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0705.2270.txt |@word roh:1 limited:6 code:4 partial:1 consider:1 llr:1 assembles:1 global:1 results:3 known:1 scalar:1 proposition:9 markers:2 computation:1 edu:2 gn:26 n32:1 devoted:1 whose:4 cardinality:1 calculate:3 subjected:1 rayleigh:1 tr:1 james:1 γk:2 finally:1 tj:1 c5:1 th:5 ti:5 analogous:1 sent:1 case:5 orthogonal:3 choice:8 sons:1 cellular:2 entries:3 application:2 uncoordinated:1 condition:3 transmission:3 list:1 solution:1 t1:2 large:4 vector:11 hanly:1 small:1 λi2:1 upper:16 employing:2 maximization:1 direct:2 approximation:7 rate:60 athematical:1 further:1 estimated:1 substitute:2 spectral:1 index:2 appear:1 bϕ:4 diag:3 sum:27 near:2 uniform:1 current:2 above:3 sup:1 international:3 ˆj:1 increasing:1 equivalent:3 multivariate:2 full:2 simultaneously:1 respectively:5 jointly:11 packing:2 directions:1 extreme:4 obtained:1 involved:1 vectors:5 muirhead:1 throughput:2 implement:1 glt:3 tt:1 involves:1 via:1 useful:1 extra:1 unitary:3 sloane:1 achievable:1 apply:1 total:1 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0705.2271.txt |@word partial:3 remarkable:1 illustrates:1 rev:18 4ac:1 y2:3 four:8 roy:1 generalize:1 computation:2 foundations:1 denotes:2 referring:1 tr:13 nonlocal:3 does:1 yˆ1:2 yˆ2:2 under:1 must:3 tb:14 division:1 supported:1 ρtb:4 advantage:1 orthogonal:1 very:1 choice:1 p1:1 lecture:1 experimentally:1 matrices:1 kwek:2 vast:1 leads:1 kaszlikowski:3 presented:1 notes:1 t2:7 applicable:1 vector:2 demonstrated:1 inscribed:1 chuang:1 lines:1 revolution:1 james:1 edu:1 2x1:1 second:3 chen:3 linear:4 blue:1 established:4 appear:1 sum:2 expressed:2 ˆa:2 ˆb:2 version:1 above:3 ˆi:1 increasing:1 coefficient:2 led:2 degree:1 respectively:4 equals:1 here:1 china:2 address:1 active:1 fifteen:1 chen1:1 great:2 institute:2 study:1 studied:1 allows:2 spheres:1 suitable:1 makes:1 honor:1 y12:1 via:1 tightness:1 family:2 f1:4 iph:1 marked:1 outcomes:1 hardy:1 unitary:1 p44:1 p43:1 p42:1 unit:7 projector:3 would:1 massar:1 distinct:1 positive:2 tightly:1 program:1 call:1 therefore:1 type:3 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0705.2272.txt |@word roh:1 limited:5 monte:1 code:12 consider:2 exponentiation:1 global:1 results:10 antennas:12 markers:1 edu:2 gn:32 compares:3 compact:1 calculate:1 rayleigh:1 those:4 include:1 sent:1 g6:3 random:6 orthogonal:3 g8:3 corollary:3 entries:1 difference:1 exact:7 riemann:1 presented:1 transmission:1 rao:1 applicable:1 large:12 vector:1 small:4 evs:1 upper:12 consistent:3 sin2:1 measurable:1 approximation:14 rate:54 design:1 estimated:1 carlo:1 substitute:1 established:1 dept:1 onclusion:1 section:5 near:1 uniform:4 above:1 icassp:1 expresses:1 multivariate:1 full:1 simultaneously:1 respectively:5 here:2 water:1 packing:9 extreme:1 obtained:3 receive:5 vectors:3 completely:1 p2:4 military:1 glt:2 composed:1 prints:1 useful:1 projection:1 addressed:1 sloane:1 achievable:1 apply:2 unit:3 use:6 asymptotic:10 usa:2 codewords:1 remains:1 positive:1 contains:1 chooses:1 distinct:1 vol:10 therefore:1 m2:2 vj:1 more:2 flat:1 award:1 particular:1 known:3 hold:2 iii:2 high:1 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0705.2273.txt |@word roh:1 limited:5 monte:1 code:12 consider:2 exponentiation:1 global:1 results:10 antennas:12 markers:1 edu:2 gn:32 compares:3 compact:1 calculate:1 rayleigh:1 those:4 include:1 sent:1 g6:3 random:6 orthogonal:3 g8:3 corollary:3 entries:1 difference:1 exact:7 riemann:1 presented:1 transmission:1 rao:1 applicable:1 large:12 vector:1 small:4 evs:1 upper:12 consistent:3 sin2:1 measurable:1 approximation:14 rate:54 design:1 estimated:1 carlo:1 substitute:1 established:1 dept:1 onclusion:1 section:5 near:1 uniform:4 above:1 icassp:1 expresses:1 multivariate:1 full:1 simultaneously:1 respectively:5 here:2 water:1 packing:9 extreme:1 obtained:3 receive:5 vectors:3 completely:1 p2:4 military:1 glt:2 composed:1 prints:1 useful:1 projection:1 addressed:1 sloane:1 achievable:1 apply:2 unit:3 use:6 asymptotic:10 usa:2 codewords:1 remains:1 positive:1 contains:1 chooses:1 distinct:1 vol:10 therefore:1 m2:2 vj:1 more:2 flat:1 award:1 particular:1 known:3 hold:2 iii:2 high:1 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0705.2274.txt |@word partial:1 consider:2 saves:1 results:9 illustrated:1 antennas:7 proposition:6 cooperative:2 edu:2 denotes:1 whose:4 calculate:3 rayleigh:2 γj:1 finally:3 inite:1 γm:2 ti:5 insights:4 worth:1 case:2 random:8 2ri:1 orthogonal:4 very:1 maximized:1 focus:1 every:1 decide:4 summarized:1 difference:3 level:1 transmission:3 turns:2 who:1 solution:1 occurs:1 large:6 vector:3 indices:2 upper:2 smaller:1 computation:2 fairness:5 dimensional:9 empirical:1 rate:16 design:7 further:2 recalculate:1 spectral:1 index:2 nalysis:1 sub:1 onclusion:1 section:9 selected:2 http:2 while:4 access:1 version:1 above:5 sup:2 ˆi:4 method:2 coefficient:2 full:2 respectively:4 realizations:4 sinr:1 equals:2 here:4 desired:1 others:1 directions:7 path:4 strong:2 change:1 obtained:2 search:2 spacial:1 vectors:5 reason:3 amount:1 throughput:13 usually:1 surely:1 studies:1 involves:1 appropriately:2 projection:1 elaborated:1 ls:3 unitary:2 turning:1 achievable:2 apply:1 total:2 unit:1 use:5 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0705.2275.txt |@word sci:1 consider:12 remarkable:1 caused:1 forbidden:1 desirable:4 results:2 leads:6 scalar:14 denotes:1 contributions:1 causes:1 vev:18 whose:1 inverse:2 aug:1 tr:15 finally:3 does:3 those:5 under:18 ev2:1 include:1 b147:1 yr:1 far:1 differently:1 splitting:1 maskawa:1 mixing:15 affect:1 exact:2 condition:3 wsb:6 hamiltonian:9 vu:5 irreducible:2 michael:1 solution:4 leave:1 discrete:1 convenience:2 science:1 small:3 majorana:2 jhep:1 εm:4 uei:1 zi:1 mνl:3 zero:2 nelsen:1 further:1 fusaoka:3 even:1 index:3 what:4 appear:6 diag:4 section:8 current:1 version:1 above:1 new:2 satisfy:1 devoted:1 respectively:7 machikaneyama:1 mei:7 here:3 understanding:1 objects:1 free:2 address:1 concluding:1 ratio:6 appears:1 z2:19 z3:7 obtained:6 b120:1 institute:1 eri:1 suggests:1 superpotential:22 permutation:1 usually:2 erk:1 mν2:4 uniquely:1 although:10 forbid:1 requiring:2 merely:2 explained:1 neutrino:19 m2π:2 kobayashi:1 m2σ:2 d73:1 conventional:3 er1:1 er2:1 er3:1 give:6 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0705.2277.txt |@word gw:3 precise:1 δg1:1 partial:3 consider:10 gv:1 rev:19 global:2 ours:1 results:14 gy:4 leads:3 gf:3 scalar:1 concept:1 computation:2 parameterization:3 go:1 follow:3 gl:12 contributions:8 efficients:1 gh:1 vev:1 rd:1 calculate:1 integral:1 simplify:1 tr:19 corrections:5 c6:2 presents:1 must:3 program:1 those:18 under:6 pay:1 include:3 divergent:1 faz:3 division:2 g4:8 amplitudes:5 g2:33 straightforward:2 δw:2 threepoint:2 hagiwara:7 assuming:3 exception:1 induce:1 gz:42 falk:2 wµa:1 wavy:1 interpreting:1 herrero:1 summarized:1 mixing:4 affect:3 difference:1 matrices:4 condition:2 four:15 ρg:1 vv:1 level:6 vu:3 ref:11 list:3 correct:1 large:15 discrete:2 chivukula:1 vector:11 haidt:2 small:8 relation:1 barbara:1 noted:1 termined:1 zl:14 smaller:3 ga:6 findings:1 cgh:5 consistent:1 g2g:4 sin2:3 prediction:3 sign:3 approximation:1 βv2:1 imply:1 premature:1 manner:1 further:1 dynamics:1 tev:30 linear:11 even:5 matsuzaki:1 nonlinear:4 adds:1 cast:2 section:6 coef:1 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0705.2278.txt |@word code:19 consider:4 isotropically:3 results:9 antennas:2 edu:1 go:1 gn:37 compares:2 compact:1 whose:1 hold:3 calculate:1 rayleigh:1 tr:2 finally:3 those:1 awgn:9 p2:4 supported:1 orthogonal:2 choice:1 corollary:5 entries:2 matrices:2 g8:1 riemann:1 presented:2 transmission:3 large:7 