text
stringlengths 0
190k
|
|---|
0704.0661.txt |@word replacing:1 araujo:1 gt:4 partial:1 consider:15 chain:24 rx:7 global:1 results:15 oqn:1 eds:2 proposition:56 grateful:2 vectoriel:1 consists:1 follow:2 denotes:1 assembled:1 gi:3 whose:15 γy:6 maximally:2 tx:20 ty:13 equivalence:8 contained:14 factoring:1 finally:1 those:4 hulek:1 under:9 connecting:2 analogous:9 include:2 lake:1 norm:1 degeneration:1 applied:4 conjecture:5 fac:1 consequently:1 straightforward:1 very:22 kleiman:1 reader:1 connects:1 induce:1 choice:6 suggesting:1 corollary:4 every:32 lecture:2 affect:1 exact:7 deformations:1 condition:9 dim:65 induced:2 immediately:2 turns:2 notes:2 large:1 aiming:1 convenience:1 vector:21 sniewski:3 shows:4 gruyter:2 homomorphism:1 des:1 says:3 lefschetz:1 harder:1 miur:1 milano:2 rulings:2 second:8 pass:1 further:3 reine:1 linear:8 even:3 index:2 giving:2 section:29 contracted:3 cohomologie:1 find:3 version:3 above:17 hyperquadrics:1 new:1 construction:5 consisting:1 supporting:3 full:1 notions:3 excludes:1 respectively:2 component:19 proc:2 here:8 desired:1 identifications:2 q2:7 tangent:6 groups:2 address:5 isomorphically:1 along:1 quite:1 observing:4 z1:2 contraction:7 obtained:8 remark:26 divisor:10 forum:2 technical:1 items:1 study:4 studied:5 alta:1 ampleness:4 resulting:2 adv:1 pick:1 suitable:7 changes:1 sup:1 sci:2 quotient:18 via:9 useful:5 projection:1 classification:5 f1:1 inducing:5 namely:2 explained:1 f2:1 proves:6 assertion:6 addressed:1 generality:6 apply:6 should:1 univ:1 linearly:8 use:9 quasi:1 would:4 prove:8 distinct:3 positive:10 h0:10 give:3 bundles:20 negative:6 next:2 comparing:1 mori:19 call:6 m0:14 means:1 type:5 minor:1 more:9 introducing:1 loci:3 said:10 initiated:1 relax:1 city:1 aware:1 surjection:4 berlin:7 exposition:1 particular:22 known:4 projective:53 cases:3 hold:2 iii:2 account:2 isomorphism:20 word:2 tokyo:1 recall:4 work:1 det:8 sweeps:1 theories:1 obvious:4 codimension:6 den:1 determining:1 following:27 making:1 quadrics:1 andreatta:2 example:3 proof:48 claim:2 compare:4 stated:1 fibration:35 suggestions:1 rc:4 generically:11 ut:1 mannigfaltigkeiten:1 assumptions:4 numbers:2 hyperplane:4 sense:4 exclude:1 counting:1 conversely:1 breaking:1 guarantee:1 respective:4 goal:2 rather:1 beweis:1 discussion:1 hom:50 department:1 occur:1 maps:4 ochiai:2 reducible:1 resolution:1 pure:1 simplifies:2 extensions:1 verlag:4 parameter:1 classify:2 map:24 product:1 mar:1 ft:1 intended:1 singular:1 may:4 fz:3 after:4 different:6 diagram:24 applications:5 fundamental:2 ova:1 coming:1 cambridge:3 fi:8 fj:4 parallel:1 types:1 fo:1 cokernel:1 stress:1 short:4 natural:11 varieties:25 third:1 whenever:2 lemmas:1 fibers:28 lines:7 parameterized:2 element:2 extremal:13 fernex:17 so:16 sect:1 allow:1 definitions:3 acknowledges:1 order:4 restriction:20 eron:1 holds:5 abelian:1 produces:1 indeed:7 over:15 fall:1 vary:1 satisfied:5 paper:4 through:6 connexit:1 hypersurface:2 existence:5 satisfies:5 still:1 vari:1 its:11 before:1 le:2 group:3 thank:1 acknowledge:1 chosen:1 picard:7 fix:12 writing:1 according:1 cofin:1 criterion:1 main:5 might:2 deformation:3 maximal:4 non:7 h1:2 polarizations:1 inductively:1 impossible:1 yg:16 primary:1 break:1 mention:1 parameterizing:5 they:1 grenzgeb:2 now:12 smoothness:2 pz:1 easily:2 finite:19 equality:1 duality:3 always:1 university:4 drop:1 arrows:1 potier:2 sufficiently:2 universita:2 inequality:2 irreducible:49 lanteri:20 found:1 soc:3 higher:2 side:1 mean:2 subset:18 domain:1 schemes:2 meets:1 series:2 idea:1 related:3 conventions:1 milan:2 literature:2 factorization:2 combining:1 into:3 our:13 special:7 out:6 clarity:1 space:12 restricted:1 furthermore:2 since:48 induces:12 valeurs:1 research:2 content:1 similarly:3 posteriori:1 dominated:1 rational:80 istituto:1 denoted:5 formula:1 get:5 dominate:1 suffices:3 occurs:4 math:22 rk:10 fiber:38 theory:6 circumstance:1 mapped:3 little:1 free:19 standard:2 admits:2 oy:1 base:9 put:1 beginning:2 generate:2 definition:29 unique:1 hg:3 geometry:7 phrases:1 could:1 πe:2 keep:1 turn:1 length:2 place:1 compactification:1 hence:17 view:3 onto:1 think:1 south:1 first:16 rang:1 already:2 einer:1 adjunction:7 relate:1 number:5 rank:6 restrict:2 clear:1 dima:1 adopted:2 directly:2 neighborhood:2 precisely:1 open:8 passes:1 given:18 cartesian:1 likely:1 needed:2 introduction:2 adjoint:2 system:2 least:3 their:6 assumption:3 listed:1 statement:8 scheme:10 structures:3 smoothed:1 speaking:1 gives:3 commutativity:2 relationship:1 tommaso:1 contains:4 exactly:1 proving:1 because:4 authors:1 than:3 observed:1 polarized:3 determines:1 effective:3 characterizations:1 sections:10 require:4 dans:1 zero:9 project:1 classes:10 supposed:1 were:3 naturally:2 treated:1 trento:1 projections:2 springer:4 pointed:1 tracts:1 cn:1 subvarieties:19 ann:4 concludes:1 argument:4 generalization:4 needs:1 fail:1 say:4 angew:1 close:2 disjoint:3 seen:1 sees:1 obviously:1 any:20 viewed:3 ray:9 lie:2 bayreuth:1 convenient:1 latter:1 internat:2 able:1 sendai:1 polarization:4 instance:1 ideal:1 lifts:1 take:7 quadric:19 zu:1 unimi:1 added:1 relatively:1 gβ:2 normal:20 collaboration:1 reach:1 algebraic:13 regular:13 connected:58 plan:1 conic:2 remarks:1 acknowledgements:1 intrinsic:1 class:10 tensor:1 bound:1 ka:1 kg:5 kf:2 considered:6 ki:2 later:1 countably:1 face:1 countable:1 nef:10 proceedings:2 points:7 camb:2 ky:5 kx:10 salt:1 notion:1 fact:24 mrc:3 precise:1 gz:4 scrolls:1 particularly:1 show:9 supported:3 spaces:4 relation:3 2r:1 campana:3 trivial:3 injection:2 faces:1 fibrations:44 based:1 holomorphe:1 situations:3 outside:3 completes:3 values:1 lemma:24 only:18 saldini:1 local:1 interested:1 continuity:1 do:4 his:1 dominant:7 birational:6 notation:21 di:5 dg:4 genera:1 de:23 beltrametti:17 manuscripta:1 soon:1 hartshorne:5 cannot:2 words:1 allowed:2 du:1 secondary:1 closure:4 subscheme:3 evident:1 genova:1 covering:28 irrational:1 arxiv:1 yield:1 rcv:19 contain:1 cycles:1 qm:13 qn:5 set:5 modulo:1 exists:3 surjectivity:1 national:1 relative:7 see:29 geometrically:1 result:16 discussions:1 pi:3 theoretic:1 acts:2 subject:1 surfaces:1 preparation:1 detect:1 extend:5 ways:1 positivity:3 currently:1 fano:4 dodecaneso:1 state:1 un:1 various:1 closed:9 between:4 rem:1 geometric:3 conditions:10 letting:1 restricting:1 terms:2 jy:4 vertical:1 complementary:1 weak:1 complement:1 attention:1 focus:1 however:2 wi:3 vanishing:4 inclusions:1 hypothesis:11 key:1 codimx:10 comb:1 come:2 ker:5 both:6 essentially:1 positif:1 last:2 reverse:1 cov:4 many:3 taking:7 la:1 equal:3 conference:1 admit:2 geom:1 equidimensional:2 context:2 interesting:1 passing:3 genus:4 adapted:2 sheaf:1 considering:1 comment:1 among:3 ci:3 rcw:3 point:31 reasons:1 each:4 cohomology:1 cf:2 except:1 dimensional:11 grants:1 simply:1 assertions:1 spans:1 sequences:1 constant:2 throughout:3 miyaoka:4 precious:1 speak:1 specializing:1 most:2 light:1 described:1 submanifold:11 union:7 due:5 been:2 springerverlag:1 interest:2 basic:1 collected:1 morphisms:11 pn:14 universal:5 empty:4 define:10 surjective:20 stud:1 referee:2 corresponding:3 ionescu:5 restrictions:4 composing:2 sufficient:2 propositions:2 subspace:4 coincides:2 gap:2 matematiche:1 observe:6 recalled:1 curves:59 mail:3 catania:1 improved:1 c1:2 general:61 universitext:1 manifolds:9 case:43 p3:2 p0:1 p1:129 jx:3 splits:1 subsets:2 defining:2 contradiction:4 kodai:1 value:1 choices:5 will:20 rationally:29 near:1 ar:7 suppose:14 monodromy:2 applies:2 situation:5 property:12 debarre:1 theo:1 commutative:17 vg:8 almost:1 endowed:1 von:1 thus:14 them:2 iv:7 ii:12 need:6 good:3 im:4 cone:5 dual:1 ambient:3 ia:1 vy:59 sits:1 ig:1 capture:1 containing:8 italy:3 stein:2 author:2 generic:2 things:3 make:2 connection:1 same:15 clearly:3 complex:6 arguments:6 widely:1 largest:1 survey:1 reminder:1 several:2 evidence:1 freeness:1 independent:4 used:2 embedding:5 maeda:4 numerical:12 upon:1 hand:7 subvariety:10 moment:1 harris:2 uses:1 purpose:1 supposing:1 changing:1 normalization:7 cycle:2 multiplicities:1 lower:1 indeterminacies:3 rationnelle:1 keeping:2 possibly:3 makes:1 well:7 roughly:1 deal:1 antonio:1 thought:1 without:2 components:12 sets:1 undertaken:1 model:3 fujita:3 dimension:15 severi:1 meet:1 manifold:9 op1:3 being:2 generally:2 resp:8 obtain:9 identify:1 transforms:1 integer:2 facts:2 previous:11 blow:1 note:33 intersection:2 family:79 generator:2 application:1 conclude:14 seems:2 fitting:1 discuss:1 iψ:1 setting:12 extends:9 easy:2 theorem:77 necessarily:2 ruled:1 remaining:1 generalized:2 ample:79 utah:2 possible:1 spanned:4 corresponds:1 quelconque:1 vα:17 vβ:15 philos:2 know:3 press:1 using:5 opn:1 subfamily:4 occurring:1 loss:2 imposed:3 like:2 semi:1 follows:20 reduces:1 enriques:1 unnecessary:1 specific:1 collect:1 steps:1 either:14 arbitrary:7 subschemes:2 works:2 reduced:7 terminology:1 del:1 exceed:1 right:1 unsplit:18 often:3 classical:4 sequence:8 some:15 back:6 deduce:7 semipositive:1 examples:1 choosing:1 moreover:17 proper:17 koll:7 proofs:2 zariski:6 separately:1 dense:23 dimensions:2 properness:1 cut:1 mukai:1 does:4 uniruled:1 kobayashi:2 edu:1 assuming:8 lazarsfeld:1 torsion:1 imply:1 minimal:2 refer:4 differential:2 core:1 dipartimento:1 june:1 equivalent:2 additively:1 bh:4 bi:4 amer:1 restrictive:3 step:4 although:2 standpoint:1 casagrande:1 tautological:1 biregular:1 properties:7 injective:4 quotients:9 chapter:1 usa:1 extension:18 extending:3 og:1 theorems:4 o:4 essential:4 recalling:3 ensure:3 surjections:2 ox:5 introduced:5 slightly:2 other:9 morphism:42 homogeneous:3 hypotheses:4 contractions:7 statements:1 suited:1 inclusion:24 image:11 within:2 numerically:19 isomorphic:9 nsf:1 locus:43 lies:1 appropriate:1 square:1 references:2 wβ:4 determine:2 elementary:2 proportional:1 fibr:1 shrinking:2 theoretically:2 east:1 rely:1 fill:1 additional:4 pezzo:1 assumed:2 support:2 there:27 transform:2 smoothing:1 start:2 restricts:2 way:5 starr:3 notices:1 exceptional:1 unige:1 was:6 strict:1 assumes:1 therefore:28 complete:2 form:1 enough:1 sequel:2 denoting:3 but:4 kodaira:1 properly:1 ec:1 matematica:3 line:19 true:3 divisors:9 partially:1 pull:2 made:3 applying:1 mat:1 embedded:7 meeting:1 inside:1 smooth:42 up:4 us:3 ur:1 international:1 below:3 dms:2 submanifolds:3 problem:2 pm:16 similar:4 called:3 obtains:1 adopt:1 associated:7 ag:1 pencil:2 defined:19 certain:1 abstract:1 pic:29 proven:4 denote:16 images:2 associates:1 exist:1 formulation:1 nazionale:1 families:16 commuting:1 mauro:1 again:2 proalgebraic:1 variety:20 whereas:1 nc:3 when:18 ne:9 nf:10 sommese:8 ny:27 priori:1 jong:1 es:1 ergeb:2 mathematics:4 concerning:1 conclusion:2 expositions:1 elements:4 generates:1 remains:1 time:1 problems:1 bundle:54 includes:1 replace:2 generated:9 important:1 allowing:1 additionally:2 structure:8 independently:1 implies:29 assume:35 graber:2 factors:2 curve:25 together:1 lift:1 deg:3 lying:1 teeth:1 n1:31 requires:1 original:1 others:1 once:3 |
0704.0662.txt |@word partial:1 consider:1 results:6 invent:2 leads:1 sci:1 contributions:2 compact:2 whose:1 ihes:1 analytic:2 equivalence:1 adically:1 speh:1 under:3 analogous:1 norm:1 alternating:1 division:1 conjecture:5 very:2 pek:4 corollary:2 isomorphism:3 calegari:3 exact:5 dim:21 level:1 newform:1 try:2 discrete:21 multiplicities:7 recall:4 indices:1 eigenvalues:1 noted:4 upper:3 lefschetz:1 rate:2 infimum:1 zp:4 linear:2 spectral:6 established:3 filtration:1 appear:1 gk:27 sum:1 version:1 xvii:1 subspaces:1 sup:1 new:1 gl2:1 contributes:1 acknowledgments:1 coefficient:1 homology:1 full:1 ibid:1 respectively:2 here:1 groups:3 consideration:2 obtained:1 remark:3 gln:6 prior:1 domains:1 studies:1 quotient:2 via:1 projection:1 apr:1 namely:1 replace:1 analyzing:1 apply:2 should:1 tools:1 imaginary:1 fef:1 use:2 additive:2 takes:1 would:1 cohomological:7 contains:1 comparing:1 therefore:1 reductive:1 taken:1 associated:5 type:6 more:3 fractions:1 flat:1 compositio:2 duality:1 initial:1 israel:1 virtue:1 particular:7 known:1 lazard:2 hold:1 account:1 valued:1 tokyo:2 local:3 equation:1 mn:1 cancellations:2 following:8 example:3 stimulating:1 proof:9 control:1 weaker:1 stated:1 pieces:1 states:2 assumptions:1 numbers:1 evidently:1 end:1 goal:1 xue:4 occur:1 write:5 how:1 e2i:2 fp:6 may:6 derived:1 collection:1 consequence:1 produce:1 representations:22 short:2 natural:7 varieties:1 imply:1 light:1 schneider:1 summing:1 su:2 quadrant:1 so:5 fundamental:2 representation:11 order:1 neighbourhoods:1 elic:1 indeed:3 over:12 displayed:1 paper:1 through:1 banach:5 cole:1 its:5 before:1 group:7 thank:1 decay:1 interesting:1 fix:8 wallach:4 forms:5 degrees:1 choose:1 lp:1 main:6 semisimple:3 maximal:1 cusp:3 non:11 return:1 isomorphic:2 they:2 now:4 discuss:1 above:1 february:1 equality:1 betti:1 invariants:3 corank:9 rohlfs:1 establishing:1 applied:1 inequality:4 l2:2 each:11 subset:1 square:1 cocompact:4 another:1 series:20 ef:2 related:2 reader:1 poincare:1 our:10 category:4 large:3 matrix:3 space:10 spectrum:1 closure:2 furthermore:1 since:11 denotes:4 studying:1 vector:2 geom:1 rational:1 conjectured:1 formula:4 rn:5 induced:1 induction:1 occurs:1 math:10 shows:6 theory:5 frank:1 free:3 admits:7 ask:1 estimate:2 publ:1 remainder:1 correction:1 unique:1 language:2 hyperbolic:1 cofree:1 conversation:1 length:1 adic:2 hence:2 first:3 formulas:1 already:2 dime:14 franke:1 powerful:1 number:1 rank:5 restrict:1 long:1 directly:1 hochschild:1 ring:3 precisely:3 open:2 similarly:1 introduction:5 system:3 least:3 their:3 borel:1 manifolds:1 statement:1 gives:2 relationship:1 ity:1 continuous:15 part:1 e20:1 translation:1 than:4 coefficients:4 finitely:7 showed:1 princeton:2 require:1 second:1 determined:2 eigenforms:1 minus:1 projections:1 rad:1 pro:3 argument:2 flatness:1 any:7 functors:1 lie:2 depending:2 odd:1 latter:1 note:9 ideal:3 useless:1 subject:1 even:1 trace:1 index:1 systems:1 falls:1 most:2 regular:2 connected:2 definitions:1 class:1 prove:1 considered:1 hcusp:8 subgroup:7 section:2 fact:3 precise:1 show:2 spaces:5 relation:1 rubric:1 trivial:1 find:1 completion:1 situations:3 state:1 topological:3 completes:1 lemma:10 only:5 annals:1 equipped:4 integrable:1 commensurable:2 abelian:4 dl:1 dk:1 notation:4 admissible:13 dg:1 closely:2 lattices:2 quantifies:1 prime:6 qp:3 automorphic:4 introduced:1 arxiv:1 consisting:1 common:1 multiplicity:2 fixed:2 view:1 set:3 computed:2 exists:5 differentials:1 kernels:1 module:7 see:5 radius:2 result:20 w0:2 subquotient:1 techniques:1 degree:2 rings:1 preimage:1 tend:1 symmetric:4 enough:1 classes:2 between:1 invariant:1 terms:5 hecke:1 attention:1 however:4 p2k:1 key:1 relying:1 improve:1 concentrated:2 both:1 many:2 taking:3 equal:2 admit:4 pdk:8 embedding:3 passing:1 sheaf:3 point:1 cohomology:15 harmonic:1 dimensional:6 anti:1 sequences:2 moreover:2 torsion:1 coadmissible:1 pp:2 commutative:1 three:1 sl2:4 savin:2 bianchi:1 interest:1 pk:28 pn:1 ann:2 define:3 direction:2 contribute:3 corresponding:3 else:1 noncommutative:1 yk:29 denote:15 those:1 case:10 inertial:2 splits:1 leave:1 pgl2:1 value:1 will:5 dense:1 suppose:5 error:1 situation:1 serre:1 unitary:2 vol:1 characteristics:1 vk:17 thus:11 them:2 ii:1 itself:1 dual:3 vw:4 claimed:1 noetherian:2 different:1 descent:1 author:1 make:1 same:3 matthew:1 proved:2 finite:10 infer:1 interpolation:1 ball:1 forced:1 hand:3 v0:2 action:4 harris:3 contribution:1 identity:1 subgroups:3 lower:1 proceed:1 bootstrapping:1 ingredients:1 analysis:1 thm:4 lim:4 quantitative:1 arising:1 dimension:6 left:4 teitelbaum:1 manifold:1 graded:1 less:1 being:1 resp:3 obtain:7 topol:1 λe:14 integer:3 eli:4 application:1 conclude:1 improvement:4 lattice:3 dunfield:2 easy:2 theorem:35 input:1 euler:2 real:4 depends:2 sums:1 term:3 admitting:1 descending:1 press:2 using:2 intersection:1 mod:1 appearing:1 like:1 follows:3 yields:2 either:2 alternatively:2 equivariant:1 tower:2 university:2 right:3 methods:2 classical:2 sequence:10 spheres:1 some:10 back:2 tempered:10 deduce:1 growth:1 peter:1 describing:1 dimensions:2 sufficiently:1 prop:1 does:6 decomposition:1 provides:2 assuming:1 power:1 ps:1 relating:1 injectivity:1 injective:1 quotients:3 integers:1 ok:1 extension:1 algebraic:1 oe:7 theorems:4 o:13 compatible:3 efforts:1 acyclic:2 iwasawa:4 duke:2 statements:1 into:1 successive:1 obtaining:1 bound:2 lies:1 weighted:1 references:1 strictly:1 there:12 question:2 sarnak:5 quadratic:1 way:1 was:1 naturally:2 tight:1 complete:1 form:6 but:2 volume:1 analytiques:1 hn:1 functor:1 true:2 pull:2 characteristic:1 attached:1 bounds:6 us:1 discarding:1 below:1 limit:3 called:1 duals:1 constant:4 ad:1 certain:1 congruence:5 cuspidal:1 covers:2 general:2 single:1 exist:1 adiques:1 inj:1 functions:1 groupes:1 no:11 when:8 vanishes:1 nf:3 field:3 other:5 mathematics:1 nt:1 arithmetic:6 briefly:1 preceding:1 generated:5 bounded:1 proceeding:1 sides:1 structure:1 implies:5 assume:2 emerton:2 modules:4 together:2 implied:2 ramification:2 lying:2 recalled:1 |
0704.0663.txt |@word limited:2 measurements:1 partial:1 consider:4 squared:1 suggests:2 desirable:1 results:1 integration:1 leads:3 quadrature:1 commute:4 uner:1 c2:1 managed:1 expressions:2 shorthands:1 gh:7 diffusive:5 preserves:1 inverse:3 terms:5 calculate:1 integral:2 eα:4 tt:6 eˆ:2 c6:1 tn:13 finally:2 tm:1 squeezing:12 c5:1 under:1 semenov:2 tg:1 analogous:1 include:1 worth:2 sent:1 amplitudes:1 very:3 unavoidably:1 conditions:1 kristensen:1 electron:1 frequencydependent:1 sensitivity:1 refractive:1 experimentally:2 difference:2 exact:12 condition:3 indicate:1 dominate:1 moderate:2 level:1 transmission:8 evaluation:1 t2:2 scalar:1 correct:1 large:5 solved:4 vector:1 small:6 enhance:1 optics:2 equation:9 hasegawa:1 upper:2 smaller:2 compensated:2 carter:2 renormalized:1 consistent:5 pulse:50 l3:1 approximation:11 elegant:1 second:16 design:1 enhancement:26 manipulating:1 dynamics:1 estimated:2 theory:4 spectral:6 index:1 nonlinear:11 adds:1 appear:1 rate:1 clock:1 section:8 expressed:2 current:3 version:2 new:1 net:5 contributes:2 waveguide:2 method:1 coefficient:14 focuses:2 ibid:5 respectively:2 even:1 component:3 here:6 desired:1 amplification:1 excess:1 depend:2 along:1 equations:4 change:1 obtained:2 guassian:1 institute:1 study:3 studied:6 completely:2 exiting:1 prior:1 accomplished:1 resulting:2 lightwave:2 complicated:1 fourier:3 studies:2 via:2 useful:1 apr:1 vii:1 magnitude:6 achievable:1 condensates:1 total:3 use:5 would:1 tn2:1 remains:4 positive:7 contains:1 negative:7 next:1 few:1 depicted:1 noting:2 opposed:2 m2:2 survive:2 associated:1 theoretical:3 minor:1 more:11 duality:1 infinitesimally:1 advance:1 artner:2 solitons:7 operators:14 envelope:6 odinger:4 validity:1 berlin:1 appendix:8 controlling:1 virtue:1 varying:3 known:2 central:1 cases:4 hold:1 iii:2 must:5 high:2 account:3 quantized:1 science:4 setup:3 work:2 lβ:5 london:1 cm2:2 glauber:2 remain:3 fock:5 values:2 following:9 drops:2 root:1 example:2 performed:2 control:8 figure:6 give:2 predict:2 organized:1 ottir:1 states:7 numbers:1 coincident:2 arise:1 particles:1 dominant:2 nonnegative:1 evidently:2 absolute:1 information:9 needs:2 end:4 provide:1 purpose:1 means:1 steepening:1 how:3 strategy:1 ent:1 resolution:1 pure:2 opt:8 instead:6 derivations:1 profile:3 simplicity:4 fs:2 chernikov:1 lai:7 algebra:1 may:5 overall:2 after:1 derived:6 minimized:1 yanov:1 applications:1 produce:1 value:2 andersen:1 derives:1 constants:2 times:1 short:4 third:3 sech:3 sensitive:2 explicit:1 departure:1 complexity:1 cannot:1 so:14 correlation:2 definitions:2 subsequently:1 heuristically:1 order:17 least:1 help:1 reservoir:3 developed:4 over:2 top:3 mainly:1 satisfied:2 timing:27 thermal:1 paper:12 pulses:4 jakobsen:1 statistical:1 cuts:1 argued:1 satisfies:2 still:5 its:5 before:1 derive:2 group:3 symmetry:1 temporal:5 solving:1 c18:1 boson:1 better:1 lossless:2 quant:2 might:2 easier:1 aeff:2 eur:1 maximal:2 non:9 fourth:1 than:8 obtaining:1 practice:4 fig:5 investigated:3 functional:1 framework:2 effects:11 they:5 half:1 front:1 inelastic:1 february:1 gets:1 hereafter:1 always:3 university:1 kerr:3 did:2 inequality:3 transmitted:1 mode:4 positions:1 found:2 2n:3 difficult:2 2i:1 mean:1 filtering:1 square:1 significantly:4 lam:2 generation:1 energy:1 barnett:3 reduce:1 gaussian:7 related:3 applicable:1 operator:19 frequency:7 measurement:1 quantum:60 our:1 approximated:1 beyond:4 eq:51 special:1 giovannetti:8 shown:2 gur:1 furthermore:1 since:3 rev:17 denotes:2 increase:6 suggesting:1 induced:5 ref:13 viable:1 shows:4 fiber:36 linear:7 analagous:1 maintains:2 standard:16 approaches:3 kodama:1 california:1 term:19 ask:1 estimate:5 hand:11 rewritten:2 definition:2 maˆıtre:2 derivation:6 route:1 positioning:1 linearized:4 motion:3 length:5 period:3 gordon:18 hence:4 investigates:1 neglected:2 neglect:1 first:16 dmr:1 intuition:1 utilizes:1 probability:3 enhances:1 variables:1 number:18 reaches:1 transform:1 channels:2 improvements:1 simplified:1 approximately:3 another:2 reached:1 profiles:1 spread:1 dispersive:8 given:25 management:4 iω0:1 likely:1 similarly:1 introduction:1 leading:3 eqs:8 attenuated:1 system:7 relations:1 heights:1 their:5 cooling:1 assumption:1 convention:1 dt1:1 scheme:14 final:5 speaking:1 gives:2 relationship:1 huttner:1 bowen:1 relative:4 exactly:1 accurately:2 transverse:2 technique:1 optical:31 yurke:2 requisite:1 buchler:1 sˆ:26 thz:1 distance:3 kind:1 determines:1 effective:3 bachor:2 zero:13 picosecond:1 loudon:1 annihilation:5 minimize:1 determined:2 amplitude:3 amount:1 perturbative:1 function:1 san:1 fluctuation:8 spectrum:2 dash:1 say:1 conjugate:2 seen:1 any:6 relatively:1 shelby:1 convenient:2 latter:1 able:7 theses:1 instance:1 ideal:4 potential:2 take:1 online:4 performance:2 accuracy:11 heisenberg:32 refocusing:1 b3:2 experienced:2 electric:2 shall:3 most:4 optimized:1 said:1 propagate:1 unitless:1 significant:4 analytically:1 measured:1 jørgensen:2 causality:1 soliton:24 nonlinearity:8 considered:5 average:4 km:12 part:1 principle:5 exp:6 velocity:3 dispersed:1 normally:2 sum:1 quantity:2 show:4 supported:1 merit:3 fini:3 corney:1 relation:1 lloyd:4 substituting:1 rough:1 trivial:1 eliminated:3 fifth:1 impact:5 ratio:10 just:3 parameters:8 situations:3 print:1 state:22 negligible:2 should:8 analytic:1 only:9 explicitly:5 factor:7 equally:1 achieve:2 dn:1 insight:1 handle:1 therefore:3 get:1 dependent:1 beams:1 express:1 db:9 synchronization:1 dz:33 drummond:4 despite:5 dv:1 during:1 dt:23 tsang:4 dp:1 dtn:1 adiabatically:1 evolution:14 increasing:1 fields:1 arxiv:1 shape:2 factorization:1 acknowledgments:1 reid:1 prokhorov:1 investigate:4 financially:1 predicted:1 through:2 fixed:1 approaching:1 satisfy:4 achieved:5 frame:2 correlations:2 uses:1 grosse:1 detection:1 opposite:1 intensity:3 sec:9 result:4 enhanced:6 fail:1 close:4 acquires:1 fails:2 satisfying:1 commutation:2 phonons:2 subsequent:1 review:1 nature:1 justifies:2 propagates:1 materials:1 importance:1 written:2 future:1 various:2 between:9 ωm:1 subscript:1 approach:3 recently:1 opening:1 initially:1 darpa:1 however:4 dougherty:1 jointly:5 analyzed:1 longitudinal:2 dimensional:1 tion:2 abruptly:1 suggested:4 both:3 essentially:1 improved:1 limits:12 0z:1 many:3 taking:1 uncertainty:7 according:2 called:1 propagation:11 fiorentino:1 dated:1 retarded:2 exceeds:1 variance:8 contribution:1 expression:5 regarded:2 0l:1 otherwise:1 relevant:2 jitter:49 color:5 ca:1 homodyne:1 nˆ:15 semiclassical:2 maintained:1 bose:1 ordered:2 narrowed:1 throughout:2 considering:1 ps:3 described:1 aˆ:102 due:9 been:8 quickly:1 reduction:3 describes:1 slowly:4 z2:3 compensating:3 ph:2 improve:1 systems:9 arises:1 corresponding:3 commutes:2 quantities:1 coherence:2 photon:17 further:4 6n:2 coherent:16 observe:1 representative:1 c12:2 c3:1 last:2 c1:1 c7:2 former:1 those:3 c4:2 case:4 laser:3 processes:1 pacs:1 variances:1 expanded:1 evaluated:2 c16:1 will:1 while:12 optimization:1 abrupt:1 c15:1 maccone:5 identical:1 larger:3 coupled:2 phenomenological:1 vi:1 refs:1 t1:9 thus:3 them:1 iv:10 ii:2 leuchs:1 technology:5 nielsen:1 righthand:1 multiphoton:3 fibers:5 cross:3 same:6 clearly:1 shorter:3 adverse:1 complex:1 potentially:1 split:1 schematic:1 largest:1 units:1 regime:5 solution:1 higher:8 independent:3 used:10 infinity:1 diego:1 numerical:9 effect:21 possible:2 mandel:1 codes:1 moving:2 appreciable:3 coh:8 infinite:3 a2:1 normalization:3 ments:1 lower:2 schr:4 center:7 scenario:1 fully:1 nevertheless:1 well:5 roughly:1 analysis:11 obviously:1 academic:1 approached:1 without:1 experimental:1 components:1 coordinate:1 position:27 parametric:1 self:1 usual:1 distances:1 proposed:4 less:2 shapiro:1 denser:1 obtain:4 sources:1 bandwidth:15 lossy:4 identify:2 ps2:2 followed:2 doran:1 scattering:3 eigenstates:2 previous:4 memory:1 density:2 absorption:1 photons:10 wandel:1 smith:1 except:2 iω:2 source:1 valid:5 lett:12 c13:2 input:1 c11:1 c10:1 c17:1 excited:2 momentum:18 c14:1 real:2 iκ:5 increased:3 depends:2 iα:2 evaluate:1 haus:30 corresponds:1 rumyantsev:1 increases:4 ultrashort:2 vacuum:4 press:2 using:17 gr:1 overwhelms:1 photonnumber:1 loss:32 necessary:1 like:2 follows:1 reduces:1 adiabatic:19 extremely:1 noted:1 specific:2 arbitrary:5 become:4 conclusion:2 reduced:8 because:8 classical:9 treps:2 creation:2 some:1 springer:1 b4:1 b5:1 b6:2 growth:1 b1:2 b2:10 respect:3 process:1 soc:4 b8:1 b9:1 provided:2 scale:1 describing:1 realistic:4 cavity:2 affects:1 avoid:2 tainty:1 langevin:2 extensively:1 per:1 conservative:1 does:2 tially:1 provides:1 assuming:3 fom:1 beating:1 demonstrated:1 2a:2 particular:2 noise:18 slight:1 sixth:1 expansion:1 step:1 wong:2 although:5 plots:7 analyses:1 properties:2 rearranging:1 cn2:1 chirp:11 introduces:1 dependence:2 o:3 side:8 practical:2 moores:1 carrier:1 wolf:1 obeys:3 mixed:2 technol:2 slightly:1 other:6 electromagnetic:1 a0:3 cambridge:2 presence:5 into:5 a6:1 numerically:5 bound:2 three:1 b7:2 hermitian:2 right:7 primarily:1 einstein:1 balanced:1 proportional:4 nb2:1 reducing:5 theoretically:2 vaughan:2 uncertainties:2 statistics:16 additional:1 area:1 assumed:10 initial:16 question:1 approximate:4 long:4 dispersion:44 width:14 much:5 low:1 way:4 sections:2 assumes:1 naturally:1 raman:5 medium:2 form:2 governs:1 anywhere:1 specialty:1 but:16 nn:6 pj:1 correlated:4 gain:2 scope:3 true:1 relaxes:1 coupling:2 applying:2 prevents:1 inside:1 up:1 below:1 owing:4 limit:33 ωn:18 fluctuations:2 problem:3 define:1 similar:8 calculated:3 ac:1 required:3 constant:10 jeffers:1 defined:11 certain:1 describe:3 am:4 general:4 tˆ:96 engineering:2 miroshnichenko:1 formalism:4 lithography:1 defines:1 again:3 compared:9 raised:2 nm:1 national:1 no:1 sˆt:16 when:7 cˆ:1 reality:1 rewriting:1 field:16 narrowing:2 pasadena:1 electrical:1 becomes:9 department:1 4b2:5 nr:3 out:1 acceptable:1 expected:2 deviation:1 picture:5 regardless:2 fabre:3 preceding:1 agrawal:1 a1:1 commutator:6 a3:1 important:2 a5:1 a4:1 a7:1 sql:8 dissipation:3 a8:2 decoherence:13 suffers:1 longer:4 dω:8 assume:3 4b:1 bottom:3 c9:1 approxima:1 4n:12 depth:1 c8:1 mass:1 time:2 n2:7 starting:1 normalized:7 |
0704.0664.txt |@word represent:1 gr:1 rev:2 lack:1 results:2 month:2 follow:1 faster:2 issues:1 gh:1 devoted:1 whose:2 inverse:11 paris:1 lillo:2 tail:2 preserved:1 stable:4 norm:1 fat:2 rzesz:2 difference:1 minute:4 level:2 did:1 issue:1 companies:3 gopikrishnan:3 leave:1 evy:3 indices:6 drop:1 averaged:2 findings:1 zd:5 direct:1 past:4 further:2 dynamics:3 even:5 index:15 what:1 nonlinear:3 business:1 favour:2 consistently:1 abs:1 above:3 new:1 increasing:3 method:1 full:3 led:1 respectively:1 realizations:1 here:2 behaviour:4 reported:1 asymmetry:1 possibility:1 represented:1 along:1 z1:1 logarithmic:1 obtained:3 institute:2 study:5 changed:1 completely:1 suggests:1 dro:5 studies:1 followed:1 family:1 scales:8 apr:1 outcomes:2 decrease:1 kwapie:5 market:12 positive:1 continuous:1 negative:1 type:1 theoretical:3 more:4 under:2 normalized:2 actual:3 cases:2 effort:1 amaral:2 hour:1 tokyo:1 work:1 swi:2 column:2 sudden:1 values:5 following:1 dec:2 example:1 f1:2 taq:1 ummer:1 give:1 process:2 december:1 high:1 indicates:2 axis:1 information:3 rather:1 oslo:1 feature:2 how:1 instead:1 parameter:2 stock:8 mat:1 mendes:1 may:10 after:1 hong:1 fits:1 law:4 revealed:1 short:3 attempt:1 spectra:3 lines:2 st:1 cannot:1 so:3 decreasing:3 order:1 noteworthy:1 indeed:1 over:5 displayed:1 soon:1 kong:1 symbols:3 paper:1 london:1 statistical:1 differs:1 existence:2 still:2 its:2 before:1 fit:2 interesting:2 temporal:1 better:1 absence:1 fig:13 farmer:2 fin:1 return:5 finance:2 scaling:21 tails:9 they:1 half:1 formulating:1 documented:1 dax:10 day:2 easily:1 university:1 traced:1 sufficiently:2 each:2 accompanied:1 side:1 characterized:1 mean:1 financial:5 significantly:2 krak:1 series:2 hypergeometric:1 gaussian:9 related:2 frequency:4 variety:1 our:6 approximated:1 eq:1 out:1 shown:4 factors:1 restricted:1 since:2 crucial:1 research:1 increase:1 gaussians:2 denoted:1 ref:2 shows:1 foundation:1 earlier:3 governing:1 small:2 recordings:1 dependencies:1 rises:1 shortest:1 additional:1 starts:1 could:1 transition:1 days:8 american:6 exponentially:1 first:1 already:3 striking:1 tsallis:2 number:1 randomized:4 open:1 tively:1 differ:1 data:23 top:3 approximately:1 their:2 returns:19 intermediate:1 statement:1 gives:1 free:1 academy:1 exactly:1 stylized:1 than:4 wide:1 kind:1 showed:1 see:4 submitted:1 were:3 outcome:1 poland:2 exhibit:2 turned:1 spectrum:1 curves:1 crossover:1 compression:1 sen:1 seen:1 apparently:1 clearly:2 acceleration:1 min:30 note:1 sciences:1 potential:2 plerou:3 towards:2 trace:1 opposite:1 price:2 extending:1 gauss:1 significant:1 observation:2 considered:3 calculated:2 sometimes:1 physica:7 points:2 subsequent:1 physics:2 fact:1 show:1 german:2 contemporary:3 principal:1 finally:1 based:3 shuffling:2 daily:1 written:1 flights:1 version:1 rich:1 factor:2 means:2 econophysics:1 anteneodo:1 ones:1 words:1 despite:1 years:2 comply:1 volatility:1 processes:1 covering:1 arxiv:1 comprising:1 europhys:1 characteristic:1 set:1 exists:2 correlations:6 up:6 observed:3 depends:1 individual:1 result:2 stanley:5 uncorrelated:1 best:3 subject:1 detect:1 exponent:1 lux:1 nuclear:1 µq:1 tend:1 outside:1 between:3 tens:1 consecutive:1 richer:1 terms:1 nature:2 plastino:1 however:1 efficiency:3 key:1 both:3 stages:1 fitted:2 according:1 called:2 etc:1 context:1 com:1 finds:1 experimental:1 among:1 huang:1 point:1 period:6 sampling:7 pol:1 table:3 considering:1 described:1 three:4 been:1 quickly:1 much:4 interest:1 abstract:1 pl:2 mike:1 enable:1 corresponding:2 argument:2 systematic:1 prices:1 presented:1 c7:1 present:4 case:2 look:3 pacs:1 solid:2 might:2 empirical:2 value:2 while:1 revisited:1 property:1 economics:1 almost:1 middle:2 examined:1 cond:1 elsevier:1 regression:2 different:5 monofractal:1 suggest:2 cumulative:5 same:4 shorter:1 quant:2 largest:3 several:3 infer:2 independent:1 used:1 http:1 gabaix:1 cubic:11 numerical:1 effect:2 counterparts:1 hand:1 normalization:1 recent:5 scenario:1 changes:2 underlies:1 depending:1 well:3 analysis:4 comes:1 model:1 left:3 multifractal:3 proposed:1 less:1 mandelbrot:2 sources:2 shape:1 intervals:4 facts:1 polish:3 speed:1 singularity:3 previous:1 unique:1 preprint:1 source:1 lett:1 theorem:1 extensive:1 acta:1 showing:1 aggregation:1 corresponds:1 early:1 increases:2 world:2 highly:1 like:3 systematically:1 separately:1 satisfactory:1 right:2 truncated:1 some:2 back:1 osorio:1 nonextensive:1 borland:1 bottom:3 recorded:1 tends:1 multifractality:4 noise:1 power:6 processing:2 ruf:1 agreement:2 bq:2 references:1 multiscaling:1 properties:2 meyer:2 comparison:3 central:2 most:4 row:3 o:2 range:2 tailed:2 ow:3 introduced:1 slightly:2 thinner:2 www:1 due:2 down:1 rising:1 1990s:1 nowadays:1 nunes:1 statistics:1 log:4 constantly:3 question:1 specifically:1 lags:1 appl:1 was:11 assumes:1 naturally:1 function:1 medium:1 phenomena:1 but:5 convergence:2 rak:1 line:1 removed:1 he:1 absent:1 made:1 evident:2 markets:6 mantegna:1 capitalized:1 below:1 limit:1 autocorrelation:2 fluctuations:3 distribution:8 panels:1 minutes:1 display:1 mechanics:1 later:1 associated:1 classic:1 universal:1 evidence:1 together:2 formulation:1 speth:2 distributions:15 regime:1 functions:1 compared:1 no:2 other:2 details:1 nq:2 picture:1 develops:2 stocks:3 aggregated:1 ago:1 longer:3 p500:9 interval:5 persistent:1 governed:1 presenting:1 time:18 n1:1 frankfurt:1 original:2 |
0704.0665.txt |@word dist:4 consider:1 chain:1 rev:1 global:15 results:4 invent:1 2c1:3 leads:1 commute:1 2n2:2 follow:1 localized:4 compact:2 depend:1 ginibre:7 theorique:1 young:1 nonlocal:2 finally:2 tj:2 tk:2 norm:3 ingredient:3 applied:1 advantage:3 zhang:3 2re:1 recursively:1 choice:1 corollary:6 endpoint:1 every:1 lecture:1 lrx:4 iut:8 notes:1 tokyo:1 t2:4 solution:16 t0:47 t1:7 large:8 admissible:3 convenience:2 proposition:14 interpolating:1 dealt:1 small:12 anal:1 velo:6 prevent:3 abbreviated:1 estimates:7 direct:1 sign:1 rate:1 l2t:1 l2x:3 linear:2 even:1 readability:1 nonlinear:16 ct0:2 appear:2 section:12 labeled:1 uniform:2 3n:17 above:3 fractional:1 3c:2 new:7 increasing:1 method:1 3d:1 respectively:1 equals:2 here:2 china:2 free:3 strong:3 equations:14 implicit:2 change:1 contraction:3 box:1 remark:1 sobolev:8 weinstein:1 institute:2 study:1 studied:1 contradiction:1 amount:1 fourier:1 spacetime:5 boundedness:2 useful:1 convolution:1 classification:1 claim:7 apr:1 namely:1 explained:2 hardy:1 summation:1 apply:2 total:3 derivatives:2 use:12 asymptotic:1 would:2 intensively:1 distinct:2 contains:3 strauss:2 next:4 vol:1 call:2 therefore:5 consecutive:4 type:5 until:1 subcritical:2 operators:3 odinger:17 merle:1 adapt:1 eη:1 hold:2 iii:1 annuli:2 must:3 ii:1 balls:1 henri:1 recall:2 equation:26 ik:2 zhao:3 ij:55 subdivide:1 following:6 proof:24 control:3 beijing:1 figure:2 give:4 process:1 relativistic:1 organized:1 contradicts:1 v0a:2 sense:1 sharp:1 tao:6 occur:2 absolute:3 exceptional:6 dydx:6 kenig:1 write:1 maps:1 occasionally:1 criterion:3 pure:1 instead:2 profile:1 map:3 may:6 after:1 derived:1 mapping:2 consequence:3 inst:1 law:2 data:10 constants:2 natural:1 spherically:1 hypotheses:2 sj:9 so:3 asserts:1 tiled:2 origin:3 holds:2 dx:26 ith:1 produces:1 developed:1 over:3 find:1 satisfied:2 paper:6 through:1 banach:1 existence:6 satisfies:1 derive:1 group:1 thank:1 decay:3 ln:1 fix:1 lt:2 6c3:6 lr:1 choose:1 lp:2 derivative:1 main:2 lx:16 maximal:2 non:3 yj:4 return:2 duhamel:1 practice:1 introduce:2 bound:7 they:4 acta:1 now:5 discuss:1 term:5 several:1 university:1 sufficiently:7 inequality:21 l2:7 2a:16 radial:10 2m:1 2n:25 higher:2 side:1 constraints:1 defocusing:4 ei:2 bump:3 energy:37 reduce:1 related:1 used:4 measure:1 our:2 out:4 lt2:3 shown:1 divide:1 space:12 res:1 furthermore:1 since:4 lagrangian:2 denotes:1 re:4 ajj:1 ajk:4 dxdy:3 evacuation:1 dxdt:7 formula:3 rn:54 suffices:5 ri:2 math:19 shows:1 theory:8 interactions:2 differ:1 possibility:4 standard:1 indices:2 york:3 estimate:24 beginning:1 additional:1 definition:3 pairs:1 interaction:1 r1:1 r2:1 r3:3 sinica:1 times:1 length:3 keel:2 place:1 hence:5 onto:1 assign:2 first:12 xj:23 xk:1 initial:2 symmetry:2 upper:2 u1:1 nc2:3 takaoka:1 number:10 visan:4 invariance:2 xu:4 1p:1 given:1 perturbation:5 similarly:1 introduction:1 least:4 assumption:2 convention:1 killip:2 gives:2 udx:2 continuous:1 l3t:4 part:1 authors:1 norms:1 x0:13 x1:2 completes:4 finitely:1 bubble:4 18n:1 second:3 modified:4 were:1 providing:1 colliander:1 permitted:1 rewrite:1 ann:3 argument:3 already:1 say:1 further:1 need:2 concentration:11 slab:4 any:17 min:2 lim:1 miao:4 note:1 sciences:1 take:6 quadric:1 subintervals:1 completed:1 calculus:1 subscripts:1 fundamental:1 shall:2 most:9 pair:1 plays:1 acknowledgements:1 class:2 exponent:3 nonlinearity:4 later:2 flow:1 staffilani:1 principle:2 quadratic:2 physics:1 morawetz:21 fact:1 quantity:2 nls:2 show:5 supported:3 notations:5 focusing:1 spaces:4 solutions:6 analogue:1 trivial:1 translation:2 dilation:1 based:3 than:2 lemma:20 only:1 integrate:2 constant:4 local:14 continuity:2 triangle:4 strichartz:9 viewpoint:1 meanwhile:1 dependent:1 sup:4 nearly:1 words:3 dy:4 dt:1 du:4 ds:15 differentiating:1 qu:1 arxiv:2 yield:1 sum:1 wish:1 kurata:1 set:1 exists:11 iteration:3 δjk:1 hα:1 j1:1 up:5 depends:2 cascade:3 radius:1 result:7 discussions:1 forthcoming:1 3c1:17 surfaces:1 exploited:2 inequalities:4 uλ:1 please:1 symmetric:1 contained:1 invariant:1 previous:1 approach:1 blow:4 initially:1 concentrate:1 hypothesis:1 key:1 jk:1 τj:4 amer:3 come:1 last:2 many:4 region:1 chosen:2 embedding:4 comm:4 adapted:1 otherwise:5 cn:3 vav:13 appeared:1 cb:1 ce:1 dimensional:1 iterations:2 respect:1 ogawa:1 restriction:1 union:2 due:1 been:2 appears:1 gevrey:1 cauchy:5 basic:2 define:10 obtained:2 corresponding:1 sufficient:1 tranform:1 6n:20 gap:2 hayashi:1 observe:2 c3:4 c2:13 c1:39 those:1 case:8 p1:2 eit:3 ap:2 will:2 contemp:1 suppose:2 ǫv:1 exist:2 inspired:1 larger:2 lx2:1 almost:1 metric:1 thus:5 iv:1 obeying:1 disjoint:2 regularity:2 itself:1 im:3 dual:1 wave:7 containing:1 develop:1 lqt:6 belong:1 same:1 poincar:2 parts:2 arguments:1 dimensionless:1 finite:3 interpolation:2 independent:5 ball:5 infinity:1 see:3 again:3 i1:1 hand:5 potentials:2 lxn:12 hartree:19 identity:6 schr:17 reflection:1 older:10 gaps:3 depending:2 well:15 posedness:14 nnsf:1 dimension:4 usual:3 λx:1 2c:2 obtain:19 rest:1 intervals:21 ozawa:2 immediately:1 scattering:22 abbreviate:1 homeomorphisms:1 preprint:1 family:2 lebesgue:1 density:1 hℓ:1 9n:2 smoothness:1 priori:1 extends:1 lett:1 combing:1 theorem:7 transformation:1 gave:1 know:1 using:4 ams:1 unique:4 modifications:1 nakanishi:2 necessary:2 δv:1 follows:6 schwarz:1 integrals:2 leaves:2 mathematical:1 sketch:1 because:3 often:1 classical:3 some:15 cazenave:1 choosing:2 moreover:2 iji:1 ijk:30 ijm:2 provided:1 scale:2 dimensions:4 integration:1 2c3:1 providence:2 critical:12 l3:1 ij1:4 ij2:2 blowing:1 journal:1 each:6 step:1 refers:1 cη:1 properties:2 l1x:1 prove:4 o:16 2i:1 range:4 obeys:2 mixed:1 2k:2 duke:2 soc:1 computational:1 m0a:4 into:2 within:1 integral:3 functional:1 remarks:1 weighted:1 references:1 pigeonhole:2 operator:2 consecutively:1 deal:2 removing:1 there:20 4re:2 long:5 generation:6 conservation:9 low:1 way:1 perform:1 was:1 function:5 complete:1 form:3 regard:1 removes:1 repeated:1 construction:1 compute:1 tsutsumi:1 ut:2 uv:4 bounds:2 us:1 4im:1 below:1 frequency:1 uk:4 uj:4 problem:4 similar:3 bourgain:2 ac:3 ab:1 associated:2 certain:1 abstract:1 aj:12 35q55:1 denote:8 littlewood:1 conserved:1 right:1 rule:5 partly:1 dα:1 l6t:6 completeness:2 courant:2 no:3 mathematica:1 when:3 other:7 role:1 spatial:2 mathematics:3 concerning:1 variation:2 generated:2 important:1 log:5 variable:1 implies:6 algorithm:2 assume:7 interval:27 together:1 2im:2 mass:39 volumes:1 time:16 appl:1 n2:1 laws:1 semilinear:1 |
0704.0666.txt |@word limited:1 since:1 micheletti:1 consider:3 crucial:2 varying:3 dynamic:1 leads:1 roy:2 scalar:4 edu:1 gn:1 primes:1 3a0:1 contributions:1 causes:1 gr:4 devoted:1 whose:1 shiraz:3 const:2 sahni:3 caldwell:2 linder:1 shanghai:2 finally:3 th:11 under:1 tegmark:1 worth:1 brown:1 rabcd:3 string:2 moschella:1 returning:1 babichev:1 onemli:1 2ra:1 figs:1 stays:1 affect:1 condition:3 four:2 riemann:1 sundrum:4 t5:6 guo:1 solution:9 large:2 convenience:1 math:1 small:6 equation:24 ichiki:1 vikman:2 upper:1 employing:1 occurrence:1 riess:1 braneworld:20 past:2 second:3 chen:1 further:2 dynamics:2 remarkably:1 substitute:1 tetradis:5 what:1 plays:4 appear:1 giving:1 diag:2 section:4 3p:5 lengthy:1 3h:1 chaplygin:1 above:2 8πgn:1 aaν:3 crossed:2 contributes:2 acknowledgments:1 contrast:4 satisfy:1 iran:2 exchange:11 respectively:4 component:3 edmund:1 here:5 understanding:1 odintsov:3 grav:1 explore:1 china:3 ansatz:2 jcap:5 quite:1 equations:14 appears:1 z2:3 obtained:2 great:1 glm:1 suitably:2 inspired:1 studied:2 allows:1 experience:1 discoveries:1 usually:3 suitable:1 spacetime:2 padmanabhan:3 extra:2 requiring:1 addressed:1 decrease:1 total:1 unit:1 derivatives:2 use:1 d71:1 figure:10 would:1 positive:1 negative:1 next:1 scenarios:2 noting:2 therefore:8 theoretical:2 more:3 tsujikawa:2 definition:1 started:1 line:25 curvature:5 yahiro:1 pasquier:1 particular:3 known:1 shahid:1 iii:2 crosses:1 integrating:2 challenge:1 work:4 modified:3 theories:2 cai:3 values:1 three:2 following:5 strategies:1 root:1 example:2 dxj:1 references:1 impose:1 wang:11 cosmological:13 ds2:1 organized:1 weinberg:2 high:2 way:1 numbers:1 tab:5 daν:1 copeland:1 educational:1 apostolopoulos:3 holds:2 located:2 cline:1 sheykhi:1 influences:4 parameter:20 profile:3 tension:5 constraint:1 kahya:1 may:5 after:1 different:2 λgab:1 mota:2 consequence:1 produce:1 studies:1 law:5 data:7 constants:1 realized:1 attempt:1 effective:9 resemble:1 troisi:1 parameterized:1 cosmology:1 accelerated:4 so:3 allow:1 enter:1 nojiri:3 lined:1 order:6 zlatev:1 kajino:1 indeed:3 perlmutter:2 insight:1 years:1 paper:3 through:4 argued:2 kinetic:1 still:3 its:2 galaxy:1 observational:3 derive:1 but:1 fit:1 chosen:2 interesting:1 fix:1 lm:2 decreases:1 li:4 better:1 choose:3 constitutes:1 derivative:2 defining:1 alter:1 versus:8 them:3 good:2 motivated:1 combination:5 break:1 effects:5 now:4 bigger:1 barrow:1 2t:7 easily:3 term:19 holographic:2 spacetimes:1 always:1 university:4 2d:1 sufficiently:1 2a:2 reasonable:1 l1:1 crossing:5 found:3 side:2 referred:2 significantly:1 simplicity:1 density:6 energy:51 reduce:2 investigated:1 expect:1 our:23 eq:12 special:2 out:1 try:1 shown:1 kerman:1 space:9 restricted:1 rep:1 cubic:1 lagrangian:1 qc:4 viability:1 content:15 investigation:1 ra:1 induced:1 correct:1 tomaras:3 shows:1 earlier:1 theory:3 written:4 discontinuity:3 free:3 standard:4 complicated:1 besides:2 randall:4 incorporates:2 hubble:2 interaction:1 r2:1 ministry:1 zwiebach:1 transition:3 cosmic:5 moment:3 david:2 motion:1 quintessence:2 h02:1 corrections:1 onto:1 eqs:8 first:4 exotic:1 flood:1 symmetry:3 jhep:3 omitted:1 bonnet:31 clear:1 simplified:2 jaeckel:1 fine:2 boulware:1 differ:2 introduction:1 interact:1 saini:1 their:2 conservation:7 observations:4 calculations:2 dt2:1 behaved:1 gives:1 lot:1 explanation:1 continuous:8 alam:2 shinji:1 assumption:1 part:1 too:1 overwhelming:1 than:3 coefficients:1 jump:1 observatory:1 require:1 namely:3 matter:20 future:1 powers:1 tamvakis:2 exhibit:1 rab:2 generality:1 rewrite:1 correction:14 modern:1 argument:1 lin:2 vilenkin:1 need:1 acceleration:3 newtonian:1 zero:1 ratra:2 convenient:1 speculative:1 responsible:2 gravity:4 mechanism:1 fitting:1 take:2 ωeff:4 singh:1 play:3 towards:1 mathews:1 normal:1 friedman:1 koivisto:2 metrics:1 most:2 propagate:2 gauss:31 steinhardt:2 bernardis:1 class:1 tensor:4 especially:1 consequences:3 into:4 adopt:1 constrain:1 left:2 physics:4 fact:2 deceleration:1 cde:1 phenomenon:3 show:9 supported:1 attempts:1 relation:1 solutions:1 astrophys:6 substituting:1 d4:1 d5:2 trivial:1 find:7 decade:1 deser:1 astron:4 cardone:1 parameters:7 state:12 should:3 only:3 going:1 factor:1 employed:1 partially:1 do:3 invoke:1 get:4 dependent:1 kamionkowski:1 de:1 redshift:3 cannot:1 devising:1 during:1 maartens:2 aν:3 subscript:1 evolution:24 wρ:1 fields:3 arxiv:1 ahmad:1 investigate:2 nakamura:1 choudhury:1 view:1 set:3 lbrane:1 lovelock:2 ricci:1 imposing:2 observed:2 opposite:1 see:6 result:3 discussions:2 satisfying:1 interacting:1 review:1 currently:1 symmetric:1 behind:1 ρeff:3 between:6 ωm:4 geometric:1 conditions:2 across:3 wide:1 available:2 terms:5 nature:2 wm:1 however:2 huang:1 tensors:1 2αh:1 suggested:1 both:4 last:1 dxi:1 conclusions:2 according:2 etc:1 figures:4 iv:1 γij:2 contribution:1 hρ:1 whole:1 nnsf:1 among:3 hold:1 cn:1 point:2 appeared:1 ca:4 period:1 dimensional:6 gong:3 starobinsky:2 respect:2 cq:1 throughout:1 moore:1 considering:2 late:4 described:1 tuning:2 addition:5 due:1 been:8 racbd:1 increase:5 much:1 combined:1 interest:2 ph:15 fudan:2 disclosed:1 dots:1 corresponding:3 received:1 lgb:3 quantities:1 gas:2 t55:2 bulk:43 dave:1 dramatic:3 mail:1 maximally:1 djorgovski:1 gab:3 present:9 sami:1 case:8 pacs:1 appearance:1 value:7 will:8 while:4 piao:2 behavior:5 pressure:4 rbc:1 study:4 real:3 metric:5 ir:2 thus:1 non:2 surface:1 equal:1 ii:5 cluster:1 ij:3 junction:2 zhang:8 containing:1 radiation:4 cross:1 same:1 complex:1 quant:1 mukherjee:1 kofinas:3 several:1 higher:2 independent:4 used:1 stefancic:1 trivially:1 absorb:1 numerical:3 effect:8 hand:3 action:5 dgp:1 purpose:1 kamenshchik:1 expand:2 recent:3 early:1 lower:1 kept:1 scenario:3 fully:1 changes:1 well:3 analysis:3 without:4 components:2 coordinate:1 position:1 model:22 dimension:1 usual:5 just:1 being:2 accurate:1 obtain:6 rest:1 verses:1 world:1 doran:1 previous:2 begin:1 adding:1 4rab:1 hab:2 except:1 confirmed:1 other:3 lett:14 easy:1 5d:1 extensive:1 momentum:7 generalized:1 bin:1 around:3 represents:1 showing:1 spatial:1 dark:28 test:1 increases:1 five:4 mon:2 confined:3 using:3 mod:2 loss:1 modifications:1 feng:2 semi:1 particle:1 follows:1 reduces:2 accelerating:1 abdalla:3 δh:2 arbitrary:2 setups:1 become:2 qualitative:1 replacement:3 therein:1 rrab:1 right:3 deal:1 some:3 back:1 choosing:2 provided:2 scale:3 describing:2 dimensions:1 lead:2 shall:1 does:1 assuming:1 inserting:2 bold:9 indicated:1 plot:3 equivalent:1 agreement:4 expansion:5 broken:1 anisimov:1 although:7 super:3 hilbert:2 papantonopoulos:2 central:1 carried:1 ωm0:3 universe:28 o:6 tomi:2 range:1 a2:1 plus:1 constraints:2 consequently:1 kiritsis:3 soc:2 rev:19 presence:2 h2:10 puzzle:1 latter:1 down:1 variable:1 accounts:1 determine:1 einstein:3 nb2:1 hep:12 commission:1 assumed:1 support:1 quadratic:1 fraction:1 was:6 function:6 elsewhere:1 form:8 brane:52 jul:1 hu:1 astro:14 gain:1 dy:1 auxiliary:1 embedded:1 gravitational:1 up:5 us:1 until:1 below:1 limit:4 uk:1 similar:1 called:1 straumann:1 ac:2 ab:3 constant:11 b2:1 ln:2 defined:1 describe:5 influence:1 liddle:1 general:13 weff:10 single:1 education:1 check:2 constructed:1 phantom:2 friedmann:7 functions:5 want:2 variety:1 dashed:9 zang:1 when:1 rs:1 field:11 interested:5 role:9 papers:1 department:3 jenkins:1 nu:4 peebles:2 denote:2 separate:1 models:10 variation:1 deriving:1 a0:7 important:4 included:2 daly:1 ghost:1 jeon:1 coupling:4 assume:2 required:1 observe:1 mass:2 capozziello:1 time:10 n0:3 n2:1 |
0704.0667.txt |@word concept:2 dist:1 funct:2 induces:1 uw1:1 focus:1 invent:1 ge:5 proposition:13 entropy:59 computation:1 edu:2 follow:2 centers:2 devoted:1 whose:1 cardinality:11 depend:2 calculate:1 aug:1 auf:1 aui:1 γr:61 auj:1 haagerup:1 tm:9 tj:6 γm:4 ti:2 include:2 equalities:1 norm:16 p2:2 random:1 orthogonal:2 very:1 induce:1 choice:1 corollary:2 isomorphism:3 every:14 entries:2 parameter:2 matrices:8 die:1 having:1 list:2 t1:6 large:8 au2:4 rj:1 small:5 λi2:3 λi1:3 homomorphism:2 upper:4 zn:3 neighborhood:2 haar:1 direct:4 approximation:8 second:1 einer:1 reine:1 αi1:3 canonical:1 index:1 subadditivity:1 semicircular:2 diag:11 section:14 version:1 goes:4 sup:27 new:2 consisting:13 compact:1 full:2 respectively:2 here:5 packing:7 groups:2 represented:2 along:5 strong:2 z1:2 change:1 obtained:1 remark:8 eij:2 technical:2 study:3 contradiction:2 paris:1 bw:1 products:1 sci:2 quotient:9 via:1 ii1:2 projection:1 family:32 limr:2 vii:1 durham:1 indecomposability:1 subfactors:2 use:2 zis:2 usa:1 prove:4 distinct:3 positive:28 hilbert:5 few:1 m1:18 therefore:10 m3:9 ki2:2 type:2 metric:8 linearer:1 more:1 introducing:1 4c2:1 operators:4 equipped:2 nm1:2 enveloping:1 normalized:2 known:3 cases:1 hold:4 iii:2 balls:18 ma:1 zi1:2 mm:42 recall:5 der:2 mn:2 mi:2 mk:59 mj:2 mt:8 values:4 ms:18 following:25 trans:2 example:3 proof:31 f2:3 indicated:1 brown:1 states:3 contradicts:3 numbers:11 information:2 mutually:2 verify:1 s1:8 holds:5 hampshire:1 acta:1 voiculescu:20 sin:1 sublemma:3 u21:1 fp:30 map:1 product:4 irrational:5 algebra:96 may:1 max:14 after:1 mapping:4 collection:3 microstate:4 representations:1 constants:6 natural:3 ultrafilter:7 lemmas:2 grant:1 element:22 sj:3 so:9 sn:2 sm:10 definitions:3 divided:2 separable:1 developed:1 pointed:1 tj1:2 16c1:1 paper:5 including:2 aθ:4 y1:68 existence:2 still:1 imbedding:1 its:3 group:8 τk:5 tˆj:7 chosen:3 microstates:5 adaption:1 actually:1 absence:1 parts:1 systems:1 cred:31 image:2 uhf:3 non:3 skipped:1 ym:76 greater:1 eigenwerte:1 introduce:3 number:23 das:1 yp:11 rotation:5 now:2 polish:1 2r:2 always:3 university:1 inequality:4 l2:2 each:14 2n:7 circular:1 2k:1 subset:9 weyl:2 directly:4 t2:1 hard:8 γtop:1 tracial:19 equivalence:1 measurement:1 quantum:1 our:1 out:1 au1:2 matrix:40 unital:62 is2:2 is1:2 since:3 crucial:1 denotes:3 contained:3 geom:2 rational:5 denoted:8 rm:5 get:2 induced:2 suffices:1 ri:1 math:25 shows:1 theory:7 diagonal:7 free:89 orbits:2 quick:1 approaches:1 eigenvalues:2 subalgebras:2 publ:1 beginning:1 generate:1 card:6 definition:25 r0:6 applications:3 pimsner:1 isn:1 u22:2 hence:9 onto:6 adjoint:55 ultraproduct:8 xj:2 xi:3 xn:195 probability:4 xm:1 variables:1 primary:1 approximate:1 exact:4 anwendung:1 another:1 electronic:2 ser:1 given:2 1r:8 similarly:2 introduction:1 top:65 construct:1 assumption:1 gives:1 progr:1 relationship:2 tuple:10 centered:3 explanation:1 upperbound:1 part:5 x1:195 than:1 coefficients:5 finitely:5 distance:2 showed:1 was:5 interpolated:1 contrary:2 projections:2 generality:2 prm:28 boston:1 ann:4 measure:4 spectrum:13 4k3:1 need:4 any:38 warsaw:1 lie:1 ubu:2 min:23 convenient:1 self:55 able:2 note:10 k2:6 ideal:5 k0:1 mit:1 calculus:2 trace:9 sets:1 αr:2 preliminary:1 homogeneous:1 class:1 indeterminates:3 don:2 observation:1 kj:10 ki:1 later:1 cover:1 kn:17 km:22 hadwin:4 ks:1 kr:12 ext:1 kt:5 sum:4 fact:3 nω:18 popa:1 stefan:2 show:7 german:1 supported:1 spaces:1 keywords:1 analogue:2 trivial:1 agrees:1 d1:4 o:10 theorie:1 enough:10 topological:53 lemma:31 only:3 going:3 generators:16 subsection:6 factor:2 over:1 dn:4 abelian:1 above:9 notation:3 means:1 µj:1 upperbounded:2 altogether:1 applying:2 secondary:1 hyperfinite:3 covering:17 arxiv:1 tj2:2 london:1 fixed:1 ik2:8 ik1:9 set:32 computed:1 exists:5 banach:1 j1:4 j2:4 see:21 mcduff:1 radius:2 result:12 w1:1 parking:1 primality:1 alternative:1 subject:1 amalgamated:1 satisfying:16 capacity:5 tensor:2 consequence:1 state:16 identification:2 closed:1 between:3 invariant:3 email:1 terms:1 confusion:1 combining:4 shanghai:1 ikj:2 amer:4 ikn:4 ikm:6 topology:2 last:1 generator:1 ism:1 many:1 equal:7 iv:1 context:1 unh:2 estimation:1 asymptotische:1 simple:11 dimensional:10 article:1 associated:1 analogues:2 pr:65 2cθ:1 basis:1 union:1 af:1 copies:4 been:1 ai:1 faithfully:2 workshop:1 1the:1 basic:1 pj:21 algebras:31 pn:1 abstract:1 define:15 generating:1 arises:1 families:1 natl:1 argument:1 arkiv:2 noncommutative:10 proven:1 c3:2 c2:4 c1:21 diffuse:2 case:2 p1:63 subsets:1 might:3 value:2 will:9 contemp:1 suppose:38 international:1 exist:1 property:12 k1:32 maximal:1 unitary:21 engl:1 played:1 cartan:1 vi:2 von:21 thus:14 according:1 ii:9 ik:2 ia:3 ib:1 µk:1 szarek:1 author:1 journal:1 angew:1 complex:5 largest:1 proved:1 finite:9 subalgebra:7 independent:6 ball:7 infinity:4 embedding:8 i1:4 i2:7 hand:2 v1:3 v2:14 birkhauser:1 dykema:2 infinite:11 identity:6 recent:1 lower:4 center:1 well:2 analysis:1 without:3 lim:24 organization:1 dimension:66 usual:1 obtain:2 rest:1 integer:15 λk:4 λj:17 λi:10 λn:19 λm:23 classification:1 lebesgue:1 infinitely:1 except:1 add:1 lett:1 easy:6 theorem:35 real:9 results:5 know:15 using:2 unique:15 moreover:1 loss:2 follows:21 8c1:9 either:1 arbitrary:1 reduced:2 acad:2 functional:3 neumann:21 sequence:4 shen:3 sequences:1 some:67 pacific:2 shen1:1 equivalent:1 b1:19 b2:8 respect:3 dense:2 dimensions:4 ak:2 providence:1 does:2 decomposition:2 proc:3 preceding:5 minimal:5 selfadjoint:1 slight:1 bm:8 bn:11 2c:10 aj:4 cθ:16 olsen:1 jung:5 imaginary:1 properties:2 integers:10 central:1 extension:1 discussed:1 factors:7 oa:4 sake:1 whence:2 introduced:4 block:2 duke:1 soc:4 contractions:1 differentialgleichungen:1 presence:4 h2:2 into:2 shlyakhtenko:1 bound:8 nsf:1 references:1 operator:10 1990s:1 k12:1 statistics:1 span:1 log:40 m4:1 mt2:8 mkm:20 there:47 u1:19 mkj:1 specifically:1 u2:19 mkr:8 unitization:1 sections:1 m0:1 function:1 complete:1 m2:6 but:2 volume:2 u11:2 construction:2 kf:9 ideals:1 u12:1 compute:5 consist:2 us:5 um:11 below:3 ui:6 uk:2 uj:4 pm:5 similar:1 called:4 strongly:1 partition:2 constant:6 computing:1 defined:22 universal:6 uij:6 am:20 covers:1 denote:4 single:2 ar:6 au:5 aw:1 inf:4 check:3 nh:1 again:1 nj:1 nk:7 completeness:1 nm:2 no:16 when:15 application:1 other:3 role:1 department:1 mathematics:2 nt:2 polar:1 elements:28 generates:5 sided:1 uniformly:1 polynomials:10 a1:58 hausdorff:1 generated:14 a2:5 bounded:7 anal:2 variable:6 fisher:2 implies:2 assume:26 space:22 orbit:17 notion:2 exhausting:1 4m:10 4k:6 n1:1 4d:1 original:1 |
