vˆee:4 transformation:3 real:23 available:1 optimizations:1 eigenfunction:1 depends:2 alternatively:1 showing:1 possible:4 spanned:6 possibly:1 immediately:1 unique:5 reconsidering:1 scuseria:18 counterintuitive:1 appearing:1 like:3 particle:1 follows:6 specific:1 casida:1 yields:11 starting:1 integrals:2 arbitrary:6 multiplicative:7 become:6 works:2 reasonably:1 towards:3 replacement:1 therein:1 right:10 methods:26 creation:1 some:4 back:1 added:2 acad:1 b1:2 b2:2 moreover:6 oscillations:3 treatments:1 diagonalizing:1 happens:2 provided:5 scale:3 lead:7 realistic:1 demonstrates:5 nonpositive:1 overlap:1 contributing:1 does:16 unit:6 proc:1 demonstrated:2 either:2 ecut:50 run:1 obey:1 minimization:1 infinitely:3 equivalent:3 martin:1 oscillating:6 agreement:1 expansion:7 bk:11 bt:1 broken:1 step:1 symp:1 using:1 refers:3 panel:2 comparison:1 about:7 energetically:9 carried:3 constraint:1 discussed:3 dependence:5 o:1 practical:3 dependency:5 aℓ:1 a2:1 plus:2 obeys:2 ov:1 comp:1 manyelectron:1 consequently:1 block:5 cutoff:20 equally:1 into:8 within:10 numerically:2 functional:10 three:6 appropriate:2 because:17 references:2 raises:2 determine:1 operator:20 scheffler:2 a3:1 rely:1 rows:1 span:1 assumed:1 there:10 question:4 long:2 start:3 describes:1 low:2 way:4 series:1 krieger:1 was:8 lowest:5 north:2 complete:16 form:6 urnberg:1 differences:1 analyse:1 but:13 searching:1 erlangen:2 properly:3 φl:6 larger:5 highest:1 hf:89 enlarging:1 he:1 kℓ:5 consist:2 whether:5 smooth:10 up:6 us:1 ur:1 crystal:1 below:3 limit:4 approaches:1 demonstrate:1 problem:1 panels:2 display:1 examples:3 constant:9 defined:9 certain:6 abstract:1 b3:2 direction:2 denote:5 chooses:1 proper:8 single:7 exist:1 formulation:1 formalism:1 constructed:7 incorrect:3 again:5 functions:52 beyond:1 nl:1 varga:1 no:11 whereas:1 when:7 vanishes:1 virtual:9 sharif:1 other:12 becomes:1 department:1 xks:2 out:9 conclusion:3 poor:1 picture:1 briefly:1 elements:23 gross:1 includes:1 a1:1 generated:3 important:2 additionally:2 variable:1 sides:1 auxiliary:68 coulomb:3 assume:4 resolution:1 curve:3 rule:1 dr:7 equivalently:1 itself:2 fact:6 time:1 qualitatively:1 nuclei:1 requires:2 original:2 |
0705.1718.txt |@word limited:1 monte:1 vorticity:1 consider:6 chain:1 broaden:1 particular:2 results:9 projected:3 leads:3 roy:2 mild:1 parametrisation:1 perturbations:1 contributions:2 row:3 extra:4 looking:1 detects:1 caldwell:1 effort:1 tr:1 program:1 indicate:1 contours:5 excluded:1 under:1 include:4 probe:2 mpc:2 very:2 supercomputer:1 ostriker:1 emphasized:1 jha:1 four:1 groth:1 level:2 positions:1 cmb:5 ri:6 large:5 red:3 team:1 small:2 markov:1 silberman:1 degeneracy:2 upper:1 10h:1 smaller:3 zi:3 zj:3 riess:6 consistent:1 estimates:1 prediction:1 approximation:2 zero:2 evaluated:1 birkinshaw:1 further:2 estimated:1 carlo:1 monteagudo:1 theory:2 factory:1 aim:1 ˆr:1 nonlinear:1 christ:1 beaten:1 while:3 uniform:2 current:5 experiment:1 ˆrij:2 above:2 flowing:1 new:1 duplicated:1 method:5 edited:1 full:2 respectively:2 compilation:1 component:2 here:1 agreement:1 pedro:1 separation:2 others:1 alone:1 ratio:1 table:5 obtained:2 search:1 leaves:1 larger:1 allows:2 example:1 prior:4 survey:10 usually:5 fourier:2 studies:1 sci:1 useful:3 although:1 δdl:3 offset:1 technologies:1 decrease:1 apply:1 extinction:1 insti:1 wang:1 derivatives:1 use:4 pushes:1 hudson:2 suppl:1 comparing:2 therefore:7 conley:2 type:3 theoretical:1 more:2 flat:6 greene:1 apparent:1 lightcurve:2 instrumental:1 appendix:2 excellent:1 iv:1 iii:1 must:2 high:11 indicates:2 avoiding:1 equation:3 work:1 measures:1 values:1 thin:1 following:2 scatter:2 compare:4 repectively:1 cosmological:9 give:1 ˆri:2 lewis:2 sample:1 effectively:1 minimum:1 degenerate:1 magnitudes:3 exclude:1 times:1 absolute:1 information:3 rather:1 discussion:2 δka:1 δk:2 astronomers:1 how:1 vital:1 parameter:6 sin:2 sne:51 undergoing:1 outlier:1 may:1 broad:1 after:2 different:4 diagram:1 mag:1 fits:1 data:13 parallel:1 bonvin:2 marginalize:1 short:1 effective:2 sets:2 negligibly:1 light:4 sq:3 separations:1 cosmology:9 accelerated:1 negligible:1 sn:5 allow:2 correlation:2 order:1 ith:1 over:9 vary:3 soc:2 through:1 statistical:3 jimenez:1 still:1 galaxy:1 ηb:3 dwb:1 thank:1 ln:4 coordinates:1 better:2 estimating:1 detected:1 rubin:1 compelling:1 fig:10 main:1 into:2 eventually:1 them:5 than:5 conversations:1 a0v:1 investigated:1 bang:1 effects:2 oxford:3 now:5 gasparini:1 schommer:1 term:3 gets:1 mcmc:4 zehavi:2 λcdm:3 sugiyama:1 l7:1 magnitude:3 each:1 instability:1 feldman:1 mean:3 weighted:1 significantly:4 energy:2 reduce:1 gaussian:1 related:1 inverted:1 society:2 used:6 eisenstein:1 combining:1 our:11 nonlinearities:1 out:1 try:1 shown:3 matrix:8 space:4 3rh:1 rev:6 investigate:2 research:1 increase:4 fellowship:1 dominate:1 cause:1 correct:1 rj:6 shows:1 dataset:7 cosmomc:1 linear:3 confidence:2 galaxies:1 given:12 free:3 standard:4 completely:1 corrects:2 estimate:6 likelihood:5 generate:1 pyne:1 l91:1 hubble:5 kunz:1 cosmic:2 days:1 keep:1 american:2 gordon:1 δij:1 davis:2 first:2 spergel:2 relate:1 number:2 done:1 another:1 thick:1 angular:1 size:1 surveys:4 perturbation:1 checked:3 needed:2 unduly:1 vasey:1 their:4 assumption:1 observations:1 hypothetical:1 wildly:1 gained:1 futile:1 linearities:1 σv2:1 contribute:2 accurately:1 suntzeff:1 believe:1 peculiar:21 megaparsec:1 distance:4 was:5 approximations:1 namely:1 aims:1 normalizing:1 project:1 matter:5 lmax:1 future:6 were:1 lines:3 modern:1 spectrum:4 dilday:1 dash:1 challinor:1 aldering:2 seen:1 any:1 acceleration:1 robertsonwalker:1 unsuitable:1 marginalizing:1 latter:1 nucleosynthesis:1 slosar:1 note:2 phillips:1 fitting:2 potential:1 take:1 wmap:11 underestimating:1 even:3 begin:1 towards:1 multiple:1 shall:1 who:2 hui:1 errors:13 bridle:1 overlapping:1 letter:2 formulae:1 pair:2 nuisance:3 intrinsic:3 probes:2 kb:2 ka:7 observation:1 considered:1 average:1 stronger:1 km:2 kr:1 verde:1 funded:1 velocity:11 constrain:5 physics:2 bulletin:2 dot:1 quantity:1 eldar:1 text:1 random:4 progress:1 astrophys:13 find:5 based:1 parameters:16 distributed:3 ox1:1 should:1 only:4 wood:1 black:2 factor:1 perlmutter:1 cooray:1 continuity:1 do:3 dl:13 dk:1 overall:2 methods:1 datasets:4 dz:1 radburn:1 combinations:1 blue:1 dt:1 silk:1 freedman:1 prime:1 runs:1 densities:2 luminosity:6 arxiv:5 remove:2 rotationally:1 bad:1 4πd:1 predicted:1 analytical:1 including:8 fixed:3 ignored:2 pvs:14 set:5 constructing:1 observer:1 sep:1 correlations:6 j0:1 j1:1 up:1 observed:1 see:7 college:1 eliminating:1 recently:1 uncorrelated:5 particle:1 incorporating:1 detect:2 spectrophotometric:1 away:1 dipole:1 vol:2 vki:1 state:1 jth:1 between:6 seljak:1 invariant:1 approach:1 available:2 lasenby:1 comparable:1 multicolour:1 ability:1 extend:1 supernova:4 weak:1 however:9 joe:1 modeling:1 cosmos:1 comparably:1 both:2 cos:4 fαα:1 improved:1 σm:7 many:1 region:1 uncertainty:3 juszkiewicz:1 sensitive:2 present:1 context:1 σs:1 variance:1 contribution:1 σv:7 nearby:4 among:1 co:1 necessary:1 conclude:2 smith:1 cg:1 period:1 ii:1 non:2 gorski:1 church:1 respect:2 throughout:1 cv:6 watkins:1 considering:1 bbn:3 pp:2 pv:9 second:1 addition:1 due:3 been:1 combined:2 expected:1 degrees:3 ph:30 θj:3 tytler:1 θi:3 vkj:1 subscripts:1 covariance:10 snap:6 coherent:3 cor:1 systematic:2 astron:5 astronomical:2 denote:1 irrelevant:2 those:5 case:1 randomly:3 limits:2 supernovae:11 thomsen:1 solid:2 budget:2 marginalised:7 rectangular:1 will:5 near:1 fiducial:1 evaluating:1 error:14 situation:1 conformal:2 study:1 procedure:1 computed:1 almost:1 marginalise:1 vk:2 thus:1 herein:2 vo:3 obeying:1 ik:1 bias:1 rij:2 discoveries:1 ia:3 ignoring:1 id:1 confirmed:1 wolff:1 baseline:1 perform:1 make:1 cross:1 same:3 underestimate:1 largest:1 units:1 resulting:1 several:2 durrer:2 higher:3 independent:2 literature:1 dobs:2 numerical:1 effect:3 forecasts:1 inhomogeneities:1 constraining:2 codes:1 moving:1 gelman:1 tyson:1 lower:4 suitable:1 snfactory:6 modeled:2 analysis:7 academic:1 without:3 components:1 priors:3 position:1 model:2 ccc:1 usual:1 distances:1 excessive:1 just:2 generally:1 obtain:1 underlying:1 differentiation:1 ωm:13 alternative:1 speed:1 sugiura:1 cut:3 density:2 hamuy:1 scales:1 sky:1 source:1 valid:1 combine:3 lett:1 samples:1 relevance:1 increased:1 depends:1 big:1 decomposed:1 kirkman:1 dark:2 increases:3 mon:2 background:1 press:2 using:7 imposed:2 like:5 excluding:1 δw:3 reduces:1 velocities:13 separately:1 flux:1 keble:1 continue:1 either:1 arbitrary:1 become:2 reduced:1 because:1 often:3 some:2 play:1 meara:1 growth:2 b1:1 statistic:1 neglecting:1 kirshner:4 provided:1 ferreira:1 scale:1 highlighting:1 lead:1 demonstrates:1 avoid:1 measurements:1 integration:1 microwave:1 provides:1 assuming:2 chains:2 refer:2 noise:2 power:4 d73:3 equivalent:1 perpendicular:1 expansion:1 broken:1 hst:3 found:3 properties:1 panel:2 pβ:1 comparison:1 about:3 pα:1 bars:3 universe:7 dependence:2 o:1 essential:1 range:3 krl:1 constraints:5 slightly:1 road:1 cutoff:3 perturbed:1 significant:2 ηa:3 redshift:19 h2:1 h0:3 numerically:1 bound:3 three:1 down:1 included:5 lucey:1 reducing:1 dodelson:1 telescope:2 rows:3 log:1 area:1 redshifts:3 long:1 low:18 way:1 astrophysics:3 log10:1 suzuki:1 function:3 considerably:1 underestimated:1 δkb:1 lubin:1 enough:1 analyse:1 but:4 hu:1 astro:30 posterior:2 correlated:7 outweighed:1 convergence:1 line:2 removed:1 lowz:1 made:3 absence:1 default:1 gravitational:1 systematics:1 maximum:1 avaliable:1 limit:2 uk:2 lightcurves:1 fαβ:2 demonstrate:1 distribution:1 ωb:6 similar:2 baker:1 hernandez:1 constant:2 defined:1 flow:1 hosted:1 evidence:1 dashed:3 examine:1 simulations:1 accounting:2 distributions:2 check:1 sasaki:2 friedmann:1 compared:1 dotted:1 no:7 eq:4 when:12 highz:1 field:4 other:5 role:1 details:1 dekel:2 test:1 ns:6 deviate:1 stat:1 hannestad:1 models:1 stay:1 meaning:1 important:1 camb:1 variable:1 fisher:3 structure:1 land:1 longer:2 assume:3 neill:1 odds:1 required:1 curve:1 implied:1 weights:1 time:5 far:1 starting:1 astier:1 |