discrete:2 convenience:1 differential:1 small:10 upper:15 haar:1 consistent:1 sin2:2 measurable:1 approximation:10 rate:53 design:1 infimum:1 follow:1 further:3 index:2 errors:1 onclusion:1 section:2 selected:1 http:2 expressed:1 uniform:1 version:3 above:1 icassp:1 international:2 method:2 multivariate:4 respectively:6 explore:1 groups:1 ratio:1 appears:1 extreme:2 obtained:3 remark:2 receive:1 vectors:4 krieger:1 spheres:1 recently:1 throughput:2 published:1 usually:1 studies:1 technique:1 useful:3 addresses:1 sloane:1 achievable:6 unit:3 use:1 additive:4 asymptotic:7 codewords:1 sake:1 next:2 rao:1 therefore:3 selects:1 minor:1 more:3 permutations:1 knows:1 comparison:1 becomes:1 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0705.2283.txt |@word gu:1 code:5 partial:6 consider:1 chain:1 believed:1 caused:1 global:2 preparations:1 results:9 existing:2 illustrated:1 computation:3 edu:1 consists:1 follow:4 expressions:1 disk:39 causes:1 whose:5 certainly:1 c0:1 terms:4 calculate:2 zone:3 description:1 technique:10 kawata:2 tn:10 mahadevan:1 2004a:2 critical:2 chaps:1 those:1 th:7 stable:17 circumstances:1 worth:1 sound:2 kπ:1 wavefront:1 advantage:1 very:17 frequencies:1 keeping:2 subject:1 choice:1 every:3 figs:7 formula:2 discretizations:1 difference:2 continued:1 collocated:1 condition:14 common:1 entire:1 beginning:2 exponential:1 question:1 level:6 did:1 turns:1 incompressible:1 shock:1 solution:16 occurs:1 leave:1 discrete:4 adjust:1 demonstrated:1 subscript:1 small:4 enhance:2 becker:2 shows:1 noted:2 added:1 fujian:1 upper:1 janiuk:2 averaged:1 slower:1 occurrence:1 oscillation:1 10m:1 miller:12 consistent:3 kato:8 direct:1 literature:2 u1d:1 microquasar:1 grant:1 rate:8 value:5 equal:2 chen:3 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0705.2284.txt |@word partial:4 consider:5 results:5 unweighted:2 minors:1 row:2 whose:7 15a18:1 graph:29 young:5 finally:1 tj:1 th:5 tg:3 very:1 corollary:5 every:2 matrices:1 condition:2 discrete:2 convenience:2 mi:4 discover:1 second:1 even:1 xω:1 complexities:3 sum:6 celebrated:1 birkhoff:1 en:1 binet:1 new:9 method:1 gµ:3 lee:6 degree:2 newyork:1 respectively:2 diagonal:1 address:3 obtained:6 bartholdi:4 study:1 products:1 wig:1 fµ:2 classification:1 wij:2 ek:4 counts:1 use:1 proceed:1 prove:1 positive:1 tutte:4 bundles:1 negative:1 next:1 few:1 call:2 m2:8 taken:2 more:2 submatrix:1 adjacency:2 doob:1 particular:3 known:2 mm:4 equation:1 mn:12 det:34 mt:2 values:1 ms:12 following:6 example:1 proof:11 νg:42 minimum:1 numbers:4 spanning:15 counting:1 end:2 provide:3 how:2 adjacent:3 instead:1 sato:2 map:1 product:5 algebra:1 may:1 fg:11 fits:1 natural:1 outline:1 lemmas:2 spectra:2 complexity:31 combin:5 order:1 cofactors:2 over:1 fλ:6 paper:2 london:1 vaintrob:1 its:3 bridges:1 enseign:1 choose:1 derivative:3 ωki:1 main:3 chromatic:4 now:3 yu:2 easily:1 invariants:2 university:5 each:9 found:3 2n:2 individually:1 weighted:41 ei:3 05c50:1 ed:1 our:1 shown:2 matrix:30 res:1 since:4 research:2 combinatorial:1 rg:2 denoted:1 formula:5 induced:2 ri:12 math:10 disclose:1 theory:9 given:2 e1:1 e2:1 definition:2 r1:4 r2:7 phrases:1 counterpart:1 int:1 first:1 variables:1 number:4 rank:1 ihk:2 another:1 ring:7 differ:2 similarly:2 cambridge:1 least:1 appl:1 siam:2 exactly:1 completes:3 tree:18 were:1 arborescences:1 ann:2 spectrum:1 generalization:3 tω:1 any:9 subgraph:3 min:1 general:2 admittance:3 note:2 instance:1 generalized:5 εg:5 cofactor:6 gω:76 though:1 incidence:2 gλ:7 iwi:1 most:1 regular:1 pair:1 pathes:1 considered:2 clear:1 kn:2 bipartite:1 graphs:20 sigma:3 section:2 fact:2 show:2 supported:1 kwon:5 threshold:1 hypercube:1 find:8 principal:2 coloring:2 explain:1 lemma:6 only:3 factor:1 columns:1 trees:7 words:1 µd:1 compute:2 kyungpook:1 covering:1 arxiv:3 common:2 qn:6 hλ:10 set:7 ser:5 national:1 see:4 result:3 w1:1 hammer:1 subject:1 tensor:1 ways:1 review:1 symmetric:1 µi:1 between:1 invariant:1 notice:2 korea:3 terms:1 extend:1 transpose:1 wi:2 ws:1 key:3 cayley:1 kruskal:1 many:1 σg:1 contribution:1 finds:2 otherwise:2 ci:8 co:3 point:2 simple:1 2nd:1 dimensional:1 grants:1 simply:1 polynomial:8 moreover:1 zeta:7 considering:1 pp:2 commutative:4 mizuno:2 sachs:1 laplacian:10 defined:9 much:1 pg:1 colorings:1 define:3 determinant:14 corresponding:2 propositions:1 observe:1 whitney:2 mail:3 c2:4 c1:4 denote:1 ǫg:2 evaluated:2 will:2 aij:1 orientation:1 played:1 vh:2 vi:2 vj:1 thus:1 ii:1 ij:5 different:1 same:3 biggs:1 complex:2 knuth:1 finite:3 couple:1 assigns:1 hand:1 cvetkovic:2 edges:15 kim:7 identity:4 vertices:6 well:1 academic:1 edge:6 coordinate:2 entry:1 knu:1 obtain:4 underlying:2 λi:2 previous:3 preprint:1 tuples:1 corollaries:1 theorem:24 harary:1 real:1 taegu:1 showing:1 press:2 using:4 ams:2 follows:3 occasions:1 classical:1 some:3 b1:1 b2:1 respect:2 kmn:1 provides:1 proc:2 refer:1 bg:5 problems:1 bn:1 expansion:1 variation:4 although:1 properties:1 algebraic:1 column:2 theorems:1 a2:1 km2:1 km1:1 chow:1 introduced:2 consequently:2 other:2 subset:2 contains:1 previously:1 soo:5 square:2 references:1 weight:11 removing:2 there:1 u2:7 start:1 cauchy:1 m1:8 was:4 function:22 complete:5 form:1 sequel:1 but:2 line:1 ωx:2 applying:3 orlin:1 characteristic:5 ωs:8 differentiable:2 ωi:3 masbaum:1 ωn:4 demonstrate:1 similar:5 ki:1 ac:3 constant:1 digraphs:1 ai:2 abstract:1 generating:1 proven:1 hµ:3 functions:9 kr:3 application:1 setting:2 role:1 department:3 mathematics:4 vertex:1 kirchhoff:1 polynomials:4 a1:1 important:1 algorithm:1 weights:11 having:1
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0705.2285.txt |@word vorticity:10 global:5 results:4 essai:1 scalar:2 proposition:3 edu:1 partial:3 research:1 relationships:1 analytic:1 paris:1 bx0:16 editors:2 uniqueness:2 kokyuroku:1 geom:1 norm:1 applied:1 orthogonal:2 far:1 wave:1 corollary:4 condition:5 die:2 solution:14 t0:73 vector:2 small:1 div:4 says:1 estimates:1 measurable:1 integrability:1 revista:1 aim:1 nonlinear:2 appear:1 annali:1 version:1 sur:1 above:7 sup:6 new:2 method:1 3d:1 satisfy:1 lee:1 component:3 here:1 struwe:1 operating:1 directions:2 z0:14 nachr:1 obtained:2 remark:3 institute:1 lomi:1 study:1 riviere:1 espace:1 suitable:16 sci:1 dxdτ:2 cylinder:1 fefferman:1 univ:1 derivatives:3 use:1 asymptotic:1 prove:2 positive:2 next:3 vol:1 call:1 therefore:2 criteria:2 indiana:1 associated:1 type:2 more:1 qz0:26 levich:1 particular:1 known:2 iii:7 integrating:1 recall:3 equation:1 work:1 temam:1 following:13 proof:10 claim:1 magnitudes:1 prodi:1 numbers:2 sense:2 r22:22 absolute:4 holds:6 numerous:1 criterion:1 pure:3 instead:1 iberoamericana:1 product:1 mat:2 singular:5 may:1 after:2 consequence:1 data:1 2l2:2 so:1 lγ:20 fundamental:1 irregularity:8 over:1 satisfied:2 paper:1 existence:5 satisfies:4 r2γ:1 its:2 before:1 controllable:1 derive:1 chosen:1 actually:1 caffarelli:5 lp:4 mail:1 main:3 lx:8 scaling:1 beir:4 acta:1 singularity:2 now:1 veiga:4 easily:1 term:1 2p:1 university:1 l6:5 sufficiently:2 inequality:7 l2:75 l3:5 each:2 domain:5 qz:2 another:1 kang:1 leray:2 related:2 measure:4 our:5 space:5 gradient:1 electronic:2 since:3 rev:1 denotes:1 contained:1 millennium:1 rational:1 dxdt:4 occurs:1 math:13 constantin:2 theory:1 surveys:1 tian:1 york:1 estimate:7 c02:1 definition:2 r1:14 r2:15 r3:3 followings:1 nonnegative:1 navier:22 hence:5 promotion:1 βi:2 first:2 initial:3 intuitively:1 simplified:1 directly:1 orszag:1 precisely:1 open:2 campanato:1 given:2 similarly:2 introduction:2 arch:2 system:1 xin:1 their:2 1d:1 continuous:1 immediate:2 direct:2 part:4 norms:2 x0:3 than:1 roles:1 zero:3 determined:1 skku:1 outstanding:1 argument:1 already:1 say:2 disjoint:1 lim:6 lin:2 heywood:1 