0704.0668.txt |@word limited:1 quarks:5 gs:2 chinese:3 switched:1 gupta:1 caused:2 gz:1 leads:1 eds:2 lindfors:2 gb:1 ga:1 partial:1 research:1 contributions:21 extra:1 transiting:1 b268:1 depend:4 gq:6 b289:1 shanghai:2 hypergeometric:1 finally:4 present:2 th:1 lin:1 worth:1 ta:2 division:1 supported:1 amplitudes:1 r13:1 outside:1 far:1 studied:2 rise:2 srivastava:1 octets:1 results:8 putting:1 figs:11 summarized:1 resonant:1 experimentally:1 little:1 rapidities:1 four:5 dominate:3 magnea:2 presented:3 turns:1 nucl:10 wittmann:1 large:7 shuryak:2 offering:1 small:3 kolhinen:2 hospitality:2 dip:7 evai:1 configurations:1 upper:9 smaller:1 renormalized:1 miller:1 estimates:1 direct:3 cosh:11 likely:1 evaluated:4 equal:1 invariant:1 b156:2 tev:3 even:1 gl:2 ranft:1 abe:1 dominantly:1 dr1:2 section:33 dr2:2 exclude:1 expressed:2 thickness:1 mueller:2 above:1 abx:2 obvious:2 except:10 contrast:3 uckl:1 completion:1 evolving:1 full:7 exchange:2 respectively:20 component:2 here:7 fairly:1 china:1 pub:1 sinh:11 others:1 represented:1 ratio:15 along:2 tevatron:2 change:4 calculate:1 box:2 incoming:1 singapore:2 institute:3 root:2 study:4 drr:2 matsui:2 controversy:1 vogt:3 amount:3 b509:1 resulting:11 stressed:1 resonance:2 fourier:1 studies:1 involves:1 φki:1 formulated:2 gluons:11 scales:2 apr:1 maksymyk:1 ipi:1 troost:1 gluon:43 frame:1 summation:1 cassing:1 total:1 renormalization:2 quasi:1 takes:3 commun:2 positive:3 contains:3 visit:1 predictions:1 next:1 depicted:3 therefore:4 qcd:6 taken:7 until:1 more:2 fractions:1 flat:3 partons:11 upcoming:1 becomes:4 operators:1 competes:1 bodwin:1 normalized:1 proceed:2 loss:2 φk1:5 φk2:2 hold:1 producing:1 evolves:1 account:8 mc:13 indicates:2 fugacities:2 work:5 c48:1 mh:1 abundant:1 labeled:1 bureau:1 values:6 transparency:1 following:2 confining:1 ingredient:2 averages:1 address:1 history:1 compare:1 persists:1 prompt:2 reasonably:1 indicated:1 escapes:1 process:4 expanding:4 neglected:3 originates:1 amundson:1 states:14 collision:32 numbers:2 want:3 allowed:1 xmin:5 dyx:4 strikman:2 r23:1 species:1 dominant:2 vanish:1 end:1 ocker:1 rather:2 divided:1 s0:11 feature:1 freezes:1 chemical:1 hot:2 fourth:1 dotted:18 occur:1 lbnl:1 dominance:1 fq:2 product:1 proc:2 ft:1 may:8 photoproduction:1 after:1 brodsky:2 fa:8 modest:2 produce:2 lepage:3 fg:17 fi:1 wave:22 data:2 concerns:1 constants:1 short:4 lhc:27 dynamical:1 third:1 sr:3 b167:1 lines:20 plateau:2 su:2 st:1 si:3 so:4 solely:1 correlation:1 sa:11 order:14 gastmans:1 typical:2 interpretation:1 subsections:1 nucleon:38 over:2 fall:2 mainly:1 soon:1 produced:39 thermal:41 experiments:9 through:18 during:3 existence:4 still:2 its:7 before:2 sciences:3 difference:1 longitudinal:3 symmetry:1 thanh:1 energies:11 masses:1 lj:31 varies:1 coordinates:3 forms:1 estimating:1 production:37 fig:27 setting:1 overcome:1 s1:19 versus:14 peskin:2 greater:1 combination:1 tov:1 greiner:1 processes:9 primary:1 break:1 yx:11 repulsive:2 subtraction:1 they:2 now:1 bigger:3 densities:3 restrict:1 term:1 2p:3 gev3:4 kharzeev:4 2s:31 characterizes:2 university:2 accompanying:1 sin:3 akiba:1 d49:1 magnitude:1 πra:4 radial:2 found:3 jacak:2 d47:3 d46:1 d45:1 2k:3 heavy:3 reactions:12 arxiv:1 directly:1 independent:1 hadronic:1 stirling:1 energy:43 hard:3 kopeliovich:2 related:1 group:1 each:1 sinha:1 decays:1 ey:4 expect:1 uttner:1 measure:1 quantum:2 laboratory:1 approximated:2 eq:17 b366:1 out:2 travels:1 shown:14 superscripts:1 shadowing:19 factors:4 furthermore:1 since:16 squared:2 2m2c:1 denotes:2 increase:3 collisions:40 ra:3 denoted:1 xu:2 ref:10 occurs:2 rj:1 m2c:2 leibovich:1 theory:3 interactions:4 1s:1 free:3 quark:5 formation:3 van:2 flatness:1 shortest:1 c52:1 driven:2 pairs:18 interaction:1 r0:2 r1:7 r2:7 created:2 eskola:11 transition:5 fb:4 used:2 heinz:1 motion:2 isi:1 place:1 assumed:2 consequence:2 degeneracy:2 martin:1 first:1 caswell:1 initial:34 probability:11 prevent:1 xb:9 omitted:1 variables:3 xa:9 number:51 reaches:2 references:1 channels:5 antiquark:2 rini:14 approximately:1 another:3 impossible:1 size:16 manuscript:1 given:15 kodama:1 temperature:4 their:1 introduction:1 leading:2 eqs:3 neutralizing:1 system:37 relations:1 fm:1 needed:3 assumption:1 normalization:1 calculations:3 show:8 signature:2 final:2 too:1 gyulassy:2 hoyer:2 aurenche:2 rest:1 arneodo:1 academy:3 alam:1 transverse:31 part:4 b334:1 sˆ:3 distance:3 determines:1 roles:3 was:3 tree:1 rate:2 collinear:2 matter:1 future:1 supposed:1 amplitude:1 bare:2 toward:2 steep:2 bination:1 perturbative:1 pre:15 lowest:2 comput:2 curves:6 ming:1 πa2:1 ka0:2 variable:1 need:1 my:1 picks:1 any:5 contents:1 relatively:1 depict:2 angle:1 uncertainty:1 latter:3 doorn:1 able:1 mechanism:1 beneke:1 extracted:1 k1:17 potential:6 thermometer:1 thoma:1 destroy:1 scatterings:3 b304:1 channel:3 begin:1 jain:1 though:1 track:1 collaboration:1 object:2 alexopoulos:1 singlet:23 charm:1 d51:1 pair:8 colliding:1 acknowledgements:1 intrinsic:4 3πr:1 milana:1 considered:7 average:2 flow:1 kr:1 exp:15 mechanical:1 brookhaven:1 gerland:1 chromoelectric:1 normally:1 8gev:1 dot:18 cdf:4 set:3 phenomenon:4 τf:18 asakawa:1 probe:1 dependences:1 fleming:1 dissociate:3 attempts:1 12s:1 c49:1 keywords:1 baier:1 gavai:1 d3:9 fifth:1 partonic:50 q0:13 indicator:2 q2:6 based:2 mehen:1 nonperturbative:4 explain:1 enough:2 sniak:1 than:13 only:9 subsection:9 factor:8 various:3 alde:2 local:1 frankfurt:2 2gev:1 equilibrium:2 do:1 hit:1 gev:22 notation:1 ralston:1 moehring:1 expectation:3 satisfied:1 cannot:1 instance:1 nonequilibrium:2 dy:1 dw:1 dt:11 dp:2 symbols:1 evolution:9 d53:1 continuum:2 d54:1 differential:5 dipping:1 assuming:1 yield:4 sum:4 armesto:1 bhanot:1 d56:1 favors:1 including:7 fixed:1 pire:1 ruuskanen:1 colorless:1 omission:1 mustafa:1 achieved:1 undergoes:1 national:1 j0:3 j1:3 j2:2 freeze:1 relative:3 depends:1 radius:16 result:6 enhanced:1 discussions:2 4m2c:2 quite:1 observed:6 λi:2 annihilation:1 αs:4 b302:1 interacting:1 b369:1 nuclear:24 away:1 kajantie:3 pajares:1 dipole:1 propagates:1 b360:1 initially:4 state:15 determined:5 identification:1 between:9 bulging:3 drawn:3 d52:1 reading:1 conditions:1 d55:3 berkeley:1 d57:1 landshoff:1 comparable:2 terms:3 wa:1 importance:1 6gev:1 weak:1 however:3 wang:11 rapidly:1 spectroscopic:1 incident:1 le:1 separately:1 configuration:5 come:1 kinematic:2 quack:1 both:13 cos:6 last:1 σn:6 bulges:2 region:14 density:3 space:8 ln:6 negative:2 b298:1 braaten:1 smearing:2 b291:1 disappears:1 referring:1 τiso:25 among:2 blaizot:1 point:4 color:65 χcj:4 narrower:1 corresponds:4 proton:8 parametrization:3 bratkovskaya:1 written:1 anti:2 cs:2 respect:3 gavin:1 cp:2 uck:2 c56:4 second:1 pr:3 destroyed:1 strong:1 collider:3 pt:23 fortran:1 addition:2 disintegrate:1 px:4 radiative:2 due:4 been:14 int:3 reduction:2 much:1 ensured:1 involve:1 pj:6 figure:24 ph:3 pi:4 pn:2 universal:1 b426:1 define:1 obtained:12 arises:1 corresponding:3 reaction:1 formed:4 gas:2 hits:1 gap:1 offers:1 observe:1 understand:2 stems:1 plasmas:1 careful:1 xiong:1 former:1 those:2 p2:2 k2:15 p0:6 exponential:1 pacs:1 solid:20 value:8 will:3 cern:1 while:11 suppose:1 weber:1 applies:1 irrespective:1 taking:2 procedure:1 a20:1 larger:5 capella:2 induced:1 λqcd:2 refs:3 thus:3 xiao:1 surface:1 according:1 b323:1 characterize:1 vt:26 amer:1 kapusta:1 ready:1 seattle:3 heiselberg:1 2j2:1 different:1 gs2:4 verified:1 sensitive:1 φx:4 suggest:2 make:1 cross:45 same:15 slac:1 c51:2 big:1 modification:2 gets:2 couple:1 higher:2 evolve:4 investigated:1 see:1 colorsinglet:1 numerical:2 upon:2 effect:12 αs3:3 ion:2 v2:1 compared:4 purpose:2 vrel:26 v8:1 expand:1 relies:2 lower:12 center:5 nevertheless:3 c67:1 no:7 well:2 tran:1 bohr:1 αs2:4 without:6 around:1 sets:1 exponentials:4 model:2 arising:1 b178:1 fermilab:2 spherical:1 distances:2 λq:2 proposed:2 less:1 being:2 ultrarelativistic:2 λg:4 λb:1 λa:1 via:5 identify:1 atomic:1 aspect:1 uller:4 momenta:5 scattering:3 dissociation:27 conclusions:3 zakharov:1 absorption:1 σgc:34 nonrelativistic:3 seems:1 fitting:2 simple:1 c19:1 internal:2 attractive:3 throughout:2 braun:1 mod:1 plasma:15 momentum:41 real:1 rosati:1 aspects:1 dφx:1 disappearance:1 ufner:4 survival:9 antiquarks:4 possible:2 iη:2 cho:1 fusion:3 five:1 world:2 hijing:3 bir:1 detector:1 rhic:30 prominent:3 melting:1 showing:3 wu:1 bulge:10 follows:1 performing:1 isotropy:1 scatters:1 yields:3 always:1 become:1 nucleons:1 essential:1 deconfined:9 because:4 parametrizations:2 sridhar:1 some:5 back:1 competition:1 productions:7 semihard:1 specified:1 proper:5 rapidity:37 eiqr:1 nonzero:1 dissociated:1 scale:4 dense:2 lead:1 confirm:1 resonances:1 measurements:3 octet:43 thank:3 b214:1 b295:1 does:3 a10:1 dissociates:1 o8:11 bessel:1 measuring:1 assembly:2 scientific:2 rep:3 confluent:1 expansion:2 step:1 wong:5 ratios:7 2m:3 salgado:2 refers:1 hadron:1 stage:43 comparison:1 about:4 central:13 carried:1 dependence:21 o:2 reduced:6 yk2:3 yk1:7 important:3 plus:4 trajectory:1 mean:1 consequently:2 enhancement:1 individually:4 rev:37 inclusion:1 into:15 within:3 washington:2 bound:1 nonperturbatively:1 three:4 phase:2 square:4 rising:1 parton:30 c53:2 proportional:1 binding:1 factorized:1 geiger:3 theoretically:1 relativistic:3 uncertainties:5 c55:1 c54:1 hep:3 additional:1 elastic:2 measured:2 support:1 there:4 transform:1 c59:1 start:3 anderson:1 fraction:1 sections:19 function:22 project:1 medium:23 complete:1 form:1 becoming:1 m2:6 nontrivial:1 but:7 expected:1 construction:1 b438:1 kaidalov:1 line:11 level:1 considerable:1 coupling:4 made:1 hornbostel:1 prevents:1 inside:4 up:2 us:1 theoretical:1 v1:1 growth:1 thermalization:1 distribution:32 stages:21 similar:2 calculated:13 correspond:7 ex:2 raha:1 ab:21 constant:3 reya:2 charmonium:6 defined:5 certain:1 abstract:1 contribute:3 influence:3 denote:1 twist:1 au:22 qiu:2 exist:1 education:1 distributions:39 proceeds:1 physical:3 grv:3 high:1 functions:10 codes:2 gg:22 ingredients:1 amounts:2 dashed:38 whereas:1 when:3 virtual:1 ng:28 d44:2 field:1 other:3 normal:1 spatial:1 department:2 overwhelms:1 massless:1 conclude:1 explaining:1 elements:4 generates:1 calculating:4 separate:1 models:1 excite:1 searched:1 hwa:3 a1:1 a0:2 a2:2 nucleus:17 peak:1 suppression:30 velocity:3 included:2 matrix:4 nakhleh:1 correlated:1 implies:1 longer:1 coulomb:2 assume:1 physics:1 dτ:29 equilibrating:2 curve:10 dσ:11 mass:7 fact:1 time:10 nuclei:3 once:1 expands:2 lett:22 satz:7 |
0704.0669.txt |@word represent:1 concept:3 partial:8 consider:14 limited:1 zˆs:8 results:10 integration:1 leads:1 kuleuven:1 scalar:5 commute:1 hove:1 computation:1 edu:1 alv:2 iu2:1 gk:4 localized:4 gr:2 compact:2 whose:3 preserves:2 inverse:7 depend:1 referring:1 integral:1 asymptotics:2 γs:12 tt:2 equivalence:2 canonical:4 acting:1 presents:1 commonly:1 finally:5 tj:1 present:5 th:1 under:8 stochastic:17 include:2 norm:1 pillet:5 case:10 belonging:1 comm:6 straightforward:2 md:7 very:2 frequencies:4 2re:1 rise:1 choice:2 corollary:4 isomorphism:1 every:4 traced:1 approximate:1 little:1 al2:2 condition:24 al1:3 identity:5 believed:2 υk:1 level:4 turns:2 notes:9 henri:1 υa:2 t0:13 t1:9 large:4 lendi:1 woods:2 flows:1 small:18 eigenvalues:5 markov:43 antiunitary:5 cmp:2 spohn:1 says:1 haar:1 lecture:7 among:1 za:2 nski:7 approximation:2 go:4 second:6 tℓ:7 further:2 dynamics:46 implemented:1 volovich:1 zr:43 linear:12 even:5 what:3 ˆs:6 plays:2 stands:1 invertible:1 ǫr:6 aν1:1 section:13 version:8 conjugations:1 d0:3 above:11 ǫw:4 d1:15 method:1 developments:3 satisfy:8 impact:1 full:1 complex:1 leg:1 respectively:1 concepts:1 equals:6 jointly:1 diagonal:2 friedrichs:13 objects:2 possibility:2 du1:2 represented:1 aυ:2 shortness:1 strong:2 equations:4 transformation:3 tn:6 obtained:5 remark:2 balance:16 rigorously:1 institute:2 shift:2 study:1 larger:2 allows:1 reason:1 through:2 later:2 aνj:2 olkiewicz:1 published:1 usually:5 verri:1 fourier:5 studies:1 involves:3 uniquely:3 zametki:1 useful:2 projection:1 family:3 devoted:1 tr:34 f2:1 replace:2 iz:1 names:3 apply:2 total:4 univ:1 derivatives:2 use:9 asymptotic:14 prove:5 distinct:2 positive:25 contains:1 itk:10 uniqueness:2 hilbert:25 phenomenological:1 chr:2 call:5 therefore:10 m2:2 survive:1 associated:1 meyer:1 von:1 more:11 formally:5 operators:36 constructs:1 odinger:4 berlin:4 particular:10 known:6 iii:3 iτ:1 circumstances:1 me:4 kraus:2 springer:10 araki:2 ma:2 viewed:1 integrating:1 recall:11 equation:11 work:1 fock:5 obvious:1 publications:1 majewski:2 freedom:3 following:25 ith0:2 star:1 history:2 beautiful:1 f1:1 compare:2 νv:1 renormalization:1 νs:5 give:2 justifications:1 states:3 spk:7 numbers:1 arise:2 dj:4 νn:1 conversely:1 fysica:1 νk:2 νj:10 afl:7 versions:3 needs:1 erratum:1 end:1 kυ:1 awkward:2 noises:15 dγ:17 verify:1 discussion:2 holds:6 differences:1 feature:1 enn:4 write:9 maps:11 thermodynamics:1 get:3 sij:4 white:2 verlag:1 explains:1 map:12 fr:6 description:3 algebra:5 replacing:1 after:1 containing:1 substitute:2 maa:4 fa:4 physik:1 irreversible:2 multiplication:6 representations:2 fj:2 data:1 sz:1 realized:1 short:1 natural:4 dynamical:6 imply:2 resemble:1 parameter:4 maes:1 explicit:1 correspond:1 mjj:1 st:3 pautrat:1 perhaps:1 so:21 sect:1 fundamental:2 correlation:3 representation:5 βk:30 words:2 order:4 talk:1 ito:1 least:1 interpretation:3 dx:6 reservoir:36 devote:1 over:1 ite:1 choose:4 interpreted:1 course:1 thermal:13 paper:1 itz:16 da1:5 da2:4 banach:1 equip:1 satisfies:17 still:1 its:19 before:1 τn:5 djp:3 difference:1 group:11 τk:2 singular:5 unitaries:1 energies:2 interesting:7 zˆ:20 vicinity:1 conjugation:4 li:4 forms:6 annales:1 lu:3 degrees:1 systems:17 mail:2 τt:3 main:6 defining:1 h0:14 outside:1 yi:1 them:4 yj:1 gibbs:1 combination:1 trh:7 ǫ2r:1 bjk:4 material:4 evolution:1 introduce:18 isomorphic:2 scaling:1 mention:5 complete:2 sψ:1 they:18 now:6 discuss:10 it0:3 dj1:5 eigenvalue:2 finite:11 name:7 always:7 university:1 presented:1 hermitian:3 orthonormal:1 realistic:5 iff:19 inequality:3 l2:27 l1:3 found:3 soc:1 ρa:1 side:3 sketches:1 el:2 domain:3 en:1 ei:1 directly:2 arbitrariness:1 ej:1 ed:1 energy:9 journ:4 reduce:1 idea:2 related:9 derezi:7 line:1 literature:17 obtains:2 b1:4 positivity:1 quantum:75 our:14 operation:1 special:5 out:3 rt:1 eith0:1 matrix:4 ejj:1 space:48 restricted:3 rep:1 since:3 rev:2 semi:1 denotes:4 contained:2 vector:6 denoted:5 formula:11 instituut:1 xu:2 math:22 shows:1 commutation:1 earlier:1 theory:9 interactions:2 sudarshan:2 differ:1 free:4 standard:1 completely:13 perturbation:4 complicated:1 york:2 besides:3 imagine:1 ask:1 microreversibility:1 publ:2 e1:1 warszawa:2 minimality:1 definition:6 interaction:9 applications:3 could:1 atj:2 βy:16 voor:1 dissipated:1 length:1 dublin:1 atp:2 invitation:1 hence:7 view:1 onto:1 think:1 first:7 xi:4 features:1 evans:1 u1:7 pa:2 assumptions:1 number:4 theoretische:1 restrict:4 kadison:2 enlarged:2 long:1 another:10 takesaki:4 precisely:2 open:9 several:1 illustrate:1 stochastics:1 given:11 toy:8 temperature:7 covariant:1 similarly:3 introduction:4 adjoint:32 system:19 construct:2 eitk:8 their:5 perturbations:2 1e:2 fierz:15 1h:5 1k:26 scheme:1 behaved:1 final:1 functor:1 gives:4 attach:1 gough:1 preserved:2 mostly:2 academy:1 explanation:1 continuous:12 measurable:1 assumption:3 part:12 somewhat:1 schr:5 believe:3 than:4 lebowitz:1 haake:1 jump:1 kind:1 resolvent:3 dtn:2 edition:1 sections:1 df1:6 namely:1 df2:2 annihilation:5 classes:1 parthasarathy:2 treated:1 projections:1 siedentop:1 tracts:1 false:3 derivative:1 kossakowski:3 rewrite:2 ann:1 modern:1 measure:2 spectrum:3 direct:1 talking:1 say:15 decomposition:2 ible:1 emission:1 conjugate:1 need:4 seen:2 ccr:2 apparently:1 clearly:11 contents:1 warsaw:1 generalizes:2 constructions:1 relationship:1 zero:3 academic:1 convenient:2 gks:4 responsible:1 ideas:2 note:33 sciences:1 k1:16 contact:1 take:2 davies:7 zs:4 analogs:2 gω:4 sn:2 calculus:3 spectral:3 play:1 sure:1 trace:3 though:2 singles:1 denoting:1 barchielli:1 birkh:1 most:3 involving:2 plan:1 definitions:2 pair:1 ˆt:1 νi:1 closable:2 class:8 interacting:4 kn:3 constructed:2 especially:5 considered:1 clear:1 sometimes:3 cover:1 curiously:1 physica:1 possesses:1 giving:1 roeck:19 ku:1 mechanical:1 north:1 usual:5 physics:9 away:1 fact:7 applied:2 show:3 lewis:2 dbc:28 atom:1 scattered:1 anyway:1 nagy:4 purely:9 spaces:5 ummerer:1 determined:2 d2:10 find:1 dilation:22 λv:2 completion:1 based:6 ith:1 foias:4 e11:4 situations:1 explain:2 written:7 jan:2 only:11 explicitly:2 generators:4 subsection:12 various:6 hamiltonians:5 equilibrium:1 do:3 dm:3 sense:9 goes:1 notation:2 means:3 de:19 joye:5 satisfied:3 next:7 aγ:1 closely:4 new:3 compute:1 dt:9 du:11 aν:1 gen:1 differentiating:1 holland:1 closure:1 processes:2 bar:4 conclusion:1 converge:1 conditions:1 arxiv:1 remove:1 twice:2 common:1 including:1 fixed:1 discussing:1 wrote:1 looks:2 hλ:10 set:24 statistical:3 exists:15 physically:5 δjk:1 da3:4 ends:1 lnm:1 differentiation:1 see:23 justification:2 result:4 existence:3 terms:5 theoretic:1 particle:2 close:1 closer:2 appear:4 satisfying:5 tensor:4 nondegenerate:2 review:1 definite:1 functionals:1 attal:7 symmetric:2 state:7 proof:12 identification:3 between:2 invariant:24 approach:9 discovery:1 multiplied:1 notice:1 recently:1 extend:4 rims:2 arises:1 attention:1 weak:75 however:7 wi:4 wj:1 jn:2 ws:2 here:3 bose:1 contractive:7 trotter:1 suggested:1 both:5 essentially:1 improved:1 limits:1 modular:4 energetic:1 many:3 taking:1 density:2 equal:2 presentations:1 quantization:5 dipole:1 involve:3 hω:8 poincar:1 context:3 absorption:1 quite:1 argue:2 adapted:1 fix:4 etm:28 strongly:5 relevant:3 cn:18 characterization:1 simple:3 others:1 harmonic:1 ce:2 2nd:2 dimensional:10 ii:3 anti:1 master:3 right:4 article:9 respect:4 ae:4 k2:12 considers:1 semigroups:43 kernels:1 pp:4 amer:1 described:6 transformations:1 basis:5 addition:4 help:2 oder:1 due:1 alicki:3 reduction:1 describes:11 treat:1 basic:5 pj:8 transformed:2 ph:3 algebras:3 pn:8 pl:1 define:24 direction:1 rather:2 θn:2 received:1 concerning:1 gas:1 coincides:1 argument:1 δtk:2 sobolev:2 iu1:1 demand:1 c2:2 c1:2 general:6 1ik:2 those:2 accardi:5 fuw:1 intriguing:1 p1:8 cyclicity:1 look:1 ǫk:4 ij:1 ǫn:3 choices:1 will:47 invoking:3 suppose:8 probability:2 involved:1 exist:7 du2:2 property:5 zξ:1 inspired:2 procedure:1 subsect:9 identical:1 unitary:41 gorini:3 commutative:1 coupled:4 vh:2 vi:5 vj:3 ir:13 thus:10 non:5 reversal:3 disjoint:2 ik:51 cocycle:4 liouvillean:1 interacts:1 id:2 agarwal:1 different:8 formalism:3 generic:1 arguments:1 make:3 belong:1 radiation:1 same:2 any:14 parts:1 split:1 pauli:15 dilations:9 relatively:1 isometries:4 difficult:1 independent:2 used:9 eds:7 embedding:5 eitz:4 u0:5 hand:3 multitime:1 mij:3 auser:1 invariance:6 eij:2 opportunity:1 refreshed:1 eith:2 recent:4 garbaczewski:1 weakly:2 off:3 center:1 matters:1 nevertheless:4 expression:3 poland:1 well:10 analysis:3 bohr:3 concrete:2 without:4 relations:1 lim:11 model:4 σt:4 arising:1 self:29 left:2 rescales:1 just:4 less:2 true:5 when:2 obtain:10 chebotarev:3 product:9 belgium:1 body:1 ch:2 identify:5 facts:1 polish:1 alternative:3 scattering:1 yet:2 z0:8 previous:1 adv:1 cut:2 preprint:1 generator:22 instance:1 haa:2 cl:2 seems:2 aψ:1 mathematically:1 iω:9 cc:2 setting:3 extends:3 ψdx:1 easy:4 theorem:52 relevance:1 semigroup:43 apart:1 iυ:7 remaining:2 generalized:1 real:2 iθ:10 iλ:13 aspects:2 around:3 easily:1 iβ:2 implications:1 possible:7 fys:1 background:1 vacuum:1 wojciech:2 using:4 unique:8 advanced:1 formal:1 appearing:1 like:2 tomita:4 follows:11 δt:12 dt1:2 golden:1 0s:1 steps:2 schwarz:2 arbitrary:1 evolutions:3 sesquilinear:4 pointwise:3 probabilty:1 reduced:27 terminology:3 replacement:1 mathematical:2 leuven:1 methods:1 classical:17 continual:1 creation:5 some:20 back:2 identified:1 regularized:1 equivalent:4 examples:2 choosing:2 curious:1 extended:36 proofs:2 ourselves:4 transport:1 confusing:1 ǫy:1 dense:1 lead:2 eiλ:4 measurements:1 langevin:27 sketching:1 subclass:1 selfadjoint:2 does:3 kms:9 heat:2 yields:2 three:1 proc:1 symbol:1 minimal:4 either:1 differential:2 considering:1 noise:2 rescale:2 kyoto:1 jumps:1 each:1 bi:2 bj:13 defines:1 how:1 step:5 includes:1 subtract:2 properties:7 simpler:3 a1:8 about:4 central:2 extension:3 extending:1 dd2:7 dd1:9 theorems:3 discussed:1 meaning:2 o:1 j1:2 de0:3 aℓ:3 a2:5 aλ:2 treatment:1 frigerio:5 introduced:6 bath:1 mechanics:2 hudson:2 statements:1 markovian:5 jλ:33 press:1 unbounded:4 into:3 within:1 obtaining:1 functional:3 latter:1 down:2 dissipation:1 appropriate:3 because:2 references:1 operator:90 actually:3 reducing:1 bosonic:9 often:7 schrodinger:1 van:1 additional:4 famous:1 anticommutation:1 there:22 question:2 transform:2 fast:1 u2:5 quadratic:18 bosons:2 physicists:1 way:3 m1:5 analyze:3 was:6 assumes:2 naturally:3 function:4 eit1:2 elsewhere:1 form:33 enough:2 hr:67 hp:5 converse:2 jun:1 independently:1 but:8 regularization:1 volume:1 hk:6 repeated:2 construction:15 ho:1 pk:1 convergence:3 lindblad:13 dissipative:10 nv:1 auxiliary:5 commun:1 applying:2 places:1 instructive:2 whether:1 ut:23 mat:1 up:8 us:29 probabilists:1 below:2 un:2 limit:82 sum:1 continuously:1 fluctuations:1 eβk:5 similar:5 called:24 expect:2 detailed:15 ab:1 constant:1 b2:4 ag:3 classic:1 defined:15 certain:6 universal:1 describe:23 proven:1 denote:11 single:1 ar:1 reservoirs:9 rule:1 corresponding:4 1k1:1 hamiltonian:9 check:9 physical:13 again:2 functions:4 paradox:2 differentiable:2 no:4 whereas:1 commutes:3 generally:1 stinespring:8 nf:2 streater:1 application:1 other:4 role:3 th0:4 papers:2 department:1 mathematics:6 ns:6 sufficient:2 realize:2 nice:1 kinds:3 generates:1 models:4 subspace:2 why:1 resembles:1 chem:1 variation:1 much:2 deriving:1 generated:3 important:2 bounded:1 anal:1 additionally:1 studied:1 variable:5 describing:2 needed:2 structure:1 algebraic:4 axi:1 implies:11 coupling:79 coulomb:1 assume:14 values:1 dτ:10 together:2 having:1 reports:1 delta:1 mast:2 time:5 observables:2 func:1 original:1 fermi:1 |
0704.0670.txt |@word represent:3 code:2 angles:1 yasuhiro:1 both:3 results:5 woods:1 controversial:1 edu:1 contributions:1 ver:1 byrd:2 tp:6 charles:1 charge:1 foster:3 noro:2 cm2:1 indicating:1 henderson:1 probe:1 amplitudes:1 ihara:1 hintz:2 wave:3 experimentally:1 condition:1 entire:1 dii:12 supports:1 morlet:2 large:6 arndt:1 small:1 graw:1 noted:2 employing:2 grateful:1 ullmann:1 miller:2 consistent:7 prediction:3 approximation:2 second:1 enhancement:2 rigorous:2 qualitatively:1 estimated:2 zr:1 perimental:1 mercer:1 takashi:1 interactions:2 tohoku:2 thickness:1 current:1 version:1 carey:1 lallena:2 international:1 filled:2 σf1:4 quenched:1 full:1 lee:1 ibid:1 exchange:14 respectively:9 component:1 strakovsky:1 reported:1 mev:43 address:1 represented:1 along:1 mcclelland:2 sagawa:1 deduced:4 obtained:2 luther:2 study:4 larger:1 allows:1 polarimeter:1 resulting:1 suggestion:1 resonance:2 studies:2 fujita:3 yamada:1 love:2 helmer:1 apr:1 plenum:1 neutrons:1 analyzing:1 total:6 suda:1 use:1 dnn:1 quasi:1 sports:1 nucl:6 edward:1 taken:1 meyer:1 theoretical:9 more:3 separated:1 quantitatively:1 raynal:1 normalized:1 impulse:2 particular:1 high:3 mg:1 mb:1 thaler:2 science:2 work:2 vetterli:1 values:14 lindgren:1 ishihara:1 f1:16 compare:1 wang:2 figure:2 give:2 ann:1 saito:1 states:3 indicates:2 jackson:2 performed:1 hutcheon:1 yang:1 information:4 comfort:1 regions:2 larsen:1 deviated:1 description:1 flip:8 plane:2 demonstrating:1 waves:1 choice:1 data:8 response:2 realized:1 natural:4 effective:8 ichihara:1 sr:1 spectra:5 lines:3 parameterized:1 sendai:2 gwdac:1 so:1 sect:2 representation:1 order:4 bins:2 typical:1 timeof:1 help:1 nucleon:2 over:2 mainly:3 takeda:1 distortion:1 experiments:3 including:1 statistical:6 japan:1 peterson:1 still:1 excitations:2 its:1 colorado:1 longitudinal:1 thank:1 energies:2 coordinates:1 li:1 microscopic:1 fig:9 saxon:1 mail:1 cls:1 non:1 good:1 greater:2 fukuoka:1 effects:2 they:1 half:1 sorted:2 nor:1 nos:1 wambach:1 represents:1 hatanaka:4 name:3 gamow:1 93c:1 telluride:1 university:5 2b:3 each:3 found:7 characterized:1 reactions:1 differential:2 clausen:1 as6:1 osaka:3 reduce:1 gaussian:2 extended:1 isospin:2 ex:23 manley:1 our:3 transitions:1 out:1 atsushi:1 shown:1 kerman:2 acknowledgment:1 twice:1 unnatural:9 furthermore:1 rev:14 dss:5 research:3 re:1 asymmetries:1 formula:1 ref:5 shows:6 howell:1 θlab:6 sideways:1 free:4 beatty:2 york:1 shun:1 okamura:5 interaction:24 masanori:1 bowman:1 ministry:1 transition:9 phy:1 instrum:2 due:2 transfer:16 first:2 already:1 powerful:1 ohnishi:1 tetsuo:1 open:2 angular:1 given:3 quality:1 fl:10 top:8 system:1 millener:1 fm:9 indicate:4 intermediate:1 listed:2 calculations:6 unpublished:2 gives:1 storm:1 tool:1 park:1 dwia:7 direct:1 optical:1 than:6 wide:1 polarized:1 target:1 double:2 enabled:1 transferred:1 suzuki:3 amplitude:1 were:9 tion:1 providing:1 exhibit:1 schwandt:1 gubler:1 cohen:2 spectrum:1 chen:1 distorted:2 seen:1 concentration:1 clearly:1 strength:12 sdr:6 depending:2 sakamoto:4 polarization:9 extracted:1 fitting:3 potential:1 take:1 green:3 detector:1 strengths:2 eff:2 circles:2 normal:1 radioisotope:1 sethi:3 letter:5 tanaka:1 measured:8 probes:1 exn:1 calculated:1 typeset:1 proceedings:1 part:3 exp:1 nuclear:5 sd:7 physics:3 section:5 show:3 supported:2 expressed:1 keywords:1 agrees:2 parameters:2 otsu:3 yen:1 should:3 only:5 kunihiro:1 dn:7 his:1 dominant:3 means:1 de:1 beam:2 watson:1 goulding:1 new:1 during:1 ema:1 continuum:9 workman:1 arxiv:1 summary:1 kurath:2 investigate:1 predicted:2 scott:1 bars:2 set:10 edited:1 sensitivity:2 correlations:2 maximum:1 relative:2 culture:1 see:1 computer:2 result:1 tornow:1 cyclotron:2 best:1 said:1 tensor:15 fwhm:1 dipole:4 dll:7 state:1 mcmanus:1 yuji:2 yamashita:1 program:1 george:1 jp:1 however:2 jr:2 incident:1 omp:2 no:1 huang:1 carbon:1 suggested:1 observable:7 σc:1 region:1 equal:1 gwu:1 sensitive:2 contribution:1 experimental:4 proton:2 grants:1 simply:1 stretched:1 kev:1 table:3 crew:1 conference:1 hiroaki:1 pt:13 three:2 been:9 expected:1 ishida:5 lett:3 direction:4 flight:1 reaction:13 observe:1 systematic:2 spin:25 present:5 aid:1 solid:5 value:7 pwia:1 while:1 error:2 investigating:1 real:1 studied:1 schaeffer:1 jpn:4 almost:2 madey:1 thus:2 sekiguchi:2 examined:1 technology:1 different:2 author:3 make:1 cross:9 same:2 unity:1 moss:1 finite:1 neutron:4 kyushu:2 independent:3 jeffrey:1 used:4 http:1 peaks:8 maeda:1 assignment:1 hand:2 sults:1 recent:3 center:4 rcnp:2 analysis:1 calibrated:1 components:4 model:1 sorenson:1 kawabata:1 less:1 briscoe:1 shape:1 yamamoto:1 scattering:5 previous:2 gt:3 smith:2 goodman:4 spread:1 teller:1 nanda:3 excited:1 momentum:7 identical:1 march:1 possible:1 jpsj2:1 using:7 prominent:1 theor:1 whitten:2 extremely:1 either:2 sakai:5 alford:1 parity:16 because:3 methods:2 predominance:4 deduce:1 was:8 cooper:1 bottom:7 resonances:1 willis:2 measurements:3 kmt:1 provides:1 assuming:1 prog:1 baldwin:1 rapaport:3 scientific:1 power:1 s12:6 radial:1 sasano:1 qˆ:2 panel:12 about:1 kinematical:1 carried:1 hicks:1 stephenson:1 discussed:1 dependence:2 o:2 range:1 slightly:1 soc:4 greenfield:2 previously:1 into:2 within:1 predictions:1 assess:2 appropriate:2 tostevin:1 operator:1 katoh:1 uncertainties:6 van:1 elastic:1 assumed:1 support:1 there:2 width:1 anderson:1 sections:4 energy:7 function:2 fragmented:1 insensitivity:1 complete:9 form:1 differences:1 but:2 esbensen:1 ling:1 line:2 he:1 fragmentation:1 consist:1 whether:1 up:3 us:2 fluctuations:1 panels:2 similar:1 agree:1 detailed:1 ac:1 defined:2 gaarde:1 evidence:1 single:1 reliability:1 laboratory:2 ay:2 corresponding:2 education:1 distributions:1 functions:1 compared:2 calibration:1 na:1 other:4 department:1 2dn:2 shimizu:1 conclusion:2 nonaka:1 excitation:3 models:2 tanabe:1 lucia:1 generated:1 peak:3 lichtenstadt:1 transfers:3 structure:3 jones:3 garcia:1 baker:3 mass:1 res:2 walker:1 observables:17 nuclei:3 resolution:1 |
0704.0671.txt |@word limited:1 code:5 partial:2 consider:7 springer:3 secondly:1 ppendix:1 results:4 gy:2 sketching:1 illustrated:1 eds:1 generalize:1 edu:1 consists:1 follow:1 restrictions:1 compact:2 whose:1 inverse:1 depend:1 concerned:1 finally:3 under:9 norm:1 ingredient:1 p2:5 supported:1 risk:6 straightforward:2 zhang:3 very:2 dispense:1 assuming:1 dobrushin:5 lyapunov:1 corollary:1 wishes:1 every:17 bounding:1 difference:2 electronics:1 pt1:1 costly:1 obvious:1 todd:1 notes:2 t1:1 noiseless:1 admissible:1 vector:2 dealt:1 entropy:7 shows:1 upper:1 zn:1 y0:3 zi:9 measurable:3 approximation:4 rate:31 infimum:2 even:1 plays:1 power:1 invertible:1 section:2 learner:16 uniform:6 version:2 goes:1 sup:22 expresses:1 net:5 change:1 method:1 satisfy:1 led:1 notions:1 gathered:1 jointly:4 modular:2 operating:7 compressed:8 separation:1 excess:3 directions:2 along:1 respect:4 z1:1 z2:1 remark:2 sobolev:1 institute:1 study:1 yˆ:1 prior:2 cardinality:1 suitable:3 makes:1 control:1 via:3 useful:1 classification:2 apr:1 merely:1 convexity:1 replace:3 achievable:8 apply:1 establish:1 causal:1 standing:1 fed:1 takes:3 would:2 prove:1 stated:3 next:1 vol:8 call:1 therefore:4 taken:2 type:1 separated:1 nauka:1 optimizing:1 decoders:3 formally:2 thus:2 pfm:2 uiuc:1 effect:1 appendix:3 everywhere:1 normalized:1 particular:7 known:2 cases:2 hold:1 iii:2 must:3 keeping:1 quantized:1 science:1 work:6 haussler:2 minimum:3 values:5 lipschitz:3 following:8 erm:3 trans:2 example:8 unconditional:1 proof:8 f0:6 continuity:2 weaker:2 figure:2 give:1 allowed:2 sample:5 assumptions:8 numbers:1 arise:1 triangle:1 nonnegative:1 jensen:1 information:26 predictors:2 minimax:2 discussion:1 holds:9 write:3 maps:1 nontrivial:1 optimal:1 allowable:1 guarantee:1 parameter:1 simplicity:1 continues:1 binary:1 may:7 after:1 derived:2 tracking:1 walk:1 applications:2 machine:1 abuse:1 designed:1 burnashev:4 law:1 data:13 fm:4 fn:57 goal:1 short:1 chiefly:1 simplistic:1 sets:2 whenever:1 lines:1 hypotheses:2 inform:4 algorithms:3 fundamental:1 decreasing:1 operate:1 order:1 dx:1 over:6 dy:22 satisfied:2 nonparametric:8 distortion:12 paper:3 london:1 statistical:6 y1:3 ntroduction:1 satisfies:8 ieee:2 its:1 before:1 perfect:4 superior:1 derive:2 fix:3 expectations:1 actually:1 better:2 mendelson:2 absence:1 concavity:3 fig:1 listing:1 main:4 lz:6 lx:8 yi:20 vidyasagar:2 yn:3 yb:6 framework:1 now:3 coleman:1 reconstruction:1 represents:1 finite:9 2r:2 always:1 university:1 concave:1 capability:1 applied:1 inequality:5 l2:1 each:5 done:1 cliffs:1 side:15 constraints:4 subset:4 en:19 just:1 ed:2 hard:1 gaussian:4 related:2 decays:1 measurement:1 our:7 eq:2 special:1 might:1 large:1 shown:3 network:3 space:6 furthermore:2 urbana:1 squared:2 ry:5 rd:2 fellowship:1 papers:1 performs:1 denoted:2 lecture:1 learners:1 induced:1 sensor:7 correct:1 math:1 rk:1 multiterminal:2 theory:14 divergence:1 little:1 free:3 standard:2 york:2 ask:1 sensors:3 log:2 definition:1 training:14 r1:2 r2:1 could:4 messages:1 so:3 keep:1 length:1 place:1 exponentially:1 leading:1 hence:3 generalizations:1 first:2 major:1 xi:16 xn:2 zak:1 probability:5 encoding:1 relate:1 variables:5 coding:7 number:6 simplified:1 least:1 another:1 says:1 array:1 ℓf:7 size:1 given:19 kol:1 unknown:2 approximately:1 needed:2 assumption:4 observations:4 statement:1 scheme:11 bits:4 listed:1 kolmogorov:1 kohler:1 relationship:2 cope:1 moscow:1 continuous:3 proving:1 immediate:1 part:9 x1:2 than:2 outline:1 distance:1 variational:1 roles:1 zero:4 future:4 reproduction:3 were:1 result:2 comput:1 acknowledged:1 ann:1 measure:1 locations:2 generalization:8 say:2 ℓn:16 compression:1 close:2 need:4 constrained:1 clearly:2 generalizes:2 min:6 efficient:1 lim:18 tuple:1 able:1 ideas:1 note:1 other:2 internal:1 square:1 generalized:1 analogy:1 performance:6 reals:1 channel:3 lectures:1 begin:1 unless:1 asserts:1 shall:4 object:1 most:1 letter:1 pair:3 probabilistic:1 class:14 observation:5 considered:2 parametric:2 average:1 cover:1 reflecting:1 verlag:1 dispersed:1 typically:1 technical:1 fact:3 quantity:1 show:7 random:12 spaces:1 relation:2 substituting:1 networks:1 based:3 knowledge:2 distributed:4 enough:1 operational:1 penalty:1 lemma:9 only:5 attained:1 integrable:1 constant:1 nj:1 dn:18 sense:1 above:1 notation:2 get:4 designing:1 expectation:1 joint:2 october:1 words:1 probably:1 dv:8 prentice:1 dp:2 dq:1 gray:2 densities:2 covering:2 approach:4 arxiv:1 yield:1 acknowledgments:1 optimally:1 lossy:5 statist:1 fixed:1 communicated:5 requirement:1 set:8 constructing:1 exists:7 achieved:1 mind:1 2c:3 bounds:4 relative:1 depends:2 decided:1 sec:7 quantitatively:1 wyner:1 arg:2 discussions:1 terms:3 theoretic:8 best:4 techniques:1 instance:1 satisfying:4 capacity:3 currently:1 convex:1 state:3 smallest:1 various:1 between:9 drawn:3 justified:1 conditions:5 quantities:1 available:3 lf:2 triples:1 deliver:2 however:1 wi:4 gratefully:1 hypothesis:6 iscussion:1 extent:1 amer:1 distribution:10 both:3 essentially:1 region:1 uncertainty:1 beckman:2 according:3 quantization:1 converses:1 variance:4 estimation:5 otherwise:1 detailed:1 necessary:2 characterization:1 simple:1 asymptotically:1 eferences:1 simply:1 ahlswede:4 learning:27 cs:1 2nr:4 throughout:1 ensures:1 basis:3 copies:1 springerverlag:1 belongs:1 pf:18 pg:2 interest:3 basic:2 expected:5 orfi:2 define:6 corresponding:1 finishes:1 received:1 suppress:1 sufficient:1 precision:1 new:2 argument:2 gains:1 general:3 present:1 case:6 p1:6 leave:1 empirical:3 will:6 euclidean:1 while:7 suppose:6 behavior:1 error:7 situation:2 property:2 taking:4 existence:3 memoryless:1 metric:4 agnostic:3 iv:2 ii:3 regularity:1 il:1 triple:1 ave:1 supremum:1 regression:10 capture:1 author:1 estimate:2 identities:1 cumulative:1 same:2 any:17 member:2 pac:3 emphasize:1 proved:2 gets:1 independent:7 used:3 infinity:1 see:5 mutual:2 hand:1 moment:2 encoders:3 robust:2 adopting:1 reference:1 lower:5 task:1 proceed:1 neural:1 onedimensional:1 well:1 without:1 mathews:1 consistency:1 model:2 laboratories:1 sensing:2 stating:1 usual:2 interpret:1 construct:2 proposed:1 2dy:1 accurate:1 adjustments:1 obtain:2 rest:1 sources:1 underlying:6 redesign:2 inference:1 family:9 han:2 density:3 nats:1 had:1 except:1 hall:1 source:11 setting:9 location:4 easy:1 theorem:12 input:6 remaining:1 take:2 real:1 motivating:1 replaced:1 spatial:1 possible:3 amari:2 deployment:1 using:9 bit:1 2nd:1 moreover:1 pinsker:1 advanced:1 loss:14 englewood:1 imposed:1 follows:7 unified:1 separately:1 imposes:1 steps:1 either:2 arbitrary:2 output:6 because:6 often:2 namely:1 sequence:11 absolutely:2 conditional:7 some:25 maxim:2 specified:4 proofs:1 march:1 δn:1 informationtheoretic:1 decision:2 measurements:2 xample:1 per:2 fbn:1 equal:1 exposition:1 tends:1 minimal:2 limitations:1 noise:2 minimization:1 rep:1 uniformly:1 statistician:1 pose:1 pp:8 step:1 substitution:1 asymptotic:2 about:2 central:1 extension:1 constraint:1 pθ:2 theorems:1 dependence:1 o:1 2i:1 whence:1 referred:1 slightly:1 predictor:6 block:1 berger:4 soc:1 presence:3 previously:1 into:5 bound:7 right:1 pairs:1 methods:2 computer:1 additional:2 few:1 assumed:1 strictly:2 there:10 approximate:1 incurred:1 smola:1 was:4 assumes:1 asymptotics:1 function:29 complete:1 form:6 sequel:1 but:2 encoder:9 volume:1 here:1 decoder:10 russian:1 implies:3 role:1 true:2 he:1 made:2 consist:1 stanford:1 minkowski:1 up:2 us:6 placed:1 limit:1 problem:11 pm:2 called:3 viewpoint:1 associated:1 defined:3 abstract:1 describe:1 condition:11 denote:5 transl:1 proves:2 exist:2 formulation:2 inf:8 distributions:9 constructed:1 ser:2 ni:5 functions:7 codes:1 no:6 when:7 illinois:1 geographically:1 interested:2 coded:1 normal:3 digital:1 tech:1 nr:3 problemy:1 symbol:1 problems:1 bounded:4 variable:4 singleton:1 structure:2 correlated:1 remote:3 longer:1 algorithm:5 assume:9 interval:1 together:1 n2:3 mean:3 having:2 |
0704.0672.txt |@word ibid:1 holman:1 dewitt:6 partial:1 consider:5 rev:12 global:1 kanai:1 leads:1 scalar:3 generalize:1 research:2 contributions:1 issues:1 gr:4 devoted:1 glimpse:1 th:2 under:3 anharmonic:1 division:2 string:2 evolves:2 far:1 onemli:2 noncommuting:1 wave:1 socorro:1 hµν:2 little:1 condition:3 hamiltonian:37 turns:1 notes:1 t2:5 solution:3 t1:2 large:2 solved:2 jhep:1 employing:1 riess:2 direct:1 8πgtµν:1 zero:1 dissipation:2 perspective:1 further:6 canonical:7 even:1 aim:1 nonlinear:2 plays:1 combined:1 sun:2 cosmologists:1 dr2:1 current:4 3h:2 above:7 new:7 3a:4 acknowledgments:1 coefficient:1 27a:1 27b:1 degree:1 trivedi:1 modify:1 here:7 odintsov:3 china:2 jcap:1 address:1 ignore:1 equations:20 appears:1 change:2 obtained:5 institute:1 study:5 studied:3 completely:1 commonly:2 p2:5 poisson:3 action:1 spacetime:2 kachru:1 winkler:1 projection:1 bertolami:1 integrations:2 logarithmic:1 santini:1 apply:1 wang:3 use:2 asymptotic:2 would:1 commun:1 contains:1 properties:2 comparing:2 linear:2 sitter:9 call:2 therefore:7 taken:1 theoretical:4 possible:1 more:3 separated:2 flat:2 duality:2 becomes:2 operators:1 odinger:4 curvature:5 appendix:2 particular:1 known:1 cases:3 iii:2 must:1 comoving:1 account:4 quantized:2 science:1 equation:48 work:8 oscillator:11 modified:3 era:1 universe:8 following:10 example:7 f1:19 f2:16 f3:1 renormalization:1 cosmological:21 give:8 ds2:1 organized:1 topic:1 claimed:1 numbers:1 sense:1 pinto:1 oliveira:1 provide:1 discussion:1 very:2 instead:1 ordinary:1 parameter:7 glinka:1 simplicity:3 de:9 description:5 kahya:1 replacing:1 after:8 derived:3 different:4 fluid:6 applications:1 lay:1 fits:3 law:3 data:5 constants:2 dynamical:2 effective:15 chern:1 introducing:1 cosmology:20 so:2 make:5 gµν:3 nsfc:2 jiri:1 perlmutter:1 insight:1 mainly:1 satisfied:2 paper:1 through:2 cold:2 its:2 perfect:1 jie:1 group:1 ln:7 presence:1 coordinates:1 systems:1 derivative:2 horvat:1 defining:3 h0:1 correspondence:2 motivated:1 propose:1 investigated:1 framework:7 effects:3 oxford:1 rotation:1 now:4 yu:6 discuss:2 developments:1 eigenvalue:1 february:1 name:1 university:4 applied:5 lemos:3 2a:3 reasonable:1 2m:4 side:1 characterized:3 eηt:1 individually:2 differential:1 directly:1 kani:1 energy:13 silva:1 idea:1 related:3 inhomogeneous:1 used:2 expect:1 combining:3 quantum:13 our:14 eq:40 special:10 out:8 rw:3 matrix:1 space:1 tianjin:2 nuovo:1 since:6 lagrangian:6 qc:4 denotes:3 intriguing:1 ren:2 rel:3 transfer:1 ref:4 math:1 foundation:1 theory:6 favored:1 singularities:1 galaxies:1 sheer:2 standard:3 admits:1 approaches:1 york:1 ofer:1 dω2:1 hubble:2 interaction:1 r2:1 geometry:1 cosmic:6 motion:10 turn:1 period:1 h02:4 quadratically:1 major:1 initial:1 shapiro:2 simplified:4 xin:1 another:1 ostriker:1 electronic:1 given:10 guberina:1 checked:1 similarly:2 introduction:1 eqs:1 achieved:1 system:13 construct:3 their:1 conservation:1 observations:1 dt2:1 scheme:1 relations:2 gives:7 authors:1 eliminated:1 believe:1 coefficients:2 18b:1 18a:2 determines:1 stefanˇ:2 cimento:1 matter:11 future:2 bridge:1 generality:2 pˆφ:3 bhe:1 generalization:3 husain:1 vilenkin:1 ans:1 need:1 contents:1 ijmpd:1 acceleration:1 built:1 pa:2 nikoli:1 able:1 gravity:3 abrowski:1 liu:1 subjects:1 generalized:10 gρ:1 spergel:1 upside:2 λcdm:12 heisenberg:1 though:1 bk21:2 object:7 viscosity:8 simplify:1 eroshenko:1 steinhardt:1 remarks:3 naidu:1 bahcall:1 why:1 commutation:2 observation:1 consequences:1 calculated:1 order:1 bracket:3 exp:10 mechanical:1 physics:5 section:1 fact:1 quantity:1 neto:2 3p:1 show:4 supported:2 discovered:1 relation:5 substituting:1 d2:1 find:4 caldirola:1 cardone:1 proposed:3 parameters:3 explain:3 written:4 should:2 only:1 explicitly:3 ambiguity:2 factor:14 heun:1 meng:4 hotmail:1 dh:1 means:1 dependent:1 simplest:2 straightforwardly:2 da:5 cannot:3 dz:1 kiefer:1 3b:3 during:2 dt:1 gen:3 differentiating:2 dq:11 prime:2 evolution:4 arxiv:1 yield:2 4πg:1 investigate:1 valid:1 2p0:1 sep:1 accompanied:1 respect:2 see:5 sec:5 discussions:1 terms:5 satisfies:1 quantizing:1 uν:3 appear:1 tensor:6 review:1 state:2 difficulties:1 between:6 invariant:1 overduin:1 approach:6 choose:1 observational:5 korea:1 p2a:1 attention:2 however:2 jr:1 sola:1 hypothesis:1 jj:1 jk:1 both:11 essentially:2 last:1 many:4 according:1 quantization:5 vishwakarma:1 dated:1 filho:1 babichev:1 contribution:1 com:1 ck:2 aa:1 ci:2 solving:1 point:1 simple:1 seems:1 harmonic:9 anti:1 elizalde:1 moreover:2 pervushin:2 pq:3 described:6 transformations:1 simplification:1 been:6 difference:1 bianchi:3 frw:8 damping:4 basic:2 ph:5 define:1 contribute:1 corresponding:13 tµν:1 observable:3 quantities:2 concerning:2 wheeler:5 bulk:7 ordering:2 ρuµ:1 curves:1 systematic:2 astron:1 evidence:1 present:7 case:18 p0:10 p1:3 supernovae:1 pacs:1 evaluated:2 will:3 braz:1 cooperstock:1 conformal:1 changed:1 vi:1 refs:2 thus:8 iv:3 ii:2 quantize:1 dual:2 ia:2 containing:1 formalism:13 seoul:1 same:5 quant:7 widely:1 independent:2 literature:2 effect:3 hand:1 usually:2 moving:7 potentials:2 identity:3 schr:4 safely:1 variety:2 well:3 without:4 solve:1 components:1 consistency:1 coordinate:1 model:32 possesses:5 unified:1 just:1 increasingly:1 generally:2 rµν:1 obtain:7 λa:1 thanks:1 aspect:1 previous:1 candidate:1 density:3 regarded:5 had:1 except:2 nojiri:2 appeared:1 add:2 potential:16 transformed:2 lett:11 rosu:1 transformation:10 momentum:5 take:5 around:1 easily:1 term:12 corresponds:7 dark:4 inflation:4 background:1 vacuum:2 press:1 using:3 bit:1 8πg:3 advanced:1 mod:1 helpful:1 follows:1 accelerating:2 specific:2 arbitrary:1 works:1 reduced:3 newton:2 right:2 classical:6 some:15 pφ:4 examples:3 specified:2 nonzero:1 provided:1 ferreira:1 scale:14 bento:1 shall:2 conservative:1 does:1 eliminate:1 provides:3 timelike:1 prog:1 prof:1 power:1 equivalent:1 grav:11 expansion:3 although:1 found:3 atze:1 hilbert:1 eψ:3 comparison:3 extension:1 constraint:6 freedom:1 based:1 o:5 practical:1 consequently:1 mathematical:2 redshift:2 h2:1 into:5 sergio:1 sol:2 down:2 variable:24 appropriate:5 ηt:2 einstein:3 operator:1 proportional:1 significantly:1 hep:2 assumed:2 there:3 transform:1 sne:2 class:7 start:2 describes:4 physicists:2 way:2 was:1 hanyang:1 function:2 form:6 regard:1 but:2 hu:1 astro:5 dissipative:2 illustrative:1 he:1 applying:1 cosmol:1 intuitive:1 dokuchaev:1 until:1 dφ:2 ωm:7 problem:6 mechanics:2 constant:26 af:1 defined:2 ah:1 describe:2 general:7 conserved:2 exist:1 nankai:2 woodard:1 education:1 check:2 metric:3 constructed:1 friedmann:25 functions:10 no:6 uµ:2 whereas:2 when:2 field:9 other:2 role:1 capozziello:2 department:1 mathematics:1 theor:2 conclusion:2 picture:3 generates:1 models:8 brevik:3 problems:1 a1:1 a0:1 a3:2 a2:8 a5:2 a4:2 a6:1 linearization:2 lution:1 3h02:1 gao:1 ge:1 implies:2 assume:6 veneziano:1 eos:14 mass:8 time:6 walker:3 serious:1 starting:4 once:1 |
0704.0673.txt |@word secondly:1 concept:1 consider:9 remarkable:2 illustrates:1 brownian:1 results:23 leads:6 scalar:1 nunn:1 entropy:54 comments:1 computation:2 edu:1 consists:3 anggi:1 expressions:10 ward:4 kluwer:1 whose:1 simon:1 depend:1 calculate:2 re:1 clarke:1 solution:1 simplify:1 young:1 presents:1 must:2 award:1 present:1 th:3 under:4 stochastic:9 include:1 hill:1 lindner:1 consequently:1 straightforward:2 very:5 implants:2 implicitly:1 focus:1 nadal:1 pierre:1 p1:25 anonymous:1 emphasized:2 difference:7 exact:25 condition:8 illustrated:3 school:2 fluct:4 discretely:1 stimulus:4 cause:1 pearce:4 correct:2 large:60 discrete:9 differential:2 interpolating:1 science:1 small:4 biological:1 inspection:2 noted:2 upper:1 smaller:3 maclaurin:2 consistent:1 maximization:1 direct:1 replicates:1 approximation:30 superimposed:1 pmf:11 evaluated:3 further:6 functioning:1 even:5 reviews:1 what:2 nonlinear:1 minimization:1 invertible:1 morse:5 complexities:1 section:3 l205:1 near:1 expressed:2 uniform:9 aperiodic:2 above:1 referees:1 new:9 increasing:3 method:4 thin:1 satisfy:1 justification:5 led:2 behavior:1 respectively:1 microelectronics:1 component:1 here:5 laughlin:1 herz:1 address:1 ratio:6 along:2 quite:3 respect:3 appears:1 change:9 obtained:6 solid:2 almost:1 parameters:4 rigorously:1 receive:1 studied:1 allows:2 prior:3 periodic:1 olivier:1 action:1 resonance:9 proof:1 changes:1 involves:1 plotted:4 via:10 regardless:4 figure:1 scales:3 apr:1 requiring:1 summations:1 fig:17 neiman:1 modifying:1 bulsara:1 limn:1 pp:1 achievable:2 summation:3 pdfs:10 des:2 conventional:1 additive:4 proceed:1 would:2 improves:1 remains:1 positive:1 contains:2 negative:7 cauchy:2 optimize:2 process:2 snrs:3 derivation:5 call:1 therefore:7 taken:1 associated:2 leaky:1 theoretical:6 more:8 nagumo:1 optimizing:8 multiplying:1 comparison:3 outputs:2 archer:1 validity:1 nguyen:2 iid:5 appendix:6 excellent:1 known:9 actual:1 cases:7 hold:2 iii:8 huxley:1 cochlear:3 states:3 springer:1 valued:5 integrating:3 wiesenfeld:2 recall:1 originally:1 work:6 modified:1 quantizer:3 erf:2 itself:1 values:10 rewritten:1 following:1 making:3 perturbs:1 example:3 performed:1 compare:2 acoustics:1 wang:1 indicated:1 give:4 calculation:1 amblard:2 role:1 bennett:1 share:1 sample:3 indicates:1 numbers:1 council:1 sense:1 standard:6 transactions:2 np1:6 occur:3 axis:1 information:81 needs:2 united:1 2σx:1 viewpoint:2 optimised:1 rather:2 describes:2 write:1 holds:9 utilize:1 makes:1 located:1 varies:1 numerous:1 get:4 significance:2 optimal:27 guarantee:1 parameter:1 max:1 rousseau:2 fq:51 product:1 fs:19 mat:1 fx:70 fy:7 wiley:2 derived:12 epsrc:1 diagram:1 hence:1 snr:1 improving:2 end:1 minimizes:1 derives:2 response:5 consisting:1 gaussian:30 introduced:1 physical:2 dynamical:1 whenever:1 sr:9 lines:1 provide:2 sons:2 so:8 verify:1 definitions:1 subsequently:1 order:1 worsens:1 fβ:2 acts:2 valid:2 fη:50 indeed:3 thresholds:1 speech:1 distortion:4 paper:7 including:1 statistical:1 differs:1 still:1 ieee:3 its:8 hoch:1 before:1 thomas:1 strikingly:1 derive:3 thank:1 la:1 ln:11 interesting:1 solving:4 decreases:2 forms:2 previously:2 absence:2 verifies:1 biomedical:1 derivative:2 encapsulates:2 main:1 marchesoni:1 setting:2 arguments:1 correspondence:1 non:3 good:1 motivated:1 greater:1 barron:1 integral:3 randomness:3 emphasised:1 scaling:1 laplacian:4 they:1 identically:1 bialek:2 now:7 provision:1 outlines:1 matched:4 easily:1 february:1 finite:6 stated:1 publication:1 always:8 university:5 sin:3 transmission:3 iff:1 magnitude:1 each:16 found:10 entirely:2 mean:13 mcculloch:1 just:1 significantly:3 generation:1 series:1 hypergeometric:1 idea:1 related:1 proportion:1 used:5 static:1 connect:1 exceeded:1 our:14 approximated:3 eq:101 event:1 special:3 out:3 noiseless:1 shown:13 network:1 3rd:1 solved:2 restricted:1 furthermore:5 since:12 rev:16 research:4 increase:1 may:1 contained:2 vector:1 dxdy:1 wide:1 maximized:1 denoted:1 formula:7 electronics:1 illustrate:1 supports:1 occurs:11 shows:8 plotting:1 abbott:4 arizona:1 log2:98 theory:9 circumstance:1 rieke:1 divergence:1 free:1 unimodal:1 sensory:1 analytical:8 approaches:6 carried:1 formation:2 york:2 roper:1 simplifying:1 pierson:1 remainder:2 additional:1 signaux:1 definition:1 digitization:1 agree:2 could:1 saddlepoint:1 motion:1 derivations:2 assumed:4 consequence:1 hodgkin:1 first:1 nigel:1 features:1 probability:5 clinical:1 researcher:1 variables:2 coding:5 number:4 improvements:3 done:1 array:7 precisely:2 electronic:2 several:1 size:2 given:36 necessarily:3 asymptotic:3 indicate:1 introduction:1 leading:1 eqs:11 system:2 approximately:1 parallel:6 their:2 assumption:1 listed:1 calculations:1 john:2 bits:4 final:1 gives:17 shifted:1 testing:1 relationship:2 square:1 sin2:1 reversed:2 continuous:7 lists:2 compression:3 spiegel:1 authors:1 natural:1 than:17 outline:2 begins:1 relative:14 showed:1 approximations:8 crosses:1 cimento:1 see:4 preparation:1 patients:1 determined:1 oregon:1 amplitude:3 were:3 identical:7 collins:1 rate:1 solely:2 e2:2 motivation:1 comput:2 modern:1 curves:1 substantial:1 manner:3 need:2 seen:1 demonstration:1 any:6 synapses:1 relatively:1 conversion:3 fxy:3 zero:16 min:2 efficient:1 studying:1 able:1 pdf:70 note:3 liu:1 high:4 derek:1 best:1 simplified:2 academy:1 finding:5 performance:5 require:1 explanation:1 channel:43 accuracy:3 circles:2 formulas:1 begin:2 exactly:4 centre:1 l169:1 measures:1 most:3 beta:7 plus:1 significant:2 2e:2 device:9 histogram:1 sa:1 7al:1 reduces:3 nonlinearity:2 considered:7 average:9 cover:1 inferred:1 physica:1 giving:1 michel:1 exp:4 hastings:1 physics:1 sum:3 fact:5 cdf:11 particularly:2 intensity:5 show:8 nπ:4 text:1 detection:1 random:32 approx:2 obtains:1 durrant:2 afferent:1 threshold:24 substituting:3 algorithms:1 find:7 subtracting:4 o:14 feng:1 based:3 knowledge:1 dp1:1 situations:1 distributed:4 enough:1 ed:1 only:8 version:1 integrate:1 greenwood:4 over:3 achieve:1 do:1 notation:2 means:12 dependent:1 syst:1 lehmann:1 overall:2 ssr:46 joint:2 cannot:5 nearly:1 dx:20 progress:1 evans:1 differentiating:3 converter:1 gray:1 regarding:1 peacock:1 conditions:4 arxiv:1 stirling:2 mannella:1 acknowledgments:1 circuits:1 investigate:1 common:1 logistic:2 release:1 through:1 peak:3 fixed:4 inside:1 nas:3 set:3 schreiber:1 achieved:6 achieves:1 summed:1 bounds:2 observed:1 mentioned:1 depends:5 individual:2 sec:16 result:22 enhanced:1 tables:1 discussions:1 close:5 2πn:3 theoretic:5 analog:3 subject:3 capacity:52 probable:1 ways:1 review:1 plymouth:1 label:2 written:13 between:19 drawn:1 justified:1 approach:4 σx2:1 discovery:1 publishers:1 sompolinsky:1 terms:11 fitzhugh:1 extend:1 missing:1 importance:1 weak:1 however:12 deterministic:4 quantizers:4 problem:6 gammaitoni:1 improve:1 both:23 cos:2 improved:5 2n:2 limits:1 gratefully:1 many:2 biologically:2 acknowledge:1 equal:6 quantization:8 subthreshold:1 dated:1 context:3 variance:13 estimation:1 expression:20 finds:6 otherwise:6 relevant:1 abbreviate:1 point:3 simple:3 ca:1 asymptotically:1 taylor:2 simply:3 invariant:1 iterations:1 sequences:1 yi:6 table:8 throughout:1 conference:1 ensures:1 sine:1 described:3 tuning:1 second:3 basis:1 addition:1 simplification:1 cv4:1 py:51 three:1 been:6 mark:1 much:4 replicate:1 basic:1 expected:1 extends:1 proposal:1 tan2:1 mcgraw:1 systems:3 resultant:4 easy:1 fire:1 sufficient:7 formed:1 ensuring:1 optimality:3 tan:1 σo:17 denote:2 those:2 aid:1 case:23 novel:1 unlike:4 pacs:1 coventry:1 variances:5 blahut:2 engineering:3 value:25 will:5 while:3 optimization:3 suppose:8 evaluating:1 error:7 situation:6 liebler:1 taking:1 real:1 larger:3 a4:5 memoryless:1 funded:1 neuron:3 them:1 discrepancy:2 ii:12 neurons:4 cond:1 io:5 wave:1 nikitin:1 rearranging:2 different:11 verified:4 russell:1 grant:1 journal:1 alphabet:1 make:4 cumulative:1 same:21 clearly:3 unity:8 σx:13 potentially:1 virtually:1 schematic:1 adelaide:2 brunel:1 breaks:1 independent:7 jeffrey:3 literature:2 infinity:3 receives:1 laboratoire:1 numerical:8 effect:1 possible:5 usually:2 uses:4 purpose:1 potentials:1 infinite:1 neurophysiology:1 recent:1 relies:1 prescribed:1 lower:3 mech:1 off:1 scenario:1 neural:11 studies:1 stimuli:1 no:3 well:11 full:1 analysis:2 thought:1 academic:1 without:2 log:5 firstly:1 obermayer:1 model:42 preprints:1 justify:1 stringent:1 proposed:2 less:5 being:2 when:12 accurate:5 half:2 valuable:1 shape:3 lossy:2 aspect:1 sufficiently:1 uller:1 alternative:2 previous:6 letting:2 heuristic:1 generous:1 accepted:1 integer:1 density:4 percent:1 signals:5 source:6 wu:1 other:6 transformed:1 lett:11 samples:3 marginal:1 relevance:1 input:21 euler:2 take:1 kingdom:1 australia:1 increased:1 showing:1 papers:1 thicker:1 term:9 possibly:1 increases:4 five:1 know:2 substituted:1 using:19 highly:2 casella:1 like:1 semi:1 signal:101 strictly:1 specific:8 communications:1 either:2 integrals:3 arbitrary:3 multiplicative:1 output:47 stationary:1 qualitative:2 mathematical:1 a15:2 versa:1 old:1 often:4 sequence:1 conditional:10 some:4 back:1 hair:3 calculated:7 elements:1 examples:2 convey:1 specified:3 images:1 arimoto:2 nonzero:2 provided:4 vol:1 describing:3 a13:1 lead:1 realistic:1 boyle:1 integration:5 per:3 does:7 provides:6 assuming:1 proc:1 demonstrated:1 refer:1 noise:91 inaccurate:2 power:1 a19:2 equivalent:4 processing:2 use:8 expansion:2 how:1 binomial:5 although:4 substitution:4 eye:1 approximating:1 properties:1 noisy:3 corresponding:6 about:7 pα:1 central:2 bimodal:3 constraint:2 discussed:12 optimized:1 recognized:2 essential:1 mutually:1 range:1 estimator:1 extensions:1 chow:1 a5:4 constraints:1 slightly:4 functions:2 a17:2 computational:2 moss:3 presence:2 arcsine:3 noting:1 into:6 numerically:10 bound:1 ηi:4 due:2 down:1 phase:1 because:1 inverting:1 determine:1 fisher:15 france:1 methods:1 a3:2 performing:1 analytically:1 devices:2 comparing:1 transfer:3 support:7 there:5 question:1 approximate:4 why:1 width:1 cosine:1 handbook:1 inner:1 way:2 kang:1 analyze:1 was:6 a2:1 function:21 form:4 a9:2 duan:1 warwick:1 agrees:4 but:8 pitts:1 state:2 ho:4 uncorrelated:1 delta:1 line:2 ear:1 true:5 australian:2 made:1 2πe:4 consequences:1 consist:1 versions:1 whether:3 wish:1 cells:3 maximum:7 us:2 achieving:7 resolved:1 below:2 frequency:1 limit:3 verification:3 uk:1 continuously:3 distribution:47 define:1 similar:2 clear:4 bethge:1 expect:1 instead:1 interval:4 constant:8 defined:3 abstract:1 proven:1 general:10 single:3 au:1 formulation:1 dη:2 exist:1 distributions:12 regime:2 again:1 mutual:52 compared:4 variety:1 amounts:1 nonlinearities:3 whereas:2 generally:1 ne:1 ep:1 arcsin:4 interested:2 electrical:1 shannon:4 digital:3 mcdonnell:5 kullback:1 deviation:4 a14:3 stat:1 a16:2 a11:2 a10:8 calculating:2 a12:1 models:4 remarked:1 uniformly:4 a18:2 jung:1 a1:1 meaning:1 important:2 nucleus:1 allowing:1 a7:1 a6:2 variable:29 neuroscience:4 stocks:9 sides:2 incurred:1 independently:3 auxiliary:4 algorithm:2 vice:1 assume:1 resolution:4 dτ:11 required:4 curve:1 dσ:1 equivalently:1 a8:3 carrying:2 mass:1 time:2 international:1 validation:1 requires:2 nuovo:1 |