0705.1719.txt |@word represent:2 monte:2 consider:5 chain:3 interference:1 green:2 global:1 commun:4 splitting:20 tested:1 existing:3 four:16 mrenna:4 during:1 originally:1 go:3 expressions:2 disk:1 issues:2 restrictions:1 looking:2 dimensionality:1 depend:3 calculate:1 million:2 b289:1 similar:1 iii:2 concerned:1 pirjol:2 tr:63 tn:1 finally:2 does:5 restriction:1 tk:2 ti:13 analogous:1 include:4 ingredient:1 nason:3 applied:3 supported:1 amplitudes:1 advantage:3 evolves:1 very:6 desired:1 rise:1 results:4 me:1 putting:1 under:1 reweighted:3 affect:1 difference:6 exact:7 skands:5 rejects:1 look:3 leads:4 indicate:1 basics:1 moderate:2 level:4 did:1 turns:1 t2:4 solution:1 t0:64 t1:9 large:11 solved:1 pronounced:1 phase:19 section:7 small:7 provided:1 markov:3 reshuffling:1 enforce:4 zl:22 correct:7 zn:1 smaller:4 compensated:1 zi:12 zk:2 regained:1 gev:1 fit:1 generic:1 direct:1 gieseke:4 consists:1 second:11 evaluated:2 equal:1 further:8 estimated:3 carlo:2 remarkably:1 zr:13 even:7 employ:2 what:3 kuhn:2 adds:1 nagy:1 sum:1 uniform:1 current:1 consistently:1 mueller:1 version:1 optional:1 above:9 selecting:1 new:24 increasing:1 boost:7 consisting:1 contrast:1 satisfy:4 impact:1 evolving:1 full:10 christian:1 cwb:1 desires:1 eliminated:1 respectively:2 doing:1 never:3 modify:2 onnblad:3 here:2 ranges:1 following:1 asymmetry:1 test:1 free:3 berkeley:2 quark:2 z0:50 z1:2 z2:2 violate:1 obtained:10 solid:4 balance:1 daughter:25 ac02:1 involved:1 study:6 vectors:1 allows:6 completely:2 commonly:1 amount:1 resulting:3 yield:1 usually:5 complicated:5 implement:1 narrow:1 makes:7 involves:2 via:3 shuffle:4 mc:1 viewpoint:1 namely:1 explained:1 natural:2 thrust:3 decrease:4 frame:12 apply:1 total:5 tools:2 unit:2 use:8 feb:1 takes:7 would:9 failed:2 probabilities:9 contains:3 predictions:2 flat:1 next:4 distributing:1 few:6 depicted:1 program:1 kinematics:13 therefore:1 qcd:2 taken:2 themselves:2 simpler:1 type:2 theoretical:9 more:7 introducing:2 zh:1 partons:23 furthermore:3 successful:1 becomes:3 starting:4 emission:3 realized:2 terminates:1 normalized:3 particular:2 known:8 rare:1 cases:3 hold:1 effort:1 opens:1 must:5 choose:1 states:3 account:3 err:1 illustration:1 science:1 setup:1 work:6 modified:1 flight:1 hardest:2 itself:2 values:19 splittings:2 erl:1 ernest:1 example:9 performed:1 control:12 compare:5 norrbin:1 reasonably:1 indicated:1 give:1 process:1 introduces:2 allowed:3 parametrizing:1 purposes:1 accept:1 dzl:2 high:4 effectively:1 application:2 numbers:2 employs:1 arise:1 unphysical:1 counting:2 occur:1 collider:1 axis:1 information:2 needs:3 possibility:1 end:3 straightforward:3 rather:1 describes:2 discussion:3 acts:3 department:1 workshop:1 write:1 how:11 nontrivial:1 dzr:2 pure:1 dedicated:1 simplifies:1 instead:2 allowable:1 parameter:2 nonsingular:2 simplicity:3 product:5 de:1 krauss:5 description:2 may:5 ostrand:8 after:11 derived:4 different:12 corrections:22 wrong:1 produce:3 coming:1 twofold:1 choice:7 data:12 teor:1 shuffled:4 stress:2 short:1 lhc:2 effective:1 occasions:1 whenever:2 light:2 lines:4 gustafson:1 element:13 provide:2 branched:11 algorithms:9 expression:1 fundamental:2 decreasing:1 representation:3 increase:2 order:13 talk:1 typical:4 exclusive:3 holds:1 office:2 cutoff:2 indeed:1 over:11 move:1 restframe:1 satisfied:7 produced:1 held:1 paper:3 through:5 mlm:1 statistical:4 cuts:1 mentioned:1 satisfies:3 still:13 its:7 before:2 pt:2 render:2 correctly:1 acknowledge:1 chosen:5 masses:9 decreases:2 actually:1 estimating:1 fq:2 fig:17 pcm:1 orange:7 showered:2 main:1 might:1 pittau:1 eur:1 maximal:1 them:2 good:2 return:1 thereby:1 entire:3 matches:1 numerically:1 practice:3 introduce:4 framework:1 course:2 effects:3 they:8 implementations:1 now:13 discuss:5 matched:2 pps:13 term:1 finite:2 gev2:5 bengtsson:2 fully:6 university:1 2z:4 had:1 realistic:5 magnitude:3 each:26 found:3 difficult:2 side:2 characterized:1 constraints:4 el:15 differential:4 determine:1 weight:4 branchings:5 generation:5 tackmann:2 energy:18 hard:3 idea:1 related:3 webber:7 sj:8 remove:1 entering:1 proportional:1 quantum:1 laboratory:1 happen:1 beyond:2 eq:58 event:27 special:1 out:7 leave:1 shown:6 matrix:24 space:21 van:1 integrates:1 since:11 crucial:2 particles:5 similarly:3 adjust:1 05ch11231:1 get:2 illustrate:2 issue:1 occurs:2 shows:4 theory:10 lawrence:1 frank:1 enforcing:1 dealt:1 governing:1 standard:7 resums:2 reason:5 carried:2 california:1 ldrd:1 boosting:1 put:1 facilitates:1 estimate:7 remainder:1 generate:9 care:1 pairs:1 interaction:1 βr:3 applications:1 recast:1 starts:4 could:7 impose:1 running:2 feasible:1 turn:1 pdf:1 virtuality:2 incorporated:1 unknown:1 hence:9 scheme:2 hadrons:1 indispensable:2 colliders:1 first:17 already:5 probability:45 jhep:17 variables:8 dσ:2 powerful:2 number:4 getting:1 linking:1 improvements:3 done:2 construct:1 directly:4 impossible:3 luke:1 miss:1 angular:3 divided:1 size:7 given:22 necessarily:1 checked:1 their:4 introduction:3 leading:6 eqs:5 stewart:3 least:1 needed:3 intermediate:2 observations:1 calculations:8 hindered:1 efficiently:1 branches:15 final:20 store:2 too:2 attach:1 e0:17 shell:13 way:14 behind:1 explanation:2 acquire:1 lower:1 rejected:1 transverse:1 b238:1 part:2 simulate:3 attempt:1 tive:1 than:5 alternative:1 translate:1 impractical:1 third:4 dtl:1 double:15 require:1 tree:4 see:15 collinear:4 determined:9 speaking:1 amplitude:2 were:3 bauer:6 dtr:1 gives:4 perturbative:8 enforced:2 comput:4 shrinks:1 dada:1 correction:4 turned:2 generalization:1 randomly:1 discussions:1 medium:5 violating:1 unlikely:1 showers:18 need:3 unaffected:1 clearly:1 elsewhere:1 helpful:1 implemented:2 angle:5 zero:3 min:2 efficient:2 pursued:1 latter:1 fnal:1 able:2 ideas:1 violates:1 note:6 instance:1 fitting:2 promising:1 take:3 timelike:2 alwall:1 schematically:2 so:5 detector:11 miu:2 tool:2 relevant:1 blue:5 begin:1 relatively:1 though:2 any:13 sets:4 lbnl:1 phases:1 most:4 thank:1 encodes:1 retaining:1 grateful:1 analytically:2 extremely:3 why:1 exponent:1 branching:23 fiz:1 treats:1 conversations:1 clear:1 later:8 doe:1 kr:2 properly:1 principle:2 exp:3 b306:1 left:14 physics:3 consumes:1 quantity:2 precise:7 incorporate:1 efficiency:1 think:3 stephens:2 show:9 text:2 random:1 dependences:1 fleming:2 attempts:1 pedagogical:1 calculable:1 ridolfi:1 find:2 oji:1 partonic:1 access:1 trying:1 based:3 knowledge:1 parameters:10 shuffling:12 implementation:5 original:16 distributed:3 written:3 poles:2 should:3 analytic:46 only:20 explicitly:5 generators:4 subsection:1 factor:8 employed:2 distributes:3 interested:1 achieve:1 do:4 hit:1 goes:2 notation:2 means:1 there:3 diamonds:2 expectation:1 soper:4 cannot:1 dz:5 nearly:1 words:2 invariant:18 determines:3 dt:8 conjunction:1 amer:2 qq:1 gray:4 evolution:9 simplest:1 reweight:3 tcut:15 conditions:1 arxiv:40 βl:11 factorization:1 method:1 investigate:2 diagrammatic:3 qg:3 fixed:8 hadronization:1 view:1 enhances:2 bars:2 set:8 computed:3 physically:1 iteration:5 national:1 correlations:2 relative:4 depends:7 individual:3 sec:5 result:13 holding:1 fail:2 terms:9 particle:2 best:1 subject:1 shower:67 αs:7 satisfying:1 er:14 ways:2 subsequent:1 review:4 currently:1 state:12 classes:1 various:2 closed:2 between:15 understood:1 progress:1 subscript:2 moretti:1 approach:6 checks:1 available:5 ends:1 suppresses:2 recently:1 reproduced:2 opening:3 initially:1 restricting:2 however:10 effec:1 p2t:3 recent:1 manual:1 jets:1 phasespace:1 come:1 problem:4 pull:2 observable:3 cos:31 last:2 ell:1 limits:15 implementing:1 many:3 tmax:24 conclusions:2 catani:1 according:16 against:1 sov:1 somewhere:1 merging:1 sudakov:6 quite:2 estimation:1 whole:1 reweighting:9 experimental:6 otherwise:6 comment:1 eksp:1 adjusted:1 βi:1 point:4 simple:10 seems:2 ca:1 address:2 corresponds:3 pole:2 simply:5 respect:2 assign:1 considering:1 ensures:4 ei2:2 described:9 tuning:8 kinematic:6 addition:5 suppressed:2 inclusive:1 three:6 been:7 quickly:2 much:3 change:12 basic:3 expected:8 ph:40 tini:11 define:1 dots:5 generating:4 corresponding:7 easy:1 θl:11 both:5 quantities:2 sufficient:1 2z0:5 pettersson:1 accommodate:1 jettiness:1 ordering:5 understand:2 systematic:2 θr:4 consecutive:1 denote:1 those:1 case:12 exception:1 splits:1 contexts:1 reliable:1 expanded:1 appearance:1 aip:1 value:29 choices:2 will:8 while:8 momentum:19 error:2 b603:1 property:1 procedure:1 b632:1 bin:2 changed:2 inaccuracies:1 almost:1 vi:2 refs:1 ir:1 thus:11 non:1 iv:3 ii:1 reads:1 altarelli:2 converts:1 contract:1 conf:1 unbranched:4 vanish:1 conserve:1 acknowledgments:1 capture:1 containing:1 sample:1 righthand:1 anymore:2 sensitive:1 parisi:2 things:1 make:1 cross:4 same:10 check:6 unity:4 virtually:1 widely:1 uncertainty:1 several:7 events:38 daughters:34 higher:3 independent:4 used:9 http:1 peaks:1 trivially:1 boosted:1 essential:1 numerical:4 upon:1 effect:8 hand:1 director:1 squared:1 uses:1 purpose:2 necessity:1 skip:1 sisters:1 changing:3 tune:3 keep:5 experiment:2 subleading:2 off:3 undefined:1 older:1 nevertheless:2 changes:5 no:5 well:10 roughly:1 picks:1 thought:1 concrete:1 without:2 characterizing:1 simulated:5 mz:1 comparisons:1 model:2 johan:1 arising:5 fermilab:1 usual:3 spherical:1 mind:1 newest:1 schwartz:1 just:2 less:1 when:10 distribute:5 obtain:6 rest:8 assigns:1 sources:1 underlying:6 pnew:5 jetp:1 immediately:1 useful:1 momenta:2 zcut:14 yet:1 previous:5 adding:1 cut:3 generator:5 mother:32 hameren:1 regarded:2 evolve:1 transparent:1 signals:1 reasons:2 valid:3 combine:1 lett:5 versa:2 elr:1 input:2 vetoing:1 remaining:1 match:4 generalized:1 real:2 aspects:1 reuse:1 alternatively:1 checking:1 breaks:1 possible:13 b126:1 cf:2 dark:3 finding:1 increases:3 know:4 background:1 using:18 integrated:3 accepted:2 gleisberg:1 apart:1 modifications:3 tl:88 frixione:3 like:7 lost:1 follows:3 reduces:2 performing:1 orlando:1 serves:1 translates:1 specific:6 oct:1 steps:8 either:3 always:13 el2:2 become:3 soft:4 reduced:1 fnew:1 because:8 old:9 classical:3 picture:3 e02:1 perturbation:1 some:10 back:4 experiments:1 another:4 examples:1 choosing:1 moreover:1 home:1 peter:2 matching:2 nonzero:6 separately:1 scale:3 proceeding:1 logarithms:3 illustrated:1 support:1 avoid:1 measurements:1 integration:3 per:1 sch:2 everything:1 efficiencies:1 eliminate:1 provides:5 assuming:2 propagating:1 proc:1 corcella:1 limitations:1 destroys:1 varying:1 measures:1 run:5 power:24 vertex:5 equivalent:4 processing:1 consuming:2 expansion:2 translated:1 step:34 mangano:2 although:3 drawn:1 analyses:1 dictated:1 stage:3 comparison:3 sister:3 kinematical:2 ok:2 working:2 extension:2 constraint:5 scet:1 discussed:4 factors:1 o:7 simulation:10 practical:4 convenient:1 range:2 statement:1 greatly:1 act:1 insufficient:1 introduced:1 automatically:4 lowering:1 considerations:1 rev:7 orders:1 into:17 within:3 integral:2 functional:2 due:3 down:3 included:5 right:11 inverting:1 parton:90 returning:1 eini:13 fixing:1 forcing:1 technically:1 uncertainties:13 rely:2 hep:40 additional:10 shading:4 sherpa:13 measured:1 strictly:1 initial:6 nucl:6 long:1 start:2 accordingly:1 conservation:14 low:2 fraction:1 call:1 analyze:1 was:7 assumes:1 function:12 recompute:1 complete:2 form:19 energies:4 pme:8 adjusting:2 regard:1 agrees:3 but:11 failure:1 gov:1 construction:1 integrations:3 larger:7 ref:2 encoded:1 line:4 removed:1 true:2 considerable:1 absent:1 compute:1 largest:1 instructive:1 wish:1 up:3 us:2 marchesini:1 limit:13 emissions:2 iterated:1 approaches:1 distribution:31 minutes:1 average:2 expect:1 detailed:1 required:6 ordered:3 conserves:2 computing:1 defined:5 certain:4 describe:3 direction:2 general:11 single:19 violated:4 our:7 formally:3 distributions:4 proceeds:2 triangles:3 physical:3 again:2 functions:9 compared:3 ideally:1 gg:1 variety:1 amounts:1 dashed:4 whereas:2 generally:2 detail:4 invalid:2 field:2 other:13 details:2 branch:43 correlation:6 weights:5 massless:3 gaining:1 happens:1 elements:11 immediate:1 generates:4 separate:6 models:1 problems:2 update:2 includes:1 treelike:1 generated:22 important:6 track:1 pythia:4 suppression:2 studied:1 variable:3 soff:2 structure:4 searches:1 independently:3 implies:3 faster:1 algorithm:71 vice:2 assume:2 typically:3 proposed:1 timeconsuming:2 coherent:1 together:2 having:3 equivalently:2 factorizes:1 mass:12 time:10 far:1 richardson:1 requires:1 cpu:1 once:3 |