generalized:1 interior:5 incompressible:3 unless:1 birkh:1 most:1 regular:15 preliminary:1 pair:2 class:1 neighborhoods:1 considered:1 adopt:1 stronger:1 countable:1 points:3 exp:2 velocity:9 physics:1 notion:3 fact:2 moehrd:1 show:1 supported:3 solutions:23 substituting:1 find:2 escauriaza:1 foias:1 basel:1 completes:1 lemma:4 only:1 mouvement:1 parabolic:2 local:5 hopf:2 continuity:1 scheffer:2 ladyzhenskaya:1 notation:1 di:3 kosef:1 ϕv:8 fluid:3 manuscripta:1 da:4 dx:11 dv:10 dt:18 du:32 boundary:1 rademacher:1 takahashi:1 closure:1 evolution:1 qt:13 conditions:7 arxiv:1 implication:1 set:11 ser:1 exists:6 imposing:1 turbulent:2 j1:2 j2:3 see:2 result:2 japan:1 sem:1 incorporating:1 satisfying:1 written:1 serrin:2 closed:1 αi:1 invariant:1 geometric:1 approach:1 korea:1 rims:1 weak:30 however:1 le:2 hypothesis:1 problem:6 instant:1 region:4 equal:1 comm:7 estimation:1 zapiski:1 uber:1 point:15 simple:1 dimensional:3 simply:1 moreover:2 diff:2 pp:22 equations:22 due:2 much:1 basic:1 choose:1 direction:4 concerning:2 spectrum:1 fund:1 observe:3 equazioni:1 c1:4 c0:3 case:4 yakhot:1 rat:1 value:2 will:1 near:2 suppose:4 property:1 taking:1 seven:1 almost:1 vj:2 kohn:5 ii:6 regularity:23 vt:1 containing:1 grant:2 epoch:8 proved:6 interpolation:2 used:3 i1:3 i2:3 effect:1 flows:7 v0:4 v1:1 v2:1 v3:1 identity:1 recent:1 pures:1 mech:2 off:1 older:2 well:3 analysis:3 patterns:1 r01:1 obtain:5 intervals:1 showed:1 previous:4 cut:1 preprint:2 conclude:3 smoothness:2 valid:1 lett:1 theorem:17 guarantees:1 navierstokes:2 2u:6 advances:1 possible:11 plenum:1 department:1 press:1 using:2 follows:3 fabes:1 either:1 clay:1 regularizing:1 reduced:1 beltrami:4 therein:1 acad:2 sungkyunkwan:1 conditional:1 some:2 b1:4 b2:18 specified:1 majda:1 ohyama:1 integration:1 per:1 fluide:1 proc:1 pressure:2 step:1 bx:2 properties:2 simpler:1 stokes:22 choe:1 eqns:2 o:1 wolf:2 introduced:3 krf:1 mathematical:3 into:1 integral:3 refines:2 remarks:1 appropriate:1 references:2 refined:2 seregin:1 nirenberg:5 there:11 appl:4 inner:1 viscous:2 was:4 energy:1 function:3 gronwall:2 form:1 phenomena:1 but:1 russian:1 true:5 partially:1 applying:1 versions:1 smooth:4 us:1 ur:1 below:5 un:2 distribution:1 similar:1 called:2 mechanics:2 later:1 constant:4 chae:5 int:1 flow:2 abstract:1 combining:3 ao:4 denote:2 ap:1 exist:4 curl:1 check:1 traditional:1 functions:2 no:5 d2u:20 d2v:1 field:1 other:1 spatial:1 test:2 mathematics:2 ns:8 conclusion:2 repeat:1 suwon:1 problems:1 galdi:2 hausdorff:4 important:1 bounded:2 anal:3 structure:1 jones:1 scient:1 implies:2 assume:5 interval:1 together:2 implied:1 time:13 backward:1 starting:1
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0705.2286.txt |@word represent:1 eriksson:1 consider:12 chain:4 illustrates:1 recombining:1 alleles:14 forbidden:1 excellent:1 results:15 leads:5 stops:1 follow:3 expressions:3 research:1 2r2:1 causes:2 soc:1 sx:1 certainly:1 replacements:2 calculate:1 graph:2 segments:1 deterministic:24 editors:2 environment:1 finally:2 critical:3 tk:17 ewens:1 under:4 stochastic:9 maximum:1 eliminate:1 applied:1 random:2 consequently:1 advantage:3 evolves:1 very:9 frequencies:1 bm:1 rise:1 springer:2 sons:1 putting:1 figs:4 affect:2 difference:7 exact:2 condition:2 states:1 entire:1 squares:1 beginning:1 solves:1 level:2 die:1 urns:1 crossovers:1 t2:10 solution:6 fewer:1 occurs:5 large:13 small:14 markov:5 favoured:17 upper:1 smaller:4 monotonous:1 incremented:1 consistent:1 direct:3 literature:1 modified:2 approximation:24 elegant:2 second:11 pass:1 manner:1 dynamics:3 implemented:4 quite:1 theory:4 blue:6 will:9 what:3 sub:10 advantageous:4 t2n:13 section:26 selected:35 signature:2 brief:1 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0705.2287.txt |@word dist:3 consider:4 results:9 leads:1 computation:1 edu:3 partial:5 contributions:1 2r0:2 whose:3 c0:8 depend:1 integral:1 paris:2 graph:1 technique:1 tr:1 tp:15 uniqueness:24 elliptic:19 under:3 up2:1 up1:2 applied:2 straightforward:1 2γk:1 very:2 tends:2 translations:1 electron:1 matrices:1 condition:9 entire:1 school:1 dij:6 die:1 solution:23 large:6 indices:1 eigenvalues:2 markov:2 upper:6 lw1:1 neighborhood:2 estimates:1 measurable:3 second:4 further:1 linear:4 established:1 nonlinear:11 iterating:2 chicago:2 3r:1 section:3 while:1 uniform:7 above:4 sup:1 replaced:1 increasing:3 method:4 satisfy:5 2kr:1 respectively:1 b2r:2 here:5 behaviour:2 desired:4 address:3 path:1 standard:2 equations:21 appears:2 obtained:1 remark:5 sobolev:1 subsolutions:1 study:2 larger:1 contradiction:4 domains:6 studies:1 sci:1 boundedness:1 γp:3 useful:1 transformations:1 classification:1 bounds:1 gilbarg:2 minnesota:2 analyzing:1 summation:1 mckenna:2 unit:1 readily:1 k0p:2 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0705.2288.txt |@word represent:1 monte:2 qiang:1 sci:1 consider:1 similarity:1 gupta:1 rev:11 people:1 results:7 ruyter:1 illustrated:1 grateful:1 edu:2 consists:1 cases:2 issues:1 layers:2 γy:1 γx:1 depend:1 unanimity:1 ali:1 james:2 program:1 preserved:1 th:1 ti:4 tc:4 indicating:1 supported:1 amplitudes:1 zhang:4 very:3 choice:4 electron:1 figs:5 experimentally:2 difference:1 leads:3 squares:1 manep:1 hamiltonian:3 did:1 positions:1 proposals:1 t0:6 large:3 solved:1 annihilates:1 dopings:1 small:1 marezio:1 strongly:1 smaller:1 periodicity:1 labb:1 renormalized:3 consistent:3 estimates:1 approximation:2 zero:1 chen:1 qualitatively:2 estimated:2 carlo:2 substitute:1 even:2 index:1 overdoped:1 http:2 near:1 swiss:1 cell:5 consistently:1 experiment:2 above:2 new:1 hajime:1 commensurate:1 method:1 bi:4 full:2 simultaneously:2 lee:5 degree:1 respectively:5 trivedi:2 modify:1 here:4 understanding:2 reported:5 mev:5 alone:2 along:6 appears:1 superconductor:1 acceptor:1 obtained:2 apical:2 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0705.2289.txt |@word 2kµ:1 monte:2 concept:1 sci:1 gr:1 dick:1 results:2 four:1 scalar:1 parker:1 mp2:1 contributions:1 hole:1 localized:1 consider:4 simon:1 depend:2 noncompact:2 spirit:2 supported:1 kβ:1 late:1 sepangi:2 worth:1 rabcd:3 orthogonal:3 very:1 geometrical:5 hµν:4 condition:1 dominate:1 riemann:3 sundrum:1 notes:1 solution:3 large:3 vector:1 science:2 small:2 gauge:1 setup:1 smaller:2 neighborhood:1 cabcd:1 braneworld:1 consistent:3 sin2:1 approximation:1 8πgtµν:2 second:1 manus:1 antoniadis:1 even:1 established:1 power:1 giving:1 section:2 codazzi:3 near:3 3k:2 fifth:1 above:4 method:2 new:1 3a4:2 consisting:1 contrast:1 full:3 iran:3 respectively:2 qµν:6 here:2 free:1 xν:1 along:4 equations:19 interpret:1 box:1 institute:2 study:3 vectors:1 allows:1 completely:1 usually:2 spacetime:3 4a4:1 via:5 extra:13 merely:1 planck:10 unit:1 derivatives:1 proceed:4 would:2 remains:1 contains:1 scenarios:2 comparing:1 possible:2 more:1 flat:12 owen:1 knows:1 l191:1 started:1 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0705.2290.txt |@word partial:1 angles:1 uℓν:2 exponentiation:1 global:1 results:18 four:2 parametrisation:11 lcsrs:4 follow:2 contributions:2 whose:1 lcsr:6 determinations:3 include:1 dramatically:1 updated:2 charles:1 ofthe:1 advantage:2 φnp:1 very:1 induce:1 choice:1 mixing:5 experimentally:4 difference:1 matrices:1 presented:2 turns:1 large:4 small:4 enhance:1 jhep:7 semileptonic:1 prediction:2 rate:1 invariant:1 theory:3 what:2 errors:2 sum:4 networks:1 current:1 experiment:1 above:1 obvious:1 full:3 respectively:1 lange:2 others:1 ratio:7 khodjamirian:3 obtained:7 noticeable:1 involved:1 study:1 larger:2 hfag:10 g2f:1 suggests:1 resulting:3 resonance:1 narrow:1 m3b:1 control:1 ratios:1 ippp:1 private:1 durham:2 gluon:1 total:1 m2π:2 plot:1 impacts:1 would:1 kaidalov:2 predictions:7 comparing:1 