0704.0674.txt |@word systematic:2 chinese:1 caused:1 focus:1 projected:2 four:3 allgood:1 selection:3 edu:1 consists:1 spaced:1 disk:2 voids:1 centers:1 consider:1 arcsec:1 spin:1 shanghai:4 environment:1 finally:3 program:2 under:1 conservation:1 case:1 supported:3 mpc:1 very:5 void:1 innovation:1 induce:2 results:11 l5:1 orientations:4 illustrated:1 level:2 positions:1 guo:1 radii:4 large:14 adjust:1 small:7 enhance:1 mo:4 upper:1 smaller:1 carter:2 findings:2 trend:1 consistent:4 direct:13 sign:1 hirata:1 likely:6 displays:1 dynamics:1 yw:1 linear:1 blue:10 what:2 errors:1 croft:2 selected:3 dr4:2 agrees:1 version:2 cheng:2 new:4 consisting:1 contrast:1 stripping:1 body:1 statistically:1 full:1 lee:3 degree:1 respectively:2 bailin:2 here:1 l21:1 hawley:2 china:1 ober:1 groups:6 adelman:2 along:7 obtained:4 search:3 institute:2 study:6 larger:3 onigstuhl:1 preferentially:6 survey:3 shaded:2 studies:3 brightest:3 buote:1 divide:1 scales:11 bullock:1 vir:1 macclesfield:1 amherst:1 apply:1 total:1 planck:2 use:4 contains:1 next:1 few:1 kinematics:1 therefore:3 luminosity:1 survive:2 themselves:2 assessment:1 prep:1 marginally:1 more:14 hoffman:2 corrected:1 pairs:4 tested:1 normalized:1 particular:3 cases:1 aligned:5 iii:1 must:1 high:1 orner:1 ma:1 conf:1 weighting:1 equation:1 work:1 ishak:1 reproduce:1 values:1 den:5 mr:2 following:2 history:1 relative:1 compare:1 weaker:1 wang:2 sample:6 indicates:2 magnitudes:1 axis:5 information:2 colless:2 discussion:1 means:1 nyu:3 how:1 methodology:1 significance:1 constraints:1 parameter:2 massive:1 de:2 may:7 max:2 derived:1 confirmed:1 bcgs:1 catalog:1 data:7 types:3 short:1 natural:1 dynamical:1 emphasize:1 schneider:2 grant:1 cosmology:3 green:5 theuns:1 halos:6 subsequently:1 sackett:1 order:1 bins:4 nsfc:1 interpretation:1 astronomical:1 mainly:2 years:1 report:1 paper:1 including:1 still:1 its:16 galaxy:33 fardal:2 style:1 group:19 fit:1 located:2 masses:5 expectations:1 li:3 forms:1 detected:3 primordial:1 fig:14 clusters:5 main:1 shear:1 underestimate:1 non:1 good:2 weakness:1 material:1 evolution:1 primary:1 band:2 effects:1 they:4 satellites:21 rotation:1 discuss:1 bank:1 easily:1 february:2 porciani:3 university:3 classified:2 identified:1 l7:2 kpc:3 radial:22 found:5 higher:1 tracer:2 mean:3 homogeneous:1 significantly:2 kang:7 gaussian:1 applicable:1 carvalho:1 literature:1 interplay:1 measure:1 our:13 happen:1 orient:1 refregier:1 shown:3 space:1 gradient:1 restricted:1 since:8 rvir:12 mccarthy:2 gaussians:1 emerged:1 sloan:2 induced:1 cause:1 red:10 shows:3 sk11:1 theory:1 libeskind:2 frank:1 confidence:3 galaxies:42 given:2 possibility:1 orbits:1 fainter:2 formation:3 york:3 members:1 span:1 impulsive:1 hubble:2 created:1 readjusting:1 similarly:1 cosmic:1 frenk:1 caption:1 fleck:2 isotropic:1 first:2 origin:2 major:6 natarajan:1 struble:3 number:2 randomized:1 reflects:1 least:4 directly:1 changing:1 carry:1 carretero:1 angular:1 size:1 surveys:2 necessarily:1 brighenti:1 indicate:3 introduction:1 system:1 construct:1 their:7 ciotti:3 accretion:3 draft:2 mao:3 analytical:1 white:1 perfectly:3 bosch:4 final:1 dutta:3 originating:1 mostly:1 academy:1 explanation:2 exactly:1 accurately:1 rejected:2 prediction:1 astrophysics:2 assumption:1 apjs:2 than:12 chomiuk:1 l43:1 wide:1 observatory:3 showed:1 gottl:1 double:1 see:3 matter:16 determined:1 were:8 tion:1 toward:1 tangential:1 heymans:3 zentner:1 84th:2 astrophysical:2 headings:1 allen:1 null:1 any:3 ray:1 lie:1 angle:7 min:1 ypj:1 latter:1 able:1 isolated:1 mechanism:1 oriented:1 sciences:1 potential:1 strazzullo:2 forces:1 observationally:1 finding:1 so:1 projects:1 tool:1 l111:1 added:1 relatively:3 opposite:2 most:2 germany:1 letter:1 intrinsic:4 why:2 sub:1 latex:1 considered:1 average:2 adopt:1 implications:1 inferred:1 km:1 typeset:1 memberships:1 yang:11 ferrari:1 li1:1 aip:1 velocity:1 physics:1 fact:3 precise:1 axes:3 particularly:1 pope:1 show:1 cdm:1 random:5 colors:1 manchester:1 inconsistent:1 carefully:1 earth:1 heavens:4 find:4 impact:1 based:9 knowledge:1 explain:2 distributed:2 outside:1 patiri:2 king:2 only:7 unable:2 rich:1 thompson:2 bernstein:3 over:4 achieve:1 above:2 distance:1 kamionkowski:1 prada:1 preferred:3 l107:1 joint:1 cannot:1 subhaloes:1 holmberg:2 rejection:1 areas:1 regarding:1 sources:1 numerous:1 arxiv:2 method:1 navarro:1 blanton:2 investigate:5 cheshire:1 release:2 fixed:1 16th:2 cole:1 reveals:1 9dl:1 set:1 predicts:1 fair:1 imposing:1 sensitivity:1 correlations:1 detection:2 depends:1 centric:3 radius:3 close:1 observed:2 subject:1 detect:2 yields:1 yepes:1 tend:1 catalogue:6 percentiles:2 various:1 tendency:3 between:22 2002a:2 limit:2 2002b:2 encounters:1 recently:1 kuhn:5 parent:2 importance:1 gg:3 weak:8 however:7 hypothesis:1 magn:1 extent:1 contamination:3 coma:1 virial:2 limits:1 lensed:1 region:1 according:2 etc:1 improves:1 norberg:3 l25:1 steinmetz:2 binggeli:3 reside:2 detailed:1 key:1 timescale:1 point:1 reasons:1 relaxation:1 cf:4 simply:1 framework:1 associated:2 throughout:2 conference:1 benoist:1 described:1 addition:5 west:3 locally:1 due:2 been:6 mark:1 pa:3 combined:1 basic:1 expected:1 ph:2 define:1 direction:5 precision:1 arkiv:1 gal:1 understand:1 representative:1 angles:6 evidence:1 djorgovski:3 those:2 applied:2 exception:1 dilute:1 mandelbaum:2 align:1 vagc:3 value:1 will:3 subsample:1 while:2 momentum:1 longo:1 unlikely:1 styles:1 studied:1 orientation:17 fujimoto:2 prolate:2 thus:2 surface:1 ii:1 cluster:6 owes:1 orbital:1 different:8 pas:2 assure:1 acknowledgments:1 virialized:1 locking:1 kjcx2:1 same:3 clearly:2 shorter:1 split:1 contaminate:1 resulting:2 nanopoulos:1 several:2 difficult:1 independent:3 satellite:29 used:2 http:1 effect:1 hand:2 constraining:1 uses:1 robust:2 bggs:1 single:1 recent:1 early:1 lower:2 supports:1 kept:1 center:3 nandan:1 weinmann:3 well:1 analysis:3 obviously:1 mathews:2 sets:1 l101:1 position:1 blandford:1 kauffmann:1 left:1 plionis:5 basilakos:1 less:1 being:1 accurate:2 obtain:1 mo4:1 subsamples:1 violent:1 aspect:1 alignment:57 previous:2 note:1 preprint:1 guhathakurta:1 prints:1 cl:1 sky:2 except:1 jodrell:1 signals:2 source:2 falsely:1 crittenden:2 halo:22 samples:9 2006a:2 heidelberg:1 finder:2 bin:4 tests:1 around:2 2006b:6 absence:1 possible:2 l89:1 corresponds:1 dark:14 department:1 increases:1 preference:1 press:1 using:10 unique:1 color:6 apj:20 propris:1 semi:1 exploiting:1 signal:10 velocities:1 isotropy:2 shapes:1 detections:1 indication:4 follows:1 become:1 pereira:3 alignments:8 reasonably:1 spins:1 indications:1 old:1 often:2 brainerd:13 some:1 catelan:2 understood:1 towards:9 redshifts:1 extended:1 trujillo:2 confusing:1 metcalfe:2 scale:5 projection:1 lead:1 affects:1 avoid:1 measurements:5 moon:1 2dfgrs:3 pen:3 magnitude:1 connecting:3 tends:1 hosts:1 sdss:7 proc:1 anna:1 biased:1 noise:1 power:1 each:6 agreement:5 illustration:1 host:4 filaments:2 tidal:13 refers:1 emulateapj:1 properties:1 helly:1 central:2 bgg:28 brinkmann:1 discussed:1 dependence:2 range:3 haloes:3 johnston:2 introduced:1 consequently:1 road:1 equally:1 significant:9 redshift:3 h0:1 within:6 three:6 down:1 lensing:6 references:1 determine:1 maurogordato:1 jing:9 statistics:1 van:5 log:2 shells:1 removing:1 there:5 spiral:1 long:1 noticed:1 dispersion:1 much:1 low:1 ed:1 resulted:2 was:1 function:3 filamentary:1 faltenbacher:4 criteria:2 jun:1 but:13 astro:2 repeated:1 hierarchical:1 mnras:21 line:4 partially:2 compute:4 embedded:1 whether:2 prevents:1 inside:1 gravitational:1 theoretical:1 isophote:1 ωm:1 minor:1 uk:1 distribution:6 similar:3 clear:4 puddu:1 strongly:1 metzler:2 required:1 ordered:1 contributors:1 af:1 defined:1 stronger:1 abstract:1 aj:4 influence:1 general:3 yang1:1 examine:1 periods:1 research:1 simulations:1 babul:1 distributions:2 constructed:2 again:1 mutual:1 discriminate:1 weakened:1 no:8 percent:3 field:10 other:3 dekel:3 digital:2 test:2 jenkins:1 t05:1 seljak:2 realize:1 picture:1 briefly:1 peebles:2 pronounced:1 models:1 astronomi:1 radially:2 important:3 flattened:1 massachusetts:1 paolillo:1 astronomy:2 structure:2 correlated:2 longer:1 typically:3 bcg:2 together:1 neighbouring:1 mass:5 time:3 debris:1 accreted:3 strings:1 |
0704.0675.txt |@word magnetically:4 consider:2 qian:1 magnetic:14 luminosities:2 results:3 gb:1 edu:3 winds:16 gm:4 torquing:1 rot:2 millisecond:3 inverse:1 zone:3 ergs:6 removal:1 quasi:2 outwards:1 th:16 under:1 case:1 bionta:1 presently:1 r10:14 continues:1 superluminally:1 electron:3 figs:1 affect:1 condition:1 ref:3 shock:8 occurs:1 lever:3 woosley:1 miralles:1 force:1 pms:11 centrifugal:1 approximation:1 morphology:1 rate:7 alfv:1 timescales:1 further:1 wilson:1 even:2 while:1 mv:1 poles:1 above:3 collapsar:1 net:1 thin:1 satisfy:1 outgoing:1 explosion:2 respectively:1 component:1 asymmetry:1 mev:2 threads:1 ωs:2 berkeley:4 arons:1 along:3 strong:1 change:1 ωa2:1 obtained:1 zanna:1 hydrostatic:1 action:1 proportionality:1 chang:1 via:1 useful:1 scales:2 apr:1 requiring:1 antineutrino:3 apj:7 neutrino:15 total:5 unit:2 readily:1 flavors:1 asymptotic:1 remains:2 positive:2 arms:1 metzger:2 m1:8 therefore:1 relativistic:9 taken:1 type:2 theoretical:1 more:2 successful:3 binding:2 enormous:1 excellent:1 cases:1 producing:1 must:3 me:1 majority:1 rotational:6 rν:21 equation:6 modified:1 erg:3 values:2 mp:1 ms:3 making:1 drops:2 example:1 attain:1 nearest:1 del:1 process:3 thermally:3 pons:1 νe:7 way:1 reviewing:1 occur:1 axis:1 turn:1 rather:1 write:1 brian:1 hot:2 flow:1 sin:2 φ2b:1 galactic:1 communicating:1 may:3 overall:1 after:8 different:1 corrections:1 modest:2 produce:2 mag:8 efficiently:1 stress:1 short:1 physical:1 light:1 cools:6 element:1 fraction:3 accelerated:1 so:3 sn:8 lν:5 order:1 wind:8 typical:5 indeed:1 over:2 ejecta:1 years:1 thermal:5 including:3 erot:5 kinetic:4 still:2 its:2 derive:1 rapidly:7 chosen:1 vth:2 φb:4 decreases:1 detected:1 latitude:2 pcf:4 easier:1 weber:1 eventually:1 non:3 motivated:1 thereby:1 material:1 scaling:2 effects:1 they:2 rotation:8 now:1 hall:3 possess:2 represents:3 fully:1 university:2 crudely:1 bursts:5 reasonable:1 luminosity:3 accompanied:1 mean:1 en:1 significantly:1 energy:19 grbs:2 astrophysical:1 todd:1 substantially:1 our:2 eq:1 emerges:1 dominates:2 rev:1 denotes:1 increase:1 dominated:4 rel:6 newly:1 dominate:2 evaluation:1 correct:1 scalings:1 theory:1 mω:5 free:1 quite:3 base:1 california:1 estimate:4 rises:2 allocation:1 pairs:1 transition:1 times:2 σνn:1 exponentially:1 hence:1 first:2 hoop:1 powerful:1 pulsar:1 thick:1 open:11 angular:3 given:4 necessarily:1 temperature:3 indicate:2 unknown:1 behaves:1 their:1 cooling:6 conservation:1 rates:1 too:1 calculations:4 precipitously:1 low:2 collapse:3 trapped:1 asymmetric:1 pns:48 sn1987a:1 favorable:1 than:5 princeton:3 likely:1 matter:2 sr:1 dynamo:1 quataert:4 gives:2 extracting:1 ρdr:1 dynamically:1 torque:2 substantial:2 manner:1 ray:6 acceleration:1 forced:2 conversion:1 angle:1 efficient:2 responsible:1 gravity:1 mechanism:2 arm:2 sciences:1 high:1 potential:2 combining:1 deposit:1 begin:1 normal:2 hirata:1 gν:2 neutrinos:4 most:2 significant:1 pair:1 cleared:1 measured:1 tν:2 considered:1 kh:4 steady:1 km:3 exp:3 velocity:1 physics:1 fact:1 atmosphere:2 show:2 rotating:3 purely:1 keywords:1 find:1 ratio:1 parameters:1 duncan:1 explain:2 outside:1 analytic:1 only:3 explicitly:1 factor:2 thompson:5 helmholtz:1 means:1 davis:1 familiar:1 freezing:1 cannot:2 during:2 dr:1 peyton:1 evolution:1 4πr:1 fields:4 arxiv:1 through:4 latitudinal:1 traverse:1 set:2 modulo:1 hν:2 declines:2 plausible:1 see:7 radius:8 enhanced:5 outward:2 review:1 definite:1 dipole:4 state:1 closed:6 between:3 affecting:1 subscript:1 jω:1 supernova:1 weak:1 however:3 efficiency:2 vanishing:1 rapid:2 τj:4 abruptly:1 concentrated:1 both:3 stages:1 last:1 outflows:3 region:1 heating:6 assure:1 cylindrical:1 receives:1 exceeds:2 argue:1 expression:1 finds:1 extractable:1 relevant:2 co:1 timescale:2 point:1 simple:1 ca:2 excess:1 period:1 height:1 dimensional:1 pole:1 cs:3 bν:7 capable:1 addition:1 poloidal:2 due:1 quickly:1 rν2:6 extraction:1 magnetized:3 much:2 deposited:1 progenitor:1 expected:1 ph:1 engine:1 releasing:1 observe:2 spin:3 sound:1 extracted:4 multi:1 supernovae:2 pacs:1 solid:1 value:1 near:1 corotate:1 promising:1 rotator:1 balance:1 extracts:1 cylinder:1 sizeable:1 reddy:1 equator:1 endowed:2 thus:4 surface:12 vr:5 itself:4 ivy:1 ρr:1 increased:1 capture:1 l52:8 verified:1 proto:10 perhaps:1 cross:2 epoch:4 split:1 relatively:2 neutron:4 used:1 context:1 somewhere:1 kelvin:1 numerical:3 drives:1 hand:1 driven:11 moving:1 bucciantini:1 totally:1 normalization:1 recent:1 magnetosphere:4 center:1 roughly:2 concrete:1 accreting:1 possesses:1 spherical:4 nucleosynthesis:1 just:1 less:1 being:1 generally:1 lorentz:1 axisymmetric:1 campbell:1 speed:3 neutrinosphere:1 4m1:1 loading:3 vφ:2 density:4 absorption:2 photons:1 conclude:2 seems:1 except:1 source:1 magnetar:8 constant:1 plasma:1 momentum:3 sonic:1 around:1 easily:1 lνe:7 cf:1 early:2 dipolar:1 birth:3 vacuum:1 press:1 using:1 τkh:6 generated:1 loss:10 rotate:1 reduces:1 pnss:6 accelerating:1 specific:1 flux:12 either:1 lose:1 become:2 exceed:1 because:8 some:1 bounce:2 born:4 escape:1 duration:2 neglecting:1 provided:1 scale:2 cavity:1 avoid:1 per:2 conservative:1 lattimer:1 efficiencies:1 provides:1 assuming:2 inserting:1 core:4 particular:1 equipartition:1 power:5 reaching:1 seconds:2 reach:1 agreement:1 stellar:2 pressure:1 bw:1 bp:4 although:3 relating:1 properties:2 out1:1 central:1 dependence:1 pν:1 distinct:1 carries:1 other:1 gamma:5 considerations:1 thermore:1 letters:1 mantle:1 prakash:1 into:1 magnetars:3 down:3 lies:1 right:1 references:1 primarily:3 lastly:1 log:1 few:1 assumed:1 support:1 initial:2 long:2 bp2:1 collimated:1 outflow:7 leconte:1 stars:1 astrophysics:1 sections:2 launching:2 form:2 but:3 astro:4 heat:1 mnras:1 line:1 considerable:1 ωy:20 pulsars:2 gravitational:3 until:1 limit:1 ωl:18 ωa:9 monopole:2 similar:2 detailed:2 viable:1 later:1 intersects:1 defined:1 recognize:1 abstract:1 fνe:2 resultant:1 periods:1 simulations:1 eliot:2 internal:2 defines:1 again:1 nj:1 compared:1 when:2 field:5 b15:6 grb:2 becomes:5 department:3 nr:4 optically:2 polar:2 star:3 models:2 durations:1 uniformly:1 develops:1 important:3 allowing:2 astronomy:1 structure:1 ago:1 lane:1 implies:1 longer:2 bcf:2 required:2 persistent:1 mass:20 bethe:1 time:7 nuclei:1 requires:2 initiating:1 once:1 |
0704.0676.txt |@word precise:1 abundances:1 consider:2 remarkable:1 arcminutes:1 caused:1 particular:1 results:6 existing:1 eds:4 markova:2 garching:1 tenuous:1 winds:1 remarkably:1 centers:1 relationships:1 whose:2 fronts:1 simon:1 wc:1 ız:3 send:1 protostars:1 environment:1 kaper:2 finally:1 caha:1 determinations:3 under:3 atlas:1 l133:1 indicating:1 2mass:2 ρa:1 very:16 pierce:1 unchen:1 simbad:1 rotational:1 lockman:2 summarized:1 mixing:1 affect:2 difference:2 clouds:1 presented:4 turns:1 shock:21 list:1 physics:1 large:4 heger:3 vector:2 asp:2 small:1 markov:1 refer:2 midplane:1 noted:1 tenths:1 upper:1 approximately:3 o6v:1 ten:1 l93:1 repolust:4 consistent:1 estimates:1 literature:2 past:2 go:1 likely:6 omez:1 weigelt:1 booth:1 spectrograph:1 further:2 estimated:7 hucht:1 spectral:12 transfer:1 errors:2 rate:1 sun:2 section:1 selected:1 bruijne:2 while:2 expressed:1 current:2 noriega:4 experiment:3 carey:1 above:2 new:4 3a:1 increasing:1 bonnell:3 processing:2 explosion:1 meynet:8 mechanisms:3 mccray:4 iraf:1 residual:5 jointly:1 reported:1 tracks:3 objects:1 hillier:2 directions:1 iras:3 strong:2 appears:2 change:1 alto:3 notably:1 instituto:1 naval:1 noticeable:1 pressure:1 institute:2 µl:8 studied:1 allows:4 bow:18 amount:1 resulting:1 milky:2 dickey:2 california:2 studies:2 der:1 pasquali:6 plotted:1 tasks:1 followed:1 ratios:1 classification:8 gredel:1 apr:1 ls:2 marked:2 apj:10 visible:2 addressed:1 aimed:1 support:3 extinction:4 univ:1 planck:1 cloud:1 ıa:1 use:4 takes:1 would:1 msx:7 positive:1 niii:3 intense:1 few:3 asser:2 kinematics:2 therefore:1 luminosity:1 taken:2 micron:1 astr:1 type:13 until:1 more:5 separated:1 flat:1 ejected:2 layer:2 zinnecker:2 apparent:1 emission:2 leonard:5 missile:1 blaauw:2 kinematical:1 nomad:3 apjs:2 heii:7 known:3 actual:3 producing:1 must:1 abundance:1 account:3 ucac2:1 ma:3 origins:1 science:4 supergiant:2 work:2 mi:3 longitude:1 theories:1 reproduce:1 suggestive:1 mv:3 obvious:1 temperatures:1 growing:1 woodward:1 ingredient:1 stanishev:1 andaluc:1 dedicated:1 hamburger:1 indicated:2 give:1 ambient:1 high:10 indicates:2 slit:1 usno:1 magnitudes:1 tan:1 crespo:4 axis:2 information:3 provide:1 kinemuchi:1 discussion:1 feature:1 hofman:1 regions:2 located:3 vanbeveren:5 absolute:2 preferable:1 sin:6 classify:1 circular:2 fp:1 simplicity:1 mas:6 galactic:15 binary:2 may:6 max:1 earlier:1 derived:2 containing:1 diagram:2 davis:1 catalog:5 plane:6 inst:1 mag:4 date:2 choice:1 data:4 types:2 poveda:2 stress:1 dynamical:9 effective:1 elmegreen:2 scheffler:2 approximation:1 ruiz:1 lines:5 fraction:1 spain:1 sect:3 fundamental:1 clusters:3 pleasure:1 subsequently:1 order:2 wind:9 typical:2 bull:1 evolutionary:4 zacharias:2 office:1 laboratory:1 indeed:1 pointed:1 mainly:1 schaller:1 interpreted:1 course:1 episodes:1 paper:1 through:2 motions:2 clumping:1 existence:3 facilitates:1 its:23 galaxy:2 tonantzintla:1 observational:1 chemical:1 kiminki:2 symmetry:1 fit:2 ratioed:1 masses:1 kluwer:1 vicinity:3 coordinates:1 actually:1 better:1 absence:1 conti:1 systems:1 latitude:1 mail:2 main:3 might:2 alter:1 them:2 good:1 rodighiero:1 greater:1 matches:2 bound:1 band:3 aniz:3 effects:3 they:3 cep:4 odlseder:3 rotation:3 now:1 discuss:1 association:5 february:1 several:1 products:2 even:1 cygnus:27 university:1 esteban:1 identified:4 explode:1 alem:1 magnitude:2 2a:1 2b:1 radial:2 2l:2 2m:1 photometry:6 side:1 characterized:1 warner:1 homogeneous:1 telescope:1 due:5 colder:1 energy:1 universities:1 motte:1 bolton:2 related:1 frequency:1 expect:1 entering:1 measure:1 separating:1 our:8 transitions:1 eq:6 special:1 out:3 shown:5 space:6 garmany:3 quality:1 since:2 rev:1 projected:1 research:3 content:1 walborn:3 shull:2 photometrically:1 constants:1 supports:2 red:1 shows:1 foundation:2 arizona:1 theory:1 interactions:2 favored:2 8a:2 ısica:1 rayet:1 possibility:2 standard:1 formation:5 org:1 estimate:10 companion:1 pup:4 massey:3 interaction:3 r0:1 derivation:1 argument:1 fitzpatrick:1 inferred:1 times:1 motion:12 place:1 massive:24 lte:1 unknown:1 consequence:2 projection:1 travel:2 grism:1 caii:1 first:4 origin:4 intervening:1 already:1 features:2 manuscript:1 aeronautics:2 opez:1 number:1 ob1:1 smaller:1 unspecified:1 spanish:1 thick:2 open:1 angular:2 size:1 given:7 herrero:2 temperature:6 strasbourg:1 introduction:1 leading:2 charbonnel:1 system:3 least:1 their:4 cooling:2 accretion:1 rates:1 listed:2 hypothetical:1 iau:1 ballistic:1 trend:1 signature:1 observations:11 urban:1 way:2 relationship:1 ratio:1 schwarzschild:1 oort:1 kirkpatrick:1 accurately:1 nearby:1 assumption:3 part:1 cyg:11 hks:1 on1:1 than:4 population:2 distance:14 bei:1 unfortunately:1 dgani:2 ipac:1 martins:3 grey:2 aims:1 project:2 arc:1 str:1 were:3 pasp:1 providing:2 steep:1 schneider:2 jet:1 springer:1 mpia:1 irwin:1 ram:1 mind:1 spectrum:5 peculiar:1 l31:1 case:2 unlikely:1 allen:2 clearly:4 karl:1 relatively:1 gives:1 angle:6 triggered:1 zero:1 depending:2 astronomie:2 latter:1 mechanism:1 note:2 extracted:1 potential:1 take:1 negligible:1 modulus:3 blue:2 towards:3 multiple:2 price:2 centro:1 most:10 involving:1 germany:2 bouret:2 organization:1 phase:1 acknowledgements:1 intrinsic:1 cause:1 observation:1 average:2 adopt:1 metal:1 kn:3 km:12 counted:1 ks:2 points:1 verlag:1 funded:2 uncertain:1 propulsion:1 velocity:15 normally:1 fact:1 slope:1 currently:2 heap:2 show:1 german:1 bromm:1 infrared:3 discovered:1 colors:1 cds:1 rough:1 find:2 decade:1 ground:1 arcmin:1 larson:1 execution:1 based:10 parameters:2 duncan:3 similarity:1 distributed:1 defense:1 should:1 surroundings:2 only:3 black:1 rich:2 factor:3 thompson:2 identification:3 circle:1 hispano:1 local:6 astronomical:1 merged:1 ser:2 do:4 dm:2 dominant:1 means:2 there:3 de:12 joint:1 observatory:2 words:1 3b:1 report:2 during:1 respectively:3 dr:1 reveal:1 evolution:2 continuum:1 loore:2 numerous:1 coalescence:1 arxiv:1 iraf1:1 remove:1 summary:1 investigate:1 vacca:2 torra:2 view:1 calar:3 bars:1 computed:1 exists:1 supporting:1 hγ:1 national:4 astrometry:1 comparable:1 hδ:1 maxplanck:1 ara:1 see:5 individual:3 radius:1 submitted:1 enhanced:1 operated:4 close:4 luminous:2 observed:4 lanz:2 page:9 detect:1 catalogs:1 berrington:1 subsequent:1 away:2 nebula:1 µm:7 wo:1 determined:1 hipparcos:3 between:9 probably:2 boundary:2 conditions:2 across:1 favor:2 µb:8 available:4 apell:3 stagnation:1 terms:1 aas:1 parental:2 importance:1 component:1 supernova:7 however:1 equals:1 spectroscopic:5 csic:1 derive:3 here:3 key:1 reipurth:1 thank:1 received:1 dates:1 toward:1 improved:1 reverse:2 many:1 region:4 conclusions:1 according:1 contract:2 puls:2 exceeds:1 requests:1 bever:1 expression:1 comer:13 among:3 extent:1 cm:1 sky:7 deviating:1 environments:1 coincidence:1 pole:3 filippis:1 path:1 polynomial:1 siiv:3 levine:1 runaway:21 considering:1 forms:1 combines:1 alvez:1 described:1 kinematic:1 buren:10 addition:1 mizuno:1 three:5 been:5 mart:1 pc:2 much:1 combined:1 progenitor:1 collected:1 ph:1 hardly:1 ak:2 fig:8 woosley:1 obtained:4 direction:7 adopted:6 corresponding:3 both:4 wycoff:1 quantities:3 sufficient:1 formed:3 gas:6 cos:16 tycho:2 locations:1 maps:1 dave:1 astron:2 diffuse:1 present:3 astrof:1 sound:1 exception:1 classifications:1 ahead:2 subtypes:1 reliable:1 ejection:9 aip:1 value:2 expelled:1 near:4 ar:1 neat:1 error:3 taking:1 real:1 detailed:2 uncertainty:6 orientation:1 almost:1 cafos:1 simulations:1 thus:5 non:2 surface:1 cluster:4 conf:2 vw:2 odyssey:1 limit:1 technology:2 jewitt:1 orbital:1 capture:1 different:5 thronson:1 generic:1 administration:2 same:4 any:2 member:1 units:1 survey:3 inc:1 composition:1 higher:2 evolve:1 satellite:2 used:2 imply:1 unlabeled:1 numerical:1 hand:3 isochrones:5 v2:1 moving:3 gies:2 niv:3 contribution:2 recent:2 kept:1 center:6 scenario:4 database:1 changes:1 preibisch:2 calibration:1 well:7 remain:1 analysis:2 peculiarities:1 calibrated:1 components:1 convenient:1 position:17 model:1 binaries:2 supergiants:1 left:1 noao:1 monet:1 quoted:1 less:1 being:1 captures:1 accurate:1 midcourse:3 obtain:2 acknowledge:1 sources:1 shape:1 shocked:1 northern:1 speed:1 previous:4 yr:7 candidate:1 density:9 absorption:5 wei:1 had:2 source:2 treatment:1 samples:1 wilkin:2 els:2 apart:1 heidelberg:1 details:1 associations:1 egan:1 kobulnicky:1 around:2 22b:2 bands:5 showing:1 papers:1 possible:2 spanned:1 early:6 possibly:3 increases:2 netherlands:1 makes:1 voigt:1 press:3 using:3 accepted:1 fryer:1 prominent:3 atmospheres:1 loss:4 hoogerwerf:7 shaped:1 velocities:5 byproduct:1 gaume:1 always:1 become:2 reduced:1 therein:2 omico:1 densest:1 methods:1 sequence:2 staff:1 plausible:1 some:2 back:2 born:2 strongest:1 ejections:1 acad:1 examples:1 respect:8 images:5 imager:1 absent:1 provided:1 vol:1 scale:1 dense:3 lead:1 keil:1 broad:1 bedding:1 measurements:1 comments:1 kpc:5 donder:2 assuming:4 eso:3 o5:2 o4:3 ob2:36 either:3 bd:41 core:2 location:2 each:2 aj:7 agreement:1 constructive:1 stellar:16 hǫ:1 onigstuhl:1 symp:1 although:3 found:3 tokunaga:2 zeeuw:2 rensbergen:4 properties:3 russell:1 comparison:3 about:1 census:1 central:3 carried:1 increasingly:1 package:1 tracing:1 sternwarte:1 basis:1 ob:5 o:8 langer:4 range:1 wolf:1 greatly:1 publ:1 obs:2 massachusetts:1 balega:1 bate:2 hubeny:1 burning:1 presence:2 previously:2 into:3 within:1 interstellar:11 22a:2 dataset:1 cox:1 because:1 references:3 determine:2 kuchar:1 refined:1 france:1 monson:1 significantly:2 uncertainties:2 van:16 additional:1 her:2 measured:1 astrometric:2 initial:3 approximate:1 overestimate:1 encounters:1 low:2 stars:31 ed:1 astrophysics:1 analyze:1 was:11 hei:1 assumes:1 calibrations:4 medium:9 north:4 form:2 hr:1 forming:2 bol:1 but:3 astro:1 expected:2 neutral:1 hi:1 segregation:1 solar:7 larger:1 mnras:1 magellanic:2 line:1 true:1 birthplace:1 schaerer:1 blanketing:1 bontemps:1 made:2 builds:1 places:1 whether:1 up:2 us:3 ur:2 placed:1 below:1 astrophysical:1 those:4 nasa:2 distribution:1 similar:5 clear:1 reddened:2 b1:1 strongly:1 associated:2 introducing:1 defined:2 abstract:1 myr:3 life:1 evidence:1 proper:10 referee:1 right:1 planets:1 wavelength:1 lifetime:1 moves:2 archive:1 physical:1 nh:2 compared:2 brighter:1 dotted:1 no:7 image:1 when:2 nal:1 reality:1 field:1 other:6 neighbourhood:1 spatial:7 5r0:1 concerning:1 star:41 models:3 time:6 includes:2 metallicity:5 important:1 allowing:2 hanson:3 astronomy:2 unless:1 sides:1 exposure:1 offprint:1 maeder:6 values:6 age:10 curve:2 orbit:1 together:2 having:1 runaways:4 warm:2 mass:16 ortiz:1 institut:2 far:1 8µm:1 resolution:4 original:2 |
0704.0677.txt |@word limited:1 code:2 sci:2 astron:18 focus:1 spectrograms:1 month:1 although:1 roy:1 systemic:3 heliocentric:2 suspected:1 follow:1 disk:2 piskunov:2 layers:4 whose:1 inverse:1 lamers:3 referring:1 vexp:1 decin:1 swan:7 brault:1 pierce:1 removal:1 presents:2 finally:2 program:2 present:1 th:1 under:1 atlas:21 te:1 spec:1 applied:1 alcolea:1 supported:2 synchronized:1 far:3 conditions:1 results:2 every:2 figs:1 mixing:1 uncertain:1 gillet:3 difference:1 mcclure:1 categories:1 entire:2 kinematic:1 level:3 positions:4 shock:2 list:2 dib:1 sri:1 differential:2 minimal:1 mnii:5 arkhyz:1 small:3 kitt:1 concluded:4 upper:2 smaller:1 trend:2 consistent:1 estimates:1 direct:2 surrounding:2 second:3 noise:1 pasp:1 spectrograph:6 observ:4 further:1 canonical:2 spectral:26 established:1 errors:2 appear:1 fine:1 section:4 selected:4 brief:1 find:1 current:1 bipolar:1 version:2 above:9 new:3 nes:18 meixner:1 shocks:1 slicer:1 full:2 led:1 chose:1 degree:1 mem:1 respectively:5 even:1 component:11 residual:5 here:4 atoms:2 hours:1 asymmetry:2 objects:15 operating:1 groups:1 excess:2 represented:1 iras:9 along:1 bakker:16 respect:1 change:2 obtained:9 great:1 kurucz:1 shift:2 study:3 studied:2 allows:2 commonly:1 adopt:1 significantly:1 p2:6 periodic:1 products:3 published:3 usually:2 complicated:1 hors:1 fourier:1 studies:2 control:2 via:1 lasts:1 overabundance:1 tau:4 apr:1 explained:1 volk:1 highly:2 visible:2 anomalies:3 outer:1 use:9 reflected:1 russell:1 photospheric:2 remains:1 niii:4 next:1 spectrogram:1 vol:2 therefore:4 distortions:1 taken:4 associated:3 type:12 minor:1 more:3 mauron:3 rich:1 envelope:7 emission:12 award:1 absorptions:10 primarily:1 depth:2 particular:2 known:3 given:1 must:3 sample:1 account:1 graphic:1 recall:1 supergiant:6 averaged:1 modified:1 measures:1 ferro:1 remain:1 values:7 evolved:1 universe:1 following:1 example:4 numbers:1 protoplanetary:1 ions:2 weaker:3 figure:9 give:2 process:3 expanding:1 near:1 high:15 indicates:4 performed:5 allowed:3 sharp:2 p15:1 hydrogen:2 longest:1 axis:2 needs:1 monitoring:2 ocker:2 rather:2 feature:3 trammell:2 chemical:6 located:1 varies:2 numerous:2 criterion:1 fourth:1 es:5 sii:7 ermakov:1 profile:13 galactic:3 description:1 undergoing:1 may:9 unidentified:1 immersed:1 earlier:2 containing:3 collection:2 diagram:1 plane:1 disproved:1 date:7 wave:1 data:16 types:1 short:3 natural:1 dynamical:2 pulsations:5 light:1 sp:2 lines:49 element:31 ones:1 metalpoor:1 allow:2 correlation:3 wing:3 wind:6 typical:4 wavelengths:1 bull:1 superimposing:1 midas:1 laboratory:1 over:8 move:1 vary:1 facilitated:1 nii:8 years:7 stability:2 report:1 episodes:1 paper:3 motions:3 signs:3 mentioned:2 cold:1 its:9 crii:62 observational:1 rostov:2 position:4 group:2 wallace:1 dinerstein:1 temporal:4 hot:2 coordinates:1 circumstellar:11 better:1 absence:1 html:2 fig:11 constitutes:1 latitude:2 main:5 into:1 confidently:2 yi:1 them:3 good:1 combination:1 descendants:1 fragment:3 similar:2 kupka:1 elliptical:1 processes:1 ppn:5 band:1 p12:1 superhigh:2 effects:1 they:3 half:5 p18:1 p19:1 now:2 discuss:1 february:1 ryabchikova:1 galazutdinov:1 oxygen:1 publication:1 always:1 university:3 presented:1 identified:6 hinkle:1 2d:1 sufficiently:1 radial:40 found:11 soc:1 referred:1 heavy:1 development:1 sb1:1 mni:28 telescope:5 hundred:1 energy:2 used:7 astrophysical:11 undertake:1 measure:1 wavelength:13 beyond:1 extract:1 special:9 out:1 ru:2 rv:4 fundamentally:1 space:1 gradient:1 quality:2 furthermore:1 surrounded:1 rev:1 research:3 produced:1 illustrate:2 cause:2 waters:6 red:3 shows:7 foundation:2 classification:1 doppler:1 galaxies:1 differ:3 standard:2 clarify:1 base:2 formation:1 brightest:2 members:1 companion:2 generate:1 additional:2 her:1 r2:23 r3:25 widths:1 could:1 transition:1 cosmic:1 days:3 motion:2 benedict:1 produce:2 hence:3 onto:1 caii:4 first:4 origin:1 features:17 reveals:1 variables:1 supplement:2 number:3 peculiarity:2 methodological:1 electronic:2 angular:1 size:1 passes:2 unexplained:1 nebulae:3 likely:1 introduction:1 revealed:3 top:1 yii:44 system:5 least:1 their:10 ionospheric:1 intermediate:1 observations:9 1k:2 molecular:6 fokin:1 ranging:1 gives:7 shifted:1 shell:3 companions:3 mostly:1 ratio:3 asymmetric:3 academy:9 relative:1 acquire:1 took:1 lists:1 optical:11 cyg:3 manifestation:1 believe:1 representing:1 than:6 peaked:1 wide:2 kind:1 observatory:10 determines:1 unfortunately:1 showed:3 dredge:1 depressed:1 double:1 zero:3 preparation:1 matter:2 individual:5 intensities:8 attention:1 were:4 naturally:1 russia:2 contr:1 exhibit:9 binarity:4 spectra:43 sao:2 remained:1 rao:1 unchanged:1 ms:1 spectrum:38 waelkens:4 ras:1 close:1 seen:1 confirms:1 any:3 bujarrabal:2 studying:1 latter:1 nucleosynthesis:1 mechanism:1 note:3 sciences:10 take:1 photosphere:3 so:3 accuracy:2 echelle:7 differences:7 goswami:1 fundamental:1 trace:1 normal:1 object:6 molecule:4 paid:1 depths:5 most:4 regular:2 eight:3 plan:1 successive:1 phase:3 measured:8 class:2 conspicuous:1 don:1 observation:1 dwarf:1 ki:4 nasmyth:1 neutral:2 km:14 order:1 part:6 subsequent:2 velocity:37 blend:1 bulletin:1 fact:3 criteria:2 planetary:2 atmosphere:9 phenomenon:1 intensity:4 show:5 kwok:1 blended:1 authors:8 furenlid:1 multicomponent:1 mnras:5 bright:2 radio:2 inconsistent:1 astrophys:19 baii:16 font:1 d2:2 agrees:3 symmetric:1 giant:1 based:6 proposed:1 parameters:1 much:2 ueta:1 state:3 peculiar:3 spectrographs:4 being:1 only:11 unable:1 deepest:1 molecules:4 equipped:1 employed:1 pointed:1 columns:6 hertzsprung:1 do:1 hit:1 invoke:1 means:1 dependent:1 mgi:10 foremost:1 ssl:2 polarized:1 listed:2 supergiants:2 klochkova:55 interpreted:1 barlow:4 secondary:1 reveal:4 evolution:2 continuum:4 luminosity:3 arxiv:1 median:1 yield:2 consisting:1 intervals:1 cri:10 inferred:8 preserve:1 set:6 ser:1 hβ:5 hγ:1 national:1 hα:22 hδ:1 observed:5 telluric:2 see:3 sed:2 slanted:1 p20:1 fail:1 sporadic:1 ebre:7 points:2 project:1 mgii:6 nuclear:1 civilian:1 nebula:4 cai:24 mayor:1 µm:2 outside:1 determined:4 identification:3 between:8 contrary:1 neither:2 approach:1 available:6 variability:14 triplet:1 terms:1 amplitude:4 nature:3 importance:2 p25:1 ppne:18 weak:6 however:7 tiii:107 spectroscopic:7 white:1 hypothesis:1 no:20 livingston:1 distinguish:1 carbon:4 vald:2 problem:1 ads:1 both:5 dates:3 parentheses:1 limits:1 many:2 region:8 barely:2 escape:1 according:3 against:1 agree:2 propagation:1 connection:1 manifestations:1 figures:1 context:1 coi:4 l25:1 crdf:1 comment:1 among:4 ci:56 ch:3 co:2 cn:4 siii:9 conclude:3 simple:1 narrower:1 period:6 height:1 dimensional:1 analyzed:5 exhibits:3 nonspherical:1 blending:1 constant:3 forms:3 radialvelocity:1 strong:5 leads:1 corroborates:1 addition:5 observing:1 create:1 due:8 been:6 basis:1 blueshifted:1 reduction:2 describes:2 combined:1 interest:1 judging:2 ph:1 crawford:4 systems:1 atlases:1 lived:1 corresponding:4 deeper:1 thousand:2 precision:1 observe:1 determination:1 representative:1 systematic:1 nizhnij:1 trams:2 c2:101 former:1 those:9 case:5 szczerba:3 p1:2 atmospheric:1 identifications:2 reliable:2 ejection:2 profiles:21 promotes:1 while:1 behavior:7 situation:1 taking:2 mexico:1 almost:2 averaging:2 ir:7 thus:1 surface:1 equal:3 ii:1 vr:81 itself:1 comparative:1 orbital:6 binary:7 different:15 stimulates:1 perform:4 acknowledgments:1 make:1 belong:3 radiation:1 same:8 orders:1 princeton:2 shifts:2 complex:6 roland:1 largest:1 proved:1 several:11 composition:4 status:1 extended:6 http:2 blue:2 disagree:1 effect:1 asymptotic:1 driven:1 ion:1 kii:1 uses:1 necessity:1 dust:2 recent:1 lower:4 task:3 database:1 makes:1 variety:1 well:5 analysis:8 peculiarities:2 temperature:2 components:14 very:4 ccd:2 binaries:2 possesses:1 researchers:1 subgroup:1 confirm:1 multiplets:1 zhao:1 quoted:1 less:2 increasingly:1 nd:1 accurate:1 p17:1 detail:1 shape:3 unclear:1 identify:2 atomic:3 spherically:1 multiplet:1 spectrophotometric:1 previous:1 tables:4 preprint:7 family:1 candidate:1 conclusions:2 absorption:10 point:1 sky:1 confirmed:1 source:6 lett:2 extensive:2 remaining:1 match:1 tii:17 photometric:6 definitive:1 depends:1 bands:13 boundaries:1 measurement:1 comparing:2 increases:1 indicative:6 using:1 unique:1 moreover:1 wings:2 apart:1 atmospheres:5 maybe:1 pertinent:1 like:3 lost:1 systematically:1 signal:1 velocities:23 specific:3 informative:1 history:1 yields:1 either:3 night:1 become:1 overtone:1 accessible:1 www:2 because:3 methods:1 classical:1 sequence:1 some:3 afgl:1 strongest:2 table:14 images:1 infall:1 scales:1 basic:1 scale:3 bottom:1 demonstrates:1 annu:1 measurements:10 recorded:1 per:45 when:4 oudmaijer:4 panchuk:9 simbad:1 pattern:4 fragments:4 chentsov:1 demonstrated:1 bd:1 core:2 who:1 ba:1 indicated:1 bl:2 each:5 expansion:2 stellar:6 lamps:1 hst:2 accompanied:1 plots:1 post:11 p27:1 properties:1 stage:3 comparison:4 about:4 central:5 would:2 oi:16 oh:1 column:5 feii:134 months:2 anomalous:3 recognized:1 dibs:1 r1:32 presidium:1 nat:3 winckel:5 mean:3 obs:2 vi:3 astronomical:1 presence:5 owe:1 lambert:2 image:1 within:3 interstellar:8 three:4 references:1 56m:1 determine:2 contrib:2 fei:327 vii:27 often:3 liege:1 van:5 log:1 possible:1 shells:1 extremely:1 question:1 planesas:1 long:2 outflow:5 low:4 stars:18 slopes:1 analyze:3 was:3 hei:1 synthesis:2 head:1 medium:2 complete:2 form:8 hr:6 hq:2 but:9 astro:1 repeated:1 hi:2 solar:5 hm:1 russian:10 line:29 highest:2 hd:98 absent:1 made:4 portions:1 evident:3 interiors:1 variations:19 up:7 us:4 tucson:1 gaps:1 emissions:2 spectroscopy:46 lynx:9 demonstrate:2 distribution:1 minutes:1 average:1 detailed:7 later:2 hotter:1 moore:3 defined:2 certain:1 abstract:1 mirror:1 metals:1 evidence:2 single:1 ar:1 asynchronous:1 periods:1 our:15 work:3 physical:2 ni:6 compared:3 calibration:1 na:2 whereas:3 nai:16 generally:1 leftward:1 barth:5 p14:1 field:3 other:11 compares:1 details:2 branch:2 papers:1 scii:25 techn:1 concerning:1 dishoeck:1 optically:1 briefly:1 elements:5 star:36 excitation:4 separate:2 models:1 databases:1 gradations:1 shown:1 variation:1 includes:1 metallicity:1 important:1 peak:1 variable:7 structure:4 goodrich:1 independently:1 longer:1 interval:4 agb:13 portion:1 nasa:1 mass:8 time:7 cores:2 resolution:16 rep:3 |
0704.0678.txt |@word partial:1 consider:5 switched:1 rev:14 green:1 amplifier:1 idealised:2 yellow:1 existing:1 four:4 continual:1 scalar:1 computation:2 edu:1 research:1 reˆ:1 causes:1 poorly:1 feeding:2 knill:1 subjected:1 deterministic:1 finally:6 squeezing:2 preserved:1 th:1 under:1 include:2 resources:1 ingredient:1 spekkens:1 amplitudes:1 string:1 orthogonal:3 far:1 account:1 results:4 manipulated:2 every:4 sonja:1 summarized:1 mixing:1 affect:2 difference:5 exact:1 condition:1 mathis:1 splitter:21 beating:3 num:1 cable:2 altering:2 ref:2 notes:1 proposals:3 ryan:1 correct:1 large:6 o1:1 klm:1 small:4 shows:1 optics:9 challenge:1 open:1 smaller:1 direct:2 sign:1 approximation:2 rate:2 cost:2 cosq:1 manipulating:1 dynamics:2 implemented:2 port:7 linear:12 will:1 what:1 nonlinear:2 sum:1 favour:1 debate:1 current:2 ˆb:3 experiment:4 steinberg:1 increasing:3 method:4 gyroscope:1 coefficient:2 magnetometry:1 processing:1 lee:2 reverses:1 exchange:1 respectively:3 burnett:1 component:1 here:5 atoms:2 localisation:3 desired:2 cos2:1 address:2 represented:1 path:3 obtained:2 convert:2 rigorously:1 institute:2 shift:3 study:2 studied:1 commonly:2 prior:2 describing:1 resulting:1 walther:1 suggestion:1 action:3 implement:1 suitable:1 makes:2 numerical:2 corrects:1 composed:1 rotator:1 absorbers:1 divide:1 aˇsek:1 scales:6 apr:1 inducing:1 shifters:5 outcomes:6 improbable:1 decrease:1 saleh:1 condensates:2 counts:2 total:15 sensors:1 linearly:1 readily:1 use:1 superpositions:1 would:3 army:1 probabilities:3 positive:1 laflamme:1 negative:1 next:5 classically:2 depicted:5 noting:1 therefore:2 ψl:4 encode:1 jonathan:1 achieving:1 more:4 advance:1 outputs:3 operators:3 starting:1 corrected:2 odinger:7 normalized:1 proceed:1 particular:3 known:1 cases:1 iii:8 must:4 boixo:1 kraus:1 none:2 valued:1 kasai:1 science:2 setup:3 work:2 oscillator:1 measures:1 cat:25 labeled:5 fock:5 values:7 concepts:1 following:2 making:3 averages:1 example:7 challenging:1 lπ:8 process:6 choice:1 share:1 purposes:2 pro:1 high:5 performed:7 degenerate:1 tan:1 occur:1 absolute:1 information:4 notation:3 disruptive:1 rather:2 verify:2 six:1 feature:1 orthogonality:1 how:3 varies:1 ψg:2 oˆ:1 instead:1 axis:1 parameter:4 sin:2 rπ:2 inputs:1 intended:1 may:4 earlier:2 derived:2 applications:5 independent:3 mesh:1 improving:1 baton:1 response:1 efficiently:4 iθj:1 si2:1 si1:1 transitive:1 physical:1 outline:2 third:5 diffraction:1 whenever:4 light:6 explicit:1 yielding:1 provide:2 algorithms:1 fundamental:3 decreasing:2 representation:2 subsequently:1 typical:2 operations:2 feed:7 acts:3 reversal:1 office:2 produces:1 developed:1 over:4 move:1 displayed:1 cols:1 produced:2 experiments:3 through:2 lasers:1 existence:1 fidelity:8 its:4 before:1 derive:1 symmetry:2 acknowledge:1 procedures:2 better:2 detected:7 according:3 itano:1 fig:10 inspecting:1 might:4 incorporate:1 macroscopic:1 non:4 ikθ:1 combination:1 propose:2 material:1 heinzen:1 processes:2 scaling:5 effects:2 they:5 half:4 rotation:1 now:5 s0:1 maintaining:1 outweigh:1 going:1 finite:1 2s:1 university:1 requires:1 labeling:1 possibilities:1 applied:1 mode:24 each:8 found:2 2n:14 quarter:1 ports:3 glasser:1 referred:1 schemes:2 transform:2 populated:1 generation:5 there:1 gaussian:2 constitute:1 deterministically:1 extended:1 expect:1 measurement:17 quantum:28 our:20 lithography:2 beyond:1 eq:7 hugo:1 giovannetti:2 shown:3 reducing:1 watanabe:1 quality:1 since:2 interference:2 denotes:3 acting:1 investigation:1 adapt:1 impart:1 size:1 suffices:2 occurs:1 excess:1 predicted:1 after:3 turning:1 theory:1 localization:2 differ:1 possibility:1 standard:3 attributed:2 sanders:2 imaging:2 detecting:1 remainder:1 generate:2 milburn:1 definition:1 speedups:1 mølmer:1 english:1 inspection:1 could:1 transition:1 horace:1 times:1 n00n:3 length:2 exponentially:3 circuit:43 arccos:3 hence:6 onto:1 first:10 origin:1 already:1 probability:7 relate:1 wave:2 number:35 condense:1 bartlett:2 choose:1 caves:1 another:2 knight:2 electronic:1 angular:1 engineer:1 given:4 destructive:1 asymptotic:1 achieved:1 system:1 relations:1 fiction:1 their:1 intermediate:1 too:3 scheme:4 final:5 speaking:1 exploring:1 imperfect:1 liang:1 ratio:2 exactly:1 serve:1 yield:1 immediate:1 optical:15 shifter:2 authors:1 translation:1 than:9 specify:1 modes:27 relative:36 perfectly:1 critically:1 effective:1 taken:1 approximations:1 reinforce:1 annihilation:2 matter:1 states:41 determined:2 intensities:7 amplitude:1 were:2 ber:1 outcome:3 minus:7 romalis:1 sult:1 ψab:4 measure:2 say:1 rau:1 further:2 seen:2 any:1 lie:1 conversion:1 zero:1 efficient:1 convenient:2 trapped:1 note:2 ideal:2 square:2 generalized:1 analogy:1 online:1 finding:1 so:6 techniques:3 analogs:1 adjusting:1 heisenberg:1 begin:1 broglie:2 asin:2 correlation:2 prevedel:1 fails:1 thank:1 occurred:1 phase:61 acknowledgements:1 measured:2 takes:2 nonlinearity:1 considered:2 average:4 later:2 detectors:1 principle:1 exp:20 mechanical:1 resch:1 typically:2 fact:1 precise:1 optimal:1 shot:1 show:1 text:1 transmissive:1 least:1 purely:1 attempts:1 relation:1 lloyd:2 rouge:1 label:2 thirds:2 find:6 principal:4 multichannel:1 photodetector:2 based:6 popescu:1 implementation:1 proportion:1 should:2 only:7 explicitly:1 generators:3 factor:2 attained:1 constant:1 population:4 local:1 achieve:3 do:3 dl:5 mixture:1 gains:1 localizing:1 beat:1 beams:3 connections:1 de:2 overall:3 degradation:1 beam:27 ones:2 closely:1 clarify:1 dr:6 schrodinger:1 lossless:1 stability:1 regarding:2 exhibiting:1 resource:1 fields:2 arxiv:1 microscopy:2 consisting:3 investigate:2 lsu:1 common:1 photodetectors:8 analytical:1 creates:1 fixed:3 require:1 view:1 reveals:1 requirement:1 set:1 computed:1 reference:5 ancillae:3 sensitivity:1 correlations:17 condensed:1 topics:1 transferred:1 detection:7 intensity:8 actively:1 result:3 enhanced:2 discussions:1 close:2 kok:3 jeong:1 subject:3 flammia:1 phases:4 runs:2 record:2 ways:1 subsequent:1 currently:1 ralph:1 tend:1 symmetric:2 qubits:2 state:60 between:8 invariant:1 αj:2 approach:3 across:1 speed:1 available:1 terms:1 vertical:1 nature:5 initially:1 combining:1 however:8 jr:1 implementing:1 incident:1 extent:1 article:1 distribution:2 improve:1 suggested:2 both:4 cos:10 limits:4 reported:1 many:3 taking:1 uncertainty:3 equal:5 against:2 april:1 dated:1 context:1 behaviour:1 estimation:1 0n:1 regarded:1 experimental:2 allowance:1 ck:1 splitters:6 cn:2 supply:1 simple:5 asymptotically:1 corresponds:4 height:1 active:1 exploit:1 configured:1 losses:1 polynomial:1 normalisation:2 cq:1 superselection:3 second:2 considering:1 kominis:1 described:2 transformations:1 cavities:1 basis:2 atomic:2 three:4 been:11 devise:1 much:2 combined:4 interest:4 basic:1 expected:4 degrees:1 ph:5 anomalously:1 louisiana:1 correction:1 define:2 adapting:1 generating:1 enable:1 corresponding:2 insulator:1 0s:1 suppress:1 sufficient:1 coherence:3 photon:33 precision:2 coherent:3 external:2 denote:4 spin:1 case:9 multi:2 laser:2 exponential:1 engineering:2 value:7 remaining:4 aim:1 while:4 suppose:2 evaluating:2 applies:1 squeezed:1 situation:2 maccone:2 mitchell:1 elaborate:1 procedure:6 reflectance:2 unitary:3 induced:3 coupled:1 00n:27 systems:1 conditioned:3 ii:14 good:2 mott:1 anticipating:1 dual:3 zhang:1 different:4 bollinger:1 metrology:4 multiphoton:1 proto:1 estimate:1 suggest:1 make:2 indistinguishable:1 same:5 wherein:1 shifts:3 unity:1 complex:1 quant:5 geremia:1 several:1 events:1 higher:2 magnetometer:1 evolve:2 used:4 see:3 i1:3 restraint:1 i2:3 effect:1 counterparts:1 hand:1 moving:1 entanglement:7 yuan:1 implements:3 lower:1 weakly:1 schr:7 whereby:2 scenario:2 expression:1 no:2 well:7 roughly:1 analysis:8 evolves:4 thought:4 without:1 components:11 lim:1 position:1 parametric:2 left:4 transmittance:2 teich:1 rudolph:4 aborted:1 proposed:3 less:1 being:2 obtain:1 photonic:1 sources:3 identify:4 transforms:2 useful:2 alternative:2 scattering:1 previous:4 like:2 monitored:1 generator:10 application:1 absorption:1 photons:26 point:2 mathematically:2 source:9 other:3 transformed:1 lett:4 problematic:1 relevance:1 input:20 iσ:1 mod:1 transformation:8 iχ:2 iφ:1 opt:1 iθ:2 iλ:1 increased:1 depends:3 rules:1 couple:2 normalise:1 possible:7 dark:2 ancillary:2 five:1 entangled:6 vacuum:4 using:11 modifying:1 color:2 apart:1 loss:1 necessary:4 lost:3 success:2 follows:3 twin:2 noted:1 specific:1 detections:10 yields:1 either:2 exploiting:1 output:13 essential:1 mathematical:1 allred:1 because:1 methods:1 classical:6 sequence:2 maintained:1 conditional:2 some:2 back:2 supplementary:3 examples:1 mirror:1 ups:5 generates:4 happens:1 discarded:2 proceeding:1 cavity:4 leak:1 measurements:5 extensively:1 overlap:1 depletion:1 assuming:1 propagating:2 bose:2 prob:2 demonstrated:3 illustrate:1 noise:2 run:1 obey:1 power:1 reaching:1 equivalent:2 additively:1 agreement:1 step:1 binomial:3 dunningham:1 eiφ:1 plots:1 super:2 entirely:1 stage:4 comparison:1 central:1 oj:1 freedom:1 nondeterministically:1 o:1 simulation:1 practical:1 range:6 plus:7 act:1 mixed:1 ou:1 2k:1 rendered:1 wineland:1 into:8 photodetection:7 numerically:2 predictions:2 fidelities:6 device:1 right:3 references:3 einstein:1 frames:4 fiur:1 conceptually:1 bosonic:2 approximately:2 often:1 terminated:1 rely:1 statistics:2 additional:7 leaks:1 normalised:1 assumed:4 support:1 initial:3 question:1 approximate:1 specifically:1 start:3 cats:2 low:2 fraction:5 forward:9 lundeen:1 translate:2 was:2 assumes:1 iˆ:1 function:3 creation:2 complete:3 form:5 phenomena:2 registered:4 minimise:1 denoting:2 but:3 sophisticated:1 failure:2 correlated:2 atom:1 helpful:2 technologies:2 removed:3 faster:1 normalising:1 made:3 compute:1 full:1 interferometer:1 circuits:6 pn:1 up:1 theoretical:1 crystal:1 frequency:3 limit:6 fluctuations:1 problem:1 stages:1 similar:2 called:1 strongly:2 adopt:3 associated:1 play:1 computing:5 defined:10 packets:1 describe:1 general:2 single:2 rule:1 dθ:2 wavelength:3 zou:1 ing:1 check:1 regime:1 variety:3 when:20 dowling:4 field:2 setting:1 role:1 department:1 eiθ:1 conclusion:1 poor:1 elements:2 superposition:5 ubs:16 preceding:1 interferometric:3 generated:13 important:2 terry:1 variable:4 transfers:1 maximally:1 astronomy:1 building:1 condensation:2 individual:1 longer:2 assume:5 physics:3 required:1 resolving:4 together:2 time:3 resolution:1 having:1 degrade:1 |
0704.0679.txt |@word homomorphism:1 four:13 consists:5 analiz:1 whose:14 quadruple:1 γi:4 under:4 aux:1 coeffcients:1 rise:1 intriguing:1 every:4 dubrovin:1 solution:82 vector:2 math:27 indices:5 ups:1 degeneracy:2 consistent:1 direct:3 α2n:5 surrounding:1 second:17 even:3 established:2 en:1 above:4 neat:1 coefficient:3 κi:26 κj:26 κk:25 aten:1 equals:1 here:10 represented:10 path:1 logarithmic:3 obtained:10 rigorously:1 study:6 approaches:1 suitable:1 settled:3 classification:5 total:2 univ:1 linearly:2 would:3 tabulated:1 call:1 therefore:5 care:1 type:68 fragmentary:1 qz2:1 adjacency:5 berlin:1 dessins:1 andreev:1 must:19 springer:1 quartic:10 work:3 ere:1 root:31 example:32 mz:39 tritangent:2 give:4 preserving:2 indicates:1 caution:1 cartan:2 degenerate:4 counterpart:1 thing:2 verify:1 takebe:1 how:2 nontrivial:2 ordinary:3 classify:1 description:1 replacing:2 earlier:1 diagram:12 parallel:1 types:10 infinte:1 stratifications:1 order:14 operations:1 origin:17 over:9 satisfied:8 london:2 japan:4 satisfies:2 enfants:1 before:1 fix:13 eventually:1 them:4 combination:1 xj2:1 they:6 singularity:8 eigenvalue:1 classified:2 asymptotique:1 properness:1 each:21 d41:1 side:1 mean:2 lifted:10 series:11 combining:1 jimbo:2 gradient:1 restricted:2 rz:4 multiply:1 rh:16 linear:9 strata:22 standard:3 admits:10 detecting:1 publ:2 r0:5 r1:3 r2:4 pfaff:1 onto:1 already:1 conjugacy:2 dynkin:12 rank:1 ℓk:3 ℓj:37 ℓi:1 another:3 rewritten:1 similarly:9 top:2 observations:1 centered:1 finitely:4 zero:2 classes:1 derived:1 rewrite:1 manner:6 seen:1 convenient:2 latter:9 thorough:1 2εj:2 2εk:2 2εi:2 though:1 object:1 riccati:62 regular:2 phase:4 doi:1 observation:1 professor:1 vertices:1 points:74 principle:2 sum:9 labels:5 solutions:105 substituting:23 d4:94 d2:1 d0:1 situations:1 theme:1 summarizing:3 constant:2 do:7 dk:2 klein:4 di:5 df:1 de:8 dz:7 new:1 du:1 dp:1 dq:3 angers:1 die:1 covering:4 θj2:1 observed:1 depends:1 w4:4 w3:3 w2:3 w1:3 w0:5 initiales:1 subject:1 birational:1 exponent:4 symmetric:3 approach:1 terms:22 nature:1 modify:1 restricting:1 wk:1 however:5 wi:3 gτ:1 essentially:3 une:1 argue:1 character:2 polynomial:8 diff:1 2nt:1 commutative:5 union:10 three:15 been:3 much:1 basic:3 expected:1 ann:4 θj:9 θk:9 ergodic:2 θi:5 families:6 iµ:6 confinement:1 kitaev:2 applied:1 transformation:28 euclidean:1 suppose:1 property:7 leaves:1 mistake:1 a21:1 a22:1 a23:1 a24:1 ii:11 need:1 ij:2 cone:1 subdiagram:1 make:5 brieskorn:2 intersecting:2 complex:3 accumulating:2 grows:1 independent:3 i1:3 i3:2 i2:11 i4:2 hand:10 prescribed:1 fourier:1 changes:1 except:2 easily:2 left:7 just:9 newton:14 identify:2 transforms:4 yes:2 yet:3 previous:1 adding:3 infinitely:1 had:1 belongs:2 easy:2 possible:9 unique:12 g32:3 appearing:1 permuting:5 arbitrary:2 componentwise:1 boalch:2 right:6 truncated:2 sends:2 fot:1 hirzebruch:2 bottom:1 θk2:1 properties:1 proceed:1 eεi:3 o:4 eight:2 slightly:2 primitive:7 transcendents:2 statements:1 bound:5 combine:9 lies:6 acad:1 loday:1 nodal:1 support:1 initial:3 transform:11 class:1 way:2 gin:1 form:2 converse:1 forgetful:1 encodes:1 true:2 gi2:4 compactification:2 attached:1 considered:1 b1:6 qii:2 codimensions:1 abstract:15 convergent:5 exist:2 check:5 constructed:7 marking:1 no:32 when:4 vanishes:2 interested:2 describe:4 variable:6 transfers:1 assume:18 together:2 time:5 xk2:1 remarkable:2 global:7 invent:1 leads:2 l12:1 computation:1 technique:2 recurrence:4 quasi:1 elliptic:1 x03:1 x02:2 orthogonal:1 erale:1 keeping:1 dokl:3 choice:1 coprime:5 entries:2 kazuo:1 riemann:30 presented:2 irreducible:5 discrete:1 settle:1 accumulation:1 upper:3 ekvac:2 sign:14 g22:3 stands:1 xτ:3 uniform:1 current:1 satisfy:4 cos2:1 groups:2 address:1 along:16 change:3 knowledge:1 sending:1 shift:7 vectors:1 simultaneous:5 studies:1 emerge:1 logically:1 inverses:1 planck:1 prove:1 perj:56 peri:1 france:1 etude:2 theoretical:2 germs:5 surjection:17 everywhere:1 cases:3 cardinality:3 valued:28 values:3 following:12 claim:1 dedicated:1 δθj:3 figure:56 saito:6 topic:1 conversely:4 occur:1 s3:8 discussion:4 s0:8 s4:18 write:4 pura:1 pure:2 parameter:29 obius:9 map:15 product:2 may:27 applications:1 iwasaki:9 birthday:1 representations:3 data:1 natural:4 dynamical:4 lemmas:11 explicit:1 branched:3 so:33 representation:1 indeed:2 soc:4 stability:1 course:2 derive:1 group:21 interesting:2 coordinates:9 mail:1 main:9 correspondence:33 closure:3 non:11 thereby:2 acklund:13 introduce:1 identically:1 now:15 discuss:3 nor:2 term:3 equality:4 x12:1 qz:13 ei:25 ek:18 ej:25 expansions:4 hypergeometric:6 ez:7 happen:1 es:3 shown:3 space:30 lagrangian:1 u2i:3 u2k:3 contained:2 rational:12 formula:10 shows:5 after:1 theory:2 variant:1 possibility:1 quite:2 e4:11 e1:3 e0:22 e3:3 e2:3 qj:9 βq:1 c4θ:1 turn:1 think:3 first:29 xj:40 xk:37 xi:62 symmetry:5 omitted:2 signifies:1 directly:1 impossible:1 xq:2 open:4 little:1 necessarily:1 permutation:4 constants:1 realization:2 1m:1 speaking:2 gives:5 continuous:1 x2:14 x3:11 x0:8 x1:11 representing:2 than:8 coefficients:15 effective:2 accordance:1 require:1 were:1 correction:1 turned:1 argument:5 say:8 occupied:1 any:44 emes:1 efficient:1 note:8 take:5 online:1 coincide:1 formulas:2 begin:2 multiple:8 trace:2 normal:2 falls:5 algebraic:39 automorphism:5 successive:1 pair:7 monodromies:1 especially:3 discarding:1 gk2:3 g12:3 precise:2 show:9 leibniz:1 fifty:1 spaces:1 decompositions:1 injection:20 enough:1 analytic:7 only:47 explicitly:2 equipped:2 parabolic:22 get:3 cannot:2 sibuya:1 aν:4 gen:1 prime:6 yield:1 summary:1 appear:2 hitchin:2 characteristic:9 αn:1 discussing:2 voisinage:1 j2:21 connections:7 namely:9 surfaces:13 αp:1 review:2 label:2 outside:1 between:7 geometric:4 x21:1 x23:1 x22:2 notice:5 vertical:1 jp:1 erard:2 inclusions:1 comm:4 article:6 come:3 x2i:9 many:13 vk2:1 according:4 laplace:1 sketchy:1 embedding:1 expression:4 γim:1 among:1 solving:1 characterization:8 period:9 pole:1 anti:2 assertions:1 proved:2 considering:3 enable:1 observe:3 weierstrass:1 former:5 those:8 case:48 uehara:2 zp2:1 trick:1 situation:4 fibration:2 different:4 verified:1 author:1 same:13 shifts:1 arguments:7 kyushu:2 investigated:1 ness:1 octahedron:1 edges:3 πim:1 relies:2 without:1 solve:1 components:7 coordinate:1 being:4 generally:2 rest:1 eorie:1 blow:10 gj2:20 parametrization:7 treatment:1 around:52 represents:1 biholomorphism:4 certains:1 using:3 moreover:12 x4:1 identifying:1 reduces:1 either:13 characterizes:1 multiplicative:2 reduced:1 table:23 nonzero:9 provided:1 2xk:1 2xj:1 confirm:1 critical:5 inject:3 provides:1 x3i:1 refer:1 power:13 sixth:12 equivalent:3 found:3 x32:1 discussed:2 mutually:2 act:2 2k:1 jν:1 inclusion:5 image:1 references:1 halphen:1 operator:3 log:7 area:2 removing:1 strictly:2 there:50 strict:17 slopes:1 complete:5 meromorphically:1 technologies:1 downstairs:8 applying:2 multiplicity:1 casorati:1 liouville:1 grothendieck:1 multiplications:2 ac:1 ag:2 exhausted:15 certain:4 ak:18 aj:1 deep:1 general:1 formulation:1 fill:1 again:3 field:2 juin:1 valid:2 remarks:1 shimomura:1 mathematics:2 briefly:2 symbol:1 vertex:16 includes:2 a1:34 a3:30 a2:20 a4:3 included:2 tricks:1 curve:25 appl:2 resolution:22 represent:2 sci:3 consider:36 follow:2 expressions:2 disk:1 preserves:1 tz:8 equivalence:2 tr:3 tq:2 c5:1 th:12 ti:2 nodes:2 norm:1 degeneration:1 very:5 gz:1 corollary:1 difference:3 deformations:1 condition:27 hamiltonian:2 t4:1 t2:4 t3:1 t0:5 t1:5 large:3 small:1 b24:25 b23:2 b22:2 b21:2 b20:2 painlev:58 further:3 reine:1 canonical:2 what:3 nonlinear:14 funkcial:2 section:3 sur:1 intersect:5 sup:1 abbildungen:1 method:4 component:25 ranges:2 modular:1 b2k:27 b2j:26 b2i:13 investigating:1 equations:25 search:2 divisor:2 periodic:23 published:1 action:11 kaneko:1 uniquely:13 via:4 family:40 ask:1 equivariant:2 establish:1 readily:2 takes:3 uniformity:1 distinct:7 contains:20 finally:1 more:11 flat:2 corrected:1 basically:1 particular:7 known:3 projective:5 none:2 recall:3 equation:90 des:1 paragraph:3 x4i:1 pick:1 f1:3 f4:10 stated:3 contradicts:3 hyperplane:1 sense:2 rather:3 acts:20 enlarge:1 maps:1 explains:1 fr:1 algebra:1 angew:1 singularities:19 mapping:1 faculty:1 horizontal:2 associ:1 fundamental:1 developed:2 paper:1 through:6 signs:3 y1:2 existence:5 y3:2 y2:2 its:23 roots:11 icosahedral:1 picard:1 affine:22 coarser:1 actually:1 systems:1 deformation:1 finer:1 yi:5 yk:13 yj:17 entire:1 differential:20 yz:6 smoothness:9 restrict:1 2r:2 always:1 level:4 2z:20 conic:1 turns:2 2m:1 2n:25 referred:2 upstairs:4 reduce:2 idea:4 extended:2 loops:2 really:1 given:49 since:44 induces:11 denotes:3 acting:2 denoted:7 induced:2 issue:4 occurs:1 fiber:2 reformulated:1 reason:3 base:1 put:10 beginning:4 definition:11 pairs:5 exponentially:1 avec:1 consequence:3 number:4 done:1 least:5 polygons:5 passes:1 introduction:1 leading:4 osung:1 tata:1 construct:6 echet:1 assumption:2 statement:3 scheme:3 exponents:2 listed:1 holomorphic:30 calculations:1 recursively:10 immediate:2 part:17 jordan:2 translation:1 kleinian:6 kind:3 determines:1 cyclic:2 double:4 dans:1 eguli:1 determined:13 treated:1 outstanding:1 affirmative:1 2t2:3 null:2 lie:7 depending:10 internat:1 hyperplanes:2 k2:1 lifts:3 generalized:2 k4:1 play:1 rhz:6 3z:1 most:2 plan:1 nothing:2 singled:1 kj:1 ki:15 kl:13 reflections:1 ku:1 subgroup:1 phenomenon:1 multiplicities:1 relation:4 parameters:10 assertion:6 transcendental:2 factor:2 integrable:2 his:1 notation:1 dependent:3 uroku:1 express:3 closely:5 resolve:1 transversal:1 arxiv:2 factorization:1 investigate:4 common:1 set:38 ses:1 ser:1 see:32 pvi:14 various:1 permutes:1 takano:1 conditions:10 attention:4 both:6 last:5 connection:7 les:1 arbitrarily:1 point:93 simple:9 seems:1 corresponds:18 coincidence:1 dimensional:1 bε:2 sakai:1 consideration:2 bν:1 described:6 transformations:16 discriminant:2 due:1 strategy:1 reduction:1 asymptotics:1 pj:12 pk:11 pi:7 biholomorphic:5 pm:3 surjective:2 puiseux:3 fund:1 representative:1 p2:8 p3:6 p0:15 p1:49 look:1 p4:3 while:21 replaced:4 loop:13 garnier:1 von:1 conjugate:1 triple:2 resulting:5 composition:1 higher:2 used:1 purpose:2 lower:2 analysis:1 edge:6 sixtieth:1 simi:1 fuchsian:1 egrale:1 theorem:30 remaining:8 isomorphisms:2 big:3 emanating:2 cardinalities:1 integer:12 formal:10 semi:2 follows:9 holomorphically:4 translates:1 yields:25 pointwise:4 essential:1 terminology:2 parametrizations:2 subdiagrams:1 some:23 back:1 b4:189 understood:1 b0:9 examples:3 b2:5 b3:4 erentielles:1 shall:5 per:4 singularit:4 connecting:3 tends:3 proc:2 minimal:17 bl:1 bi:151 bj:138 bk:127 hilbert:26 integers:4 pα:2 f33:1 into:44 isomorphic:1 locus:21 appropriate:1 next:13 u3:1 gauss:5 repeatedly:1 line:41 espaces:1 collapses:1 cij:2 up:26 us:8 ui:48 uk:52 uj:53 continuously:1 similar:9 called:13 uber:1 associated:4 defined:7 globally:3 single:27 defines:1 polygon:12 fixing:11 application:1 nice:1 2xi:1 elements:3 exp:4 critiques:1 polynomials:5 generated:1 allowing:1 structure:6 independently:1 implies:15 orbit:1 equivalently:1 far:2 having:2 once:2 scratch:1 results:10 existing:1 exceptional:34 gj:1 gi:3 excludes:1 factoring:1 stable:10 include:1 putting:1 antipode:1 continued:1 fukuoka:1 notes:1 try:1 inspection:1 smaller:3 zi:1 zj:3 zk:1 zf:1 dynamics:6 zq:5 index:2 3r:1 expressed:3 poles:3 kyoto:1 degree:2 respectively:22 desired:2 objects:1 others:1 sing:8 z1:1 z2:1 z3:1 remark:19 dividing:1 involved:1 leaving:1 survey:1 makes:1 formulated:4 apr:1 apply:4 resolutions:3 clockwise:1 tools:1 use:2 germ:5 depicted:3 doubt:1 sort:1 ecole:1 becomes:3 feuilletages:1 iii:4 account:1 isomorphism:17 riemannhilbert:5 unknowns:1 meet:3 proof:30 something:2 holds:1 located:1 instead:1 mazzocco:2 singular:36 inst:3 multiplication:1 realized:2 discusses:1 computations:1 classe:1 lines:20 correspond:8 element:3 lε:2 s1:6 six:1 move:1 including:1 mentioned:4 le:1 outer:1 chosen:1 2e0:1 lj:2 lk:2 li:15 lq:8 derivative:4 greater:1 hands:1 transparent:1 establishes:1 university:1 identified:3 sufficiently:1 l2:2 l3:3 l1:2 subset:3 weyl:7 related:2 elementary:5 our:17 special:3 out:5 matrix:4 res:4 chaos:1 geom:1 stud:1 lecture:2 suffices:1 announced:1 completely:1 backwards:1 geometry:18 determining:1 feasible:4 algebraicity:1 hence:34 third:1 congr:1 poncelet:1 precisely:6 unknown:2 system:25 relations:6 πm:7 their:5 intermediate:1 explanation:1 exactly:17 foliation:6 reflecting:1 varieties:1 punctured:2 distinguished:1 result:4 behaviors:1 curves:7 disjoint:8 clearly:1 viewed:2 able:1 εn:3 εi:3 εk:19 εj:11 said:3 connected:1 preliminary:2 intrinsic:1 why:1 parametrize:3 laurent:5 counted:1 fact:6 trivial:4 q1:12 q0:11 based:4 q4:2 should:1 lemma:47 candidates:1 2bi:2 local:8 preliminaries:1 hope:1 ordre:1 δxk:2 means:2 syst:1 words:4 qq:1 2b4:1 fixes:4 contain:1 qi:9 qk:5 fixed:63 view:8 moduli:17 multiplying:1 modulo:2 constructing:2 exists:14 pattern:1 rims:1 identification:3 bruno:3 closed:1 invariant:4 boundary:3 meromorphic:17 inaba:4 wj:1 hypothesis:1 key:3 configuration:1 distribution:1 2θi:1 2θk:1 2θj:1 taking:3 fulfilled:1 admit:1 estimation:1 otherwise:9 ck:4 cj:1 ci:5 relevant:1 cm:3 conclude:4 wall:16 cz:2 sequences:1 respect:3 copies:3 ai:6 treat:1 define:5 determinant:2 arises:1 corresponding:15 truncations:1 sufficient:1 cos:6 bull:1 c3:2 c2:3 c1:3 present:2 c4:5 subsets:4 appearance:1 value:7 will:4 monodromy:18 wild:1 chaotic:1 vi:35 vj:11 vk:13 thus:27 surprisingly:1 surface:38 compactified:2 higashi:1 generic:7 unity:7 finite:22 difficult:1 phi:6 infinity:14 cubic:19 upon:1 effect:1 parametrized:8 v3:2 infinite:1 identity:3 reflection:3 well:4 patterns:2 sets:4 position:2 usual:1 monomial:6 obtain:9 underlying:1 adv:1 conjugated:1 stratum:46 divided:3 vε:2 press:1 immediately:1 intersection:13 necessary:2 helpful:1 because:9 classical:2 sequence:5 phenomena:1 okamoto:5 choosing:1 proper:4 pinpoint:2 lead:1 injects:5 does:6 assuming:1 blowing:12 2q0:1 expansion:2 although:1 injective:1 stage:1 about:2 getting:1 dependence:1 carries:13 important:1 introduced:3 homogeneous:1 stratification:14 square:1 sl2:2 bombay:2 restricts:3 quadratic:2 inner:1 ed:1 notices:1 function:5 sequel:1 but:20 repeated:1 construction:3 convergence:4 truncation:4 made:2 wish:1 smooth:26 below:2 limit:1 empty:2 problem:15 pii:2 pij:2 pik:2 intersects:3 int:1 universal:1 denote:6 proceeds:1 functions:1 qβ:5 qν:1 detail:1 other:23 details:1 branch:40 expositions:1 repeat:1 expressible:1 bundle:1 pi4:2 ranks:2 factors:2 rule:1 lift:10 indirectly:1 |