0705.1720.txt |@word secondly:3 monte:1 faber:1 ams:1 consider:1 remarkable:1 global:1 concern:1 results:7 elongations:1 four:2 σj2:2 proposition:1 teukolsky:1 during:1 edu:1 go:2 follow:1 contributions:1 causes:1 poorly:2 ebeling:2 simon:1 fits:3 calculate:1 integral:1 centres:1 governato:2 volume:2 description:2 technique:2 ρs:4 extraneous:1 containing:6 simplify:1 finally:3 does:2 those:2 lewis:1 include:2 lake:2 case:10 keck:2 lack:1 mpc:1 takes:2 outside:1 very:10 discrepant:1 3aa:1 rise:2 balcells:1 relatively:1 distort:1 splitting:8 grid:8 l5:1 every:4 anonymous:1 approximate:1 24th:1 difference:3 matrices:1 condition:1 common:1 generalised:1 entire:2 school:1 kinematic:1 lindner:1 presented:1 did:1 positions:1 list:1 cf24:1 fewer:2 integrated:1 large:8 sand:4 vector:4 form:2 small:6 referred:2 optics:1 noted:1 programme:1 application:1 smaller:6 recipes:1 ten:1 consistent:20 galax:1 approximation:2 morphology:8 likely:3 noise:4 basile:1 value:11 growing:1 qualitatively:1 ruled:3 estimated:1 carlo:1 quite:1 theory:1 spectral:1 will:1 what:2 errors:10 adds:1 appear:1 improvement:3 complexities:1 section:19 stars:1 http:1 brief:1 debate:1 current:5 mullis:2 version:1 reconstruction:7 vetterling:1 increasing:1 method:10 exercise:1 satisfy:1 full:1 submitted:2 excludes:1 respectively:2 l1:4 component:40 residual:1 here:5 diagonal:2 following:6 fairly:1 amplification:1 smearing:1 separation:3 meet:1 krist:2 layout:1 along:2 strong:13 transformation:1 z2:3 contraction:4 obtained:10 convert:3 gavazzi:3 arc:2 ellipsoid:1 nevertheless:1 institute:2 slow:1 study:1 changed:1 allows:3 contradiction:1 adopt:2 eh:5 trial:2 amount:1 resulting:4 loop:2 sphere:1 published:1 implement:1 bullock:2 studies:4 ies:1 elongated:1 brightest:2 spatially:1 although:11 figure:11 scales:2 problematic:1 triaxial:1 prefer:1 wij:2 magnitude:3 highly:2 scaled:1 visible:2 lenticular:1 apply:1 total:13 establish:2 unit:1 orientation:10 plot:2 use:7 towards:1 eye:1 cosmological:1 would:8 brighter:4 distinct:1 positive:4 h0:1 charge:1 next:3 comparing:2 magnification:5 camera:4 therefore:8 bender:1 taken:4 3le:1 exhaustive:1 noisy:1 type:2 creates:1 minor:3 more:14 beyond:1 initial:2 acceptable:2 easterly:1 emission:2 hii:1 berlin:1 surface:21 particular:2 known:1 further:4 cases:1 hold:2 rubin:1 must:6 spekkens:2 reconstructed:18 account:2 royal:1 integrating:1 science:1 equation:3 work:7 modified:1 nagai:1 column:1 labeled:3 isodensity:2 values:2 minimisation:7 evolved:1 smear:1 believed:1 making:2 l129:1 springel:4 example:3 covariant:1 point:6 claim:1 compare:2 rhodes:1 swinbank:4 indicated:4 give:8 process:1 discussed:1 referee:1 sense:3 grant:1 sigad:1 high:2 unbiased:2 minimum:2 degenerate:1 allowed:5 concordant:1 isothermal:3 axis:14 dominant:1 manner:1 respective:1 end:1 advantage:2 pure:10 provide:4 verify:1 discussion:3 s0:3 caustic:3 regions:3 how:7 varies:2 suggested:1 criterion:2 sie:18 elliptical:8 instead:1 guarantee:1 parameter:6 circular:2 profile:44 map:3 buildings:1 contribute:2 intended:1 information:1 may:2 overall:1 reconciled:1 after:2 different:16 constraint:1 less:1 testament:1 plane:24 kneib:3 designed:1 mag:6 date:3 findings:2 law:16 data:7 marginalised:1 aj:3 dynamical:4 moments:1 negligibly:1 light:15 schneider:4 counter:6 elongation:16 poggianti:1 cosmology:4 annealing:1 pixelisation:2 so:4 sn:3 allow:3 keeps:1 halos:4 sa:2 acknowledges:3 eds:2 divided:3 unmasked:1 upon:1 reproduced:1 holds:1 interpretation:1 developed:1 over:11 vary:9 xh:3 years:1 produced:1 whilst:1 paper:9 through:3 motions:1 dye:11 cold:1 hook:2 its:5 galaxy:33 warren:10 observational:2 chemical:1 accepted:2 lb:12 thank:2 fit:51 somewhere:1 interesting:1 fix:2 redshift:16 exhibits:1 edge:1 better:3 absence:2 according:1 degrees:12 systems:14 omitted:1 fij:3 fik:1 argentina:1 main:1 defining:1 into:8 archival:1 s1:1 yh:3 non:4 good:2 affected:1 contention:1 thereby:2 press:6 numerically:2 average:5 practice:1 investigated:1 tinytim:5 break:2 band:7 exponentially:1 simply:2 serendipitous:1 they:4 half:1 change:3 rotation:3 now:3 day:1 halo:22 represents:3 inversion:7 assessed:1 double:1 hereafter:1 brightness:16 fully:1 university:3 level:2 determine:1 nfw:5 micro:2 morris:1 kpc:3 reasonable:1 each:14 found:5 identifies:1 quarter:1 constraints:9 constructing:1 square:2 successively:1 telescope:2 weight:2 evolve:1 generation:1 reduce:1 bolton:3 solution:9 carry:1 extended:3 search:1 measurement:5 substantially:1 our:19 summary:3 extract:1 shearing:1 special:1 out:9 leave:1 shown:1 divide:1 matrix:5 space:2 restricted:1 since:7 crucial:1 projected:5 detailed:2 adhere:1 increase:2 rf:2 optical:1 dominated:1 xaxis:1 reader:2 suggesting:2 adaptive:10 squares:1 significance:5 ri:2 red:2 shows:8 foreground:4 quinn:4 gerhardt:2 turning:1 linear:16 disagree:1 confidence:2 galaxies:10 surveys:1 free:1 standard:4 extraordinary:1 completely:2 perturbation:1 formation:2 imaging:3 members:5 usual:1 ask:1 beginning:1 telescopes:1 software:1 degeneracies:3 hubble:2 r0:7 marshall:1 created:3 geometry:2 starts:1 could:2 persists:1 cosmic:1 frenk:4 times:2 filter:3 4th:1 place:2 massive:1 incorporated:1 assumed:2 hence:3 sersic:18 south:3 first:5 johan:1 major:7 there:3 shears:2 features:2 suyu:3 prevent:2 third:1 dithered:1 powerful:2 number:12 nested:2 stsci:3 wilman:1 multiplying:1 directly:1 comprises:1 impossible:2 ring:33 quality:1 angular:1 size:2 given:22 ian:3 temperature:1 kochanek:6 similarly:4 introduction:1 cambridge:1 top:11 saglia:1 system:7 approximately:4 yij:2 their:10 perturbations:2 observations:2 importantly:1 analytical:1 white:4 scheme:2 bosch:1 final:1 flannery:1 low:3 way:3 mostly:1 trapped:1 ity:1 baryon:3 relative:1 exactly:2 zeroth:1 accurately:3 rejected:1 required:2 assumption:1 part:3 bower:1 extensions:1 honolulu:1 parameterisation:3 brightnesses:2 july:2 than:13 outline:1 peaked:1 wide:2 target:1 showed:4 accordance:1 ersic:2 require:1 regularised:5 second:5 modelled:3 reconstructing:1 matter:11 appealing:1 computer:1 aas:1 were:3 quarters:1 contribution:5 exposures:1 treu:16 minus:1 covered:1 perturbative:1 contradicts:1 spectra:1 nsrc:2 correction:11 modern:1 mind:1 spectrum:3 curves:3 chapman:1 randomly:1 already:1 headings:1 lbg:8 close:1 need:2 seen:3 constrained:2 clearly:3 template:3 gives:7 conversion:1 tangential:1 angle:5 minimally:1 presents:1 cimatti:1 self:1 propagation:1 verlag:1 delivered:1 predominantly:1 six:3 extracted:1 fitting:5 potential:3 take:1 finding:3 negligible:4 parameterisations:2 subject:2 singular:1 evaluated:1 cl:1 added:1 multiple:4 centre:7 quote:1 who:3 reach:1 burles:3 positionally:1 most:4 regular:3 experiences:1 significant:2 baryons:10 future:1 measured:15 jean:1 queens:1 annulus:2 cause:1 episode:1 subtracted:1 blumenthal:2 considered:1 chosen:2 later:4 stronger:3 drive:1 km:3 order:2 2nd:1 giving:1 simplex:2 accounted:2 snapshot:1 exp:2 chris:1 velocity:3 constrain:1 left:4 physics:1 away:3 fact:2 satisfactorily:2 slope:24 incorporate:3 paul:1 contracted:1 ivison:1 apj:21 show:2 cdm:10 luminos:1 probe:1 anyway:1 degeneracy:4 converge:1 discovered:2 mnras:11 radii:1 keeton:2 convolved:1 degraded:1 determined:3 find:8 cordoba:1 par:1 nearer:1 proximity:1 removed:1 ratio:6 just:2 parameters:24 baryonic:16 implementation:1 explain:2 heavily:1 written:1 supported:1 should:1 analytic:1 only:12 originally:1 irs:1 factor:7 nyquist:1 µi:2 constant:1 he:1 local:9 astronomical:1 discuss:2 do:1 predict:2 dj:2 above:1 degrade:1 means:6 constructive:1 de:6 quantified:1 klypin:2 simplistic:1 cannot:2 dz:1 listed:1 gnfw:24 combinations:1 reconstruct:2 distortion:1 den:1 secondary:1 evolution:2 reading:2 continuum:1 held:2 luminosity:3 latex:1 arxiv:1 collapsed:1 comprising:1 consisting:1 navarro:7 meylan:2 investigate:1 predicted:3 fitted:7 characteristic:1 fainter:3 including:4 jetzer:2 fixed:9 inside:4 view:2 financial:1 rms:1 set:8 computed:6 exists:1 achieved:1 acquired:1 problem:4 frame:2 testing:1 observed:23 edition:1 see:20 individual:2 radius:16 result:3 enhanced:3 separately:1 terms:7 observatorio:1 springer:1 satisfies:1 best:30 techniques:1 error:8 exponent:1 ways:1 somerville:1 review:1 giovanelli:2 bias:1 ensures:1 macros:1 state:1 difficulties:1 barnab:3 between:9 probably:1 geometric:2 before:1 approach:1 multiplied:1 various:1 recently:3 ability:1 nature:1 weak:2 aesthetic:1 combining:1 however:9 acknowledgements:1 spectroscopic:1 gratefully:1 extent:1 outer:1 psfs:1 configuration:2 pixels:35 swaters:2 both:5 enables:1 improved:1 θh:3 many:1 taking:1 uncertainty:4 equal:1 against:1 fkj:1 enabling:1 sensitive:1 objects:1 f606w:6 improving:1 passing:1 mean:1 lenses:6 nearby:9 minimises:1 generalisation:1 ci:1 co:2 groups:2 conclude:4 simple:3 effective:2 address:1 corresponds:4 except:2 minimised:6 differ:2 iterations:1 consideration:1 table:9 throughout:1 lends:1 adaptively:1 smith:4 considering:2 complication:1 described:6 lyman:2 vanzi:1 addition:3 computing:1 due:5 been:5 ai:1 much:4 slowly:1 treat:1 interest:1 contained:1 expected:2 applying:1 ph:6 pi:1 fig:4 concentrated:1 direction:3 weighted:1 westerly:1 σj:1 photon:2 covariance:2 modelling:8 ndof:2 hayashi:6 offers:1 finished:1 ensuring:1 j2135:7 external:3 angles:1 clusters:1 bayesian:3 moustakas:3 v5:1 evidence:3 kronawitter:1 present:3 applied:1 laser:1 seds:1 wfc:3 straight:1 primack:2 budget:1 profiles:6 pixel:17 middle:2 sd:1 near:3 ongoing:1 shear:32 coppin:3 procedure:4 pack:1 scatter:1 seven:1 barely:1 ve:2 averaging:1 distorted:3 thus:1 discrepancy:2 faintest:1 ii:1 cluster:42 itself:2 contract:1 dual:26 massey:1 motivated:1 rusin:2 lsbs:2 borys:1 primary:2 circumventing:1 perform:1 suggest:1 madore:1 belong:1 intrinsic:1 same:8 any:1 another:1 potentially:1 split:2 modification:1 several:4 quoted:1 dan:1 higher:9 independent:1 calculation:1 used:11 infinity:1 peaks:8 hobson:1 numerical:1 koopmans:23 effect:5 mesh:1 blandford:1 diemand:2 levels:1 uses:1 purpose:2 v6:1 blain:1 changing:1 bosma:3 opportunity:1 stack:2 recent:2 early:1 lower:2 weakly:1 off:1 whereby:1 penalised:1 changes:1 colour:8 parameterised:1 well:9 analysis:8 magnified:2 without:4 residuals:6 components:1 simulated:3 firstly:3 ccd:2 model:74 plotted:1 arising:1 dh1:1 latest:1 arbitrarily:1 proposed:1 30th:1 being:3 generally:1 accurate:1 keeping:2 rest:2 ellipticals:5 assigned:1 sources:3 mannucci:2 predicts:3 alternative:2 λh:2 lessened:1 yet:1 alignment:1 based:2 lensed:3 note:1 preprint:1 density:10 absorption:1 ease:1 extra:3 sky:2 woodlawn:1 outlines:1 source:97 unambiguously:1 combine:1 attractive:1 samples:1 formal:1 blok:6 remaining:5 measure:2 gave:1 real:1 npar:2 sub:4 around:1 read:1 outermost:1 showing:1 astronomico:1 psf:6 possible:1 dark:11 interior:1 five:5 makes:2 background:1 jenkins:2 unlikely:1 using:14 apart:1 sampling:1 correcting:1 advanced:3 sheared:2 richard:3 brought:1 like:3 semi:8 follows:4 signal:1 adiabatic:2 extremely:2 sized:1 flux:9 durham:2 hosts:2 arbitrary:1 become:1 works:2 reduced:3 cooled:1 empirically:1 exceed:1 sum:2 33rd:2 parade:1 grids:1 course:2 χ2min:1 some:2 searching:2 deflection:3 aligned:1 repeat:1 examples:1 sight:1 redshifts:4 images:7 macs:3 little:2 practical:1 provided:4 scale:15 ellis:6 bottom:5 demonstrates:3 measurements:2 comments:1 smail:10 centroid:1 masked:2 provides:1 assuming:2 indication:1 minimal:1 measuring:3 object:3 resolve:1 power:17 treating:1 isophotes:1 radial:1 uniform:1 agreement:4 infra:2 stellar:1 carollo:1 step:3 biases:1 hst:3 offset:1 prepared:1 normalisation:3 properties:3 panel:4 uncontracted:1 comparison:4 about:1 neighbours:1 central:2 carried:1 extension:1 package:1 row:10 freedom:11 www:1 introduces:1 factors:1 o:2 simulation:1 acs:6 dependency:1 range:3 606w:2 ensure:2 greatly:2 stadel:5 desktop:1 apjl:1 introduced:2 slightly:3 contours:3 road:1 peak:7 seeing:1 purported:1 computational:1 inclusion:1 alongside:1 image:45 within:16 obtaining:1 satisfactory:2 three:4 lies:4 perturbing:4 lensing:5 accounts:1 primarily:1 einstein:18 cardiff:2 pairs:2 reducing:1 downhill:2 significantly:7 unambiguous:1 uncertainties:1 rows:1 van:1 additional:3 area:4 gridding:4 support:3 placing:1 question:1 spiral:1 stark:2 smoothing:1 dispersion:3 spread:4 kravtsov:2 inner:13 fraction:5 suit:1 forward:1 slopes:1 was:16 assumes:1 function:1 multidrizzle:1 north:3 complete:2 wambsganss:4 mcgaugh:3 becoming:1 fortran:1 agrees:1 but:11 back:1 astro:6 failure:1 repeated:4 hi:1 gain:2 convergence:5 line:1 imaged:3 gnedin:2 especially:1 count:1 isophotal:1 made:1 compute:3 society:1 whether:5 assessment:1 gravitational:3 daddi:1 maximum:1 quantitatively:1 until:2 below:1 ωm:1 critical:1 spectroscopy:2 planes:7 demonstrate:1 distribution:7 define:1 similar:1 called:1 averaged:5 strongly:5 400s:1 associated:1 moore:4 minima:2 defined:1 abstract:1 describe:4 life:1 proven:1 general:3 dashed:1 single:7 proves:1 right:1 regularisation:18 natarajan:2 simulations:10 corresponding:1 bary:1 graham:1 worse:2 steeper:1 functions:2 compared:6 completeness:1 unique:1 no:4 fixing:1 when:8 proceedings:2 dlog:1 preventing:1 field:4 other:7 compares:2 details:2 holding:1 spatial:1 weights:1 solely:1 references:1 briefly:1 elements:1 star:1 flores:1 separate:4 models:27 june:1 return:1 subtraction:1 includes:3 lens:86 important:1 allowing:3 additionally:1 included:1 pparc:2 astronomy:2 structure:4 delineate:1 zemp:1 condensation:1 pozzetti:1 algorithm:3 assume:1 quantifying:1 age:1 rs:4 mask:2 original:1 neighbouring:1 mass:32 lying:3 time:3 clockwise:6 once:1 resolution:6 having:5 8th:1 |