nucl:3 call:1 m2:6 taken:1 3le:1 themselves:1 theoretical:14 more:2 fractions:2 th:1 equipped:1 nieves:1 validity:1 subclass:1 basically:1 particular:1 known:1 iii:1 c45:1 mb:6 challenge:1 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0705.2291.txt |@word monte:2 chain:1 similarity:1 vlaanderen:1 knotted:15 results:8 yellow:1 leads:1 disc:1 francesco:1 follow:5 displaying:1 issues:1 whose:3 biol:2 monomer:3 paris:1 subjected:1 presents:2 finally:1 investigation:1 stochastic:1 supported:1 g3:14 g1:7 far:2 plausibility:1 govern:1 presented:1 turns:1 fewer:1 occurs:2 solved:2 vector:1 math:2 small:1 upper:1 force:1 consistent:7 miur:1 second:3 gyration:9 zt:13 further:2 dynamics:13 estimated:2 carlo:3 bacteria:1 theory:1 even:1 localization:1 melt:1 pippenger:1 current:1 localized:1 establishes:1 new:5 method:1 movement:3 full:1 lee:1 respectively:2 equals:1 here:2 behaviour:10 focused:1 governing:1 path:1 along:2 strong:3 appears:1 obtained:1 search:1 fwo:1 study:2 stretching:1 leaving:1 stella:2 resulting:1 studies:1 plotted:1 departement:1 scales:2 environment:1 dna:5 takes:1 plos:2 distinct:1 contains:1 predictions:1 mirny:1 calculation:1 therefore:2 taken:2 black:3 associated:4 type:2 creates:1 more:1 flat:3 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0705.2292.txt |@word code:1 angles:2 ali:1 rev:1 magnetic:3 graphics:1 results:12 produce:1 leads:3 eds:3 computation:7 vary:1 consists:5 cases:1 sch:5 layers:2 depend:1 patches:4 superspace:1 languages:1 quasi:1 critical:1 tanaka:1 matlab:4 nodes:1 alternating:5 applied:1 supported:1 amplitudes:1 presently:1 orthogonal:1 very:2 frequencies:1 straße:3 springer:2 unchen:1 balancing:1 discretizations:2 difference:8 exact:2 electronics:1 condition:2 entire:1 intersections:1 moderate:1 solves:1 solver:14 transmission:3 cause:1 eigenmodes:1 solution:4 correct:1 large:4 admissible:1 vector:2 optics:2 programme:3 smaller:2 compensated:1 findings:1 direct:1 burger:13 gmbh:2 cost:1 design:6 enclosed:1 rigorous:10 further:5 implemented:1 even:1 index:2 errors:2 phaseshift:1 nano:1 unknowns:8 giving:1 assisted:1 selected:1 near:3 find:3 cell:3 optimization:2 reconstruction:1 designing:1 new:1 increasing:1 waveguide:1 method:13 filled:1 3d:43 coefficient:1 full:1 degree:10 component:1 here:2 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0705.2293.txt |@word homomorphism:6 gr:2 induces:6 global:2 results:2 invent:2 extensively:1 gf:24 proposition:20 ozaki:17 consists:2 gn:4 gm:1 research:1 gk:23 2r2:1 gi:12 whose:7 certainly:2 yahagi:2 auf:1 young:1 finally:2 th:5 under:2 golod:1 norm:1 p2:3 conjecture:2 abelian:27 g0:1 far:1 instructional:1 choice:4 every:12 exact:12 f111:7 condition:1 school:1 presented:1 die:1 solution:10 ri:3 large:2 solved:1 recall:5 zl:1 application:2 submodules:2 exten:1 direct:10 zero:1 reine:1 zp:33 primes:19 even:1 aim:2 what:8 plays:2 stands:2 giving:1 section:9 subextensions:1 goes:1 scientists:1 consisting:1 q1:1 chose:1 degree:40 respectively:8 l1:8 here:4 modular:1 groups:14 morphisms:1 institute:1 idele:1 contradiction:2 action:1 suitable:3 studies:1 honor:1 ihre:1 via:5 divide:2 classification:1 assertion:1 functoriality:1 rχ:15 annihilator:1 janusz:1 rψ:3 rω:1 unit:5 prove:2 distinct:3 eχ:2 only:3 sports:1 noting:1 therefore:14 reciprocity:1 brighton:1 type:1 kinokuniya:1 duality:1 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0705.2294.txt |@word proposition:3 consider:5 similarity:2 excellent:1 brownian:1 results:4 integration:1 leads:1 αr1:1 scalar:1 disc:9 edu:2 consists:1 centers:1 dα:1 devoted:1 whose:9 inverse:1 depend:1 calculate:1 paris:1 γr:6 technique:1 intensive:1 finally:1 investigation:1 petersburg:4 th:3 under:5 breach:1 norm:6 p2:2 conjecture:1 amplitudes:1 consequently:5 abelian:2 orthogonal:12 very:2 dokl:2 corollary:3 valued:4 every:2 summarized:1 2rs:1 trudy:1 condition:2 immediately:1 presented:1 bn:5 suffices:1 osipov:2 solution:5 md:1 large:1 au0:1 vector:5 eigenvalues:1 upper:1 nineties:1 periodicity:1 haar:56 direct:4 riesz:2 second:1 α2s:19 dynamics:1 zp:2 canonical:4 spectral:2 index:1 what:3 appear:1 giving:1 sum:7 http:1 expressed:1 abs:1 en:1 causes:1 above:9 fractional:21 new:4 consisting:3 contrast:3 satisfy:1 multivariate:4 padic:3 2ks:1 respectively:9 never:2 here:6 understanding:1 refinement:17 objects:1 pennsylvania:1 groups:1 xν:12 represented:10 ba2:2 strong:1 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0705.2297.txt |@word represent:2 delaware:1 partial:1 consider:1 ceases:1 rev:2 suggests:1 results:7 godoy:4 four:10 ciudad:1 catalina:1 cooperative:1 mimic:1 consists:1 remarkably:1 magnifying:1 synthetic:2 content:3 paris:1 ıa:4 finally:1 aut:1 ti:4 exit:1 td:5 include:1 applied:1 amplitudes:6 very:2 frequencies:25 keeping:1 wave:102 tanks:1 summarized:1 resonant:55 atmospheric:1 difference:1 sj:1 condition:6 common:1 induced:2 catherine:1 level:6 proc:3 leveled:1 t2:8 solution:1 flute:1 damped:1 large:2 convenience:1 recall:1 small:2 inertial:1 des:1 force:4 oscillation:18 oscillator:1 consistent:1 prediction:10 past:1 second:4 design:3 ρa2:1 distinctly:1 estimated:1 linear:5 subscripts:1 what:1 nonlinear:2 combined:1 section:7 selected:1 near:2 dχ2:3 dχ1:3 dominates:1 above:6 del:2 direcci:1 increasing:2 method:1 contrast:1 body:3 compresses:2 full:3 shoreline:1 channeled:1 respectively:3 component:22 here:5 water:42 reported:4 fiorentino:1 focused:1 compressed:1 separation:1 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0705.2299.txt |@word tµ:2 sep:1 tˆµν:11 m20:1 ak:4 ii:1 mp4:2 mp2:1 o:1 tˆ:1 teq:10 d4:2 ev:2 λgµν:1 nº:1 nbe:4 gev:1 gφ:1 nk:3 hep:1 matter:1 uµ:1 h0:1 tsb:4 3v:2 tp:29 mµ:1 k2:1 tii:1 ψl:3 m2:10 t2p:1 ph:1 φl:7 ρrel:1 pm:3 3h0:1 dψl:1 tµν:23 iγ:3 zφ:1 m4:2 a0:2 vacuum:1 pv:8 gλ2:1 8πg:2 aeq:2 ρc:2 tº:2 λm2:2 dψ:2 t4:1 arxiv:1 ρm:5 t0:25 2m20:1 ln:3 ωk:9 δm:1 pˆµ:3 mp:12 exp:3 ρv:11 tˆ0:1 gµν:6
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0705.2302.txt |@word gt:11 sci:1 analiz:2 results:1 gy:6 grateful:1 gi:6 finally:1 under:2 stochastic:6 worth:1 case:4 rtn:7 g1:26 springer:2 splitting:1 every:2 formula:1 difference:6 condition:1 school:2 subsets:1 notes:1 solution:2 solved:1 vector:1 anal:1 barles:1 martingale:1 fτi:3 estimates:5 measurable:9 approximation:2 rate:8 summer:1 linear:2 filtration:3 appear:1 itˆ:1 section:2 xτ:2 abs:1 above:2 sup:34 new:3 increasing:3 method:3 exercise:1 satisfy:1 notions:1 equals:1 les:1 ongy:6 xα:1 equations:11 change:1 differential:1 obtained:1 remark:1 larger:1 allows:1 p2:13 published:1 control:9 via:1 followed:1 formulates:1 apply:2 use:1 quasi:1 would:1 prove:2 remains:1 positive:1 contains:2 negative:1 next:1 few:1 associated:1 gained:1 tions:1 operators:1 berlin:2 eξ:2 everywhere:1 normalized:2 known:4 cases:1 hold:1 eα:3 pagination:1 integrating:1 recall:1 equation:1 mn:4 obvious:1 lipschitz:2 following:3 proof:7 f0:2 degenerate:1 do:1 process:7 suggestions:1 bellman:9 sample:1 assumptions:1 numbers:1 contrˆ:1 david:1 information:1 needs:1 end:2 straightforward:1 dwu:1 means:1 optimal:11 parameter:3 priori:1 edinburgh:1 buildings:1 fs:6 ft:12 algebra:1 may:3 cadlag:1 constants:1 si:1 so:1 progressively:4 holds:4 developed:2 wiener:2 paper:1 jakobsen:4 banach:1 differs:1 existence:1 integro:1 τn:2 du:23 1a1:8 1a2:3 fix:1 better:1 resort:1 unbounded:2 jacobi:1 mail:1 main:2 defining:1 non:1 motivated:1 bernoulli:2 noticing:1 introduce:1 hamilton:1 they:2 smoothness:1 bank:1 karlsen:2 easily:1 equality:1 university:1 stochastique:1 inequality:1 each:5 found:1 1an:3 1ai:2 el:1 schemes:2 eh:1 ed:3 revised:1 reduce:1 related:1 applicable:1 breakthrough:1 our:2 special:1 rt:16 ru:21 matrix:1 space:2 furthermore:1 since:6 rev:1 semi:1 