0704.0680.txt |@word snia:5 l17:1 consider:1 rev:17 alternatives:1 results:5 month:2 scalar:1 edu:1 adjustment:1 gr:5 inverse:8 calculate:1 sahni:2 caldwell:1 concerned:1 finally:2 monotonically:1 those:1 lewis:1 summarizes:1 p2:2 mpc:1 very:1 choice:2 condition:1 school:1 cmb:2 t0:15 large:4 solved:1 evades:1 small:2 smaller:1 neighborhood:1 riess:2 astrophys:6 zero:1 design:2 further:1 dynamics:1 substitute:1 what:3 appear:2 availability:1 access:1 3h:6 above:1 new:1 filled:1 iran:2 component:4 here:1 odintsov:2 shafieloo:1 test:1 ansatz:1 others:1 concluding:1 path:2 equations:3 implicit:1 change:1 box:2 arrive:1 institute:1 leaves:1 compliance:1 allows:1 adopt:1 action:4 adopting:1 stipulated:2 spacetime:5 plotted:5 followed:2 scales:2 transit:1 brought:1 plot:5 use:3 freese:1 takes:1 sake:1 positive:3 negative:2 flat:1 next:5 scenarios:2 nucl:1 robertson:1 type:4 more:2 introducing:1 tsujikawa:1 bennett:1 becomes:1 company:1 corrected:1 known:4 evolves:1 account:1 equation:14 work:2 ρm:7 modified:9 entertained:1 theories:1 remain:2 values:3 universe:13 following:2 nonsingular:2 scherrer:1 dec:1 f1:1 compare:1 wang:2 cosmological:3 give:1 attribute:1 rgµν:1 sample:2 numbers:1 sought:1 presently:1 copeland:1 goal:1 s2:1 feature:1 recovers:1 write:1 wspc:10 answer:1 instead:2 parameter:2 economy:1 galactic:1 singular:1 may:1 earlier:1 dx2:1 designed:1 deducible:1 data:2 compatibility:1 constants:1 attempt:1 dynamical:1 third:1 candles:1 cosmology:1 accelerated:3 so:1 nojiri:2 gµν:2 zlatev:2 perlmutter:1 expects:1 course:2 paper:10 letters:1 cold:1 its:7 perfect:1 fit:2 chosen:1 starobinsky:3 writing:1 choose:3 versus:6 eventually:1 non:1 propose:3 fig:12 effects:1 they:1 ys:1 now:1 day:2 barrow:1 february:10 deffayet:1 hereafter:1 always:1 university:1 possibilities:1 2f:1 reasonable:1 2h:3 differential:1 energy:18 revised:1 reduce:1 related:1 solution:3 inhomogeneous:1 obtains:1 year:2 our:4 eq:13 es:1 out:2 rv:10 factors:1 since:1 lagrangian:3 content:3 rf:4 hill:1 torres:1 after:1 tully:1 galaxies:1 free:2 standard:3 approaches:2 put:1 movahed:4 language:1 transition:2 cosmic:7 times:4 place:1 hence:1 neglect:1 first:1 spergel:1 question:1 spiral:1 done:2 unspecified:2 another:1 guess:1 eqs:2 system:3 adopted:1 zanjan:1 indicate:1 observations:7 hypothetical:2 dt2:1 white:1 structures:1 final:1 gives:2 serve:1 alam:1 deceleration:1 authors:1 tehran:1 shortly:1 eliminated:1 than:1 distance:4 ahmed:1 instruction:10 exponents:1 matter:2 future:1 light:1 exhibit:1 modern:1 argument:1 curves:1 environments:1 ρde:5 turner:1 acceleration:2 ratra:2 gravity:4 note:2 sciences:1 emphasis:1 modulus:3 circles:1 begin:3 ds2:1 though:1 algebraic:1 letter:1 phase:4 analytically:1 stands:1 deviations:1 observation:2 considered:1 calculated:1 later:3 tβ:1 porrati:1 points:1 physics:3 dot:1 emerging:1 gold:2 cdm:5 converge:1 mnras:1 relation:1 solutions:3 calculable:1 keywords:1 find:3 subtracting:1 based:1 parameters:5 baryonic:2 explain:4 state:5 should:4 only:1 black:1 factor:8 integrate:1 adequate:1 accurate:1 discuss:1 continuity:1 do:1 dl:3 means:1 df:3 fluid:1 dr:3 comply:1 luminosity:1 arxiv:1 greene:1 reveals:1 ser:1 epochs:3 see:1 sec:1 eliminating:2 facilitates:1 best:2 hilbert:1 gravitation:10 away:1 tend:2 favor:1 written:1 between:5 limit:3 boundary:4 conditions:3 knowing:2 observational:1 recently:1 however:3 indicial:1 rudiments:1 jk:1 intelligent:1 come:1 received:1 last:1 equal:1 attributed:1 etc:1 pde:4 finds:2 otherwise:1 arbitrarily:1 adjusted:1 point:1 simple:1 whatever:2 maintained:1 simply:1 70km:1 throughout:1 publishing:1 basis:1 addition:2 been:1 frw:11 basic:1 ph:1 pm:4 obtained:2 corresponding:1 tµν:1 both:2 6h:1 dave:1 astron:1 c2:3 c1:3 dvali:2 present:1 reddening:1 case:3 extracted:1 p1:2 supernovae:2 solid:3 empirical:4 value:1 will:4 while:1 behavior:3 larger:2 almost:2 endowed:1 metric:4 thus:2 ia:1 mod:3 technology:1 examine:1 sami:1 sensitive:1 suggest:1 make:3 same:2 epoch:1 dimensionless:3 several:1 sorkin:1 numerical:3 counterparts:1 possible:1 purpose:2 recent:1 early:3 explains:2 scenario:1 matters:1 studies:1 kept:1 without:1 solve:2 model:9 possesses:1 observed:2 obtain:4 underlying:1 alternative:1 speed:7 yet:2 letting:1 waga:1 density:4 seems:1 evidences:1 lett:6 extensive:1 formal:1 remaining:1 momentum:1 rahvar:12 unaccounted:1 advances:1 term:5 dark:18 department:1 increases:1 makes:1 background:1 rµν:1 world:1 unique:1 8πg:1 advanced:1 2q:1 reduces:1 resorted:2 discarded:1 either:1 become:2 mathematical:1 classical:1 some:2 back:2 deduce:1 redshifts:2 proper:2 universes:1 scale:9 lead:1 yousef:1 measurements:1 integration:3 microwave:1 manipulations:1 does:1 eliminate:1 provides:1 scientific:1 equivalent:7 conventional:8 expansion:4 pressure:5 optimize:1 asymptotic:2 about:1 constraint:2 dzh:1 gabadadze:2 o:2 decelerated:2 range:1 ensure:1 recourse:1 introduced:1 revise:1 outset:1 dilemma:1 steinhardt:3 redshift:4 h0:2 numerically:3 suppl:2 down:1 remarks:2 appropriate:1 references:1 stebbins:1 einstein:2 refined:1 dodelson:1 log:1 there:2 available:2 approximate:1 way:3 translate:1 function:1 form:3 differences:2 but:2 hu:1 astro:1 verde:1 solar:3 elimination:1 line:4 rotation:1 clifton:1 instructive:2 inside:1 up:9 us:2 3t0:1 demonstrate:1 similar:1 dτ:1 aa:1 diverges:1 constant:2 classic:4 int:3 liddle:1 general:1 single:1 file:10 moves:1 functions:1 compared:1 frieman:1 no:2 dashed:2 sharif:2 field:8 wetterich:1 other:3 normal:1 dimmer:1 2hf:1 peebles:2 models:2 ttrans:2 polynomials:1 generated:2 studied:1 variable:1 fisher:1 algorithm:2 sawicki:1 assume:3 age:2 required:1 curve:1 time:5 walker:1 peiris:2 |
0704.0681.txt |@word replacing:1 limited:1 concept:1 sci:3 amon:1 rev:8 trappe:4 dynamic:18 focus:1 icf:2 illustrated:1 sergey:1 follow:2 disk:1 contributions:1 localized:2 sch:1 content:2 terms:2 technique:4 micrometers:5 former:1 keeping:1 charge:1 critical:1 backscattered:1 th:1 under:6 breach:1 heterogeneity:1 incompressible:1 applied:4 g2:5 far:16 brownian:1 implicitly:1 amorphous:1 wave:7 nanomaterials:1 refractive:1 mrtn:1 polymeric:1 capillary:1 inset:1 squares:1 solves:1 presented:2 trc:7 lequeux:2 humidity:5 large:6 unrelated:1 phase:8 minimal:1 succession:1 small:3 referred:1 optics:3 configurations:2 intermittency:5 upper:1 dries:1 glassy:4 disordered:1 ten:2 monodisperse:1 penetrates:1 heterogenous:2 direct:5 approximation:1 second:5 timescales:1 subtle:1 further:2 dynamics:20 estimated:1 theory:3 even:1 index:1 nonlinear:1 sub:1 speckle:24 diffusing:4 selected:1 while:2 thickness:1 access:3 experiment:14 3l:4 new:11 falling:4 increasing:2 method:7 contrast:2 publications:1 coefficient:2 subdivided:1 condensed:4 full:4 evanescent:1 submitted:1 component:1 residual:1 here:1 understanding:1 hours:1 growing:1 intercept:2 focused:2 pecora:1 address:1 path:4 along:1 respect:1 obtained:3 dashed:1 oxford:1 study:4 studied:1 allows:4 commonly:1 example:1 spheres:1 amount:1 periodic:2 usually:1 formation:1 changes:1 york:2 composed:1 diameter:1 spatially:11 scales:4 editors:1 conditions:3 harden:1 addressed:2 analyzing:1 motor:5 illumination:3 outer:1 should:1 viscoelastic:1 select:1 suspensions:4 use:2 eye:1 would:1 remains:2 contains:2 comparing:1 magnification:1 camera:12 therefore:5 vi:2 taken:3 themselves:1 panel:1 type:1 until:2 more:2 fractions:1 attractive:1 becomes:1 company:1 distribution:3 glass:12 controlling:1 normalized:5 particular:1 known:3 cases:3 mounted:2 iii:3 opin:2 must:1 high:3 mg:1 evolution:2 indicates:1 mm:4 science:6 equation:1 averaged:6 strain:1 mw:1 itself:1 values:4 thin:5 ms:2 following:1 webster:1 crocker:1 averages:1 scramble:1 compare:2 figure:9 plate:1 process:13 confused:1 agent:1 dependence:1 sample:22 sphere:2 performed:1 sharp:1 spanning:1 durian:2 absolute:1 information:3 rays:1 monitoring:3 provide:3 drying:21 differences:1 feature:1 pine:2 delay:2 maps:2 influences:1 beams:1 opt:5 instead:1 ensemble:5 mat:2 dws:3 may:2 immersed:1 after:2 variant:1 collection:1 consolidation:1 applications:2 plane:13 blood:2 waves:2 revealed:2 parallel:1 introduced:2 dynamical:5 liquid:10 diffraction:1 light:27 acknowledged:1 think:1 rather:2 correlation:16 tsay:1 subsequently:1 increase:2 order:8 typical:3 breaking:1 valid:1 biroli:1 radiation:1 over:8 vary:1 biomedical:1 cohen:1 lsi:1 produced:2 speckles:6 experiments:3 decays:1 statistical:7 still:4 its:1 perfect:1 rapidly:1 monitor:5 fit:2 decay:1 chosen:1 interesting:1 lateral:2 accompanying:1 better:1 laponite:1 static:1 systems:8 weeks:1 main:2 spot:1 pixel:3 shear:1 eur:1 correspondence:1 non:3 within:1 skipetrov:2 combination:1 fig:9 reflected:4 often:1 records:1 resolve:2 penetration:1 half:1 sweeping:1 rotation:1 now:3 transparent:1 developments:1 structural:1 easily:1 finite:4 name:1 2s:2 characterizes:1 university:3 level:1 advent:1 grows:1 into:3 good:2 stopped:1 mode:1 l0:7 each:3 found:4 characterized:1 mean:4 homogeneous:3 el:1 financial:1 directly:3 weight:2 zurich:1 energy:1 hard:3 positioned:1 gaussian:7 related:3 mm2:2 rojas:1 meta:3 solvent:2 expect:1 σ2d:11 measure:3 substantially:1 our:14 beyond:1 eq:1 description:1 shown:5 pigments:1 matrix:1 space:3 quantify:1 since:2 rx:1 particles:6 modulation:1 conclusions:1 dominated:1 scaling:2 current:1 illustrate:2 occurs:2 excess:1 shows:1 foundation:1 condens:2 complicates:1 fribourg:5 linear:1 barrier:1 interactions:1 frank:1 contain:1 transfer:1 free:3 standard:3 orn:1 nth:1 completely:1 ramos:1 advantages:1 imaging:19 lacoste:1 bouchaud:1 maret:2 atzel:1 pendular:1 geometry:6 starts:1 could:1 transition:5 motion:4 aging:2 length:7 ohler:1 editor:1 gordon:1 signature:2 undergo:1 onto:1 isf:13 first:3 berthier:1 major:1 probability:1 prevent:2 omitted:1 number:13 biomed:1 echo:6 spinning:1 set:8 done:1 long:2 suspended:1 changing:1 results:3 ring:1 open:1 size:14 given:3 smaller:2 tio2:1 introduction:1 data:3 sep:1 amsterdam:2 system:4 approximately:3 retreats:2 paint:11 observations:2 sian:1 white:2 scheme:3 aiche:1 speaking:1 inner:1 originating:1 tool:1 continuous:3 serve:1 5µm:1 binned:1 optical:4 foams:1 than:5 greenwood:1 diffusion:1 distance:2 polarized:2 determines:1 effective:2 bubble:1 require:1 evaporates:2 rate:7 bed:1 recording:3 matter:5 states:1 individual:2 recovered:1 were:2 bare:1 enables:2 hz:2 quantitative:1 dynamically:2 7l:1 few:1 case:5 manner:1 qualitatively:1 need:1 elsevier:1 concentration:2 occupied:1 any:4 ray:1 paths:2 zero:1 general:2 studying:2 latter:1 able:1 relaxations:1 note:3 goodman:1 materials:9 take:1 detector:7 diffusive:1 berne:1 channel:1 accuracy:2 acquire:1 multiple:2 investigations:1 probed:4 enter:2 reach:1 falls:1 most:3 optimized:1 exploited:1 germany:1 significant:1 echoes:1 device:1 marie:1 measured:2 dispersing:1 probes:2 bound:1 deviations:1 chemistry:1 give:1 observation:3 calculated:1 flow:4 drifts:1 face:1 traditional:6 curie:1 part:1 cortex:1 exp:1 flux:1 dispersed:4 physics:2 fact:2 quantity:2 slope:1 show:3 text:1 detection:1 random:2 scattered:8 evaporation:4 bring:1 relation:1 scarce:1 scatterer:1 determined:1 d2:22 find:1 decade:1 ground:7 cell:3 feng:1 slow:4 based:3 crp:5 µl:1 enough:2 short:1 only:3 sequential:1 gradual:1 curr:2 local:1 achieve:1 do:2 slows:1 means:1 air:2 overall:1 fluid:1 beam:9 report:2 during:6 nanometric:1 areas:1 reveal:1 processes:2 gels:2 course:1 nicely:1 outperform:1 schofield:1 arxiv:3 ceram:1 l02:2 microscopy:2 acknowledgments:1 network:1 europhys:1 activity:3 switzerland:3 distinguishes:1 view:2 scanning:1 multiplying:1 backscattering:2 reference:1 achieved:1 generally:1 national:1 correlations:1 evolving:1 pathlengths:1 observed:4 intensity:7 computer:1 sec:1 result:1 discussions:1 close:1 techniques:5 inversely:1 said:1 revolution:1 attempting:1 subsequent:1 equal:1 µm:8 colloids:1 state:2 depolarization:1 boundary:1 approach:10 email:1 pastes:1 choose:1 publishers:1 comparable:1 harris:1 recently:2 statistically:3 extend:1 importance:1 alexander:1 steady:1 however:5 analyzes:1 continuously:1 incident:7 selectively:1 demonstrate:2 analyzed:3 article:3 configuration:1 suppressed:1 pixels:4 thank:1 suggested:1 both:6 panels:4 last:2 brown:1 gratefully:1 many:4 density:1 according:1 called:1 sensitive:2 dated:1 heterogeneities:10 contribution:1 temporal:1 experimental:7 albeit:1 detailed:1 ch:4 co:1 cm:1 point:6 rheological:1 relaxation:3 period:7 dimensional:2 interface:2 jammed:2 consideration:1 disturbing:1 constant:4 decline:1 described:1 leads:2 source:2 create:2 radiative:1 due:3 been:6 homogenous:1 slowly:1 interest:1 unchanged:1 pco:1 concentrated:1 direction:1 controlled:3 quantities:1 sufficient:1 formed:3 photon:3 andrew:2 binning:1 bulk:1 observe:2 diffusely:4 expander:1 careful:1 diffuse:2 present:1 ultraslow:1 novel:2 laser:10 look:1 solid:11 expanded:1 lemieux:2 value:3 deformation:2 intimately:1 reviews:1 near:15 replaced:1 weber:1 behavior:1 weitz:3 situation:2 balance:2 leaves:1 polymer:2 larger:2 lindner:1 coupled:1 diaphragm:1 averaging:6 hene:1 thus:6 surface:9 iv:2 ii:4 characterize:2 sudden:3 cond:2 heidelberg:1 loosing:1 different:5 inc:1 grant:1 perform:2 media:4 timeresolved:1 stepper:3 cross:1 same:5 another:1 complex:4 coworkers:1 emulsions:1 several:1 events:8 neutron:1 ochoa:1 independent:4 used:7 see:1 instrumentation:1 foam:1 munch:1 effect:1 flows:1 hand:1 driven:2 moment:2 journal:1 kin:1 koper:1 variance:6 frequently:2 normalization:1 recent:2 approaching:1 lower:1 kept:3 center:2 scenario:1 intermittent:6 studies:2 no:2 well:2 roughly:2 analysis:6 solids:3 without:3 lenses:1 sets:2 swiss:1 ccd:1 paradigm:1 left:1 less:1 when:7 nanoseconds:1 obtain:1 rest:1 front:3 sufficiently:1 stabilization:1 scattering:29 previous:1 superficial:2 enters:1 monitored:3 application:2 zakharov:4 photons:1 characterization:2 except:1 arrest:2 potential:2 lett:4 theorem:1 input:1 mod:1 remaining:1 resolved:8 saturation:1 advances:2 breaks:1 spatial:7 absence:2 possible:3 early:1 increases:2 netherlands:2 compaction:3 press:1 using:9 moreover:1 like:1 neutrons:1 phenomena:2 depolarized:1 particle:4 aqueous:1 follows:2 signal:3 porous:4 temporally:5 chamber:1 clay:1 invaluable:1 weiner:1 inter:1 soft:13 reduced:2 masri:1 scatterers:1 right:1 methods:2 arrested:2 village:1 some:1 springer:1 proportionally:1 polynomial:1 specified:1 images:3 home:1 precautions:1 nanometer:1 colloid:2 transport:4 investigating:1 vol:2 scale:7 colloidal:11 kegel:1 µm2:2 measurements:8 recorded:2 fluids:2 per:1 does:1 exit:1 linearly:1 provides:3 tends:1 propagating:1 trautman:1 esi:6 blaaderen:1 biology:1 noise:10 power:1 seconds:2 viscosity:1 jumps:1 radial:1 oscillating:1 agreement:2 step:1 chaikin:1 super:1 properties:12 stage:3 chapter:1 about:7 central:1 carried:1 stationary:3 completing:1 ob:1 o:1 practical:1 distinct:1 range:2 wolf:1 glasses:2 additives:1 soc:4 real:1 presence:4 previously:1 image:15 boundaries:1 cipelletti:6 usa:2 three:2 down:1 multiply:2 haskell:1 references:1 scherer:1 determine:1 proportional:2 initially:1 technically:1 statistics:3 van:1 additional:1 area:16 removing:1 support:1 initial:3 available:1 fast:1 pages:2 dispersion:1 occupy:1 collimated:1 low:1 fraction:4 was:3 assumes:1 function:13 project:1 medium:2 reduce:1 retina:1 roberts:1 but:4 volume:10 films:1 construction:1 brain:1 line:2 manifests:1 made:1 wise:1 rejuvenation:1 characteristic:1 inside:1 up:3 us:3 theoretical:1 below:2 frequency:3 limit:3 spectroscopy:5 heterogeneous:7 fluctuations:9 problem:2 stages:5 similar:3 display:1 strongly:2 d22:1 associated:1 ag:1 fans:1 defined:2 roberto:1 measurement:3 am:4 evidence:2 levitt:1 ap:1 single:3 pores:1 wavelength:1 request:1 corresponding:1 dawson:1 work:1 eric:1 film:10 physical:1 again:2 functions:3 compared:2 nm:1 calibration:1 extract:1 whereas:1 water:6 4l:1 field:33 other:4 details:2 digital:6 department:1 out:1 conclusion:1 optically:1 briefly:1 narita:1 kout:1 calculating:1 separate:1 uniformly:1 includes:1 lens:2 important:1 modelling:1 dense:4 aggregated:1 structure:9 exposure:3 correlated:1 faster:1 algorithm:1 proximately:1 realtime:1 resolving:1 uncovered:1 depth:3 mass:1 time:30 dover:1 resolution:9 |
0704.0682.txt |@word represent:1 observatorio:2 results:9 systemic:1 cooperative:1 layers:3 amplification:1 tx:1 technique:2 should:1 send:1 finally:1 spain:2 under:4 details:1 overlaps:1 alcolea:5 lack:1 alcal:1 figs:1 summarized:1 socorro:1 difference:1 dwingeloo:1 vibrational:2 presented:2 bright:2 vlba:4 upper:3 consistent:1 direct:1 second:1 correlator:1 further:1 estimated:2 situated:1 calibrators:1 universities:1 errors:1 appear:1 section:2 current:2 template:1 new:2 method:1 contrast:1 compact:1 cam:1 iram:1 understanding:1 reported:2 along:1 change:1 obtained:1 institute:1 study:3 larger:1 contradiction:1 simultaneous:3 studies:1 followed:1 apr:1 total:4 asymptotic:1 would:1 humphreys:2 predictions:2 comparing:1 therefore:3 december:1 jive:1 type:2 theoretical:2 more:1 diamond:1 molecules:1 envelope:6 mira:2 particular:3 antennas:1 rotational:1 science:1 supergiant:1 work:1 det:1 reproduce:1 temperatures:1 evolved:2 making:1 example:1 figure:3 process:2 expanding:1 sample:1 performed:3 coincident:1 magnitudes:1 occur:1 information:3 divided:1 six:1 regions:9 located:2 symposium:1 sio:40 circular:1 map:6 mas:2 description:1 derived:3 mapping:4 snr:1 fits:4 data:8 types:1 beam:11 light:1 spectra:2 lines:9 ghz:14 omez:1 correlation:1 subsequently:1 mainly:1 produced:4 paper:1 lsr:1 mentioned:1 observational:1 delay:1 derive:1 outer:1 maps:6 collisional:2 circumstellar:7 better:1 previously:2 detected:1 production:1 multiline:1 fig:3 mail:1 non:1 polarizations:2 material:1 innermost:1 band:1 february:1 netherlands:1 cotton:3 evn:1 oxygen:4 level:2 each:2 found:3 mean:1 significantly:1 fr:1 our:5 transitions:8 ring:3 out:1 shown:4 since:2 crucial:1 detailed:1 angular:1 dominated:1 vlbi:2 l39:1 integrated:2 shows:1 foundation:1 theory:1 spot:3 mechanisms:2 pumping:6 standard:1 reason:1 anchez:1 could:1 transition:2 desmurs:2 corrections:3 think:1 first:3 already:1 manuscript:1 xc:3 variables:1 number:1 done:2 spots:2 spanish:1 array:1 several:2 size:1 given:1 mennesson:1 indicate:1 introduction:1 xii:1 structured:1 system:1 their:2 rates:1 observations:7 calculations:2 molecular:1 final:2 recovered:1 scans:1 shell:1 continuous:1 centroids:1 than:2 observed:8 observatory:1 namely:1 aims:1 matter:1 oj287:1 amplitude:1 were:11 providing:1 pulsation:2 exhibit:1 few:2 alfonso:1 emission:18 clearly:1 bujarrabal:8 rout:1 mechanism:1 fitting:2 channel:1 circles:1 spectral:1 molecule:1 significant:1 phase:2 alez:1 acknowledgements:1 measured:1 average:1 km:11 chemical:1 clean:1 velocity:2 constrain:1 latest:1 drastically:1 particularly:2 intensity:4 show:2 supported:1 infrared:1 radii:1 radio:2 find:1 giant:1 ratio:2 parameters:1 explain:1 1994a:2 soria:15 only:4 rich:5 factor:1 emitting:1 constant:1 ruiz:12 do:1 predict:1 means:1 occuring:1 de:1 overall:1 joint:1 nearly:1 words:1 procedures:1 gray:1 processes:1 continuum:1 arxiv:1 mapped:1 www:1 reveals:1 national:2 deconvolution:1 relative:4 see:3 individual:1 radius:2 result:1 operated:1 contour:2 closer:2 compounds:1 subsequent:1 rings:1 state:2 envelopes:3 between:6 irc:1 conditions:2 europe:1 jy:10 vertical:1 key:1 leo:14 received:1 irregular:1 many:1 region:3 context:1 requests:1 among:1 simple:1 period:1 coincidence:1 table:3 radiative:2 been:8 reduction:1 expected:1 ph:1 arises:1 maser:27 both:2 occurs:1 formed:2 spectrum:3 understand:1 astron:2 present:1 3c273:1 applied:1 multi:1 aim:1 layer:1 mexico:1 characteristics:1 thus:1 discrepancy:2 rin:1 different:10 baseline:3 perform:1 distributions:1 cross:1 same:3 any:1 epoch:1 complex:1 units:2 physical:2 yc:2 difficult:1 evolve:1 http:1 colomer:5 dgi:1 hand:2 henares:1 numbered:1 lower:2 center:3 yates:1 nevertheless:1 calibration:2 well:2 components:6 very:7 left:1 1994b:1 proposed:1 less:1 sources:1 financially:1 farther:1 useful:1 yet:1 previous:2 unique:1 ease:1 nacional:2 source:2 location:2 relevance:1 masers:4 aspects:1 around:1 lcp:2 outermost:1 milliarcsecond:1 consisted:1 using:3 accepted:1 projects:1 helpful:1 necessary:1 specie:1 sizes:1 follows:1 either:2 iramfr:1 omico:2 right:2 methods:1 madrid:1 some:2 imaged:2 understood:1 confirm:1 overlap:1 provides:1 assuming:1 eso:1 restoring:1 power:3 selecting:1 equivalent:2 agreement:1 stellar:3 how:1 step:1 although:2 plots:1 properties:1 panel:7 comparison:1 postbus:1 central:2 carried:1 oh:2 fringe:1 o:5 compatible:1 introduced:1 slightly:1 software:1 facility:1 h2:2 image:1 within:2 shed:1 included:1 references:1 determine:1 contreras:1 shells:2 support:1 rcp:1 planesas:1 long:4 width:1 inner:4 stars:12 astrophysics:1 was:4 interferometry:2 mcyt:1 astro:1 gain:1 line:6 removed:1 gildas:2 made:2 masing:3 characteristic:1 those:1 emissions:1 distribution:4 panels:1 similar:3 aa:1 bearing:1 ac:1 associated:1 defined:1 abstract:1 package:1 single:1 apartado:1 gonz:1 inc:1 nl:1 antenna:1 no:2 dashed:2 whereas:1 when:2 proceedings:1 other:8 mas2:1 branch:1 spatial:4 test:2 concerning:1 star:4 excitation:1 models:4 interferometric:1 important:1 peak:2 variable:3 astronomy:2 offprint:1 correlated:1 algorithm:1 assume:1 agb:4 time:1 resolution:1 8th:1 |
0704.0683.txt |@word consider:4 gq:2 bourges:1 magnetic:10 results:1 existing:1 leads:1 maxima:2 consists:3 follow:1 expressions:4 lonzarich:2 contributions:2 demagnetization:1 inverse:1 depend:1 29k:1 intensive:1 gatchina:1 finally:1 does:2 petersburg:1 under:1 tc:1 case:3 jensen:3 very:2 rise:1 wave:27 condition:1 inset:2 hamiltonian:2 forth:1 anisotropy:11 vector:3 bq2:1 small:4 gor:1 noted:1 unexpected:1 zh:1 disordered:8 10l:1 sin4:1 edu:1 sin2:4 prediction:2 sign:2 approximation:1 second:8 evaluated:2 estimated:3 theory:4 bilinear:1 established:1 giving:1 3q:1 axes:1 while:1 uniform:2 ˆb:1 experiment:3 above:3 3l:1 new:1 principal:3 q1:1 full:2 exchange:2 respectively:1 component:2 equals:1 perpendicular:1 cos4:5 cos2:11 address:1 directions:3 consideration:1 along:11 extrema:1 appears:5 obtained:2 ref:1 spite:1 institute:1 vectors:1 abrikosov:1 stiffness:1 studies:2 apr:1 semiconductors:1 explained:3 ǫq:6 order:10 decrease:2 total:1 unit:1 use:2 takes:1 commun:1 remains:1 positive:1 contains:2 negative:7 kataoka:1 sample:1 program:1 m1:3 m2:2 e2:3 theoretical:4 diagrams:2 more:2 becomes:6 operators:1 stable:1 bogdanov:1 particular:1 known:1 cases:1 hold:1 must:2 logarithm:1 high:2 account:6 endoh:1 mo:1 work:1 theories:1 mt:2 remain:1 fock:2 mq:4 following:4 f0:3 dzyaloshinskii:3 weaker:1 give:2 predict:1 neglected:2 model13:1 contradicts:1 numbers:1 spb:1 attract:1 axis:2 rather:1 means:1 parameter:1 sin:8 fq:4 mat:1 replacing:1 after:1 derived:2 ζr:1 law:2 data:1 parallel:3 sr:8 sq:4 sp:1 lines:1 correspond:1 sh:2 negligible:1 decreasing:1 representation:2 sf:1 ege:1 s0:1 saturated:2 hierarchy:1 indeed:1 stability:1 paper:1 london:3 statistical:1 signs:1 existence:1 excitations:2 its:2 2e2:1 ǫ2q:4 expectations:1 fig:8 fade:1 main:1 decades:1 h0:1 non:4 h1:4 processes:1 chetverikov:3 they:3 now:1 yu:3 february:1 several:2 2s:4 drop:1 sufficiently:1 mnsi:5 instability:2 el:1 square:3 energy:6 macmillan:1 decays:1 expect:1 quantum:4 eq:10 shown:6 since:1 rev:10 research:1 may:3 bragg:5 oni:2 ossler:1 get:1 evaluation:1 occurs:1 note:1 shows:1 earlier:1 8n:1 linear:1 interactions:2 ecl:2 ex:1 reason:1 complicated:1 york:1 e1:4 e0:4 temperature:1 hc2:2 interaction:15 chiral:4 v1:3 transition:9 so:1 length:1 place:1 signature:1 hence:2 teor:1 neglect:1 first:8 initial:1 features:1 ignored:1 feel:1 ql2:1 erroneous:1 neglects:1 another:3 umklapp:1 electronic:1 given:8 1t:2 district:1 needed:1 eqs:1 system:1 their:1 quadratic:1 calculations:1 gives:1 part:8 ivanov:1 polarized:2 eq2:1 zero:3 matter:1 determined:1 contrary:1 str:1 were:4 kov:1 russia:1 sak:2 julian:2 ishida:1 spectrum:9 sf0:4 need:1 depending:1 thoroughly:1 responsible:3 oriented:1 materials:1 take:2 green:1 subject:1 l111:1 begin:1 correlation:1 formulae:1 phase:1 measured:1 why:1 divergences:1 ka:6 fiz:1 observation:1 koyama:1 chosen:1 later:1 physica:1 kl:1 electrons:1 reflections:2 nuclear:1 shadowed:1 physics:2 phenomenon:1 intensity:4 text:3 supported:1 scattered:1 rotating:2 purely:1 reznik:1 trivial:1 line:1 d0:7 ground:2 saturate:1 ratio:3 parameters:2 hf:1 should:1 only:3 helix:9 factor:2 di:2 dependent:1 belitz:3 dq:3 evolution:1 arxiv:1 qa:1 bak:3 reveals:1 set:1 frame:1 j0:2 j1:1 observed:3 in22:2 depends:2 result:4 close:2 conductivity:1 macroscopic:1 away:1 state:25 between:1 invariant:2 discovery:1 terms:3 nature:4 attention:1 weak:3 jq:12 however:5 jk:1 analyzed:2 configuration:1 both:5 cos:7 parentheses:1 last:2 region:1 according:4 zeeman:1 etc:1 dated:1 contribution:11 expression:4 experimental:3 detailed:1 adjusted:1 cl:1 simple:2 cf:1 diverges:1 belyaev:1 ordered:2 cq:3 strong:2 pfleiderer:4 chirality:3 due:6 been:1 anisotropic:2 ph:1 direction:3 corresponding:2 gap:16 6t:1 external:1 presented:2 spin:33 former:1 present:1 applied:4 p0:2 pacs:1 solid:2 plain:2 georgii:2 value:2 will:1 near:2 b02:1 behavior:1 situation:1 taking:4 loop:1 larger:1 orientation:1 jpn:1 almost:1 thus:1 them:3 surface:2 equal:2 ii:1 helimagnets:2 cond:1 cone:1 ambient:3 conical:3 disappear:1 rfbr:1 began:1 same:2 parts:1 modification:1 gets:1 neutron:5 independent:3 peaks:1 see:7 cubic:12 fluctuations:1 ion:1 v2:4 v3:1 hartree:2 a2l:2 destruction:1 reflection:1 programs:1 changes:1 well:1 analysis:1 solids:1 without:1 comes:1 components:2 model:1 left:1 spherical:2 magnetization:2 just:1 superconductors:1 obtain:1 vanishes:1 facts:1 momenta:1 scattering:5 yet:2 polarization:5 point:4 iω:5 lattice:3 fermiliquid:1 spread:1 lett:2 plumer:1 misprints:1 around:1 breaks:1 sums:1 term:7 increases:3 using:3 projects:1 neutrons:2 nakanishi:1 qualitative:1 e02:1 unstable:3 arbitrary:1 soft:1 spins:1 therein:2 right:2 leningrad:1 classical:2 mitsuda:1 goto:1 competition:1 b0:4 iˆb:1 neglecting:1 lead:1 measurements:1 whole:1 critical:4 connecting:1 disappears:1 ξr:1 demonstrated:2 2a:4 spinwave:1 agreement:5 stem:1 pressure:3 bq:5 although:2 in15:9 properties:1 ohneysen:1 vishwanath:1 ferromagnetic:11 disorder:2 discussed:3 dependence:2 o:5 range:4 important:3 coexists:1 circumstance:1 nsi:4 soc:1 sd0:2 pergamon:1 into:6 helical:7 three:4 tanaka:1 hermitian:1 macrophysics:1 references:2 determine:1 sov:1 proportional:5 methods:1 additional:1 helimagnetic:1 there:2 long:2 noticed:1 dispersion:1 width:1 conservation:1 low:1 decisive:1 was:9 pintschovius:1 function:2 yanase:1 form:2 usp:1 but:4 grigoriev:4 russian:2 hc:41 eksp:1 true:1 aqk:1 partially:8 directed:1 smooth:1 up:1 us:1 below:6 demonstrate:2 problem:1 similar:4 obtains:2 strongly:2 garst:1 centrosymmetric:1 constant:2 ln:1 ak:15 metals:1 general:3 aq:6 single:2 ar:3 crystals:1 tedious:1 functions:1 2dq:1 no:1 whereas:1 when:2 cˆ:6 handed:2 field:26 papers:1 dipolar:1 binz:1 conclusion:2 condens:1 reorientation:1 in2:1 a1:1 a0:3 a3:1 a2:4 a4:1 structure:6 correlated:1 interval:1 pseudo:1 together:1 4n:2 4l:1 walker:1 |
0704.0684.txt |@word limited:1 magnetic:1 dynamic:45 four:7 ginzburg:4 entropy:1 sch:1 looking:1 paris:2 mcs:8 presents:2 neighbours:1 δhj:1 δhi:1 under:17 slowest:1 conjecture:1 amorphous:1 every:1 jack:2 summarized:1 experimentally:4 encounter:1 cianci:1 solution:11 vector:3 guiding:1 straight:1 10k:5 glassy:51 force:2 consistent:7 10a:1 direct:2 approximation:4 surrounding:1 second:11 chem:9 even:11 established:2 struik:1 selected:4 constrast:1 establishes:1 zippelius:1 net:1 increasing:3 evolving:1 whose:1 divergence:5 here:10 atoms:2 refinement:1 represented:2 logarithmic:1 obtained:5 study:11 yoshino:2 completely:2 pinning:1 spacetime:1 projection:2 explained:5 total:3 linearly:1 derivatives:6 would:5 call:1 m0:1 lennard:4 type:7 tell:2 separated:2 skewness:1 relax:1 composite:2 glass:22 separates:1 hold:2 must:5 dominicis:2 springer:1 ma:1 room:1 pursue:1 work:4 theories:4 temperatures:6 concepts:2 example:7 renormalization:1 indicated:3 give:2 generically:1 indicates:3 want:1 absolute:1 aging:55 end:7 provide:1 verify:1 how:13 nontrivial:1 ens:1 answer:4 orientational:1 description:2 undergoing:1 transforming:2 thermodynamic:2 oscillators:1 after:5 summarize:2 law:2 parallel:2 types:1 attempt:2 third:1 summing:1 parisi:3 green:4 correlation:69 order:19 interpretation:4 enter:1 over:16 vary:1 satisfied:3 satisfies:2 before:1 monotonicity:1 symmetry:47 fiz:1 fix:2 better:4 distinguishing:1 fig:14 weeks:3 easier:2 shear:5 eventually:1 them:5 band:3 they:9 mimicking:1 structural:8 represents:3 oxygen:1 grows:1 arrow:3 each:6 side:2 hypersphere:1 mean:21 financial:1 list:1 principles:2 joined:1 literature:1 trading:1 laboratory:2 recognizable:1 rt:1 restricted:2 particles:3 rg:1 reader:1 surprise:1 rn:1 sluggish:1 ri:1 scalings:1 i2:3 turning:2 linear:23 little:1 ramos:1 reparametrizations:16 checked:1 estimate:1 r1:4 r2:5 r3:4 starts:2 days:1 silicon:1 lozano:2 corrections:1 liquids:6 onto:1 biroli:4 already:6 features:3 restrict:1 another:5 thick:4 electronic:1 illustrate:1 similarly:4 berthier:6 eqs:5 approximately:3 needed:1 perturbations:4 master:8 too:6 ordered:1 collapse:3 centered:2 keldysh:2 took:1 positively:1 distance:1 showed:5 correlators:4 project:3 matter:4 classes:2 solely:1 rag:7 quench:2 boston:2 manner:3 seem:1 seek:1 contents:33 relatively:1 forced:3 convenient:5 latter:5 reparametrization:62 acquire:1 shall:3 impurities:1 boltzmann:1 regular:1 quantitative:3 phase:13 nussinov:1 dummy:1 observation:2 dom:2 lpt:1 flow:1 points:9 principle:1 sum:7 labels:1 gauge:1 solutions:3 tempted:1 hypercube:1 just:18 became:1 delays:1 appreciated:1 do:13 mixture:1 above:8 dd:7 de:5 dc:1 da:1 report:1 dt:10 eme:1 runs:1 fields:9 acknowledgments:1 thanks:1 reference:2 testing:2 observed:8 depends:7 radius:1 result:4 supercooled:4 discussions:1 techniques:1 away:2 symmetric:1 saddlepoint:1 simplest:5 drawn:1 approach:18 accord:1 terms:19 nature:7 weak:7 however:4 extent:3 irregular:1 bray:2 against:9 heterogeneities:11 contribution:3 argue:2 confronted:1 height:2 factorize:1 lennardjones:1 basis:1 three:15 been:15 much:8 interpret:1 interest:2 expected:5 dynamically:1 location:1 dots:1 life:1 quantities:8 worked:1 spin:34 manifolds:1 applied:3 spontaneously:1 aim:4 near:1 gumbel:6 applies:6 property:5 leaves:1 characterizing:2 phenomenological:1 ip:4 iv:2 ii:3 characterize:3 ij:1 cond:13 disappear:1 perform:1 make:6 linked:1 complex:3 mixtures:1 dimensionless:1 several:5 characterise:1 independent:7 i1:1 laboratoire:1 numerical:10 monotonic:4 counterparts:1 hand:4 potentials:1 normalization:3 kept:1 scenario:13 changes:1 materials:3 claims:2 left:11 unified:1 proposed:5 newton:1 transforms:2 bellon:1 yet:3 previous:2 poses:1 eln:2 candidate:1 infinitely:1 had:1 belongs:1 transformed:1 easy:1 gave:1 bands:1 posed:1 possible:8 eorique:1 boxes:1 vibrations:1 unique:4 advanced:6 steps:3 arbitrary:1 cooled:12 right:12 dean:5 entropic:1 dropping:1 normal:1 when:12 plot:7 elucidate:1 illustration:1 binder:2 super:12 properties:17 o:5 slightly:1 automatically:1 considerations:1 presence:3 dyson:8 rotations:3 hallmark:1 bath:4 down:4 acad:1 sov:1 ezard:1 refined:1 rely:1 support:3 initial:2 approximate:11 lowering:1 lags:1 anderson:6 way:13 was:6 form:31 differences:5 analyse:2 cedex:1 encoded:1 absent:1 assessment:1 inside:1 maximum:2 crystal:1 crider:1 panels:3 phil:1 ln:6 abstract:2 conserved:1 exist:6 simulations:7 nagel:1 distributions:1 check:3 constructed:1 nn:1 no:4 nc:1 generally:2 vanishes:4 schwinger:10 unambiguously:1 role:4 holding:1 papers:1 test:5 nr:1 picture:2 models:36 welcome:1 variable:6 picco:2 jones:4 younger:3 regime:38 longer:2 typically:2 dτ:2 time:187 observables:3 annu:1 trappe:1 global:73 activated:1 focus:5 leads:2 morphology:1 discern:1 layers:1 certainly:1 depend:3 aron:1 environment:3 answered:1 finally:5 monotonically:3 marks:1 advantage:3 grigera:1 locked:1 exact:4 presented:6 proposals:1 skewed:2 solved:2 science:1 dis:1 upper:5 measurable:2 lpthe:1 htw:6 cost:1 appear:9 axes:1 uniform:8 current:1 goes:3 suppress:1 satisfy:3 understanding:6 alone:3 along:5 appears:2 change:4 bu:1 institute:1 studied:6 pictorial:1 usually:1 hospitality:1 therein:2 studies:2 emerge:1 useful:2 modifying:1 translational:1 wang:1 angell:1 additive:3 working:4 prove:4 sake:1 positive:3 visit:1 predictions:12 france:3 scenarios:3 opposed:1 memory:1 associated:10 selects:2 theoretical:8 introducing:1 everywhere:2 cases:11 effort:1 rotational:2 modified:2 reviews:1 labeled:1 values:8 slowness:1 following:3 jstat:1 cag:20 nearest:1 figure:10 predict:2 arise:2 sample:8 performed:3 allowed:2 kennett:5 rescaling:1 verlag:1 requirements:1 discussion:5 write:3 fourth:2 dotted:1 parameter:17 product:1 mar:1 mat:13 may:10 mag:1 date:1 data:5 man:1 stress:1 natural:3 dynamical:11 liquid:10 st:2 sk:3 sj:4 si:13 so:12 sn:1 representation:2 thirumalai:2 typical:2 noteworthy:1 indeed:14 displayed:3 entity:1 experiments:4 ϕr1:1 statistical:2 argued:1 still:9 derive:6 group:1 thank:2 acknowledge:1 interesting:3 jij:3 coordinates:1 forms:6 window:2 decreased:1 main:4 non:21 matches:1 introduce:2 scaling:45 now:6 discuss:10 possess:1 susceptibility:20 term:4 name:2 drop:2 realistic:4 ji2:1 ji1:2 goldstone:4 domain:4 vanishingly:1 ea:14 approximates:1 inhomogeneous:1 entering:1 wavelength:3 eq:18 emerges:2 shown:7 100k:5 space:9 furthermore:2 miyazaki:1 increase:2 shows:2 theory:6 state:14 mechanisms:3 quite:4 dependencies:1 complicated:1 transition:10 motion:1 turn:1 place:2 think:1 first:15 origin:4 surviving:2 lequeux:2 omitted:1 variables:15 xy:1 long:34 directly:3 array:2 open:2 angular:2 size:9 kurchan:9 given:5 necessarily:1 sheet:1 unitarity:3 indicate:2 1e:21 1k:5 gives:1 mostly:1 kirkpatrick:6 continuous:2 transverse:1 absorbs:1 than:8 effective:20 garrahan:5 were:1 accessed:1 outcome:1 generality:1 correction:1 argument:3 crossover:3 say:11 any:4 ideas:8 note:5 ideal:4 potential:4 take:9 cnrs:1 aspen:1 opposite:3 cugliandolo:20 decreasing:3 clearer:1 falls:1 algebraic:2 importantly:2 rationale:1 multiply:1 analytically:1 xµ:1 especially:1 average:10 later:5 implications:4 sigma:1 quantity:1 slope:1 show:8 justifies:1 spaces:2 diverge:2 slow:30 ratio:2 histories:1 analytic:11 only:14 explicitly:3 black:2 get:1 tilting:1 expects:2 cannot:4 nearly:1 ferromagnets:1 geometric:1 yield:5 summary:2 predicted:3 though:9 physically:1 namely:1 uncorrelated:3 surfaces:1 inequalities:1 ways:1 excitations:2 review:6 definite:1 sites:8 energetics:1 behind:1 enumerated:1 between:26 justified:1 checks:1 notice:1 sompolinsky:1 vertical:3 ascribed:1 multiplier:1 analyzed:1 article:1 jetp:1 many:3 region:2 propagation:1 tour:1 traded:1 among:1 jammed:1 lagrange:1 moreover:4 considering:2 fabricius:1 oder:1 ξeq:3 production:1 borders:1 direction:3 observe:1 external:9 careful:1 irrelevant:3 former:1 those:2 case:16 developing:1 intimately:2 conformal:1 polymer:1 characteristics:1 couples:1 peliti:2 baths:1 different:32 develop:1 sicilia:2 coexisting:1 same:28 arguments:1 ciliberto:1 propose:2 physical:3 pan:1 status:1 trivially:1 companion:2 running:1 invariance:61 relies:2 modes:9 zerotemperature:1 expression:2 roughly:1 ogren:1 without:9 solve:1 model:33 charbonneau:2 dimension:1 justify:2 manifold:2 being:3 captures:2 guided:1 rest:1 speed:2 rose:2 parametrization:1 cc:2 interested:2 treatment:4 grempel:1 real:5 aspects:1 around:2 rules:1 sums:2 early:1 otze:2 world:3 meaning:1 particle:5 velocities:1 serves:1 either:2 integrals:4 characterizes:3 inter:1 stationary:20 reduced:1 satisfactory:1 cr:25 matching:1 reasons:1 dimensions:3 langevin:3 fluids:1 critical:5 provides:1 refer:1 reasonable:1 power:3 broken:5 ratios:2 inherent:1 central:1 ferromagnetic:5 discussed:4 generated:3 ezin:2 act:1 mixed:1 perturbed:1 cambridge:1 spreading:1 numerically:8 cipelletti:2 dissipation:7 references:2 determine:2 conceptually:1 theoretically:1 technically:2 kivelson:1 assumed:1 unmodified:1 there:18 start:2 workshop:1 low:10 series:1 slopes:2 strict:1 assumes:1 complete:2 enough:6 makse:2 displacement:1 trying:1 faster:1 applying:4 embedded:1 buisson:1 operationally:1 obtains:1 detailed:3 diverges:2 ag:2 certain:5 sketched:2 general:3 arises:1 controlled:2 moves:1 again:5 ideally:1 stationarity:1 field:24 valid:2 spatial:12 forcing:2 briefly:1 separate:1 drift:1 walker:1 important:10 ising:7 included:1 curve:12 describable:1 mimic:1 mass:2 resembles:1 starting:2 original:1 represent:1 sci:1 consider:1 restated:1 follow:3 tw:169 vs:3 program:1 preserved:1 th:1 stochastic:2 td:5 tc:5 ınguez:2 song:1 very:21 conjectured:1 fall:3 difference:7 condition:1 hamiltonian:1 t4:2 t2:64 t3:47 t0:7 t1:46 large:11 small:7 appearance:2 tef:8 past:1 zero:16 displays:2 further:3 what:12 nano:1 clock:9 section:6 dtν:3 falsify:2 contrast:2 quenched:9 condensed:2 full:7 ranged:4 modify:2 behaviour:7 relaxation:26 strong:1 equations:31 transformation:5 search:1 tµ:6 allows:3 pics:1 stiffness:1 published:1 action:56 via:2 family:3 requiring:1 semiconductors:1 analyzing:1 pdfs:13 viot:1 silva:1 twa:1 takes:3 distinct:1 contains:2 quasi:2 taken:9 more:16 flat:1 tested:3 basically:3 particular:6 known:2 recall:1 equation:8 remain:2 paragraph:1 del:1 compare:1 stated:2 neglected:1 ann:1 states:3 sphere:2 minimum:1 sense:6 sharp:2 needs:1 rather:8 breaking:7 cst:6 explains:1 ensemble:2 simplicity:3 fr:1 tried:2 derived:4 treatments:1 fc:36 fd:1 waves:3 horizontal:4 derives:1 response:15 short:14 twisting:1 perhaps:1 negligible:1 sect:9 help:2 developed:2 trade:1 held:3 thermal:9 paper:2 through:4 existence:5 avenue:1 its:11 rapidly:2 energies:1 actually:1 absence:1 microscopic:3 systems:46 argentina:1 might:2 good:1 schematic:1 universality:5 framework:5 stariolo:1 spinglass:1 develops:5 easily:2 fully:13 level:3 fluctuate:6 2d:2 stopped:1 fχ:12 found:3 2n:1 characterized:5 weight:1 generation:1 mesoscopic:2 energy:3 hard:1 idea:5 numeric:1 expect:6 measurement:1 quantum:10 beyond:1 rheology:1 really:2 since:7 research:2 evaluation:1 occurs:1 localization:1 reason:3 imagine:1 put:4 teach:1 generate:1 pairs:3 universidad:1 consequence:2 probability:6 number:11 done:4 least:4 perturbation:1 temperature:37 introduction:6 leading:5 kob:2 construct:2 assumption:5 statement:3 molecular:2 recovered:1 listed:1 calculations:1 immediate:1 prediction:3 part:7 translation:2 believe:3 unrealistic:1 diffusion:2 kind:2 scheme:1 double:1 largely:1 plateaus:1 grained:20 determined:7 treated:2 etage:1 ages:6 randomly:1 elsevier:1 hexagonal:1 orders:2 lie:3 constructions:2 jour:1 sellitto:2 lim:6 self:6 extracted:1 generalized:2 analogy:4 sherrington:2 kac:2 play:1 towards:3 reckon:1 measures:2 reach:1 most:4 nothing:1 measured:6 ccg:2 deviations:1 tν:8 clear:7 physica:3 tα:5 clean:2 velocity:1 physics:5 particularly:1 phenomenon:1 session:1 relation:22 spacings:1 causality:5 parameters:4 distributed:1 subsection:2 factor:2 his:1 dominant:1 notation:1 dependent:9 ϕr:3 wolynes:4 actions:1 arxiv:1 common:3 fluidized:1 vincent:1 set:1 achieved:1 see:12 close:7 contour:1 preparation:2 currently:2 pisa:1 smallest:1 eksp:1 conditions:3 knowing:1 recently:1 responses:5 vanishing:3 ferromagnet:5 both:2 collaborators:1 last:3 reverse:1 dtw:1 sensitive:1 improves:1 context:2 retarded:6 pdf:15 whole:2 finds:4 experimental:4 arbitrarily:1 point:23 simple:10 asymptotically:12 corresponds:4 whatever:1 dimensional:14 simply:4 described:9 transformations:2 glotzer:2 due:5 reduction:1 describes:3 coarse:35 shorttime:1 chandler:2 lett:16 generating:4 else:2 understand:6 equilibration:3 replaces:1 δsj:1 look:1 exponential:2 δsi:1 solid:6 siggia:1 evaluated:1 pace:1 while:13 replaced:1 behavior:4 costly:1 saturation:1 encountered:1 itself:2 kinetically:3 santos:1 lengths:7 belong:1 read:1 widely:1 qab:3 higher:2 development:3 used:9 t21:1 moment:1 levels:1 uses:4 purpose:1 stack:1 eigenvectors:1 lower:7 older:3 analysis:11 concrete:2 solids:5 equilibrated:1 parametric:16 stating:1 distances:1 λt:3 reviewed:1 questions:2 using:18 spatially:5 cut:1 conclusions:3 plateau:4 theorem:3 relevance:1 remaining:3 forces:1 phenomenology:2 couple:3 weitz:1 quest:1 apt:1 integer:1 emergence:2 helpful:1 modifications:1 success:1 follows:10 interestingly:2 manifest:1 imposes:1 yields:4 reichman:3 translated:1 disorder:10 essential:1 spins:7 mathematical:1 polymers:1 sketch:5 some:13 understood:2 examples:1 bramwell:1 scale:28 describing:6 kegel:1 affects:1 glassiness:3 measurements:1 integration:2 behave:2 prog:1 proc:1 minimal:1 varying:5 run:2 restrictive:1 step:3 br:2 relating:1 dictated:1 developped:1 concretely:2 constraint:2 kawasaki:2 completing:1 simulation:2 range:4 consequently:1 qea:49 into:13 within:10 integral:2 nsf:2 perturbing:2 next:1 statistics:6 institut:1 extremely:2 sequence:1 question:6 fast:8 forward:1 analyze:2 considerably:1 ioffe:1 line:11 characteristic:2 probabilistic:1 up:3 us:18 fdt:4 heterogeneous:5 fluctuations:48 similar:18 called:3 partition:1 constant:8 defined:8 metals:1 single:1 formalism:4 defines:4 amounts:1 dashed:1 edwards:4 rewriting:1 priori:1 department:1 deviate:1 draw:1 elements:1 problems:9 001e:1 fisher:2 structure:4 correlated:1 implies:8 age:5 graining:15 equivalently:1 weights:1 presenting:3 far:7 requires:1 having:2 once:4 results:7 illustrated:1 eds:1 houches:1 edu:1 manipulations:1 contributions:3 issues:1 gases:1 concerned:2 excluded:1 stable:1 statics:1 random:11 wave:3 incoherent:1 diverging:1 notes:1 inspection:2 zh:1 disordered:5 claudio:1 picked:1 zt:4 dynamics:40 scientific:2 plays:1 expressed:2 find:3 waiting:8 concisely:1 renders:1 3d:13 body:1 lee:1 respectively:6 spacing:3 growing:6 packing:2 les:1 separation:23 others:3 great:1 technical:2 involved:2 larger:2 leaving:1 suggests:7 products:1 proof:1 explain:4 examining:1 formulated:1 scales:22 apr:1 reparametrized:1 limt:4 scaled:1 addressed:1 arenzon:2 apply:10 causal:2 cloud:1 use:5 asymptotic:27 usa:2 remains:3 guideline:2 few:1 vollmayr:1 themselves:1 panel:10 χst:5 becomes:5 carrying:1 sharply:1 iii:2 account:7 crosses:1 averaged:2 obvious:3 thin:1 crocker:1 averages:1 scatter:1 dropped:1 control:1 purposes:1 pieces:1 high:2 assumptions:4 something:2 plata:1 sip:1 decaying:2 holds:5 delay:1 located:1 varies:2 instead:5 universitaire:1 coarsegrained:1 philosophy:1 trieste:1 bertin:2 si2:1 si1:1 introduced:4 lines:7 correspond:3 starr:1 allow:5 jussieu:3 lined:1 s1:1 fastest:1 houston:1 facilitated:2 symbols:1 doussal:1 saturates:1 including:3 looks:1 mentioned:2 envisage:1 regions:2 le:1 longitudinal:1 decay:15 chosen:8 temporal:2 coarsening:8 degrees:2 setting:2 eur:1 material:6 landau:3 mention:3 front:1 rotation:1 university:2 identified:1 sufficiently:4 magnitude:3 mode:14 identifies:1 constraints:2 commonwealth:1 lfc:3 related:7 constitute:1 static:2 measure:7 separating:1 our:16 transitions:2 special:2 out:9 matrix:1 res:1 rep:1 rev:28 behaviours:1 lecture:1 wick:1 ref:1 integrated:6 limτ:1 interactions:2 maintains:1 clarify:1 approaches:2 surely:1 franz:5 bouchaud:6 interaction:4 determining:1 could:10 times:41 length:30 derivations:1 hence:6 teor:1 diminishes:2 strictly:2 scene:1 reaches:3 reached:2 precisely:4 hyperbolic:1 ordering:1 system:15 relations:16 their:8 intermediate:3 ictp:1 explanation:3 exactly:1 realized:1 regards:2 manifestation:1 july:1 resist:1 claim:5 negatively:1 sillescu:1 symmetries:4 fluctuation:9 unchanged:1 curves:7 interrupted:1 need:2 curved:3 constrained:1 border:1 clearly:2 min:1 studying:1 physique:1 gravity:1 mechanism:5 instance:2 unless:1 collaboration:1 mimics:1 connected:6 but:34 nuisance:3 formalisms:1 why:10 hj:1 parametrize:1 χr:3 consequences:9 ξst:1 face:1 graphs:1 proceedings:1 hi:1 prefactor:1 normally:1 χj:1 fact:19 selection:1 insulators:1 text:2 superimposes:1 trivial:4 based:9 knowledge:2 holdsworth:1 should:34 dalibard:1 attained:1 local:75 equilibrium:20 slows:1 means:4 ttw:7 donati:1 overall:1 feigel:1 joint:5 ones:9 words:2 exchanges:1 evolution:5 paramagnetic:1 differential:1 europhys:2 contain:1 qi:1 fixed:11 nist:1 view:7 requirement:2 constructing:2 exists:4 correlations:48 computes:1 interacting:2 dmr:2 tend:1 favor:1 written:5 closed:1 invariant:12 boundary:2 mainly:1 saddle:1 chamon:10 reproduced:1 hypothesis:2 key:1 problem:8 observable:1 instant:1 limits:2 taking:4 equal:3 barrat:3 etc:2 admit:1 regimes:3 otherwise:1 cj:1 relevant:3 wall:1 cg:6 harmonic:1 environments:1 ab:1 decreases:2 respect:12 crystalline:2 addition:1 slowly:4 proposal:6 describe:7 corresponding:4 bulk:7 present:9 c4:3 multi:4 novel:1 harder:1 value:19 choices:1 will:3 frameworks:2 layer:1 refs:1 thus:16 site:4 surface:3 equilibrate:1 quantize:1 vr:3 examined:1 lifetime:1 claimed:1 generic:4 member:1 parts:2 castillo:6 gibbs:1 units:1 finite:36 difficult:1 practice:2 infinity:1 cubic:1 upon:3 effect:6 parametrized:1 infinite:11 mech:1 off:1 center:1 nevertheless:1 nonetheless:1 well:16 sets:1 position:6 arising:3 usual:1 spherical:9 ediger:2 magnetization:5 less:1 obtain:5 underlying:1 predicts:2 macroscopic:2 rapid:3 density:5 nacional:1 lattice:9 book:1 extends:1 natl:1 c13:1 identical:5 tests:10 fluctuating:11 increased:1 criticality:1 sytems:1 increases:9 five:1 know:2 immediately:1 domains:2 fradkin:1 massless:1 necessary:2 like:8 lost:1 sizes:1 alternatively:1 qualitative:1 susceptibilities:18 martin:1 become:4 soft:7 accessible:1 because:4 classical:2 smoothly:1 phenomena:3 algebraically:1 growth:8 fluctuationdissipation:1 proper:5 koga:1 highlighting:1 condens:2 overlap:1 instantaneous:1 does:14 assuming:4 limitations:2 blaaderen:1 noise:2 vertex:2 analysed:1 expansion:1 approximating:1 simpler:1 about:5 carried:4 getting:1 freedom:2 introduces:1 dependence:1 glasses:29 homogeneous:1 outset:1 rendered:2 letters:1 h2:2 h3:2 h1:2 functional:19 mere:1 pinton:1 additional:1 elastic:1 spread:1 restricts:1 quadratic:1 tg:1 frustration:2 tarjus:1 function:25 triangular:14 ht:12 gaussian:9 volume:6 construction:8 compute:2 whether:6 wish:1 brackets:2 smooth:3 below:4 limit:39 distribution:5 display:2 int:1 universal:11 slowing:1 denote:1 replica:2 relates:1 hautes:1 functions:29 variety:1 detail:3 envisaged:1 other:22 details:4 droplets:1 conclusion:1 stat:1 class:6 variation:1 ultrametricity:4 coupling:13 factors:1 volumes:1 searched:1 |
0704.0685.txt |@word sci:3 consider:3 forbidden:1 results:1 proposition:3 generalize:1 grateful:1 whose:4 inverse:1 tn:5 tm:3 tk:6 th:29 ti:1 cm2:1 cm1:1 p2:1 conjecture:5 orthogonal:1 very:1 connects:1 corollary:1 wishes:1 rationality:2 involution:1 cmr:2 sign:1 approximation:1 second:1 odd:1 even:7 index:1 appear:1 morse:1 section:2 above:2 new:1 t2s:1 consisting:1 coefficient:5 respectively:3 equals:2 here:6 mev:5 subword:14 groups:1 path:4 appears:1 remark:1 studied:1 permutation:1 deg:2 changes:1 apr:1 boolean:1 ayk:1 prove:2 positive:1 contains:2 sµ:7 call:2 therefore:5 ayt:1 more:1 flag:1 springer:1 orner:9 word:1 tns:3 recall:1 mn:1 mi:6 mr:1 following:3 trans:1 ay1:1 example:1 proof:21 claim:4 σli:1 give:6 s1:2 holds:5 forest:1 answer:1 obius:9 map:5 description:2 algebra:1 advice:1 chow:1 derived:22 sx:5 natural:1 st:2 sk:9 si:5 so:2 sn:9 sm:12 sl:6 definitions:3 order:10 s0:1 matsumoto:1 daisuke:1 paper:4 through:1 its:1 ima:1 τk:1 τi:4 interesting:2 fix:1 main:1 τr:1 τs:4 correspondence:1 non:2 tableaux:1 they:2 now:15 easily:1 2s:3 university:1 modd:5 each:2 2l:1 found:1 side:2 cl2:4 series:3 hypergeometric:1 related:1 our:1 special:1 shown:1 discrete:2 since:1 induces:1 combinatorial:2 geom:1 formula:3 induction:4 math:8 theory:2 subsequences:1 york:1 put:12 compositions:1 definition:5 starts:1 times:15 length:6 hence:19 qn:13 first:6 reversing:1 xn:15 rooted:3 xm:2 bijection:1 number:8 rank:1 ql1:5 morita:1 passes:1 introduction:1 system:1 their:1 posets:4 σki:2 x1:10 kind:3 see:6 mobius:6 were:1 comput:3 cohen:1 generalization:4 affirmative:1 take:8 element:2 orders:9 paths:8 ax1:3 k1:1 ck1:6 generalized:10 ck2:6 combin:1 most:10 position:1 reutenauer:1 axt:5 professor:2 kr:1 ckr:1 axk:1 chebyshev:18 show:4 notations:1 ki:7 relation:4 tks:7 analogue:1 trivial:2 q1:26 q2:2 lemma:33 only:1 t0s:3 factor:3 partially:1 his:1 notation:4 aβ:1 words:1 arxiv:3 ql:9 sho:1 set:2 reference:1 j1:10 j2:4 namely:1 result:15 stanley:4 best:1 ways:1 pattern:1 symmetric:1 enough:1 vatter:3 between:1 invariant:1 notice:5 jp:1 jm:6 ji:16 jk:4 σq1:1 amer:1 thank:1 σk:22 σj:1 σi:14 σm:6 σl:1 embedding:12 σp:1 expression:1 sα:3 ck:28 among:1 ci:1 co:3 cn:54 cm:28 point:1 simple:1 cf:1 cd:2 polynomial:4 cq:22 cp:14 ps:6 transformations:1 west:1 px:2 locally:1 enumerative:1 ai:4 basic:2 pk:12 pi:3 pl:2 define:7 θj:1 θk:1 generating:1 θi:7 θr:17 c2:3 case:12 p1:55 splits:1 suppose:5 vectors:3 vol:4 macaulay:1 author:1 any:1 finite:3 composition:3 qji:10 used:2 context:1 hand:2 shellable:1 acknowledgement:1 studies:1 well:1 analysis:1 obviously:1 sets:1 claims:1 left:1 shellability:1 being:1 generally:1 obtain:14 valuable:1 transforms:1 σnk:5 σni:2 cl:2 theoret:3 easy:2 theorem:4 gave:3 involutions:1 press:1 using:2 unique:1 poset:14 advanced:1 helpful:1 follows:10 right:11 sequence:1 some:1 tsukuba:1 comments:1 l2:5 bl:2 l1:3 bj:9 binomial:1 integers:1 algebraic:1 ob:13 cl1:2 t1s:3 obp:10 soc:1 cambridge:3 letters:1 into:10 determine:2 combinatorics:2 appl:1 way:1 was:1 function:10 jun:1 but:1 sagan:4 construction:2 true:1 he:2 arranged:1 pm:43 called:2 ac:1 ordered:1 defined:2 recognize:1 ak:3 describe:1 am:24 minneapolis:1 denote:2 ay:4 ax:16 functions:7 no:2 ends:1 when:4 forests:1 other:1 mathematics:1 elements:3 kinds:1 polynomials:15 a1:31 |
0704.0687.txt |@word ϕj:47 u2i:1 uvj:1 λk:7 λj:2 αk1:8 rot:52 λn:7 hloc:1 q1:4 k3:21 ld:2 x1:7 ny:2 ln:4 tr:4 µj:2 lq:4 µh:10 u1i:1 g2:9 g1:11 df:2 dλ1:16 dx:26 dy:1 4c21:3 dt:28 ds:27 2p:1 2r:1 arxiv:1 t0:28 t1:1 au1:18 l4:1 au2:8 l2:9 l0:3 2c:5 2l:7 2m:2 div:7 qm:57 2k:1 zn:3 zj:21 q1m:31 b1:30 d¹:1 ess:1 3k2:2 3r:1 d0:4 qº:1 2c0:5 nº:1 2c2:4 wº:1 gi:1 sup:15 rn:1 ek2:3 math:1 λkr:3 pm1:1 lei:3 l1:1 wk:4 wj:4 bi:1 qi:2 e1:1 2n:1 e2:1 c21:8 r2:2 2h:15 ξj:1 4c41:5 qn:8 cˆ2:3 cˆ3:9 cˆ1:5 xj:5 xi:5 xn:3 cn:2 ri:1 apr:1 h1:1 cf:1 8c2:1 k13:8 k12:5 log:2 u1:64 u0:10 u3:1 u2:59 1d:3 λm:6 pn:6 4c4:3 pm:23 2c21:1 hp:3 x2:5 c2:11 c1:49 c0:13 p2:1 p0:4 p1:7 ut:2 ρk:4 ωt:2 ωi:4 8c:1 ωk:3 un:1 ui:4 uk:6 uj:5 ua:2 dτ:5 hº:2 f1:13 f2:11 νr:39 vj:26 dξ:3 ap:1 au:40 av:1 inf:4 rid:1 dα:1 dh:1 min:4 lim:16 2νr:58 k2:37 k1:60 2c1:4 hpm:5 max:5 a1:36 ξi:2 a3:1 a2:1 ξn:1 fi:1 fk:4 fn:2 2l2:12 νk2:1 νk1:6 k22:3 k23:6 hp1:1 αa1:2 2f:1 exp:10 n2:2 4c:2 |
