text
stringlengths 0
190k
|
|---|
0704.2236.txt |@word partial:1 consider:15 chain:4 results:7 tripartite:4 proposition:10 entropy:19 comments:1 grateful:1 edu:2 go:1 follow:1 informatics:1 research:9 whose:3 preserves:1 hold:4 depend:4 calculate:1 leung:1 contained:1 λn0:2 presents:1 finally:2 christandl:6 protocols:4 γm:5 under:27 teaching:1 analogous:7 insights:1 presentation:2 sent:2 ingredient:1 applied:7 straightforward:1 song:3 far:1 implicitly:1 rise:2 account:2 primed:1 corollary:4 valued:1 zhejiang:2 anonymous:1 govern:1 difference:2 condition:15 paz:1 dim:8 school:1 magic:1 presented:2 meant:1 turns:5 notes:1 tre:1 accidentally:1 minimization:2 convenience:1 math:5 recall:3 dit:1 generalize:3 trr:1 alternatively:1 upper:19 illustrating:1 monotonous:1 findings:1 slepian:1 lecture:1 σa1:6 maximization:3 direct:4 tucci:1 outcomes:2 limǫ:1 second:4 cost:2 ρa1:14 value:1 infimum:8 pass:1 maurer:2 cover:1 reina:1 theory:15 subscripts:1 index:1 what:10 abc:1 abe:1 rate:13 3s:2 section:17 selected:1 mechanics:1 dephasing:1 public:4 pawel:1 version:14 goes:1 sup:5 new:7 increasing:1 method:2 contrast:1 satisfy:2 condensed:1 ensure:1 ρaa:6 degree:4 ρab:11 respectively:2 even:2 equals:1 here:12 bi:4 china:8 others:1 represented:4 σab:2 σaa:1 quite:1 respect:1 alicki:2 logarithmic:1 ensembles:2 obtained:13 great:1 ref:1 antisymmetric:1 institute:4 inspired:1 larger:1 allows:1 approaches:1 χa1:1 koenig:1 amount:10 products:2 professor:2 permutation:1 usually:1 warsaw:1 bob:5 fourier:1 involves:1 patrick:1 qn:2 via:8 useful:2 secure:4 family:2 tensored:1 marginal:1 merely:1 explained:1 convexity:3 private:3 tracepreserving:1 ask:1 weaker:1 apply:3 outer:1 operational:1 univ:2 linearly:2 recurrence:1 use:10 additive:8 takes:4 would:5 prove:10 remains:4 positive:6 stated:2 negative:4 next:1 few:1 partite:10 bases:1 call:1 therefore:2 ip:2 taken:6 black:1 jonathan:3 theoretical:4 more:11 optimizing:1 formally:3 th:1 distillation:15 eferences:1 aca:1 concatenation:1 needed:4 manybody:1 normalized:1 particular:7 known:3 foundations:3 hole:1 conditioned:3 iii:2 appointed:1 negativity:1 had:1 ρa:3 helped:1 ρc:1 ρb:2 fulfils:2 mul:1 ρi:11 science:9 work:1 modified:3 roof:20 ρn:4 ρq:2 values:1 γe:2 cam:1 following:19 trans:3 example:9 proof:30 locc:13 gravity:1 transition:1 tap:1 processing:3 give:2 organized:1 states:38 indicates:1 numbers:2 want:1 sense:1 onclusions:1 γdn:1 nonnegative:2 paweł:3 corrolary:1 gains:1 information:91 needs:3 end:2 notation:1 regains:1 rather:2 ie:4 discussion:1 get:13 savov:2 feature:2 entangled:2 revisit:2 how:6 commutative:1 vancouver:1 thermodynamics:1 pure:5 assistant:1 answer:4 instead:3 verlag:3 ensemble:5 map:1 product:7 explores:1 communicating:1 replacing:1 ancilla:6 after:5 michał:3 mapping:2 straightforwardly:1 diagram:1 applications:1 produce:1 faculty:2 computation:2 choice:1 data:2 types:1 winter:6 realized:2 introduced:2 attempt:1 third:2 onto:1 sq:1 register:21 augusiak:2 ghz:1 purification:4 s3:23 complexity:1 cannot:1 so:14 realizes:1 sm:25 correlation:4 definitions:1 acknowledges:3 bipartite:37 operations:21 separable:4 holds:10 interpretation:2 help:1 produces:1 developed:2 over:14 brandao:2 choose:1 interpreted:1 course:1 paper:8 through:2 wolf:3 thesis:3 mentioned:1 existence:1 satisfies:17 still:5 ieee:3 its:11 matter:2 before:1 superadditive:1 anhui:1 manuscript:1 acknowledge:1 chosen:1 interesting:3 fix:1 cryptology:1 actually:2 forms:1 broadcasts:1 according:1 systems:16 omitted:1 mail:2 main:4 maximally:1 dyson:1 ideal:2 maximal:1 them:2 good:5 combination:4 press:1 propose:2 fig:1 isomorphic:1 framework:1 they:4 optimal:12 sσ:3 sρ:4 now:14 umber:1 discuss:3 wiley:1 suppose:1 represents:1 term:2 finite:2 equality:5 2s:1 always:1 university:24 drop:1 2z:1 2d:1 inequality:10 reasonable:2 each:6 renner:4 found:2 difficult:1 side:2 associative:1 mean:1 subsystem:4 en:1 another:8 