0705.1721.txt |@word aided:1 represent:1 abundances:1 measurements:2 transitions:1 illustrates:2 believed:1 hint:1 excellent:1 results:3 produce:1 indicates:4 facilities:2 systemic:3 per:2 bergmann:1 morphology:5 follow:2 amplified:1 disk:9 cases:1 benson:1 whose:2 amplification:3 depend:1 calculate:3 werf:1 statistics:1 should:1 young:5 supported:1 contract:1 critical:1 award:1 contours:4 bressan:1 blended:2 sustain:1 td:1 must:5 dramatically:1 indicating:3 starbursts:2 mpg:1 comparatively:1 mpc:1 far:12 could:6 listed:1 rise:3 accu:1 weighting:1 smg:1 inclinations:3 difficult:1 anonymous:1 uncertain:2 significantly:1 mstars:3 common:2 four:1 school:1 clouds:1 alma:4 lindner:1 1000µm:1 positions:1 mirror:1 solution:2 correct:1 large:8 discrete:1 detected:2 interpolating:1 brevity:1 small:3 society:1 inspection:1 caltech:2 configurations:1 granato:1 upper:4 employing:1 trend:1 consistent:9 l13:1 estimates:3 direct:1 surrounding:1 second:3 cost:1 calzetti:2 enclosed:1 correlator:1 manner:1 further:4 dynamics:5 estimated:10 wmap:1 spectral:4 what:1 appear:6 seaquist:3 giving:2 selected:2 near:2 supplied:1 tremaine:2 current:13 version:2 absolute:2 reconstruction:2 selecting:1 new:2 gildas:1 boost:1 consisting:2 contrast:3 helou:3 coefficient:3 supporting:2 mea:1 transparency:1 leitherer:2 iram:7 respectively:8 error:3 component:9 understanding:1 reported:1 bulge:1 midinfrared:1 address:2 alone:1 based:6 november:1 strong:4 observing:2 appears:8 change:1 extreme:2 obtained:3 convert:2 deriving:2 institute:2 study:3 larger:3 barmby:1 step:2 domaine:1 gravitationally:1 astrophysique:1 suggests:4 amount:1 resulting:4 milky:5 california:5 adopting:5 deg:3 studies:5 koornneef:1 imaging:5 magnifications:3 diameter:2 spatially:1 hst:4 states:1 scales:3 information:1 win:1 extending:1 photometric:1 casoli:1 sample:2 marked:4 highly:6 order:6 durham:2 pp:1 irac:11 total:10 univ:2 ivison:5 swinbank:4 plot:2 use:12 eye:4 usa:2 intense:1 subtract:2 faint:2 negative:1 france:3 lbgs:40 magnification:12 camera:2 kinematics:2 therefore:5 those:2 m2:1 taken:2 3le:1 associated:5 preview:1 type:1 tell:1 reflects:1 more:17 separated:4 populations:6 composite:1 conclusions:5 starburst:5 corrected:7 emission:45 drivers:1 henkel:1 unstable:3 dunne:2 apjs:3 particular:2 rare:1 increasing:1 insights:2 md:1 rotational:1 mc:2 steidel:11 mm:2 science:4 der:1 work:4 modified:1 mk:1 sensitivities:1 erg:1 nine:1 24µm:1 ms:1 growing:1 making:1 drops:2 example:3 dither:2 smail:18 point:3 compare:9 weaker:1 wang:2 cosmological:1 give:1 process:1 choice:2 lewis:1 frenk:1 high:18 unbiased:2 assumptions:2 walsh:2 taking:3 coincident:2 magnitudes:5 blvd:2 spanning:1 chapman:6 axis:1 plausible:1 mix:1 ebeling:1 caption:1 provide:1 discussion:2 six:1 chemical:1 submillimeter:6 keel:1 criterion:1 elliptical:1 lfir:10 instead:5 ordinary:1 universitaire:1 guilloteau:2 circular:1 profile:1 map:5 continues:1 galactic:1 description:1 spitzer:12 arcs:3 may:6 max:1 insu:1 after:1 derived:8 different:2 constraint:2 reflect:3 modest:2 plane:6 kneib:4 value:4 demonstrating:1 fits:2 law:7 data:7 practical:1 efficiently:1 aj:1 short:2 natural:1 dynamical:23 effective:1 light:9 bootstrap:1 correspond:1 ghz:1 cosmology:2 perhaps:1 so:6 emissivity:2 allow:4 seems:1 greve:12 increase:1 silva:1 mjy:9 typical:13 evolutionary:1 poor:1 help:1 reservoir:11 september:1 over:3 toomre:1 restframe:11 confirm:1 interpreted:1 stability:2 whilst:2 paper:1 through:2 statistical:1 pdbi:4 existence:1 cold:14 still:2 fwhm:5 its:4 galaxy:33 before:1 piscine:1 regions:3 style:1 derive:10 outer:1 thank:2 fit:4 la:1 lo:1 masses:15 epoch:2 edge:1 better:1 age:2 window:1 continue:1 degrees:1 fig:14 exposures:1 wales:1 bout:2 main:1 h0:1 lacey:1 maximal:2 good:1 motivated:1 entire:4 even:1 significance:1 primary:1 break:3 band:13 resolve:1 course:1 effects:1 they:5 half:2 own:1 employed:1 scatter:2 yr:15 discuss:3 association:3 densities:4 easily:1 february:2 hereafter:2 under:1 brightness:2 pc2:10 fully:1 university:2 traced:3 gmcs:2 identified:1 alter:1 events:1 lifetime:1 csc2:7 kpc:20 visibilities:1 mode:4 reasonable:2 each:5 found:1 photometry:13 traces:2 tracer:1 σgas:5 referred:1 subset:1 templates:1 bruzual:2 fication:1 ed:1 energy:1 hard:2 reduce:1 gaussian:2 related:2 interferometer:1 owing:1 yield:1 measure:1 substantially:1 our:24 mapping:1 beyond:1 extract:1 ring:1 out:3 borys:3 shown:1 space:2 2πgσ:1 σsfr:3 rep:1 since:3 gbt:1 content:4 re:1 extrapolate:1 dominated:2 boosted:1 suggesting:2 accessible:1 integrated:4 red:1 shows:4 foreground:6 huang:1 l17:1 astronomers:1 jwst:1 kennicutt:7 mapped:1 galaxies:31 attempt:1 free:1 diagnostic:1 bursts:1 formation:48 brightest:1 van:1 estimate:17 telescopes:1 millimeter:3 hubble:1 unresolved:1 jet:1 geometry:1 widths:4 just:3 transition:2 cosmic:4 catalog:1 fortuitous:1 noted:1 turn:1 mab:1 place:5 massive:4 assumed:3 hence:12 propulsion:1 repeats:1 support:2 south:1 first:7 knots:1 carilli:2 major:1 spergel:2 features:2 miralles:3 knudsen:1 possessing:1 irs:1 number:2 references:1 channels:6 clear:1 smaller:1 s0:1 approximately:2 directly:1 comprises:4 impossible:1 array:1 dominating:1 angular:1 size:1 given:5 ian:1 bracket:1 temperature:4 likely:3 similarly:5 introduction:1 unknown:2 top:1 precludes:1 system:17 offset:3 their:12 assumption:1 draft:2 observations:27 saint:1 tom:1 iau:1 rates:1 molecular:12 normalisation:1 frame:6 gives:2 disks:6 vigorous:1 way:6 relationship:1 centered:6 sin2:5 binney:2 forward:1 binned:1 part:2 gyr:1 somewhat:1 blindly:1 off:2 representing:1 than:20 intrinsically:2 population:20 observed:11 unlensed:1 unfortunately:1 princeton:2 double:2 require:1 typically:2 rate:7 resampled:1 luminosities:3 solomon:9 actively:1 sured:1 germany:1 were:8 timescales:2 providing:3 indicators:1 files:1 rab:1 few:1 look:1 correction:2 ages:3 spectrum:4 attenuation:2 yielding:2 randomly:1 discussions:1 substantial:1 headings:1 lbg:97 need:1 north:1 element:2 any:2 relatively:2 lie:3 conversion:10 angle:2 uncertainty:10 mopex:1 imf:1 latter:1 mid:3 apj:27 note:11 majority:1 fitting:5 potential:1 build:1 finding:1 coincide:1 mir:3 analogs:2 contursi:1 channel:4 pello:3 blue:1 begin:1 towards:1 unless:1 redshifted:4 investigations:1 replenished:1 caustic:2 siphon:1 indication:1 insets:1 most:7 eight:1 significant:6 laboratory:1 phase:5 baryons:2 mdyn:5 sfe:1 intrinsic:6 r32:11 fco:2 latex:1 acknowledges:1 constructed:1 subtracted:1 dordrecht:1 consumed:2 adopt:6 implications:1 inferred:4 km:27 typeset:1 ks:2 cameron:1 optical:9 proceedings:1 principle:1 pattern:2 velocity:8 constrain:2 sfes:1 physics:3 dow:1 respect:1 kristen:1 starburst99:2 selection:1 particularly:1 kg:1 show:5 overlaid:2 text:2 random:1 spain:1 least:2 infrared:19 radford:1 bright:6 quiescently:1 relation:5 argues:1 interpretation:1 armus:1 find:5 decade:1 subtracting:1 fadda:1 giant:1 highest:1 ratio:7 proposed:1 parameters:2 baryonic:2 merger:1 distributed:4 histories:1 hrs:1 discretionary:1 values:6 brighter:2 only:8 going:1 ellingson:1 arcseconds:1 rich:4 factor:25 acknowledge:1 emitting:1 constant:1 local:21 achieve:1 cb58:37 do:4 predict:2 dumke:2 dominant:3 template:3 means:1 occuring:2 hunt:1 de:4 overall:3 etrique:1 beam:6 cannot:1 stars:9 nearly:1 closely:1 probably:2 report:2 dye:7 du:1 ssc:2 alexander:2 following:3 evolution:2 exhibiting:1 bar:2 continuum:3 sources:3 evolved:1 luminosity:25 arxiv:1 median:2 rived:1 remove:2 across:1 investigate:2 convolve:2 predicted:6 activity:8 fainter:3 including:3 cycles:1 occupy:1 scoville:3 cole:1 traverse:1 set:2 above:1 questions:1 smgs:24 burst:1 wielebinski:1 sensitivity:3 farinfrared:1 astrometry:1 hosting:1 detection:10 ara:1 see:10 individual:2 radius:7 charlot:2 operated:1 close:2 luminous:7 analog:1 subject:2 eres:1 detect:4 exponent:1 combes:1 subsequent:1 review:1 currently:2 below:2 smallest:1 µm:26 halves:1 outside:1 converted:1 cambridge:2 between:5 understood:1 progress:1 warren:1 approach:1 email:1 discovery:1 comparable:11 terms:2 uk:3 receivers:1 mags:1 kinney:1 weak:1 however:8 jr:1 efficiency:11 cut:1 key:2 flats:1 analyzed:1 modeling:1 configuration:1 lirgs:17 barrett:3 giavalisco:3 observable:1 oiii:2 last:2 erb:3 limits:5 outflows:2 immense:1 coppin:5 vanden:2 5z:1 against:1 storchi:1 sensitive:2 f606w:2 exceeds:1 contribution:6 mean:3 whole:1 pdb:1 ago:1 strongly:4 adjusted:1 relevant:1 co:88 extent:5 timescale:2 gone:1 wall:2 had:1 corresponds:1 environments:1 lk:6 active:2 exploit:1 simply:2 morphologies:1 moreover:1 factors:3 along:1 intercloud:1 complication:1 described:1 µjy:2 lyman:2 uncomfortably:1 addition:1 west:2 locally:1 due:5 been:5 mark:2 pc:6 reduction:1 yan:1 radii:1 basic:1 expected:4 ska:1 ph:1 wait:1 derives:1 sanders:4 colors:1 adopted:3 corresponding:4 both:6 formed:3 gas:90 dave:1 observe:2 understand:2 angles:1 soifer:4 sfrs:1 evidence:1 present:7 reddening:2 multi:1 schmidt:7 atmospheric:1 resides:1 exponential:1 solid:1 reliable:2 primack:2 examine:2 hz:1 pixel:2 will:8 dusty:1 while:7 reliably:1 lensed:8 global:1 dickinson:3 region:6 constructive:1 unlikely:1 identical:1 jy:2 sizeable:1 reddy:6 rix:1 determination:1 averaging:2 bohlin:1 thus:9 lehnert:1 surface:12 helped:1 cluster:1 cant:1 bias:1 commonly:1 seen:6 pipelines:1 limit:1 myrs:8 technology:1 geach:2 3l:1 result:1 confirmed:2 diagram:2 baseline:1 considerable:1 perform:1 suggest:4 expect:1 same:4 millim:1 potentially:1 arguments:1 steps:1 units:1 survey:1 several:2 infer:4 higher:7 status:1 calculation:1 used:5 slightly:2 closest:1 laboratoire:1 lutz:1 nj:1 director:2 constraining:1 levels:1 uses:1 photometer:1 blain:8 dust:15 mips:3 opportunity:1 normalization:1 scaling:1 lower:8 argue:1 sed:5 center:6 makes:2 no:3 well:3 roughly:2 analysis:4 magnified:7 episode:1 calibrated:2 solve:1 does:3 components:5 position:6 model:4 plotted:1 arising:2 apertures:1 dh1:1 comparably:1 blackbody:1 carlberg:1 knot:1 quoted:1 less:6 being:1 percent:1 accurate:2 fueling:1 yee:2 obtain:1 rest:6 align:1 bandwidth:1 underlying:1 predicts:4 lco:1 years:1 useful:2 somerville:2 yet:1 adding:1 now:2 preprint:1 arcsec:2 kluwer:1 density:12 absorption:2 conclude:4 sky:1 capabilities:1 day:1 source:16 add:1 pasadena:2 combine:2 plateau:1 collapse:1 stable:2 extensive:1 east:3 mh2:3 remaining:1 match:1 pparc:1 resolved:1 explained:1 around:1 alternatively:1 nearinfrared:1 measurement:3 comparing:1 period:2 early:1 increases:4 background:1 ign:1 press:2 using:11 ams:1 unique:3 correcting:1 radioastronomie:1 color:1 l1500:1 naturally:1 like:1 reconstruct:1 follows:4 signal:1 faber:2 alice:1 translates:1 ignore:1 flux:15 detections:1 history:1 yields:6 either:2 martin:1 bs:11 log10:2 decimal:1 