0704.0688.txt |@word neighbors:8 limited:4 dist:5 consider:6 pointing:5 represent:2 depends:5 results:1 tendrils:2 interpret:1 helped:1 commute:1 edu:4 gn:3 denotes:1 causes:1 soc:1 devoted:1 rd:18 c0:6 depend:4 patches:1 tx:2 vacuous:1 deterministic:4 unanswered:1 tn:18 finally:3 those:2 th:4 under:4 analogous:4 include:3 norm:1 γd:32 applied:1 supported:3 jensen:1 far:4 could:2 assuming:1 mg:1 aszl:1 corollary:1 valued:1 every:7 summarized:1 cook:3 ui:1 difference:4 bringing:1 condition:2 induct:1 impressive:1 exits:3 made:1 positions:1 t2:4 t1:5 large:6 discrete:6 sand:3 proposition:8 succession:1 small:1 div:8 caltech:1 martingale:3 zn:1 des:1 says:2 organised:1 zd:55 consistent:1 priezzhev:2 sign:1 located:2 zero:2 infimum:1 pass:1 further:1 estimated:1 toppled:1 even:2 trick:1 what:1 diam:4 plays:2 giving:1 fine:1 section:8 axes:1 analogously:1 find:1 current:2 abs:5 transformed:1 above:6 sup:1 learned:1 increasing:1 ever:1 consisting:1 satisfy:1 κm:1 2h2:11 whose:2 never:1 here:4 tangent:3 8d:1 berkeley:4 directions:5 path:2 along:2 strong:2 appears:1 z2:6 intersect:1 box:3 sending:1 remark:5 increments:2 colored:1 superharmonic:12 study:3 studied:2 leaving:1 amount:5 resulting:3 graph:1 suitable:3 exited:1 useful:3 although:2 extra:1 pling:1 paradise:1 visible:1 inductive:1 apply:1 clockwise:1 univ:2 unit:7 use:5 metaphor:1 asymptotic:6 prove:7 distinct:1 positive:3 asz:1 contains:2 visit:2 negative:2 odometer:8 distributing:1 comparing:1 topples:4 m0:1 vi:9 mysterious:1 indiana:1 h1c:1 type:1 until:4 ψd:8 fey:6 diamond:2 integers:1 started:10 ti:2 everywhere:3 wilfried:1 particular:3 known:5 hole:4 td:2 tx1:1 must:4 high:2 keeping:1 endpoint:1 rα:1 cluster:1 wiesenfeld:1 recall:1 work:1 mk:1 mt:2 remain:1 values:3 three:1 den:2 following:14 topplings:2 example:2 fulton:1 proof:31 control:1 method:1 theorems:2 figure:13 abelian:21 process:3 chip:1 organized:2 near:5 sake:2 topic:1 minimum:3 performed:1 hyperplane:4 sense:2 triangle:1 nonnegative:6 occur:2 νk:2 information:1 thank:2 provide:1 s1:1 holds:5 rapport:1 regions:2 very:2 cardinal:1 adjacent:3 simplifies:1 instead:1 hi:9 parameter:2 circular:1 map:2 de:2 2cj:2 spitzer:1 algebra:1 may:3 max:2 after:8 derived:1 different:2 constraint:1 diagram:3 plane:1 inst:1 heuvel:2 quadratically:1 improving:2 fk:1 grow:1 constants:5 times:1 xte:1 natural:1 outline:1 imply:1 coupling:3 whenever:2 lemmas:3 yielding:1 assign:2 sk:17 perform:2 hic:1 negligible:2 sn:17 enter:1 enti:1 order:3 xj:3 circularity:3 s0:2 indeed:2 over:5 stays:2 uchiyama:2 paper:2 through:2 thesis:1 existence:2 satisfies:3 still:2 its:10 before:9 perfect:2 write:14 le:6 outer:11 treat:1 πr2:1 chosen:4 fix:7 jim:3 expectations:1 coordinates:1 writing:3 html:1 degrees:1 choose:5 ent:1 main:2 defining:6 easier:1 sandpile:34 h1:25 inductively:1 primary:1 scaling:2 answer:1 reaches:11 they:3 half:7 sρ:29 now:8 wiley:1 mystery:1 represents:1 term:5 stated:1 name:1 2r:1 intuitively:1 fully:6 university:2 intelligencer:2 2z:1 grows:1 2d:58 sufficiently:4 inequality:4 stopped:9 each:34 2m:1 entirely:1 higher:4 side:9 algorithmic:1 constraints:2 subset:1 domain:7 square:1 weight:4 independent:7 dωd:1 idea:2 related:1 ball:23 expect:2 our:10 operation:2 beyond:1 event:1 routed:1 out:3 principles:1 matt:1 factors:1 since:29 rev:2 research:2 particles:35 fellowship:1 settle:1 adapt:2 performs:2 maximized:1 denoted:1 newly:1 2k:19 math:11 shows:2 earlier:2 mρ:4 linear:3 2h1:1 change:1 million:3 divergence:1 borgne:5 possibility:2 standard:2 indices:1 base:1 california:1 org:5 estimate:12 spencer:1 e1:4 markov:1 additional:3 definition:1 r1:6 r2:6 agree:1 starts:4 just:1 inferred:1 lawler:6 turn:4 length:3 place:2 avec:1 hence:22 router:26 probab:5 think:1 south:1 first:25 origin:19 xk:33 intuition:1 initial:4 features:1 probability:13 kernel:3 thereafter:1 faculty:1 number:21 walkers:2 infinite:1 enlarged:1 another:1 blows:1 xt:15 size:1 rossin:5 given:14 necessarily:1 their:1 introduction:2 1x:1 crossings:1 least:9 parallel:2 needed:1 draft:1 convention:1 fonctions:1 dhar:2 white:1 final:8 shifted:1 shell:5 fraction:1 firing:1 centered:5 estimates:6 explanation:2 unoccupied:5 8d2:3 authors:1 x2:4 absorbs:1 x0:2 x1:9 than:4 center:1 diffusion:4 distance:10 showed:1 divisible:17 rate:1 extraordinarily:1 limiting:3 classes:1 were:1 visited:4 treated:1 springer:1 vector:1 comput:2 rend:1 ann:4 cept:1 argument:2 generalization:2 summing:4 already:2 need:4 rotors:6 occupied:16 any:18 viewed:2 rotor:43 diaconis:1 depending:18 lim:3 self:2 τk:3 converges:1 note:12 internal:15 absorbed:1 generalized:1 xi:25 so:14 coincide:1 circles:1 lectures:2 begin:1 shvets:1 multiple:1 opposite:1 who:2 reach:5 birkh:1 extending:1 connected:3 net:2 remarks:1 oil:1 extremely:1 why:1 bound:6 give:1 observation:1 petite:1 neighboring:2 clear:1 stronger:1 vertices:2 dh2:1 points:7 reflections:1 subharmonic:1 h2d:2 senior:1 usual:1 normally:1 microsoft:1 fact:6 quantity:2 saying:1 phenomenon:1 show:8 nρ:21 retains:1 random:26 rotating:1 colors:2 spaces:3 keywords:1 analogue:3 trivial:1 d3:2 q0:1 ratio:1 knowledge:1 explain:1 distributed:1 outside:1 should:1 xm:1 lemma:62 only:26 factor:3 attained:2 oct:1 centrally:1 do:5 en0:1 dm:23 topple:5 gains:1 µj:3 stop:1 expectation:1 xdi:1 cannot:3 δxy:1 despite:1 during:6 dt:2 αk:4 secondary:1 portion:1 evolution:1 arxiv:6 acknowledgments:1 gbr:3 source:2 scott:1 qk:10 fixed:1 bak:1 remains:1 monochromatic:2 bramson:2 set:9 unpublished:1 2c:2 lazy:5 up:5 observed:1 see:8 individual:1 radius:7 result:11 discussions:2 close:6 sem:1 3c1:2 best:4 subject:2 closer:1 eres:1 dla:7 sites:21 tend:1 symmetric:2 rˆole:1 state:5 propp:5 routing:1 µk:15 between:3 crude:1 invariant:1 boundary:13 αj:2 pictured:1 tent:1 available:2 notice:1 attention:1 terms:6 initially:3 complement:2 emitted:6 however:1 contribution:1 derive:1 hypothesis:1 group:1 configuration:3 optional:1 improve:1 received:2 hits:1 c21:1 last:2 reverse:1 limits:5 many:4 region:9 60g50:1 according:3 called:1 personal:1 improves:1 grain:3 receives:3 faces:2 pde:1 adapted:1 asked:2 comes:1 otherwise:3 arbitrarily:1 among:2 co:1 point:10 simple:12 excess:2 corresponds:1 walk:24 dimensional:1 concluding:1 pol:1 simply:1 lagrange:1 moreover:6 throughout:1 pr:2 cycling:1 second:1 basis:1 addition:2 west:1 px:19 griffeath:2 due:4 laplacian:9 hitting:13 much:1 logarithmic:1 basic:3 expected:3 pk:5 oded:1 empty:1 define:7 direction:4 general:2 antisymmetric:2 inradius:2 formed:5 observe:1 covers:1 τw:1 c3:5 c2:22 c1:18 evidence:1 present:6 lionel:1 case:5 intriguing:1 toppling:7 classifications:1 bρ:9 grains:10 tang:1 empirical:1 value:1 choices:2 will:17 euclidean:4 while:4 replaced:2 error:7 stopping:4 property:9 taking:9 london:1 c4:4 larger:1 attains:1 coupled:3 averaging:2 simulations:2 thus:13 site:26 discrepancy:2 equal:3 ii:1 disjoint:1 itself:1 exiting:4 containing:2 criticality:2 grant:2 perhaps:1 make:2 recurrent:1 lett:2 same:6 complex:1 modification:1 figures:1 proved:3 finite:5 infer:1 difficult:1 disc:2 evolve:1 used:7 http:7 closest:3 holroyd:1 kleber:1 v1:1 v2:1 edges:4 auser:1 aggregate:3 sodin:1 eulerian:2 identity:1 lower:1 fourier:1 shortly:1 maximizing:1 torino:1 uml:1 min:3 well:2 spent:1 analysis:3 without:1 patterns:2 thm:1 edge:4 c5:2 thi:1 sets:1 coordinate:6 model:24 dimension:3 left:3 spherical:6 proposed:1 rotated:2 obtain:15 rest:1 vanishes:4 sources:1 shape:17 identify:2 questions:1 using:8 txk:1 ng:2 previous:1 move:1 heuristic:1 infinitely:4 la:1 conclude:2 had:1 lattice:7 add:1 potential:3 pile:3 location:1 theorem:25 ex2:1 east:1 remaining:1 take:3 real:1 rescaled:3 aspects:1 yuval:1 rules:1 couple:2 aggregation:15 harmonic:3 game:3 know:2 combin:2 integer:6 height:1 grenoble:1 weights:4 mod:2 rotate:1 δx:1 particle:16 follows:14 vd:1 performing:2 immediately:1 shapes:1 continue:2 yields:4 either:6 arbitrary:1 bisecting:1 inversion:1 terminology:1 exceed:1 right:5 methods:3 classical:14 sequence:5 sends:1 huss:1 some:8 draw:1 growth:5 choosing:1 cr:1 extended:1 proofs:1 mat:1 nonzero:1 provided:4 total:9 cooper:1 dimensions:10 majorant:3 2c0:2 πt2:1 prop:1 does:2 exit:5 summand:1 tends:1 redig:6 steps:3 intersections:1 proc:1 noise:1 run:1 power:1 reaching:1 vertex:5 l1:1 bh:1 bi:1 expansion:2 likewise:2 step:7 cube:2 misha:1 br:68 found:1 approximating:1 emits:3 seeded:1 takes:1 comparison:1 about:6 central:2 harvard:1 most:16 www:1 levine:6 discussed:1 o:37 union:1 plus:1 obeys:1 neighbor:6 introduced:1 slightly:1 equally:3 convergent:1 assignments:1 h2:13 communication:1 image:3 within:2 eo:2 nsf:3 son:1 references:1 fruitful:1 subsets:1 next:1 often:1 schramm:1 h1h:1 van:2 log:32 shells:2 segment:1 support:2 there:11 question:4 long:2 start:5 quadratic:1 lov:1 inner:8 way:1 fasc:1 analyze:1 was:4 asymptotics:2 function:30 hx:7 north:2 complete:1 form:1 enough:3 hr:6 denoting:1 hw:5 but:3 gaussian:1 volume:10 construction:1 repeatedly:1 convergence:1 hd:6 partially:1 directed:3 begins:2 october:1 improved:1 evident:1 whether:5 characteristic:1 inside:1 variations:1 bounds:8 signed:1 below:2 dms:2 limit:6 uk:11 sum:12 fluctuations:1 distribution:2 more:5 similar:2 ωd:17 strengthens:1 ex:23 his:1 taylor:2 constant:25 ad:4 defined:6 coincides:2 abstract:1 contribute:1 deep:3 ordering:1 peres:5 single:1 proves:1 exist:3 together:3 walks:15 corresponding:1 inf:1 moves:3 distributions:1 regime:1 hit:2 again:2 functions:3 compared:1 completeness:2 polygon:1 no:14 simulating:1 fixing:3 when:13 green:7 graduate:1 application:1 other:5 role:2 2dc:2 warehouse:1 mathematics:1 2dn:2 nt:1 bc1:12 2dk:1 stat:2 denote:7 completes:1 models:2 setting:3 uniformly:2 shown:1 visits:1 propositon:1 a1:3 a3:1 a2:1 bounded:9 ξd:8 implies:2 faster:1 sheffield:1 space:4 holes:4 rule:1 depth:2 mass:33 lying:1 krishnamurthy:1 time:21 n1:2 4d:6 subdiffusive:1 starting:7 stacks:2 once:2 |
0704.0689.txt |@word precise:1 sco:19 chinese:1 l167:1 reviewers:1 magnetic:1 results:5 gx:33 four:4 eds:1 comments:1 grateful:1 hole:6 millisecond:8 boutloukos:5 quasi:20 applied:3 updated:2 zhang:17 frequencies:11 migliari:3 none:1 wave:3 anonymous:1 resonant:1 difference:3 qpos:21 presented:5 list:3 applicable:1 smale:1 lewin:1 noted:1 upper:9 smaller:1 oscillation:12 miller:4 consistent:1 prediction:1 approximation:1 alfv:2 spectral:5 index:5 appear:2 wijnands:7 incompatible:1 aν1:3 section:2 l12:1 above:1 increasing:3 coefficient:1 compact:1 pose:1 simultaneously:2 respectively:1 l1:2 l21:1 reported:1 l23:1 china:1 l24:1 separation:16 l26:1 accretion:4 strong:1 table:2 j1807:3 obtained:1 study:3 larger:2 stella:3 amount:2 periodic:20 usually:2 resonance:2 plotted:1 magnetospheric:1 apr:1 highly:1 apj:23 decrease:5 would:1 until:1 xte:4 few:1 therefore:1 candidates:2 belloni:9 theoretical:1 more:1 jonker:9 naive:1 varying:1 known:2 cases:2 states:1 account:1 der:40 averaged:2 reviews:1 zhao:2 values:1 l125:1 l129:1 beijing:1 νs:2 give:3 relativistic:3 share:1 high:3 minimum:1 tab:7 lamb:1 rays:1 scorpius:2 varied:1 di:3 influences:1 l9:1 description:1 alfven:1 noise:1 horizontal:1 law:20 data:34 j1808:1 maybe:1 lines:5 correspond:1 extrapolation:1 so:1 decreasing:3 lamost:1 typical:2 horne:1 interpretation:1 correlation:8 quasiperiodic:1 astronomical:1 endez:17 paper:3 including:1 argued:1 still:1 its:1 tendency:3 sciences:1 swank:3 fittings:4 thank:1 fit:6 chosen:2 masses:1 decreases:1 li:2 better:2 detected:5 fig:23 main:1 might:1 versus:1 them:1 mention:1 they:3 half:3 1b:2 now:2 discuss:1 bigger:3 hereafter:2 brightness:2 always:1 university:1 sideband:1 2e:1 2f:1 l5:2 2b:2 each:1 found:3 lorentzian:1 mean:1 individually:1 en:2 significantly:1 bursa:2 linares:3 related:1 frequency:37 our:2 approximated:1 explorer:1 shown:4 l97:1 space:1 furthermore:1 since:2 research:1 increase:2 appreciate:1 outburst:1 shows:1 linear:20 org:1 pairs:2 straaten:6 features:3 l95:1 l35:1 approximately:1 pulsar:4 rxte:2 l39:1 given:2 publication:1 introduction:1 twenty:1 yin:3 system:1 relations:3 their:2 1c:1 assumption:1 1e:1 listed:3 1f:1 rates:1 observations:2 shifted:1 correlations:9 psaltis:9 academy:1 abramowicz:6 l99:1 cyg:1 somewhat:1 x1:1 than:11 peaked:1 wide:2 showed:1 namely:1 classes:1 hasinger:2 were:1 providing:1 function:9 qpo:19 circinus:1 separations:6 curves:1 sax:1 clearly:1 ray:29 vietri:3 instance:1 fitting:16 2006a:2 l119:1 l117:1 klis:40 markwardt:2 towards:1 who:1 most:1 eight:1 accreting:5 acknowledgements:1 kilohertz:15 barret:1 observation:1 consequences:1 behaviour:1 inferred:2 ks:1 points:3 fitted:5 slope:1 show:4 radii:1 scattered:1 discovered:2 bright:3 relation:2 inconsistent:1 lense:1 find:4 ratio:6 parameters:1 sood:1 peculiar:1 black:6 do:1 means:2 beat:4 strohmayer:5 cannot:5 words:1 timing:8 homan:9 precession:3 qu:1 luminosity:2 arxiv:1 summary:1 investigate:1 predicted:1 set:1 reference:2 burst:2 national:1 testing:2 observed:3 ara:1 see:2 individual:7 discussions:1 close:1 luminous:2 exploited:1 tend:3 future:1 various:1 between:14 2002a:2 2002b:3 email:1 discovery:5 variability:4 notice:1 recently:2 statistically:1 nature:1 however:4 key:1 analyzed:2 meaningful:1 both:6 interpretations:1 equal:2 against:2 personal:1 exceeds:1 among:1 point:1 simple:3 harmonic:1 distinguish:1 twin:19 consideration:1 observatories:1 powered:2 addition:2 three:1 been:3 much:1 ph:3 colors:1 diversity:1 systematic:2 evidence:3 spin:5 those:1 case:1 multi:2 value:4 will:1 behavior:1 promising:1 studied:2 j1701:1 cluster:1 vs:10 binary:4 different:2 l54:1 anymore:1 l57:1 perhaps:1 fender:2 same:4 any:3 several:1 neutron:10 higher:1 peaks:1 zhao1:1 normalization:1 lower:6 well:5 roughly:1 obviously:2 patterns:1 sets:2 firstly:4 comparisons:2 model:17 binaries:15 unified:1 salvo:3 less:7 being:1 distribute:1 sources:48 atoll:40 rapid:1 conclusions:4 except:4 source:20 sonic:1 tests:7 march:1 around:1 advances:1 showing:1 2006b:2 increases:1 press:2 accepted:1 occurring:1 helpful:1 systematically:2 follows:1 mhd:1 disks:1 separately:1 flux:1 either:1 bulik:1 because:2 successfully:1 some:2 moreover:1 oscillations:15 lead:1 measurements:1 l4:1 paradijs:2 does:1 morsink:1 thirring:1 power:21 2c:1 stellar:1 powerlaw:2 ratios:6 plots:4 properties:3 comparison:4 about:1 discussed:3 o:9 range:6 constraints:1 cambridge:1 communication:1 references:2 rossi:1 1999a:1 1999b:1 van:48 support:1 there:1 fast:1 low:15 stars:2 was:2 lowest:1 offer:1 differences:1 but:3 ford:2 astro:3 l66:1 link:1 mnras:6 true:1 l100:1 pulsars:2 lmxb:1 cir:3 altamirano:1 lmxbs:4 fluctuations:1 distribution:3 hz:31 khz:36 constant:14 chjaa:1 abstract:1 general:1 no:1 generally:5 detail:1 field:1 other:5 branch:1 ns:5 explaining:1 star:8 kuulkers:1 models:6 time:1 peak:26 variable:1 structure:1 correlated:3 l60:1 l63:1 neill:2 4u:62 mass:11 fact:1 remarked:1 |
0704.0690.txt |@word secondly:1 similarity:2 magnetic:3 four:12 obstruction:1 entropy:10 ωp1:1 crete:1 nwo:1 localized:1 whose:5 under:3 worth:1 summarizes:2 conjecture:1 φns:1 φnr:4 every:1 summarized:2 solution:70 vector:23 indices:11 degeneracy:8 jhep:11 aiv:1 excited:4 consistent:3 direct:3 10d:2 approximation:5 likely:2 2aα:4 implemented:3 even:10 lunin:4 above:7 new:5 net:3 increasing:1 ˆn:1 coefficient:2 simultaneously:2 evaluating:3 4nt:1 wrapping:4 abstractly:2 here:41 refinement:1 active:1 obtained:10 rigorously:1 leaves:1 approaches:1 aki:7 fourier:2 spacetime:1 cancellation:1 appropriately:1 projection:2 classification:1 explained:1 replace:1 visible:2 rρ:1 total:13 unit:4 would:39 motivate:1 negative:1 m4:2 m1:3 therefore:21 m3:2 m2:1 type:34 duals:8 brings:1 naive:6 lightcone:1 curvature:3 hole:36 hold:2 must:10 ma:3 ml:8 work:11 mi:2 theories:2 mq:7 ms:2 mr:4 root:1 example:13 renormalization:3 give:5 generically:2 involve:4 indicates:1 cartan:1 henningson:1 david:1 guarantee:1 verify:1 feature:2 how:11 answer:1 ψii:1 description:8 oscillators:13 earlier:2 microstate:2 2g3:2 summarize:4 parallel:1 constants:1 dω23:2 effective:2 chern:8 correlation:4 democratic:5 order:8 restriction:2 interpretation:7 over:17 expects:1 xi:4 satisfies:4 before:4 asymptotes:1 onl:1 harmonics:22 persist:1 easier:1 them:7 combination:2 prevented:1 proca:1 break:3 they:15 sixteen:2 netherlands:1 backgrounds:2 hepth:2 reasonable:2 each:15 theta:1 cl2:1 mean:3 lifted:1 24n:1 onr:4 j3r:7 combining:1 extract:6 rr:20 rs:3 quantify:1 crucial:2 ry:2 angular:14 content:2 rg:3 ra:1 rc:2 rm:1 rn:2 size:2 rk:5 mρ:1 linear:2 free:6 standard:5 proportionality:1 flows:2 ramgoolam:1 estimate:1 r4:30 ds2m:1 chiral:45 r2:21 fµ1:1 behrndt:1 r8:1 corrections:4 uses:4 onto:2 already:2 features:2 subtlety:1 primary:5 rank:2 2a5:1 another:3 rewritten:2 similarly:2 xii:2 top:1 twisted:1 needed:2 perturbations:1 too:2 unbroken:1 collapse:2 2aa:2 gyn:1 gym:3 α1n:3 2ai:4 πz:1 α2n:1 2aq:1 gyy:5 tities:1 target:1 showed:1 approximations:3 second:1 correlators:3 minus:3 extracting:1 sees:1 behavior:2 correlator:1 spectrum:5 return:2 emphasizing:1 seen:3 contents:1 strength:4 convenient:11 latter:17 isolated:2 kaya:1 acquire:13 tyi:2 shall:1 anatomy:1 simplify:2 involving:6 treats:1 partition:5 flow:7 points:1 sum:2 incomplete:1 labels:4 infrared:1 radii:2 gauge:27 solutions:113 d8:1 d9:1 d6:6 subtle:2 d5:48 d3:3 d1:51 just:2 explain:2 hrs:1 aspinwall:1 coefficients:5 axion:1 dn:12 do:12 dk:1 klein:4 df:5 de:9 db:6 dc:8 da:12 periodicity:1 dz:2 dy:16 dv:35 dw:1 dt:10 du:2 dr:2 ds:1 runs:5 f52:6 fields:81 acknowledgments:1 mihailescu:1 testing:1 padm:1 depends:1 radius:6 result:2 w1:3 discussions:2 dµ:1 best:1 techniques:1 tensor:19 fn1:2 worldsheet:9 µq:2 supergravity:84 symmetric:4 simplest:2 approach:3 µb:1 terms:48 extend:1 nature:1 wn:3 wm:1 restricting:1 weak:1 however:23 wi:1 wv:9 wu:4 picking:1 e2ψ:1 cos:3 gµνρ:1 cµ:7 argue:1 presumably:1 factorize:1 non:25 dsm:2 polynomial:1 2nr:1 hijk:1 mathur:5 decoupling:7 basis:27 three:35 been:10 quickly:1 frs:1 much:2 interest:5 basic:4 describable:1 supersymmetric:10 quantities:5 iµ:2 coherent:7 lift:2 applied:1 tanh:2 hat:1 2aρ:1 remaining:4 near:3 ain:2 suppose:3 property:2 characterizing:1 unlikely:3 iy:1 iv:5 ii:12 characterize:4 ik:19 ij:11 uplift:2 ie:2 id:2 perform:1 suggest:2 make:7 wound:1 complex:1 quant:2 split:1 dimensionless:1 several:2 independent:1 dǫ:4 i1:11 dvdv:1 i3:5 i2:1 i5:3 i4:10 potentials:11 a2i:1 a2n:1 cycle:7 weakly:2 scenario:1 quantitative:2 eiπ:1 left:6 proposed:8 attractor:1 newton:2 lorentz:1 assigned:1 eigenstates:3 previous:7 ham:1 candidate:1 haa:1 had:2 proeyen:1 5r:1 easy:1 requiring:2 iρ:1 occurring:1 interprets:1 breaks:2 possible:4 background:6 unique:1 apart:1 strengths:26 appearing:1 specific:14 bps:6 steps:3 schwarz:1 arbitrary:9 dualities:14 deal:1 ˆik:1 ˆin:2 bottom:1 yki:6 hodge:15 linearly:1 meanings:1 properties:19 peet:1 takes:3 kinematical:3 theirs:1 o:30 plus:1 horizon:10 slightly:1 ǫijkl:9 presence:1 selfduality:1 obtaining:2 bound:4 chooses:1 down:1 multiply:1 right:3 amsterdam:2 reducing:1 often:2 suffice:1 sundell:1 transform:3 why:3 conservation:9 way:5 was:21 cγ0:1 iˆ:2 lowest:1 form:45 simplifications:1 becoming:1 denoting:4 encoded:1 removed:1 true:1 vevs:77 coset:1 wσ:2 wρ:7 compactification:9 heterotic:23 examples:2 diagnose:1 zeroes:2 computing:5 abstract:1 conserved:5 exist:2 dλ:2 dδ:2 a1i:1 check:3 a1j:2 ni:2 ijk:4 nl:4 nm:3 no:30 na:5 wavefunction:1 generally:2 vanishes:1 interested:3 role:4 holding:1 papers:1 np:2 nr:6 ns:20 nt:14 nw:1 picture:2 superposition:31 a12:2 models:3 describe:8 russo:1 coulomb:4 αjn:2 pseudo:2 dσ:2 together:1 time:2 n1:5 n2:2 n4:4 n5:4 dualizing:7 chain:14 switched:1 skip:1 varying:1 ost:2 leads:1 computation:8 primes:1 vev:17 depend:4 summarises:1 noncompact:1 charge:58 analogous:5 ωt2:3 ωt1:4 brown:1 string:49 orthogonal:3 frequencies:9 choice:14 h36:1 hatted:1 papadimitriou:2 exact:3 charac:1 level:7 irreducible:1 leave:1 science:1 mn:8 sign:10 mnpq:1 nδn:1 spectral:4 appear:1 xρ:5 current:1 switch:2 satisfy:12 αin:16 αij:3 multipole:5 understanding:1 tangent:3 address:3 alone:1 based:1 along:33 xα:4 change:5 ds23:1 institute:1 shift:1 vectors:1 conveniently:2 cµi:1 emerge:2 supertube:4 useful:7 extra:1 eψ:4 working:1 covariant:2 positive:5 eφ:9 eρ:11 selfdual:1 dλα:1 encode:2 arutyunov:1 associated:49 compactly:1 theoretical:2 dudv:3 smeared:3 introducing:1 duality:76 dλρ:1 dxµ:4 distribution:1 fµν:2 appendix:23 everywhere:1 cases:9 capturing:1 fermionic:4 parameterize:1 rotational:2 deformed:1 oscillator:2 labeled:8 fock:3 values:5 following:37 making:1 reviewing:1 nearest:3 expanding:2 sample:2 dxi:35 allowed:2 spanning:1 counting:2 conversely:1 uˆi:1 requirements:1 s3:2 discussion:5 s5:3 write:1 pure:3 map:6 dx8:2 may:13 dx4:2 respective:1 expectation:2 pqr:2 explored:2 lω1:1 date:1 representations:1 data:4 stress:8 natural:7 dynamical:2 higgs:3 explicit:3 su:7 sj:1 si:10 aβ:1 so:84 automatically:1 sl:1 definitions:1 typical:2 acts:3 indeed:11 ǫi1:1 years:1 course:2 statistical:2 differs:4 still:1 derive:4 group:5 thank:2 interesting:6 sα:1 coordinates:8 forms:34 dxρ:4 correspondence:16 dxν:2 rotations:1 introduce:7 half:2 eµ:1 now:28 discuss:10 nor:4 term:7 holographic:21 drop:2 orthonormal:1 domain:1 square:1 fixes:1 commuting:2 conventions:8 ey:1 eu:1 approximated:1 emerges:1 space:10 furthermore:4 algebra:2 squared:1 contained:5 emerged:1 formula:2 correct:2 asymptote:1 after:2 theory:32 hull:1 contain:5 quite:1 romans:2 complicated:1 ori:3 fixed:5 derivation:1 impose:1 βy:1 ql:5 motion:13 turn:2 βh:1 βj:2 first:8 origin:3 simplifies:1 vacua:7 symmetry:24 variables:1 directly:4 carry:4 ring:2 open:1 singling:1 fijk:1 constructing:3 given:86 checked:1 1y:3 fmp:1 fmn:1 indicate:1 realization:2 speaking:1 gives:6 fraction:3 transverse:30 x8:1 quan:1 copy:1 than:10 specify:1 accordance:1 require:1 fm2:2 fm3:1 fm1:1 were:12 bination:1 bilinears:1 argument:2 winding:28 20d:1 any:7 20n:1 symmetrized:1 papadodimas:1 note:42 ideal:1 potential:2 take:7 primaries:29 switching:1 formulas:2 begin:2 sure:1 multiple:1 trace:1 removes:1 importantly:1 formulae:1 pair:1 gρσ:5 surprising:1 average:2 later:2 implications:5 mrs:1 harvey:1 sigma:1 quantity:1 precise:9 show:8 jµ:1 fuzzballs:10 ground:48 aρ:27 aπ:2 state:24 collapses:2 only:68 explicitly:11 black:48 aini:1 normalizations:1 correctly:1 get:1 rept:2 ki:1 straightforwardly:2 satisfied:2 aα:34 aγ:3 cannot:9 progress:3 aν:2 neither:2 closure:1 intrinsically:1 summary:1 cf:1 source:2 mapped:3 fqr:1 discussing:2 ricci:2 imposing:1 j1:1 bδ:2 j3:24 relative:4 namely:8 eliminating:2 existence:1 rmn:3 surfaces:1 satisfying:1 commutation:1 subsequent:1 review:8 definite:7 label:1 outside:1 between:35 geometric:9 αm:1 αn:4 jy:1 jt:1 ju:1 jv:1 jp:1 suppressed:1 parentheses:1 acquiring:1 σn:2 many:5 region:3 according:1 contract:1 embedding:2 expression:3 among:1 sampling:1 anti:16 spans:2 lagrange:1 moreover:13 branes:6 considering:2 locally:1 workshop:1 combined:1 oα:9 differently:1 6a:2 direction:24 6d:1 6f:1 bmn:2 jacobi:1 irrelevant:4 former:3 those:8 case:29 disconnected:1 aijk:1 conformal:3 coupled:4 metric:24 middle:15 motivated:1 technology:1 different:10 d10:2 distributions:1 formulations:1 same:18 dγ:2 shifts:1 arguments:1 valckenierstraat:1 extended:2 assigns:1 trivially:1 running:2 arose:1 invariance:1 modes:24 charges:48 kallosh:1 without:3 components:6 rychkov:1 coordinate:5 model:6 dimension:20 charged:10 boonstra:1 vˆm:2 manifold:14 being:25 captures:1 ne:1 am2:1 captured:4 blow:2 heuristic:1 seems:3 parametrization:1 setting:1 lett:2 eigenstate:1 momentum:20 ross:1 aspects:1 around:5 rules:34 multiplets:5 hm1:1 test:3 vacuum:1 using:20 supergravities:3 janssen:1 particle:7 identifying:1 reduces:3 either:2 integrals:1 always:1 tower:5 callan:1 stationary:2 reduced:4 comˆ:1 specifies:1 itfa:1 e4π:1 table:1 matching:3 provided:5 dimensions:24 2e:3 maoz:2 donder:5 o8:1 propagating:1 o1:9 wavefunctions:1 broken:1 refers:1 central:4 oj:6 oi:6 package:1 og:4 smear:2 discussed:23 oa:1 srr:2 2j:1 neighbor:3 ov:1 os:11 youm:1 ηv:1 qrs:2 references:2 determine:4 einstein:5 operator:20 conceptually:1 het:1 hep:39 dkγ:1 assumed:1 strictly:3 there:42 start:1 low:1 delocalized:1 ortin:3 complete:5 enough:2 respec:1 formalisms:1 alday:1 aµ:2 i19:5 applying:3 ωp:2 quantitatively:1 agree:3 obtains:1 detailed:2 kostas:1 ab:13 ai:35 certain:6 aj:4 am:1 ao:9 general:24 ap:2 av:2 controlled:1 dvb:1 uplifts:1 again:3 extending:2 field:76 valid:1 spatial:2 roest:1 massless:1 balasubramanian:1 polar:1 briefly:3 ads5:1 ads3:11 separate:1 includes:2 deriving:2 a2:12 a5:1 included:5 a8:1 conclusive:1 building:1 curve:31 mass:5 stringy:1 starting:1 strings:10 consider:27 pth:1 mnp:4 goa:1 forbidden:2 splitting:2 scalar:13 follow:4 expressions:6 ty:5 tr:7 kγ:20 program:6 th:39 kδ:1 nsns:1 norm:1 subtleties:2 amplitudes:5 straightforward:6 sitting:1 very:7 induce:2 fall:1 ln:5 difference:3 deformations:6 condition:3 treating:1 t8:1 hamiltonian:3 π2i:1 t4:3 applicable:2 large:14 small:12 ds26:1 holography:4 ten:23 b26:3 zero:36 perspective:1 qmn:2 further:8 gm:9 canonical:1 subscripts:4 what:9 y1i:1 y1j:2 section:23 bαβ:1 intersect:1 solitonic:8 method:4 contrast:3 full:3 2kq:1 excludes:1 component:1 modular:5 ansatz:2 directions:18 strong:2 equations:36 generalizing:1 antisymmetric:1 tµ:3 allows:1 periodic:2 pick:1 action:19 formation:1 via:15 followed:2 fµ:7 family:1 marginal:6 proceed:1 distinct:1 contains:4 finally:4 nucl:15 ψn:3 taken:2 more:21 flat:14 ramond:5 operators:87 surprisingly:1 tested:1 particular:16 known:5 none:1 quantized:2 recall:9 equation:3 det:1 remain:3 could:6 f1:80 f2:2 f3:5 f5:79 ds2:13 share:1 states:82 sphere:5 numbers:5 cubic:1 information:5 needs:12 compactify:3 rather:11 breaking:4 maps:2 larsen:1 explains:1 fp:4 fq:2 fr:1 cjk:2 derived:12 mapping:4 fa:1 plane:4 saxena:1 unsurprising:1 waves:2 fi:4 fm:6 fn:4 transposed:1 parameterized:1 fundamental:7 jevicki:1 developed:4 e2φ:14 paper:9 y1:2 uva:1 excitations:48 its:4 microstates:27 boson:1 microscopic:1 systems:7 recombined:1 might:2 deformation:2 supersymmetry:4 yi:1 yk:1 good:2 ym:6 pauli:1 ya:1 anticipated:1 yy:3 remarkably:1 motivates:1 cosh2:3 smoothness:1 easily:2 gets:1 2p:2 2q:3 2r:1 fully:2 presented:1 labeling:4 2d:2 fρ:2 2f:5 2a:5 2b:1 found:5 2n:12 polynomially:1 2h:3 characterized:17 2k:2 haro:1 energy:8 reduce:3 idea:1 bosonization:1 expect:2 quantum:9 beyond:4 unnatural:1 since:14 induces:2 denotes:17 acting:2 flowed:1 denoted:14 issue:9 mmt:2 reason:2 ask:1 definition:2 pairs:2 reinforces:1 a4n:1 twenty:1 waldram:1 assign:1 number:25 done:1 least:1 wadia:1 fluxes:2 tively:1 passes:1 differ:6 temperature:2 introduction:2 leading:2 construct:3 assumption:2 expand:2 calculations:1 dt2:2 listed:1 shifted:2 relationship:5 required:4 part:8 authors:1 focusing:2 cosh:4 2f1:1 2f5:1 horizons:3 determined:4 fˆ:3 y1α:5 b2ρ:2 eiπτ:1 supertubes:1 null:10 solitons:2 lie:1 built:8 self:30 a34:2 k3:78 k2:3 k1:3 internal:37 build:1 finding:1 play:4 towards:1 pqrs:1 electric:2 singles:2 measures:2 singlet:14 most:8 plan:1 singled:1 deviations:1 constructed:6 kk:3 torus:22 km:3 ks:2 kq:1 exp:3 usual:4 physics:8 gabc:1 lying:1 sector:19 eˆµ:2 relation:7 find:10 parameters:4 generators:1 subsection:1 factor:2 circle:13 abelian:4 notation:3 dependent:1 express:1 sixdimensional:2 closely:1 combinations:9 freedman:2 resolve:1 arxiv:41 factorization:2 common:2 minasian:1 set:9 achieved:1 see:17 sen:2 theoretic:1 contour:1 evaluation:1 probable:1 currently:2 dipole:1 various:2 subscript:2 conditions:4 knowing:1 recently:1 creating:1 characteristic:3 vanishing:7 distinguish:6 gmn:4 both:22 collaborators:1 last:3 dualise:2 f2i:4 mrtn:1 quantization:3 connection:2 context:4 whole:1 finds:3 point:38 simple:6 asymptotically:14 ga2:1 except:1 dimensional:79 superstring:1 bζ:1 simply:3 bα:3 bγ:11 nr2:1 throughout:2 pq:5 described:20 transformations:2 py:5 due:3 reduction:18 dropping:2 coarse:3 pn:1 holographically:1 pl:4 pm:4 understand:4 representative:5 systematic:1 nrs:1 replaces:1 classifications:2 bρ:13 exponential:4 expanded:4 reliably:3 error:1 couplings:2 loop:1 h3n:2 reads:1 triple:3 vanish:1 currents:4 3l:1 confirms:1 grant:2 i20:4 i21:3 i22:2 i24:4 shorter:1 read:1 products:1 higher:12 used:8 sym:1 h32:2 h31:1 moving:10 purpose:1 h35:1 recent:2 lower:4 picks:1 boer:2 reviewed:4 bµ:3 questions:2 λk:5 regardless:1 λi:1 readers:1 guaranteed:1 kinematically:3 location:1 mandal:1 mod:1 transformation:9 gs:4 bij:3 couple:2 φ0i:2 appendices:1 integer:1 imposed:2 follows:17 manifest:3 flux:1 imposes:1 yields:2 methods:3 some:11 back:5 b4:1 understood:1 economic:1 b1:2 b2:10 oscillations:1 biµ:7 scale:4 describing:12 behave:1 inserting:1 ba:1 bm:8 bn:8 bi:10 bj:13 bk:2 restrictive:1 step:5 relating:8 asymptotic:16 constraint:4 range:1 block:1 therein:1 martinec:1 into:19 within:9 integral:7 appropriate:10 proportional:1 physical:1 span:6 eleven:1 question:8 long:1 u2:1 walls:1 analyze:1 sections:4 considerably:2 elsewhere:1 bǫ:1 properly:2 ns5:15 raising:1 cij:14 uv:1 up:7 us:19 2πn:4 2πr:2 ui:1 civ:1 planes:1 fluctuations:6 2πz:1 similar:4 called:2 skenderis:12 constant:27 defined:29 single:9 formalism:8 kdv:1 defines:4 paradox:2 rederive:1 fixing:1 multipliers:1 rewriting:1 application:3 b12:1 elements:1 excitation:2 sides:1 structure:9 independently:1 implies:9 i16:2 holes:11 graining:2 implied:2 requires:6 having:2 once:2 partial:1 results:14 gy:1 ge:2 ga:16 go:4 bvi:2 contributions:4 issues:3 compact:13 λij:5 longstanding:1 hats:4 stable:2 differing:1 include:7 g5:1 breathing:1 g3:5 provides:2 implicitly:2 wave:2 putting:1 hµν:1 matrices:10 entire:2 notes:1 try:1 assignments:1 dealt:1 manifestly:4 noted:2 averaged:1 sin2:1 imply:2 picked:1 substituting:1 cft:31 odd:9 eik1:1 index:15 vakkuri:1 2q1:1 analogously:1 expressed:11 consistently:2 infinitesimal:3 flowing:1 expresses:1 3a:2 3d:2 degree:12 respectively:19 believed:1 explore:4 focused:1 sinh:1 others:2 implicit:2 z2:1 dualised:1 convert:1 rdr:1 larger:1 cty:4 metry:1 suggests:1 resulting:6 implement:1 makes:1 grained:1 apr:1 maldacena:3 addressed:2 condensates:2 apply:2 use:14 superpositions:14 commun:2 remains:1 next:6 few:1 themselves:1 cδ:2 bρσ:4 untwisted:1 carrying:4 iia:27 normalized:6 iib:31 bena:1 account:12 integrating:1 ρi:2 when:30 reproduce:4 anywhere:2 coincident:1 process:1 inaccessible:1 purposes:3 high:2 effectively:1 assumptions:2 daα:1 ijkl:1 dh:4 vielbein:13 dilaton:6 distinguishable:6 six:51 regions:2 reinstated:1 mnr:1 warner:1 sin:5 circular:4 singular:10 µab:1 realized:2 advocated:1 lines:1 correspond:6 element:1 extremal:1 destroying:1 gravitons:1 gˆµν:1 sezgin:1 whilst:18 including:6 looks:1 atypically:1 mentioned:2 defects:1 orbifold:4 thence:1 chosen:4 ll:3 lm:2 byn:1 h2:1 lt:5 bym:2 choose:2 defining:14 ly:15 symmetrization:2 spell:1 graviton:3 rotation:2 reconstruction:1 betti:1 university:2 sufficiently:4 l4:1 magnitude:1 l2:5 mode:6 l0:1 accounts:2 constraints:3 subset:1 weyl:1 related:28 ρi2:2 elementary:1 frequency:6 measure:3 relates:2 alambertian:1 out:21 matrix:24 integrates:1 rev:4 m2s:1 lecture:1 supports:1 integrated:1 math:2 tildes:1 dictionary:8 interactions:1 ρit:1 diagonal:10 completely:3 dω3:2 geometry:34 route:2 linearized:3 length:4 mab:1 hence:9 retain:1 phrased:1 blown:2 precisely:6 f1i:2 πj:2 πk:1 adjoint:2 behaves:4 system:50 relations:3 their:11 intermediate:1 wrapped:4 final:6 townsend:1 sugra:2 completed:1 exactly:6 solodukhin:1 zν:1 branches:1 amplitude:3 f12:2 naturally:2 distinguished:16 w2:3 symmetries:4 hµa:1 maharana:1 unchanged:4 curves:34 factorizations:1 enforces:1 need:9 curved:2 clearly:2 viewed:1 angle:1 dαβ:1 able:1 gravity:7 instance:1 sn:2 unless:3 eight:4 representation:1 class:3 duff:1 neighboring:1 atypical:1 stronger:1 construction:1 prefactor:1 fact:5 selection:22 dba:1 rings:1 supported:3 12n:1 rotating:3 bring:2 superimposed:1 trivial:4 agrees:1 principal:1 q1:39 q2:2 q5:54 should:15 candidates:1 kaluza:4 hope:1 inσ:3 means:5 overall:2 ones:2 db2:1 qq:1 liu:1 processes:3 µa:3 gbm:2 expansions:6 grav:2 fuzzball:61 qf:2 cycles:6 qm:2 traceless:4 view:1 moduli:8 computed:6 exists:3 hν:1 frame:7 bty:3 computes:1 computer:1 acquires:1 interacting:1 written:10 einσ:1 closed:2 invariant:13 boundary:3 comparable:2 reproduced:2 theisen:1 importance:1 dabholkar:1 reproduces:1 key:3 2pm:1 tensors:3 limits:2 taking:6 equal:2 etc:2 admit:2 masses:2 grounds:2 comment:5 relevant:12 cl:7 cohomology:32 harmonic:48 taylor:7 decreases:1 respect:2 ct:1 ǫabc:3 singlets:2 geometries:58 addition:2 copies:2 bianchi:2 proposal:15 recurring:1 define:4 arises:2 corresponding:36 scalars:9 sufficient:1 bulk:1 c2:7 c1:2 c0:15 present:3 c4:1 multi:2 splits:1 dyonic:1 choices:7 will:50 simons:9 vi:1 formulation:1 thus:51 vm:15 vn:2 vv:2 vy:1 conical:1 compactified:2 fki:5 generic:9 indistinguishable:2 parts:1 diagonalize:3 largest:1 φi:2 finite:3 supercharge:1 infinity:8 parametrizes:1 absorb:1 upon:4 v1:3 v2:3 v4:2 infinite:1 identity:6 off:6 center:1 nonetheless:2 well:16 sets:1 firstly:6 arising:3 subgroup:3 spherical:15 samir:1 less:3 moments:5 obtain:15 cˆ:3 sources:5 underlying:1 momenta:7 macroscopic:4 vρ:1 vidi:1 ads:18 density:12 reasons:1 usage:1 adm:3 match:5 ellipses:1 resolved:1 tests:1 henneaux:1 keski:1 corresponds:2 increases:1 know:6 immediately:3 intersection:3 loss:1 necessary:2 like:4 become:2 δa:6 accessible:1 because:2 classical:3 gauntlett:1 σi2:1 growth:1 kdx:1 q25:1 choosing:2 dc4:1 dc2:1 lead:1 cρ:1 overlap:2 does:15 assuming:3 intersections:1 chains:5 limitations:2 slight:1 σik:3 expansion:8 although:3 cγ:7 cβ:1 perspectives:1 about:3 actual:2 carried:1 extension:1 saddle:2 freedom:1 introduces:1 dependence:1 important:1 bounded:1 introduced:1 equally:1 bergshoeff:4 previously:3 h3:18 h1:7 weighted:1 bosonic:10 van:3 additional:10 vˆ:1 restricts:1 describes:4 quanta:1 crucially:1 var:2 asymptotics:5 function:13 hr:1 brane:16 buv:3 but:23 volume:9 hk:5 hi:1 hn:5 hm:6 truncation:1 count:1 made:5 compute:5 instructive:1 whether:13 wish:1 gravitational:2 smooth:5 below:5 projecting:1 limit:12 problem:1 intersects:1 dual:91 int:1 universal:3 contribute:3 denote:7 twist:3 our:21 families:2 4q:2 functions:71 compared:1 susskind:1 ingredients:1 detail:5 other:14 details:3 branch:4 conclusion:2 star:1 bνρ:1 log:3 coupling:4 fˆµ:2 factors:1 rule:7 original:12 4n:4 anomaly:2 4b:9 |
0704.0691.txt |@word replacing:1 discards:1 monte:2 sci:2 forget:1 chain:1 limited:1 sousa:1 caused:1 edn:1 results:7 existing:4 interpret:1 eds:6 avalanche:1 drastically:1 stops:1 physik:1 edu:1 go:2 faster:1 saved:1 children:3 issues:1 retention:1 whose:1 simon:1 terms:1 chinese:1 tx:1 concerned:1 involve:1 father:2 acting:1 including:1 realities:1 languages:89 finally:6 constituted:1 under:2 atlas:2 dominated:1 include:1 presentation:1 sent:1 applied:3 blackwell:2 presently:1 advantage:1 geology:1 very:3 rise:1 conditions:1 splitting:4 verb:1 every:3 trough:1 join:1 difference:2 logarithmically:1 strand:1 entire:1 linguists:10 roy:1 ageing:1 who:4 having:1 eve:1 try:2 solved:1 differential:3 dealt:1 small:14 biological:2 originally:1 20th:1 favoured:1 upper:4 work:1 leaders:1 ten:8 10m:2 trend:1 10a:2 among:2 b267:1 understanding:1 aip:1 jump:1 consists:1 second:4 estes:1 deutscher:1 enhancement:1 experimentalphysik:1 further:2 dynamics:2 estimated:1 carlo:2 even:1 reproduce:1 what:3 developed:1 cover:1 witnessed:1 fine:1 section:1 selected:15 contributed:1 near:1 agrees:1 current:1 switch:1 19th:2 version:2 above:6 scientists:1 new:12 learned:5 occupation:1 contrast:2 halley:1 coefficient:1 widely:1 drastic:1 million:4 submitted:2 never:1 modify:1 dissipates:1 here:4 bi:1 anthropology:1 growing:1 china:1 possibility:1 groups:1 others:1 represented:1 novotny:2 quite:1 equations:2 teacher:4 change:14 simulating:2 obtained:1 search:1 trans:1 institute:3 shift:11 elaborate:1 changed:1 allows:1 ignoring:1 resulting:1 published:2 usually:1 unsymmetric:1 suitable:1 changes:4 regularity:1 coast:1 plotted:1 parisi:1 prints:1 via:1 followed:4 perspectives:1 family:6 scales:1 apr:1 millennia:2 important:1 pp:1 replace:1 brought:1 conditionally:1 darwinian:1 apply:1 extinction:2 tools:1 planck:1 everybody:10 plot:2 use:3 barab:3 conferences:1 would:1 probabilities:1 give:3 maybe:1 neighbours:10 nobel:1 predict:1 modelling:5 call:3 therefore:1 taken:3 length:2 means:2 preview:1 selects:3 theoretical:3 today:3 more:23 separated:2 sharing:1 abrams:6 populations:2 started:2 becomes:2 stable:2 mira:1 site:18 berlin:4 appendix:3 adult:2 particular:1 known:3 actual:2 cases:2 iv:1 iii:1 carried:1 reconstructed:1 none:2 characterised:1 word:2 springer:3 bits:4 ed:2 science:2 equation:3 created:1 modified:5 mk:1 pr:1 reviews:3 remain:1 anywhere:1 values:4 publications:1 learn:2 following:2 meet:1 arrive:2 grimes:2 help:3 nearest:3 transition:10 percolates:1 wang:2 figure:12 stated:1 process:8 india:2 purposes:2 agent:2 castell:3 high:3 mixture:1 numbers:1 allowed:4 christiansen:1 surge:1 yet:1 native:2 information:2 needs:1 united:1 rather:1 int:4 six:1 feature:4 regions:1 how:12 extended:2 vancouver:1 group:1 freshly:1 shifts:1 instead:9 widespread:1 absolute:1 parameter:1 ensemble:1 tried:1 pater:1 capture:1 may:16 max:1 after:8 variant:1 wrong:1 lot:1 designed:2 structure:4 coming:1 date:1 ties:2 horizontal:2 fk:1 data:4 grow:2 times:1 alps:1 collecting:1 short:3 natural:2 chiefly:1 four:2 martins:1 ges:1 wins:2 sq:5 lines:1 correspond:4 egu:3 element:1 inform:1 complexity:1 ones:2 so:2 allow:2 april:1 quantifiable:2 order:6 interpreting:1 evolutionary:2 interpretation:1 dx:1 institutional:1 indeed:2 over:7 capacities:2 romania:1 drozd:2 years:4 stability:2 course:1 paper:1 through:4 same:6 statistical:5 during:1 mentioned:1 japan:1 still:1 masse:1 its:6 boer:1 before:4 pressures:1 linguistics:10 accepted:1 rapidly:1 manuscript:1 decay:3 ln:1 interaction:5 decreases:1 actually:1 better:1 age:3 continue:1 fig:17 saxon:1 persist:2 potentially:1 paths:1 culture:1 decades:1 easier:1 northwest:1 versus:2 eventually:1 them:6 usa:2 somebody:1 geographical:4 parabola:3 gets:3 patriarca:2 runs:1 investigated:1 units:1 walls:1 precisely:1 effects:1 they:5 half:5 oxford:5 grows:1 documented:1 now:4 bigger:1 finite:1 grammar:3 transitional:1 fully:1 university:5 publishing:1 advent:1 leading:3 dominance:14 schulze:26 coexistence:1 each:16 crossing:2 found:1 traces:1 side:1 characterized:1 mean:1 development:2 domain:1 square:3 england:1 evolve:1 generation:1 there:2 revised:1 solution:1 frequency:1 obtains:1 amsterdam:1 separating:1 our:3 transitions:1 adequately:2 out:3 large:8 100m:2 dominates:2 100k:5 network:7 factors:1 vch:1 restricted:2 since:9 crucial:1 semi:1 research:8 looking:2 re:1 contained:1 multilingual:1 sustain:1 print:1 newly:3 millions:2 issue:1 situations:3 shows:8 provide:2 theory:1 barrier:3 interactions:1 qf:1 mechanisms:2 story:1 free:6 standard:1 completely:3 necessarily:1 complicated:3 york:1 members:1 imagine:1 put:1 org:3 asi:3 hysteresis:1 beginning:1 spread:1 additional:1 definition:2 uiuc:1 fixed:4 language:116 english:8 starts:2 could:5 computers:1 days:1 round:1 american:1 choices:1 place:2 assumed:1 onto:1 unmodified:1 south:1 first:7 grammatical:1 major:1 already:4 features:9 probability:20 10k:2 spoken:19 omitted:1 number:25 romanelli:1 xy:1 dominating:5 relations:1 another:6 spanish:3 carry:1 reached:1 clarity:1 sutherland:1 fj:1 size:15 given:5 ancient:1 checked:1 temperature:1 likely:1 similarly:1 introduction:1 unknown:1 top:5 moderately:1 least:2 franca:3 their:10 joseph:1 1e:5 too:2 phd:1 lifetimes:1 rates:1 1k:4 molecular:1 structures:2 final:1 speaking:12 low:4 numbered:1 way:5 mostly:3 paredes:1 bit:10 continuous:1 albert:3 took:1 lists:1 binned:1 part:7 sociology:1 somewhat:1 authors:2 x2:2 branches:1 unrealistic:1 than:8 population:24 diffusion:6 distance:6 iterations:1 temporal:1 1m:5 approximations:1 immigrants:1 iteration:4 rate:5 extraordinarily:1 youth:1 mobility:1 states:1 future:2 pairwise:1 weinheim:1 historical:2 were:11 design:1 gives:2 powers:1 russia:1 kilometers:1 migration:7 behaviors:1 bridge:1 comput:1 enhanced:1 exert:1 multiplicative:3 modern:2 locations:1 curves:1 randomly:13 paulo:1 chambers:1 need:2 events:2 concentration:1 border:2 clearly:1 mountain:1 speakers:7 strength:1 engin:1 zero:5 depending:2 babel:1 latter:1 cambridge:3 able:1 recourse:1 mechanism:3 note:1 oliveira:9 emphasis:1 contact:1 take:3 interior:1 hgg:2 coincide:1 techniques:1 tool:1 channel:1 play:1 towards:2 beyond:1 normal:5 object:1 molecule:1 most:6 attempt:1 involving:2 connected:2 moss:2 comparisons:1 phase:3 prestige:5 measured:1 why:1 cavalli:1 deviations:1 chemistry:1 wiley:1 fitter:1 average:2 later:5 differ:1 physica:10 looked:1 proceedings:2 yang:2 verlag:3 principle:1 exp:1 physics:17 fact:1 gain:1 permeable:1 lexical:1 particularly:1 simulate:3 festschrift:1 german:3 random:9 favour:1 discovered:1 area:1 nowak:1 ortmanns:1 threshold:4 earth:1 determined:1 thirds:2 networks:4 decade:1 geography:3 rev:1 resisting:1 based:4 knowledge:2 parameters:6 bilingual:1 romanian:1 explain:1 less:3 distributed:1 behind:1 should:5 tries:1 entities:1 only:21 kilometer:1 molecules:1 factor:1 employed:4 adequate:2 thousands:2 hope:1 equilibrium:5 borrowed:1 do:5 dl:1 his:1 dominant:1 notation:1 get:3 dependent:1 econophysics:1 de:10 dominate:1 account:1 soon:2 joint:1 amazon:1 cannot:2 sociophysics:1 nearly:1 words:4 exchanges:1 lattices:3 dt:2 tsang:1 platz:1 areas:1 evolution:7 increasing:1 invaded:1 geographically:1 approach:2 arxiv:3 speaks:4 throughout:1 typology:1 investigate:1 europhys:1 common:2 logistic:1 contain:1 clean:2 linguist:2 require:1 wrote:1 view:1 diversity:1 set:2 thesis:1 count:3 tree:1 aerts:1 humans:1 maximum:5 cologne:1 differs:1 see:4 computer:3 result:1 sea:1 operated:1 close:3 uncorrelated:1 subject:1 brazil:1 instance:2 fails:1 learns:1 capacity:2 exponent:2 review:3 laureate:1 sites:2 continent:2 boundaries:3 halves:1 written:1 smallest:2 various:5 correctly:1 between:11 progress:1 numerous:2 across:1 law:3 europe:1 partha:1 latin:3 recently:1 majority:1 nature:5 initially:6 processes:1 exceptions:1 focus:3 however:3 physicist:1 adept:1 chatterjee:1 hypothesis:1 french:3 bose:2 hundreds:1 come:1 both:5 prospects:1 toward:1 last:6 irregular:1 many:12 region:2 according:1 against:1 agree:1 stauffer:10 etc:1 roman:2 und:3 acquisition:1 share:1 whole:5 lima:2 otherwise:2 ck:1 cj:5 ci:1 separation:2 agents:3 chakraborti:1 leipzig:2 corresponds:4 community:1 except:3 homogeneously:1 simply:1 learning:7 article:1 extinct:1 trust:1 speak:4 conference:2 epistemology:1 unusual:1 strong:1 described:1 tuning:1 argued:1 addition:2 west:1 lep:1 three:3 been:9 defined:1 genetic:1 much:3 replicate:1 combined:1 basic:1 linguistic:9 ph:1 dozens:1 meeting:1 empty:1 systems:1 sforza:1 field:3 direction:2 lived:2 families:6 easy:1 retrospective:1 influence:1 thousand:1 lepp:1 binning:1 neighbour:10 pacific:1 understand:2 child:1 selten:2 spirit:1 present:2 case:9 gender:1 unify:1 look:1 unlike:1 might:2 straight:1 empirical:4 value:3 air:1 will:6 forgetting:3 while:8 replaced:4 teachers:1 behavior:2 involved:1 situation:1 happened:1 solomon:1 london:2 seven:1 economics:1 costly:1 portugal:1 century:5 pool:1 characteristics:1 thus:12 non:2 profiles:1 equal:1 ii:3 exchanging:1 grammars:2 itself:1 holman:3 elsevier:1 limit:3 foreign:12 everyday:1 replacement:2 grown:1 binary:2 different:18 develop:1 residence:1 logos:1 lengths:1 occupied:12 appreciable:1 sokal:1 start:5 check:1 member:1 regularities:1 unity:1 complex:3 speaker:3 split:1 coworkers:1 largest:7 avoids:1 success:2 several:3 characterise:1 higher:3 status:3 independent:4 used:6 http:1 centuries:3 trivially:1 economic:1 social:2 effect:2 flows:1 hand:4 assessing:1 arrived:1 purpose:2 necessity:1 fraser:1 infinite:2 changing:1 validate:1 tradition:1 recent:2 simulates:1 schw:2 lower:2 verhulst:1 shortly:1 whereby:1 nevertheless:1 studies:2 dallas:1 well:2 roughly:5 ocean:1 person:6 without:9 modelled:1 mother:15 san:3 quantitative:3 model:42 mutating:1 fittest:1 left:3 summer:1 meyer:1 fast:1 just:2 sentence:1 being:3 when:5 observed:3 hands:1 briscoe:2 presumably:2 reviewed:2 identify:2 anglo:1 human:3 using:3 alternative:1 speed:2 variants:3 reduced:1 adv:1 mmax:1 patt:1 death:2 classification:1 inventories:1 density:1 similarities:1 monolingual:2 percent:5 had:1 empirically:2 mathematically:1 lattice:24 internal:1 lett:1 samples:1 natl:2 compares:1 mod:5 remaining:1 gave:2 real:2 fluctuating:1 march:1 around:1 depends:1 comparison:2 kirby:1 survival:2 spatial:1 progressed:1 possible:3 mutations:5 early:1 catalan:2 increases:2 dryer:1 five:3 makes:1 birth:2 press:5 world:6 emergence:2 chakrabarti:1 string:5 apart:2 loss:1 modifications:1 theor:1 simulational:1 like:6 excluding:1 sizes:11 follows:1 extremely:1 mit:1 separately:2 flux:1 individuals:4 unstable:1 arbitrary:1 translated:1 become:5 tower:1 works:1 page:1 italian:1 mathematical:1 portuguese:1 www:2 right:2 old:4 often:2 people:29 shen:1 belonged:1 some:8 begin:1 oln:1 trends:1 growth:2 acad:2 proper:1 strogatz:6 investigating:1 happens:6 morphology:1 total:4 lead:1 sufficiently:2 support:1 schilling:1 opposite:2 integration:1 per:3 14th:1 coupled:2 everything:1 critical:1 mutation:6 komarova:2 fragments:2 moderate:1 proc:3 refer:1 core:1 biology:4 noise:3 power:4 dropped:1 mitt:1 fitness:3 agreement:2 wichmann:6 overall:1 pressure:1 step:2 shifting:3 urban:1 takes:3 zur:1 viviane:15 about:10 central:1 working:1 extension:1 coexist:1 universe:1 discussed:1 dependence:3 o:4 simulation:5 melbourne:1 remains:1 range:1 regular:1 plus:1 historically:1 done:1 concentrations:1 germany:3 tongue:2 introduced:3 slightly:1 allowing:1 accessible:2 soc:3 own:3 simulated:6 niyogi:2 previously:2 generalized:1 into:9 within:5 due:1 down:1 lies:2 gomes:1 en:1 references:1 einstein:2 computational:7 proportional:3 france:2 minority:6 van:1 log:6 few:2 transfer:4 suffice:1 initial:3 populated:1 gift:1 long:3 sides:3 mutated:2 inasmuch:1 miguel:3 handbook:2 physicists:11 fraction:8 brazilian:2 gil:1 was:13 war:1 opposed:1 function:4 fragmented:2 north:1 newtonian:1 offer:1 sound:3 differences:2 but:18 back:1 neutral:2 shorter:1 game:1 competition:10 larger:4 line:4 hg:1 he:1 directed:4 fragmentation:12 made:5 builds:1 places:1 wish:1 anen:1 up:10 us:1 until:1 dordrecht:1 below:2 decays:1 retaining:1 minor:1 syst:1 distribution:12 stages:1 similar:3 called:4 detailed:1 fractions:4 constant:2 adults:3 heidelberg:2 migrate:1 certain:2 abstract:1 describe:4 history:1 life:1 general:1 penna:1 exist:1 simulations:12 flight:2 moves:1 distributions:5 empire:1 constructed:1 again:3 compared:2 nichols:1 quantitive:1 no:6 weaken:1 storage:1 reality:4 application:1 other:12 role:1 details:2 papers:2 department:1 mathematics:1 ns:7 little:2 ıluz:3 nice:1 picture:2 included:1 apparent:1 kinds:2 hamming:1 separate:3 models:14 dies:1 june:1 shown:2 variation:4 includes:1 meaning:1 scale:4 bounded:1 ising:1 studied:2 variable:1 transfers:1 formal:1 cooperate:1 needed:1 died:1 ago:3 independently:2 condensation:1 longer:1 assume:2 normally:1 tricks:1 bottom:6 together:1 original:1 carrying:2 fitted:1 time:23 far:1 characterising:1 accidents:1 4b:2 strings:8 4a:1 |
0704.0692.txt |@word partial:1 consider:1 zhang:1 electrondoped:2 equalities:1 results:14 existing:1 four:4 gf:31 consists:1 follow:1 expressions:11 denotes:4 contributions:8 hole:17 gh:2 relationships:3 depend:2 essentials:1 zone:2 technique:3 worth:2 gab:2 charge:10 νij:10 subband:23 those:2 under:6 tc:2 summarizes:1 doped:8 straightforward:1 r11:1 very:1 translations:2 induce:1 wave:4 electron:5 every:1 stays:2 fab:1 difference:1 matrices:1 condition:1 kinematic:1 level:5 solution:1 solved:2 vector:2 rj:4 small:8 upper:2 xiσ:11 occurrence:5 f21:3 renormalized:1 consistent:1 uef:1 estimates:2 b22:1 b21:1 approximation:12 second:8 j22:1 j21:1 rigorous:8 χb:1 cfs:4 canonical:1 spectral:4 established:3 g22:1 xi22:6 richard:1 adjustable:2 anton:1 section:3 2c21:1 expressed:1 cell:1 goes:1 coordination:2 method:1 degree:1 exchange:7 respectively:12 component:1 equals:1 here:2 diagonal:1 correlating:2 address:1 corrections:1 strong:1 equations:4 extreme:1 obtained:6 remark:2 parameters:6 rigorously:1 institute:2 vectors:1 allows:3 implementation:1 products:1 fourier:5 makes:1 anticommutators:1 involves:1 χs1:1 χs2:1 shorthand:1 projection:3 apr:1 summation:1 total:1 use:12 would:1 commun:1 distinct:1 quasi:1 next:2 anticommutation:1 noting:1 therefore:2 4t2:1 νim:2 type:1 theoretical:1 3ev:1 becomes:1 operators:6 carrying:1 particular:1 known:1 cases:1 hold:3 iii:1 fermionic:3 high:3 account:1 crosses:2 equation:9 mn:1 dab:3 2c22:1 remain:1 ij:17 values:2 following:10 rij:3 averages:17 decoupled:1 dropped:1 nearest:2 compare:1 schmitt:1 calculation:1 anomalous:9 states:9 numbers:2 allowed:1 r22:1 r21:2 afm:2 needs:1 carriers:1 provide:1 siz:2 secured:1 holds:4 chemical:1 stemming:1 hos:4 pure:1 simplifies:1 parameter:3 secures:3 simplicity:1 product:1 express:1 description:2 information:1 may:3 thermodynamic:3 advice:1 derived:3 dx2:2 reflect:1 hence:1 coming:2 multiplication:2 representations:1 derives:1 fm:2 constants:2 effective:5 yielding:1 element:1 sj:2 si:9 green:30 temp:1 enter:2 representation:14 order:17 g11:1 superscript:1 hierarchy:1 over:7 summarized:1 mainly:1 satisfied:2 siσ:2 paper:4 through:2 statistical:10 omitting:2 y2:2 its:5 roots:1 geometrical:3 derive:1 exclusion:1 paa:1 fiz:1 exact:2 solving:1 boson:14 forms:2 faa:1 complex:1 systems:3 workable:1 mail:1 image:1 non:7 gibbs:1 unveiling:1 runs:1 cˆσ:3 band:9 effects:1 identically:1 inelastic:1 gλµ:2 oudovenko:4 eigenvalue:1 term:3 finite:1 always:1 hamiltonian:5 ensemble:1 2d:1 plakida:10 found:2 assume:1 characterized:3 mean:20 domain:1 schemes:2 financial:1 rink:1 gfs:7 energy:26 enables:1 reduce:2 related:3 abrahams:1 ifin:1 martin:1 frequency:17 entering:7 quantum:1 laboratory:1 eq:13 χij:11 special:1 mat:1 predefined:1 ru:2 shown:3 matrix:48 factors:4 algebra:6 rev:11 cuprate:1 research:2 particles:2 replacing:4 investigation:2 weighted:3 get:12 ri:4 math:1 shows:5 theory:1 subbands:1 free:1 effect:4 reason:1 convolutions:1 dubna:1 e1:10 e2:23 definition:2 pairs:2 interaction:5 derivation:11 english:1 damascelli:1 so:1 motion:5 exponentially:6 δij:12 consequence:3 onto:1 eqs:7 first:3 xj:2 copper:1 romania:1 xi:2 features:3 symmetry:4 xm:2 omitted:2 nhi:4 number:3 reaches:1 d22:4 obeying:1 done:1 relations:1 another:2 array:1 open:1 interchange:1 given:10 perturbation:1 temperature:1 similarly:2 introduction:1 πk:3 adjoint:1 system:6 occupancy:1 their:3 ci0:1 zeros:1 too:1 structures:1 frame:1 relationship:1 moscow:1 exactly:2 interband:5 part:4 authors:1 kept:1 translation:7 representing:1 coefficients:3 distance:1 third:2 aab:2 jumps:2 was:3 approximations:1 matteo:1 depends:2 submitted:1 annihilation:4 doubly:1 identical:1 p21:2 providing:1 treated:2 russia:1 descriptions:1 magurele:1 lowest:2 formulated:1 symmetries:2 raa:1 fluctuation:1 spectrum:5 manuscript:1 current:1 cumbersome:1 occupied:2 any:2 relatively:1 zero:2 βe2:1 convenient:2 self:1 able:3 εp:1 aa:1 phillips:1 potential:1 generalized:3 εd:1 2c11:1 heisenberg:1 kab:4 normal:13 correlation:20 singlet:26 algebraic:1 involving:4 but:1 significant:1 position:1 pair:5 extremely:1 tpd:1 χs:3 consequences:2 considered:1 average:2 physica:3 points:2 principle:2 χa:1 quadratic:1 physics:1 sum:2 fact:2 quantity:1 incorporate:2 emerging:1 show:4 labels:5 relation:2 solutions:1 principal:1 henceforth:1 aσ:1 finally:4 based:1 securing:1 conduction:1 romanian:1 state:8 negligible:3 only:2 explicitly:1 2ax:1 factor:3 various:2 rice:1 jab:2 do:2 above:1 notation:4 means:2 dependent:2 there:2 between:3 overall:1 hussain:1 antiferromagnetic:1 joint:1 brillouin:2 reversal:14 gen:1 matsumoto:2 processes:4 densities:1 qy:2 qx:2 transposition:1 arxiv:1 yield:1 acknowledgments:1 bab:2 contain:1 inside:4 set:1 reference:2 phenomenologically:1 national:1 correlations:4 nambu:4 maximum:2 see:2 sec:6 result:8 p22:1 forthcoming:1 incorporating:1 xi0:2 commutation:2 consistency:1 nuclear:2 review:1 sites:5 label:5 symmetric:2 written:2 identification:5 simplest:3 invariant:8 mathematical:2 reading:1 approach:4 horia:1 multiplied:1 ends:1 terms:12 iπδ:1 however:3 vanishing:5 uω:2 jetp:4 jb:1 originates:2 c22:24 both:5 essentially:1 c21:24 last:1 reported:1 hayn:2 region:1 conclusions:2 reproduces:1 fulfilled:1 raimondi:1 negative:1 retarded:4 contribution:7 expression:7 comes:1 con:1 collecting:1 2e1:1 characterization:1 evaluate:1 dyson:1 dimensional:2 ab:2 simply:1 doping:3 gratitude:1 zubarev:2 most:1 singlets:3 described:5 decoupling:4 basis:1 simplification:5 due:4 been:2 varma:1 reduction:8 describes:1 pd:1 ph:1 2σc:2 differently:1 determinant:3 corresponding:3 quantities:8 cos:6 300k:1 argument:3 neighbour:3 denote:1 spin:43 c11:24 present:3 c222:4 eiq:1 reciprocal:2 pacs:1 solid:1 reliable:1 single:8 value:4 rectangular:1 will:2 rests:2 while:8 irrespective:1 di:1 property:2 procedure:7 cab:3 a21:3 a22:6 unitary:2 approximate:1 played:1 iq:1 im:1 site:37 iv:1 ii:1 cluster:1 superconducting:14 hulubei:1 cond:1 mod:1 vanish:1 containing:3 hubbard:36 develop:1 d11:3 spheres:2 same:1 rules:1 parts:1 pauli:1 grand:1 avoids:2 resulting:1 several:3 higher:3 hermiticity:1 independent:6 nih:3 used:1 imply:1 iε:19 numerical:1 fulfilment:1 nj:8 u0:1 possible:1 v0:2 v2:1 levels:1 uses:1 infinite:1 invariance:18 identity:3 mentioning:1 lower:2 off:1 hopping:27 p11:1 k22:25 k21:25 well:3 double:1 stanescu:1 does:1 components:2 sets:1 organization:1 model:38 usual:1 cuprates:9 being:1 isolated:1 underlying:3 identify:1 transforms:2 differentiation:1 useful:1 alternative:1 macroscopic:1 yet:1 now:2 corroborated:1 density:1 yu:1 point:5 exclusively:1 mathematically:1 iω:1 lattice:18 jefferson:1 lett:2 theorem:4 xjν:3 iσ:7 occurring:1 transformation:1 take:1 real:1 iθ:1 around:2 iα:2 bands:1 iβ:1 sums:2 2v:2 vacuum:1 using:3 unique:1 moreover:1 calculate:1 advanced:4 like:4 necessary:1 adams:1 particle:6 follows:6 superexchange:1 specific:7 roth:1 yields:4 either:3 integrals:1 niσ:4 essential:1 spins:1 bucharest:1 right:1 namely:2 discrete:1 shen:1 creation:4 some:1 2qx:1 2qy:1 q21:2 c211:3 respect:2 proper:1 a11:1 eβω:1 provided:1 describing:1 feiner:1 cσ:1 shall:1 overlap:1 critical:2 provides:1 assuming:1 prof:1 denominator:1 scientific:1 equivalent:1 each:7 bi:1 constructive:1 villani:1 imaginary:3 properties:14 simpler:1 comparison:1 asks:2 constraint:1 column:1 discussed:1 dependence:5 nonvanishing:1 sake:1 carries:1 underway:1 constraints:2 therein:1 equally:1 previously:1 into:1 within:8 integral:3 three:6 accommodate:1 hermitian:2 square:2 references:2 sov:1 operator:12 proportional:1 bosonic:2 approximately:1 k12:1 k11:25 support:1 pairing:20 question:1 transform:3 u2:2 start:2 ijσ:21 low:1 jinr:2 sections:3 function:14 project:1 therefrom:1 complete:1 form:9 cuo2:1 usp:1 extended:1 hh:1 lowered:1 incorporation:1 ho:2 elimination:4 technologies:1 j11:1 embedded:1 characteristic:6 supr:1 monic:1 up:2 us:1 different:2 crystal:2 limit:1 planes:1 avella:1 similar:1 jσ:5 originating:4 nnn:3 definitions:1 defined:6 abstract:1 contribute:1 general:4 transl:1 engineering:1 together:1 ay:8 ax:9 proceeds:1 authority:1 physical:1 ni:12 functions:32 completeness:2 nn:3 no:1 whereas:3 edwards:1 vanishes:1 elemental:5 reality:1 field:21 other:3 role:1 details:1 investigations:1 b11:1 out:1 conclusion:1 elements:10 kinds:2 superconductivity:19 models:2 variation:1 commutator:1 generated:1 ξk:3 fermi:5 gap:1 structure:3 zhetf:1 implies:1 anticommutator:2 coulomb:1 dω:5 d21:3 space:4 emery:1 rule:4 mancini:2 neighbouring:3 adam:4 time:1 observables:2 starting:1 gαβ:1 |
0704.0693.txt |@word code:1 partial:4 remarkable:1 illustrates:1 magnetic:2 results:4 four:1 eckern:1 covalent:1 contributions:2 ıt:3 zone:1 environment:1 finally:2 program:2 under:1 dramatically:1 egami:1 ın:3 fax:1 very:4 rise:4 helpful:1 choice:1 electron:2 verg:1 leads:1 dominate:1 presented:1 transmission:1 irreducible:1 solution:1 large:1 small:2 dreher:1 configurations:2 unexpected:1 direct:1 approximation:1 second:1 displays:1 untiedt:1 dynamics:1 chem:2 linear:22 even:2 established:1 interatomic:2 plays:1 luitz:1 3s:18 3p:7 near:1 above:1 values:3 net:4 principal:2 consisting:1 full:1 lee:1 exchange:1 respectively:1 component:1 orbitals:10 atoms:3 behaviour:2 reported:2 magnetism:1 flores:1 mes:1 address:2 represented:1 consideration:1 along:5 table:3 obtained:1 great:1 shift:2 spacial:2 stretching:6 completely:2 leaving:2 spheres:1 periodic:2 chang:1 studies:1 elongated:2 via:3 nearest:3 apr:1 apw:1 visible:1 addressed:1 apply:1 should:1 kobayashi:1 ıa:2 use:1 sharper:2 duda:1 charge:12 next:1 scenarios:1 few:1 mediate:2 call:2 therefore:4 taken:1 type:8 until:1 minor:1 more:5 becomes:1 stable:1 about:3 particular:3 cases:1 account:4 stabilized:1 decouples:1 setup:1 work:1 ıaz:1 instable:1 remain:1 nine:1 jacobsen:1 following:1 spontaneous:2 performed:1 wedge:1 compare:2 modulation:1 figure:7 give:1 states:37 perdew:1 degenerate:3 lacks:1 axis:4 bonds:5 arrangement:1 chemical:5 maps:2 sim:1 map:1 levy:1 mat:2 may:1 hence:2 levi:3 plane:3 physik:2 waves:1 3s2:1 stress:2 short:1 eyert:1 neck:5 third:1 sp:3 explicit:1 yielding:1 lengths:4 fundamental:1 correlation:1 subsequently:1 order:1 restriction:2 interpretation:1 muffin:1 over:1 enez:2 years:1 course:1 including:1 same:1 still:1 its:5 ono:1 rapidly:1 thank:1 energies:5 lo:1 jim:2 vicinity:1 decreases:1 madsen:1 fig:4 main:1 versus:1 junction:1 deutsche:1 runs:1 introduce:1 reflected:1 break:1 band:7 effects:6 they:2 palacios:2 now:1 hall:1 nor:1 structural:7 february:1 2p:1 2s:1 university:1 level:2 realistic:1 urbina:1 each:4 found:3 universit:1 traces:1 characterized:1 bond:10 financial:1 significantly:3 instability:4 energy:9 ef:3 µb:2 joyez:1 conductance:4 literature:1 expect:2 changed:1 quantum:1 our:5 ev:13 es:1 minority:2 rt:1 shown:2 mediates:1 gradient:1 restricted:2 rep:1 since:4 rev:14 increase:2 attracted:1 seriously:1 dominated:1 size:6 burke:1 shows:2 turning:1 theory:3 given:2 crystallographically:1 reason:1 thygesen:1 van:1 beginning:1 rearrangements:1 geometry:12 widths:3 insulating:1 length:5 mesh:1 isotropic:3 transfer:6 consequence:2 first:1 nieminen:1 features:3 symmetry:3 wave:1 coming:1 number:4 channels:1 smaller:4 comprises:2 reached:1 electronic:15 agra:3 1s:1 afner:1 width:1 ordering:2 top:1 system:4 lapw:1 their:1 calculations:10 molecular:1 structures:3 ribeiro:1 augsburg:3 addition:1 forschungsgemeinschaft:1 ogl:6 larger:3 part:1 simulate:1 authors:1 udo:1 pyramidal:18 scheme:1 see:3 submitted:1 matter:1 determined:1 enables:1 treated:1 addressing:1 cohen:1 curves:1 delin:3 mater:1 elsevier:1 hexagonal:1 occupied:2 any:2 lie:1 sandwiched:1 layer:2 omez:1 efficient:1 convenient:1 note:1 majority:2 potential:2 generalized:1 new:1 subject:1 interfered:1 divers:1 channel:1 play:1 towards:1 serena:2 investigations:2 precluded:1 most:3 fcc:4 connected:3 letter:1 acknowledgements:1 sfb:1 consequences:1 calculated:2 metal:1 giving:3 points:1 electrons:3 reflections:1 mechanical:2 nanocontacts:6 fact:1 particularly:1 show:2 rodero:3 radii:1 tsukada:1 participate:1 find:1 piezoelectric:1 based:1 than:4 only:4 adequate:2 local:8 dominant:1 means:5 occupation:2 nanowires:3 de:1 cannot:2 brillouin:1 words:1 despite:1 during:1 accomodates:1 endez:1 neither:1 evolution:1 increasing:1 bar:1 densities:6 arxiv:2 microscopy:1 across:3 investigate:1 europhys:1 predicted:1 fixed:1 view:1 scanning:1 mandatory:1 electrodes:3 violated:1 geometrical:1 depends:1 radius:1 result:1 discussions:1 herrero:1 ur:1 prototypical:2 techniques:1 wire:1 erez:2 review:1 sites:1 shiraishi:1 state:1 various:1 between:7 boundary:2 conditions:2 email:1 schuster:4 terms:2 interfaces:1 attention:1 however:4 magn:2 key:1 configuration:16 suppressed:3 both:4 last:1 taking:1 infinitely:1 according:1 against:5 sensitive:3 und:2 uni:1 contribution:1 disappears:1 comes:1 otherwise:1 relevant:1 point:2 simple:1 nanocontact:8 relaxation:1 directions:1 stretched:5 interrelations:1 moreover:2 decline:1 amer:1 geometries:5 basis:2 stretch:1 px:3 locally:1 due:6 been:6 mart:3 reduction:2 pd:1 expected:3 hardly:2 corresponding:2 concerning:1 precision:1 schwab:1 bulk:3 observe:1 angles:1 spin:5 present:2 case:7 gustafsson:1 pacs:1 value:1 will:2 amounting:1 while:3 theoretical:1 situation:1 tunneling:1 study:1 seven:1 studied:2 orientation:2 almost:3 thus:4 site:15 arrangements:1 cond:2 affected:1 technology:1 orbital:8 different:1 decoupling:2 pauly:1 author:1 art:1 aluminium:17 clearly:1 shifts:1 units:3 finite:2 higher:2 used:2 prohibits:1 bollinger:1 hand:2 parametrized:1 moment:1 conductors:1 kim:1 louis:1 infinite:2 puska:1 lower:1 off:4 largely:1 changes:2 well:3 bohr:1 contact:50 does:1 simulated:1 quantitative:1 model:2 comprise:1 left:2 distances:2 magnetization:2 3p1:1 obtain:1 nordgren:1 tosatti:2 atomic:10 coordination:1 previous:1 oriented:1 yeyati:4 preprint:1 density:7 discuss:1 reasons:1 concerns:1 extends:1 lett:11 electrical:5 polarized:1 hybridization:9 increased:1 couple:1 increases:2 using:1 breakage:3 formal:1 modifications:3 like:1 obvious:1 schmitt:1 specific:3 wien2k:2 yields:1 schwarz:1 rearrangement:1 become:1 valence:3 essential:1 satisfactory:1 because:4 deal:1 back:1 respect:1 transport:8 pronounced:2 lead:1 contacts:5 opposite:1 integration:1 overlap:5 when:3 critical:1 chains:1 demonstrated:2 core:1 equivalent:1 pascual:1 accompanied:1 properties:5 conducting:1 neighbours:4 central:5 ferromagnetic:4 extension:1 package:1 discussed:1 o:1 reduced:3 pz:1 oshiyama:1 mixed:1 germany:1 consequently:1 brandbyge:1 py:3 garc:2 significant:1 hirose:1 into:2 within:2 splitting:1 functional:3 three:1 neutrality:3 right:2 references:1 okano:1 cuevas:3 rely:1 institut:1 comparing:1 assumed:1 support:1 occupy:1 accordingly:1 appl:1 way:1 scheer:1 vienna:1 differences:2 but:1 gain:1 atom:6 nanowire:5 true:1 directed:2 characteristic:3 us:1 schwingenschl:6 crystal:5 owing:1 fermi:10 planes:1 similar:1 jellium:1 strongly:5 ab:2 nanotechnology:1 likewise:3 abstract:1 influence:2 covers:1 general:1 single:2 esteve:1 blaha:1 sasaki:1 constriction:1 again:2 compared:2 devoret:1 no:1 amounts:2 whereas:3 hybrid:3 vanishes:2 planar:2 tin:1 other:2 role:2 details:5 conclusion:1 elements:1 calculating:1 condens:1 initio:1 medina:2 prepared:1 bonding:10 important:1 dos:19 sides:2 structure:17 longer:1 resembles:1 serious:2 nielaba:1 augmented:1 |