zurich:1 ee:18 nagel:1 eg:6 silva:1 reduce:1 idea:1 related:4 applicable:1 society:2 extended:1 ex:1 measurement:8 quantum:68 laboratory:2 operation:9 differ:1 eq:10 special:3 out:10 canada:2 divincenzo:1 shown:8 flower:9 matrix:1 devetak:3 space:2 mq:1 since:12 rev:6 δi1:1 detailed:1 denotes:1 increase:9 hayden:2 acting:6 adapt:1 reader:1 denoted:5 formula:2 rn:4 issue:3 achieving:1 shows:1 achievements:2 foundation:1 provide:3 turning:1 linear:20 assured:1 easily:1 monotone:12 guess:1 standard:1 assures:1 completely:4 formation:3 conditioning:30 members:1 put:1 region:1 monotonic:1 axioms:6 compression:2 definition:25 pairs:1 omit:1 messages:1 british:1 ist:2 turn:1 terhal:1 asserts:3 place:1 due:2 hence:6 monotones:9 bilities:1 generalizations:3 south:1 first:12 blind:1 informations:9 already:4 ntroduction:1 features:2 probability:5 u1:1 variables:1 coming:1 number:16 system:17 channels:5 clear:2 xy:1 done:1 least:2 dong:3 simplifying:1 reached:1 imperial:1 open:5 several:1 york:2 squashed:81 given:28 necessarily:3 rewritten:1 telecommunication:1 similarly:1 unitarity:1 eqs:2 ρabc:1 ρabe:2 construct:2 unruh:1 their:6 assumption:1 brevity:2 normalization:3 statement:5 rates:3 scheme:1 bits:2 final:1 relations:1 gives:3 interests:6 behind:1 completed:1 continuous:7 proving:1 immediate:4 broadcast:1 outcome:3 short:1 authors:2 natural:5 copy:1 uhlmann:2 than:4 toronto:2 distance:1 kind:2 perfectly:1 unfortunately:1 sections:1 namely:3 distill:1 lim:6 contrary:1 were:3 college:1 providing:1 treated:1 schneider:1 decompose:2 mini:1 addressing:2 twisting:1 wyner:1 rewrite:1 ccq:2 modern:1 measure:20 argument:1 generalization:9 say:1 ℓn:1 fannes:5 need:2 seen:1 any:23 indeed:2 multipartite:95 realm:2 built:3 zero:2 output:3 convenient:1 latter:7 2aa:1 able:1 ideas:1 note:9 supremum:2 unnecessarily:1 generalized:4 analogy:1 ancillary:3 φaa:1 channel:1 lecturer:1 formulas:3 begin:1 added:1 optimizes:1 axiomatic:1 aba:1 trρ:1 whole:1 measures:22 subadditivity:4 singlet:1 most:3 wire:1 but:4 representation:4 nothing:1 uncertainty:1 acknowledgements:1 intrinsic:11 class:2 tensor:5 γi:6 don:1 observation:2 ke:1 kd:12 considered:8 average:4 adopt:1 coincides:1 order:1 yang:4 τa1:1 χn:4 χm:2 physics:15 notion:1 fact:23 quantity:7 thomas:1 l57:1 show:21 entanglements:2 analogously:2 registers:2 relation:1 seems:1 decompositions:5 carefully:3 wigner:1 analogue:1 trivial:3 find:1 subtracting:1 pe:2 based:18 proposed:5 simulation:2 distributed:2 written:2 should:2 lemma:15 only:21 explicitly:3 candidates:3 subsection:3 factor:2 constant:4 local:28 achieve:1 continuity:24 do:10 his:10 above:6 cryptography:3 means:5 fellow:1 radtke:2 referees:1 karol:3 da:1 joint:5 dyn:2 ones:2 nearly:1 lui:2 combinations:2 during:1 initial:1 approach:6 arxiv:6 yield:1 summary:3 twice:1 hangzhou:1 common:1 informationally:1 contain:1 qi:4 qk:8 fixed:2 valid:2 thanks:1 cǫ:1 pioneering:2 set:3 constructing:1 exists:2 achieved:2 σa:1 correlations:4 ends:2 bounds:5 relative:7 see:21 computer:4 sec:1 result:13 group:1 discussions:1 close:2 theoretic:1 yes:2 analog:1 techniques:1 hilbert:2 satisfying:3 inequalities:3 multiparty:3 dn:4 review:1 currently:4 consequence:1 λn:4 state:66 ua:2 various:1 between:15 invariant:3 conditions:4 email:5 wide:1 l55:1 notice:2 realizations:1 terms:6 supn:2 extend:2 nature:1 comp:1 uj:2 however:12 hefei:1 implementing:1 vanishing:1 jointly:1 key:48 monotonicity:21 come:1 distribution:17 improve:1 σk:9 both:12 essentially:1 enables:1 prescription:1 σn:2 resides:1 gratefully:1 many:4 taking:2 τi:2 equal:5 ln:3 merging:2 became:1 present:3 context:2 attributes:1 qubit:2 argue:2 expression:2 comes:10 sake:1 arbitrarily:2 among:1 cn:5 study:1 bell:1 simple:4 guaranteed:1 ca:3 asymptotically:4 cf:2 cd:10 povm:1 grants:1 simply:2 dephase:1 nsk:16 proved:11 venn:1 considers:1 simpler:1 pp:20 transformations:1 basis:2 addition:2 associativity:2 