rd:4 optim:1 denoted:1 lecture:1 rn:3 illustrate:1 math:7 ftn:1 numerical:4 theory:4 monotone:1 surely:1 york:1 org:1 inductive:1 times:3 isi:2 place:1 hence:8 probab:1 shiryaev:1 first:2 separable:1 major:1 probability:2 variables:3 randomized:10 xr:1 xs:1 electronic:2 xt:18 xu:2 stochastics:2 given:2 introduction:1 dft:11 1a:4 needed:2 1b:8 rates:1 statement:1 siam:1 insightful:1 saint:2 moscow:1 continuous:8 assumption:3 authors:1 than:1 coefficients:6 finitely:1 king:1 approximations:8 classes:1 generality:1 argument:1 krylov:9 say:1 need:1 null:2 any:6 indeed:1 paths:1 lim:4 note:1 gτ:2 take:1 price:1 viscosity:1 nothing:1 analytically:1 class:2 doi:1 ke:1 later:1 kn:8 show:1 random:4 notations:1 spaces:1 solutions:4 keywords:1 pdes:1 minnesota:1 lemma:10 only:1 equipped:1 parabolic:1 integrable:2 continuity:1 diffusion:10 his:1 notation:1 get:1 ϕt:13 expectation:1 ϕs:1 dt:21 reprint:2 dr:5 ds:6 processes:17 fields:1 arxiv:3 contain:1 fixed:1 nδ:1 require:1 set:8 constructing:1 exists:1 hβ:1 see:8 result:4 terms:1 subject:1 3jz:1 αs:1 satisfying:2 αu:2 αt:7 comp:1 conditions:3 available:1 notice:2 recently:1 numer:1 wn:3 however:1 jn:3 wt:3 ws:1 article:1 both:2 last:1 many:1 taking:2 τi:5 equal:2 embedding:1 hypothesis:1 adapted:4 hτ:7 simple:1 2nd:1 dimensional:3 sequences:1 proved:1 pr:1 ps:1 estimating:1 locally:2 due:2 been:1 transformed:1 pi:5 pn:10 define:4 referee:1 controlled:11 received:1 general:5 those:2 applied:3 p1:10 gnt:2 discrete:1 will:2 error:1 stopping:28 almost:1 metric:1 thus:2 ii:1 disjoint:3 karoui:1 march:2 semimartingales:1 pay:4 clearly:3 parts:1 flour:2 finite:10 independent:1 unboundedness:1 i1:6 i2:2 hand:1 infinite:1 recent:1 off:4 expression:1 kne:1 well:1 without:2 comes:1 sets:3 reward:1 sdes:1 diffusions:3 moments:1 ninth:1 using:2 useful:1 lebesgue:1 source:1 setting:1 ska:6 easy:2 theorem:21 nicolai:1 real:2 aspects:1 typographic:1 know:1 integer:1 bit:1 unique:1 loss:1 like:1 lost:1 follows:1 either:1 right:1 methods:3 sequence:3 some:2 respect:1 peter:1 vol:1 provides:1 refer:1 uniformly:1 jumps:1 bs:2 cα:2 chapter:1 piecewise:1 http:1 dependence:1 o:1 h2:16 pays:1 into:2 h1:19 because:1 references:1 ole:1 acknowledgements:1 there:5 borel:1 way:1 function:5 complete:1 ht:38 hi:6 hn:11 convergence:9 removed:1 true:1 made:1 applying:2 supt:1 bounds:1 us:2 eh9:1 below:2 limit:2 uk:2 problem:3 ac:2 constant:1 nauka:1 ai:5 proven:1 denote:3 proves:1 exist:2 inf:1 check:1 ni:7 functions:4 no:1 when:1 detail:1 application:3 other:1 mathematics:1 nt:1 models:1 problems:8 istvan:1 a1:13 ξi:4 generated:1 a2:2 bounded:3 variable:2 assume:4 values:3 approxima:1 time:6 appl:2 original:2
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0705.2303.txt |@word consider:1 caused:4 magnetic:1 results:7 05t:1 computation:1 tomioka:1 consists:1 research:5 causes:1 forget:1 devoted:1 ver:1 calculate:3 tx:1 bx2:1 charge:8 program:1 th:7 ingredient:1 case:2 supported:1 peaks:3 wave:1 electron:4 matsuda:1 ishikawa:1 summarized:1 mixing:2 experimentally:1 hamiltonian:4 issue:1 large:4 wulff:1 small:11 speculation:1 dimer:14 spinsinglet:1 force:1 grateful:1 consistent:1 kato:1 direct:1 approximation:1 second:2 holon:15 further:2 koda:3 odd:1 approached:1 even:1 what:1 nonlinear:1 ohno:2 section:2 tohoku:1 3t:1 current:1 switch:1 dimerized:12 new:1 method:1 contrast:1 dimerization:2 condensed:1 full:6 lee:1 here:8 understanding:4 adachi:1 address:2 change:2 obtained:3 great:1 institute:1 larger:5 approaches:2 perfetti:1 resulting:3 studies:2 fujita:4 lowers:1 via:1 projection:1 classification:5 color:4 yitp:1 1st:1 summation:1 apply:1 unit:1 use:2 nagaosa:2 would:5 quasi:2 eσ:7 next:2 calculation:2 ψi:2 therefore:1 taken:1 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0705.2304.txt |@word limited:2 magnetic:25 dynamic:7 four:3 entropy:1 heliocentric:3 consists:3 woody:3 localized:1 consider:1 fronts:13 calculate:1 paris:1 freytag:5 under:3 characterised:3 alternating:1 desirable:1 connects:1 figs:2 solution:1 convenience:1 organisers:1 direct:4 approximation:1 likely:4 correlator:3 qualitatively:2 estimated:1 even:12 holweger:3 selected:4 steiner:2 above:13 chromosphere:49 new:5 increasing:10 consisting:1 shocks:1 coefficient:3 evolving:1 simultaneously:1 equals:1 here:21 atoms:1 study:13 controversy:1 complicated:3 fourier:3 changes:2 diameter:4 prints:1 slices:1 explained:5 highly:6 visible:10 bruls:1 achievable:1 opacities:2 total:5 linearly:2 would:11 therefore:2 until:1 populations:1 successful:1 excellent:1 hold:1 must:1 mm:138 work:2 erg:1 temperatures:17 ms:1 example:3 give:5 feasible:2 absolute:2 provide:7 very:12 hot:9 significance:1 cadence:1 oscillatory:1 description:3 thermodynamic:4 after:2 dietrich:1 demanding:1 millimeter:8 mesh:5 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0705.2306.txt |@word urbana:1 yields:1 gr:1 remarkable:1 conform:2 out:1 find:2 results:1 meltzer:1 use:1 rotating:1 press:1 thermal:3 entropy:1 stimulating:1 statistical:2 ttt:1 perturbations:3 tend:1 its:3 substituting:1 consider:2 whose:1 based:1 thank:1 decay:3 interesting:2 will:1 dynamical:2 should:1 thermodynamics:2 finally:1 smallest:1 black:30 systems:4 nollert:1 must:2 correction:1 momentum:1 equilibrium:3 real:1 supported:1 return:2 takes:1 saturating:1 than:1 demonstrated:1 possible:1 hashitsume:1 number:3 tbh:5 units:1 commun:1 focus:2 front:1 now:1 gruzinov:1 name:1 february:1 dominate:1 approach:1 exponential:1 turns:1 arxiv:1 kerr:3 berlin:1 grav:1 damped:4 large:1 discrete:1 qc:1 settle:1 unstable:1 mode:3 science:1 2m:3 4πm:1 explicitly:1 stationary:3 noted:1 characterized:5 established:1 upper:2 another:1 colder:1 some:1 back:1 lett:1 connections:1 astrophys:1 namely:1 frequency:3 result:1 rph:7 quantum:2 our:1 dynamics:1 soc:1 eq:6 event:1 shannon:1 canonical:1 respects:1 fundamentally:1 4m:1 resonances:1 away:1 algebra:1 rev:4 below:1 per:1 denotes:1 reminiscent:1 state:3 behave:1 τmin:2 radiated:1 between:1 limit:10 mathematical:1 increasing:1 proc:1 acknowledgments:1 law:1 discovery:1 foundation:1 accord:1 after:1 recently:2 theory:3 deduces:1 respectively:1 ωn:2 mω:1 however:1 here:2 standard:1 strong:1 relaxation:20 put:1 outer:1 imaginary:6 configuration:2 weaver:1 shortest:1 shahar:1 verify:1 cos:2 last:1 institute:1 many:2 taking:2 larger:1 o:6 times:4 turn:1 negative:1 hω:1 dated:1 horizon:1 resonance:3 discussions:1 spacetime:1 finds:1 considerations:1 perturbed:8 azimuthal:2 term:1 timescale:3 bell:1 communication:1 numerically:1 bound:14 eqs:1 down:1 infinite:1 perturbing:2 references:1 least:3 determine:2 qnm:4 actually:1 correspondence:1 jerusalem:1 univ:1 angular:2 unit:1 math:1 straightforward:1 given:4 perturbation:3 temperature:7 would:1 prove:1 previous:1 andrei:1 system:5 been:3 review:1 returns:1 describes:1 axis:1 inner:1 πt:2 detweiler:1 extreme:3 was:1 theoretical:1 gives:1 function:1 mundane:1 israel:2 corresponding:1 hawking:3 form:1 kb:1 am:1 leaver:1 photon:1 blackhole:1 mashhoon:2 magnitude:2 quiescent:1 external:1 realms:1 excellent:1 known:2 hole:20 spirit:1 present:1 longer:1 iωt:1 keshet:1 reciprocal:1 cluster:1 horizons:1 characteristic:1 gravitational:1 12m:1 toda:1 verlag:1 limiting:1 ωi:3 near:3 long:1 values:1 eikonal:1 tones:1 were:1 demonstrate:1 problem:1 property:1 discoveries:1 characterizing:1 attain:1 springer:1 hωi:1 detailed:1 required:1 ringing:2 process:1 universal:3 thus:3 spectrum:2 deep:1 uri:1 ii:1 oscillations:3 list:1 kepler:1 manner:1 research:1 allowed:1 null:1 orders:1 physical:4 ruppin:1 information:2 hod:2 rays:1 thermodynamical:2 minimally:1 dying:1 generic:1 suggest:1 self:1 radiation:1 gravity:2 same:1 illinois:1 field:2 complex:1 pure:1 frequencies:3 test:1 new:1 gets:1 circular:2 description:1 see:1 shall:1 may:2 thermodynamic:3 class:1 decreasing:1 derived:2 quasinormal:5 kubo:1 a2:3 bounded:1 studies:1 velocity:1 corresponds:2 analytically:2 revealed:1 response:1 bekenstein:2 equatorial:1 implies:4 center:1 third:1 hωn:1 typically:1 calculated:1 saturate:1 holes:10 orbit:2 analysis:1 extremal:5 academic:1 part:6 mass:2 fundamental:7 time:7 qualitatively:1 quantitative:1 physics:3 order:2 fact:1