0704.0694.txt |@word ybco:20 sci:1 consider:2 chain:7 caused:1 ceramic:2 resistance:6 four:1 revealed:2 calculate:2 technique:2 young:2 removal:1 charge:2 sr1:2 under:2 andreev:5 cm2:2 p2:2 keck:1 supported:1 federation:1 very:2 choice:1 electron:1 figs:1 bottleneck:8 illustrated:1 presented:3 tanh:2 large:1 small:2 path:1 glued:1 hysteretic:9 smaller:3 prediction:1 zero:1 further:2 estimated:4 nonlinear:1 sum:5 selected:1 stauffer:1 thickness:1 current:31 experiment:5 above:1 scientists:1 nev:3 new:1 jumps:2 filled:1 coefficient:3 full:1 led:1 modify:1 equals:1 here:4 feldmann:1 mev:7 ummarino:1 2kb:2 excess:2 based:2 imperfections:1 superconductor:7 pb0:2 stresses:1 almost:1 tunneling:2 institute:1 ekf:1 larger:1 allows:1 reports:1 htsc:1 resulting:4 usually:1 conveniently:1 narrow:1 members:1 apr:1 iph:1 explained:2 gurevich:1 replace:1 decrease:2 use:2 links:35 remains:1 ca2:2 contains:1 quasiparticles:1 vol:4 program:3 therefore:1 characteristics:15 type:1 reflects:1 more:4 composite:6 neglected:1 emission:1 correspondingly:3 known:2 kgn:8 me:1 sample:14 account:2 room:1 mm:3 work:1 peeters:1 mk:1 tc:25 arches:1 krasnoyarsk:1 values:7 temperatures:4 bent:1 figure:13 division:1 calculation:1 share:1 topic:1 weighting:4 numbers:1 slip:1 la1:2 junctions:20 axis:1 influenced:1 varied:1 verify:1 breaking:1 parameter:1 simplicity:1 description:2 may:3 fy:1 earlier:3 sns:11 fits:2 president:1 arch:4 parallel:6 realized:1 intergranular:5 effective:1 lines:5 so:1 decreasing:1 banks:3 dispersing:1 order:1 sd:1 help:1 ith:2 daghero:1 indeed:2 over:3 displayed:1 siberian:1 thermal:1 scientist:1 through:4 signs:1 y0:2 its:1 before:1 constituted:1 difference:1 group:1 chosen:1 decreases:4 fruitful:1 narrowest:1 mail:1 main:2 non:2 junction:8 combination:1 break:18 units:1 kopnin:1 subtraction:1 inelastic:1 yu:2 represents:1 larbalestier:1 drop:3 arrows:2 realistic:1 reasonable:1 each:2 accompanied:1 higher:3 mean:2 em:1 differential:2 series:6 energy:4 mv:3 mm2:1 used:4 measure:1 quantum:1 our:1 ev:3 eq:11 out:2 ru:1 network:20 rev:6 smp:1 increase:1 investigation:1 rn:5 shows:3 theory:2 mechanisms:2 voltages:2 free:1 standard:3 approaches:2 dependencies:3 formation:1 disposition:2 estimate:2 e1:3 inevitable:1 synthesized:4 dramatically:1 times:3 massive:1 circuit:1 substrates:1 first:1 initial:3 quasiparticle:1 number:11 peculiarity:9 simplified:2 size:2 given:2 temperature:7 introduction:1 data:5 least:1 1a:1 their:3 1b:2 structures:1 shifted:2 academy:2 obtained:1 reflecting:1 simulate:1 believe:1 than:4 coefficients:1 determines:1 correlate:1 second:1 project:1 determined:4 were:11 russia:1 result:1 exhibit:2 polycrystalline:8 resistivity:1 contradict:1 supercond:1 resistive:3 few:4 curves:36 ras:1 distorted:1 screws:1 seem:1 paths:3 angle:1 responsible:1 metallic:1 sciences:2 high:21 potential:1 negligible:1 circles:6 multiple:3 investigations:1 simplify:1 petrov:8 connected:6 significant:1 phase:1 acknowledgements:1 measured:2 kf:3 gorkov:1 considered:5 calculated:5 stronger:2 physica:5 mod:1 graphs:1 part:6 reflections:5 exp:1 mechanical:1 subharmonic:3 lsco:12 dispersed:1 typical:16 physics:3 section:8 shot:1 show:1 probe:1 theories:1 relation:3 svistunov:1 dyachenko:1 rough:1 d2:2 networks:4 d1:1 ba2:2 parameters:12 should:3 only:5 version:1 rich:1 developed:1 employed:1 hatta:1 ip:1 usp:2 dm:1 nanowires:1 de:2 evolution:2 substrate:1 approach:3 arxiv:1 nauk:1 fixed:1 scanning:2 computed:6 achieved:1 undergoes:1 observed:2 individual:2 sec:1 powder:1 discussions:1 conductivity:1 draws:1 nature:1 materials:1 boundaries:5 state:3 various:1 jth:2 between:3 macrophysics:1 conditions:1 multiplied:1 controllable:1 weak:44 however:1 bscco:10 yba2:3 jetp:1 suggested:4 many:1 region:2 gonnelli:1 according:2 fiz:1 connection:4 figures:3 contribution:1 estimation:1 expression:4 experimental:16 con:1 among:1 cm:3 simple:1 coincidence:1 consideration:1 loaded:1 considers:1 considering:1 described:3 addition:1 due:5 been:1 mark:1 much:2 percolating:1 pi:6 lu0:2 corresponding:2 formed:1 gap:6 bulk:6 clusters:2 case:1 p1:5 pacs:1 solid:8 ij:2 value:8 likharev:1 while:1 pressed:1 shift:1 cracked:1 ultra:1 layer:2 studied:1 orientation:1 chaotic:1 vi:4 thus:1 discrepancy:1 ii:2 cluster:1 superconducting:1 bias:4 cond:4 ic:5 technology:2 currents:2 different:8 grant:1 cross:5 member:1 parts:1 modification:1 grain:1 finite:1 difficult:2 independent:1 investigated:4 percolation:2 i1:1 i2:1 effect:1 flows:1 hysteresis:1 v1:2 v2:2 ripamonti:1 kresin:2 lower:1 well:1 peculiarities:7 contact:3 s27:1 components:1 simulated:1 firstly:1 position:1 model:8 otherwise:2 less:2 crystallites:1 superconductors:20 obtain:2 voltage:16 predicts:1 facts:1 bi1:2 preprint:3 density:4 fitting:3 valid:1 lett:2 samples:6 crack:1 sectional:1 joynt:1 possible:2 tunnelling:1 increases:2 using:1 emergence:1 projects:1 heightened:1 cu3:7 like:5 follows:1 specific:1 either:1 alternatively:1 works:2 satisfactory:2 because:3 spring:1 some:2 competition:1 suppl:1 table:5 aleksandrov:2 transport:4 provided:1 scale:1 contacts:3 measurements:2 sr0:2 critical:3 provides:1 assuming:1 o7:5 chains:5 measuring:1 equivalent:1 bj:7 popkov:2 substituted:1 ummel:6 references:1 found:1 zimmermann:1 comparison:1 about:1 central:1 most:1 dependence:4 simulation:1 sake:1 range:2 wolf:3 presidium:1 ox:2 mixed:1 functions:1 thinner:1 polished:1 decreased:1 negative:2 down:2 thankful:1 appropriate:1 right:1 bjs:6 sov:1 reducing:2 ovchinnikov:1 area:3 support:1 there:3 describes:2 low:3 resulted:2 analyze:1 was:11 hightc:1 cuo4:2 granules:2 form:1 forming:1 m2:1 but:1 stepanov:1 heat:2 link:9 russian:3 line:1 piraux:1 compute:2 mat:4 arrays:1 characteristic:2 supr:1 up:2 us:1 sapphire:2 demonstrate:2 distribution:1 display:2 ohm:2 ag:12 metal:5 abstract:1 describe:4 influence:2 metals:1 evidence:1 single:2 moves:1 physical:1 mutual:2 dotted:1 no:1 when:3 detail:1 smears:1 other:2 normal:4 becomes:1 nv:9 conclusion:1 prepared:1 important:1 technol:1 velocity:2 sensibility:1 structure:4 haslinger:1 curve:38 together:1 mass:1 resembles:1 pellets:1 |
0704.0695.txt |@word sci:1 consider:6 squared:1 magnetic:1 eκ:1 splitting:53 kernphysik:1 four:8 facilities:2 selection:1 gn:6 expressions:7 contributions:7 compact:3 increase:1 repetition:1 depend:3 calculate:1 strakhovenko:2 technique:4 tr:3 worth:1 intensive:1 charge:2 does:2 tj:2 those:8 ωs2:2 cm2:6 mpg:2 supported:1 amplitudes:60 presently:1 g1:14 very:8 conditions:1 results:5 electron:7 wavy:1 putting:1 experimentally:4 difference:1 matrices:2 xtr:3 condition:1 iν2:4 presented:4 t2:8 t3:10 d2:41 t1:10 large:6 vector:21 fourier:1 small:11 relation:5 becker:2 shows:1 lines:1 application:1 fµν:1 zh:11 zj:1 d3:42 direct:3 pulse:4 sign:2 approximation:6 fold:2 rate:13 design:1 me3:6 pass:3 iσ3:3 iσ2:3 iσ1:3 eik3:3 eik2:3 4x1:5 linear:7 even:3 index:1 nonlinear:1 trivial:1 assisted:1 analogously:2 expressed:2 uniform:2 experiment:5 above:4 lifshitz:1 crossed:6 net:1 principal:1 technical:1 method:1 suppress:1 viii:2 coefficient:1 edited:1 lundstr:1 lee:2 tabulation:1 respectively:1 never:2 modify:1 here:5 atoms:1 natural:1 asymmetry:2 mev:3 κx:2 free:2 address:3 represented:1 consideration:1 along:6 strong:4 observing:2 z1:21 change:2 extreme:3 obtained:13 delbr:2 incoming:1 iπ:1 2x2:4 institute:2 studied:3 allows:1 periodic:1 products:1 permutation:1 t21:8 hospitality:1 t23:8 t22:4 makes:1 golden:1 eˆ:4 spatially:1 projection:4 dϑ2:1 a21:1 split:1 problematic:1 namely:1 vii:2 compare:1 highly:1 inequality:1 decrease:1 summation:2 total:7 planck:2 linearly:13 use:5 asymptotic:2 usa:1 commun:1 probabilities:1 positive:2 fel:7 contains:6 visit:1 finally:4 eσ:3 next:2 equipment:1 calculation:9 nucl:1 noting:1 kinematics:1 therefore:14 m3:9 m2:24 taken:2 simpler:2 theoretical:1 today:1 more:3 corrections:1 initiated:3 successful:2 becomes:4 operators:2 under:2 line:5 emission:1 carrying:1 proceed:1 particular:2 known:2 cases:2 iii:2 bremsstrahlung:1 e2µ:1 account:1 rotational:1 hour:2 permits:1 equation:3 mn:44 ρn:3 values:7 following:9 arrive:1 root:1 example:1 mσ1:5 numbers:3 f0:5 f1:1 f2:6 f3:6 figure:1 chosen:1 process:11 relativistic:1 sense:1 organized:1 high:7 indicates:1 lorentz:2 performed:4 allowed:1 exclude:1 spanning:1 axis:1 provide:2 verify:1 discussion:3 means:5 regions:1 pair:2 rλ1:24 answer:3 instead:1 ordinary:1 parameter:7 sin:9 ρ2n:3 circular:2 rfbr:1 applicability:2 express:1 mourou:1 intended:1 max:2 after:2 derived:3 containing:3 diagram:4 applications:1 shukla:1 plane:9 fj:2 wave:19 parallel:12 dw3:1 short:3 eµi:1 imply:2 light:3 explicit:3 correspond:3 su:1 element:1 perform:3 cannot:1 green:6 allow:1 s2:22 representation:5 acknowledges:1 order:9 transformation:1 restriction:1 tagged:7 s3:16 baier:5 help:3 developed:2 over:18 ϕj:2 mainly:1 confirm:1 course:1 paper:4 through:2 lasers:2 during:1 mentioned:1 existence:1 satisfies:2 still:2 dt:1 before:3 write:3 derive:2 τj:2 symmetry:1 energies:4 exact:1 2e1:2 d32:1 affleck:1 decreases:1 forms:2 h2:1 according:2 fig:9 main:1 moskalev:1 s1:11 maximal:1 measurement:1 non:1 photonphoton:1 polarizations:2 investigated:4 differential:1 effects:3 they:5 oxford:1 now:7 2s1:2 easily:2 february:1 dirac:3 2s:4 invariants:2 appropriate:1 fs:2 2e:4 x21:2 2z1:2 each:6 found:2 difficult:1 2i:5 mean:1 square:1 ei:5 g2:16 accelerator:1 generation:2 there:4 energy:16 ea:2 fr:1 related:1 ea1:2 brodin:1 frequency:5 aλj:4 measure:1 quantum:3 laboratory:3 meth:1 ev:2 eq:30 out:6 shown:6 matrix:2 factors:1 restricted:2 rep:4 since:2 lagrangian:4 denotes:3 content:2 contained:2 investigation:1 d21:3 reader:1 formula:2 size:3 ref:2 integrated:2 note:5 mκ:3 log2:1 theory:2 mσ:2 circumstance:1 parseval:1 possibility:11 quite:1 indices:2 reason:2 loa:1 term:5 besides:3 lundin:1 hep:1 e1:6 e0:7 e3:4 e2:5 collimators:1 interaction:1 derivation:1 starts:2 ds2:10 ds3:9 ds1:10 iz1:1 iz2:1 instrum:1 fiz:7 transfer:1 consequence:2 nω0:3 symbolize:1 first:5 xj:3 simplifies:1 probability:2 upper:1 omitted:1 variables:5 xa:1 dˆ1:1 number:7 dˆ2:1 clear:1 employing:1 simplified:1 nonperturbative:2 another:2 impossible:1 thick:1 precisely:1 electronic:3 angular:6 illustrate:1 k3µ:1 received:1 given:7 perturbation:1 checked:1 interesting:2 introduction:1 leading:15 eqs:12 achieved:1 system:1 relations:5 needed:1 intermediate:1 calculations:5 aλ3:24 aλ2:24 aλ1:24 scheme:4 approximately:2 final:18 speaking:1 gives:1 sin2:2 sdn:3 centimeter:1 transverse:4 optical:5 contri:1 x2:29 x3:26 x1:13 than:4 coefficients:14 wide:1 aλi:4 polarized:30 effective:1 accordance:1 sections:2 depends:5 aims:1 limiting:3 project:1 future:1 amplitude:17 were:1 powers:5 russia:1 perturbative:1 synchrotron:1 rad:1 marklund:1 generality:1 electrodynamics:2 ann:1 turned:1 argument:1 berestetskii:1 already:1 smaller:2 further:1 seen:1 cumbersome:2 orders:1 ray:2 strength:6 kˆ2:3 kˆ3:3 zero:9 k32:1 convenient:7 latter:3 pdf:2 4x2:3 k3:23 k2:27 coplanar:2 potential:6 εi:2 take:2 εj:1 so:9 coincide:3 modulus:1 accuracy:2 heisenberg:3 spectral:1 play:1 added:1 electric:8 trace:2 investigations:1 any:11 twodimensional:1 reach:1 z2:23 germany:2 but:10 definitions:1 nothing:2 analytically:1 measured:2 why:1 δn1:2 observation:7 considered:6 ki:2 implications:1 z3:23 sf:1 feynman:2 part:2 ξx1:1 principle:1 exp:15 azimuth:4 physics:2 section:12 fact:3 2m3:1 drastically:1 cot2:1 bj:6 show:2 hatsagortsyan:3 notations:1 bring:1 gauge:2 k1ν:1 threshold:1 mitter:2 d4:4 determined:1 fine:1 find:6 d1:37 sj:2 q2:1 ratio:3 parameters:9 explain:1 state:1 zα:1 bernard:2 only:11 difficulties:1 factor:1 employed:1 inφ:1 pointed:2 substitutions:1 dn:6 do:2 his:1 gev:2 notation:1 di:3 beams:3 de:2 beam:6 closely:1 ones:3 instance:2 negative:3 dx:2 progress:1 report:1 dw:13 aλ:2 du:9 ds:7 dp:1 dq:2 prime:1 hall:1 processes:6 dpt:1 fields:2 ie3:4 arxiv:1 dw1:1 twice:2 common:1 though:1 contain:4 pulses:3 fixed:6 pitaevskii:1 monochromatic:12 ik1:3 set:1 sep:1 eˆ1:2 frame:9 up:5 observed:2 differs:1 intensity:7 sec:2 result:9 arg:1 discussions:1 recently:1 2me:1 momenta:5 overlapping:1 collinear:2 revolution:1 tensor:2 bulanov:1 nuclear:3 teor:7 e1µ:2 propagates:1 its:1 symmetric:1 written:1 converted:1 various:5 between:11 tens:1 invariant:3 bunch:1 numerous:1 x23:1 x22:1 available:2 dν2:1 infrastructure:3 terms:21 2pt:1 useful:3 budker:1 importance:1 ωn:8 weak:1 however:7 rapidly:2 jl:1 gratefully:1 jn:1 enters:1 butions:1 distinguish:2 kev:2 understanding:1 suppressed:1 holds:1 thank:1 both:8 essentially:7 planned:2 efµν:1 cot:2 limits:1 many:1 taking:1 compton:1 b1:2 equal:8 called:1 propagation:2 dated:1 absorption:5 focused:2 contribution:11 estimation:1 expression:3 experimental:8 cos2:1 4z1:1 eksp:7 4z2:1 cm:1 point:2 simple:2 corresponds:3 kiµ:1 parametrization:1 analyzed:1 exploit:1 grants:1 anti:3 conjugation:1 keitel:3 respect:7 throughout:1 uck:2 second:2 configuration:1 described:3 pt:17 agree:1 pz:1 equations:2 three:4 been:7 ting:1 tesla:1 magnetized:1 production:2 asymptotics:10 interest:1 eiϑ:2 ph:1 δλi:1 choose:2 direction:4 rather:1 corresponding:11 σj:3 quantities:4 photon:99 σi:7 new:1 dθ2:1 coherent:2 observe:2 external:13 angles:2 hamburg:2 mandelstam:1 denote:1 present:3 case:29 p0:1 laser:89 pacs:1 solid:3 value:6 k2µ:1 will:8 brilliant:1 while:3 euler:3 behavior:1 cancelled:1 situation:1 eur:1 region:3 procedure:1 schumacher:1 ix:1 a22:1 vectors:11 coupled:1 almost:6 vi:2 refs:5 thus:3 iv:2 ii:2 ih:2 reads:2 ij:1 limit:4 vanish:2 id:1 around:2 jz:7 φq:4 different:5 circularly:15 acknowledgments:1 radiation:1 cross:7 same:1 slac:1 read:1 unity:1 complex:1 emphasize:1 units:4 relatively:1 events:3 higher:3 g3:18 independent:2 used:5 http:1 rescattering:1 see:11 i0:15 numerical:1 ansel:1 hand:3 average:1 v4:1 introduce:5 distinction:1 angle:11 invariance:2 noticeably:2 identity:1 narrow:1 piazza:3 pµ:2 k22:1 disappears:1 kˆ1:3 well:4 double:1 without:3 comes:1 components:1 dashed:2 om:1 ritus:1 lin:2 usual:4 less:1 being:5 generally:1 obtain:14 rest:1 sources:2 via:2 atomic:2 jetp:8 summed:2 λj:3 alternative:1 scattering:14 based:2 polarization:21 eli:3 conclusions:2 furry:4 photons:35 instr:1 k1:18 discuss:2 add:1 valid:7 lett:10 theorem:2 absorbed:6 mod:2 plasma:1 heidelberg:1 momentum:11 emphasis:1 real:1 tests:1 desy:3 rev:17 2u:3 fulfillment:2 bialynicki:1 dφq:3 possible:2 increases:1 helicity:8 background:2 vacuum:8 press:1 using:20 projects:1 formal:1 positron:1 loss:1 necessary:5 like:3 follows:4 performing:1 specific:1 remind:1 arthur:1 mhz:1 either:3 integrals:2 arbitrary:11 become:1 suitable:1 essential:1 replacement:5 unexplored:1 because:8 qed:4 classical:1 some:2 strongest:1 pφ:3 2xj:1 b2:1 moreover:1 restrictive:1 ourselves:1 nonzero:8 vol:1 clockwise:1 flux:5 electromagnetic:6 avoid:1 opposite:2 integration:5 per:5 id1:1 circ:2 critical:1 unit:1 provides:1 assuming:1 bessel:1 demonstrated:2 refer:1 lowest:1 λi:7 reaching:1 mpi:2 11n:1 agreement:2 expansion:4 eiπ:1 calorimeter:3 great:1 substitution:6 properties:2 stage:1 about:6 would:1 discussed:4 dependence:3 o:1 bialynicka:1 financial:1 range:1 a2:24 done:1 2x1:6 2x3:2 introduced:7 abbreviations:2 automatically:1 sh:2 nsk:1 statements:1 mλ1:1 presence:3 previously:1 pergamon:1 into:5 integral:3 due:12 variable:3 odd:8 schemes:1 ηs:3 novosibirsk:1 sov:3 operator:8 proportional:3 valuable:1 tabulated:1 nowadays:1 milstein:8 theoretically:2 k12:1 e3µ:1 statistics:1 institut:1 log:2 mork:1 u4:2 support:1 initial:11 u1:2 reduction:1 u3:2 u2:3 moulin:1 restricts:1 conservation:6 accompanied:1 way:4 m1:22 analyze:1 was:14 propagator:1 pg:1 function:13 considerably:2 form:15 reduce:1 opt:2 tajima:1 hundreds:1 nn:5 reminds:1 aµ:1 ec:10 hz:1 larger:2 dy:6 adler:2 hd:3 he:1 directed:1 absent:1 made:1 elliptically:3 ig1:2 stanford:1 characteristic:1 uw:1 maximum:1 us:4 ur:1 dφ:5 below:4 astrophysical:1 fermi:1 diagrams:1 sum:3 heinzl:1 b0:3 distribution:2 helicities:1 similar:2 calculated:5 distance:2 strongly:2 interval:1 constant:4 defined:3 coincides:2 abstract:1 describe:1 inp:1 general:6 duration:3 single:2 pˆ:9 together:1 our:5 crystals:1 work:1 eaµ:1 simplest:1 again:1 functions:7 k1µ:2 no:1 cos:7 nc:4 when:5 detail:5 aleksandrov:1 field:86 other:7 role:2 papers:1 ns:1 conclusion:2 polar:2 perpendicular:3 elements:1 superposition:1 saupfercheckweg:1 subtraction:1 a1:23 meaning:1 important:3 averaged:2 included:1 birula:2 structure:4 independently:1 ig3:1 ig2:2 coulomb:3 4y:2 assume:1 d22:1 pseudo:1 dσ:1 rule:3 equivalently:1 appendix:2 mass:3 4i:1 n1:10 n2:10 n3:10 starting:3 kruglyak:1 dϑ:1 |
0704.0697.txt |@word leurer:1 sci:3 consider:3 rev:18 global:2 results:3 kernphysik:1 scalar:8 milc:1 edu:1 expressions:2 vev:3 description:1 charge:6 compensate:1 those:2 th:1 under:5 mpg:1 conditions:1 mpi:1 maskawa:3 matsuda:1 redefinition:2 experimentally:1 difference:1 matrices:12 common:1 lindner:1 fhd:2 dic:2 try:1 discrete:2 gut:3 small:4 eigenvalues:1 shindou:1 possibility:3 application:1 smaller:1 oscillation:1 miur:1 prediction:2 zero:3 evaluated:1 iσ2:1 dynamics:3 estimated:1 fusaoka:1 even:1 established:1 plays:1 appear:2 3r:1 section:1 expressed:2 above:1 new:1 method:1 simultaneously:2 lee:1 here:1 diagonal:1 b2n:1 explore:1 china:1 ansatz:3 address:1 ratio:1 standard:1 appears:1 z2:7 deduced:1 obtained:4 fritzsch:2 u3c:4 spontaneous:4 study:2 studied:2 resulting:1 permutation:3 studi:1 harari:2 although:4 scales:1 apr:1 explained:1 koji:1 1st:1 neutrino:1 planck:1 kobayashi:4 would:9 may:2 remains:2 finally:2 next:1 phenomenological:1 nucl:7 therefore:1 taken:1 type:16 more:4 introducing:2 ramond:1 successful:2 becomes:1 naive:1 babu:1 excellent:1 iii:1 must:1 md:5 keeping:2 ma:3 mc:6 mb:6 science:1 det:2 rλ:4 mu:7 mt:6 examined:2 values:7 publications:1 ms:6 following:4 root:1 example:1 beijing:1 renormalization:1 give:1 organized:1 high:1 numbers:2 unphysical:1 absolute:2 end:1 sahu:1 s3:1 breaking:4 lepton:1 how:5 amazing:1 rλ2:3 parameter:2 sin:10 simplicity:1 de:1 fu:2 fx:1 max:1 after:4 derived:1 them:2 dc:1 hence:1 multiplication:1 evaluations:1 geometrical:1 data:6 constants:2 realized:1 natural:2 higgs:2 grant:2 element:1 quadrant:3 so:4 sm:3 democratic:13 order:12 blind:1 hierarchy:5 developed:1 satisfied:1 mixing:6 paper:2 including:2 mentioned:1 japan:3 still:1 diagonalized:1 group:2 trieste:3 energies:2 masses:5 petcov:1 renormalizable:2 takasugi:1 eur:1 non:6 good:1 greater:2 introduce:3 framework:2 couples:1 tsinghua:2 they:2 das:1 now:1 yu:5 discuss:2 nos:1 several:3 always:1 university:3 tran:1 possibilities:2 realistic:2 magnitude:2 internazionale:1 reasonable:1 each:3 found:2 d3c:4 2k:1 rajasekaran:1 fθ:1 generation:4 osaka:4 lfn:1 idea:5 extended:1 expect:2 combining:1 our:3 eq:8 out:3 large:3 froggatt:5 vcd:1 matrix:13 3rd:2 u2c:4 m2t:3 furthermore:1 since:1 lagrangian:1 m2s:4 re:1 istituto:1 rattazzi:1 induced:1 evaluation:1 correct:1 m2b:4 rk:2 theory:2 interactions:3 fisica:2 free:1 quark:12 completely:1 complicated:1 superiore:1 hep:6 generate:4 r4:2 interaction:2 ministry:1 impose:1 cabibbokobayashi:1 times:1 introduction:1 choices:1 iso:4 generations:2 leading:4 consequence:1 first:4 origin:3 symmetry:19 sugawara:1 s3r:2 s3l:3 tetsuo:1 least:3 valle:1 ferrandis:1 size:1 given:9 toy:1 needed:1 unitarity:1 unknown:1 top:1 achieved:1 construct:2 their:4 assumption:1 seiberg:1 fn:32 murayama:1 gives:6 way:2 relationship:1 parida:1 kilcup:1 electroweak:3 barbieri:5 part:2 predictable:1 too:1 than:4 coefficients:3 relative:4 determines:1 tavartkiladze:1 programs:1 yoshioka:1 matter:2 hagedorn:1 determined:2 supposed:1 were:1 ko2:1 symmetries:4 generality:2 raby:1 sevilla:1 wyler:1 watari:2 close:1 m2c:3 any:1 implemented:1 angle:1 sankar:1 mechanism:7 take:3 avanzati:1 collaboration:1 d1c:4 neutrinos:1 singlet:3 most:4 germany:1 phase:24 αu:4 future:1 ckm:13 clear:1 principle:1 left:1 physics:4 sector:2 incorporate:1 show:2 violation:6 supported:2 fleming:1 rb2:7 attempts:1 d5:1 find:2 q1:4 q3:4 q2:4 based:2 scuola:1 parameters:4 explain:5 enough:1 texture:1 should:1 aubin:1 analytic:1 only:4 postfach:1 vevs:5 factor:2 fq2:1 fq3:1 fq1:1 abelian:2 cube:1 triangle:1 di:4 simplest:5 expectation:3 cannot:4 fqj:4 fields:23 arxiv:6 twice:1 predicted:4 qi:2 through:2 qj:2 weyers:2 doublet:2 set:3 phenomenologically:1 throwing:1 up:4 toyonaka:1 culture:1 see:1 sec:3 cim:1 arg:4 kek:1 incorporating:1 pakvasa:1 phases:6 satisfying:1 ei2π:1 away:2 fθ1:1 fθ2:1 written:2 difficulties:1 αd:3 between:9 ui:1 approach:1 terms:2 nature:1 jp:3 however:7 vanishing:1 tommasini:1 extent:1 fukugita:1 both:2 vud:1 vub:9 many:1 mixings:1 april:2 vus:9 context:1 exceeds:1 acceptable:3 experimental:6 cos2:2 among:1 adjusted:1 relevant:3 necessary:2 simple:4 uic:1 2nd:4 simply:1 moreover:1 cp:20 cu:9 considering:1 strong:2 addition:2 rb4:2 will:2 three:2 been:10 pomarol:1 describes:1 basic:1 expected:2 ph:6 θc:3 shinya:1 cos:9 grimus:1 observe:1 angles:5 mail:8 dvali:1 present:1 case:3 multi:1 u1c:4 nd:3 appearance:1 value:8 transformation:2 employ:1 uckm:1 promising:3 aid:1 shafi:1 couplings:6 unitary:1 almost:1 refs:1 violating:12 iv:1 ii:8 yanagida:3 ij:16 turns:2 technology:1 fermion:3 around:1 different:2 italy:2 etc:3 koide:2 same:6 orders:1 unity:1 complex:12 grand:1 modification:1 φi:1 dimensionless:1 constructed:1 nij:1 investigated:1 velasco:1 assignment:6 numerical:2 effect:1 hand:2 terao:2 nir:2 lower:1 off:2 center:1 scenario:8 nucleare:1 charges:3 patterns:1 without:2 comes:2 sets:1 model:20 effects:1 unified:2 generally:1 observed:2 rotated:1 obtain:8 assigned:2 predicts:1 using:1 flavor:18 cn:1 cut:1 conclusions:1 extra:1 except:2 hall:6 setting:1 lett:18 heidelberg:1 ross:1 yukawa:18 nielsen:5 government:1 haut:2 giusti:1 bando:2 vives:1 vacuum:3 world:1 cd:5 loss:2 theor:3 imposed:2 like:1 follows:1 sissa:2 sezione:1 works:1 italian:1 therein:1 parity:5 because:4 successfully:1 phenomena:1 b4:9 b6:2 examples:1 b2:5 kugo:2 diagonalizing:2 eiα:2 scale:5 xing:1 avoid:1 quarks:12 does:1 uma:1 assuming:1 prog:3 cabibbo:2 demonstrated:2 omura:1 run:1 power:1 agreement:2 irges:1 broken:3 ratios:7 vcb:7 comparison:1 about:1 extension:1 constraint:1 discussed:2 o:4 2i:1 distinct:1 introduced:2 consequently:1 tanimoto:3 within:1 splitting:1 hypercharge:1 due:5 down:3 appropriate:2 right:1 references:2 tiny:1 determine:1 sports:1 het:2 uncertainties:1 acknowledgements:1 institut:1 additional:1 assumed:1 there:4 start:1 rept:1 much:1 low:2 lot:1 was:1 energy:2 function:1 some:2 brane:1 koichi:1 hu:11 leptons:3 hierarchical:1 considerable:1 hd:13 infn:1 fdc:1 toyama:3 us:1 ur:1 considered:2 limit:1 ωa:1 problem:1 agree:1 ac:3 associated:1 defined:1 abstract:1 general:1 cure:1 exist:1 predictions:2 nazionale:1 education:1 eigenstate:1 physical:2 again:1 oversimplification:1 discriminate:1 no:3 when:2 handed:2 field:7 other:2 department:2 d2c:4 massless:2 nu:8 conclusion:1 elements:5 kinds:1 models:12 finite:1 shown:2 generated:2 a4:1 structure:13 coupling:2 assume:3 required:1 reproduce:1 mass:20 nelson:1 romanino:3 n2:4 requires:1 nuovo:1 cpv:12 |
0704.0698.txt |@word limited:2 four:8 obstruction:1 entropy:1 parameterization:1 consists:6 poorly:2 lenci:1 whose:19 const:48 paris:2 γt:3 presents:1 γj:5 lanford:1 under:8 rise:8 every:14 school:2 skills:1 induction:1 solution:18 convenience:10 vector:31 force:5 coordinate:4 estimates:7 second:5 rigorous:2 invariant:20 even:3 errors:2 ˆt:9 euclidean:1 8m:2 contributed:2 birkhoff:3 above:33 new:9 net:1 increasing:2 consisting:4 pioneering:1 simultaneously:2 never:2 equals:1 here:26 met:1 path:3 logarithmic:1 obtained:5 mintchev:1 rigorously:2 study:7 mentor:1 suitable:2 changes:6 appropriately:2 divide:3 discontinuous:2 explained:4 visible:1 moral:2 total:8 univ:1 rω:2 unit:11 derivatives:1 tn1:1 would:20 e1:121 motivate:1 negative:1 definiteness:3 call:1 therefore:3 m2:14 type:3 until:5 tk:143 separated:7 oscar:1 kδ:4 curvature:5 aware:1 separates:4 hold:8 must:8 me:10 springer:2 mc:19 pursue:1 work:13 mi:8 mh:9 suggestive:2 mv:3 temperatures:2 henry:1 my:14 example:21 defer:2 indicated:3 give:8 preserving:7 organized:1 involve:1 degenerate:1 magnitudes:1 keep:2 dolgopyat:9 straightforward:1 provide:3 verify:7 travel:1 neishtadt:14 ens:1 adjacent:3 answer:1 ordinary:11 oscillatory:1 lai:2 beauty:1 replacing:1 after:3 summarize:1 law:7 parallel:4 constants:3 effective:18 summing:1 hypotheses:1 order:17 restriction:2 over:23 vary:1 expects:3 xi:7 thesis:4 satisfies:15 vari:1 before:11 monotonicity:1 xl:5 fiz:1 fix:16 writing:3 better:3 emphasize:2 versus:1 eventually:2 them:6 hryniewicz:1 collide:2 break:1 effects:4 they:16 singularity:1 represents:15 invariants:1 luca:1 reasonable:4 each:74 side:17 mean:3 independent:19 t2:21 literature:1 substantially:1 rq:1 restricted:5 angular:2 rd:5 fellowship:1 rl:8 rm:9 rk:8 foundation:1 turning:4 linear:5 barrier:1 given:14 free:11 standard:5 admits:1 sanders:1 proportionality:1 estimate:9 r4:3 r0:3 r1:4 r2:4 created:1 starts:2 ds2:1 ds1:1 corrections:3 moving:17 generalizations:5 speeds:1 separable:3 already:2 primary:1 rank:1 restrict:2 clear:2 another:5 enumerate:1 clarity:4 sutherland:1 similarly:18 approximately:4 needed:3 zaslavsky:1 too:3 tom:1 submersion:1 albert:1 requisite:1 finitely:1 distance:8 showed:5 enabled:1 zero:11 tion:1 modeldependent:1 pistons:12 modern:1 torque:1 manner:3 seen:2 seem:2 seek:1 tells:1 contents:1 relatively:5 convenient:5 absorbed:3 forces:1 indexed:4 circles:1 shallow:1 though:1 extending:1 involving:5 phase:46 acknowledgements:2 observation:1 partition:1 flow:45 points:8 principle:6 left:38 sum:5 saying:1 rayleigh:2 visitor:1 random:10 solutions:25 analogue:1 d2:30 d1:89 situations:1 constant:17 hamiltonians:3 rectangle:2 continuity:7 do:14 δq2:5 dh:22 di:23 df:6 de:2 foremost:1 dz:10 dv:10 dw:6 dt:80 du:8 dr:3 ds:125 dp:6 dq:14 traverses:2 fields:6 bad:8 bae:1 nγ:21 nε:6 riemannian:5 reference:1 observed:1 depends:9 result:33 w0:1 dµ:2 best:1 techniques:8 µx:1 away:9 pressures:4 µh:4 previous:2 approach:4 µc:3 preserve:2 terms:17 extend:3 restricting:2 weak:4 however:23 wi:3 wp:1 dedication:1 suggested:2 received:1 essentially:10 polytope:1 infinitely:1 adapted:4 presumably:1 abbreviate:2 timescale:1 height:2 applicability:1 grazing:1 speak:1 immobile:4 union:3 observing:1 three:25 been:12 much:14 interest:6 expected:4 containers:10 ergodic:30 quantities:7 concerning:2 argument:5 applied:2 suitably:1 fubini:1 near:6 suppose:12 viii:2 nonuniformly:1 applies:4 stopping:10 property:2 leaves:2 cylinder:1 tδ1:9 iw:1 iv:2 ii:2 disjoint:4 ik:10 interacts:1 perform:1 make:11 elliott:1 several:1 grows:3 fairly:1 exponents:1 hand:1 insulating:3 normalization:1 fulfillment:1 verhulst:1 immaterial:2 mother:1 claims:4 εw:22 dh0:1 just:6 diameter:3 aside:1 identify:3 facts:3 rn1:10 projection:3 adding:2 enters:2 instance:1 emphasis:1 wright:3 transformed:1 easy:2 thermodynamical:1 gave:1 cramer:1 advances:1 possible:6 caps:1 possibly:2 background:3 unique:1 occurring:3 dµh:7 dµc:2 specific:7 steps:8 dhε:4 scatterers:1 www:2 right:24 old:1 deal:3 people:2 underly:1 escape:3 critique:1 altered:1 ignore:1 proceeding:2 bottom:1 arguing:2 continue:3 exposition:1 linearly:1 participation:1 core:27 oscillating:1 substitution:3 hadamard:3 post:1 properties:3 chapter:16 dˆ:5 o:286 nonvanishing:1 ensure:2 horizon:1 orthogonally:2 slightly:2 ωh0:11 lieb:2 considerations:1 statements:1 bound:4 wε:19 s22:1 methods:2 comparing:3 sup0:19 suffice:1 initial:70 transform:1 way:1 m1:28 anosov:25 gil:1 was:8 form:6 quantity:1 simplifications:2 differences:4 hemisphere:1 true:6 responding:1 cylinders:3 nonlinearity:1 emin:4 inside:26 bounds:2 stages:1 adopt:1 proved:4 ln:7 abstract:3 proven:2 conserved:4 dν:6 exist:1 dζ:1 accounting:1 check:3 physical:5 ni:7 nj:28 no:33 na:1 generally:4 vanishes:2 setting:9 nt:2 models:4 preceding:1 uniformly:18 variable:22 faster:1 dψ:1 assume:11 dτ:25 interval:19 pseudo:2 dσ:10 governed:1 time:128 n1:32 n2:42 dϕ:13 breadth:1 customary:1 excellent:1 brownian:3 focus:2 leads:1 grateful:2 dϕ1:9 dϕ2:5 rectangles:2 inverse:1 depend:4 umd:1 elizabeth:1 father:1 recurrence:1 finally:3 analogous:3 t11:1 dϕj:2 keeping:1 choice:12 stays:3 emphasized:1 exact:1 presented:3 did:1 travels:1 solved:2 science:1 upper:1 says:3 occurrence:1 oscillation:6 dealing:1 prediction:1 sign:2 stands:2 uniform:16 reminiscent:1 axial:1 goes:1 shared:3 filled:1 satisfy:8 partners:1 lipschitz:5 understanding:6 tangent:3 cos2:2 alint:3 along:19 teacher:1 change:18 box:1 institute:2 petersen:1 studied:1 usually:9 ekt:1 studies:2 love:1 extra:1 inducing:3 merely:2 f2:11 handled:8 prove:10 ariel:1 positive:5 going:1 today:1 sharing:1 apparent:3 validity:1 eν:5 visual:2 appendix:3 eε:21 cases:2 parameterize:2 valued:2 pretend:1 values:2 achieve:1 following:26 making:1 dmitry:3 claim:1 dedicated:2 want:1 figure:16 expanding:1 dxi:2 occur:4 verlag:2 requirements:2 s2:35 discussion:7 nyu:1 write:9 fourth:1 optimal:3 parameter:11 divides:6 map:19 deviated:1 mat:6 may:25 r2d:1 dx2:1 dx1:1 applications:2 produce:2 end:7 grow:3 nikolai:1 sz:1 natural:4 outline:1 whenever:5 lemmas:6 si:4 so:80 progressively:1 definitions:2 typical:3 tagged:3 indeed:2 pointed:6 mainly:3 years:1 professors:1 course:1 motions:36 still:11 dynam:1 derive:1 thank:7 how:4 interesting:1 tori:5 coordinates:45 forms:1 suspension:1 main:16 non:1 introduce:5 scaling:4 mismatched:1 now:23 t21:2 term:16 corners:2 teoret:1 possibilities:1 cusps:2 entirely:2 domain:16 square:1 ei:41 ej:3 conventions:1 inhomogeneous:1 adequately:1 description:5 living:1 shown:1 accomplish:4 container:28 undergoing:3 space:58 furthermore:17 collisions:59 formula:2 squares:1 shows:6 earlier:1 theory:7 singularities:1 divergence:4 possibility:2 yuri:2 remainder:4 e0:1 chernov:11 e2:44 qj:6 derivation:11 impose:1 motion:23 place:13 massive:11 think:14 first:25 xj:1 xk:14 benefited:1 symmetry:1 stevens:1 pn1:1 u1:9 variables:67 approximate:6 fast:28 directly:4 impossible:5 open:4 george:1 size:20 little:2 necessarily:2 1t:1 unduly:2 indicate:3 convention:1 speaking:3 gives:2 fraction:1 mostly:2 continuous:11 proving:3 accurately:2 x2:4 x0:13 x1:15 than:30 specify:1 wide:1 impractical:1 third:1 require:2 hypersurfaces:1 future:1 were:11 decompose:2 pre:1 generality:7 ann:1 locations:1 generalization:4 say:1 distorted:2 recover:1 any:13 kevin:1 calogero:1 ideas:8 converges:1 note:34 ideal:8 potential:17 take:17 online:2 interior:2 8m1:12 8m2:4 closer:1 begin:4 multiple:7 normal:4 track:2 incidence:2 remarks:1 pages:1 especially:3 surprising:1 considered:4 average:13 later:4 steady:3 laws:3 precise:2 2m1:13 spaced:1 show:48 tkk:1 russian:1 corner:1 fifth:2 slow:49 kγ:1 starlike:1 outside:3 only:64 explicitly:4 γn:1 satisfied:3 cannot:3 nearly:3 piston:200 boundary:11 regarding:1 yield:2 predicted:1 mapped:1 homeomorphic:2 discussing:3 ables:1 differentiable:2 y0:4 postdoc:1 violates:1 satisfying:9 inequalities:1 ways:1 review:2 boundaries:1 enough:8 between:27 geometric:3 reading:1 across:1 bisects:1 fathi:1 notice:1 comm:2 come:2 motivations:2 many:12 region:9 according:8 expression:3 comes:5 learning:1 hotter:1 considering:3 submanifold:4 mark:1 foliated:1 v22:2 direction:2 enable:1 restrictions:2 dorfman:2 observe:11 those:3 countless:1 case:25 situation:7 margin:1 coupled:1 endowed:1 metric:1 dedicate:1 regularity:9 return:6 technology:1 different:4 develop:1 doctor:1 preparatory:2 same:16 dγ:2 arguments:8 constructed:2 events:3 trivially:1 assist:1 lochak:1 driven:1 koiller:1 inbetween:1 sssr:2 roughly:6 without:12 components:9 very:11 model:3 dimension:17 justify:2 manifold:1 being:14 when:107 guided:1 rest:4 speed:4 heuristic:9 lebesgue:3 except:2 interested:4 momentum:1 ross:1 real:6 nonoverlapping:1 porto:1 read:1 kifer:3 sums:2 early:1 using:28 vˆ1:1 mod:1 acute:1 particle:108 velocities:2 chamber:2 either:10 integrals:10 fully:1 xviii:1 satisfactory:1 qn1:1 madrid:1 specified:1 duration:1 provided:6 dimensions:24 tube:5 provides:1 refer:4 equivalent:5 notable:1 evolve:2 found:10 sixty:2 refers:2 collides:11 comparison:5 instantaneously:7 dzk:2 theorems:7 discussed:2 generated:2 greatly:1 perturbed:1 cambridge:4 unbounded:1 image:3 2v1:1 references:1 determine:1 operator:1 happening:1 log:4 her:8 area:7 assumed:1 there:43 start:2 strict:1 assumes:1 gronwall:23 complete:4 amongst:1 shrunk:1 longer:6 perpendicularly:1 applying:1 embedded:1 liouville:8 submanifolds:3 strongly:2 diverges:3 ai:13 certain:4 ak:6 describe:6 moved:3 fellow:1 examine:8 together:2 corresponding:8 moves:2 spends:3 again:9 inductively:4 completeness:1 graduate:4 field:18 valid:3 m1h:1 mathematics:5 poor:1 briefly:3 congress:1 separate:2 students:2 mekh:1 drift:7 a1:5 commutator:1 a2:4 bounded:25 wife:1 mass:17 starting:4 original:1 represent:5 externally:1 surrounded:1 consider:36 pointing:7 splitting:6 generalize:8 follow:10 expressions:1 disk:1 particles:77 preserves:14 referring:1 alberts:1 tn:4 tl:2 tm:2 preserved:1 th:1 ti:3 worse:1 r10:1 returning:5 far:2 induce:2 lyapunov:1 corollary:6 fall:1 difference:3 condition:20 hamiltonian:26 list:2 t0:6 t1:67 large:19 sang:2 small:35 neighborhood:2 periodicity:1 edu:2 past:1 rate:7 further:3 choices:1 dissertation:2 what:8 nonlinear:1 sub:2 section:72 nondegeneracy:1 version:4 δq1:10 subspaces:3 sup:63 method:2 outgoing:3 full:11 christian:1 component:3 relaxation:1 strong:3 equations:21 uspehi:1 inspired:2 allows:5 experience:6 amount:7 periodic:21 specialize:2 quotient:2 uniquely:2 via:5 followed:1 family:10 vii:1 research:1 readily:1 takes:15 uniformity:4 de1:7 de2:3 contains:3 quasi:3 chaotic:3 mckean:1 minor:2 more:12 flat:1 vi2:1 controlling:1 surface:4 particular:17 known:5 helped:1 none:1 recall:4 equation:101 r3:4 remain:1 history:1 f1:9 compare:9 memoirs:1 impacts:1 stated:3 neglected:1 accept:1 states:3 collision:39 numbers:7 sense:4 domokos:1 yε:15 axis:2 information:2 needs:1 goal:2 rather:1 maps:6 explains:2 simplicity:1 algebra:1 advice:1 wiley:1 derived:1 orbits:18 plane:4 ζx:5 verified:2 short:5 onto:4 parameterized:3 specifying:1 fundamental:1 dispersing:8 help:2 ith:3 developed:1 held:7 thermal:5 paper:1 through:5 existence:3 kinetic:2 poincar:2 its:19 rapidly:1 energies:7 inward:2 translation:4 actually:1 individuals:1 microscopic:5 systems:30 might:2 good:5 motivated:4 generously:2 ya:6 reflected:1 framework:3 walls:13 communities:1 bigger:2 2t:11 easily:4 2w:16 2q:13 2m2:7 always:1 level:5 2d:1 inequality:29 2m:3 referred:2 heavy:7 multiphase:3 transforming:1 energy:24 hard:17 positioned:1 deterministically:1 expect:8 quantum:1 http:2 really:2 involution:1 electronic:1 robert:2 since:10 induces:1 projected:2 denotes:3 studying:2 dominated:3 izv:1 denoted:1 dxdv:1 induced:4 issue:2 occurs:1 fiber:6 ast:1 asz:1 reason:1 base:7 put:1 beginning:1 definition:4 omit:1 imre:1 american:2 exponentially:1 consequence:3 2kδ:1 indebted:1 major:1 probability:24 number:22 preservation:4 instances:1 done:2 construct:2 slower:1 polygons:1 passes:1 guess:4 perturbation:1 temperature:1 introduction:6 leading:1 interact:10 least:9 assumption:11 statement:6 superscript:1 smoothed:2 relationship:1 akad:2 immediate:1 part:2 differentiate:1 focusing:1 spacings:1 separability:1 lebowitz:3 oscillate:1 diffusion:1 dti:1 df1:2 df2:4 determined:3 fˆ:7 toward:1 motivation:2 affirmative:1 orders:1 karl:1 paths:9 generalizes:1 depending:8 lim:2 lin:1 internal:2 lip:3 generalized:2 analogy:1 unperturbed:5 experienced:1 english:5 reach:1 most:8 experiences:5 significant:1 nothing:1 colliding:1 extremely:2 appear:2 kc:2 deviations:9 crossing:1 torus:4 kh:1 cover:2 unreasonable:1 drifts:1 kl:2 traditional:1 reflections:1 clean:9 kt:1 velocity:13 physics:5 ambiguities:2 v12:9 converge:3 find:21 polygonal:1 inductive:2 depended:1 parameters:1 subsection:15 factor:3 integrable:4 circle:1 moser:1 his:4 triangle:5 notation:14 dependent:1 ϕl:2 ϕn:1 ϕi:7 nonequilibrium:1 ϕk:6 ϕj:8 during:2 arxiv:1 investigate:2 statist:5 set:55 ser:1 emax:4 unpublished:2 see:31 individual:5 descriptions:1 chambers:3 outward:1 ergodicity:18 expert:1 halves:1 subscript:1 conditions:52 available:2 recently:2 leonid:1 initially:1 attention:1 analogues:1 preprint:1 inertia:1 both:11 last:2 bunimovich:4 context:1 finds:1 pendulum:1 point:19 simple:9 address:1 corresponds:9 dimensional:29 bε:22 simply:4 throughout:3 patiently:1 pp:1 described:10 transformations:2 due:13 hitting:1 whom:1 reduction:7 describes:1 pi:4 interparticle:2 flight:12 mind:1 gas:172 remark:8 surveys:2 p2:9 p1:9 straight:1 while:16 replaced:2 compactness:3 behavior:16 error:3 vectors:5 averaging:61 itself:1 fibers:13 belong:1 rules:1 seminar:1 higher:4 used:5 lie:1 flows:7 domains:5 uses:1 recent:5 lower:1 analysis:6 concrete:1 machinery:2 equidistributed:1 shape:5 λk:2 letting:2 tables:3 cut:1 conclusions:1 theoret:1 location:5 theorem:78 vˆ0:1 transformation:5 marco:1 insert:2 nonphysical:1 showing:3 smallness:1 projects:1 dq1:8 modifications:5 dq2:5 follows:72 adiabatic:25 separately:1 imposes:1 yields:6 essential:3 mathematical:3 sketch:1 often:6 some:26 back:1 understood:1 towards:1 b0:3 uspekhi:1 curious:1 scale:36 describing:7 affects:1 integration:4 behave:2 connecting:1 tends:8 shatah:1 measures:5 jumps:1 perpendicular:3 bk:11 restrictive:1 step:35 nowhere:1 bz:6 integers:3 pε:3 hinge:1 remains:12 range:1 regular:9 computational:1 into:18 within:2 integral:8 appropriate:6 primarily:1 proportional:4 pentagon:1 behaving:1 segev:1 measured:2 smoothly:3 question:3 gases:2 u2:7 borel:1 forward:3 translate:1 sections:2 sinai:15 etc:6 properly:1 repeatedly:1 delta:4 hopes:1 line:3 relaxes:1 directed:1 up:3 us:9 ui:3 verification:1 callen:1 fluctuations:1 similar:14 called:1 tε:81 associated:1 defined:29 doesn:2 single:5 defines:1 application:6 priori:3 department:1 mε:3 dv1:11 dv2:5 elements:1 lend:1 problems:2 drag:1 markarian:2 sides:3 independently:5 implies:1 required:3 orbit:19 depth:1 presenting:1 international:1 requires:3 having:3 once:2 chebyshev:2 partial:1 results:39 proposition:4 stochastically:1 compact:25 concerned:1 young:2 maryland:1 include:1 implicitly:2 electron:1 implausible:1 matrices:2 positions:4 notes:1 try:1 noted:2 smaller:2 zk:26 jump:1 imply:1 traveling:1 insertion:1 dynamics:43 invertible:4 giving:5 expressed:4 exercise:1 degree:1 respectively:3 desired:3 identifications:1 adjoined:1 consideration:3 z0:44 implicit:2 sina:1 great:1 wesley:1 technical:1 involved:1 larger:6 contradiction:1 resulting:2 makes:2 examining:1 scaler:1 scales:6 apr:1 limt:1 apply:3 use:19 recalling:3 next:16 few:2 depicted:2 themselves:1 sort:1 formally:1 started:1 becomes:4 arranging:1 actual:18 pieces:6 iii:2 iik:15 account:2 crosses:2 integrating:1 averaged:51 decoupled:1 proof:100 control:12 weaker:2 process:1 purposes:3 qmax:7 effectively:3 assumptions:11 umberto:1 holds:2 delay:3 located:6 varies:1 instead:1 immersed:1 philosophy:1 abuse:3 inst:1 realized:1 light:4 correspond:3 subdomains:3 diffeomorphism:1 spain:1 doklady:2 allow:1 prikl:1 s1:56 six:1 closely:2 εc1:2 produces:2 move:9 mathematicians:1 looks:1 mentioned:1 regions:1 decay:1 chosen:10 masses:5 2e1:29 estimating:3 degrees:3 choose:8 derivative:4 defining:1 eur:1 greater:5 gasses:1 material:5 billiard:52 transparent:1 dirac:2 verifying:1 university:3 sufficiently:23 2ei:2 l1:2 disregard:1 accounts:1 traces:1 constraints:2 subset:8 erisque:1 bump:2 related:1 society:2 frequency:4 measure:54 separating:4 our:75 special:2 out:7 chaos:1 performs:2 suffices:21 math:7 interactions:4 completely:3 york:4 advisor:2 monographs:1 interaction:1 vˆ:3 geometry:3 could:8 times:26 length:12 birthday:2 hence:11 heuristically:3 manuscript:1 reaches:2 precisely:9 long:16 swept:1 table:2 hyperbolic:5 system:59 their:6 intermediate:1 final:2 interests:1 completed:1 exactly:1 reflecting:2 zε:115 dynamical:8 submitted:2 limiting:3 arc:1 distinguished:1 unchanged:1 close:3 need:13 constrained:1 clearly:4 viewed:1 angle:10 εt:11 eter:3 billiards:15 able:1 εl:82 εo:2 εh:6 εf:1 unless:4 who:4 connected:4 sb:1 segment:1 why:1 volume:9 face:6 cims:1 proceedings:1 mechanical:4 occasion:2 oscillates:1 fact:17 supported:2 chapters:1 qmin:12 trivial:1 agrees:1 principal:1 q1:103 q0:31 q3:1 q2:43 should:18 jan:1 lemma:57 ambiguity:2 partially:1 local:1 hope:3 equilibrium:9 cube:1 means:5 words:4 evolution:9 differential:21 nauk:4 she:1 contain:3 qi:11 fixed:50 qn:2 strengthened:1 requirement:1 statistical:3 exists:20 national:1 correlations:1 hδ:3 hε:115 geometrically:1 acquires:1 et2:1 lyon:1 tend:2 state:3 difficulties:2 closed:3 crude:1 progress:1 neither:1 ends:2 jos:1 ability:1 wk:1 hypothesis:1 key:1 observable:2 hits:1 limits:2 taking:3 equal:2 2e2:3 figures:2 otherwise:1 comment:1 ch:1 co:7 conclude:5 wall:1 encompasses:1 meunier:1 respect:13 piecewise:10 addition:2 trajectory:4 slowly:3 define:51 oth:3 determinant:1 controlled:4 finishes:3 am:5 sufficient:4 subspace:2 cos:23 c1:7 general:15 ott:1 present:12 multi:3 novel:1 value:20 rectangular:1 will:66 almost:13 vi:9 thus:33 encouragement:1 equilibrate:2 az:4 generic:1 divergences:2 s2i:1 cross:14 gruber:2 parts:1 schematic:2 φj:6 finite:17 difficult:2 ball:1 infinity:3 effect:1 v1:102 v2:27 infinite:2 frequently:1 off:1 reflection:2 nonetheless:1 well:24 thought:4 s21:3 sets:9 position:7 arising:2 usual:1 spherical:1 heavily:1 accurate:2 obtain:11 interim:1 paul:3 macroscopic:5 bibliography:2 density:15 thermodynamics:3 extends:1 dqi:2 mh0:1 divided:1 inversion:1 elapsed:2 five:1 know:5 press:2 immediately:6 intersection:1 loss:7 necessary:9 like:11 lost:1 sizes:4 diffeomorphic:3 δq:4 δf:1 become:2 works:2 soft:11 soviet:1 therein:1 because:48 classical:8 sequence:15 discontinuities:3 growth:1 choosing:1 proper:1 proofs:10 neglecting:1 happens:1 lead:2 does:12 assuming:1 2q0:4 journal:2 pressure:8 although:15 cγ:3 periodically:2 stage:1 about:14 rare:2 extension:1 a0:4 freedom:3 dependence:7 important:1 introduced:4 enigmatic:1 previously:5 travelers:1 h0:10 h1:1 hyperbolicity:2 additional:1 elastic:9 transfer:1 justifying:1 support:2 smoothing:4 quadratic:1 function:25 stadium:2 but:42 hj:5 hk:12 santal:3 hm:1 convergence:31 he:1 made:10 compute:4 evident:1 whether:6 wish:4 smooth:27 placed:1 below:9 limit:5 demonstrate:1 problem:13 piece:3 mechanics:3 addison:1 sectional:2 denote:38 periods:3 inf:23 proceeds:1 functions:9 compared:2 qε:17 courant:3 variety:1 detail:1 ep:1 other:28 details:1 suppress:6 conclusion:1 bundle:3 stan:1 friends:1 rule:1 eor:1 portion:1 compete:1 |
0704.0702.txt |@word consider:1 dynamic:2 results:3 baroni:1 illustrated:1 ge:14 ga:1 expressions:1 research:1 negf:5 gr:5 increase:5 zone:1 γr:1 tr:2 young:1 quasi:1 does:1 under:1 gironcoli:1 straightforward:1 very:2 frequencies:2 springer:1 wave:3 fan:1 dispersions:1 transmission:10 solution:1 vector:1 small:6 optics:1 concluded:1 epitaxially:1 smaller:2 force:5 findings:1 consistent:2 approximation:1 further:1 chem:1 will:6 nonlinear:5 section:2 d3:1 current:2 3h:1 above:3 falling:1 method:2 contrast:2 3d:3 coefficient:1 interfacial:8 respectively:2 equals:1 here:3 hundreds:1 explore:1 mes:1 σal:1 directions:1 along:1 obtained:2 studied:1 suggests:1 changes:1 plotted:3 diameter:8 apr:1 semiconductors:1 explained:1 fournier:1 translational:1 wang:8 plot:2 conventional:1 therefore:1 diagrams:1 becomes:1 γl:1 berlin:1 known:1 degenerately:1 account:2 quantized:1 science:1 equation:1 work:1 reproduce:1 temperatures:9 example:2 reasonably:1 figure:1 calculation:4 high:3 giannozzi:1 recursive:1 s0:4 feature:2 pure:2 instead:1 explains:1 displacements:1 mat:2 may:1 after:1 derived:2 applications:1 faculty:1 law:4 constants:5 branches:8 third:1 si:31 so:1 brillouin:1 holds:1 years:1 thermal:58 through:3 still:1 longitudinal:1 thank:1 energies:1 interesting:1 li:2 caroli:1 choose:1 decreased:1 into:1 fourth:1 material:4 scaling:1 effects:2 hall:1 university:2 d3q:1 mode:1 reasonable:1 each:1 found:2 mean:1 nanometers:1 generation:1 energy:5 used:1 conductance:46 frequency:8 quantum:2 our:4 eq:6 shown:2 dominates:1 matrix:3 furthermore:1 rev:8 denotes:2 semiconductor:3 attracted:1 formula:2 dominate:1 ref:2 shows:3 linear:1 interactions:1 gbulk:2 interaction:1 transition:1 silicon:4 quadratically:1 exhibited:1 first:2 manuscript:1 upper:1 mingo:1 number:1 electronic:1 given:4 temperature:26 moderately:1 ballistic:1 structures:2 ranging:1 continuous:1 transverse:3 optical:3 than:1 kind:1 polarized:1 iteration:1 future:1 tion:1 treated:1 spectrum:1 crossover:6 substantial:1 need:1 seen:6 clearly:1 majumdar:2 self:6 note:1 potential:4 green:6 σrr:2 play:1 maris:2 most:2 optimized:1 letter:1 device:1 σrn:3 why:1 σrl:2 kc:2 kb:1 considered:2 calculated:8 km:3 feynman:1 part:1 velocity:1 physics:2 fact:1 stoner:1 supported:1 relation:5 substituting:1 find:3 conduction:1 enough:1 should:1 only:3 gαr:2 equilibrium:1 dominant:1 dependent:1 nanowires:42 aim:1 nonequilibrium:3 subscript:1 arxiv:1 summary:1 investigate:1 shi:1 computed:1 national:2 observed:1 depends:3 result:1 close:2 exponent:2 written:2 epitaxial:3 between:6 tens:1 boundary:1 reading:1 across:8 terms:2 nature:1 attention:1 wu:2 concentrate:1 interface:4 group:3 atoms:1 microelectronic:1 observable:1 σl:1 many:1 region:4 april:1 dated:1 retarded:4 σs:2 expression:1 experimental:4 cm:4 conclude:1 reasons:1 dimensional:23 cs:1 described:1 due:1 reduction:1 much:1 calcula:1 universal:3 fig:17 direction:2 corresponding:2 both:1 schwab:1 bulk:21 gan:1 moderation:1 understand:2 roukes:1 careful:1 present:1 unlike:1 solid:1 value:6 lesser:2 optimization:1 behavior:5 landauer:2 vectors:1 played:1 thus:1 surface:1 cond:2 different:6 verified:1 grant:1 cross:2 same:2 investigated:1 singapore:4 i0:1 phy:1 kim:1 infinite:1 invariance:1 bourgeois:1 recent:2 lower:1 center:1 pavone:1 well:2 materials:6 position:1 model:2 dimension:3 left:5 emerge:1 nan:1 germanium:2 atomic:1 haug:1 yamamoto:1 scattering:6 lattice:1 lett:3 role:2 vα:3 increases:3 supercell:1 using:7 jauho:1 advanced:1 like:1 semi:1 sizes:1 systematically:1 velocities:2 ignore:1 reduced:5 right:3 nm2:1 debye:5 matching:1 transport:8 scale:1 dimensions:1 lead:8 superlattice:2 behave:3 tends:1 tersoff:6 moderate:1 sheng:1 equivalent:1 use:1 expansion:1 acoustic:3 properties:1 comparison:4 about:3 central:2 dependence:13 o:1 range:2 km2:3 zerbi:1 optoelectronic:1 computational:1 significant:2 jian:2 dyson:1 three:11 down:2 because:1 promise:1 proportional:1 diameters:16 log:4 intrinsic:1 there:2 dispersion:3 appl:3 low:19 was:2 function:9 but:1 atom:1 nanowire:10 line:1 circuits:1 ωs:3 smooth:1 maximum:1 devices:2 below:3 limit:1 problem:1 similar:2 clear:1 abstract:1 zeng:3 substantially:2 engineering:1 reliability:1 formalism:1 compared:1 nm:21 no:1 200k:1 when:4 field:1 yang:3 republic:1 branch:2 department:1 conclusion:1 deviation:1 includes:1 important:2 included:1 60k:4 watanabe:1 coupling:3 dω:2 assume:1 kinetics:1 phonon:13 |
0704.0703.txt |@word gs:4 consider:3 rev:9 magnetic:2 global:1 results:12 leads:1 quadrature:2 computation:1 expressions:2 contributions:7 hole:2 localized:2 optical:7 whose:4 dimensionality:1 depend:3 calculate:1 zone:5 re:2 technique:3 micrometers:5 finally:3 tm:3 helps:1 under:4 dramatically:1 applied:2 amplitudes:2 impinges:1 orthogonal:1 very:7 erale:1 account:3 polarization:1 wave:66 resonant:1 experimentally:1 difference:6 exact:1 condition:3 beating:1 presented:1 transmission:10 evaluation:1 solution:2 large:3 vector:8 excellence:1 affect:1 small:3 enhance:1 optics:4 ups:1 programme:1 oscillation:2 consistent:5 direct:1 approximation:1 zero:1 design:2 ǫm:2 further:2 grooves:1 cao:1 odd:1 milled:4 spectral:1 will:5 plays:1 appear:2 advantageous:1 opaque:3 section:4 near:15 expressed:2 eiqx:8 sinc:1 experiment:4 poles:1 dominates:1 above:9 sup:1 thio:2 new:1 egion:1 method:7 contrast:1 3d:3 coefficient:9 full:8 evanescent:28 arb:3 component:15 here:5 understanding:1 reported:4 objects:3 focused:1 address:2 directions:1 along:23 standard:1 equations:1 appears:2 interpret:3 films:2 obtained:4 propagative:13 extraordinary:1 elaborate:2 studied:4 approaches:1 periodic:2 published:1 usually:1 resonance:5 fourier:7 studies:2 involves:1 plotted:3 sightly:1 useful:2 figure:2 apr:1 plasmons:1 nanostructured:1 total:6 unit:3 standing:2 plot:1 use:2 takes:1 charge:1 france:1 spp:22 therefore:1 aperture:1 theoretical:1 more:4 separated:2 flat:2 ecole:1 composite:3 becomes:2 envelope:1 ip0:1 transient:7 everywhere:1 normalized:1 diffracted:22 excellent:1 cases:1 aligned:2 iii:2 must:3 k02:17 permits:3 equation:4 midi:1 reproduce:1 ere:1 values:2 thin:1 following:1 modifies:1 example:1 history:1 compare:2 gratings:3 polaritons:1 indicated:1 calculation:5 anomalous:1 choice:1 states:1 indicates:1 slit:20 assumptions:1 performed:4 whirls:1 simulation:16 simple:5 axis:6 scalar:1 varied:1 rather:3 g0:3 en:1 write:2 located:9 varies:1 cardinal:1 low:1 adjacent:1 optimal:1 absolute:1 parameter:1 sin:15 profile:2 fr:1 express:5 may:5 broad:2 earlier:1 derived:1 vaccum:1 hence:6 evˆeque:1 plane:12 waves:11 derives:1 parallel:7 times:1 short:1 physical:1 dynamical:2 effective:16 light:8 sp:1 correspond:1 egu:1 their:2 si:4 fp6:1 green:20 media:1 acknowledges:1 order:5 typical:2 moloney:2 interpretation:1 indeed:1 over:3 insight:1 displayed:1 produced:3 seideman:1 experiments:2 through:11 thesis:1 pitch:1 differs:1 its:3 rapidly:2 decay:2 susceptible:1 interesting:1 vicinity:3 decreases:5 better:1 distinguishing:1 fig:23 pergamon:1 derivative:3 narbonne:1 might:1 maximal:1 acknowledgments:1 good:4 greater:3 similar:3 halfspace:1 band:1 effects:1 they:1 half:1 silver:8 dielectric:5 represents:6 february:1 vidal:1 subwavelength:11 organ:1 fabricated:1 corners:2 university:1 2d:2 mode:9 qx:11 found:3 universit:1 side:2 characterized:3 mean:1 homogeneous:1 el:1 domain:2 square:1 ei:8 nanometers:4 generation:3 ed:2 principles:1 numeric:2 frequency:4 ex:2 ez:21 eu:1 wavelength:20 approximated:2 beyond:2 extract:2 array:1 out:3 shown:5 sabatier:1 funding:1 network:2 lalanne:6 space:16 restricted:1 rep:2 since:1 interference:2 research:1 increase:1 replacing:3 nominal:2 dominated:1 paulus:1 formula:1 ref:4 occurs:1 shows:3 after:4 theory:2 passes:1 retrieved:1 given:4 free:12 quite:2 switzerland:1 reason:2 york:1 beginning:1 e0:11 training:1 interaction:1 r0:5 created:2 geometry:6 widths:1 route:1 accumulation:1 length:1 produce:1 consequence:1 first:10 corrugated:1 placing:2 toulouse:1 symmetry:1 reflected:2 reaches:1 overestimated:1 simplified:4 directly:2 indices:1 thick:2 precisely:1 electronic:2 size:2 multilayered:2 differ:1 xie:3 quality:1 simulated:1 introduction:1 structured:1 system:2 response:2 belongs:1 appl:1 calculations:1 structures:6 recovered:1 correctly:3 explanation:1 shallow:1 contribute:1 transverse:1 part:13 somewhat:2 constituent:1 representing:2 than:11 center:3 relative:2 nanostructures:1 polarized:4 measured:1 intensity:4 determined:2 stratified:2 amplitude:28 6th:1 zx:2 toward:3 perturbative:1 unchanged:1 conventional:1 spectrum:6 curves:3 say:1 substantial:1 sauvan:1 need:2 seem:1 null:1 slab:1 any:1 relatively:1 paths:1 eq:12 rochester:1 convenient:2 overcoming:1 metallic:9 oriented:2 k2:1 ideal:1 k0:20 generalized:1 online:3 so:3 ghaemi:1 conductivity:1 eff:2 posits:1 multiple:1 electric:12 normal:1 pyr:1 incidence:1 resonates:1 depths:2 extending:1 importantly:1 irsamc:2 phase:25 analytically:1 intrinsic:6 sfc:1 interacting:1 diffractive:1 observation:5 surprising:1 considered:1 calculated:4 metal:11 ebbesen:3 pipe:1 qualitative:1 points:5 exp:1 narrow:1 nanostructure:1 oscillates:1 physics:2 away:2 fact:7 precise:2 phenomenon:1 gold:1 show:3 scattered:11 converge:1 implying:1 relation:1 goes:1 keywords:1 scatterer:1 find:2 principal:1 µm:14 periodically:1 just:12 parameters:2 inflection:1 written:1 analytic:5 only:10 explicitly:1 black:1 factor:1 oscillate:1 closed:4 distance:9 there:3 de:5 overall:2 erieur:1 beam:1 cannot:2 legitimate:1 report:1 dt:2 dr:1 polariton:1 dq:20 evolution:16 qr:1 substrate:1 qt:1 qw:3 approach:7 arxiv:1 yield:1 summary:1 arrays:2 analytical:7 including:1 fixed:1 electrostatic:1 monochromatic:1 computed:8 reference:1 physically:1 summed:1 up:2 observed:2 see:2 lausanne:2 result:1 enhanced:1 close:3 dyadic:1 best:2 techniques:1 surfaces:4 invoked:1 tensor:17 placed:1 pattern:2 review:1 dipole:31 boundaries:1 outside:1 dereux:2 radiated:6 between:11 tens:2 boundary:9 conditions:2 interfaces:2 wide:1 multiplied:1 terms:1 reflection:9 vertical:2 nature:5 initially:3 modify:1 screen:4 however:4 supports:2 interfere:1 incident:10 strong:1 key:1 interface:22 hundreds:2 suppressed:1 distribution:1 concentrated:1 both:5 essentially:4 last:2 many:1 taking:2 infinitely:1 reproduces:2 against:1 agree:1 propagation:6 negative:1 iv:1 dated:1 refraction:1 lezec:7 contribution:5 expression:11 experimental:9 nano:1 adjusted:1 ch:1 fields:1 point:9 tlse:1 asymptotically:1 narrower:1 corresponds:1 dimensional:3 represented:1 pole:3 simply:1 right:2 associated:2 considers:1 second:2 considering:1 fib:1 nanosciences:1 sine:2 geometries:1 girard:2 radiative:3 three:2 been:4 tensors:1 defined:5 much:2 slowly:1 change:1 interest:3 expected:2 slits:2 ph:1 empty:1 lett:6 direction:4 arises:1 controlled:2 deeper:2 gay:5 concerning:1 cos:1 zlim:1 confinement:1 determination:2 general:1 present:4 case:4 p0:16 main:1 ǫg:1 exponential:1 solid:1 value:13 rectangular:1 aim:1 while:3 optimization:2 replaced:2 behavior:4 property:1 study:3 opt:5 layer:2 larger:3 almost:3 vi:1 thus:4 surface:45 equal:2 ii:2 reads:1 itself:2 im:1 different:3 wolff:1 sensitive:4 barnes:1 radiation:1 cross:1 same:5 clearly:4 stimulated:1 complex:4 uncertainty:1 units:3 finite:4 couple:1 difficult:2 independent:1 used:1 infinity:2 laboratoire:1 numerical:11 ion:1 running:1 purpose:1 changing:1 cr:1 fabrication:1 normalization:1 recent:5 relies:1 weakly:1 integral:5 modes:5 charges:1 acknowledge:1 well:4 analysis:2 dwyer:2 enseignement:1 without:2 solve:1 components:9 dashed:1 model:26 excitation:2 parametric:1 distances:3 invariantly:1 less:1 being:1 guided:4 photonic:2 detail:1 shape:3 identify:1 predicts:1 using:5 paul:1 converges:3 scattering:2 previous:2 begin:1 note:1 rapid:2 conclusions:1 absorption:2 excites:1 except:1 source:7 concerns:2 extends:2 location:2 compares:2 extensive:1 excited:4 varying:1 real:3 sub:1 around:2 depends:1 easily:1 showing:2 measurement:2 term:9 increases:2 background:3 press:1 immediately:1 color:3 displaced:1 semi:2 follows:1 signal:1 ees:1 moreno:1 polytechnique:1 martin:4 output:4 weiner:5 minist:1 reduced:1 permittivity:2 because:11 methods:1 fresnel:2 creation:2 some:3 play:1 ct:1 born:1 trends:2 evaluated:1 moreover:2 proper:1 process:1 reasons:2 dimensions:4 lippmann:1 cavity:1 electromagnetic:2 measurements:3 integration:1 grazing:1 rodier:2 does:6 exit:2 dipoles:3 provides:1 assuming:2 prog:2 propagating:4 straightforward:1 minimal:1 limitations:1 particular:1 measures:1 equivalent:1 arbitrary:1 oscillating:6 agreement:7 unity:1 step:1 although:2 epfl:1 imaginary:1 entirely:1 asymptotic:3 comparison:7 about:1 actual:1 carried:1 influences:1 aci:1 fringe:1 discussed:2 dependence:1 o:10 essential:1 range:2 recherche:1 wolf:1 introduced:1 slightly:1 presence:1 previously:2 maxwell:1 into:7 within:4 numerically:1 due:3 down:1 lies:1 appropriate:1 weighted:1 references:1 determine:1 proportional:2 few:4 inserted:1 support:1 initial:1 approximate:2 long:3 dispersion:1 width:11 cosine:1 structure:5 fraction:1 analyze:1 was:1 propagator:1 interferometry:1 function:20 illuminated:1 form:5 phenomena:1 but:13 volume:1 taken:2 hprn:1 delta:2 nanotechnologies:1 line:12 longer:2 applying:1 iqx:1 embedded:1 circuits:2 characteristic:1 inside:3 maximum:1 discretized:1 below:2 greens:1 sum:2 problem:7 groove:73 called:2 regimes:1 strongly:1 fdtd:2 diverges:1 constant:6 ag:2 int:1 curve:7 describe:1 influence:2 ist:2 denote:1 dirac:3 single:4 lived:1 exist:1 simulations:15 corresponding:3 formalism:2 distributions:1 film:1 regime:4 again:2 functions:1 compared:5 nm:25 dotted:1 index:18 whereas:2 when:6 inset:3 schwinger:1 field:56 other:1 role:4 details:3 spatial:3 dipolar:3 leveque:1 thousand:1 conclusion:1 integrand:1 picture:2 impinging:1 la:1 calculating:1 models:1 problems:1 bottom:1 variation:2 includes:1 generated:2 neff:5 chavel:1 included:2 vein:1 faster:2 garcia:1 apertures:3 confirm:1 diffraction:7 extraction:1 calculates:1 depth:11 appendix:3 plasmon:6 time:4 far:7 resolution:1 |