three:3 been:7 pb:1 ai:27 secret:4 much:3 pg:1 basic:2 marginals:1 ph:14 pi:26 pn:4 realize:1 pl:3 define:3 cerf:1 graphical:1 arises:1 corresponding:1 received:6 quantities:1 remark:13 gap:1 neumann:2 maps:1 coherent:1 versions:13 oppenheim:8 last:4 denote:7 spin:1 spirit:1 those:1 honest:4 case:36 twisted:2 xa1:12 examine:1 χnm:2 will:29 technical:5 while:6 optimization:1 replaced:1 situation:1 property:7 leaves:1 procedure:1 opt:1 purifying:2 unitary:5 subadditive:1 vol:24 vi:2 von:2 damtp:2 thus:7 non:1 iv:5 ii:6 eve:5 itself:1 im:6 dual:2 limit:1 orthogonal:2 vanish:1 technology:2 piotr:1 different:7 qap:1 grant:1 perform:1 distributions:8 corresponds:1 orner:1 locking:4 same:8 clearly:1 shorter:1 pab:1 concavity:1 quant:6 φe:2 distilled:2 modification:1 party:8 constructed:2 subalgebra:1 grows:2 interpolation:2 independent:3 used:8 columbia:1 i1:1 cptp:1 i3:4 upon:8 mutual:65 hand:6 sys:2 uses:7 implications:1 entanglement:119 build:1 invariance:2 implement:2 identity:1 recent:1 approaching:1 scenario:1 restricted:2 poland:7 min:2 well:5 inherit:2 directly:4 without:1 flags:4 representing:1 sets:2 very:3 diploma:1 paradigm:2 dimension:9 usual:3 unified:1 λq:1 protocol:30 just:10 less:1 being:1 generally:1 observed:1 newton:1 obtain:5 rest:3 csisz:1 got:1 gda:19 transforms:1 immediately:3 facts:6 polish:1 alternative:1 yet:2 previous:2 adding:2 ham:1 candidate:1 density:2 wei:3 royal:2 k1:2 sometimes:1 cc:61 add:2 other:14 combine:1 lett:5 easy:4 theorem:27 reason:3 input:6 engineering:1 mod:1 remaining:1 ic:3 take:6 real:1 extraction:1 aspects:1 nielsen:2 depends:1 2u:1 advances:1 decomposed:1 squashing:5 possible:2 additivity:9 joined:1 vidal:1 know:7 distillable:22 secrecy:6 massar:1 using:6 part:1 intersection:2 moreover:6 apart:1 lond:1 like:1 lost:1 follows:24 interestingly:1 alice:4 noted:3 coauthor:3 transform:1 γk:6 either:3 obvious:3 ivan:1 recalls:1 security:1 works:3 reduces:1 accessible:2 sketch:1 because:4 methods:1 classical:52 sequence:3 conditional:22 some:13 springer:3 regularized:1 pρ:1 include:5 convex:24 proofs:2 reasons:2 nonzero:1 provided:3 entropic:1 recently:1 esq:45 scala:1 positivity:1 measurements:2 thank:2 per:1 prop:2 confidential:1 does:13 decomposition:2 lattice:1 provides:2 steps:1 chuang:1 monogamy:1 proc:1 refer:1 measuring:1 ba:2 bb:64 bc:5 equivalent:2 arbitrary:7 notable:1 agreement:6 notably:1 although:1 ha1:1 graduated:4 avis:1 isit:1 normalisation:2 properties:8 asymptotic:18 about:1 carried:1 extension:22 eavesdropper:5 tracing:2 logn:1 commun:4 discussed:1 meaning:2 o:5 reduced:1 distinct:1 l1n:1 extensions:13 raggio:1 mixed:21 suggestions:1 discusses:1 consequently:3 restrict:1 lieb:1 soc:1 cambridge:6 statements:1 followed:1 presence:3 previously:1 communication:23 into:13 within:4 obtaining:1 bound:23 nsf:1 copies:15 down:1 pair:2 appropriate:1 right:1 parties:16 computational:1 proportional:1 classicality:1 often:1 argumentation:2 log:43 classically:1 completing:1 support:6 there:18 question:5 u0:1 noticed:1 restricts:1 pa:1 way:3 astrophysics:1 was:28 function:40 eth:1 yanase:1 irreversibility:1 form:7 enough:2 smolin:1 converse:1 jul:1 change:1 mysterious:1 construction:4 eurocrypt:1 repeatedly:1 lindblad:3 ha:7 true:4 cqq:1 he:9 made:1 compute:1 full:1 horodecki:23 whether:1 up:1 us:7 tell:1 discarding:1 below:4 projecting:1 ui:5 uk:1 sum:4 problem:1 similar:4 called:5 entropies:10 ub:2 aa:80 ac:4 ab:14 ae:7 defined:11 totic:1 abstract:1 describe:1 am:100 proven:1 general:9 eu:1 single:3 proves:3 exist:1 regularisation:2 our:5 journal:1 inf:18 formalism:1 identities:4 check:5 defines:2 again:4 functions:4 completeness:2 nm:2 no:4 werner:1 allow:3 ekert:2 when:7 application:2 setting:1 normal:1 papers:1 department:3 mathematics:4 ar:1 rid:1 conclusion:1 symposium:1 briefly:3 elements:1 completes:2 resembles:1 june:1 a1:64 a3:9 a2:26 bounded:1 a4:3 studied:1 variable:2 dephased:2 ineq:4 sides:1 structure:1 independently:3 correlated:4 implies:3 auxiliary:1 assume:2 established:1 required:1 bca:1 rule:5 having:2 reproduce:1 observe:4 ustc:1 n0:4 international:1 original:8 |