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0705.2308.txt |@word evidence:1 consider:2 rev:7 magnetic:71 results:6 integration:4 four:1 expressions:1 causes:1 compact:1 whose:2 inverse:6 transferred:2 concerned:1 posteriori:1 γt:1 lower:1 quasi:8 present:1 εijk:2 worth:1 amplitudes:1 presently:1 very:3 condition:3 immediately:1 presented:1 ref:9 t2:4 solution:4 large:10 solved:2 vector:1 verdict:1 small:10 leonardo:1 linearizing:2 configurations:1 governing:1 upper:1 smaller:1 force:3 direct:2 sign:1 approximation:6 second:1 enhancement:1 correlator:4 further:1 dynamics:2 widrow:1 linear:3 spectral:1 index:3 what:1 wavenumbers:4 deeply:2 diffusing:1 expressed:1 d3:3 current:1 merical:1 above:4 fractional:2 suppose:1 increasing:1 satisfy:1 evolving:1 full:4 ibid:1 respectively:2 here:4 bi:10 selective:4 bj:6 sinh:2 address:1 represented:1 dissipated:2 equations:20 nachr:1 logarithmic:1 differential:1 obtained:2 antisymmetric:2 suitably:1 study:2 studied:3 completely:1 usually:1 fourier:2 studies:1 useful:2 selfsimilarity:1 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0705.2309.txt |@word homomorphism:1 consider:7 results:1 proposition:17 primes:5 sung:1 toric:2 row:1 devoted:1 λij:1 c0:2 depend:1 graph:2 technique:3 tr:10 tn:3 finally:1 program:1 tj:1 th:1 stable:1 tb:15 ta:4 case:2 yr:5 straightforward:1 very:4 corollary:4 sons:1 decide:1 entries:3 ma:1 rn:4 condition:1 ve2:1 suffices:1 t2:1 solution:5 t1:5 large:1 convenience:1 vector:6 small:1 λi1:1 deleting:1 application:2 mi:1 second:4 chen:1 further:1 αi1:7 zs:2 even:1 aim:2 what:1 filtration:1 invertible:1 rd2:1 trivial:1 section:5 brodmann:2 version:1 above:9 sup:1 new:1 increasing:1 method:1 coefficient:2 degree:5 αij:1 respectively:1 mr:11 modify:1 here:3 ratliff:1 behaviour:1 address:1 trung:3 equations:1 extreme:5 obtained:2 remark:5 institute:2 akr:3 study:3 studied:1 allows:1 contradiction:1 products:1 βij:1 deg:2 quotient:2 2000e:1 useful:1 classification:1 herzog:2 total:1 use:3 asymptotic:3 would:1 prove:1 positive:2 give:3 hanoi:3 epimorphism:4 bases:1 m1:4 therefore:2 taken:2 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0705.2311.txt |@word since:2 minors:1 consider:1 remarkable:2 12a:1 magnetic:49 comparatively:1 results:1 four:4 sergey:2 scalar:1 generalize:1 follow:2 expressions:1 research:2 rot:1 sch:1 particles:13 depend:12 calculate:2 integral:6 paris:1 segments:1 similarity:1 pistons:1 isentropic:1 finally:3 program:1 those:2 under:3 breach:1 analogous:3 applied:3 belonging:3 tanh:2 g3:3 expressing:1 straightforward:1 orthogonal:8 implicitly:1 rise:4 account:2 geometrical:6 every:3 orientations:1 advised:1 exact:1 condition:7 splits:1 ovsyannikov:7 leads:3 threedimensional:1 obvious:1 streamlines:3 irreducible:1 shock:2 solution:73 t0:22 integrated:1 large:2 admissible:4 convenience:1 vector:38 math:5 small:1 entropy:2 div:4 woven:1 programme:1 locus:1 upper:1 foundation:1 consistent:1 boca:1 sinusoid:1 sign:5 zero:5 alfv:1 tangential:2 pass:2 further:2 dynamics:12 ode:1 linear:2 nonlinear:3 appear:3 rate:1 giving:1 exactly:1 axes:4 eic:1 expressed:1 ojk:3 axial:3 odes:3 intersect:2 new:9 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0705.2312.txt |@word gv:1 katz:1 consider:1 secondly:1 caused:1 results:4 four:1 entropy:1 martinis:5 computation:2 invariably:1 consists:2 2r2:1 causes:2 sch:1 compact:1 repetition:2 depend:1 calculate:2 eigenbasis:1 tr:5 pierce:1 charge:7 greentree:1 ti:2 include:2 resources:1 ingredient:1 applied:2 supported:1 jensen:1 advantage:1 very:6 none:1 readout:4 electron:43 manipulated:1 resonant:1 little:1 matrices:1 disturb:1 level:1 transmission:8 cause:3 large:1 small:5 upper:1 smaller:1 oscillation:1 sign:1 approximation:2 second:2 gorman:1 pass:1 further:4 dynamics:2 implemented:1 approached:1 what:1 superlattices:1 nano:7 sun:2 interactions:1 near:2 current:3 sequential:1 above:1 pashkin:2 method:3 nakamura:3 coefficient:2 outgoing:1 full:1 girvin:1 respectively:1 clerk:2 error:1 residual:7 here:3 diagonal:3 mev:7 capacitor:3 groups:1 alone:1 change:2 obtained:3 great:1 property:1 suitably:1 likharev:1 allows:3 example:2 prior:1 amount:3 resulting:1 resonance:1 adopting:1 fourier:1 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0705.2313.txt |@word limited:3 dynamic:3 sonja:1 integrity:2 whose:1 presents:1 neighbours:16 under:10 worth:2 alternating:1 mohammad:1 risk:7 manet:1 every:2 adaptive:1 school:1 supports:1 solution:6 correct:1 evaluating:4 incremented:1 consistent:1 guidelines:1 direct:3 approximation:1 likely:3 implemented:1 even:9 established:1 selected:1 adhoc:1 above:2 conduct:1 new:6 increasing:1 compilers:1 simultaneously:1 sinks:1 romano:2 here:1 hundreds:1 reported:1 protection:1 represented:2 path:5 property:1 study:1 economics:1 permit:1 military:1 suitable:1 changes:1 julio:1 secure:2 slices:1 explained:4 counts:1 total:6 linearly:1 plot:4 would:9 negative:1 overhead:6 therefore:2 25th:1 assessment:1 preserved:3 brings:1 aware:6 berlin:1 springer:3 permits:1 work:15 example:10 wang:1 give:4 preserving:4 want:1 guarantee:1 end:7 hoc:15 provide:2 olariu:1 feature:8 how:6 hop:36 significance:1 symposium:2 description:2 after:1 millimeter:1 minimizes:1 parallel:3 types:1 danny:1 third:2 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0705.2314.txt |@word secondly:1 quarks:3 evidence:1 consider:1 limited:1 caused:1 particular:6 desirable:1 results:1 totem:2 existing:3 illustrated:1 facilities:1 scalar:3 gb:1 grateful:1 go:1 instantaneous:1 contributions:6 increase:2 21st:1 maximally:1 coughlin:1 interactions:2 environment:1 gatchina:1 finally:2 investigation:1 petersburg:2 excluded:1 under:2 atlas:2 worth:1 c25:1 applied:1 luminosities:2 amplitudes:2 presently:1 straightforward:2 c45:1 very:6 rise:3 seemingly:1 wave:1 comparatively:2 mpp:3 c34:1 experimentally:2 forshaw:2 tagging:10 gg:9 impressive:1 presented:1 permits:1 haber:1 skewed:1 large:6 item:3 demonstrated:1 science:1 small:8 mangano:1 cms:4 noted:1 programme:3 jhep:1 gallinaro:1 c48:2 uncomfortably:1 estimates:3 direct:3 approximation:1 across:1 rate:8 perspective:2 further:5 fermilab:1 quite:6 scientific:2 even:7 optimize:1 advantageous:1 brackets:1 section:10 selected:1 contributed:1 current:4 khoze:19 greco:1 d0:1 above:4 new:9 falling:1 contributes:1 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0705.2315.txt |@word limited:1 code:1 eriksson:1 sch:5 varying:1 dynamic:2 results:7 existing:3 known:1 winds:7 consider:3 layers:1 depend:1 alamos:1 flash:3 editors:1 tp:3 must:5 amplitudes:3 advantage:1 very:6 choice:1 falk:1 every:1 affect:2 exact:1 condition:2 level:1 deals:1 prep:1 upper:1 pasa:1 consistent:2 literature:2 imply:2 oder:1 further:1 even:3 employ:1 what:2 appear:1 bergman:1 current:1 above:3 new:1 susanne:1 acknowledgments:1 contrast:1 full:1 prescriptions:5 spacing:1 here:8 understanding:1 ranges:1 explore:1 concluding:1 consideration:1 strong:7 appears:1 logarithmic:1 involved:1 study:1 steffen:2 suggests:2 amount:1 published:1 studies:2 summarising:1 scales:2 groenewegen:2 brought:1 put:1 names:1 rarely:1 predicted:1 use:1 usa:1 remains:1 almost:1 wood:3 therefore:2 theoretical:3 more:2 giuli:1 becomes:1 envelope:2 om:1 glass:1 gallino:1 particular:1 