0704.0704.txt |@word kinderlehrer:1 similarity:4 nualart:1 reversibility:1 four:2 entropy:14 consists:2 whose:2 isometric:2 calculate:1 γs:1 segments:3 γt:6 γj:1 γi:15 masayoshi:1 γm:1 under:31 dwti:2 rise:1 dobrushin:1 brenier:2 every:5 encounter:2 supports:2 solution:4 convenience:1 vector:6 markov:23 martingale:5 sturm:3 consistent:3 estimates:4 direct:2 approximation:2 second:10 tangential:1 rigorous:5 estimated:1 even:4 euclidean:1 establishes:1 new:6 increasing:9 ever:1 consisting:1 simultaneously:1 applies:1 here:19 atoms:1 represented:7 path:5 logarithmic:2 obtained:4 study:5 completely:5 paris:1 fourier:4 changes:1 projection:3 discontinuous:1 explained:1 replace:2 pβ0:16 total:2 unit:5 derivatives:2 would:4 motivate:1 xh1:1 call:1 therefore:12 type:4 until:1 curvature:4 berlin:3 reversible:6 separates:1 anatoly:1 springer:2 mn:1 mi:4 mk:6 mt:1 dg1:1 concepts:2 root:1 example:3 give:2 preserving:5 want:1 david:1 ene:3 verify:3 ent:5 ψij:7 replacing:3 after:3 minimizes:1 law:2 parallel:1 constants:1 attempt:1 effective:1 order:18 restriction:5 interpretation:6 over:13 satisfied:3 satisfies:3 integrands:1 before:10 monotonicity:2 directional:12 fix:7 exhibits:1 convexity:1 easier:1 overcome:1 maximal:4 them:1 they:4 each:113 stieltjes:1 independent:9 ιg:4 combining:2 rt:1 driving:1 gradient:14 restricted:2 unrelated:1 rm:15 rn:17 ri:1 rk:1 linear:10 yid:1 free:1 standard:2 admits:3 ψ2k:4 estimate:5 publ:1 masanori:1 r1:1 r2:1 created:1 probab:5 onto:5 separable:1 already:2 malliavin:7 restrict:4 another:3 enumerate:1 force:1 q00:3 electronic:1 rewritten:1 similarly:4 heights:2 variational:1 tool:1 weakly:8 positively:2 finitely:1 distance:14 kenji:1 approximations:8 iteration:1 integrability:1 classes:2 ran:3 ram:1 manner:2 seen:1 seem:1 latter:13 oriented:2 shall:1 object:2 simplify:4 regular:10 dom:82 partition:4 flow:11 points:6 principle:2 yann:1 notion:2 random:1 fleming:3 solutions:1 analogue:1 topological:2 geodesics:1 rich:1 constant:15 continuity:10 do:3 above:23 dh:2 df:3 dg:13 dd:2 de:3 dx:42 dy:17 dv:11 dw:27 dt:106 du:68 ds:49 rademacher:1 dq:15 covering:1 fields:3 riemannian:6 wt1:1 kolmogorov:3 depends:2 result:6 w1:2 dµ:9 µx:3 µt:18 away:2 µs:5 symmetric:10 µg:8 µf:7 approach:3 letting:3 terms:20 wn:7 wm:2 wk:1 however:10 wi:2 wt:2 wtn:1 topology:8 essentially:2 c21:1 contribution:1 argue:1 monograph:1 villani:3 basis:3 three:3 much:1 interpret:1 interest:2 basic:7 topics:1 families:1 locations:4 θz:5 θx:3 lift:1 θs:3 xxi:1 applied:1 transformation:6 aim:4 equivariance:1 aij:20 property:18 leaves:4 procedure:2 cylinder:15 played:1 iv:10 ii:41 ij:2 id:2 disappear:1 containing:1 make:6 recurrent:8 ırez:1 linked:1 split:1 several:3 isometries:1 evolve:1 trajectories:1 counterparts:4 hand:2 maruyama:1 normalization:3 suitable:7 academic:1 greatest:1 jean:1 diffusions:1 solvability:1 identify:1 facts:2 stratonovich:4 previous:22 adding:2 candidate:1 regarded:9 belongs:12 easy:2 possible:2 unique:11 steps:1 arbitrary:2 right:8 deal:1 donald:1 entropic:19 dense:18 linearly:1 core:5 rescale:1 illustration:1 super:1 kantorovich:1 chapter:8 quasilinear:1 canonic:2 plus:1 mccann:3 slightly:1 lieb:1 markovian:1 bound:3 lies:1 wδ:5 wγ:1 methods:1 existed:1 topologies:2 support:7 initial:4 approximate:1 way:1 m1:1 was:2 medium:1 form:78 converse:1 heat:6 true:2 supx:2 supp:2 bounds:2 mti:1 supn:1 supf:1 examples:1 abstract:2 convergent:2 dν:1 exist:3 distributions:7 dγ:3 dα:7 ni:7 nk:3 xkm:1 whereas:4 generally:2 interested:2 role:2 picture:3 intend:1 preceding:2 ξs:3 uniformly:10 µis:1 µit:1 variable:10 ξa:2 assume:13 interval:15 ti1:1 governed:1 time:5 push:11 n1:3 dϕ:83 concept:2 remarkable:1 particular:28 brownian:18 invent:1 leads:5 inverse:13 depend:3 passage:1 quasi:15 analogous:2 dϕi:9 dϕj:8 dϕk:33 advantage:1 orthogonal:2 choice:9 stays:1 partitions:1 level:2 did:1 turns:2 discrete:2 science:1 round:1 measurable:11 sign:4 cost:1 uniform:17 reminiscent:2 closability:8 transportation:2 lipschitz:11 tangent:15 xβ:1 along:4 xα:1 change:14 sobolev:5 studied:3 poisson:3 studies:2 diffeomorphisms:5 merely:1 prefer:2 f2:2 1st:1 planck:1 schied:1 additive:1 prove:23 positive:2 properties:10 explicitly:4 eϕ:8 duality:1 apparent:1 eε:1 cases:5 eβ:2 valued:8 originally:1 bertoin:1 values:1 probabilit:1 following:18 claim:22 dxt:1 sample:1 dxn:21 dxk:3 dxi:4 rescaling:3 conversely:1 fortunately:1 s2:5 s1:51 write:3 ockner:1 pure:4 optimal:1 parameter:3 map:44 levy:5 may:17 max:5 dx2:2 dx1:27 subordinators:1 applications:1 representations:2 lifting:1 2l2:5 natural:3 whenever:3 lemmas:2 explicit:2 sk:5 so:6 sn:1 representation:14 michel:1 indeed:7 course:3 ttn:1 statistical:1 still:1 derive:1 group:17 τh:6 gtn:9 forms:13 constitutes:2 gtx:10 main:5 non:4 tt2:1 evolution:2 introduce:1 scaling:1 equidistant:1 now:21 discuss:1 nor:1 term:8 equality:3 drop:1 orthonormal:8 gt1:9 el:3 domain:5 en:2 eg:1 gaussian:3 gaps:10 happen:1 es:1 er:1 shown:1 watanabe:2 space:45 squared:1 looking:1 contained:3 rational:1 formula:34 theory:4 hull:2 divergence:1 homeomorphism:5 univalent:1 e0:10 e2:1 βt:3 derivation:4 language:1 arnaud:1 transition:2 motion:13 turn:3 βl:1 view:1 first:19 xj:6 xk:17 xh:7 xi:62 xn:33 symmetry:1 xm:21 variables:5 carry:1 bijectivity:1 open:1 xt:3 size:1 interchange:2 given:57 1t:4 1x:2 1a:2 hilliard:1 1c:1 1b:2 convention:1 white:1 gives:1 continuous:43 proving:1 x2:9 x0:3 x1:55 specify:1 unfortunately:3 accordance:1 require:1 intensity:1 were:2 decompose:1 pre:3 generality:3 ann:3 argument:1 generalization:1 say:7 any:13 ξxi:1 converges:8 note:14 cantor:1 coincide:6 modulus:1 beta:1 formulae:3 pair:3 pages:2 considered:3 feynman:3 ξx2:1 typically:1 precise:2 show:1 leibniz:1 tkj:18 dy1:1 justifies:1 notations:3 spaces:18 xmk:3 state:1 analytic:1 only:14 going:2 lorenzo:1 equipped:7 µgn:2 closure:15 settings:2 yield:1 nondecreasing:4 kernel:1 ricci:2 closures:5 relative:6 namely:1 us:20 y0:1 satisfying:8 inequalities:1 subsequent:1 definite:2 functionals:1 lukacs:1 enough:4 between:9 αi:4 geometric:4 αm:7 densely:1 comm:3 analyzed:1 jg:33 come:1 originates:1 concentrated:1 σi:2 σn:15 x2k:2 dario:1 many:2 according:29 called:10 concentrate:1 embedding:1 expression:1 comes:1 among:1 kondratiev:1 characterization:4 assertions:4 ordered:3 semigroups:2 marc:2 barry:1 locally:2 defined:27 direction:2 observe:1 weierstrass:1 those:1 case:25 eβ0:1 proves:8 situation:1 orientation:1 metric:16 good:1 different:6 develop:2 cc1:1 same:5 verifies:2 arguments:5 otto:4 constructed:2 extended:2 assigns:3 driven:1 invariance:14 pures:1 motions:2 locality:2 without:6 coordinate:1 justify:4 isometry:5 ck:3 manifold:4 being:3 resp:8 rest:1 differentiation:2 heuristic:10 generator:25 debussche:1 yu:1 seems:4 versa:1 hino:1 real:6 aspects:1 e2ε:4 using:4 moreover:21 identifying:1 beltrami:1 deduce:2 specified:1 provided:15 conservative:3 decomposition:2 provides:1 equivalent:6 stone:1 y2k:1 central:1 meaning:3 perturbed:1 image:5 ηi:5 ηt:14 ηs:7 determine:1 bijective:5 argumentation:1 log:73 area:1 assumed:3 strictly:6 there:23 start:1 θˆs:2 complete:6 regard:2 dissipative:1 applying:1 h0s:3 frechet:1 strongly:10 taylor:3 ai:3 certain:1 ak:6 aj:14 general:11 together:3 formulation:1 ay:1 gradients:3 again:8 graduate:1 field:3 valid:1 mathematics:1 zambotti:1 polar:1 briefly:4 drift:13 dq1:2 a1:15 a2:6 bounded:19 vershik:1 natalia:1 cordero:1 mass:5 starting:7 sci:2 consider:11 restated:1 cameron:1 follow:5 expressions:2 brascamp:1 careful:1 chain:2 tt:2 equivalence:6 superprocesses:1 tn:12 tm:9 tk:20 ti:207 tf:2 stochastic:16 norm:18 straightforward:1 very:3 translations:4 corollary:17 difference:1 condition:5 hamiltonian:2 gǫ1:2 t2:14 t0:7 t1:23 large:11 p00:1 small:11 anal:8 neighborhood:1 zero:1 infimum:1 pass:2 canonical:15 bilinear:2 what:3 richard:1 section:8 varadhan:2 subspaces:1 sup:17 method:1 contrast:2 full:5 behaviour:1 friedrichs:8 directions:2 strong:4 equations:5 increments:2 tµ:5 allows:3 action:4 quotient:1 uniquely:4 via:3 homotopic:1 family:21 thalmaier:3 establish:1 proceed:2 contains:2 finally:12 ψj:1 ψk:10 ψi:13 ψn:1 taken:3 more:10 operators:3 problem:6 doob:1 basically:2 varying:2 known:7 projective:4 recall:10 equation:9 remain:1 canonically:1 f1:12 compare:1 stated:2 states:2 sphere:7 sense:7 nonnegative:4 respective:6 goal:3 rather:1 dydx:2 maps:13 acta:1 simplicity:4 ft:3 ζi:2 mapping:1 fi:14 fj:1 fm:10 fn:5 short:2 sect:1 fundamental:1 ito:6 2πkx:4 wiener:5 paper:4 through:1 y1:13 existence:2 kinetic:1 its:29 forwards:2 solving:1 actually:2 wilhelm:1 might:1 yi:16 yh:21 yk:1 yj:6 ym:13 ye:1 number:6 ξij:3 oxford:3 renesse:2 easily:7 2r:1 2s:4 always:2 presented:1 2e:1 inequality:3 found:1 1ai:2 characterized:2 energy:9 obtains:1 operation:3 event:1 robert:2 since:27 induces:6 denotes:21 acting:1 dominated:8 denoted:7 induced:5 reformulated:1 monotone:4 difficulty:1 base:1 conditioning:1 put:21 viot:3 definition:12 pairs:1 accumulation:1 american:1 consequence:6 probability:36 geodesic:2 least:2 perturbation:3 temperature:1 introduction:1 construct:9 assumption:4 statement:4 wasserstein:24 saint:2 relationship:1 immediate:6 part:4 jordan:1 norms:2 translation:2 diffusion:19 kind:3 treated:1 tϕ:16 ager:1 needs:1 randomly:1 karl:3 paths:2 depending:1 lim:36 self:3 k2:5 k1:14 costs:1 generalized:7 k4:1 2tg:1 rhs:3 measures:35 most:2 experiences:1 nothing:1 closable:14 measured:1 dηt:3 kj:20 clear:2 coincides:7 km:22 kl:9 countable:1 exp:25 converge:10 minimizing:1 completion:5 distributed:3 assertion:9 subsection:2 factor:1 ymk:1 notation:5 ϕm:2 famous:1 ϕn:3 ϕi:16 closely:4 ϕj:13 alexander:1 arxiv:1 factorization:1 common:1 wrote:1 set:25 gµ:10 see:12 close:2 fang:4 talagrand:1 various:4 conditions:1 missing:1 both:7 last:6 lebesgue:8 connection:1 oshima:1 whole:3 finds:1 arbitrarily:2 point:11 simple:1 dimensional:20 simply:2 throughout:2 pr:1 transformations:2 pt:10 px:3 py:2 due:5 laplacian:3 describes:1 asymptotics:1 marginals:1 pn:3 walter:1 surjective:1 tg1:3 else:3 neumann:3 understand:1 albeverio:1 fokker:1 semigroup:12 p0:66 replaces:1 look:2 exponential:3 ǫi:2 empirical:2 ǫm:1 replaced:2 compactness:2 behavior:1 von:2 reads:2 itself:4 belong:2 emphasize:1 modification:1 composition:2 interpolation:3 used:3 felix:2 flows:4 uses:1 dgt:2 lower:4 analysis:2 obviously:19 machinery:1 consistency:1 vαβ:2 intervals:3 alternative:1 homeomorphisms:2 guaranteed:2 theorem:40 remaining:2 euler:1 big:2 formal:5 follows:26 collect:1 yields:9 rearrangement:1 pointwise:7 mathematical:1 sketch:2 often:1 absolutely:9 some:53 back:1 understood:1 acad:1 s1n:3 ourselves:2 spdes:2 integration:11 providence:1 tends:1 minimal:2 inserting:1 bm:2 jumps:15 martin:1 bi:1 br:2 hilbert:2 pβ:22 δe:4 recalling:1 range:1 uǫ:18 gamma:13 into:7 within:1 integral:3 appropriate:5 next:2 statistics:1 span:2 probabilistic:1 gases:1 u2:1 forward:9 sections:2 governs:1 immigration:1 bǫ:3 sde:3 reed:1 line:1 intuitive:1 uw:2 uv:2 up:2 differentiable:1 un:88 ui:10 verification:1 uk:5 sum:7 uf:12 similar:5 tδ:2 associated:13 gx:2 globally:1 single:1 defines:13 priori:1 nice:1 elements:2 sided:1 problems:1 generated:2 linearization:2 sides:1 structure:3 implies:17 vice:1 required:2 equivalently:5 implied:1 having:1 once:1 gt:117 gs:46 funct:7 results:7 existing:3 proposition:19 stochastically:1 gn:11 gi:9 compact:9 simon:1 deterministic:1 dp:8 cahn:1 g2:9 g1:60 g0:362 putting:1 matrices:3 entire:1 notes:2 michael:2 try:3 zk:3 jump:7 limǫ:1 imply:3 dynamics:5 ode:1 zr:1 index:2 plays:1 anton:1 analogously:4 expressed:3 leb:60 respectively:1 objects:5 others:4 consideration:5 z0:3 z1:46 z2:9 deduced:1 masatoshi:1 remark:15 suggests:1 products:1 makes:2 involves:1 boundedness:2 apr:1 limt:4 ϕ2k:10 sgn:2 summation:2 apply:1 tools:1 use:6 asymptotic:1 remains:4 guideline:1 reflects:1 formally:2 ecole:1 normalized:3 iii:26 circle:6 isomorphism:10 lϕ:2 obvious:3 publications:1 proof:48 dn:2 links:1 process:78 assumptions:1 gǫ:3 z20:2 holds:3 instead:3 dwi:2 sin:2 inst:1 realized:1 correspond:1 element:8 diffeomorphism:12 allow:2 ϕk:49 takeda:1 interpreted:4 mentioned:3 bridges:2 la:1 chosen:6 lw:1 lu:8 choose:17 lp:2 derivative:20 defining:1 handa:1 flour:2 ferguson:1 rotation:1 dirac:3 university:1 identified:5 sufficiently:4 l2:166 l3:7 l0:1 l1:12 references:1 subset:6 product:8 related:6 constitute:1 operator:20 measure:93 our:16 out:3 matrix:1 res:1 ren:3 lecture:2 suffices:11 math:12 approaches:3 surely:6 york:1 anyhow:1 dirichlet:71 geometry:5 could:1 times:1 length:10 xσ1:1 hence:40 powerful:2 improvements:1 precisely:7 kingman:1 πa:2 θˆx:2 adjoint:3 πn:7 system:6 their:7 appl:3 siam:1 tuple:2 reflecting:1 zβ:11 subsequence:2 distinguished:1 disjoint:3 clearly:1 min:3 polarization:1 instance:8 calculus:2 lectures:1 gν:3 but:9 edric:1 definitions:1 intrinsic:10 class:10 volume:6 graphs:1 construction:15 fact:14 chapters:3 q1:4 q0:55 based:4 dp0:1 should:7 lemma:34 ambiguity:2 local:7 means:11 words:6 girsanov:3 processes:21 densities:1 differential:4 dpg:4 qk:2 fixed:8 qm:9 qn:13 requirement:3 constructing:5 exists:26 notational:1 finiteness:1 interacting:1 segment:5 written:7 identification:4 closed:1 invariant:14 boundary:1 jos:1 weak:8 job:1 no:11 key:5 configuration:1 ker:2 interpretations:1 etc:1 admit:1 comment:1 ci:1 co:1 cn:1 cc:1 poissonian:1 cf:8 sequences:1 fukushima:1 respect:9 ct:3 piecewise:3 addition:2 cauchy:2 treat:4 partial:2 define:19 arises:2 corresponding:1 sufficient:1 subspace:3 cos:2 c3:11 c2:8 c1:30 c0:2 present:3 pardoux:1 choices:3 will:69 homeo:1 inherits:1 almost:10 thus:27 vn:9 δxt:1 vw:2 φij:3 dawson:3 parts:14 gibbs:1 largest:2 finite:26 erausquin:1 infinity:1 restating:2 qβ:30 infinite:15 identity:6 reflection:2 nevertheless:1 zk0:1 well:11 theodor:3 sets:1 usual:2 sdes:1 moments:1 obtain:10 underlying:3 paul:3 adv:1 preprint:1 density:8 reasons:1 add:2 extends:4 vϕ:9 dqn:1 gruyter:1 increases:2 xe0:1 press:3 immediately:9 loss:1 dq0:54 like:3 alternatively:3 δt:1 porous:1 yor:2 δi:2 δg:23 works:1 alexandrov:1 sequence:21 choosing:3 convex:1 proofs:3 transport:4 lead:4 assuming:1 noise:4 σij:4 clarendon:1 simplex:1 approximating:3 about:1 dun:9 extension:13 carries:1 important:2 introduced:2 converging:3 previously:3 h1:3 functional:7 square:4 duf:1 additional:1 transfer:2 quadratic:9 tg:49 pg:5 function:61 borell:1 hs:4 sequel:10 ht:15 approximates:1 hj:1 neutral:2 hi:9 hn:14 convergence:17 coefficients:2 society:1 whether:2 smooth:22 below:10 limit:12 iterated:1 distribution:27 mechanics:1 sectional:1 linearity:1 denote:22 inf:10 approximated:8 functions:44 compared:2 dpβ:13 detail:2 other:14 details:1 variation:4 resolution:1 emery:1 rule:3 |
0704.0705.txt |@word limited:1 partial:3 systematic:1 represent:2 green:1 results:17 four:2 eds:1 scalar:3 1p3:7 alt:8 1p1:3 contributions:2 reasoning:1 looking:1 isobar:3 sparrow:1 removal:1 presents:2 finally:2 th:1 under:1 include:1 eikonal:47 subtleties:1 applied:1 supported:1 orthogonal:1 very:1 mn2:1 relatively:2 wave:17 rl:1 electron:2 interpreting:1 summarized:1 affect:3 difference:1 exact:4 leads:1 squares:1 moya:1 level:1 proc:1 solution:9 large:1 solved:1 vector:3 dip:1 linearizing:1 upper:4 work:3 version:1 oscillation:1 miller:1 fit:1 prediction:1 literature:1 approximation:23 second:25 enhancement:4 further:2 implemented:1 expressions:2 ˆp:5 will:1 what:1 hide:1 diamonds:1 frameworks:1 mercer:1 section:9 ryckebusch:7 expressed:1 access:1 lt:1 ito:1 new:1 increasing:1 method:1 body:2 impact:1 transparency:8 exchange:2 donnelly:1 component:7 residual:1 here:4 asymmetry:3 mev:15 address:1 ghent:1 along:1 appears:1 obtained:4 solid:4 almost:1 fwo:1 incoming:1 shift:2 gent:1 allows:1 typically:1 commonly:1 resulting:1 degli:1 usually:2 adopting:2 makes:1 involves:1 york:1 via:1 followed:1 clark:2 apr:1 integrations:1 replace:1 visible:1 modulated:1 meson:2 research:1 readily:1 cha:1 use:4 asymptotic:1 positive:1 brittin:1 predictions:7 permitted:1 ψk:5 nucl:9 kinematics:8 distortions:2 start:1 marginally:1 more:1 ejected:3 successful:1 becomes:1 odinger:2 1s1:5 impulse:3 excellent:3 account:1 ıas:3 collision:1 equation:9 mn:29 protons:2 assumptions:2 values:3 ms:6 cal:1 following:2 example:1 history:1 vitturi:1 brown:1 calculation:2 relativistic:12 neglected:4 high:8 indicates:1 lorentz:2 numbers:1 rescaling:1 scat:1 axis:1 normalize:1 sr:1 rather:3 mcneil:2 how:1 forest:1 σep:1 sargsyan:1 description:4 fv:1 may:1 demonstrates:1 derived:3 corrections:22 modest:2 plane:3 fe:4 verified:1 choice:1 data:17 response:2 jˆµ:3 short:4 outline:1 effective:2 joachain:1 lines:3 element:1 provide:1 used:2 decreasing:1 caballero:2 subsequently:1 integrand:1 order:48 exclusive:2 interpretation:1 words:1 nucleon:4 developed:2 over:3 move:1 displayed:2 distortion:1 experiments:2 through:1 lava:2 cuts:1 kinetic:1 its:1 derive:1 group:3 wallace:7 located:1 energies:4 dr:1 solving:2 khalili:1 decreases:1 better:1 absence:1 except:1 degrees:2 fig:12 orange:1 derivative:3 versus:1 good:1 affected:1 combination:2 entire:1 undergone:1 introduce:2 break:1 framework:2 effects:6 they:2 focus:1 now:1 wambach:1 easily:1 february:1 dirac:2 university:1 drop:1 ciofi:1 sufficiently:1 magnitude:1 references:1 side:1 referred:1 heavy:2 reactions:5 lectures:1 differential:5 ei:1 woo:1 knockout:6 energy:6 reduce:2 related:3 antiprotons:1 extended:1 amsterdam:1 quantum:2 our:7 eq:16 dǫ:1 rt:2 emerges:1 shown:2 matrix:1 space:2 quantify:2 furthermore:2 since:2 rev:33 denotes:1 particles:1 collisions:2 asymmetries:1 denoted:1 induced:5 ref:12 correct:1 red:1 shows:1 abbott:1 theory:2 risen:1 interactions:2 interscience:1 mechanisms:2 differ:1 standard:1 bringing:1 difficulty:1 corrects:1 brooke:1 rlt:1 rdwia:13 retained:1 dubbed:1 transition:2 linearized:1 turn:2 flanders:1 hence:4 first:7 symmetry:2 omitted:1 set:2 another:1 open:3 illustrate:1 1p:1 given:1 smaller:1 strikman:1 indicate:1 introduction:1 leading:1 eqs:2 piekarewicz:1 adopted:2 glauber:4 calculations:27 convention:1 final:1 adopts:3 shell:5 observable:2 sizable:1 optical:12 somewhat:1 authors:1 off:2 representing:1 than:6 greenberg:1 dynamical:3 wide:1 target:1 was:6 submitted:1 janssen:3 determined:2 amplitude:1 were:2 tion:1 dutta:1 garrido:1 benhar:2 correction:2 sevilla:3 turned:1 curves:5 cauteren:1 alike:1 rpwia:6 distorted:1 elsevier:2 koonin:1 seek:1 clearly:1 indeed:1 angle:1 latter:1 polarization:6 instance:1 potential:8 so:5 coincide:1 strengths:1 even:2 multiple:1 kelly:2 serot:2 normal:5 denominator:1 most:1 but:3 letter:3 phase:3 plays:1 acknowledgements:1 class:1 furnstahl:1 adopt:2 stronger:1 inferred:1 seki:2 qualitative:1 part:1 exp:3 physics:2 fact:2 quantity:2 particularly:2 show:3 jµ:1 manipulation:1 scattered:1 bring:1 gauge:1 substituting:1 guerra:1 d5:9 partonic:1 current:2 q2:13 explain:1 aldt:1 written:2 negligible:1 should:2 jan:1 only:3 experiment:1 black:1 factor:9 employed:1 darwin:4 do:1 lombard:2 gev:11 dh:1 dependent:2 de:2 overall:2 tjon:1 truly:1 inclusion:3 beam:1 ones:2 dz:20 reversal:1 despite:1 2mn:2 subscript:1 processes:3 ema:2 continuum:1 conditions:2 arxiv:1 expansions:1 predicted:1 london:1 dpm:2 multiplying:1 computed:3 subatomic:1 correlations:2 see:1 result:2 w1:1 subject:2 closer:3 yazaki:1 invoked:1 nuclear:10 tend:1 symmetric:1 state:7 between:1 fermi:1 boundary:1 approach:6 email:1 terms:11 fourmomentum:1 extend:2 missing:14 ikz:6 jv:1 attention:1 wk:2 however:4 spectroscopic:4 job:1 key:1 reaction:4 last:1 σn:5 many:2 region:2 equal:1 called:1 sensitive:1 improves:1 vopt:18 ejectile:1 contribution:1 expression:2 nonrelativistic:1 ca:4 corresponds:1 proton:10 height:3 adding:1 applicability:1 moreover:1 throughout:1 points:2 considering:1 puts:1 transparencies:4 due:2 been:5 mart:1 increase:1 dropping:1 treat:1 azimuthal:1 basic:1 expected:1 tering:1 pn:9 ann:1 pm:23 direction:1 corresponding:2 both:5 ınez:1 quantities:2 concerning:1 photon:1 gao:1 fund:1 determination:1 func:1 covered:1 spin:12 present:2 eiq:1 extracted:1 novel:1 look:2 exponential:1 pacs:1 tang:1 henceforth:1 aim:1 pwia:2 while:2 behavior:1 applies:1 aid:1 eik:1 study:2 procedure:2 planar:1 vc:17 orientation:1 phenomenological:1 refs:2 ir:2 tions:1 surprisingly:1 vs:5 vv:5 ia:1 currents:3 fabrocini:1 different:1 dε:1 righthand:1 thereby:2 occupied:1 make:1 radiation:1 cross:9 same:2 cc2:1 parts:2 underestimate:1 widely:1 largest:1 several:1 grows:1 higher:12 independent:2 formalisms:1 investigated:1 rescattering:1 numerical:3 upon:1 effect:13 hand:1 ion:2 arrived:1 purpose:2 kim:1 potentials:9 frequently:1 hartree:1 normalization:1 relies:2 lower:7 schr:2 ingredients:1 well:3 roughly:1 solve:1 dashed:4 radici:1 position:1 model:6 nb:1 left:4 spherical:2 heavily:1 accurate:1 obtain:1 spherically:1 momenta:9 scattering:13 adv:2 note:2 cut:1 preprint:1 zoller:1 conclusions:2 zakharov:2 absorption:1 point:2 parametrization:3 source:1 other:2 extends:1 treatment:1 wilkin:1 struck:1 momentum:15 insensitive:1 kaptari:1 term:6 belgium:1 highly:1 apart:1 fantoni:1 modifications:1 like:5 success:1 follows:2 reduces:1 performing:1 yields:1 either:1 become:1 reduced:2 right:4 truncated:1 madrid:3 phenomena:1 tostevin:1 table:2 neglecting:1 vso:20 pronounced:1 describing:1 nikolaev:2 confirm:1 rohe:1 affects:1 measurements:3 integration:1 closely:1 waxman:1 refer:1 inserting:1 treleani:1 scientific:1 location:1 performed:4 agreement:6 expansion:2 kohama:1 step:1 properties:1 panel:2 comparison:1 central:3 amado:1 extension:2 freedom:2 dependence:4 o:9 essential:2 compatible:1 range:4 quasielastic:2 2k:24 slightly:1 em:4 soc:1 significant:2 spinor:2 into:3 within:6 integral:2 bound:3 negative:1 down:1 lies:1 because:1 accounts:1 determine:1 operator:3 mccauley:1 next:1 van:5 additional:1 elastic:1 shells:1 transfer:4 ugent:1 sarriguren:1 long:3 hadronic:1 accordingly:1 low:4 way:2 forward:1 sections:3 function:10 aguiar:1 medium:1 form:7 ht:1 usmani:1 volume:1 bianconi:1 line:1 highest:1 true:1 made:2 compute:1 builds:1 hardly:1 petraki:1 robustness:1 up:6 us:1 theoretical:3 below:1 converted:1 limit:1 minor:1 uk:4 neill:1 ud:3 similar:4 agree:1 atti:1 cyan:1 walecka:1 constant:2 inclusive:2 defined:3 abstract:1 describe:1 influence:2 ripple:2 proves:1 hama:1 speth:2 formalism:4 triangles:2 functions:2 compared:3 dotted:4 no:1 dωp:2 whereas:1 when:4 vanishes:1 field:1 valid:3 role:3 investigations:1 brings:1 department:1 picture:1 models:2 includes:1 deriving:2 important:1 nucleus:5 suited:2 included:1 cooper:1 needed:1 implies:1 coulomb:1 practically:1 assume:1 fsi:7 baker:3 factors:4 orbit:9 itself:2 dot:1 time:1 observables:6 nuclei:1 frankfurt:1 lett:8 moniz:1 |
0704.0706.txt |@word limited:2 consider:2 represent:2 drapatz:1 forbidden:3 results:2 yellow:2 four:4 mathewson:8 asian:1 edu:1 morphology:3 particularly:1 bergin:1 contributions:1 weingartner:2 compact:2 whose:1 simon:1 iii:2 young:2 former:1 answered:1 foster:2 contours:4 excluded:2 marks:1 details:2 kaastra:1 danziger:2 2mass:1 ionizing:1 r14:1 very:2 regional:1 geometrical:1 rotational:2 putting:1 summarized:1 difference:1 multiple:1 contamination:1 northwestern:1 school:1 propagating:3 clouds:7 vibrational:2 positions:1 shock:11 colors:16 large:5 small:9 study:1 cox:1 overlaid:1 bleeker:1 concluded:1 upper:1 rejuvenated:1 unexpected:1 sturm:1 faintest:2 trails:1 consistent:3 estimates:2 tex:2 surrounding:3 likely:1 apparently:1 multiwavelength:1 sakon:2 storey:2 estimated:3 rough:2 quite:1 spectral:3 index:2 errors:1 heyden:7 takashi:1 axes:1 near:2 uniform:1 lights:1 version:1 above:1 skyview:1 petre:3 order:1 rosat:3 filled:1 shocks:12 hummer:2 simultaneously:1 lee:6 respectively:6 understanding:2 explore:1 slow:2 pantin:2 brα:3 ratio:3 along:4 strong:3 observing:1 appears:2 obtained:4 convert:1 parameters:1 noticeable:1 institute:1 richter:3 leaves:1 studied:3 exceptionally:1 suggests:3 amount:1 resulting:1 interclump:1 bon:1 milky:1 usually:2 narrow:1 studies:2 elongated:3 brightest:4 composed:2 ratios:1 classification:1 apr:1 marked:1 apj:18 visible:3 remnant:15 resolutions:2 total:3 cloud:5 use:1 would:7 msx:2 remains:1 faint:8 next:1 calculation:1 snrs:15 camera:2 therefore:4 crab:2 hri:2 australian:1 type:6 theoretical:2 minor:1 smeared:1 flat:6 rich:1 bronfman:1 suggestions:1 apparent:2 corrected:1 emission:36 curvature:1 payne:1 clumpy:1 known:3 ozaki:1 serendipitously:1 isas:5 clumps:1 abundance:3 sample:1 mg:1 crosses:1 tokyo:4 science:2 der:7 work:3 values:2 dem:1 those:2 southwest:6 example:2 performed:1 olaf:2 dedicated:1 weaker:1 wang:1 give:1 process:1 expanding:1 share:1 high:3 indicates:5 way:1 surround:1 coincident:1 dopita:1 interpreted:1 times:1 hydrogen:3 absolute:1 needs:1 rays:6 end:2 extinction:4 howe:1 rather:2 multiplexer:1 s7:28 positional:1 located:1 hot:3 pure:1 elliptical:1 sik:1 instead:2 filament:3 circular:1 map:6 galactic:9 seoul:2 spitzer:3 jarrett:1 may:3 after:1 southern:3 masks:1 spot:8 snu:7 snr:41 fe:5 mag:1 date:1 horizontal:1 data:10 short:1 effective:1 leroy:1 sr:3 spectra:1 lines:18 correspond:1 ghz:2 bunkyo:1 fraction:1 ones:1 so:5 sn:1 discussion:1 operate:1 wing:1 wind:1 wavelengths:3 remnants:1 hiroshi:1 pointed:1 fall:1 fν:1 ejecta:1 distortion:1 report:1 thermal:5 paper:2 including:2 same:5 japan:3 fwhm:3 its:10 galaxy:3 derive:2 synthesized:2 sν:1 akari:14 expectations:1 coordinates:1 2001a:1 ticular:1 detected:9 complex:1 takao:1 lagage:3 pipeline:3 might:6 pixel:1 happened:1 tentatively:2 dae:1 them:4 factor:1 entire:1 surrounds:1 impossible:1 band:9 resolve:1 unacceptably:1 serendipitous:2 they:8 3h4:1 yr:1 discuss:1 nor:1 represents:1 february:1 several:1 hereafter:3 oxygen:1 brightness:9 fully:1 university:3 identified:3 tielens:2 kpc:2 chandra:1 mode:1 reasonable:1 each:2 heyer:1 nagase:1 mean:1 turtle:1 multiphase:1 telescope:4 series:1 forets:1 gaussian:1 ishida:1 extended:6 expect:1 combining:1 our:8 beyond:2 out:2 canada:1 jackson:1 space:4 danforth:1 research:1 dominated:6 ro:2 smc:13 occurs:1 shows:9 foundation:1 asp:2 hyung:1 derived:3 brγ:1 possibility:1 standard:2 ecliptic:1 advantages:1 imaging:2 members:1 usual:1 estimate:1 bleed:1 interaction:2 rule:1 could:4 shells:14 snell:2 s125:1 filter:1 produce:1 iso:3 massive:1 ism:1 yun:1 ionic:10 support:1 south:1 first:3 origin:4 major:1 rcw:6 features:3 l95:1 number:1 channels:3 fits:1 smaller:1 another:2 pulsar:2 array:3 fluxes:13 06m:2 angular:2 moorwood:3 size:2 gruendl:1 necessarily:1 temperature:2 koo:9 needed:1 introduction:1 twenty:1 top:2 system:2 least:1 their:3 observations:6 iau:1 white:5 molecular:17 sensitivity:1 williams:3 too:5 n49:2 shell:44 collapse:2 mostly:2 centered:1 explanation:1 park:2 artifact:2 gyu:1 optical:19 somewhat:1 dissociated:1 representing:1 than:9 toronto:2 observed:12 observatory:2 showed:5 princeton:1 kaneda:1 require:1 intensity:2 submitted:1 project:2 boulanger:1 determined:1 were:6 hollenbach:6 toward:7 missing:1 san:1 sw:6 correction:3 spectrum:13 conference:1 summing:1 say:1 filamentary:3 close:2 seem:1 aged:3 occupied:2 any:1 l167:1 ray:19 conversion:2 issue:1 pineau:1 studying:1 latter:1 agency:1 able:1 mid:2 shocked:4 gaensler:1 note:2 phillips:1 fitting:1 potential:1 prototypical:2 negligible:2 detector:1 mir:17 channel:2 even:3 2001b:1 unless:1 mathews:1 opposite:1 neatly:1 molecule:1 extending:1 significant:2 ford:1 segment:1 l103:1 appear:1 annulus:1 observation:1 considered:1 into:4 metal:1 km:2 mjy:10 kr:7 proceedings:2 part:2 principle:1 ku:1 constrain:1 left:2 physics:1 section:2 fitted:2 nebula:7 spaced:1 show:6 text:3 supported:1 scattered:3 infrared:10 mnras:3 bright:29 radio:27 solutions:1 southwestern:1 convolved:1 especially:1 xmm:2 indicator:1 northeast:2 based:5 seung:1 spite:1 distributed:1 should:4 kessler:1 brighter:1 only:4 experiment:1 black:1 molecules:3 equipped:1 01h:2 emitting:1 jae:1 des:1 over:2 centrally:2 do:2 dust:4 distance:3 masai:1 diagnosing:1 expectation:1 truly:1 beam:2 cannot:2 listed:2 words:1 isophotal:1 during:1 onboard:2 ita:2 neither:1 areas:5 pearson:1 bar:2 continuum:3 m5s:1 covering:1 arxiv:1 yield:1 summary:1 reid:1 whether:1 shull:3 processed:1 fainter:2 through:2 distinguishes:1 burrows:1 reference:2 achieved:1 national:1 hα:1 up:1 detection:5 sandstrom:1 see:11 individual:1 result:2 enhanced:3 existence:1 led:1 contour:1 hydrocarbon:1 hanawa:1 interacting:13 extragalactic:1 pattern:1 away:1 nature:4 µm:27 mills:1 between:3 probably:6 boundary:2 irc:34 perfectly:1 across:1 discovery:1 available:1 sections:1 korea:2 jy:2 relative:1 ikt:3 supernova:3 jp:7 however:4 southeast:1 incident:2 ji:1 key:1 flats:1 kev:4 pixels:1 thank:1 received:1 essentially:1 fit:1 irregular:1 many:1 region:1 uncertainty:1 according:3 agree:1 grain:1 chernoff:1 contribution:3 southeastern:1 nearby:1 among:1 extent:3 cm:4 point:8 color:9 ca:1 northeastern:3 natures:1 pole:1 simply:1 decreases:1 iras:1 respect:1 november:1 considering:1 unusual:1 light:3 yeon:1 leads:1 wright:6 nyman:1 tatematsu:1 radiative:1 three:4 been:5 mark:1 garmire:1 pc:5 reduction:2 much:4 pf:1 basic:1 expected:3 grant:1 ph:1 meeting:1 cohen:2 fig:11 faintness:1 enable:1 corresponding:1 both:3 chul:1 gas:8 tycho:1 maps:1 coherent:1 astron:2 careful:1 mcs:6 diffuse:5 present:1 case:1 hughes:7 handling:1 grains:2 empirical:1 will:1 while:6 error:1 fielding:2 onaka:5 tuohy:1 pahs:1 almost:1 characteristics:1 calculator:1 ir:57 non:1 apjs:1 ii:7 middle:3 good:1 ia:4 limit:1 ic:14 binary:2 different:5 nakagawa:1 suggest:1 cross:3 filipovi:5 brightened:1 parts:2 northwest:2 pah:4 throughput:2 shah:1 relatively:3 used:4 http:1 ctb:3 numerical:1 hand:2 steps:1 levels:1 user:3 nir:14 dark:2 center:2 bolatto:1 no:4 well:6 analysis:3 recombination:1 components:1 simulated:3 position:1 model:4 joon:1 subtraction:3 heiles:2 background:4 proposed:1 less:3 generally:3 accurate:2 newton:1 resolution:3 rest:2 sources:6 lutz:1 identify:1 atomic:2 nousek:1 yet:1 previous:1 mckee:4 kanagawa:1 density:4 conclude:3 smith:2 except:1 signals:1 source:14 ofview:1 spread:1 extends:1 plateau:1 versa:1 east:1 plasma:3 gave:1 resolved:1 sagamihara:1 march:1 around:1 depends:1 bands:18 8th:1 absence:1 possible:4 collisionally:1 mok:1 possibly:3 aerospace:1 confined:1 using:11 accepted:1 prominent:2 like:5 excluding:1 sizes:1 manual:4 html:1 flux:10 ikeuchi:1 mhz:3 either:1 kawasaki:2 longmore:2 therein:2 reidel:1 www:1 because:10 old:1 smoothly:1 some:5 pacific:1 calculated:2 strongest:2 table:8 images:10 imager:1 matching:1 neufeld:1 provided:3 fov:5 scale:1 dense:1 overlay:1 myung:1 integration:1 moon:2 dwek:5 connecting:1 linearly:1 esa:1 molonglo:1 subtracted:3 participation:1 dissociative:2 core:2 who:1 hearnshaw:1 reach:6 s11:20 masked:1 how:1 although:3 filaments:7 cutri:1 comparison:6 about:1 central:1 most:2 column:3 stanimirovi:3 o:5 page:2 range:1 plerion:1 apjl:3 chu:3 cesarsky:4 astronomical:1 own:1 rho:7 h2:6 image:9 within:1 staveley:1 interstellar:3 soo:1 due:3 right:1 references:3 heated:2 oliva:5 proportional:1 ellipse:1 significantly:1 uncertainties:4 van:8 area:3 astrometric:1 there:8 chevalier:2 fast:6 lost:1 stars:2 ed:2 astrophysics:1 melnick:1 yrs:1 was:10 synthesis:1 synchrotron:3 medium:3 north:4 complete:2 progenitor:1 but:15 irac:1 astro:9 draine:5 neutral:1 magnitude:1 ho:1 scope:1 pwn:2 magellanic:6 line:5 partially:4 volume:1 bandwidths:1 inside:5 vice:1 maximum:2 us:3 dordrecht:1 exploration:1 emissions:1 spectroscopy:1 highlight:1 distribution:5 similar:3 called:1 ac:9 associated:10 defined:2 stronger:1 abstract:1 aj:3 linearity:1 direction:5 kaufman:1 balmer:1 ar:1 waveband:4 wavelength:1 partly:2 graham:5 calibration:5 amounts:1 when:2 ne:18 aromatic:1 graduate:1 field:2 other:9 ellipses:2 spatial:1 department:3 polycyclic:1 conclusion:2 poor:3 picture:1 francisco:1 star:1 users:1 separate:1 jaxa:6 bottom:2 interferometric:1 generated:1 peak:5 included:2 astronomy:3 slane:1 structure:3 exposure:1 jones:3 lee1:4 utoronto:1 starting:1 factors:1 midcourse:1 together:1 portion:2 mass:1 diagnosis:1 time:1 nuclei:1 n3:20 n4:27 fesen:3 astronautical:1 |
0704.0707.txt |@word represent:2 partial:1 consider:4 chain:3 melts:1 separates:1 results:3 leads:4 entropy:1 remarkably:1 synthetic:1 monomer:1 copolymers:5 segments:12 finally:1 stochastic:2 heterogeneity:7 indicating:1 labels:1 very:2 could:6 nφ:4 micelles:2 mixing:1 experimentally:1 exact:2 condition:2 randomness:2 purely:2 ref:3 solution:2 large:7 solved:1 markov:2 shows:4 noted:1 upper:2 α2i:2 past:1 second:5 cost:1 evaluated:1 further:2 chem:3 expressions:1 theory:8 what:4 combined:1 brief:1 expressed:1 uniform:4 access:2 above:11 fractional:1 new:2 increasing:4 full:3 degree:8 respectively:3 water:8 groups:3 excess:4 along:2 mex:3 change:2 extreme:8 obtained:3 great:1 reason:3 leaving:1 suggests:1 resulting:1 suggestion:1 situations:1 usually:1 suitable:1 changes:1 hydrophobic:1 plotted:1 useful:1 apr:1 explained:1 modifying:5 scaled:1 decrease:1 total:1 derivatives:1 undergone:1 would:10 remains:1 positive:2 negative:1 next:1 definiteness:1 examination:1 therefore:3 taken:3 associated:1 theoretical:1 more:2 formally:2 initiated:1 becomes:2 apparent:2 spinodal:21 particular:4 cases:1 account:2 crosses:1 indicates:1 ρi:25 equation:1 work:2 det:2 modified:15 remain:2 values:2 following:1 flory:10 root:1 example:3 grained:4 indicated:1 calculation:2 neglected:1 agent:3 copolymer:1 minimum:5 arise:3 occur:1 needs:1 eng:1 rather:4 clarke:2 holds:1 species:8 chemical:3 how:2 pure:1 instead:1 parameter:4 simplicity:1 product:1 blocks:2 mat:1 algebra:1 may:1 after:1 confirmed:1 mixed:1 coming:1 ties:1 effective:3 lines:1 provide:1 fundamental:1 typical:1 ith:1 developed:3 over:3 despite:1 vary:1 expects:2 stability:7 whilst:1 paper:2 satisfies:1 still:2 tendency:2 warren:4 strikingly:1 measuring:1 thank:1 la:1 interesting:1 absence:3 degrees:1 systems:2 decreased:1 main:1 greater:1 solubility:13 landau:1 ǫij:2 effects:1 they:1 now:5 discuss:1 eigenvalue:2 term:5 always:3 university:1 inequality:1 each:2 found:1 soc:1 associative:1 mean:7 energy:9 reduce:1 idea:1 inhomogeneous:1 extended:1 ex:2 beyond:1 eq:14 try:1 shown:3 matrix:1 rs:5 res:1 since:5 rev:3 include:1 behaviours:1 hill:1 demixing:4 induced:1 issue:1 occurs:2 chemically:3 earlier:1 solvent:5 approached:1 mechanisms:1 given:7 free:9 standard:1 completely:1 base:3 complicated:1 york:2 compositions:1 care:1 interaction:1 retained:1 route:1 transition:8 keep:1 length:4 gordon:1 removing:1 routes:1 undergo:1 first:3 major:2 already:3 nigel:1 probability:3 number:3 reaches:1 comprises:1 size:3 little:1 eqs:1 system:10 their:2 intermediate:1 structures:2 final:1 insightful:1 somewhat:1 than:5 specify:1 wide:1 third:2 zero:1 classes:1 supposed:2 were:1 gives:1 treated:1 remained:1 correction:1 curves:7 randomly:2 manuscript:1 buried:1 macromol:1 seen:1 concentration:6 confirms:2 any:1 lie:2 confirmation:1 depending:1 convenient:1 responsible:1 able:2 mid:2 port:1 note:2 ideal:1 materials:3 take:3 davidson:1 play:1 towards:2 though:5 reach:1 clearer:1 significant:1 phase:27 sophisticated:1 segment:1 class:1 consequences:2 calculated:2 partition:1 dissolved:2 generalising:1 principle:2 χn:2 effect:7 typically:1 dot:8 precise:1 show:2 characterisation:1 random:7 multicomponent:1 soluble:5 huggins:9 fine:3 find:1 ratio:1 much:1 proportion:1 enough:1 should:3 analytic:1 only:9 explicitly:1 truncation:1 mixture:2 correctly:1 albeit:1 dependent:1 de:1 overall:1 cannot:1 words:1 progress:1 hendriks:1 densities:5 conditions:1 arxiv:1 comprising:1 europhys:1 predicted:1 view:1 achieved:2 violated:1 correlations:3 lett:4 depends:4 individual:2 result:2 enhanced:1 insoluble:6 phases:3 arguably:1 behind:1 determined:2 various:2 envisage:2 closed:1 between:5 αi:12 probably:1 reading:1 approach:5 adv:1 comparable:1 terms:5 nature:5 however:1 wi:7 vanishing:4 extent:1 interface:1 problem:5 behaviour:12 essentially:1 many:2 conclusions:2 equal:2 heterogeneously:1 april:1 leibler:1 dated:1 variance:4 finds:1 experimental:1 con:2 relevant:1 separation:8 point:2 simple:4 had:1 coexistence:2 respect:1 considering:2 described:4 arbitrary:1 three:2 been:4 describes:1 coarse:1 basic:1 expected:5 fig:6 field:1 direction:8 arises:2 corresponding:2 fredrickson:2 reaction:2 irvine:1 determination:1 representative:1 derivative:1 present:9 case:7 dash:8 macromolecules:2 solid:2 examine:3 value:4 will:2 specialises:1 interchain:1 situation:1 polymer:18 almost:1 thus:1 itself:2 cond:1 vanish:1 id:2 φp:4 capture:1 different:3 perhaps:1 make:1 coexisting:2 cross:1 same:3 clearly:1 shifts:1 coworkers:1 modification:18 difficult:1 independent:1 emphasise:1 used:3 differing:1 driven:2 moment:7 olvera:1 heterogeneities:1 task:1 scenario:1 fully:3 milner:2 analysis:2 contact:1 firstly:1 model:17 chemistry:1 usual:1 just:1 being:6 obtain:2 shape:1 ithaca:1 previous:1 insight:2 characterised:2 density:1 cornell:1 workers:1 conclude:1 character:1 other:2 location:3 buxton:1 formal:1 polydispersity:1 identical:1 increased:1 easily:1 characterise:1 possible:1 corresponds:6 cruz:1 press:1 using:2 apart:1 crist:1 sizes:4 aqueous:5 patrick:1 reduces:2 substitution:1 unstable:1 either:1 polymers:24 translated:2 mcgraw:1 dilution:2 soft:1 summarise:1 accessible:1 because:1 often:1 namely:1 some:3 moreover:1 happens:1 scale:1 lead:1 χmin:2 critical:1 tends:2 proc:1 inserting:2 process:3 plot:2 cellulose:2 analysed:1 step:3 binomial:1 instability:10 drawn:1 properties:1 mesophases:1 simpler:1 stant:1 theorems:1 discussed:3 reduced:1 nonvanishing:1 repulsion:1 greatly:1 concentrations:3 block:11 equally:1 follows:1 into:4 numerically:2 due:1 lies:1 appropriate:3 determing:1 tiny:1 determine:1 methods:1 φmin:5 log:3 assumed:1 unmodified:7 there:7 question:1 lond:1 sunlight:1 why:1 quadratic:1 handbook:1 fraction:3 was:2 synthesis:1 function:1 form:3 but:2 principles:1 mechanistic:2 monomers:1 sollich:4 line:14 partially:1 made:1 versions:1 characteristic:1 up:1 us:4 below:3 limit:20 uk:1 continuously:1 distribution:5 similar:4 eigenvector:2 expect:3 required:1 proved:1 defined:1 configurational:1 determinant:1 general:4 single:1 ind:1 ing:1 intra:1 irrespective:1 onerous:1 no:4 dashed:4 whereas:1 when:1 vanishes:1 application:1 setting:1 role:1 conclusion:1 poor:1 draw:1 kinds:2 models:1 meaning:2 important:1 cates:2 diblock:1 variable:1 structure:1 space:2 kinetics:1 write:1 weights:1 original:1 augmented:1 |
0704.0708.txt |@word dbi:1 sci:1 consider:14 pointing:1 funct:1 schappacher:1 global:5 results:13 leads:6 scalar:3 proposition:9 computation:6 consists:2 follow:2 expressions:4 devoted:6 whose:1 inverse:22 depend:1 chain:1 integral:17 paris:1 graph:2 tt:21 simplify:1 spirit:3 tn:2 finally:5 critical:4 henrot:1 elliptic:1 under:8 kunisch:2 applied:3 expressing:1 straightforward:10 outside:1 very:1 void:1 conditions:13 geometrical:1 every:2 interpreting:1 decide:1 h2τ:25 difference:3 deformations:1 condition:7 severely:2 solves:8 presented:1 transmission:2 turns:2 t2:3 solution:13 t1:3 admissible:7 convenience:1 vector:27 differentiates:1 small:1 div:60 shows:4 neighborhood:3 concise:1 direct:3 riesz:2 split:1 jump:15 go:1 second:42 cost:5 design:1 tangential:23 pass:1 aux:1 dψ2:10 substitute:1 theory:4 bilinear:1 established:1 intersection:2 nonlinear:1 stands:5 rate:2 giving:1 sum:3 pierre:1 lengthy:2 access:3 version:1 ito:1 precisions:1 above:2 deal:1 obvious:1 subtracting:1 method:10 filled:1 body:2 compact:8 full:1 led:2 behavior:1 dψi:2 respectively:5 component:3 here:4 desired:1 σh2:3 simon:3 strategies:1 directions:2 consideration:1 along:8 equations:8 appears:2 change:1 differential:4 obtained:5 search:1 sobolev:1 rigorously:2 technical:1 study:9 allows:1 µs:1 usually:1 implement:1 postponed:1 studies:1 involves:1 via:1 useful:1 family:1 apr:1 substitution:1 apply:2 establish:1 unit:3 derivatives:22 use:18 asymptotic:1 working:1 prove:7 distinct:4 positive:2 objectives:3 contains:1 uniqueness:3 readability:3 classically:1 m1:5 therefore:6 m2:4 scope:1 type:1 start:1 more:6 introducing:1 knows:1 becomes:2 operators:13 curvature:4 hofmann:1 appendix:1 surface:1 particular:2 known:4 r1:2 topic:1 account:1 isomorphism:2 r2:4 thanks:12 integrating:2 h10:1 recall:5 equation:13 work:9 det:7 paragraph:1 values:4 hope:1 following:21 making:3 proof:23 control:3 f1:10 f2:14 impose:1 exterior:1 give:5 process:2 expanding:3 choice:3 justifications:1 organized:1 involve:3 minimum:4 want:2 sense:6 hhn:3 absolute:1 huge:1 needs:1 end:3 dh:13 dependency:2 provide:2 discussion:1 differentiability:5 feature:1 occur:1 write:18 how:4 criterion:10 optimal:1 verlag:2 parameter:3 priori:2 belongs:4 map:4 express:3 singular:1 may:1 after:10 derived:1 orbits:1 applications:4 explored:1 summarize:1 destructive:1 data:2 concerns:3 fn:2 drop:1 natural:1 third:1 computations:11 emphasize:3 approximation:1 lines:2 element:5 diffeomorphism:1 algorithms:1 realizes:1 fundamental:1 2u:2 definitions:3 order:42 restriction:1 holds:8 subsections:1 indeed:2 satisfied:1 years:1 stability:4 db1:2 paper:5 uh2:5 da1:1 da2:1 during:1 existence:9 satisfies:5 its:12 before:2 symmetric:2 continuity:3 derive:3 outer:5 manuscript:1 maps:1 chosen:1 fix:1 appl:1 vicinity:1 actually:1 choose:2 derivative:58 main:6 deformation:10 ωh2:5 focussed:1 non:1 ahi:1 return:1 ya:2 propose:1 material:20 appliqu:1 introduce:6 framework:1 sω:22 they:1 instead:2 misuse:1 multidimensional:1 now:13 discuss:1 nor:1 eigenvalue:2 february:1 dht:1 duality:1 explains:4 divτ:103 2a:1 each:7 instability:2 universit:1 higher:1 traces:1 side:2 mean:4 subset:6 domain:18 square:1 retrieve:1 directly:1 hh2:3 ed:1 hard:1 used:5 elementary:1 investigated:1 2b1:1 entering:1 measurement:4 eu:1 our:3 extract:1 special:2 out:5 arguments:2 shown:3 matrix:4 astala:2 space:4 gradient:9 quantify:1 furthermore:6 since:26 crucial:1 denotes:9 rd:30 reader:4 denoted:2 formula:15 get:28 squares:1 occurs:1 math:7 levenberg:1 maz:2 linear:2 written:7 2h1:1 discontinuity:4 divergence:8 standard:1 nth:2 approaches:1 calder:3 term:8 detecting:1 monographs:1 finite:1 definition:5 dirichlet:6 derivation:1 recovering:1 r3:4 geometry:1 determining:1 sylvester:2 similarly:2 keep:1 turn:1 plane:1 derivations:1 hence:12 moving:1 support:1 first:30 symmetry:3 kernel:3 u1:2 variables:1 assumptions:2 restrict:1 clear:1 simplified:5 relations:1 another:2 difficulty:1 open:9 several:1 given:18 minimizer:3 reference:1 their:7 introduction:2 unknown:4 adjoint:3 system:1 least:2 needed:6 perturbations:1 expand:2 statement:3 convention:1 siam:2 perfectly:2 gives:3 calculations:1 continuous:6 proving:2 part:1 differentiate:3 authors:1 translation:1 2div:1 unrealistic:1 than:1 specify:1 distance:3 kind:3 scheme:2 determines:1 target:2 double:3 require:2 depends:1 aims:3 normalizing:1 minimize:1 supposed:1 decompose:1 dtt:3 springer:3 gathering:3 nicer:1 rewrite:1 explicit:2 ann:4 modern:1 argument:3 triebel:1 manner:1 need:5 recover:5 seek:1 any:9 hessian:10 newtonian:1 zero:1 general:2 lim:1 note:6 sciences:2 fitting:1 potential:11 take:2 neither:1 objective:10 green:1 techniques:1 accuracy:1 calculus:7 spectral:1 insulated:2 converse:1 trace:2 normal:22 quote:3 object:1 reach:1 systems:3 birkh:1 extending:1 involving:2 connected:1 but:1 preliminary:3 pair:1 homogeneous:1 inserted:1 class:9 appear:2 volume:1 consequences:2 considered:2 arising:2 into:7 gather:2 curvatures:1 face:1 construction:2 overdetermined:1 left:1 typically:1 section:8 fact:6 quantity:2 precise:4 incorporate:3 paul:1 show:10 variational:1 consult:2 ωd0:6 notations:4 spaces:4 relation:6 solutions:1 keywords:1 manifold:5 d2:37 find:2 d0:2 help:1 current:1 based:2 knowledge:3 uhlmann:2 explain:2 distributed:1 state:23 should:4 lemma:10 only:6 subsection:3 σd2:15 factor:1 integrate:2 adequate:2 local:2 ematiques:2 achieve:1 dn:42 do:1 handle:1 reconstruction:1 notation:7 means:3 de:8 straightforwardly:3 chaleur:1 marquard:1 aim:2 ones:1 dx:1 new:1 dv:3 reconstruct:2 db2:1 justified:1 differentiating:2 furnishes:1 2h2:6 settings:1 fields:12 arxiv:1 2b2:1 remove:1 twice:3 investigate:3 experiments:1 li:1 common:1 fixed:2 view:3 satisfy:1 set:9 ser:1 exists:5 variations:1 sensitivity:1 testing:2 notice:1 ωt:7 differentiation:2 see:8 justification:1 injecting:1 result:12 terms:10 heavy:1 λi:1 best:1 conductivity:13 satisfying:3 degree:1 inappropriate:1 distinctive:1 user:1 consequence:2 incorporating:2 λn:4 boundaries:5 enough:1 identification:2 µk:8 between:4 progress:1 boundary:43 approach:3 checks:1 preserve:2 ends:1 matricial:2 recently:1 extend:1 numer:1 attention:1 weak:5 however:2 continuously:3 inclusions:1 interface:10 hal:2 problem:41 both:3 essentially:1 last:4 signed:2 always:1 many:4 ill:4 la:1 against:1 called:1 ln:1 connection:1 concentrate:1 context:2 estimation:1 expression:10 adaption:1 hτ:7 kirsch:3 necessary:1 point:9 appeared:2 seems:1 harmonic:8 insist:1 high:1 dimensional:1 twin:1 simply:1 coercive:2 respect:9 writing:1 points:1 considering:1 mention:1 geometries:1 piecewise:1 three:1 been:2 strategy:3 much:1 basic:1 applying:2 borders:1 define:8 direction:17 arises:3 corresponding:6 restrictions:2 concerning:6 propositions:1 remark:4 recalled:1 arinta:2 formes:1 former:4 present:3 case:5 compatible:1 look:1 subdivide:1 frozen:1 aiv:1 value:6 choices:1 will:27 information:1 while:6 optimization:15 compactness:3 shall:1 conformal:1 taking:1 layer:7 unitary:4 vd:6 vol:1 av:1 kohn:8 them:3 vn:8 decreasing:1 regularity:9 itself:1 formulae:3 technology:1 id:1 dhn:1 different:2 descent:1 combining:1 media:1 make:3 belong:1 same:7 funktsional:1 parts:10 viewed:1 proved:2 subdomain:1 composition:1 clearness:1 calculation:2 literature:1 solved:3 laboratoire:1 numerical:11 hand:5 v1:30 v2:22 uses:1 delicate:1 potentials:3 identity:2 mappings:1 off:1 older:1 nevertheless:3 adapted:1 obstacles:1 well:6 posedness:3 analysis:6 obviously:1 thought:1 without:2 solve:3 comes:5 components:2 convenient:1 jean:1 g1:5 dimension:1 dh1:25 usual:3 vogelius:8 less:1 being:2 resp:2 newton:5 obtain:28 dφ2:5 shape:48 identify:1 voltage:1 integer:1 facts:2 alternative:4 scattering:2 yet:1 oriented:1 cut:1 preprint:2 application:2 σu:1 auser:1 characterization:1 character:1 boston:1 other:3 prilozhen:1 easy:2 theorem:32 input:1 pitman:1 remaining:1 euler:1 real:1 unstability:1 easily:3 rules:1 couple:1 jacobian:2 posed:5 possible:2 corresponds:1 dφi:1 know:1 using:5 unique:2 formal:3 injectivity:1 appearing:1 tangentially:1 follows:6 ees:1 representation:2 shapes:2 flux:7 steps:1 either:1 arbitrary:1 output:1 works:2 technologie:1 page:1 beltrami:10 mathematical:2 right:3 methods:10 classical:6 some:18 begin:5 regularized:1 deduce:8 acad:1 examples:1 b2:1 moreover:4 proofs:1 matching:1 transport:3 describing:1 tools:1 avoid:2 measurements:3 integration:5 birkha:1 does:1 connecting:1 manipulate:1 provides:1 tends:1 preceding:1 refer:1 measuring:1 core:1 compi:2 bold:1 minimization:7 jumps:5 2c:1 expansion:1 step:10 found:3 th:1 properties:5 injective:2 comparison:1 about:2 simplest:1 extension:10 algebraic:1 novikov:2 oc:1 o:7 2i:1 practical:2 sake:3 range:1 a2:2 fredholm:3 done:1 ah1:48 considerations:1 discretization:3 egne:2 inclusion:5 h2:338 h3:1 image:1 h1:301 numerically:1 functional:4 h5:1 schemes:2 references:2 determine:1 operator:28 substitutions:1 neumann:6 additional:3 assumed:3 h01:2 there:5 question:4 transform:1 why:4 strict:1 cauchy:1 kω:22 way:1 series:1 analyze:1 was:1 function:24 form:8 simplifications:1 identities:1 sequel:5 gauss:3 back:1 ah2:3 hi:9 hn:17 related:1 justify:1 impedance:6 line:4 level:1 hf:1 made:1 compute:16 supp:1 characteristic:1 inside:2 smooth:14 up:2 us:20 international:1 kress:1 un:50 limit:5 hs:1 steepest:1 sides:1 ud:57 distribution:5 similar:3 laplace:12 b1:1 mechanics:1 adopt:1 constant:3 computing:2 defined:20 ah:4 abstract:1 describe:3 denote:8 single:8 formulation:5 tomography:6 gradients:1 distributions:1 check:3 fill:1 ni:1 functions:9 differentiable:5 nn:2 no:10 regroup:1 when:12 detail:1 multipliers:2 field:15 interested:1 electrical:6 details:4 cybernetics:1 test:3 mathematics:2 2dn:6 nt:2 sufficient:1 conclude:7 elements:5 models:1 remains:3 setting:1 problems:10 variation:4 transported:1 a1:2 important:2 bounded:4 anal:3 suited:1 tackle:2 dh2:12 gets:2 structure:1 algorithm:1 assume:7 sokolowski:1 dσ:8 rule:1 notion:1 time:1 determination:1 n2:1 original:1 once:1 |