0704.2237.txt |@word partial:1 consider:4 riccardo:1 rev:1 leads:2 scalar:12 commute:2 grateful:1 edu:2 consists:1 follow:2 whose:3 preserves:6 superspace:1 tr:2 tp:1 finally:1 award:1 preserved:2 th:13 under:3 include:1 ingredient:1 string:8 δw:2 far:1 choice:1 witten:1 every:3 entries:1 matrices:2 condition:1 four:1 annihilated:2 presented:1 ǫa1:2 large:8 ρi:2 convenience:1 vector:7 small:1 jhep:3 force:1 consistent:1 iτi:2 sin2:1 prediction:1 zero:1 complicates:1 further:2 cft:3 quite:1 linear:2 index:1 plefka:1 appear:1 sum:2 near:1 expressed:1 version:1 above:6 new:5 connected:1 acknowledgments:1 satisfy:1 exchange:1 respectively:2 theorist:1 here:6 tangent:2 ansatz:1 groups:1 xν:1 alone:1 path:1 along:6 strong:2 equations:3 xη:1 arena:1 institute:2 study:1 studied:2 suggests:3 periodic:1 loop:27 usually:1 hospitality:1 projection:1 family:4 extra:2 apr:1 requiring:1 planar:1 unit:5 use:2 takes:2 usa:1 few:1 nucl:4 sitter:1 therefore:3 theoretical:3 more:9 flat:2 duality:4 upcoming:1 operators:9 giombi:1 curvature:1 instantons:1 berlin:3 broke:1 known:3 cases:2 middle:1 mm:1 kaluza:1 equation:4 work:2 theories:6 infinitesimal:3 values:6 publications:1 guralnik:3 following:1 example:5 control:2 renormalization:1 calculation:2 preserving:1 high:1 sphere:4 lorentz:1 dxk:1 stereographic:1 degenerate:1 rescaling:1 g2:2 rays:1 notation:1 rather:3 supersymmetries:10 six:1 write:1 very:2 amazing:2 instead:1 parameter:1 sin:8 circular:3 product:1 description:1 algebra:1 may:6 dx4:2 dx3:2 dx2:2 dx1:2 applications:1 plane:4 features:2 physik:2 parallel:1 gaussian:3 natural:3 effective:1 twisting:3 explicit:2 su:18 provide:2 gravitons:1 gamma:1 allow:1 aviv:1 sb:1 acts:1 produces:1 indeed:1 course:1 london:2 during:1 mentioned:1 existence:1 satisfies:1 hebrew:1 before:3 semenoff:1 group:8 thank:1 acknowledge:1 energies:1 interesting:6 brook:2 coordinates:1 actually:1 better:1 choose:2 latitude:4 main:1 might:1 easier:1 supersymmetry:10 eur:1 correspondence:3 cusp:1 non:10 ym:2 greater:1 combination:1 richness:1 ξir:1 introduce:1 break:2 fiol:1 they:10 half:1 now:3 yitp:1 always:1 university:4 fiber:1 each:5 universit:1 side:1 lorentzian:1 constraints:1 σ2r:1 spinor:3 financial:1 dymarsky:1 idea:3 related:2 conventions:1 ǫijk:1 loops:32 our:5 ep:1 special:5 out:4 pullback:1 rey:1 matrix:10 rr:1 solved:1 since:2 crucial:1 zarembo:4 replacing:1 contained:1 math:1 shows:1 after:2 theory:20 diagonal:1 standard:1 base:2 complicated:1 york:1 hep:13 r4:4 r6:1 chiral:13 r3:3 geometry:2 could:1 length:1 including:2 tempting:1 corrections:1 first:1 xj:1 humboldt:1 symmetry:3 powerful:1 geodesic:1 rank:1 system:5 restrict:2 gy2:1 tel:1 singling:1 affords:1 illustrate:1 given:5 perturbation:1 sheet:1 publication:1 become:2 twisted:3 least:1 their:8 too:1 calculations:2 relations:1 gives:1 latitudes:1 tool:1 took:1 superyang:1 part:1 somewhat:1 x2:3 x3:2 x1:2 2az:1 than:1 x4:4 distance:1 erickson:1 second:1 future:1 were:4 elaborate:1 providing:1 decompose:1 perturbative:2 ingenious:1 close:1 longitudes:3 spectrum:1 curves:3 say:2 zu:1 need:1 seem:2 any:1 lie:1 wilson:30 angle:1 studying:1 mills:4 note:4 sciences:1 generalized:1 so:15 circles:6 unless:1 kulik:2 though:1 who:1 singlet:2 most:2 involving:1 germany:1 letter:1 extremely:1 class:5 xµ:6 exact:2 parametrize:1 max2:2 calculated:1 yang:4 exp:3 iaµ:1 usual:2 physics:5 fact:1 particularly:1 show:1 discovered:1 gauge:10 solutions:1 sunysb:2 determined:1 trivial:7 find:1 giant:1 commutators:1 explain:1 written:4 topological:2 identifies:1 only:9 explicitly:1 generators:5 factor:2 circle:12 local:3 hopf:4 hope:1 do:2 klein:1 get:1 de:2 expectation:11 ones:3 nearly:1 dx:4 combinations:3 σ1r:1 