provide:1 actual:1 cases:1 producing:1 circumstances:1 abundance:1 mc:1 arndt:2 work:5 mh:1 sudden:1 obvious:1 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0705.2316.txt |@word magnetically:1 represent:1 consider:1 caused:2 magnetic:14 lack:1 existing:1 eds:1 avalanche:1 gb:1 grateful:1 consists:1 causes:3 29m:1 const:1 γr:4 γp:1 tr:4 young:1 γt:1 tail:1 ucsb:1 γb:1 encircle:1 mpe:1 neuh:3 very:5 wave:11 electron:1 every:1 kϕ:4 resonant:1 condition:1 school:1 presented:3 large:2 vector:1 small:2 periodicity:1 likely:2 estimated:2 gaensler:1 repeaters:1 spectral:1 adds:1 section:4 axes:4 expressed:1 uniform:1 new:1 ever:1 acknowledgments:1 filled:1 condensed:4 component:4 equals:3 here:2 magnetism:1 cylindrical:1 arons:2 along:6 appears:3 change:8 obtained:1 larger:1 fruscione:1 periodic:2 resonance:2 chang:1 makes:1 plotted:1 blackbody:3 addresses:1 explained:1 apj:9 remains:1 quasi:2 predict:1 therefore:1 planckian:1 more:1 3ev:1 pavlov:6 georgian:1 emission:25 curvature:8 lightcurve:3 particular:1 known:2 aligned:2 must:1 none:1 mc:2 grant:1 work:3 minimum:1 values:3 thin:2 following:1 l101:1 give:1 process:1 relativistic:2 pons:4 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0705.2317.txt |@word replacing:1 slope:1 volokitin:1 consider:9 magnetic:2 resistance:6 sernelius:2 existing:2 four:1 entropy:7 computation:1 skin:5 consists:1 reasoning:1 whose:1 depend:2 attracted:1 concerned:1 presents:1 absorbing:1 charge:2 investigation:1 under:2 lin:1 analogous:5 te:3 di1:2 di2:2 ingredient:3 case:12 random:2 straightforward:1 far:2 frequencies:10 rise:2 conditions:1 geometrical:1 puzzles:2 capacitances:3 electron:1 orientations:1 remarks:1 chan:1 experimentally:1 difference:1 enter:1 leads:1 level:2 did:1 ref:2 eigenmodes:1 pacs:1 t2:1 occurs:1 large:7 small:7 inspection:1 rytov:5 strongly:1 unexpected:1 force:19 controversial:1 findings:1 dealing:1 direct:1 literature:1 approximation:2 go:1 zero:18 compensates:1 displays:1 correlator:1 qualitatively:1 substitute:1 linear:1 even:2 what:6 adds:2 appear:1 brackets:2 section:1 near:2 current:2 goes:1 lifshitz:10 deal:1 new:6 technology:1 increasing:2 method:1 temperatures:8 supporting:1 evanescent:3 degree:1 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0705.2318.txt |@word represent:3 consider:3 remarkable:1 illustrates:1 results:5 four:2 follow:1 research:2 relationships:1 ver:1 calculate:1 deterministic:1 supported:1 monotonically:6 wako:1 under:2 norm:2 division:1 updated:1 kπ:1 orthogonal:3 continues:1 figs:3 summarized:1 hirosawa:1 condition:2 school:1 t2:2 large:3 solved:3 small:2 smaller:23 japanese:2 sign:1 rate:13 value:20 incidentally:1 qualitatively:7 machines:1 linear:8 even:1 nonlinear:11 appear:2 deeply:1 section:1 uniform:1 goes:1 new:1 increasing:1 method:3 full:13 respectively:7 component:3 answers:2 following:3 address:1 equations:6 teacher:29 change:1 obtained:8 institute:1 larger:17 approaches:2 amount:1 simultaneous:3 changes:1 composed:3 sgn:7 perceptron:18 use:2 give:2 sports:1 comparing:1 therefore:9 memory:2 theoretical:1 more:14 clever:2 becomes:2 pairs:2 transient:1 normalized:1 known:4 cases:2 high:1 tokyo:1 science:2 equation:3 theories:1 values:2 already:1 averages:2 example:1 figure:3 stated:1 dxp:1 sample:2 minimum:7 bk1:1 tan:2 schapire:1 goal:1 discussion:1 answer:1 ensemble:40 simplicity:2 product:1 information:1 may:1 thermodynamic:3 bkn:1 after:1 variant:1 bki:6 faculty:1 fk:9 data:3 fm:2 dynamical:13 ones:1 order:5 executed:1 over:1 symbols:1 brain:1 paper:18 statistical:7 japan:1 satisfies:2 lg:1 interesting:1 lm:5 decreases:5 forms:1 fig:17 mail:1 cls:1 non:4 ym:1 greater:1 nishimori:1 nada:1 framework:4 they:3 oxford:2 discuss:1 represents:1 always:1 university:4 classified:1 sufficiently:1 l2:1 ji0:4 each:10 2l:1 mean:3 differential:5 inputs:1 generation:1 ed:1 gaussian:4 hara:2 society:4 eq:5 special:1 shown:4 superscripts:1 matrix:3 frontier:1 since:6 rev:3 denotes:5 rb:23 dominate:1 correct:3 rj:25 shows:7 theory:14 given:1 completely:2 nishi:1 training:2 r0:4 ministry:1 turn:3 length:1 isn:1 hence:1 moving:3 qkk:8 there:2 xn:1 xm:4 omitted:1 number:13 kobe:5 electronic:2 city:1 differ:1 introduction:2 eqs:6 store:1 imperfect:1 relationship:3 reversed:2 somewhat:1 translation:1 x1:1 than:14 zero:6 determined:1 contrary:2 were:1 merits:1 treated:6 projections:1 behaviors:19 saitama:1 generalization:52 randomly:2 clearly:1 relatively:2 min:8 self:1 able:1 chiba:1 sciences:2 internal:1 xi:3 performance:6 glasses:1 unless:1 who:2 simplify:1 errors:5 phase:1 analytically:11 fk2:2 abe:1 calculated:5 steady:13 typeset:1 ku:2 mechanical:2 physics:1 show:6 random:1 solutions:7 keywords:1 networks:2 q0:4 based:1 parameters:5 state:11 should:1 only:2 rich:1 adequate:1 dl:1 above:1 means:3 cannot:3 words:1 dt:3 arxiv:1 acknowledgments:1 common:3 analytical:1 shi:2 fixed:2 exists:1 clarified:3 intelligence:1 j1:1 observed:3 culture:1 computer:6 college:1 result:4 discussions:1 statical:1 satisfying:1 artificial:1 enough:2 vkm:4 between:19 drawn:4 perceptrons:8 conditions:11 multiplied:1 recently:1 complement:1 jp:1 however:5 jn:1 here:6 analyzed:3 both:2 limits:1 many:3 equal:3 connection:2 eta:36 figures:4 variance:1 otherwise:1 among:5 others:1 dimensional:3 grants:1 simply:1 learning:71 cs:1 moreover:3 masato:1 considering:3 krogh:1 analogies:1 been:9 ai:8 cosine:12 treat:3 direction:18 corresponding:1 covariance:4 observe:1 understand:1 curves:1 spin:1 former:1 present:1 case:13 ǫg:26 ǫe:1 batch:2 ǫm:1 rbk:9 teachers:50 error:44 aid:1 okada:5 ization:1 vectors:3 jpn:16 averaging:1 vk:3 thus:1 freund:1 triple:2 technology:2 different:7 same:1 unity:3 drj:1 infer:1 independent:7 used:5 infinity:1 monotonic:4 hand:4 uses:2 student:39 potentials:1 neural:2 well:4 roughly:1 analysis:2 solve:2 components:3 gakuen:1 model:17 paradigm:1 dimension:4 r02:3 when:10 obtain:7 underlying:1 human:3 note:1 had:1 confirmed:1 input:6 scientific:1 identical:1 around:2 rules:5 possible:1 test:1 increases:1 jpsj2:1 press:2 using:11 riken:1 necessary:2 follows:8 discarded:1 we2:1 output:2 because:1 some:1 examples:8 hebbian:18 cosines:6 integration:1 does:1 saad:1 noise:1 obey:4 journal:1 processing:1 bk:4 step:6 ratios:1 become:2 properties:6 actual:3 most:1 freedom:1 simulation:7 addition:1 supervised:1 obeys:1 introduced:2 soc:16 cambridge:2 into:1 numerically:8 references:1 theoretically:1 initial:3 long:1 inner:1 analyze:3 was:4 function:3 differences:1 sollich:1 line:9 true:22 partially:1 whether:1 us:1 um:6 limit:6 distribution:4 miyoshi:5 called:4 mechanics:3 storing:1 ac:1 constant:1 defined:3 describe:1 proven:5 general:1 engineering:3 exist:1 simulations:6 education:1 distributions:1 proceeds:1 variety:11 generally:1 graduate:1 other:21 electrical:1 outputs:2 department:2 conclusion:1 update:1 kashiwa:1 a1:1 generated:4 kashiwanoha:1 seiji:1 independently:8 auxiliary:1 rule:1 appendix:2 weights:2 time:8 once:2