replacement:1 function:1 cluding:1 shed:1 shapley:11 parade:1 oriented:1 advent:1 pettini:10 unjustified:1 some:2 cnrs:1 library:2 fgas:4 supplementary:1 j2000:5 examples:1 b2:4 table:4 images:4 extended:1 kuno:1 dissect:1 bell:2 provided:2 scale:3 dense:2 dimensions:1 mosaicking:1 broadband:1 normal:2 integration:3 best:3 ddt:3 flatten:1 depletion:3 efficiencies:1 centroid:8 cloud:1 provides:6 assuming:5 harness:1 mhz:4 many:3 moderate:1 numbers:1 inclination:6 bure:1 claimed:1 noise:3 royal:1 sfr:18 processing:1 carried:2 agreement:1 rue:1 stellar:27 how:1 host:1 powerlaw:1 although:8 datacube:1 post:2 emulateapj:1 properties:16 noisy:1 comparison:8 about:5 central:4 would:3 package:3 column:3 tuned:1 metallicity:1 realistic:1 ratios:4 acs:2 range:4 characterized:1 s850:1 act:1 adelberger:8 bolometric:2 efforts:1 constraints:1 denote:1 road:1 software:1 seeing:2 equally:2 computational:1 effectively:2 redshift:19 h2:12 material:1 into:7 within:20 interstellar:1 three:1 down:1 lies:4 appropriate:3 lensing:13 master:1 cent:2 determine:6 cardiff:2 reservoirs:1 next:3 telescope:2 placing:1 uncertainties:7 frayer:1 institut:1 log:2 synthesized:1 artifacts:1 measured:4 astrometric:1 there:5 redshifts:3 yao:4 awarded:1 dispersion:2 width:6 detectable:1 low:6 fraction:7 immune:1 hyperz:2 was:5 downes:1 interferometry:2 pwv:1 billion:1 medium:3 gaseous:2 form:4 enough:1 forming:8 younger:1 but:5 sophisticated:1 astro:1 aperture:3 magnitude:3 solar:1 mnras:5 salpeter:1 line:36 removed:2 true:1 dur:1 he:2 submitted:1 made:3 places:1 contain:1 whether:4 dangerous:1 gravitational:3 uv:21 variations:2 up:3 us:5 until:1 mauersberger:2 frequency:3 ωm:1 marginally:1 spectroscopy:1 grasp:2 demonstrate:2 distribution:5 marseille:2 similar:16 average:7 b1:6 detailed:4 fractions:2 ac:1 ab:1 proved:1 reconcile:1 exhausted:2 abstract:1 myr:5 bolzonella:3 frames:2 general:2 neri:1 single:2 referee:1 initial:1 av:1 accounting:1 gradients:1 distributions:1 unsaturated:1 august:1 physical:2 silbermann:1 tacconi:7 compared:1 improving:1 calibration:1 dashed:1 image:8 when:2 detail:1 elemental:1 other:8 details:1 ulirgs:10 spatial:6 test:4 jenkins:2 hainline:2 nw:1 dale:4 symposium:1 draw:1 apparent:1 star:47 energetic:1 respects:1 models:4 schulz:1 variation:4 interferometric:1 lens:13 generated:3 peak:4 accounts:1 studied:2 mgas:8 astronomy:1 15l:1 structure:3 searches:1 lane:1 correlated:1 implies:2 prevalent:1 assume:3 obscuration:3 baker:7 overlay:1 rather:1 waveband:1 having:1 sheth:1 inset:4 nasa:1 mass:56 lying:1 time:10 baugh:2 8µm:2 genzel:1 resolution:9 enrichment:1 seds:3 |
0705.1722.txt |@word onken:1 young:2 fuente:1 luminosities:6 results:6 existing:1 leads:1 eds:1 garching:1 edu:1 follow:1 denotes:1 contributions:1 weakly:1 bershady:2 poorly:1 flannery:1 depend:1 ergs:13 paris:1 turner:1 technique:7 editors:1 λlλ:8 program:5 those:2 under:1 reddening:2 sitko:3 subtleties:1 ionizing:2 amplitudes:3 far:6 plausibility:1 focus:1 every:1 difficult:1 sensitivity:1 month:2 wagner:1 four:6 school:1 clouds:5 presented:1 harbor:1 stirpe:1 try:1 second:1 radio:1 shows:4 reliable:1 application:1 strongly:1 smaller:3 tel:3 trend:1 consistent:4 estimates:1 past:3 zero:1 timescales:2 dordrecht:2 clavel:2 further:4 estimated:2 targets:1 spectral:1 aim:1 errors:2 sum:1 selected:1 while:2 uniform:1 current:6 erg:3 decade:2 above:3 3c:4 falling:1 increasing:1 method:4 contrast:1 fekα:3 coefficient:1 full:3 simultaneously:1 bh:11 promising:1 here:1 ionization:4 objects:11 active:5 accretion:2 along:1 strong:1 observing:1 annales:1 obtained:4 dusty:1 involved:1 study:6 ngc:9 allows:1 typically:1 experience:1 eberly:1 cetty:2 fabrizio:1 changes:1 plotted:2 examining:1 campaign:2 extrapolations:1 photometric:2 private:1 trevese:2 apj:31 addressed:1 names:1 apply:1 shemmer:4 establish:1 plot:1 use:1 cosmological:1 would:1 few:4 monotonically:1 kinematics:9 vetterling:1 taken:2 type:1 theoretical:1 more:4 israel:2 successful:1 kollatschny:3 inclined:1 apparent:1 emission:18 glass:3 primarily:1 opposing:1 known:2 actual:1 hole:2 pogge:2 iii:2 me:1 sample:5 account:2 palomar:1 erratum:2 equation:2 averaged:3 emerge:1 measures:1 reviews:2 unknowns:1 minimum:2 couderc:2 following:1 root:1 scatter:4 stimulating:1 compare:1 wang:2 figure:7 give:1 expanding:1 declinations:1 high:18 indicates:1 slit:1 assumptions:1 orbits:1 feasible:2 robinson:3 occur:1 verlag:1 information:4 needs:1 rays:1 monitoring:8 goal:1 reynolds:2 discussion:1 holds:1 s5:10 delay:3 how:2 parameter:2 profile:3 de:1 galactic:4 lα:1 may:3 lag:12 derived:2 mapping:47 23p:1 fa:1 catalog:1 plane:1 waves:1 fits:3 summarize:1 law:2 data:20 response:4 short:1 correlate:1 resemble:1 light:30 schneider:2 spectra:1 lines:7 sartori:2 ionized:1 green:2 fundamental:2 correlation:4 order:2 talk:1 horne:7 six:3 help:1 over:6 despite:1 find:4 years:1 produced:1 motions:1 during:3 mentioned:1 peterson:26 still:4 fwhm:1 its:1 galaxy:1 before:1 observational:1 regions:1 outer:1 monitor:1 fit:1 maps:3 inward:1 masses:2 baas:1 vicinity:1 coordinates:1 aviv:3 lt:1 lu:2 fig:3 hobby:1 weeks:1 main:1 decades:3 versus:3 them:1 greater:1 surrounds:1 recipes:1 dan:1 practice:1 akritas:2 scaling:1 band:1 example:1 effects:1 they:6 day:2 densities:1 term:1 shai:1 collier:1 university:3 level:1 did:1 magnitude:6 each:2 found:4 higher:9 decreasing:1 characterized:1 mean:5 square:1 financial:1 significantly:1 due:4 series:3 energy:1 mchardy:1 entering:1 measurement:7 relates:1 eq:1 out:8 shown:2 furthermore:1 since:7 crucial:1 blr:29 fellowship:1 posteriori:1 photometrically:1 squares:1 rk:3 disk:4 foundation:1 asp:4 linear:2 southern:1 vagnetti:1 galaxies:2 quite:1 campaigns:5 complicated:1 zdcf:1 trends:1 szczerba:1 put:1 intermediate:1 estimate:2 telescopes:1 geometry:7 could:1 days:7 steward:1 motion:1 turn:1 produce:2 massive:2 removing:1 hence:1 view:1 think:1 first:5 origin:1 initial:1 gondhalekar:1 fitexy:5 number:2 echo:1 date:1 least:1 directly:3 carry:3 slower:1 fluxes:1 quality:1 desroches:2 size:21 given:3 publication:1 likely:1 introduction:1 leading:1 top:1 relations:3 their:4 assumption:2 observations:5 white:2 jarvis:2 inner:3 persei:1 collapse:1 mostly:1 relative:1 optical:10 authors:1 probably:2 than:7 lengthened:1 urry:2 observatory:5 johnson:1 showed:1 bertram:1 was:6 enabled:1 intensity:1 alloin:1 project:2 future:1 amplitude:3 were:7 pasp:3 enables:2 san:1 julian:2 croom:1 measure:3 spectrum:1 curves:24 randomly:1 close:1 need:3 quasars:11 bhs:2 confirms:1 orders:4 ray:7 corbett:1 relationship:1 depending:1 studying:1 self:1 able:1 mckee:3 k2:1 fitting:3 potential:1 take:1 objective:1 so:6 becoming:1 ulrich:2 circles:1 even:1 multiple:1 allow:2 bands:1 object:4 most:2 iccf:1 bolometric:1 significant:4 preliminary:3 bahcall:2 coin:1 intrinsic:5 class:1 volume:1 deviations:1 technion:2 veron:4 considered:3 calculated:1 later:1 cover:2 km:1 wing:1 proceedings:6 points:8 principle:1 sternberg:2 mrk:3 velocity:3 physics:3 fact:2 slope:5 emerging:1 show:2 manifestation:1 implying:1 attempts:4 relation:16 suffer:1 subtle:1 torus:5 tremaine:2 dilation:1 my:1 based:4 rblr:9 title:1 explain:1 woo:2 should:2 jannuzi:3 only:5 black:2 ballantyne:2 factor:4 astronomical:2 ser:2 do:3 fλ:2 lyα:2 get:1 compiled:1 hopefully:1 watch:1 l41:1 agns:31 ones:1 rest:3 donald:1 progress:1 report:1 measured:8 respectively:1 alexander:2 reveal:1 evolution:1 continuum:30 sources:2 luminosity:52 arxiv:1 zeff:1 yield:1 summary:2 greene:1 influenced:1 bad:1 3c273:1 mapped:1 fainter:1 ohio:2 fixed:1 explanations:1 lbol:1 respond:2 rms:1 bars:1 set:1 computed:1 achieved:1 hβ:4 variations:7 frame:3 observed:6 depends:1 individual:1 result:2 recently:3 outward:1 best:2 subject:1 preparation:1 detect:2 nuclear:1 currently:1 circulating:1 wo:3 state:2 determined:4 various:1 between:9 affecting:1 ira:1 conditions:1 available:2 variability:18 comparable:1 dozen:2 ability:2 extend:1 importance:1 however:2 spectroscopic:1 gratefully:1 vanden:3 contamination:1 analyzed:1 kev:2 virial:1 bivariate:1 improve:1 suggested:2 both:2 prospects:1 toward:1 improved:1 kluwer:2 σl:2 σc:2 many:3 salpeter:2 acknowledge:1 connection:1 reverberation:50 siemiginowska:1 contribution:7 ll:1 teukolsky:1 blandford:3 among:1 unclear:1 cm:2 point:3 simple:1 overview:1 period:3 sampling:1 dimensional:3 directions:1 publishers:1 unsuccessful:1 smith:3 conference:1 broadening:2 mathur:2 geometries:1 fortran:1 three:3 been:5 reduction:1 pg:15 laor:2 expected:4 ph:3 orbiting:1 meeting:1 define:1 direction:1 corresponding:1 quantities:1 sufficient:1 gas:8 collaborators:1 observe:1 determination:3 tentative:1 univ:1 c3:3 c2:1 c1:1 lira:1 c5:1 c4:2 exception:2 supernovae:1 solid:1 might:2 straight:1 colton:1 profiles:1 will:8 near:1 none:2 error:1 situation:1 di:1 region:7 procedure:1 studied:1 courvoisier:1 vol:1 characteristics:3 ir:6 thus:6 non:2 iv:13 finds:1 suganuma:2 itself:1 la:1 conf:2 ambient:1 ic:1 regression:3 orbital:1 astrophysique:1 different:4 perhaps:1 acknowledgments:1 began:1 cross:3 same:2 epoch:3 changed:1 netzer:12 bces:5 units:3 dimensionless:1 several:5 kn1:1 fairly:1 used:9 http:1 see:7 welsh:5 numerical:1 hand:2 fabian:1 moving:1 dust:1 frequently:1 leibowitz:2 recent:4 lower:6 task:1 center:2 studies:8 maiolino:1 calibration:1 well:1 analysis:1 double:1 academic:1 sets:2 very:1 ccf:2 dimension:3 researchers:1 spherical:1 distances:1 construct:1 routinely:1 proposed:1 heavily:1 being:1 quasar:8 ccfs:1 obtain:1 baskin:2 seen:1 subsamples:1 untested:1 spectrophotometric:3 yet:1 previous:3 sampled:1 monitored:4 candidate:1 density:2 noted:1 scales:1 had:2 ideal:1 source:1 valid:2 easy:1 scheduled:1 wanders:1 advances:5 showing:1 disagreement:1 possible:5 extrapolating:1 press:4 using:11 kozlovsky:2 projects:2 like:1 excluding:2 highluminosity:2 interestingly:1 serves:1 manifest:1 specific:1 flux:7 seyfert:1 steps:1 either:3 essential:1 aimed:1 mathematical:1 poor:1 www:1 methods:4 begelman:1 successfully:1 some:4 springer:1 deduce:1 redshifts:4 images:2 star:4 giveon:3 scale:1 sergeev:1 lead:1 bottom:1 broad:9 measurements:9 thank:2 per:2 gaskell:3 l5:1 centroid:2 assuming:1 eso:2 bentz:3 considering:1 who:2 scientific:1 power:2 european:1 radial:1 notable:1 expansion:1 host:1 although:2 emits:1 after:1 stage:1 comparison:1 about:13 central:4 carried:5 column:1 months:1 discussed:2 inviting:1 o:2 range:12 insufficient:1 organizers:1 therein:3 cambridge:2 mbh:2 redshift:3 communication:1 into:3 within:2 stratification:2 latter:1 weather:1 references:4 determine:1 oliva:1 accumulated:1 telescope:3 het:2 uncertainties:1 rely:1 span:1 additional:1 comparing:1 transfer:4 support:1 there:6 alleged:1 nova:1 lags:4 width:1 low:8 way:1 ed:6 resulted:1 brandt:2 sections:1 morrison:2 function:5 wamsteker:2 hr:1 attempted:1 collapsed:1 but:1 astro:3 ho:2 larger:2 mnras:5 haifa:1 line:38 highest:3 berk:3 made:1 wise:3 largest:1 ut:1 uv:10 robustness:1 up:1 until:1 seems:1 kaspi:21 demonstrate:1 distribution:2 similar:1 average:1 distance:1 detailed:1 defined:2 abstract:1 year:3 influence:1 proven:1 general:1 balmer:5 single:3 exist:1 periods:1 our:3 perez:3 formalism:1 triangles:1 physical:2 functions:1 6th:1 mclure:2 vestergaard:4 no:3 generally:1 ng:1 field:1 other:5 details:2 ambitious:1 better:2 department:1 correlates:1 optically:1 briefly:1 francisco:1 accounted:1 models:1 time:22 problems:2 variation:1 grupe:2 important:1 nucleus:1 marconi:1 astronomy:2 structure:3 conclusive:1 ago:1 agn:16 correlated:1 implies:1 longer:1 starting:1 dτ:1 required:1 curve:3 berlin:1 together:1 declination:1 mass:12 fitted:1 maoz:13 nuclei:3 resolution:2 having:1 once:3 |