ds:1 fields:2 arxiv:2 mapped:1 through:2 wrote:1 set:2 ricci:2 differentials:1 see:2 arc:2 college:2 discussions:1 recently:1 heavy:1 brst:2 points:1 surfaces:2 satisfying:1 harvey:1 supergravity:2 state:2 protected:1 identification:1 between:7 invariant:5 conditions:1 wide:1 preserve:5 notice:1 terms:2 extend:1 weak:1 killing:1 vanishing:1 2pg:1 jk:1 come:1 concentrated:1 both:4 cos:7 last:1 2n:3 many:2 present:5 embedding:1 staudacher:1 finds:2 point:5 simple:3 seems:3 kovacs:1 cohomology:1 dimensional:5 anti:7 writing:1 considers:1 branes:1 forms:7 described:6 itzhaki:1 addition:5 chirality:1 due:1 int:1 reduction:1 combined:2 basic:1 define:1 generating:1 θi:2 supersymmetric:17 observable:1 scalars:5 subspace:1 essentially:1 ansatze:1 those:10 case:6 leave:2 straight:2 value:5 transformation:1 will:28 euclidean:1 while:3 replaced:2 gubser:1 property:1 conformal:2 couplings:6 sw7:2 maximal:3 seven:1 vectors:1 coupled:1 equator:1 them:1 ii:1 simone:1 dual:6 fibration:3 ia:1 vanish:2 superconformal:1 capture:1 different:1 perhaps:1 anymore:1 fibers:2 generic:4 belong:3 cross:1 same:4 poincar:2 shorter:1 parts:1 split:1 pauli:1 modification:2 φi:3 several:1 breaks:1 independent:3 sym:1 hand:1 parametrized:1 action:1 phy:1 dyon:1 identity:1 lower:1 supercharges:8 modes:1 charges:3 parameterised:1 well:4 calibrated:1 solve:1 components:3 model:5 arising:1 left:6 manifold:1 ξil:1 just:1 less:2 being:2 generally:1 yee:1 actions:2 vanishes:1 assigned:1 shape:1 world:1 rotates:1 macroscopic:1 captured:1 adding:1 speculate:1 ads:3 field:6 conclude:1 had:1 except:3 add:1 lett:2 guarantees:1 remaining:1 take:2 real:1 tests:2 read:1 multiplets:1 couple:6 possible:2 maldacena:2 using:1 bit:1 mod:1 appearing:1 like:2 arcs:1 follows:1 reduces:1 bps:13 unstable:1 either:1 arbitrary:8 simply:1 topologically:1 replacement:1 mathematical:1 right:6 often:1 gauntlett:1 some:7 understood:1 shortcoming:1 examples:3 happens:1 provided:1 slice:1 dimensions:1 lead:1 quarks:1 does:2 eliminate:1 expansion:1 σil:4 notably:1 σir:9 nowhere:1 posses:1 properties:2 about:1 would:2 constraint:3 freedom:1 theorems:1 factors:1 oz:1 eight:1 stony:2 specifies:1 computational:1 previously:1 subclasses:1 into:3 within:1 integral:2 nsf:1 three:7 down:2 trancanelli:1 references:1 determine:1 operator:3 proportional:2 spinors:2 institut:1 vafa:1 assumed:1 support:1 there:5 imperial:4 way:4 forward:1 hooft:1 was:1 propagator:1 function:1 form:2 phenomena:1 regard:1 but:9 hu:2 construction:9 aµ:1 line:1 true:1 vevs:1 longer:1 made:1 annihilate:1 consist:1 inside:3 smooth:1 us:2 ur:1 considered:1 below:2 uk:1 similar:2 clear:1 blackett:1 drukker:5 ac:1 constant:5 defined:2 certain:1 abstract:1 moved:2 general:1 globally:1 quantum:1 single:6 barcelona:1 laboratory:1 corresponding:1 constructed:2 diego:1 functions:1 compared:1 entirely:1 integrability:1 no:2 when:2 detail:2 ny:1 other:4 details:2 spatial:1 test:2 dxµ:2 2ǫijk:1 ads5:3 gross:1 why:1 variation:2 allowing:1 coupling:9 required:1 curve:9 together:1 strings:1 observables:2 n2:1 original:1 |
0704.2238.txt |@word now:1 since:1 midpoint:1 consider:2 remarkable:1 illustrates:1 caused:7 spie:1 results:7 indicates:2 known:6 overlap:3 broader:2 follow:2 disk:1 revealed:5 serendipitously:1 poorly:1 synthetic:1 whose:1 pointing:1 zone:1 ergs:2 technique:1 young:1 suprime:3 removal:1 tn:5 critical:1 contours:5 contaminant:1 largescale:1 blueward:1 indicating:2 masked:3 ionizing:9 yr:12 supported:2 shielding:1 mpc:8 takes:1 very:7 discrepancy:1 ostriker:2 helpful:2 hst:2 denoted:2 every:2 difficult:1 summarized:1 affect:1 difference:8 exact:1 condition:1 entire:10 school:1 ccfs:2 level:1 did:4 issue:1 who:1 selfconsistently:1 cmb:1 correct:1 large:8 detected:9 cooke:2 avoiding:1 small:8 relation:1 ueda:2 noted:1 xmmnewton:1 concluded:3 upper:4 smaller:5 grateful:1 ten:1 10m:2 trend:11 trails:1 consistent:9 estimates:4 