0704.0709.txt |@word limited:1 measurements:1 sriram:1 rev:15 magnetic:1 varying:1 results:2 four:11 ge:1 computation:9 edu:2 follow:1 remarkably:2 contributions:1 relationships:1 whose:1 inverse:1 oscillating:1 calculate:1 inin:1 technique:2 contained:1 environment:4 program:1 restriction:1 under:1 include:1 prevedel:1 resources:1 division:1 supported:1 abelian:1 orthogonal:2 very:5 rise:1 chuang:1 experimentally:1 difference:1 matrices:2 interferometry:2 magic:1 swapping:9 hamiltonian:10 bn:1 knight:1 solution:1 convenience:1 vector:3 nmr:1 eigenvalues:4 mo:1 still:1 abbreviated:1 work:2 ericsson:3 b23:11 direct:2 zero:1 basu:1 enclosed:1 rowell:1 chen:2 greenberger:1 jilin:1 theory:5 even:1 will:4 ˆr:5 section:2 expressed:2 annals:1 run:1 new:3 order:1 consisting:1 satisfy:1 edited:2 troduced:1 degree:5 respectively:2 realizations:1 teleportation:1 here:3 china:3 address:2 pati:1 equations:2 sending:1 institute:1 involved:2 study:3 allows:4 walther:1 permutation:5 usually:1 bob:3 kauffman:3 makes:1 ˇi:1 named:1 deterministic:1 useful:1 merely:1 highly:1 apply:1 unit:4 use:1 asymptotic:1 would:4 next:1 definiteness:1 nucl:1 therefore:1 noisy:3 sentation:1 theoretical:1 more:5 introducing:1 permutations:1 composite:1 trait:1 operators:14 odinger:2 correspondingly:1 normalized:1 particular:3 known:1 iii:2 evolves:3 account:1 sphere:6 originally:1 mn:1 mi:2 nonmaximally:2 longitude:1 following:6 making:1 arrive:1 example:2 decoupled:1 numbers:1 abcd:16 wang:1 give:1 bennett:4 organized:1 states:55 indicates:1 reviewing:1 degenerate:3 tan:1 ijkl:1 information:5 end:1 notation:1 xue:1 provide:3 verify:2 discussion:4 acts:2 srinivasan:1 located:1 pure:2 significance:1 gate:4 parameter:5 sin:20 brassard:1 simplicity:2 product:3 may:13 ζj:3 after:5 changchun:1 applications:4 produce:2 share:2 realized:2 short:1 natural:4 prefers:1 chern:1 explicit:1 ghz:13 their:3 inform:1 claire:2 cannot:1 so:2 allow:2 siz:1 representation:1 kwiat:1 make:3 horne:3 produces:1 indeed:1 concurrence:5 vary:1 produced:1 paper:4 through:2 satisfies:1 braid:3 its:2 jennewein:1 group:1 thank:1 chosen:2 interesting:1 actually:1 forms:1 systems:4 latitude:1 ours:1 decades:1 deformation:2 overcome:1 eventually:1 them:3 powerful:1 introduce:2 franko:1 mention:1 they:6 now:2 realize:5 possess:1 hereafter:1 university:4 presented:1 identified:1 side:1 baxter:5 ei:2 another:1 kang:1 braiding:38 reduce:2 related:2 used:1 obtains:5 measurement:8 quantum:37 our:1 eq:12 es:9 out:1 divincenzo:1 shown:3 jimbo:1 matrix:22 factors:1 tianjin:1 furthermore:1 since:3 crucial:1 particles:3 acting:6 investigation:2 print:1 ref:3 ri:2 earlier:2 linear:12 b34:10 standard:5 complicated:2 might:1 jozsa:1 generate:9 pairs:1 recast:1 timer:1 turn:4 generalizations:1 separable:8 there:4 swapped:2 vedral:2 variables:1 coding:1 number:1 channels:1 xy:2 done:1 relations:3 directly:2 ring:1 precisely:2 electronic:2 angular:2 wilczek:1 rewritten:2 similarly:1 introduction:1 eqs:1 system:1 construct:2 needed:2 calculations:1 realization:3 1i:10 wootters:3 bits:1 1n:1 excellent:1 collapse:1 danny:2 authors:1 x2:5 x3:2 anandan:1 x1:2 representing:1 than:1 distance:1 kind:2 showed:1 wiesner:1 structures:1 namely:2 future:2 similar:1 bridge:1 shrinks:1 timeindependent:1 strengthen:1 well:6 topics:1 generalization:1 case:1 su:3 kaltenbaek:1 weinfurter:2 any:1 viewed:2 multipartite:1 angle:1 raussendorf:1 lin:1 si:23 instance:2 maxi:1 generalized:2 transmit:1 singh:1 channel:1 spectral:1 shall:2 reach:1 most:2 connected:1 significant:1 successive:2 nothing:1 achilles:1 singled:1 surprising:1 coincides:1 physica:1 kl:2 yang:9 exp:3 mechanical:1 physics:4 fact:1 p34:1 ge1:1 bais:1 phenomenon:2 show:2 random:1 discovered:1 purely:1 relation:1 sj:1 northeast:1 based:8 parameters:4 e10:1 hopeful:1 topological:5 only:3 generators:2 factor:2 integrable:1 local:1 oct:1 discuss:4 do:2 cryptography:1 dependent:5 familiar:1 express:1 ones:2 words:2 exchanges:2 during:1 dt:1 du:2 adiabatically:4 arxiv:1 summary:1 investigate:4 feed:1 shi:1 view:1 set:1 fascinating:1 observes:1 oqvist:1 j1:3 j2:2 up:2 relative:1 see:2 sec:2 result:2 p23:7 discussions:2 terms:2 hall:1 phases:15 satisfying:1 review:2 definite:1 qubits:2 state:31 between:5 invariant:1 geometric:8 approach:7 recently:2 nature:1 initially:2 restricting:1 however:3 jr:1 equals:2 bose:2 come:2 originates:2 both:1 σi:4 last:1 many:1 taking:2 according:1 oh:1 hϕ:4 connection:1 berry:17 logic:1 qubit:11 branning:1 comes:1 among:1 cn:2 tong:1 point:3 simple:2 corresponds:1 cd:4 dimensional:2 werner:1 moreover:1 ohi:1 transformations:14 basis:14 locally:1 barreiro:1 due:1 been:6 int:1 describes:2 meanings:1 combined:1 expected:1 ph:2 pi:12 fig:4 generating:1 trices:1 coherence:2 photon:1 cos:23 zeilinger:8 coherent:1 observe:1 kitaev:1 angles:2 denote:2 spin:8 former:1 protocols:1 applied:1 novel:1 pacs:1 solid:1 wellknown:1 expanded:1 aim:1 while:8 suppose:1 behavior:1 error:1 property:1 loop:1 unitary:25 vf:1 century:1 thus:1 non:1 encouragement:1 iv:1 ii:5 cluster:17 reads:3 ramifications:1 zhang:1 mally:1 twofold:1 grant:1 acknowledgments:1 realizing:2 lett:11 same:4 quant:3 pauli:1 constructed:2 pan:3 independent:8 literature:1 singapore:2 hand:1 lomonaco:1 experimenter:1 purpose:1 entanglement:36 recent:1 literatures:1 schr:2 center:2 scenario:1 epr:1 analysis:1 without:1 oneway:1 latter:1 usual:5 gates:1 proposed:1 being:1 generally:1 observed:1 obtain:3 world:2 alternative:1 eigenstates:4 density:1 bell:9 iϕ:14 mathematically:3 baxterization:4 location:1 easy:2 b12:13 transformation:10 momentum:2 zou:1 badurek:1 nielsen:1 depends:2 read:1 decomposed:1 possible:1 spanned:2 zukowski:3 entangled:18 knot:1 press:1 using:8 part:1 unique:1 like:4 follows:4 reduces:2 performing:1 alice:3 e01:1 flux:1 yields:1 arbitrary:1 become:4 interestingly:1 mathematical:1 because:1 classical:1 people:2 some:3 self:1 experiments:1 understood:2 examples:1 choosing:1 cr:1 nonzero:1 dense:1 dimensions:2 affects:1 normal:1 prof:2 kwek:1 ij2:1 noise:2 eiϕ:4 scientific:2 bc:4 equivalent:2 communicate:1 bi:23 bj:2 interval:1 worthy:1 hadamard:1 cnot:1 simpler:2 about:1 actual:1 oi:2 constraint:1 discussed:1 2i:1 briegel:1 mixed:9 bloch:7 slingerland:1 cambridge:1 communication:1 into:1 within:1 disentangled:1 nsf:1 three:3 down:1 phase:13 right:1 einstein:1 operator:8 significantly:1 jing:1 additional:1 prepare:1 classically:1 assumed:1 initial:3 j3:2 transform:1 equation:4 peters:1 restricts:1 way:4 forward:1 was:2 assumes:1 naturally:1 elsewhere:1 form:2 shapere:1 smolin:1 but:1 talents:1 rauch:1 ling:1 faddeev:1 made:1 applying:2 characteristic:1 ωt:4 us:7 achieving:1 suitable:1 continuously:1 define:1 ua:2 called:2 uc:2 ub:2 mechanics:1 ab:4 ad:4 computing:1 defined:1 certain:2 universal:1 describe:3 general:3 peres:1 multiparticle:1 single:2 trix:1 nankai:3 corresponding:3 viewpoint:1 check:1 physical:3 mutual:1 bouwmeester:1 faithful:1 no:2 ekert:4 when:8 arctan:1 field:2 other:4 republic:2 becomes:1 department:1 mathematics:2 conclusion:2 briefly:3 kinds:3 superposition:1 subspace:3 nonclassical:1 epeau:1 prepared:1 important:1 prepares:1 describing:1 network:1 ago:1 independently:1 space:10 together:1 xbi:1 time:12 chaturvedi:1 starting:2 original:2 once:1 |
0704.0710.txt |@word monte:6 extrapolated:2 partial:2 systematic:12 pointing:1 rev:15 particular:1 results:2 kernphysik:4 leads:1 calorimeter:6 quadrature:2 edu:1 gk:1 layers:3 increase:1 bremsstrahlung:1 mπ0:1 γp:29 presents:1 gatchina:1 tl:1 petersburg:2 determinations:1 stable:1 kλ:2 hiskp:1 kσ:1 klempt:5 amplitudes:1 returned:1 advantage:1 very:1 induce:1 wave:2 electron:3 sidebands:1 entries:1 resonant:1 experimentally:2 difference:1 tagging:3 four:2 level:3 large:5 small:3 upper:2 smaller:2 consistent:1 ted:1 horn:1 grant:1 second:3 anton:1 dynamics:1 estimated:5 carlo:6 blue:1 established:1 what:1 errors:3 petry:2 contributions:10 section:21 selected:1 thickness:1 experiment:8 above:6 new:1 falling:1 increasing:2 consisting:1 contrast:1 counters:2 full:1 exchange:6 respectively:2 compilation:1 here:1 strakovsky:1 ranges:1 beck:2 asymmetry:1 mev:73 address:6 directions:1 based:1 strong:3 respect:1 transfer:5 obtained:3 incoming:1 difficulty:1 institute:1 study:1 losses:1 reports:1 guide:1 preferentially:1 simultaneous:1 products:2 procedure:1 resonance:1 capstick:6 diameter:1 via:4 apr:1 distributed:3 excellently:1 decrease:1 summation:1 meson:2 predicted:4 confidence:1 usa:2 probabilities:1 give:3 few:1 nucl:7 going:1 kinematics:2 centre:3 taken:2 more:4 fractions:2 entrance:1 pγ:1 acceptable:1 corrected:1 tested:1 studied:2 charged:4 known:2 eγ:53 had:3 sample:1 account:4 mc:2 integrating:1 arndt:1 setup:3 work:1 protons:9 minimum:2 values:4 nikonov:4 bent:1 escapes:1 predict:1 neglected:1 escaped:1 indicates:1 konrad:1 performed:3 arise:1 unpolarised:1 hydrogen:1 absolute:1 needs:1 sr:10 end:2 varied:1 decaying:3 photodiode:1 provide:2 feature:1 regions:1 how:1 scifi:1 sarantsev:5 instead:1 axis:1 parameter:2 ea:1 description:3 may:3 overall:1 photoproduction:17 earlier:1 derived:4 cua:1 diagram:1 produce:2 physik:1 csi:1 readout:1 data:19 parallel:1 types:1 forschungsgemeinschaft:1 natural:1 liquid:2 light:2 optimised:1 weinheimer:1 st:2 extrapolation:2 so:1 allow:2 sc:1 region:7 acknowledges:1 scintillation:2 order:4 typical:2 tagged:2 tallahassee:1 nucleon:1 over:4 breit:5 produced:1 surviving:2 experiments:2 filters:1 existence:1 fwhm:1 its:2 before:1 le:1 outer:1 probability:4 fit:13 decay:3 energies:6 masses:2 glozman:1 detected:4 production:11 fig:34 covered:2 schmidt:1 eur:11 correspondence:1 non:5 good:3 combination:1 washington:1 band:2 leps:1 subtraction:2 they:5 yu:1 discuss:1 cbelsa:1 matched:1 groningen:2 represents:1 february:1 netherlands:2 university:3 covering:3 forschungszentrum:1 identified:4 sufficiently:1 magnitude:1 bonn:6 each:4 crossing:1 found:2 universit:8 constraints:1 darmstadt:1 differential:21 financial:1 eh:2 accelerator:2 series:1 energy:19 revised:1 krusche:3 gaussian:1 decays:3 isospin:1 ex:1 measurement:3 our:2 meth:2 extract:1 event:4 out:1 magnet:2 shown:12 sonderforschungsbereich:1 space:9 restricted:1 since:1 squared:3 research:1 particles:2 combinatorial:2 dominated:1 aker:1 instituut:2 integrated:1 red:1 shows:7 foundation:2 after:1 lopatin:1 mω:2 given:3 free:1 quark:1 cut:2 barth:1 van:2 estimate:2 rises:2 beginning:1 florida:1 success:1 funke:1 length:2 instrum:2 place:1 pattern:1 unknown:1 hence:2 south:1 first:4 humboldt:1 manuscript:1 koch:1 number:8 channels:1 approximately:2 quadrupole:1 comprises:1 thick:1 angular:3 differ:1 termined:1 geant:1 indicate:1 introduction:1 fl:1 histograms:6 πn:3 system:6 least:4 zegers:1 their:5 intermediate:1 ulich:1 listed:1 calculations:1 rates:1 dfg:3 structures:1 final:5 low:2 fraction:3 baryon:3 explanation:1 serve:1 took:2 part:5 authors:1 constituent:1 than:3 filled:1 detection:2 anisovich:5 target:6 fuchs:1 sections:24 metsch:2 iteration:2 grey:3 isovector:1 roberts:4 states:5 determined:15 amplitude:1 were:36 distinctive:1 tion:1 russia:1 table:5 spectrum:4 summing:1 showers:1 further:2 seen:1 angle:4 exploratory:1 min:1 latter:1 mechanism:2 note:1 extracted:2 high:2 gwdac:1 funds:1 thoma:5 detector:12 channel:6 play:1 added:2 normal:1 collaboration:2 pmiss:1 most:2 said:2 germany:9 pair:1 baryons:1 inserted:1 bradford:1 branching:1 subtracted:2 cover:1 feynman:1 points:5 electrons:2 subsequent:1 barrel:7 left:5 physics:2 technical:1 fitted:4 unster:1 slope:3 nω:3 mainz:2 selection:1 intensity:1 show:2 nπ:3 text:1 unseen:1 crosssection:3 threshold:3 wigner:5 saphir:1 staff:1 fibre:5 taps:1 ratio:1 parameters:2 basel:1 should:1 only:10 version:1 candidates:1 convoluted:1 identification:2 helmholtz:1 misidentified:1 carolina:1 bartalini:1 mixture:1 hit:8 gev:12 klein:1 dependent:1 de:1 kopf:1 beam:9 timing:1 measured:3 dt:7 alexander:1 disentangling:1 reveal:1 processes:2 strahlen:1 workman:1 arxiv:1 yield:1 summary:1 paper:1 common:3 contain:1 switzerland:1 fixed:2 nη:2 set:1 statistical:2 dump:1 achieved:2 imposing:1 undergoes:1 wagenbrunn:1 observed:5 see:5 result:1 converting:1 chambers:2 seems:2 lotz:1 wire:2 ways:1 nuclear:1 dipole:1 case:2 state:3 future:1 various:1 between:3 invariant:2 µb:12 available:1 reproduced:1 missing:7 restricting:1 however:1 efficiency:1 derive:1 hypothesis:1 tmax:2 overestimated:1 improve:1 suggested:1 received:2 hits:12 many:1 taking:2 orfer:1 σe:1 participating:1 chosen:1 und:1 pdg:1 ernst:1 contribution:9 photons:6 experimental:2 otherwise:2 dm:2 stretcher:1 cm:2 point:1 simple:1 cb:5 granularity:1 corresponds:1 proton:9 coincidence:1 belyaev:1 deflected:1 polynomial:1 normalisation:3 kretzschmar:1 described:5 kinematic:1 acceptance:11 due:5 been:2 montecarlo:1 trigger:3 combined:1 basic:1 expected:3 ph:1 lett:7 direction:6 tr16:1 flight:1 carnahan:1 reaction:15 elsa:8 photon:18 cos:32 wires:1 angles:1 stems:2 c2:11 c1:2 c0:2 present:6 applied:2 multi:1 main:1 exponential:1 pacs:1 solid:1 value:1 will:2 receive:1 while:1 bochum:1 momentum:7 error:12 couplings:1 walther:1 schweizerischer:1 layer:3 uncertainty:5 ekin:1 deutsche:1 von:1 ir:1 thus:4 them:2 ii:1 currents:1 gwu:1 different:4 propagation:1 thesis:2 belong:1 radiation:1 cross:44 same:2 beside:1 reconstructed:3 strange:1 resulting:1 several:1 events:35 higher:2 con0:1 used:8 columbia:1 assigns:1 numerical:1 phd:1 barber:1 uni:1 lower:2 weakly:1 off:8 database:1 acknowledge:2 tains:1 well:2 kept:1 analysis:8 without:2 epj:1 components:1 simulated:3 gsi:1 model:2 consisted:1 reconstruction:5 background:15 less:2 photo:1 briscoe:1 assigned:1 sources:1 shape:1 ch:2 identify:1 thanks:1 scattering:2 yet:1 enters:1 majority:1 excites:1 character:1 fitting:1 isgur:1 signals:2 kinematically:1 spread:1 inner:6 samples:1 remaining:2 match:1 noether:1 radiator:2 couple:1 possible:1 dark:1 department:1 five:3 voigt:2 using:12 height:1 prominent:1 scaled:1 imposed:2 like:1 excluding:1 identifying:1 obvious:1 signal:8 lose:1 invaluable:1 emmy:1 clas:1 right:5 clusters:1 requested:1 sideband:2 some:3 dead:2 pπ:36 fibres:1 extended:1 pω:5 neglecting:1 matching:1 total:19 realistic:2 resonances:10 measurements:3 sfb:1 thank:1 per:1 mesons:3 does:1 exit:1 provides:1 prog:1 pee:2 umi:1 minimal:2 mode:1 tmin:13 disentangle:1 agreement:1 restrictive:1 step:1 comparison:3 about:1 pη:1 extension:1 constraint:1 http:1 dependence:1 o:5 simulation:3 compatible:2 de0:1 range:7 act:1 mean:2 peak:4 reactions:2 h2:2 into:8 within:2 numerically:1 three:6 phase:8 references:1 determine:3 proportional:1 ea2:1 uncertainties:1 statistics:1 institut:9 elastic:1 behaviour:1 assumed:1 support:3 there:5 yao:1 fast:2 width:2 conservation:1 editor:1 scintillating:1 forward:3 was:44 function:8 form:5 reduce:1 but:3 erlangen:1 larger:2 russian:1 ωx:1 characteristic:1 gießen:1 up:3 ur:6 crystal:5 below:10 physikalisches:3 fluctuations:1 distribution:8 similar:1 misidentification:3 expect:1 detailed:1 constant:2 worthwhile:1 abstract:1 contribute:3 ndof:1 single:2 simulations:2 ay:1 crystals:3 distributions:9 again:1 functions:1 compared:3 varga:1 no:4 eq:1 when:2 virtual:1 other:1 role:1 details:2 spatial:1 experimentalphysik:1 polar:1 nificant:1 excitation:2 models:2 time:2 a1:1 a0:1 foil:1 important:1 oring:2 fabry:1 suited:1 vectors:1 included:1 plessas:1 coupling:2 pion:1 dω:20 corresponding:1 typically:1 required:1 amsler:1 dσ:30 together:2 institutions:1 mass:14 electromagnetic:1 backward:2 resolution:6 |
0704.0711.txt |@word represent:3 miwa:1 gt:1 partial:1 switched:1 rev:23 truncated:1 results:21 wiringa:1 gx:1 four:3 scalar:5 ga:10 types:1 expressions:3 denotes:2 contributions:14 c1:32 row:2 relationships:1 increase:1 depend:2 graph:1 concerned:2 koike:1 tr:3 c6:1 tn:1 finally:1 tm:3 journal:1 those:9 th:2 include:4 presentation:1 worth:1 indicating:1 r1:1 summarizes:1 case:7 amplitudes:10 g2:5 straightforward:1 very:3 rise:6 account:1 wave:9 integration:1 crosses:1 putting:1 figs:4 jacob:2 han:1 vls:2 difference:2 coon:3 dominate:1 beginning:1 level:1 ref:10 notes:3 πnn:1 t2:1 t3:1 a671:1 ri:1 large:4 2np:3 vector:9 small:5 programme:2 jhep:1 smaller:3 force:3 broader:1 renormalized:2 dealing:1 consistent:1 coefficient:3 literature:2 sign:1 approximation:2 threshold:2 second:4 2fπ:5 value:9 realistic:1 further:3 dynamics:1 10q:1 odd:1 d4:2 quite:1 goes:1 residue:1 b01:1 gl:3 adds:1 sub:3 brackets:4 section:5 8m:2 labeled:1 expressed:1 d3:1 consistently:1 axial:1 version:5 3n:5 cheng:2 huber:1 new:12 net:1 compatible:1 dcd:2 nakamura:4 body:18 edited:1 full:4 ibid:1 exchange:10 multipole:2 respectively:10 component:3 here:5 ranges:2 mev:43 av18:28 making:1 represented:6 olsson:1 strong:2 equations:2 change:2 differential:1 obtained:4 instituto:1 leutwyler:5 receive:1 involved:2 study:2 larger:1 allows:2 amount:1 procedure:2 published:1 t21:6 t20:4 implement:1 fourier:2 changes:6 involves:5 a637:1 apr:1 vii:2 i31:2 replace:1 durham:1 decrease:1 machleidt:1 apply:1 write:2 seventeenth:1 propagators:3 cloud:3 derivatives:1 use:3 mb:2 would:2 covariant:3 positive:1 takahashi:2 contains:2 predictions:1 strauss:2 next:1 discrepancies:1 few:7 nucl:16 derivation:2 kinematics:2 therefore:2 qcd:2 taken:2 indistinguishable:1 themselves:1 assessment:1 theoretical:2 diagrams:14 more:8 encompassed:1 almost:2 extensive:1 door:1 definition:1 incident:2 becomes:5 operators:1 apparent:1 odinger:1 appendix:14 particular:2 known:2 ward:2 wt:1 iii:6 iτ:1 must:2 sample:1 keeping:1 works:1 ma:2 origins:1 tokyo:1 science:2 equation:6 work:6 reproduce:3 remain:1 values:11 mr:8 following:1 vt:3 modifies:1 intervene:1 example:1 def:2 numbers:1 νt:1 compare:5 figure:3 give:2 process:3 relativistic:5 permutations:2 organized:1 purposes:1 weinberg:6 pieces:1 involve:2 indicates:2 minimum:1 performed:1 arise:3 particles:1 higa:2 tan:3 counting:3 r23:9 occur:1 simple:2 dk:4 information:2 needs:4 argonne:2 end:1 rather:5 divided:2 six:2 gcm:12 4fπ:3 saito:1 kolck:6 mµ:8 how:1 b39:2 nakashima:2 fourth:1 dotted:4 b5:1 instead:1 parameter:2 divides:1 profile:4 alternative:2 c11:2 svarc:1 description:3 may:3 after:1 derived:5 confirmed:1 lab:10 treiman:3 diagram:4 consequence:3 wrong:2 produce:1 kambor:2 fe:2 coming:1 representations:1 horizontal:2 choice:1 data:9 fm:1 constants:5 status:1 short:1 dynamical:5 effective:4 ichihara:1 entem:1 sr:2 sp:1 lines:4 correspond:5 su:1 element:1 coelho:2 generic:1 hosono:1 so:4 allow:1 enter:1 representation:1 integrand:2 order:23 typical:1 unsolved:1 i23:2 words:1 nucleon:35 indeed:2 over:8 insight:1 vary:1 choose:1 years:2 produced:2 combinations:3 paper:3 through:1 thesis:1 tππ:3 japan:1 kinetic:1 still:2 its:4 tendency:1 before:1 shorter:1 derive:1 outer:1 decay:2 energies:2 procedures:1 masses:4 presence:1 τc:1 writing:1 forms:4 parts:2 degrees:1 fig:19 lecs:9 total:3 main:1 decades:1 h0:2 texas:1 eur:1 non:18 usa:1 cimento:2 combination:1 numerically:2 outlined:1 functional:1 framework:2 cutting:1 effects:15 they:9 das:1 front:1 schopper:1 now:1 discuss:3 association:1 2t:3 represents:3 february:1 hatanaka:1 dirac:1 2q:1 2m2:2 university:2 presented:1 b3:15 dominance:1 possibilities:1 applied:1 magnitude:5 2b:6 each:3 found:2 subset:3 reactions:1 square:4 ei:9 directly:4 series:4 energy:15 approximates:1 related:5 conventions:1 constitute:1 deficiency:1 owing:2 static:2 obtains:1 ez:3 loops:3 our:12 approximated:2 beyond:1 eq:20 tabulate:1 out:1 shown:10 matrix:6 space:8 gradient:2 restricted:1 nuovo:2 since:7 lagrangian:4 kondo:1 detailed:1 research:2 content:3 replacing:1 acting:4 dominated:2 recently:1 denoted:1 induced:2 evaluation:6 occurs:1 ockle:3 shows:1 rebuilding:1 working:2 theory:7 interactions:13 ısica:1 little:1 free:6 quark:1 reason:2 complicated:1 dx:1 intermediate:7 estimate:1 remainder:1 tudes:1 incorporates:1 interaction:8 retained:1 chiral:20 r2:2 r3:2 starts:1 transition:1 turn:1 ohler:6 cutoff:3 corrections:5 neglected:1 xij:1 first:3 opep:4 already:3 features:2 relate:1 variables:6 dab:2 number:3 restrict:1 simplified:3 adopted:1 another:2 epelbaum:1 xr:2 compensated:1 noticed:1 angular:3 given:18 perturbation:6 rewritten:2 become:3 introduction:5 leading:8 eqs:15 goldberger:2 πn:30 system:2 construct:1 1a:1 their:12 perturbations:1 dz:2 too:1 πt:11 normalization:1 rocha:1 structures:4 final:1 gives:9 exploring:1 a14:1 shell:5 calculations:13 relationship:2 b388:1 baryon:3 tool:1 took:1 amsterdam:1 uttiker:1 part:3 because:1 b21:1 schr:1 peccei:1 representing:1 than:6 coefficients:34 begins:4 determines:1 d02:1 roles:1 cyclic:2 was:5 distinguishes:1 tree:3 namely:7 states:3 classes:1 yang:1 assume:1 amplitude:20 were:4 land:1 denominators:1 powers:6 perturbative:3 lowest:1 pointed:1 ueno:1 explicit:2 dynamically:1 tornow:1 mind:1 curves:8 ππn:1 manipulating:1 elsevier:1 orders:3 relatively:1 strength:10 exploratory:1 depending:1 describe:1 latter:9 fettes:1 extracted:1 potential:34 absorbed:2 interconnection:1 forces:9 online:7 converged:1 require:1 channel:3 8m3:2 begin:5 ray:1 quote:1 iupap:1 involving:1 connected:1 rationale:1 possible:4 assessed:2 b307:1 class:3 stands:1 peaked:1 tpe:29 treats:2 discarding:1 calculated:4 adopt:1 vertices:1 tpv:2 iij:1 accounted:1 physics:2 3q:1 fact:2 oguri:1 precise:3 mckellar:1 v18:2 show:4 v12:3 lay:1 labels:1 scattered:1 least:1 fifty:1 purely:1 iǫ:1 relation:1 superimposed:1 rough:1 d5:1 d2:2 indicate:2 d1:1 xmn:2 based:7 quoted:2 parameters:8 implementation:1 writes:4 produces:2 outside:1 should:3 xi:4 bernard:1 only:12 explicitly:4 factor:9 chiyoda:1 employed:2 constant:3 truncation:2 local:16 interested:1 carolina:1 exchanged:1 do:3 mga:2 dominant:1 gev:1 means:5 displayed:5 de:4 db:4 preferred:1 da:3 pions:17 cannot:2 vss:3 longest:3 closely:3 taketani:2 tba:1 dw:2 dr:9 dq:19 dpv:4 processes:5 qr:16 bar:1 subamplitudes:4 conditions:2 arxiv:1 expansions:3 state:4 yield:5 bab:2 contain:2 including:1 valid:2 view:1 deuteron:12 becher:4 set:4 reference:2 achieved:1 iteration:1 sensitivity:1 a426:1 blend:1 maximum:1 sainio:2 collectively:1 depends:5 individual:1 w3:2 result:4 integrating:1 close:2 momenta:8 3c3:1 subject:1 brazil:4 appear:4 learns:2 tensor:4 nuclear:8 blatt:1 leg:1 dmr:3 label:1 symmetric:1 written:5 determined:5 various:1 chosen:1 between:5 conceptual:1 progress:1 problems:2 approach:2 x23:20 available:3 wf:8 terms:27 reproduced:2 extend:1 tables:1 emitted:1 however:2 ascribed:1 reproduces:2 concentrate:4 δab:1 group:1 configuration:5 barrett:1 both:19 essentially:1 last:3 borges:1 brown:1 many:1 c5:2 hence:1 agree:1 dipole:2 subthreshold:14 figures:1 dated:1 receives:1 contribution:8 expression:1 finds:3 experimental:7 among:2 ci:2 relevant:2 a625:1 cm:1 point:3 color:7 lagrangians:4 ga4:8 corresponds:8 proton:7 pole:3 sakai:1 iterations:1 x31:21 cs:3 proved:1 fruitful:1 k2:3 pr:3 kernels:2 described:3 acts:2 addition:1 due:8 been:7 bornstein:1 reduction:1 describes:1 basic:4 expected:1 meissner:4 ph:1 pi:1 estimated:2 systems:1 remedies:1 schiavilla:1 relations:2 corresponding:1 subamplitude:1 observable:2 quantities:1 designed:1 bmr:3 jacobi:1 c9:1 c8:1 external:1 systematic:1 c3:30 c2:27 mandelstam:2 denote:2 spin:1 former:10 present:9 c4:10 p2:9 p3:9 p0:1 p1:9 r31:6 pacs:1 solid:5 empirical:6 evaluated:2 remaining:1 employ:1 b00:1 while:2 investigating:1 designate:1 loop:11 3nf:1 layer:1 vc:2 vd:3 2fπ2:8 binding:8 vi:2 overlooked:1 thus:1 them:1 discrepancy:2 iv:4 ii:7 vq:1 ik:1 ij:2 rij:1 3np:41 tpep:7 ic:1 pseudovector:1 technology:1 gradients:4 different:2 robilotta:7 d10:2 d11:1 lengths:2 make:1 belong:2 reminded:1 cross:2 same:4 paulo:2 complex:2 split:1 unfortunate:1 gasser:2 c7:2 limitation:1 dimensionless:2 defines:1 neutron:2 higher:1 development:1 independent:1 calculation:10 used:12 see:2 maeda:2 comprehensive:1 numerical:9 effect:4 hand:7 action:1 v3:8 uses:5 purpose:2 potentials:2 attractive:5 ord:3 adopting:2 identity:1 prescribed:1 t22:4 off:6 center:2 analyzing:8 older:1 nevertheless:1 makes:1 well:4 santos:1 double:1 contact:1 solve:1 components:5 consistency:2 coordinate:1 position:1 model:2 polynomial:2 usual:3 neighborhood:1 understood:2 background:1 just:7 less:1 being:3 generally:1 λx:11 puzzle:1 reviewed:1 sources:1 transforms:1 tilde:1 cp:5 flavor:1 scattering:20 compared:1 previous:3 it11:7 4m2:1 cut:2 dqr:2 conclusions:2 chpt:2 character:1 except:2 source:1 internal:1 treatment:1 misprint:1 weise:1 input:2 iσ:1 c10:2 sin:2 transformation:1 momentum:4 take:1 identical:1 yukawa:2 around:2 demands:1 read:6 decomposed:1 term:15 ga2:34 test:1 environments:1 appendices:1 using:6 insert:1 2r:1 3ga2:1 systematically:1 follows:3 qualitative:1 performing:2 yields:6 either:5 integrals:3 bpv:4 spinor:1 friar:3 nucleons:8 b101:1 traced:1 old:1 a19:1 sequence:1 existing:1 some:4 back:1 b4:1 born:4 b6:1 pρ:3 olt:1 b1:1 choosing:1 table:15 proper:3 a11:1 neglecting:1 ourselves:1 matsuoka:1 happens:1 fπ:9 vol:1 scale:1 describing:4 2e:3 affects:1 avoid:1 quarks:1 2c1:1 cast:1 does:3 decomposition:1 prog:1 deg:12 propagating:4 proc:1 µx:1 conference:1 faddeev:2 power:6 dropped:1 drift:1 equivalent:2 conventional:2 expansion:10 bw:2 br:36 2m:11 pv:2 stoks:1 properties:1 earlier:2 stage:1 comparison:1 about:6 kinematical:5 central:1 carried:2 extension:2 constraint:1 freedom:1 discussed:4 dependence:3 o:112 melbourne:1 sake:2 range:11 a2:11 plus:3 kaiser:3 act:3 slightly:1 automatically:1 s61:1 triton:6 heavy:3 approximations:1 a7:1 inclusion:2 previously:1 into:14 within:4 integral:4 bound:3 three:24 accommodate:1 variable:4 appropriate:1 en:8 accounts:1 tiny:1 operator:5 proportional:8 exchanges:4 nowadays:1 approximately:1 a16:1 a3:1 uncertainties:1 rely:1 van:6 elastic:5 comparing:2 there:4 u1:11 transform:1 long:3 u2:22 dispersion:1 conservation:1 low:4 ed:3 forward:2 sections:3 third:1 function:14 considerably:1 medium:5 north:1 form:16 a9:1 m2:10 denoting:1 but:3 tucson:1 construction:1 aµ:1 d01:2 line:2 a1:2 especially:1 nishimori:1 made:1 tomozawa:5 versions:1 smooth:1 up:8 international:1 considered:3 below:1 limit:1 minor:1 refs:2 codes:1 isospin:3 problem:4 similar:1 display:1 strongly:1 bearing:1 later:1 associated:17 b2:1 defined:1 curve:6 abstract:1 contribute:4 influence:4 ao:2 general:2 single:3 arises:1 initial:2 scadron:1 numerators:1 formulation:1 ay:5 imai:1 encompass:1 moves:1 universidade:1 sasaki:2 physical:2 functions:16 dashen:2 syst:4 nn:6 feynman:3 amounts:2 dashed:8 whereas:9 when:8 detail:1 virtual:2 rewriting:1 field:1 other:10 role:1 better:1 department:1 theor:1 shimizu:3 ishikawa:5 a15:1 picture:2 a17:1 elements:1 kinds:1 a10:1 a13:1 a12:1 symbol:1 vertex:2 a18:1 polynomials:3 includes:2 qρ:22 generated:1 important:2 a5:1 a4:1 suited:1 a6:1 included:2 a8:1 structure:4 evaluates:1 ago:2 fπ4:15 correlated:1 implies:1 coupling:9 pion:19 fπ2:21 bcd:2 typically:1 factors:6 pseudo:1 dρ:4 multipion:1 4m:4 mass:10 time:1 far:2 observables:11 requires:4 lett:8 once:1 |
0704.0712.txt |@word limited:1 dewitt:2 sci:1 consider:6 maximum:2 caused:2 madsen:7 dynamic:1 results:3 kernphysik:1 existing:1 leads:3 eds:1 mp0:2 invariably:1 intricate:1 mason:1 contributions:14 centers:8 causes:1 rigidity:1 whose:1 certainly:1 depend:6 calculate:3 fellowship:1 experimentally:1 finally:2 monotonically:1 those:2 ti:1 lin:2 integration:1 cm2:1 p2:6 amplitudes:6 epin:1 straightforward:2 very:9 wave:9 paulus:3 electron:34 orientations:2 calegari:1 application:1 iup:3 difference:3 entire:3 dominate:1 obvious:2 vibrational:3 presented:2 opt:2 evaluation:2 guo:1 solution:3 leave:1 affect:1 small:2 becker:15 refer:1 inspection:2 upper:3 strongly:3 employing:6 lewenstein:3 sin2:1 direct:18 pulse:2 approximation:5 consists:1 zero:7 street:1 plenum:1 enhancement:2 equal:1 further:2 odd:1 substitute:1 goes:1 even:4 will:13 what:1 sub:1 deeply:1 sum:3 while:4 expressed:2 d3:2 experiment:1 lein:7 reconstruction:2 new:3 increasing:5 method:8 filled:1 satisfy:1 full:1 led:1 behavior:3 ibid:3 exchange:7 respectively:4 modify:1 orbitals:5 hundreds:1 ionization:26 iωτ:1 separation:10 exponent:1 active:1 strong:5 directions:1 κr:2 rescattered:5 obtained:2 antisymmetric:1 colored:1 shift:3 leaves:1 studied:1 allows:4 experience:1 ignoring:1 amount:1 resulting:3 action:1 proportionality:1 chang:1 spacetime:1 plotted:2 via:1 followed:1 figure:2 integrations:1 baier:1 highly:1 logarithmic:2 visible:4 addressed:1 decrease:2 apply:1 counts:1 total:3 planck:1 linearly:4 use:2 proceed:1 would:1 sake:1 ψp:1 contains:1 next:3 scenarios:7 few:2 therefore:4 taken:4 themselves:1 symmetrical:1 more:7 introducing:1 formally:1 highorder:1 ejected:2 binding:6 odinger:2 refrain:1 berlin:2 schrdinger:1 controlling:1 particular:4 known:2 cases:3 aligned:11 iii:6 states:1 account:1 context:1 defines:1 permits:1 science:2 equation:5 worth:1 remain:1 values:2 mp:44 starts:1 already:1 chin:1 hansen:1 ions:1 compare:1 indicated:1 stated:1 expanding:2 sense:1 organized:1 respective:2 high:11 slit:2 minimum:2 hhg:4 council:1 past:1 sharp:2 distinguishable:1 occur:1 axis:5 motion:1 regularization:1 united:1 end:1 advantage:1 validity:1 provide:3 comparing:1 discussion:4 acts:1 feature:3 photoelectrons:1 regions:3 how:3 topographical:1 adjacent:2 answer:1 portional:1 parameter:1 sin:5 simplicity:1 magnitudes:1 information:1 may:12 max:4 requires:1 after:1 orbits:2 applications:1 collins:1 coming:1 summarize:1 destructive:6 parallel:11 changes:2 short:1 attempt:1 anymore:1 four:3 computations:1 recombination:3 spectra:23 lines:6 correspond:2 kulander:1 element:9 rather:1 accelerated:2 cannot:1 negligible:2 allow:1 lα:3 sc:1 subsequently:1 imply:1 order:10 typical:1 ito:1 holds:1 interpretation:1 closely:1 wc1e:1 indeed:1 over:7 move:1 displayed:2 years:1 produced:1 jetp:2 experiments:2 london:2 looks:1 thesis:1 left:1 existence:2 kinetic:1 suffer:1 agrees:1 its:4 before:5 exhibits:2 strikingly:1 thank:1 chosen:2 extract:1 coordinates:1 recombines:1 detected:1 microscopic:1 harmonics:1 marangos:7 hidden:1 main:2 alter:1 rayner:1 maximal:1 acknowledgments:1 return:1 combination:5 was:3 numerically:1 ωr2:1 evolution:2 number:1 framework:1 figueira:2 effects:4 they:9 now:1 yu:3 transparent:1 nor:1 structural:1 easily:1 february:1 finite:1 2p:2 always:1 university:1 drop:1 arrows:4 identified:1 possibilities:1 2f:3 magnitude:1 2a:1 positions:2 2l:6 2n:1 simplification:1 side:1 baker:1 individually:1 ei:4 another:1 map:1 generation:4 energy:29 displacement:1 related:3 applicable:1 frequency:2 obtains:1 measurement:1 quantum:2 our:5 ev:1 eq:12 ep:1 out:2 rt:3 large:1 shown:3 saenz:1 opened:1 space:1 gradient:1 restricted:1 furthermore:2 since:8 interference:44 denotes:2 looking:1 maran:1 conclusions:1 assignment:1 term:8 formula:4 induced:2 ref:8 ri:1 gos:1 shows:3 torres:1 8i:1 linear:1 mciver:1 carr:1 mechanisms:1 differ:1 quite:2 complicated:2 imaging:1 besides:1 put:1 ridge:1 robinson:1 kleber:3 e0:16 incorporates:1 interaction:2 indent:1 r1:4 r2:6 determining:2 could:3 transition:11 positioning:1 used:2 ati:23 counterpart:1 turn:1 place:2 incorporated:2 consequence:1 facilitate:1 eqs:5 first:5 origin:2 simplifies:1 features:1 symmetry:3 reflected:1 reaches:2 restrict:1 smaller:1 long:2 directly:1 knight:3 reached:1 angular:1 given:12 introduction:1 leading:1 interact:2 tosa:1 system:2 least:1 their:6 conservation:1 rates:1 too:1 miloˇsevi:6 molecular:21 structures:1 final:4 humboldt:1 originating:2 way:2 polyatomic:1 relative:1 keldysh:2 terent:1 released:1 larger:1 manifestation:1 injected:1 off:15 than:3 specify:1 distance:21 polarized:4 coherently:1 double:2 require:1 arb:5 rescatter:4 exponents:1 matter:1 absence:1 inter:1 doubly:1 str:1 smirnova:1 identical:3 intramolecular:1 result:3 exhibit:4 lowest:1 fashion:1 false:1 separations:1 pro:1 radial:1 spectrum:21 sae:1 roughly:4 zu:1 occupied:1 clearly:2 viewed:1 reiss:2 depict:2 angle:20 patterns:15 studying:1 latter:3 responsible:1 able:1 overcoming:1 polarization:22 instance:1 emphasis:1 causing:1 take:2 online:8 so:10 detector:4 computation:1 schomerus:1 spectral:1 play:1 towards:1 unless:2 opposite:2 track:1 molecule:40 systems:1 wells:2 most:2 involving:1 germany:2 significant:3 phase:1 measured:1 why:1 uk:1 sfa:7 sali:1 lee:2 cause:4 give:2 especially:3 radiating:1 sansone:2 considered:1 neighboring:1 clear:3 later:1 inferred:1 face:1 proceedings:1 electrons:26 exp:4 pattern:2 velocity:2 prefactor:3 physics:2 section:1 fact:5 levesque:1 tron:1 intensity:2 show:5 detection:2 recipe:2 goll:1 infrared:1 purely:1 gauge:2 threshold:4 substituting:1 fine:1 debate:1 ground:4 boundaries:1 parameters:7 much:2 jar:1 outside:1 balcou:1 only:5 molecules:6 factor:11 employed:4 adequate:1 local:1 muth:2 ruiz:1 do:6 dominant:1 above:5 means:1 dependent:7 de:3 overall:6 analyzes:1 ionized:3 words:1 distinctly:2 dt:5 neither:1 becomes:3 areas:1 reveal:1 processes:11 volkov:3 continuum:3 fields:3 arxiv:1 expansions:1 faisal:6 yield:11 consisting:2 influenced:1 investigate:2 paper:4 cf:2 predicted:1 villeneuve:6 analytical:2 through:2 obscure:2 fixed:2 gibson:1 monochromatic:1 computed:1 exists:1 smooth:1 packet:1 up:23 observed:8 see:9 individual:4 college:1 tomographic:1 enhanced:2 corkum:8 discussions:1 close:1 uncorrelated:1 analog:1 techniques:1 eres:1 phases:1 still:2 interacting:1 intersecting:1 nuclear:2 away:1 nature:4 teng:1 huillier:1 symmetric:5 state:9 various:4 inset:1 between:10 consecutive:1 boundary:13 reading:1 conditions:1 wide:1 sciences:1 multiplied:1 notice:1 terms:13 amplitude:13 parent:2 missing:1 initially:1 emitted:7 weak:1 however:14 interfere:1 jl:5 efficiency:2 york:1 here:3 multiplies:1 probing:1 modeling:1 configuration:1 come:1 distribution:3 suggested:1 both:8 cos:18 instant:1 universit:1 region:8 density:1 hence:4 agree:1 energies:7 und:1 dated:1 exceptionally:1 contribution:2 whole:1 schafer:1 comes:1 otherwise:1 minima:9 ci:3 relevant:2 tong:2 point:3 color:9 overview:1 each:2 period:3 blurring:2 dimensional:1 analyzed:2 simply:1 decreases:3 middle:2 article:1 constructively:3 respect:10 throughout:3 pr:1 sine:1 described:5 hay:2 addition:1 suppressed:1 due:3 been:8 mark:3 describes:3 change:1 certain:1 expected:1 ph:2 fig:26 imal:1 generating:1 arises:1 corresponding:2 observable:1 quantities:2 sufficient:1 kanai:1 essentially:1 krause:1 observe:2 determination:2 external:2 angles:3 c2:7 c1:7 denote:2 present:3 case:31 eip:1 exception:1 laser:50 exponential:1 sakai:1 solid:2 poletto:1 engineering:1 value:1 remaining:2 employ:2 near:7 replaced:2 evaluating:1 exist:2 valleys:2 tunneling:2 taking:1 walther:3 a20:1 real:4 vectors:1 orientation:7 kienberger:1 almost:2 ip:1 refs:1 lohr:2 thus:1 iv:2 ii:3 characterize:1 reads:1 ij:1 bauer:1 2up:2 ric:1 trusted:1 increased:1 orbital:1 different:11 formalism:1 multiphoton:1 grant:1 perform:1 radiation:1 expect:1 same:16 any:4 complex:1 split:1 units:11 figures:1 dimensionless:1 several:2 shan:1 infer:3 higher:2 independent:2 dooley:1 iβ:3 rescattering:14 comprehensive:1 numerical:3 upon:3 effect:3 optik:1 hand:1 driven:1 ion:3 morisson:2 anscombe:1 purpose:2 potentials:2 infinite:2 cycle:2 mentioning:1 lower:2 elec:1 schr:2 center:32 scenario:1 largely:1 makes:1 well:6 kept:1 analysis:3 concrete:1 without:1 diatomic:12 position:1 model:5 recombine:1 possesses:1 figs:7 maxima:6 distances:6 sec:8 zhao:2 enormously:1 just:3 cj:1 generally:2 mol:1 obtain:2 sources:1 shape:1 underlying:1 identify:1 atomic:15 actually:1 integer:2 regardless:1 momenta:1 scattering:2 alignment:5 previous:1 adv:1 cut:3 dissociation:1 vibration:2 smith:1 except:2 discuss:2 internuclear:34 simple:2 add:3 potential:23 plateau:8 relevance:1 situation:1 mod:1 heidelberg:1 momentum:7 details:2 resolved:15 aspects:1 around:3 depends:2 iα:1 6bt:1 possible:1 l89:1 harmonic:6 vibrations:1 sanpera:1 spanner:1 using:1 advanced:1 apart:1 loss:2 necessary:1 like:7 semi:1 follows:1 reduces:1 popov:1 immediately:1 specific:3 yields:2 either:1 integrals:6 arbitrary:1 analyzing:1 log10:5 signal:1 imprints:1 accessible:1 nisoli:2 right:2 wavepackets:1 classical:14 phenomena:3 back:1 born:5 equivalent:1 examples:2 table:2 proper:1 neglecting:1 ourselves:1 nonzero:1 separately:1 scale:5 recently:1 zhou:1 lead:1 bottom:2 contributing:1 lend:1 bandrauk:3 extensively:1 overlap:1 contrast:1 does:7 expressing:1 assuming:1 allowing:1 bessel:3 freed:2 measuring:1 conference:1 reaching:1 reach:1 attosecond:2 photoelectron:3 oscillating:1 perpendicular:6 illustration:1 constructive:1 step:1 nowhere:1 shapes:1 plots:1 intense:1 panel:3 gained:1 comparison:7 about:1 δe:9 carried:1 saddle:2 discussed:5 dependence:5 o:1 distinct:1 range:10 theory:1 mccann:1 act:2 eight:1 financial:1 consequently:1 ivanov:5 peak:1 perelomov:1 cutoff:8 raised:1 rev:44 presence:4 owe:1 into:6 within:6 integral:3 bound:3 kjeldsen:3 down:1 useful:1 because:1 determine:4 sov:1 operator:2 proportional:2 prefactors:2 methods:2 kieffer:1 institut:2 additional:1 classically:1 support:1 there:7 question:2 specifically:5 start:1 cosine:7 low:1 fraction:1 telnov:1 subsequent:1 wunner:1 faria:2 chu:3 function:15 complete:4 form:3 dips:2 differences:4 jun:1 but:3 hu:1 corso:1 v0:8 gain:1 atom:17 highest:1 true:1 considerable:1 piraux:1 absent:1 compute:2 understood:2 characteristic:3 ponderomotive:3 ωt:1 ur:2 below:2 owing:1 limit:2 sapphire:1 problem:3 panels:3 similar:1 calculated:3 shih:1 precedes:1 detailed:3 ohm:2 enlargement:3 ae:1 li:1 defined:2 diffraction:2 geometrical:2 describe:1 influence:2 direction:14 general:4 single:10 kingdom:1 research:1 lcao:1 moves:1 distributions:1 internal:1 interferences:1 physical:6 area:1 functions:2 compared:2 ideally:1 no:3 dashed:2 whereas:2 when:6 detail:2 reality:3 field:37 zeidler:1 other:11 role:3 angstrom:1 spatial:1 department:1 picture:3 elements:4 superposition:1 saupfercheckweg:1 pronounced:1 geometrically:1 emission:4 a0:1 generated:1 important:1 pathways:3 suppression:1 included:1 fermi:1 astronomy:1 gower:1 structure:9 matrix:13 jones:2 constant:2 benedetti:1 implies:1 longer:2 practically:1 starting:1 dτ:5 factors:1 curve:1 orbit:2 together:1 scrinzi:1 perpendicularly:2 presenting:1 time:10 resolution:3 lett:10 once:1 |
0704.0713.txt |@word secondly:1 monte:15 extrapolated:4 gq:10 magnetic:1 results:12 concept:1 expressions:1 farhi:1 simon:2 calculate:2 zone:3 description:1 nonlocal:1 th:1 analogous:2 case:4 returned:1 far:1 wave:1 every:1 updates:2 exact:3 34e:1 presented:3 evertz:1 evaluation:3 nucl:1 list:1 applicable:1 discrete:1 vector:1 anal:1 reliable:1 configurations:3 upper:3 smaller:2 ten:1 consistent:1 direct:1 10e:1 second:1 value:7 rigorous:1 zu:1 carlo:15 b39:1 even:2 3z:1 errors:6 64e:1 stands:1 43e:1 sandvik:1 above:3 new:4 method:5 contrast:1 3d:2 coefficient:3 27e:1 neves:1 modify:1 equals:2 here:3 behaviour:1 ansatz:2 change:1 obtained:6 jord:1 shift:1 study:2 studied:1 contradiction:1 leaving:1 periodic:2 procedure:1 usually:1 chain:5 fourier:2 studies:1 involves:1 halperin:1 useful:1 slices:1 apr:1 s03:5 private:1 highly:1 lanczos:1 unit:1 wealth:1 prove:2 remains:1 positive:2 tasaki:1 next:1 mqi:2 depicted:1 therefore:4 m2:6 taken:1 type:2 bethe:2 today:1 more:2 introducing:2 s0z:1 constructs:1 appendix:4 particular:2 iii:4 must:1 account:2 mc:1 integrating:5 6d:1 work:3 85e:1 values:3 temperatures:5 following:5 my:1 proof:3 nearest:1 wang:1 give:2 calculation:1 sense:1 high:4 minimum:1 numbers:1 allowed:1 absolute:2 information:1 goal:1 very:1 opposite:1 parameter:2 sato:1 map:1 mat:3 thermodynamic:1 after:1 derived:1 mapping:1 expectation:2 corrections:5 produce:1 physik:1 data:15 umper:1 sy:1 sx:1 whenever:1 sq:2 extrapolation:3 so:2 allow:2 enter:1 ohmann:1 order:29 02e:1 ulam:1 indebted:1 over:9 move:1 displayed:1 satisfied:1 years:1 produced:1 paper:3 through:1 statistical:6 existence:10 still:2 its:1 derive:1 affleck:2 fit:1 how:1 energies:2 bringing:1 37e:1 systems:5 defining:1 into:2 eventually:1 return:1 combination:1 numerically:3 functional:2 effects:4 they:2 now:1 09e:1 february:1 finite:19 shiroishi:1 2e:1 inequality:6 crossing:6 06e:1 universit:1 side:2 referred:1 square:4 fq:8 generation:1 energy:9 hard:1 idea:2 numeric:1 40e:1 entering:1 changed:1 quantum:16 our:3 eq:17 out:1 shown:5 nonlinear:1 quality:1 since:4 rev:9 attracted:1 ref:9 integrated:1 math:2 shows:2 theory:1 39e:1 found:2 possibility:1 completely:2 analogon:1 estimate:1 e0:12 forbids:1 longrange:1 interaction:1 derivation:1 times:1 length:3 07e:1 incorporated:1 consequence:1 onto:1 first:3 sanchez:2 major:1 there:2 finiteness:1 number:4 theoretische:1 set:1 done:2 relations:1 directly:1 impossible:1 ulpicher:1 open:2 size:10 given:6 temperature:14 needed:2 system:9 construct:2 their:1 variational:1 final:1 beard:1 continuous:1 short:5 authors:1 x2:1 eliminated:1 45e:1 distance:7 showed:1 require:1 zero:2 determined:2 str:1 were:5 tion:1 seminal:1 lowest:1 developement:1 correction:3 modern:2 curves:1 substantial:1 need:1 clearly:1 issue:2 mermin:1 intends:1 internal:2 algorithms:5 accuracy:1 heisenberg:15 towards:1 fundamental:1 though:3 correlation:8 most:1 boltzmann:1 involving:1 germany:1 shastry:5 remarks:1 concerning:2 exponent:1 calculated:2 trotter:4 kl:1 wiese:1 part:1 sigma:1 400e:2 fitted:1 show:6 random:1 relation:1 hohenberg:1 subtle:1 d2:4 decade:1 ground:12 q1:1 41e:1 q2:1 e10:3 than:3 analytic:1 only:3 factor:1 do:3 his:1 notation:1 means:4 dd:2 overall:2 straightforwardly:1 cannot:3 brillouin:3 takahashi:2 continuum:1 conditions:2 arxiv:1 qi:3 ysis:1 approximations:1 multiplying:3 exists:3 violated:4 correlations:11 bounds:2 see:3 decided:1 w1:1 best:2 techniques:2 inequalities:4 definite:1 sites:5 state:12 crude:1 boundary:2 approach:1 attention:1 however:3 03e:1 comm:1 key:1 configuration:2 both:1 cos:11 last:1 2n:2 taking:2 fulfilled:1 ln:1 became:1 streams:1 dated:1 mean:1 whole:2 finds:2 otherwise:1 comment:1 relevant:1 point:3 had:3 corresponds:1 dimensional:10 63e:2 iterations:1 46e:1 sees:2 source:1 locally:1 due:3 been:1 combined:1 interest:2 prototype:1 ann:1 fig:2 direction:2 controlled:1 observable:2 sufficient:3 precision:5 neighbour:1 astron:1 spin:12 present:1 applied:1 73e:1 might:1 siggia:2 swendsen:1 evaluated:2 will:1 evaluating:1 error:6 situation:1 introductory:1 loop:3 seven:1 larger:3 00e:1 almost:2 drawbacks:1 thus:3 site:3 ii:4 reads:1 cond:2 perez:1 xy:1 different:2 make:1 cross:1 same:1 any:3 arguments:2 lana:1 several:1 independent:6 used:4 velasco:2 numerical:3 effect:5 hand:2 mq1:2 kubo:1 mq2:2 uses:1 infinite:4 lower:2 mech:1 oguchi:1 acknowledgement:1 onedimensional:1 well:3 analysis:3 s23:1 without:1 firstly:1 model:18 87e:1 dimension:3 distances:7 26a:1 26e:1 being:1 accurate:2 wagner:1 obtain:1 marcu:1 67e:1 coordination:1 53e:1 candidate:1 conclusions:1 extra:2 seems:2 improvement:1 lattice:7 falsely:1 lett:4 theorem:1 input:1 evaluate:1 b56:1 possible:3 21e:1 destroy:1 using:7 kennedy:6 fernando:1 eel:19 arbitrary:1 become:1 gutmann:1 right:2 neumann:1 classical:2 04e:1 stat:3 oln:2 added:1 sight:1 table:6 babujian:1 30e:1 nonzero:2 gross:2 euclidian:1 lead:1 sufficiently:1 shall:1 per:1 84e:1 magnitude:1 prof:1 chains:2 s13:1 δi:1 outreach:1 bt:1 step:2 nmc:1 b215:1 served:1 properties:2 comparison:4 actual:1 commun:1 dependence:3 o:1 range:4 sx3:2 introduced:1 lieb:9 orders:1 communication:1 dyson:2 integral:2 bound:12 three:1 assess:2 appropriate:2 en:1 methods:3 uncertainties:1 hep:1 twodimensional:2 question:1 transform:2 long:5 intention:1 low:5 was:11 suzuki:1 function:7 form:1 but:3 construction:1 delta:3 compute:2 iqx:2 evident:1 ute:1 whether:1 antiferromagnetic:5 up:4 us:1 discretized:1 below:1 fysik:1 limit:4 autocorrelation:1 demonstrate:1 problem:2 similar:1 called:1 originating:1 later:2 proved:3 defined:1 certain:2 am:1 6b:1 ao:1 proves:1 corresponding:1 again:5 functions:3 compared:5 puzzling:1 no:4 when:1 valid:1 spatial:1 deviate:1 conclusion:1 conclude:1 draw:1 models:3 update:1 hulth:1 important:2 15e:1 dimensions:1 arkiv:1 algorithm:4 carrying:1 weights:1 nelson:1 time:6 inaccuracy:1 n1:1 n3:1 starting:2 |
0704.0714.txt |@word secondly:1 dist:1 consider:6 remarkable:1 funct:1 ale:2 results:1 perelman:19 leads:1 scalar:22 proposition:19 entropy:2 asian:1 kato:3 ric:17 follow:1 gk:90 gj:1 gi:3 gh:4 compact:23 whose:2 isometric:1 technique:2 nakajima:1 finally:2 tk:59 elliptic:3 ti:5 norm:2 ta:4 applied:1 conjecture:1 zhang:27 very:1 continues:1 keeping:1 choice:2 corollary:1 witten:15 every:5 invent:4 rm:30 ui:1 difference:1 four:3 distg:6 irreducible:5 notes:2 solution:26 t1:3 large:6 differential:1 recall:1 small:5 eigenvalues:1 anal:2 rk:1 der:1 upper:2 smaller:2 neighborhood:1 zi:8 orbifolds:8 sesum:2 edu:1 estimates:4 mostow:1 modified:1 le1:2 le2:3 le3:3 infimum:1 canonical:2 index:1 iterating:1 ail:2 section:9 celebrated:2 uniform:3 3j:1 version:1 above:11 capital:3 obvious:2 contributes:1 cn:1 completion:1 simultaneously:1 ǫu:1 respectively:4 component:1 equals:1 here:2 desired:2 china:5 address:1 along:5 quite:1 equations:8 z1:1 change:2 obtained:1 tian:7 remark:2 rdv:1 tki:1 institute:1 study:3 studied:1 contradiction:4 ǫr:1 studies:1 sci:1 boundedness:2 volg:39 useful:3 divide:1 family:2 bounds:3 apr:1 jm0:11 modifying:1 4πc2:1 clifford:1 use:3 asymptotic:2 prove:11 positive:10 bundles:3 negative:2 next:1 almost:2 call:1 therefore:12 bochner:2 means:1 calc:1 type:2 more:1 flat:4 kε:2 comparison:2 initial:3 under:2 curvature:51 berlin:1 everywhere:3 normalized:25 particular:3 known:2 cases:1 hold:1 rδ:2 springer:1 balls:5 science:1 equation:13 work:3 regularity:1 mk:12 2c21:1 assumptions:2 values:1 following:10 degeneration:1 could:1 proof:29 claim:8 theorems:1 wang:1 give:3 process:1 ann:1 contradicts:1 minimum:1 numbers:1 want:1 sense:15 rescaling:3 verlag:1 normalize:1 counting:1 end:1 lemma:46 thing:1 verify:1 discussion:2 holds:4 kronheimer:1 conm:1 functionals:2 pure:2 instead:2 4k:13 simplicity:1 singular:7 may:7 suppose:1 fz:5 after:4 derived:2 them:1 fa:21 levi:3 multiplication:1 fi:3 fj:6 fk:6 parallel:1 constants:10 natural:1 sobolev:1 whenever:12 lemmas:3 chern:13 lines:1 element:1 diffeomorphism:1 so:18 decreasing:2 sc:7 cs4:1 cheeger:7 order:1 se:7 developed:1 pointed:6 paper:4 satisfies:6 its:3 before:2 orbifold:25 group:2 ln:1 4manifold:2 fix:1 solving:1 li:1 forms:5 ǫ2k:1 parts:3 choose:4 mail:1 main:4 easier:2 maximal:2 non:14 ye:2 functional:4 scaling:2 hamilton:5 optimal:1 now:11 possess:1 eigenvalue:3 several:1 dirac:2 2r:10 invariants:2 university:3 sufficiently:5 inequality:7 l2:12 each:15 found:1 2n:9 2k:33 subset:5 spinor:2 weyl:2 colding:1 ek:10 ergebnisse:1 society:1 ball:6 sectional:2 our:3 beyond:1 extract:1 out:2 rt:2 100n:1 space:16 gradient:1 res:3 furthermore:8 since:19 denotes:5 obstructions:1 acting:2 rg:6 geom:5 longtime:4 denoted:1 formula:14 induced:5 rh:6 occurs:1 math:22 shows:3 foundation:1 gromov:7 earlier:1 theory:3 fzz:5 given:2 standard:3 admits:2 completely:1 base:1 york:1 estimate:4 hand:1 r4:2 definition:5 pairs:1 qj:1 r0:8 r1:9 applications:3 geometry:1 collapsing:2 re1:1 times:4 ahler:22 american:1 maximality:1 signature:7 hence:12 suffice:2 first:11 xj:26 xk:10 xi:1 xm:10 number:6 rank:3 bonnet:8 another:2 open:1 lebrun:5 differ:1 ian:1 rmt:7 hyperbolic:4 introduction:1 least:5 their:1 assumption:4 seiberg:14 essays:1 inserting:1 kot:2 gives:1 grant:1 exactly:1 akutagawa:1 part:17 authors:1 norms:1 x0:10 x1:12 representing:1 than:4 finitely:6 distance:2 showed:2 zero:2 limiting:3 project:1 injectivity:1 subsequence:17 stw:2 negatively:1 rǫ:1 function:2 bhk:2 false:1 generality:1 ishida:1 argument:8 say:5 need:1 seek:1 any:36 extremal:1 jour:1 min:1 lim:48 self:16 isolated:7 converges:10 note:19 k1:1 k0:9 take:1 analogy:3 croke:1 normal:3 sequence:17 metrics:12 most:4 regular:12 but:6 plenty:1 an3:4 reducible:1 class:15 inequalities:1 kg:1 average:4 adopt:1 curvatures:4 dimension:8 ks:4 points:30 uniqueness:1 calculates:1 bzi:1 saying:2 show:4 supported:1 converge:6 ki:23 radii:3 spaces:1 solutions:26 civita:3 analogue:2 pki:1 trivial:1 q1:1 cr4:1 rict:6 assertion:1 rico:11 only:12 going:1 factor:2 constant:38 local:7 preliminaries:1 do:2 over:1 pde:1 get:14 dependent:2 dg:7 sup:3 da:4 new:1 dv:15 dt:4 vergence:1 evolution:5 covering:2 2ric:2 arxiv:7 assuming:2 taubes:4 qi:20 qk:36 fixed:6 ql:2 riemannian:18 moduli:1 set:7 exists:14 ricci:72 calabi:1 j1:11 maximum:16 connections:1 see:4 radius:6 result:13 rmk:3 surgery:2 violates:1 dahl:1 satisfying:14 tensor:7 fang:14 consequence:1 lott:1 state:1 classes:1 closed:8 invariant:10 geometric:3 approach:2 yamabe:3 compliment:1 wg:6 ends:1 embeddings:1 besse:1 weak:3 however:1 js:3 vanishing:1 hypothesis:3 key:3 amer:3 tensors:1 3cr:1 both:5 c21:16 last:2 many:6 taking:2 equal:1 chosen:1 admit:1 pl:2 symplectic:9 embedding:3 comm:1 passing:11 estimation:2 otherwise:3 among:2 monopoles:1 unnormalized:5 point:16 cc:4 asymptotically:2 cg:2 cf:22 dimensional:2 anti:2 sequences:6 cs:1 respect:6 actually:2 diff:3 cv:1 torsion:2 considering:1 extrema:1 described:2 second:1 addition:1 locally:3 cv2:1 three:2 laplacian:1 much:2 kodaira:1 pk:10 pi:3 universal:2 empty:1 determinant:3 senses:1 corresponding:3 duces:1 observe:2 understand:1 c2:2 c1:12 surveys:1 spin:3 manifolds:40 case:1 ǫk:1 estimations:1 value:3 will:3 euclidean:8 while:1 ǫp:1 replaced:2 compactness:3 behavior:2 freely:2 situation:2 property:3 conformal:1 procedure:1 cont:4 vol:20 vi:1 metric:38 thus:10 yk:7 surface:1 ii:1 φk:37 reads:2 cone:2 dual:15 ready:1 supremum:1 id:1 different:2 author:1 things:1 connection:8 same:13 clearly:1 complex:8 arguments:7 proved:2 finite:5 independent:12 used:2 infinity:1 dgh:13 flows:12 dimm:1 v0:3 uses:1 infinite:1 invariance:1 cr:10 ωjj:2 normalization:1 lower:1 weakly:1 center:1 depending:6 well:3 ujs:2 thm:1 without:2 components:1 possesses:1 subgroup:1 spherical:1 λr:1 manifold:28 just:3 less:3 resp:20 obtain:11 dvolg:2 immediately:2 proceeding:1 λm:50 previous:1 letting:3 oriented:11 preprint:1 candidate:1 kotschick:1 conclude:5 seems:2 setting:2 lett:3 easy:3 theorem:59 diagonalization:2 euler:5 rescaled:1 depends:1 easily:1 read:1 possible:1 harmonic:11 increases:1 using:7 advanced:1 mod:1 loss:1 rg2:2 necessary:2 follows:9 spinc:10 δk:2 works:1 essential:1 terminology:1 mathematical:1 olg:4 some:11 back:1 growth:1 choosing:1 moreover:9 proofs:2 provided:2 scale:2 dense:1 avoid:1 integration:1 ak:11 kleiner:1 critical:3 decomposition:1 provides:1 tends:2 ct:11 pinched:1 minimal:2 schwarz:2 bd:3 bg:59 compress:1 journal:1 l1:6 variation:1 xℓ:2 properties:1 cδ:1 an4:2 a0:4 bgk:34 pe1:8 pe2:3 beijing:2 deserves:1 carries:2 constraints:1 consequently:1 road:1 an1:6 soc:2 an2:4 h2:1 into:1 h1:1 integral:1 bound:6 nsf:1 lies:1 hermitian:2 references:1 einstein:40 operator:5 diameters:1 additional:1 her:1 comparing:1 strictly:1 there:47 anderson:6 var:1 translate:1 was:4 m0:2 lowest:2 isoperimetric:2 complete:15 form:10 enough:3 collapsed:4 regard:1 gauss:8 volume:15 hk:3 convergence:7 line:4 loc:2 pull:1 rigidity:2 characteristic:3 trans:1 smooth:23 up:1 us:3 below:3 ωj:19 limit:6 exhaustion:1 uk:1 uj:40 embed:1 monopole:10 similar:2 called:4 associated:2 defined:2 flow:41 abstract:1 denote:13 proves:2 exist:12 nankai:2 inf:8 kl:2 bishop:1 duality:1 again:4 nj:53 nm:1 no:1 ecole:1 when:9 other:2 details:1 papers:1 department:2 mathematics:4 ns:1 ar:1 conclusion:5 repeat:1 remarked:1 uniformly:2 bundle:2 hausdorff:5 important:1 bounded:13 genus:1 additionally:1 hirzebruch:4 structure:13 implies:7 dvk:53 assume:14 dvg:17 interval:3 together:1 4q:1 tianjin:1 mass:1 fact:3 volumes:1 time:20 n1:3 resolution:1 |
0704.0715.txt |@word neighbors:2 monte:2 scalapino:1 gs:3 consider:2 chain:1 rev:18 magnetic:1 results:9 leads:4 mila:6 remarkably:1 cases:2 particles:3 inverse:1 zone:2 environment:1 charge:5 rokhsar:2 th:1 under:2 td:1 tc:1 applied:1 supported:1 advantage:1 orthogonal:1 very:2 erale:1 electron:3 difference:1 exact:3 ladders:1 manep:1 hamiltonian:1 issue:3 large:2 fourier:1 small:6 linio2:1 dimer:21 configurations:3 upper:2 smaller:1 periodicity:1 consistent:4 plaquette:9 zero:1 implemented:1 carlo:2 even:1 what:1 errors:1 appear:1 sum:3 uniform:2 experiment:1 above:3 increasing:1 contrast:1 full:1 led:1 lee:2 implying:1 leg:1 trivedi:1 ceperley:1 understanding:1 behaviour:3 byers:1 possibility:1 separation:8 address:1 directions:1 path:1 along:1 strong:2 appears:3 change:1 luther:1 generalizing:1 colored:1 noticeable:1 rigorously:1 institute:1 larger:2 experience:1 periodic:3 narrow:1 changes:1 useful:1 ago:1 family:1 extra:1 cylinder:3 moessner:1 translational:2 total:1 use:1 negative:1 next:2 depicted:3 call:1 therefore:1 means:1 theoretical:1 diagrams:1 more:4 flat:1 ecole:1 qdm:2 curvature:2 particular:1 known:1 hole:8 states:3 middle:1 tunnel:1 science:1 challenge:1 work:2 theories:1 debated:1 values:3 already:2 cond:1 performed:2 nearest:2 compare:1 give:1 calculation:1 high:3 minimum:1 numbers:1 degenerate:1 becca:4 simple:2 hoc:1 decaying:1 carriers:2 provide:1 discussion:1 breaking:1 how:1 pure:1 parameter:7 play:1 fr:1 mat:1 binary:1 thermodynamic:7 earlier:1 derived:1 mapping:2 diagram:2 plane:1 horizontal:1 data:1 response:1 lifting:1 short:1 natural:2 effective:3 ss:1 lines:1 correspond:1 su:2 st:1 rather:1 complexity:1 green:2 decreasing:2 order:14 typical:3 indeed:3 over:3 move:2 displayed:1 soon:1 interpreted:1 paper:1 through:2 statistical:1 signs:1 senthil:1 still:1 its:2 condensation:1 sorella:1 acknowledge:1 interesting:1 hanke:1 vicinity:1 exhibits:3 better:1 penc:1 fig:19 insulator:1 clusters:6 hidden:1 main:1 might:1 lx:2 ly:2 non:1 good:1 runs:3 federico:1 scaling:4 framework:1 effects:4 half:6 kumar:1 bigger:1 possess:1 term:1 stabilize:2 alet:1 always:1 nationale:1 traced:1 2d:1 2e:4 turns:1 crossing:1 found:2 universit:1 side:1 bond:4 el:1 lifted:1 square:25 significantly:2 ed:2 energy:9 hard:2 reduce:2 idea:1 related:2 operator:1 used:3 quantum:11 our:6 eq:1 special:1 description:1 shown:3 sabatier:1 fundamentally:1 space:2 tried:1 since:2 squared:4 increase:1 bragg:5 investigation:3 seidel:1 ref:2 occurs:2 red:2 rk:9 linear:5 barrier:1 localization:1 diagonal:1 free:1 quite:2 definition:1 pairs:3 regarding:1 arnaud:1 geometry:4 transition:4 motion:2 turn:1 exponentially:1 hence:1 uses:1 undergo:1 onto:1 first:4 major:2 there:3 toulouse:1 computations:1 symmetry:4 prevent:1 xc:14 number:5 transform:1 done:1 directly:2 changing:2 precisely:1 aharonov:4 size:13 differ:2 temperature:3 similarly:1 ordering:1 leading:2 behaves:1 system:8 indicate:1 fermions:1 calculations:1 realization:1 staggered:2 bosons:1 continuous:1 transverse:1 branches:2 than:2 ivanov:1 liquid:3 castelnovo:1 see:1 superfluid:6 str:1 were:1 contrasted:1 peierls:1 explicit:1 ann:1 spectrum:3 analysis:3 close:3 concentration:5 obviously:1 clearly:2 constructions:1 physique:1 mechanism:1 note:2 instance:1 potential:1 online:6 so:2 heisenberg:1 cnrs:1 though:1 pujol:1 who:1 reach:1 triangular:25 jul:1 letter:1 phase:35 especially:1 mobile:1 clear:1 inferred:1 km:4 yang:1 exp:1 ky:1 kx:1 physics:2 fact:2 quantity:1 slope:2 nh:2 insulators:1 location:1 show:2 text:1 doped:5 soluble:1 gauge:1 d2:7 ground:2 deconfinement:1 finally:1 based:1 diagonalizations:1 kagome:1 enough:2 should:2 only:5 local:4 characterization:2 his:1 bonds:1 de:3 stripes:1 expects:1 define:1 brillouin:2 report:1 lattices:11 neither:1 processes:1 bar:1 continuum:1 conditions:1 arxiv:1 seperated:1 summary:1 investigate:4 predicted:1 switzerland:1 including:1 fixed:2 view:1 bars:1 set:2 national:1 correlations:2 up:1 observed:2 namely:1 lausanne:2 result:1 sea:1 discussions:1 terms:1 momenta:1 techniques:1 phases:4 interacting:1 away:1 sites:4 tend:1 boundaries:1 state:7 various:1 plaquettes:1 between:12 boundary:1 approach:1 chamon:1 recently:2 amplitude:1 parent:4 nature:2 however:3 jm:1 extent:1 bose:1 gfmc:2 suggested:2 both:2 essentially:1 efficiency:1 taking:1 conclusions:2 quantization:8 april:1 connection:1 dated:1 context:2 passing:1 disappears:2 minima:1 dm:2 ch:1 point:11 color:6 corresponds:1 dimensional:3 simply:1 boson:1 respect:1 throughout:1 ferrero:1 ps:9 singlets:3 second:1 crystalline:3 due:2 been:8 expected:5 columnar:4 systems:4 direction:2 corresponding:2 sectors:1 gas:1 recherche:1 fund:1 confinement:1 determination:1 representative:1 systematic:1 covered:1 general:1 spin:1 present:7 case:9 pierce:1 unlike:1 pacs:1 solid:1 value:3 spontaneously:1 will:2 precursor:1 while:2 behavior:3 error:2 property:2 region:5 vb:2 sondhi:1 thus:2 site:3 ii:3 cluster:8 superconducting:1 vs:3 mott:1 rid:1 orbital:1 capture:1 different:10 hubbard:1 perform:1 lett:4 same:1 qdms:1 arguments:1 schematic:2 units:3 finite:11 zhitomirsky:1 higher:1 independent:1 con2:1 investigated:2 laboratoire:1 numerical:4 upon:2 effect:1 mudry:1 insulating:5 strength:1 liquids:1 delicate:1 infinite:1 robust:1 recent:1 scenarii:1 lower:2 weakly:1 hopping:4 whole:1 degeneracy:4 well:2 roughly:1 undoped:4 evolves:1 bohm:4 solve:1 sets:1 swiss:1 model:12 usual:2 poilblanc:3 proposed:2 able:2 milestone:1 superconductors:2 obtain:2 torus:3 properties:3 thanks:1 paul:1 macroscopic:1 previous:1 candidate:1 density:1 scenario:1 conclude:1 lattice:27 other:1 extends:1 attractive:1 relevance:1 stable:2 extensive:1 momentum:1 real:1 dimers:2 around:1 depends:1 showing:1 agence:1 possible:1 period:2 eorique:1 calandra:1 background:3 nor:1 immediately:2 moreover:2 necessary:2 like:1 sizes:4 interestingly:1 specific:1 flux:18 polytechnique:1 arbitrary:3 valence:3 disorder:1 qualitative:1 therein:2 often:1 classical:2 some:1 back:1 calculated:1 doping:14 extended:1 transport:1 provided:1 noack:1 scale:1 describing:1 lead:3 realistic:1 investigations:1 per:1 16x16:2 critical:6 minimal:1 limitations:2 core:2 bc:4 bl:1 agreement:2 didier:1 although:2 substitution:1 losing:1 epfl:1 singlet:1 hilbert:1 bz:1 panel:3 conducting:6 puts:1 getting:1 discussed:1 dependence:3 o:2 reduced:1 range:3 repulsion:1 concentrations:1 significant:2 presence:1 maxwell:2 into:3 within:2 down:3 references:2 determine:1 elementary:2 france:2 bosonic:3 physical:2 kivelson:4 area:1 pairing:2 approximate:1 long:1 anderson:2 detectable:1 quanta:2 low:4 analyze:1 was:3 naturally:1 function:5 survives:1 differences:2 removes:1 trimerized:1 but:2 construction:2 segregation:1 hc:2 line:4 level:1 coulomb:1 la:1 inside:1 flip:2 us:1 antiferromagnet:1 below:1 limit:8 coverings:1 demonstrate:1 problem:2 fried:1 similar:1 called:2 strengthens:1 strongly:3 rvb:13 ordered:1 ad:1 defined:4 curve:2 describe:1 ergodic:1 evidence:2 single:2 exist:1 simulations:1 eric:1 constructed:1 resonating:1 no:5 dashed:3 whereas:2 nc:2 generally:1 vanishes:3 priori:1 role:2 details:1 out:1 shows:1 hayward:1 superconductivity:1 models:6 develops:1 important:1 peak:5 flippable:1 building:1 correlated:4 implies:1 longer:1 algorithm:2 holes:6 emery:1 governed:1 portion:1 time:1 once:1 |
Subsets and Splits