0705.1723.txt |@word limited:1 katz:1 deγ:2 consider:1 pointing:1 rev:3 magnetic:20 particular:1 results:3 existing:1 four:3 edu:2 morphology:1 follow:1 disk:1 worked:1 causes:1 increase:2 certainly:1 inverse:2 depend:1 chain:1 collisions:3 april:1 young:3 opportunities:1 supported:1 finally:1 critical:1 indicate:1 under:2 include:1 cm3:3 cm2:2 confirmation:1 very:7 emphasizes:1 choice:1 electron:3 every:2 should:3 uncertain:1 little:1 skymaps:1 clouds:6 exponential:1 level:3 did:4 cause:1 anisotropy:1 shock:9 gun:1 correct:1 large:6 detected:7 affect:2 10µg:4 small:5 radio:2 becker:1 tenths:1 degeneracy:1 upper:3 smaller:2 consistent:5 mediterranean:1 prediction:1 sweeps:1 approximation:1 consists:2 likely:3 arizona:1 summer:1 further:1 tev:50 even:1 established:1 rate:8 tentative:1 giving:1 section:4 schedule:1 while:6 ksenofontov:1 below:1 experiment:2 aharonian:5 above:9 new:1 antares:1 hillas:1 boost:1 equivalent:1 shocks:1 montaruli:2 escaping:1 implying:1 tibet:2 respectively:2 component:2 here:5 atoms:4 behaviour:1 reported:1 mev:1 free:1 excess:5 alone:1 path:1 j2019:11 observing:2 crocker:1 whipple:2 kistler:1 parameters:8 study:1 larger:3 allows:3 reports:1 example:1 suggests:4 fatuzzo:1 products:1 published:2 plotted:2 emerge:1 regardless:1 leptons:2 scales:1 proportion:1 explained:1 konopelko:2 julia:1 modifying:1 visible:2 remnant:16 beilicke:1 neutrino:23 total:4 τdiff:3 sensors:1 cloud:1 predicted:4 λpp:2 conventional:1 mb:1 takes:1 usa:1 combi:1 remains:1 positive:1 takahashi:1 eπ:4 few:2 sample:2 therefore:1 crab:10 taken:1 black:4 type:2 more:3 separated:1 introducing:1 initiated:1 ecole:1 initial:2 line:12 emission:1 3eg:3 introduces:1 interaction:1 normalized:1 1µg:8 varying:1 known:2 95er40896:1 physically:1 hold:2 producing:3 eγ:8 must:3 νe:1 ρe:2 integrating:1 dep:1 thousands:1 equation:1 hopkins:1 protons:11 array:1 mt:1 suggestive:2 erg:8 values:4 era:1 astrophys:4 containment:1 believed:1 kelner:1 closing:1 gyroradius:1 tau:2 transition:1 challenging:2 figure:9 escapes:1 calculation:3 expanding:3 lγ:2 grant:3 dependence:2 high:6 unphysical:1 way:2 microquasars:1 degenerate:1 allowed:2 ascension:1 science:2 pν:1 hydrogen:5 occur:1 dissimilar:1 egret:14 information:2 respective:1 rays:37 requirements:1 provide:1 technology:1 discussion:3 means:2 feature:3 regions:1 how:1 hot:4 significance:1 answer:1 symposium:1 parameter:4 priori:1 circular:1 map:1 alternative:2 galactic:19 dnγ:2 includes:1 may:6 after:5 spot:2 different:2 walk:1 dnν:3 produce:5 snr:8 gaisser:3 waves:1 end:1 law:4 revealed:2 response:1 abdo:1 curve:2 realized:1 convolution:1 effective:1 following:3 light:1 spectra:10 lines:1 granted:1 redundant:1 lang:1 generic:2 accelerated:7 maintain:1 so:3 emissivity:2 allow:1 correlation:1 cherenkov:2 order:6 typical:2 remnants:8 cutoff:5 indeed:3 over:2 vary:1 uchiyama:2 years:42 produced:8 performance:1 thermal:2 experiments:1 through:3 looks:1 nitrogen:1 left:1 converting:1 kinetic:1 put:1 energetics:2 galaxy:6 before:2 observational:3 veritas:1 derive:1 thank:1 fit:1 decay:6 energies:12 greatly:1 vicinity:3 window:1 production:5 degrees:2 choose:1 convective:3 bin:1 mail:1 main:3 into:6 aeff:2 non:2 greater:1 thereby:1 qp:1 muniz:1 outlined:1 largest:2 fig:3 number:4 scaling:1 instrumented:1 serendipitous:1 they:7 half:3 front:1 now:2 day:1 association:6 represents:6 february:1 several:5 oxygen:1 cygnus:13 university:3 accompanying:2 identified:4 drake:1 establishing:1 kpc:4 luminosity:2 found:1 quarter:1 referred:2 enigmatic:1 rodriguez:1 square:1 telescope:3 accelerator:1 energy:45 hard:1 positioned:2 idea:1 solution:1 used:1 increases:1 equate:1 calibrate:1 year:17 icecube:20 operation:3 beyond:1 inverted:1 event:11 out:2 gonzalez:2 shown:4 opened:1 space:3 gradient:1 since:4 rx:6 unknown:1 research:3 particles:9 re:1 acting:1 nominal:1 maximized:1 formula:1 get:1 ref:10 integrated:2 red:4 shows:2 counterpart:3 foundation:2 earlier:1 wisconsin:3 favored:1 southern:2 mechanisms:2 surveys:1 possibility:2 standard:1 indices:2 lister:1 proportionality:1 brightest:1 besides:2 modify:3 detecting:2 generate:1 irreducible:1 compression:1 unresolved:1 vshock:3 dubbed:1 determining:1 could:2 similarly:1 cosmic:44 times:2 filter:1 length:1 plane:3 place:1 massive:1 ism:1 transfer:2 hence:3 discussions:1 neglect:1 south:1 first:8 origin:4 already:3 probability:4 variables:1 thesis:1 microgauss:3 milagro:21 l37:1 set:2 approximately:5 l33:1 impossible:1 antarctic:1 fluxes:10 quality:1 angular:2 j2021:3 size:2 given:6 long:1 antiparticles:1 their:7 introduction:1 data:5 interact:1 least:2 subsequently:1 needed:1 rates:6 observations:8 lemoine:1 tom:1 ankle:2 molecular:5 semianalytical:1 uncomfortably:1 witnessing:1 figures:2 shell:2 accompany:1 fraction:1 centered:2 estimate:4 relative:2 obtained:3 astrophysics:1 optical:2 jordan:1 somewhat:1 butt:1 injected:2 than:6 population:3 diffusion:10 distance:5 observatory:1 gradual:1 target:1 traverse:2 anticipate:1 second:1 modified:2 final:3 posit:1 volk:1 determined:3 were:1 normally:1 gives:3 powers:1 collecting:1 function:1 ages:1 spectrum:31 τconv:2 dash:4 lne:1 chosen:4 showers:2 need:1 constrained:2 apparently:1 any:2 relatively:2 acceleration:12 instrumentation:1 conversion:1 zero:1 recognizing:1 hotspot:1 onset:1 instance:2 fitting:1 take:4 finding:1 green:4 detector:3 diffusive:2 bolometric:1 explanation:1 accuracy:1 spectral:5 multiple:1 trace:1 index:3 track:1 collaboration:10 object:5 neutrinos:38 traversal:1 took:1 most:4 eight:1 but:1 quantitative:1 phase:2 knee:4 colliding:1 sophisticated:1 measured:3 why:1 astro:22 observation:10 considered:2 mean:2 clear:3 partition:1 steady:3 hemisphere:2 km:3 kr:1 part:5 electrons:1 principle:1 velocity:2 charged:5 physics:4 fact:3 laws:1 slope:2 madison:1 maccione:1 particularly:1 show:7 detection:4 random:1 teresa:1 murchadha:2 purely:2 radii:1 planning:1 relation:2 inconsistent:1 calculable:1 superimposed:1 earth:2 find:2 decade:1 ground:1 northeast:1 based:1 northern:5 escaped:1 committee:1 produces:1 distributed:1 blue:4 deployments:2 halzen:5 failed:1 only:4 candidates:1 factor:5 adequate:1 local:1 astronomical:2 dn:3 do:2 predict:3 motion:1 gev:10 wide:1 dependent:1 de:7 amenomori:1 fluid:10 pions:10 beam:4 made:2 determine:2 international:1 report:1 during:2 dt:2 muon:6 astropart:4 net:1 becomes:1 secondary:3 reveal:2 processes:3 increasing:1 fields:5 arxiv:25 median:1 suggested:1 yield:2 method:6 garcia:2 paper:2 common:1 including:2 amanda:3 approximations:1 lipari:1 reveals:1 requirement:1 multiplying:1 constructing:1 exists:2 observes:1 imposing:1 sensitivity:2 cuts:2 grasso:1 observed:13 see:5 arc:1 radius:2 result:3 successive:1 accelerators:6 normalizing:1 hegra:4 j1745:1 subject:1 4πd:1 interacting:4 extragalactic:1 review:1 nebula:1 sites:1 its:5 state:1 kilometer:6 identification:1 boosts:1 between:4 tens:2 fermi:1 µg:14 d53:1 discovery:2 multiplied:1 recently:1 extend:1 nature:3 importance:1 deliver:1 supernova:20 weak:2 however:2 wi:1 southeast:1 incident:1 delivering:1 nν:1 motivations:1 essentially:2 last:1 sν:2 limits:1 beacom:2 minutes:1 region:12 compton:2 equal:6 propagation:1 cubed:1 context:1 exceeds:3 argue:1 whole:2 nearby:1 strongly:1 presumably:1 cn:1 cm:7 point:2 simple:4 harmonic:1 proton:17 coincidence:1 dimensional:1 directions:1 pole:1 steepen:1 simply:3 luis:1 moreover:1 throughout:1 mgro:11 considering:2 akhperjanian:1 atmosphere:3 described:1 basis:1 acceptance:1 due:11 been:13 pc:4 interest:1 inadequate:1 expected:2 ph:25 skymap:1 engine:1 box:2 direction:3 describe:1 corresponding:1 ranging:1 collaborators:1 sufficient:3 releasing:1 photon:1 coincides:1 argument:1 agrawal:1 observe:4 scrutinized:1 astron:2 smoking:1 j2032:3 diffuse:1 those:3 tsnr:5 case:4 intriguing:2 atmospheric:11 supernovae:3 ap:1 solid:5 originate:2 harder:1 maltoni:1 value:3 air:1 will:14 near:1 threshold:2 cannot:1 promising:1 investigating:1 taking:1 associations:1 almost:1 characteristics:1 refs:1 thus:2 site:1 surface:1 hardware:1 cluster:2 unit:1 optimistic:1 ambient:2 claimed:1 opp:1 convection:7 interacts:1 currents:1 parsecs:1 confirmed:1 trial:1 perhaps:1 suggest:1 make:1 same:2 reconstructed:1 potentially:3 arguments:1 widely:1 accumulating:1 resulting:6 proved:1 ray:40 events:14 consequence:1 higher:2 anchordoqui:2 evolve:1 satellite:1 extended:1 http:1 peaks:1 leonid:1 identical:1 milky:1 effect:1 counterparts:1 constraining:1 highly:1 opportunity:1 normalization:3 recent:2 lower:4 center:1 largely:1 nevertheless:1 disappears:1 astroph:1 variety:2 well:5 roughly:1 analysis:3 bohm:3 deν:5 simulated:1 sullivan:1 position:1 model:9 latest:1 spherical:1 distances:1 velocities:1 moments:1 when:3 alvarez:1 obtain:1 effects:5 imprint:1 sources:20 shape:1 identify:1 mechanism:1 advertised:1 flavor:1 hess:8 scattering:1 yet:1 down:1 previous:1 note:3 intersection:1 density:15 photons:15 conclude:1 sky:2 parametrization:1 exclusively:1 discuss:1 signals:2 source:14 valid:1 extends:1 location:2 inducing:1 constant:4 input:2 heidelberg:1 match:1 generalized:1 resolved:2 insensitive:1 measurement:3 possible:6 possibly:2 whichever:2 five:1 know:1 background:3 deployment:1 press:1 using:5 height:1 loss:1 displaced:1 tail:1 greg:1 like:1 particle:6 follows:1 signal:4 eev:2 flux:45 yields:1 byproduct:1 january:1 degree:2 fragmentation:1 interestingly:1 exceed:2 because:5 old:1 sequence:1 olk:1 some:5 back:1 sedov:2 calculated:3 accelerate:1 observatories:1 images:1 indirect:1 transport:1 happens:2 provided:1 scale:5 dense:1 pinpoint:1 lead:1 electromagnetic:3 pev:4 measurements:1 per:10 mesons:1 does:1 select:1 provides:1 assuming:3 readily:1 ob2:2 augmenting:1 waxman:1 either:2 run:1 power:8 reaching:1 pionic:6 reach:1 whose:2 each:4 alumni:1 stellar:1 broken:1 np:7 although:7 filaments:1 post:1 francis:2 christened:1 constrains:1 comparison:1 about:3 d74:1 constraint:4 tracing:1 discussed:5 ob:3 o:3 reduced:1 range:12 km2:1 steadily:1 germany:1 constraints:1 gamma:32 software:1 credible:1 seeing:1 cambridge:2 presence:1 previously:1 image:2 within:7 integral:2 interstellar:6 three:2 accommodate:2 right:1 references:1 national:1 proportional:1 uncertainties:1 ahrens:2 hep:2 additional:2 remain:1 assumed:3 unmodified:1 there:5 etas:1 spots:1 width:1 stanev:1 low:5 stars:2 resulted:1 perform:1 was:3 assumes:1 goodman:1 synchrotron:1 considerably:1 medium:7 ator:1 funds:1 precise:2 basic:1 jul:1 gaussian:1 volume:3 neutral:6 construction:2 solar:1 σpp:2 injection:7 highest:2 true:1 raising:1 especially:1 begins:2 wisc:2 circumstantial:1 compute:1 qualitative:1 drury:1 characteristic:2 kappes:1 up:8 us:5 planet:1 estimates:1 limit:4 similar:3 average:5 regimes:1 detailed:3 bearing:1 later:1 associated:7 ln:1 defined:1 detectors:3 abstract:1 escape:13 evidence:5 oscillations:4 single:1 exist:1 predictions:1 our:6 happen:1 triangles:1 steeper:1 qγ:3 compared:1 completeness:1 ideally:1 dotted:8 no:5 dashed:4 fg02:1 acknowledgments:1 generally:1 ep:9 field:19 other:2 holding:1 digital:1 department:2 finley:1 area:4 star:1 melia:1 models:1 gas:1 j1713:6 variation:4 precision:1 deriving:1 antineutrinos:1 peak:1 additionally:1 included:1 describing:2 astronomy:5 conclusive:1 building:1 eν:2 pion:3 assume:6 starting:1 age:18 required:3 modules:1 original:1 berezhko:1 declination:1 mass:1 time:17 far:2 nuclei:1 quantity:1 requires:4 strings:2 once:1 |