prediction:2 understanding:1 ation:1 surrounding:2 likely:2 suppress:1 perspective:2 j21:6 pass:1 incidentally:1 further:1 dynamics:1 estimated:11 depression:1 λcdm:1 spectral:2 established:3 errors:1 contradicts:1 rate:1 southwest:1 selected:6 brief:1 arnouts:2 current:1 below:1 dynamical:4 version:3 above:8 required:1 falling:2 order:1 l1:3 method:3 contrast:8 thin:2 body:1 impact:2 full:1 simultaneously:5 evolved:3 arcsec:1 dow:2 respectively:11 mr:1 here:2 atoms:1 met:3 tracks:2 objects:24 focused:1 possibility:2 separation:2 address:1 active:3 along:1 strong:16 respect:2 appears:4 benson:2 obtained:1 searches:1 search:3 drops:1 pressure:1 institute:1 study:6 larger:5 narrower:1 scatter:4 suggests:1 amount:1 chemical:1 survey:10 through:1 poisson:1 permit:1 usually:2 bunker:2 narrow:1 studies:5 tdelay:1 numerical:1 plotted:3 kindly:1 diameter:1 spatially:2 ratios:1 classification:1 scales:1 apr:1 photometric:3 prefer:1 marked:1 highly:1 referee:1 addressed:1 weaker:1 frame:2 stern:1 marker:1 apply:1 counts:14 extinction:3 tools:1 research:2 unit:1 predicted:1 environment:5 francis:3 indicated:1 would:2 brighter:1 remains:1 nine:1 contains:1 photoevaporated:1 pasj:3 intense:1 lbgs:61 mori:5 call:2 therefore:6 criteria:8 taken:2 candidates:1 stage:1 until:1 more:16 flat:1 kawakatu:2 stanway:1 populations:4 becomes:6 starburst:4 corrected:2 emission:18 visual:2 basically:1 pentericci:5 central:7 hole:1 chiu:1 iii:4 must:1 sample:27 account:1 tokyo:6 separations:1 science:2 equation:3 created:1 umemura:9 itself:1 values:1 emitters:7 cam:3 universe:6 following:2 meet:1 original:1 springel:1 example:3 vary:1 turnshek:2 compare:1 transition:1 figure:18 division:1 process:3 outline:1 hydrodynamic:1 near:3 weinberg:2 frenk:1 high:31 effectively:2 way:2 performed:3 magnitudes:7 yutaka:1 magenta:2 counting:1 hydrogen:1 occur:1 calculated:1 absolute:3 sr:1 sit:1 rather:1 discussion:1 means:2 thoul:2 species:1 regions:17 located:1 estimator:1 criterion:5 actual:1 influences:1 significance:2 instead:1 gebhardt:2 isotropic:2 profile:1 simplicity:1 overdense:9 highz:3 galactic:4 ferent:1 seds:2 may:3 lae:41 after:6 derived:5 laa:18 diagram:2 independent:1 stars:10 designed:1 mag:11 reaction:1 society:1 qsos:21 da:7 data:7 concerns:1 gaussian:1 timescales:1 kurk:2 johnson:1 3h:1 consequently:1 spectra:2 lines:9 cosmology:1 complexity:1 b711:20 green:11 sensitively:1 asserts:1 correlation:4 halos:3 fan:5 sa:1 j0836:1 shimasaku:9 davey:1 typical:2 unsolved:1 evolutionary:6 saturated:2 feedback:2 september:1 indeed:2 astronomical:2 restframe:1 02h:1 interpreted:2 gao:2 overdensity:8 thermal:1 paper:3 including:2 filters:4 cyan:2 strength:6 japan:7 still:6 fwhm:1 its:10 galaxy:27 before:1 lf:1 pirzkal:4 style:1 derive:1 efstathiou:2 symmetry:1 imf:1 chosen:1 ll:1 presence:3 yan:2 vicinity:6 decreases:1 williger:3 toru:1 age:4 absence:2 lu:2 firmly:1 choose:1 total:3 clusters:1 areas:1 might:8 h0:1 forest:1 downsizing:1 them:2 good:2 greater:3 later:3 matches:1 auto:1 isolation:1 largest:1 cover:1 investigated:3 break:12 band:20 effects:1 sextractor:3 6l:1 clouds:1 speculate:1 hall:2 halo:14 densities:1 represents:1 gets:1 hereafter:2 brightness:1 gawiser:5 university:6 presented:1 identified:1 capability:1 sufficiently:2 magnitude:24 lacy:2 mode:1 fields:23 found:21 photometry:4 destined:1 dif:1 constraints:1 l93:1 bridging:1 square:8 4πr2:1 telescope:2 fairly:2 energy:1 reduce:1 idea:2 inhomogeneous:1 mar:2 yoshida:8 accumulated:1 laboratory:1 ew:4 beyond:2 special:1 out:6 shown:1 missed:1 mcmahon:3 quality:1 miyazaki:2 virialization:1 projected:1 denote:5 denotes:2 increase:1 contained:2 rg:9 emerged:1 suggesting:3 formula:1 dominate:1 cause:1 occurs:1 red:11 shows:11 foreground:2 earlier:1 angular:2 l17:1 raise:1 passes:1 multicolor:1 turned:1 contain:1 galaxies:43 differ:1 free:2 standard:2 completely:2 perturbation:1 formation:26 imaging:10 