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0705.2319.txt |@word stock:1 gericke:1 cristiani:1 burnett:2 consider:2 images:1 switched:1 interference:13 comparatively:1 dynamic:7 results:2 facilities:1 per:4 computation:2 consists:2 expressions:1 contributions:1 gj:1 localized:1 rigidity:1 layers:1 whose:1 depend:1 calculate:6 zone:6 transferred:3 canonical:1 daley:1 quasi:13 squeezing:5 under:2 tc:1 indicating:1 interacting:1 labels:1 amplitudes:10 outside:1 frequencies:4 2re:1 rise:2 indication:1 putting:1 dispersions:1 stays:1 experimentally:2 condition:1 reciprocal:1 vibrational:1 hamiltonian:4 louis:2 integrating:1 large:4 solved:2 science:2 small:6 eigenvalues:2 der:1 possibility:1 smin:2 grateful:1 periodicity:1 zk:4 mi:3 uef:29 sin2:5 direct:1 pulse:1 approximation:5 zero:4 evaluated:1 manipulating:1 odd:1 obey:2 even:3 what:1 plays:1 superlattices:3 rate:1 trivial:1 section:2 near:4 current:1 vezzani:4 ˆb:6 above:3 fractional:2 new:4 ˆj:14 ground:6 jumps:2 contrast:1 body:6 quenched:2 wavefunctions:1 respectively:1 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0705.2320.txt |@word consider:3 kmk:1 results:4 leads:2 roy:1 consists:1 research:1 localized:6 depend:1 calculate:1 γs:5 description:1 th:3 supported:1 jensen:1 very:2 choice:1 affect:2 exact:1 clement:1 condition:4 entire:1 transmission:3 solution:1 large:2 independence:1 small:2 λi1:1 optics:1 dis:1 averaged:1 disordered:3 consistent:2 ghosh:1 past:1 zero:1 rigorous:2 further:1 dynamics:2 pavloff:3 theory:1 even:2 established:1 nonlinear:10 appear:1 sum:2 above:2 scientists:1 new:4 method:1 contrast:1 lee:1 degree:1 respectively:1 aubry:4 realizations:2 here:1 directions:2 equations:3 λin:1 obtained:5 great:1 parameters:1 rigorously:1 study:2 studied:3 pastur:1 paris:1 resulting:2 usually:1 makes:1 halperin:1 limx:1 useful:1 namely:3 private:1 expect:1 condensates:2 kravtsov:1 planck:4 unit:1 derivatives:1 use:1 asymptotic:1 commun:1 negative:1 binational:1 m4:1 m1:1 m0:1 m3:1 m2:3 survive:1 type:1 today:1 dudv:1 israel:3 company:1 envelope:1 odinger:3 validity:1 berlin:2 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0705.2321.txt |@word gt:12 gs:3 lboro:1 chain:1 z1:7 global:1 brownian:10 results:2 leads:2 proposition:17 dist:3 consider:4 depend:4 analytic:1 providence:1 tu:10 γt:13 tn:27 tl:1 does:1 tk:8 stable:22 stochastic:11 ingredient:1 conjecture:2 supported:1 straightforward:1 g0:1 far:1 choice:1 corollary:3 difference:2 fractal:3 ftk:1 condition:3 partitions:1 school:1 yˆa:1 bn:4 supports:1 t2:8 solution:1 t0:1 t1:13 large:1 solved:1 convenience:1 disc:1 rj:25 small:9 markov:2 ftn:11 originally:1 martingale:7 upper:1 smaller:1 2k1:12 2k2:12 10b:2 eλu:1 10a:2 estimates:12 direct:3 jump:2 zero:1 chen:3 further:4 gruzberg:3 even:1 aim:1 filtration:1 itˆ:1 section:12 uniform:4 version:3 3n:2 above:5 sup:21 suppose:8 3a:1 increasing:15 apply:3 method:3 satisfy:1 respectively:3 component:3 κb:3 ρy:2 situation:1 2kl:12 path:4 2kn:2 strong:1 equations:2 2ki:2 z2:9 deduced:1 obtained:1 remark:2 increments:2 shift:1 study:3 studied:3 steffen:2 yˆ:22 poisson:5 domains:3 complicated:1 studies:1 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0705.2322.txt |@word replacing:1 represent:1 gs:20 consider:1 gv:20 interference:1 magnetic:27 lack:1 results:2 leads:2 meinel:1 broader:1 go:1 sci:1 localized:1 21st:1 inverse:3 calculate:4 zone:1 paris:1 tu:1 matrix:3 tail:2 monotonically:1 indicate:1 those:5 excluded:1 under:3 analogous:2 specht:1 case:8 supported:1 proved:1 straightforward:1 zhang:2 rise:1 connects:1 wave:3 fak:4 electron:3 every:1 should:1 little:1 condition:3 four:1 level:20 integrating:3 t2:3 t3:1 large:4 solved:1 vector:2 small:4 relation:3 dubonos:2 gossard:2 ε2n:4 configurations:1 smaller:7 disordered:6 oscillation:12 renormalized:2 haas:2 consistent:7 za:4 zb:4 approximation:9 zero:21 zx:2 perspective:1 qualitatively:3 estimated:2 summation:1 spectral:1 index:2 rate:2 giving:1 sum:1 axes:1 3w:3 remain:1 expressed:2 cell:1 experiment:1 causes:1 above:4 replaced:1 3a:1 acknowledgments:1 contrast:1 3d:1 satisfy:1 ibid:2 ranged:21 respectively:1 spacing:5 here:9 atoms:2 beck:1 magnetism:5 mev:1 them:1 mes:1 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0705.2323.txt |@word concept:1 homomorphism:19 gr:1 green:1 wreath:10 results:7 gy:3 illustrated:1 commute:1 generalize:1 francesco:1 consists:3 gn:9 expressions:1 denotes:6 gi:28 consider:10 devoted:2 whose:5 γy:6 depend:2 concerned:1 equivalence:16 contained:1 tn:4 finally:6 dijkgraaf:2 adjoin:1 th:4 ti:1 decomposition:1 td:1 kξ:2 indicating:1 applied:1 conjecture:1 string:2 very:2 rise:1 translations:2 springer:8 choice:5 b261:1 witten:3 every:2 monster:1 lecture:2 li:2 matrices:2 categories:2 kerber:1 leads:2 obvious:1 riemann:11 presented:1 turns:1 t2:1 t1:5 large:1 discrete:8 zdn:1 uniformizing:7 gruyter:1 upper:2 zn:8 zh:3 zi:1 farkas:1 direct:1 elegant:2 second:1 go:1 cft:12 substitute:1 zs:4 even:1 will:1 what:3 plays:2 stands:2 giving:2 sum:7 interactions:1 transforms:1 expressed:1 current:1 sheeted:1 above:7 new:13 gh:2 multivariate:1 full:1 led:1 notions:1 degree:16 γz:4 respectively:1 equals:5 here:2 modular:11 groups:12 address:2 consideration:1 z0:1 z1:2 z2:2 obtained:2 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0705.2324.txt |@word ibid:2 consider:7 magnetic:1 dynamic:6 results:7 leads:2 issues:1 griffin:3 c0:1 depend:2 calculate:5 re:2 tr:3 baym:1 vef:1 γj:1 γi:2 critical:1 under:1 regal:2 iνm:21 tc:4 activities:1 4ek:1 ohashi:3 zhang:1 very:1 frequencies:1 keeping:1 wave:3 impinged:1 putting:1 figs:1 affect:1 zwierlein:4 matrices:2 condition:1 iν1:1 four:2 level:1 tanh:30 solution:2 large:10 solid:1 convenience:1 schirotzek:1 dealt:1 falco:1 degeneracy:1 concluded:1 ruostekoski:1 occurrence:1 oscillation:2 unpolarized:4 past:1 zero:9 displays:1 further:1 odd:2 what:1 sub:1 stoof:1 comparable:1 section:1 brief:1 expressed:4 uniform:3 current:1 indian:1 melo:2 above:2 illustrations:1 new:3 subtracting:1 method:4 3e:1 body:1 tollett:1 τj:3 respectively:6 component:5 here:11 atoms:29 ranges:1 selective:4 andrews:1 making:1 consideration:1 strong:2 equations:1 appears:3 change:1 κs:14 vµ:2 shift:4 study:4 studied:1 reports:1 amount:1 chemical:3 t21:4 resonance:10 fourier:1 studies:1 plotted:2 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0705.2325.txt |@word essay:1 holman:2 gr:4 rev:13 resist:1 teodoro:1 leads:1 olive:1 scalar:6 entropy:8 houches:1 consider:5 whose:1 respectively:1 concerned:2 rel:1 weyl:1 present:2 th:7 under:2 must:3 heraeus:1 di1:2 di2:2 ingredient:2 started:1 brown:1 conjecture:2 presently:1 takes:1 acoustic:1 very:1 none:2 choice:2 lyapunov:1 witten:1 ma:1 difference:1 condition:1 preuss:1 school:1 riemann:3 level:2 did:1 proposals:1 solution:5 large:1 discrete:1 small:2 relation:1 markov:1 jhep:2 holography:1 zh:1 consistent:7 among:1 ph:2 likely:2 design:1 dynamics:6 implemented:1 even:4 established:1 what:1 stands:1 clock:1 selected:1 decade:1 above:1 new:4 ever:1 acknowledgments:1 multitude:1 satisfy:1 fiz:1 ısica:2 residual:1 here:1 understanding:1 modular:1 les:1 possibility:3 address:1 along:1 strong:4 equations:2 change:5 instituto:2 oxford:2 shift:1 studied:1 allows:1 typically:1 ast:2 suggests:2 survey:1 action:1 suitable:4 spacetime:8 involves:1 composed:1 emerge:1 via:3 bertolami:20 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0705.2326.txt |@word represent:1 logarithms:1 consider:6 chain:1 limited:2 directions:1 both:6 splitting:7 integration:3 four:2 rephrased:1 lla:1 contributions:1 poorly:1 inclusively:3 whose:1 depend:2 referring:1 b134:1 equivalence:1 29a:1 quasi:1 dz2:3 those:1 excluded:1 under:3 analogous:1 include:1 futhermore:1 advantage:1 md:2 far:1 mn1:1 construction:1 coloured:1 b261:1 novel:2 every:1 difference:1 exact:1 skands:1 condition:2 common:2 materialize:1 tran:1 incoherent:1 level:8 induction:1 t2:2 t0:3 occurs:1 large:3 solved:1 restoring:1 sassot:1 indices:3 inspection:2 originally:1 dis:6 zn:6 mn:5 zi:1 zk:1 renormalized:1 dealing:2 direct:2 prevents:1 approximation:2 pkj:2 second:1 α2s:1 insertion:2 trentadue:6 dynamics:5 zq:2 even:1 index:1 sud:2 developed:1 stands:1 iterating:1 sum:6 expressed:1 access:1 experiment:2 eventually:3 fractional:7 expresses:3 ˆj:2 increasing:1 method:1 unintegrated:2 y2:4 pictorially:1 q2k:4 respectively:2 hera:2 chekanov:1 here:1 lack:1 abandon:1 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