0705.1724.txt |@word externally:1 extrapolated:2 consider:1 caused:1 magnetic:7 results:1 facilities:1 avalanche:1 seaborg:1 skin:1 follow:3 revealed:1 causes:1 layers:1 number:1 alamos:4 technique:4 presents:2 tl:8 does:1 ti:1 flattening:1 cm3:2 tc:17 indicating:1 supported:1 amplitudes:2 evolves:1 very:1 rise:2 wave:4 electron:2 bottleneck:5 tri:3 induced:2 modulator:1 transmission:1 ginzburg:3 large:1 damle:1 small:3 3b:3 upper:1 smaller:1 consistent:4 3c:1 rate:2 chen:2 nmr:1 dynamics:9 estimated:1 depression:2 even:1 picoseconds:2 giving:1 sun:1 burch:1 remain:1 τsc:20 cell:2 experiment:1 goes:2 pristine:1 new:9 3a:3 commensurate:2 method:1 contrast:1 3d:2 body:1 agreement:1 full:1 lee:2 27k:1 component:6 understanding:1 ranges:1 focused:1 relaxation:10 ratio:3 strong:2 change:2 obtained:2 apical:2 gay:1 institute:1 study:2 current:1 resulting:2 resonance:1 suitable:1 studies:3 emerge:1 via:4 useful:1 ldrd:1 explained:2 logarithmic:1 modulated:1 unit:2 tn:1 use:2 charge:2 usa:2 morr:1 ca2:1 negative:3 next:1 few:2 depicted:1 program:1 therefore:1 taken:2 type:1 theoretical:2 more:3 introducing:1 ascribe:1 pairs:3 transient:2 normalized:1 excellent:1 hole:1 must:1 schrieffer:1 keeping:1 crosses:1 ma:1 science:3 setup:2 work:4 halperin:1 cm2:1 suggestive:1 values:8 temperatures:4 following:2 85k:1 figure:3 thermally:2 sample:4 effectively:1 minimum:2 o:2 exclude:1 sharp:1 chia:2 kyu:1 axis:1 monitoring:1 recovery:3 photodiode:1 elbert:1 laughlin:1 zhang:2 whence:1 delay:4 how:1 la2:1 pure:17 parameter:5 arovas:1 fs:1 mat:1 23k:1 may:2 earlier:1 spot:5 kallin:1 diagram:1 sprik:1 plane:1 55k:2 fits:3 rameters:1 averitt:2 data:20 response:2 types:1 short:1 gluing:1 third:1 recombination:2 extrapolation:1 increasing:1 fundamental:1 decreasing:1 sc:23 subsequently:2 hfb:2 order:38 superscript:1 produces:1 indeed:1 over:2 insight:1 hwan:1 years:1 experiments:2 pulses:5 ce0:1 existence:1 excitations:2 its:7 before:1 τn:3 outer:2 fit:15 decay:3 energies:1 temporal:3 exhibits:1 microscopic:1 systems:3 ours:1 1c:2 might:1 versus:1 mukuda:1 fourth:1 thereby:1 material:5 devel:1 break:1 discuss:1 130k:1 easily:1 february:1 finite:1 oxygen:2 university:2 vibrations:1 pan:1 each:2 acoustic:1 characterized:1 commonwealth:1 domain:1 square:1 interlayer:1 series:2 energy:5 related:1 frequency:1 obtains:3 quantum:2 our:18 ev:1 eq:6 out:2 rt:9 shown:7 closest:1 open:1 furthermore:1 since:2 rev:17 cuprate:4 research:2 increase:2 fellowship:1 mediated:1 dominated:1 squares:1 ref:1 occurs:2 shows:4 condens:1 theory:4 interactions:2 possibility:2 asc:9 reason:1 formation:1 members:1 put:1 demler:1 carbotte:1 homologous:1 competes:3 created:1 determining:1 transition:2 times:2 turn:1 isotropic:1 hence:1 onto:1 ultrathin:1 first:6 origin:1 ability:1 perturb:1 quasiparticle:2 powerful:1 reflected:1 xin:1 another:2 precisely:1 electronic:4 lagendijk:1 given:2 perturbation:2 temperature:24 needed:1 ordering:2 unknown:1 condensate:1 system:4 least:1 1a:1 their:1 underdoped:3 1b:1 45k:1 hundred:1 low:4 17k:1 mostly:1 accurately:1 artifact:1 assumption:1 part:1 than:5 reflection:1 distance:1 pyramidal:1 depressed:1 double:1 65k:1 expt:6 matter:1 states:6 amplitude:3 were:2 gives:1 polycrystalline:1 sees:1 boston:2 tϕ:16 spectrum:1 curves:2 crossover:2 qps:3 20k:1 confirms:1 orders:3 zero:11 self:1 governs:1 mechanism:2 onset:1 high:7 materials:3 detector:1 circles:4 multiple:1 normal:1 any:1 correlation:1 took:1 photoinduced:3 letter:1 phase:18 measured:1 class:1 acknowledges:1 observation:4 average:1 physica:1 accounted:1 electrons:2 exp:5 nuclear:1 typical:1 physics:2 lying:1 show:2 kotegawa:1 probe:9 postdoctoral:1 inconsistent:1 line:9 fifth:1 ground:2 depth:1 finally:1 ba2:1 parameters:1 explain:1 state:5 quasiparticles:1 aϕ:8 mihailovic:1 thompson:1 constant:1 population:1 equilibrium:1 do:2 demsar:3 dominant:1 above:3 dependent:1 between:4 quantified:1 dc:1 beam:3 cannot:1 competing:23 penetrate:1 bardeen:1 qp:14 resolve:1 densities:1 podolsky:1 arxiv:1 excellently:1 nayak:1 though:1 characteristic:1 through:1 fixed:1 fledged:1 reveals:1 exists:3 national:2 kink:1 observed:1 intensity:2 discussions:1 techniques:2 tl2:1 αt:2 avenue:2 µw:1 nature:6 circulating:1 µm:3 pump:9 platelet:1 various:1 µj:1 across:1 notice:1 korea:3 spectroscopy:4 labelled:1 opening:3 importance:1 weak:1 however:2 daejeon:1 31k:1 reproduces:1 jo:1 suppressed:3 both:1 apure:5 enables:1 sacrificing:1 many:2 region:3 acknowledge:1 heating:1 enabling:2 layered:12 dated:1 experimental:8 con:1 unclear:1 timescale:2 coexistence:14 lake:1 gong:1 initiative:1 boson:1 wider:1 moreover:2 points:1 2nt:1 ps:6 described:2 second:3 source:1 addition:1 due:6 been:3 ting:1 reduction:1 describes:1 complicated:1 superconductor:3 basic:1 expected:1 degrees:1 fig:18 enable:1 general:1 samples:2 relaxing:1 requires:1 θd:2 gap:32 bulk:1 dramatic:1 deep:1 basov:1 repetition:2 spin:2 present:2 applied:3 multi:5 laser:3 external:2 solid:9 appearance:1 value:4 while:4 situation:1 nucleate:1 layer:1 larger:1 phenomenological:1 dumped:1 thus:2 surprisingly:1 obeying:1 superconducting:25 cond:1 inhibiting:1 technology:1 around:2 grown:1 different:3 lengths:1 clearly:2 underestimate:1 modification:1 decreases:3 infer:1 neutron:4 higher:2 development:1 independent:2 used:3 see:3 upon:1 effect:1 stripe:1 kim:2 landau:3 recent:2 lower:2 pa3:1 center:1 minimize:1 changes:2 well:1 analysis:3 without:3 solve:1 entry:1 model:9 recombine:1 responsible:1 cuprates:8 diameter:3 being:1 superconductors:6 obtain:2 shape:1 reformation:1 immediately:1 scattering:4 coordination:2 han:1 density:11 smith:1 fitting:3 lattice:2 priori:1 lett:8 versa:1 evidenced:1 excited:2 resolved:2 aspects:1 increased:1 showing:2 possible:1 increases:2 five:2 makes:1 using:10 emergence:3 unique:2 insert:1 cu3:1 like:1 sizes:1 follows:2 signal:6 temporally:1 manifest:1 flux:1 vortex:1 mhz:3 pohang:2 lends:1 namely:3 successfully:1 back:1 competition:1 b0:1 debye:1 doping:2 chakravarty:1 scale:2 cooper:5 cavity:1 affects:1 measurements:1 per:1 creative:1 magnitude:3 provides:2 assuming:1 nd1:1 yields:1 noise:2 tmin:2 power:1 elucidate:1 bn:4 conventional:3 properties:1 berlinsky:1 oh:1 freedom:1 dependence:9 recognized:1 range:4 carrier:1 oy:1 positive:3 srx:1 slightly:2 sarrao:2 jian:1 presence:7 into:7 within:1 obtaining:1 reflectivity:1 determine:3 75k:1 varma:1 additional:2 intrinsic:2 support:2 pairing:1 long:1 los:4 accordingly:1 much:2 inner:2 kang:1 was:6 opens:4 lowest:1 cuo4:2 only:7 illuminated:1 form:1 cuo2:2 femtosecond:3 kabanov:1 denoting:1 but:1 volume:2 optical:7 highest:1 relaxes:2 especially:1 zhu:2 temp:1 whether:1 antiferromagnetic:9 supr:1 up:1 us:3 crystal:3 below:14 gaps:1 limit:2 sapphire:1 planes:3 fluctuations:3 distribution:1 define:1 similar:1 strongly:2 fluence:2 taylor:4 associated:2 describe:1 metals:2 photoexcitation:2 single:7 exist:2 tabletop:1 laboratory:2 lifetime:1 regime:1 again:2 compared:3 nm:3 dotted:1 no:1 dashed:3 when:1 inset:3 field:10 photoexcited:5 other:8 republic:2 department:2 nt:12 deviation:1 excitation:2 superconductivity:13 a0:2 meaning:1 peak:2 suppression:2 structure:1 correlated:3 coupling:1 vice:1 assume:1 thermalization:1 required:1 governed:1 crease:1 95k:1 observe:3 compete:1 fitted:3 time:13 ultrafast:4 once:1 resolution:1 having:1 bcs:7 |
0705.1725.txt |@word arbitrarily:2 saturated:5 gr:1 proposed:2 accurate:2 shahar:1 obtain:1 notations:1 course:1 thermal:1 lucile:1 immediately:1 follow:1 still:1 its:1 calculate:1 remarkable:1 decay:3 ln:2 continued:1 explain:1 solving:1 should:2 finally:1 smallest:1 black:7 lett:1 slowest:4 might:3 equilibrium:1 maximal:2 do:2 saturation:2 supported:1 around:1 means:1 frequencies:5 practice:1 possible:1 results:1 smallness:1 example:2 makes:1 formula:1 press:2 using:1 rotation:4 now:1 exact:3 ds:1 2s2:1 eigenvalue:1 iδ:4 follows:3 university:1 arxiv:1 kerr:6 scalar:2 damped:6 large:1 qc:1 inequality:2 mode:5 arbitrary:1 further:1 identifies:1 works:1 notes:1 because:1 force:1 computed:1 our:3 2iδ:5 brute:1 some:2 astroph:2 rate:5 frequency:4 violated:1 expect:1 oscillations:1 gruzinov:1 violates:1 mat:1 ωis:8 confirm:1 rev:2 while:1 kleban:1 does:2 above:1 sup:4 new:2 proc:1 acknowledgments:1 coefficient:1 foundation:1 more:1 recently:1 obey:3 useful:1 infinitely:1 agreement:1 here:1 small:2 approaches:2 york:2 relaxation:2 imaginary:2 extreme:6 obtained:1 comparison:1 cos:2 derivation:2 numerically:2 many:2 leaver:2 equal:1 o:2 noted:1 introduction:1 obeys:1 positive:1 expression:6 finds:1 teukolsky:2 first:1 origin:1 david:1 unclear:1 statements:1 lond:1 washington:1 bound:18 approximate:1 pole:1 references:1 angular:2 denominator:1 given:2 checked:1 temperature:4 their:1 remains:3 transfer:1 support:1 system:2 dispersion:1 strict:2 perturbations:2 slowly:6 damping:2 interest:1 rates:2 was:1 universal:1 pl:1 gives:5 function:2 πt:1 precision:1 but:1 part:2 normalized:1 particular:1 hole:6 true:2 those:1 he:2 case:1 packard:1 whether:1 double:1 gravitational:1 work:1 value:3 ωi:4 near:4 individual:1 limit:3 amplitude:1 property:2 minus:1 real:2 compare:1 iz:1 constant:1 give:5 defined:1 holes:5 abstract:1 detweiler:2 discussions:1 say:1 im:4 dθ:2 sense:5 close:2 seen:3 seem:2 times:1 inf:2 numerics:1 information:1 hod:10 soc:1 decaying:3 lim:6 when:1 check:1 ny:1 other:1 take:2 department:1 dimensionless:1 parameter:3 sin:3 briefly:1 exp:2 may:1 numerical:1 quasinormal:7 hand:1 meaning:1 a2:1 thank:1 law:1 cases:1 tighter:1 bekenstein:4 prove:1 assumed:1 modes:9 considered:1 values:3 calculated:1 saturate:2 explicit:2 fraction:1 mass:1 fundamental:3 time:2 definitions:1 physics:1 equation:7 fact:1 once:1 |
0705.1726.txt |@word schlegel:2 luminosities:10 dynamic:1 four:2 relationships:2 rines:3 calculate:3 dalcanton:1 incurs:1 dominate:3 supports:3 consistent:10 bacon:1 direct:3 budget:10 second:3 qualitatively:2 estimated:1 even:6 errors:6 cheng:3 new:2 contributes:3 centric:1 here:3 dore:1 pratt:1 obtained:2 rests:1 study:4 complicated:1 changes:1 prints:6 divide:1 seven:1 total:63 plot:3 would:8 therefore:6 type:6 fractions:36 populations:2 starburst:1 disruption:1 excellent:1 must:4 work:5 mi:2 hansen:6 example:1 bennett:1 indicates:1 caution:1 magnitudes:4 absolute:4 end:3 provide:6 feature:1 revisit:1 how:1 hot:3 rudick:2 significance:1 bressan:1 merritt:3 minority:1 after:3 predicated:1 hence:4 modest:1 types:2 las:1 third:2 schneider:3 summing:1 davies:1 underprediction:1 decreasing:3 acknowledges:1 order:2 willman:3 feedback:2 over:9 vary:1 undetected:8 murray:1 ramella:2 before:1 fit:18 imf:1 highlights:1 expectations:1 better:1 production:3 compelling:5 fig:5 versus:2 combination:1 band:5 effects:1 they:3 structural:1 oemler:1 brightness:2 reasonably:1 reasonable:2 each:7 calibrations:1 mean:12 financial:2 telescope:2 independent:5 used:5 combining:2 driving:1 murante:6 fellowship:1 reader:1 foundation:1 arizona:1 turning:1 little:1 overprediction:1 formation:9 estimate:7 r1:1 cosmic:1 steward:1 xue:1 corrections:5 already:1 adopted:5 similarly:1 top:2 observations:4 ranging:1 insightful:1 volmerange:2 gyr:1 somewhat:1 target:1 roles:1 likely:1 zaritsky:9 project:1 matter:1 fashion:1 quench:1 guggenheim:1 seen:2 ray:23 latter:2 isolated:1 predominantly:2 circles:4 monaco:2 exercised:1 tozzi:2 constancy:2 dom:1 calculated:1 accounted:1 left:1 quantifying:2 section:2 planetary:1 reductions:1 probe:1 halpern:1 implying:1 radii:11 diminish:1 damen:1 just:1 explain:1 rich:4 constant:4 do:6 above:1 de:4 dz:2 increasing:8 mergers:1 testing:1 observed:10 depends:1 radius:18 result:16 discussions:3 best:12 techniques:1 unable:1 approach:5 reiterate:1 terms:1 extend:1 nature:5 overestimates:1 mcbride:1 weak:2 however:2 wu:3 ellipticity:1 clues:1 modeling:1 fukugita:1 uncertainty:6 ciardullo:4 fagotto:1 exceeds:3 distinction:1 contribution:13 argue:1 l149:1 presumably:3 quinn:2 phy99:1 basis:2 three:2 been:1 ting:1 much:5 progenitor:1 expected:3 ann:1 25l:1 concerning:1 exception:1 