bruzual:2 eisenhardt:1 intermediate:1 estimate:4 1000k:1 telescopes:1 log:1 definition:2 pairs:2 derivation:1 selections:1 could:13 area:5 cosmic:2 so:2 times:6 filter:3 turn:1 conducted:1 plane:3 place:2 massive:6 ism:2 transfer:1 hence:3 discussions:1 loud:1 support:1 first:7 major:2 there:4 features:1 probability:2 chance:1 omitted:1 number:34 comprised:1 inhibits:1 spots:1 another:4 blank:1 mvir:8 thick:2 fluxes:5 open:5 bertin:2 size:4 overzier:12 given:5 law:1 checked:1 nebulae:1 indicate:2 introduction:1 test:1 top:2 achieved:1 system:3 least:1 electronic:1 their:21 cooling:1 finding:1 observations:5 passed:1 miller:1 white:1 cycle:1 structures:3 final:2 speaking:1 exposures:1 exploring:1 inefficient:1 wavelength:4 baryon:2 completed:1 exactly:3 park:1 took:1 rejected:1 direct:1 environmental:1 assumption:1 optical:1 too:1 somewhat:2 than:42 l9:1 population:7 wide:4 observatory:2 target:5 showed:1 1m:1 double:1 distinguishes:1 evaporates:1 zero:1 charlot:3 limiting:9 matter:2 incompleteness:1 future:3 contrary:1 amplitude:4 were:24 identical:1 radius:3 gives:2 result:4 νl:8 hz:2 motivation:2 superwind:2 quantitative:1 reionization:1 unchanged:1 mind:1 spectrum:1 interpretation:5 dash:1 already:6 manuscript:2 width:2 headings:1 lbg:25 madau:2 seen:6 concentration:1 unaffected:1 apparently:1 any:3 relatively:3 comoving:3 proximity:2 nights:1 triggered:1 able:1 interlopers:1 efficient:1 laes:116 self:1 hubble:1 carswell:2 chiba:1 fitting:1 causing:2 2006a:8 take:1 2006b:9 spergel:2 negligible:1 coincide:1 mit:1 l65:1 circles:2 even:5 play:1 added:2 allow:1 opposite:1 track:5 object:4 fails:1 wells:1 overdensities:2 most:5 bias:1 intergalactic:1 experiences:1 overlapping:1 significant:6 comparisons:2 phase:8 baryons:2 kazuhiro:1 measured:3 had:5 inconsistency:1 latex:1 picture:2 chemistry:1 constructed:2 especially:4 average:5 adopt:1 stronger:1 inferred:1 typeset:1 underdensities:1 hawthorn:2 definitely:1 wind:1 diagnostics:1 velocity:1 satisfying:1 semianalytic:1 physics:1 naively:1 incomplete:1 slope:1 impression:2 selection:9 intensity:8 show:5 text:2 detection:9 random:7 infrared:1 discovered:5 bright:12 radio:7 inconsistent:1 carefully:2 ccds:1 rough:1 epochs:4 find:1 arcmin:1 ghost:1 giant:1 northeast:1 based:8 just:1 parameters:2 extending:1 explain:1 heavily:1 distributed:6 outside:2 woodgate:1 should:6 jan:2 hierarchy:1 only:14 venemans:8 black:3 rich:1 ouchi:5 acknowledge:1 b704:1 circle:7 he:3 local:16 loeb:2 kashikawa:12 do:2 over:6 his:1 triangle:2 lyα:20 distance:2 arcmin2:5 de:7 overall:1 hamana:3 trees:1 degradation:1 agns:3 october:1 nearly:2 closely:2 during:5 suggest:2 procedures:1 magorrian:2 unfortunately:1 λc:1 evolution:4 wolfe:2 continuum:11 explore:1 luminosity:11 arxiv:1 bland:2 consisting:1 coincidence:1 network:1 investigate:1 common:1 activity:6 fainter:4 identify:1 eyles:3 automatic:1 mergers:1 view:1 cole:1 rms:1 aspect:1 higher:6 physically:1 national:2 hα:4 bajtlik:2 relative:6 edition:1 see:4 sed:8 sec:1 quantitatively:1 enhanced:4 operated:1 close:2 luminous:4 laas:35 subject:1 phases:2 detect:1 probable:1 16h:1 placed:1 define:1 pattern:1 diluted:1 sites:1 artificial:1 tend:1 favor:1 state:1 determined:5 identification:1 tendency:1 between:27 probably:1 boundary:1 previous:3 conditions:1 mainly:1 tent:1 observational:8 comparable:1 restricting:1 recently:2 right:2 nature:5 targeted:2 jp:1 suppresses:1 weak:2 however:8 spectroscopic:3 efficiency:1 hypothesis:1 1mpc:1 extent:2 contamination:5 distinguish:2 virial:2 fukugita:2 exposed:3 suppressed:4 problem:1 thank:1 suggested:5 both:10 essentially:1 providing:1 colors:1 triggers:1 region:24 uncertainty:1 heating:1 attributed:1 intema:2 sensitive:2 merging:1 accre:1 context:1 exceeds:1 variance:1 masses:1 mean:5 σw:1 photons:1 nearby:3 among:4 comparative:1 co:3 cm:3 point:1 color:10 connection:2 excess:8 protocluster:9 corresponds:5 