aiz:2 castro:1 dept:1 applies:1 gerhard:5 balance:1 mader:1 played:1 tions:1 ii:13 insensitive:1 confirmed:2 perform:1 cumulative:1 complex:1 potentially:1 avoids:1 several:2 grows:2 fairly:1 satellite:1 peaks:2 hand:1 isochrones:1 normalization:2 sextractor:1 mezzetti:2 mathews:1 simulated:1 maxima:1 quoted:2 yen:1 distribute:1 ctio:1 thanks:1 sabbatical:1 yet:2 previous:4 cherry:1 had:1 dubinski:1 passive:1 wright:1 east:1 plasma:3 l83:1 possible:3 boxes:1 background:12 unique:1 unexplored:1 right:1 old:1 harassment:1 speybroeck:1 icm:2 icl:126 properties:1 meyer:1 limitation:1 census:1 o:6 lacked:1 slightly:2 contains:1 ahg:1 presence:4 lies:1 pimbblet:1 often:2 support:4 width:1 kravtsov:6 fraction:71 astrophysics:7 ettori:7 was:4 lowest:2 medium:7 gaseous:3 form:1 attempted:1 differences:3 verde:1 underestimates:1 loveday:1 inside:1 mgal:1 tucson:1 later:1 moore:3 computing:1 abstract:1 evidence:4 exist:2 simulations:8 accounting:8 triangles:3 physical:6 stellarity:1 dotted:2 no:12 whereas:1 generally:1 ny:1 interested:2 digital:1 kuntschner:1 picture:1 superposition:2 models:4 tabulations:1 peletier:1 abscissa:1 assume:2 bottom:1 together:1 chiosi:1 uncovered:1 stripping:3 pointecouteau:1 time:2 laws:1 meiksin:1 precise:1 overplotted:1 varying:1 blanchard:1 focus:2 inverse:1 giuricin:2 mahdavi:1 environment:4 2004b:3 2004a:4 compensate:1 ven:1 oversight:1 advantage:1 zhang:4 choice:1 fontanot:1 presented:2 discrete:1 l93:2 trend:7 literature:6 spectrograph:1 adds:1 appear:2 uniform:1 current:7 falling:1 filled:4 supporting:1 den:1 understanding:2 groups:30 alone:4 along:1 appears:1 change:1 commonly:1 suggestion:2 hospitality:1 vogeley:1 studies:16 plotted:1 buote:1 bullock:2 zibetti:8 tidal:4 bertelli:2 entities:1 stacking:1 criteria:1 theoretical:3 today:2 apparent:2 clus:1 cases:1 annuli:1 impey:1 values:11 following:1 making:1 figure:9 predict:3 sense:2 sample:35 weighting:1 performed:3 dennis:1 conversely:1 discussion:3 nyu:2 chemical:1 may:12 bcgs:2 produce:1 mag:6 date:1 data:19 grow:1 natural:1 dynamical:2 zentner:1 cosmology:3 so:2 definitions:1 noteworthy:1 indeed:1 years:1 course:1 statistical:4 still:1 observational:3 derive:5 group:7 thank:2 mardirossian:2 decreases:7 forms:1 ours:1 non:3 evolution:3 tucker:1 half:1 now:3 discuss:1 campanas:1 possibilities:1 entirely:1 photometry:1 ters:1 weighted:4 significantly:4 astrophysical:3 ex:1 year:1 adequately:1 gonzalez:14 shown:4 napolitano:1 space:1 increase:2 contained:6 investigation:1 suggesting:1 squares:2 shows:2 contain:1 mechanisms:2 possibility:1 dependencies:1 advantages:1 valdarnini:2 stefano:1 care:1 arnaud:2 impose:1 massive:9 first:7 origin:3 spergel:3 comprised:1 directly:7 open:3 size:1 given:3 necessarily:2 brighenti:1 kochanek:2 indicate:1 white:5 1m:1 williams:1 gives:1 mostly:1 dolag:3 than:30 population:7 wide:1 effective:1 require:4 were:3 correction:4 argument:1 any:5 conversion:1 efficient:2 note:5 potential:2 observationally:1 interior:1 multiple:2 probed:1 correlation:3 baryons:16 latex:1 average:3 adopt:3 typeset:1 typically:3 quantity:2 slope:6 threshold:1 feng:1 ratio:6 analytic:1 only:11 munn:1 expectation:3 nearly:1 regarding:1 median:2 yield:2 predicted:3 fainter:3 rms:2 bautz:5 physically:1 relative:10 christlein:3 subsequent:1 bureau:1 between:20 across:1 vertical:1 wechsler:2 jr:1 come:1 motivations:1 kogut:1 region:3 enabling:1 nearby:5 among:5 moreover:2 considers:1 considering:1 intracluster:20 capable:1 west:1 combined:6 concentrated:2 direction:1 andrey:1 observe:5 those:8 case:4 stacked:2 profiles:5 invoking:1 fiducial:1 wadsley:1 discrepancy:5 cluster:98 bias:5 sarzi:1 different:7 same:6 shifts:1 underestimate:1 driven:3 relies:1 boehringer:1 largely:1 minimize:1 roughly:3 macri:1 severe:1 without:2 components:20 fixing:1 model:8 when:6 rest:1 relevant:2 summed:1 durrell:4 sheldon:1 samples:4 swope:1 real:3 papers:1 early:1 department:2 using:20 correcting:1 particle:2 either:3 twelve:1 redshifts:1 images:2 sommer:4 matching:2 girardi:5 confirm:1 finkbeiner:1 depletion:1 critical:5 deficit:1 provides:1 refer:4 measuring:1 markevitch:1 power:1 biases:1 ratios:3 emulateapj:1 comparison:8 central:7 package:1 discussed:3 zappacosta:1 decreased:2 redshift:4 image:1 ltsa:2 references:1 determine:10 strip:1 valuable:1 lastly:2 log:5 area:3 removing:1 there:16 dispersion:19 low:11 stars:23 morrison:1 jones:1 illuminated:1 mnras:10 applying:1 stanford:1 ωm:5 ωb:3 strongly:3 ab:1 describe:1 deep:1 resultant:1 examine:1 enable:1 az:1 again:1 completeness:2 field:2 valid:1 emsellem:1 krajnovi:1 poor:2 separate:3 drift:3 nichol:1 includes:1 important:4 included:5 building:1 enrichment:1 mass:121 resolution:1 original:3 consider:2 lack:3 unweighted:1 mccarthy:3 zabludoff:9 arnouts:2 causes:1 removal:1 diluting:1 program:1 barroso:1 mpc:3 straightforward:2 very:1 discrepant:2 czoske:1 interpreting:1 dispersions:11 falc:1 difference:3 sauron:2 large:10 past:2 pasp:1 further:1 ter:1 wmap:12 gunn:1 sum:2 fractional:1 method:3 full:4 component:29 strong:2 published:6 brightest:5 via:5 hogg:1 magnitude:3 limon:1 extinction:3 uniformity:1 distinct:1 faint:4 mihos:2 strauss:1 comparing:3 monotonically:1 aperture:2 1r200:2 more:20 corrected:1 particular:2 presumed:1 science:1 equation:1 tanvir:1 subcluster:1 impacts:1 scan:3 rodriguez:1 suggestions:2 contradicts:1 arise:2 axis:4 information:1 rather:3 utilize:1 maps:1 larsen:4 explains:1 ensemble:3 m500:1 jarrett:2 derived:7 reflect:2 fb:7 fg:2 horizontal:1 fl:1 short:1 extrapolation:3 fundamental:1 paper:14 through:1 existence:1 avenue:1 its:2 style:1 jacoby:3 actually:1 peng:2 detected:1 systems:42 bypass:1 might:1 good:1 number:2 speculate:1 fioc:2 bryan:3 moscardini:2 hereafter:3 level:7 connolly:1 radial:3 found:3 bruzual:2 weight:1 reduce:1 expect:3 measurement:9 dominates:1 dominated:1 hill:1 sloan:1 issue:1 ast:1 favored:3 dressler:1 confidence:1 difficulty:1 reason:1 imaging:1 members:5 definition:1 unresolved:2 conducted:1 fallen:1 major:1 reflected:1 instances:1 schectman:1 least:3 fluxes:1 introduction:1 leading:1 construct:1 assumption:3 arnaboldi:4 hundred:1 listed:2 relationship:4 baryon:63 part:2 bower:1 authors:1 observatory:1 charlot:2 determined:3 cept:1 substantial:1 headings:1 blanco:1 lin:18 majority:1 internal:1 build:1 extrapolating:1 reach:1 most:9 significant:8 britton:1 bahcall:1 measured:6 cover:1 km:21 optical:4 velocity:30 physics:4 bulletin:1 lying:1 hippel:1 mcdermid:1 particularly:1 relation:9 entity:1 find:12 giant:3 parameters:2 distributed:1 factor:8 circle:1 bernstein:1 kashikawa:1 dominant:13 dependent:2 eprints:1 rocca:2 during:1 morgan:5 csabai:1 blanton:4 bars:1 set:3 sep:1 declines:1 see:7 individual:4 close:1 soucail:1 mckay:1 fang:2 smallest:1 various:3 targeted:1 spectroscopic:1 subdividing:1 alters:1 annis:1 both:13 improved:3 context:3 whole:1 sadat:1 reside:1 point:1 simple:1 smith:1 corresponds:4 dimensional:1 simply:4 throughout:1 decline:1 due:5 yasuda:1 reduction:1 ph:1 generating:1 referee:1 gas:31 convert:3 anthony:1 determination:5 systematic:13 intriguing:1 empirical:1 while:7 behavior:10 error:1 resolved:1 rix:1 von:1 apjs:1 grant:4 barnes:1 vikhlinin:16 survey:1 relatively:1 conflict:2 higher:7 weinberg:1 robust:4 recent:3 dark:1 lower:20 analysis:7 odegard:1 subsamples:1 conclusions:2 source:1 deliberately:1 lacking:1 suffering:1 forman:1 formal:1 excluding:2 systematically:2 follows:1 consensus:1 flux:3 yields:5 methods:1 creation:1 some:3 trends:7 infall:1 scale:1 diaferio:3 measurements:8 l13:1 minimal:1 ponman:4 bm:1 annular:1 agreement:1 step:1 plots:1 brinkmann:2 range:12 consequently:1 tornatore:2 into:7 within:43 shed:1 nsf:1 appropriate:1 uncertainties:13 span:2 few:4 placing:2 question:2 specifically:3 balogh:1 cappellari:4 rasmussen:4 line:4 padova:1 up:1 5r200:2 similar:6 purcell:2 associated:4 reservoirs:1 l500:4 steeper:1 dashed:1 gainesville:1 points:2 shallower:1 dashes:1 calculating:1 lucia:2 structure:1 agn:1 correlated:1 implies:3 required:1 nasa:2 nasi:1 requires:3 having:2 katz:2 results:12 winds:1 roussel:2 concerned:1 helps:1 tegmark:1 include:10 random:2 continues:1 dependences:1 fewer:1 smaller:4 biased:2 enclosed:4 index:1 abell:27 obvious:1 sigurdsson:2 degree:2 respectively:2 explore:1 focused:1 separation:1 implicit:1 great:1 larger:13 suggests:1 resulting:2 antecedents:1 examining:1 kurtz:1 scales:1 photometric:1 apj:29 overestimating:2 decrease:4 apply:2 use:11 remains:2 jarosik:1 hydra:1 camera:1 reflects:1 sort:1 governato:1 formally:1 becomes:1 iii:3 account:3 integrating:1 boschin:2 reproduce:2 crossed:1 scatter:3 weaker:1 calculation:2 high:6 assumptions:1 hinders:1 regions:1 located:1 varies:1 elliptical:3 instead:3 circular:3 blocks:1 harding:1 kneib:1 demonstrating:1 bertin:2 efficiently:2 light:22 lines:1 evrard:1 american:1 shimasaku:1 evolutionary:1 astronomical:1 interpreted:1 overdensity:1 including:4 converting:2 accrete:1 galaxy:39 aj:5 lgal:1 exclusion:2 masses:13 inclusion:6 li:1 choose:3 clusters:52 defining:1 freeman:3 contention:1 richness:2 subtraction:7 university:2 identified:1 sufficiently:1 kpc:7 l0:1 l1:1 rising:1 arxiv:8 related:1 inverted:1 society:1 measure:2 our:52 out:5 cause:1 integrated:1 interactions:6 galaxies:49 approaches:1 york:1 okamura:2 determining:2 could:3 florida:1 frenk:1 times:1 davis:1 humphrey:1 diminishes:1 precisely:1 nebulae:1 system:14 relations:2 their:7 accretion:2 schwarschild:1 bosch:1 final:2 wollack:1 contribute:3 environmental:1 nolta:1 constituent:1 detection:1 limiting:1 inversely:1 exhibit:2 correspond:1 unlikely:1 apparently:1 clearly:1 angle:1 studying:1 able:1 mechanism:2 mix:1 subject:1 borgani:5 dimming:1 who:2 finoguenov:1 class:2 r200:18 artificially:1 constrain:1 fact:1 selection:6 supported:1 kitp:1 purely:1 principal:1 based:4 knowledge:1 baryonic:6 should:2 virgo:1 brighter:1 constituents:1 emitting:1 local:1 nag5:1 means:1 overall:2 bean:1 ones:1 argues:2 processes:4 luminosity:64 tuned:1 navarro:1 ascertain:1 fixed:3 requirement:1 computed:1 national:1 phases:2 xray:1 conroy:2 identification:2 krick:3 crude:1 comparable:2 reproduced:1 importance:4 interpolate:1 efficiency:4 key:1 comparably:1 interpretations:1 salpeter:1 komatsu:1 detailed:1 unclear:2 conclude:5 contamination:1 environments:6 cd:1 feldmeier:9 table:4 kinematic:1 addition:1 slowly:1 aguerri:3 arises:2 corresponding:2 bulk:2 shortfall:4 covered:1 general:2 present:3 contexts:1 value:21 will:2 kimball:1 thus:4 surface:2 vs:4 against:2 largest:1 difficult:2 hinshaw:1 upon:3 effect:2 ferguson:1 romeo:1 dust:1 ponent:1 center:2 com:1 modeled:1 well:1 position:2 recasting:1 kauffmann:1 usual:1 routinely:1 less:4 increasingly:1 obtain:5 geller:3 generous:1 preprint:1 density:8 sky:3 lake:2 reasons:1 combine:1 spirals:1 identical:1 increased:1 sytems:1 increases:2 five:1 know:1 necessary:1 like:2 lost:3 become:1 works:1 page:1 r500:36 exceed:1 because:13 mohr:5 smoothly:1 growth:1 nagai:1 choosing:1 gastaldello:6 lead:2 demonstrates:3 overlap:1 does:5 masked:1 sdss:1 slight:1 selecting:1 journal:2 stellar:49 although:6 zeeuw:1 analyses:1 panel:3 gained:1 about:4 extension:2 column:2 universe:1 introduces:1 dependence:12 own:1 previously:2 h0:1 estimators:1 van:3 additional:1 spiral:1 galfit:1 function:15 reduc:1 north:1 basic:1 but:14 astro:1 ho:1 highest:1 he:3 made:1 compute:7 whether:6 portinari:1 variations:3 huchra:2 below:3 limit:2 distribution:2 universal:9 tormen:2 denote:2 functions:1 compared:1 calibration:2 percent:1 detail:1 other:7 details:3 conclusion:1 star:4 astronomy:1 weiland:1 apertures:4 bcg:89 rule:1 4m:1 kaib:1 peiris:1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.