environments:1 sampling:3 ii:4 reported:1 non:1 dr4:1 leads:1 constant:2 throughout:1 effective:1 points:2 second:3 landolt:3 targeting:2 clusterings:1 lyman:24 basis:1 addition:3 locally:1 radiative:2 due:11 been:13 pixels:3 reduction:3 pa:1 runs:1 combined:1 delay:7 basic:1 expected:9 intensities:1 ph:11 fig:8 photoionization:15 life:1 adopted:3 corresponding:8 samples:7 received:2 ages:2 imag:1 formed:3 qso:105 interpretations:2 smoothed:2 aperture:2 orange:4 coherent:1 observe:1 corner:1 covers:1 systematic:1 ours:1 improved:2 general:5 importance:1 those:3 aid:1 case:9 randomly:1 main:1 external:4 solid:8 reliable:1 collapse:5 evaluated:4 pixel:2 will:6 dusty:4 while:8 ellis:2 replaced:2 cannot:7 promising:1 irrespective:1 property:1 discoveries:1 manner:1 susa:2 versus:1 szalay:2 categorized:2 almost:17 characteristics:1 simulations:2 thus:4 site:1 surface:7 according:2 helped:1 cluster:37 vs:3 properties:1 against:2 turns:2 maximal:1 limit:3 helium:1 examine:1 comments:2 grown:1 confirmed:3 l25:1 excludes:1 grant:1 generic:1 dithering:2 radiation:28 cross:4 same:17 clearly:3 shorter:2 prevented:1 epoch:5 potentially:1 bands:1 web:1 several:5 residing:1 templates:1 evolve:1 dearth:1 used:8 peaks:2 blue:5 effect:8 ferguson:1 hand:3 devoid:1 running:1 edges:2 dust:4 completeness:10 validate:1 recent:1 relies:1 recognized:1 lower:5 shaded:5 center:2 scenario:3 older:1 pennsylvania:1 restricted:2 calibration:1 well:4 analysis:2 without:8 solve:1 temperature:2 redshifted:2 consistency:1 position:4 model:13 ccf:8 dark:2 whereas:3 kauffmann:2 left:1 spherical:3 they:4 proposed:3 less:8 being:1 generally:5 observed:6 distribute:1 yee:2 rest:7 j0924:2 sources:4 distant:3 questions:1 positions:2 hongo:1 absorbers:1 yet:1 alignment:1 projection:1 onset:2 rgs:9 preprint:1 timescale:3 density:17 absorption:4 regarded:2 sky:7 except:2 counted:1 discuss:2 source:9 potential:1 5h:1 easy:1 poissonian:3 duncan:2 ranging:1 east:1 hat:1 details:2 real:2 pair:2 saturation:1 around:47 depends:1 mitaka:3 showing:2 possible:7 early:5 department:4 kpc:2 background:14 clustered:7 using:9 accurate:3 accepted:2 correcting:2 advanced:1 essential:1 generated:1 apj:31 mpc2:1 like:3 semi:1 identifying:1 bulge:1 follows:2 interestingly:1 specific:1 flux:5 homogeneously:1 index:1 either:6 night:1 barkana:2 photodissociation:1 reduced:1 cooled:3 making:1 sharp:1 because:7 old:1 often:2 habitat:2 sequence:3 shen:2 flatter:1 plausible:2 some:7 under:2 steidel:7 j2000:1 trends:1 examples:4 promotion:1 redshifts:4 images:5 conclusions:2 kitayama:4 pronounced:1 fov:3 scale:6 mately:1 confirm:1 broadband:4 scalo:1 avoid:8 measurements:3 integration:1 markers:1 ikeuchi:2 kms:1 deficit:3 provides:2 assuming:2 prog:1 sdss:19 imply:1 funabashi:1 biased:1 noise:2 assembly:1 scientific:1 power:1 slight:2 equivalent:2 each:18 aj:4 expansion:1 stellar:10 how:1 host:3 ztot:5 giavalisco:2 although:12 described:3 includes:1 emulateapj:1 supermassive:1 panel:3 comparison:1 about:3 rare:2 carried:4 oh:1 coexist:3 tracing:1 125m:1 discussed:1 haehnelt:2 o:8 simulation:3 acs:2 deserves:1 range:6 important:5 furusawa:1 greatly:1 adelberger:4 connected:1 2k:1 slightly:5 block:1 peak:1 seeing:1 faint:1 redshift:14 h2:2 landy:2 into:3 within:6 bound:1 down:9 lies:1 subaru:4 shapley:7 references:1 determine:1 speculated:2 actually:1 valuable:1 mere:1 significantly:2 clustering:12 uncertainties:3 statistics:2 mask:4 few:7 assumed:1 strictly:1 initial:5 stark:5 smoothing:1 dispersion:3 start:1 much:6 low:19 fraction:4 astrophysics:1 dickinson:2 analyze:1 was:40 contiguous:1 assumes:1 function:4 tight:1 filamentary:6 form:5 forming:4 collapsed:2 differences:1 delayed:1 but:10 hu:3 astro:11 collected:1 neutral:1 hierarchical:1 segregation:5 solar:1 estimation:1 mnras:12 mentioned:1 line:5 removed:3 substructures:1 considerable:1 observation:1 count:12 teplitz:1 approxi:1 made:3 middle:1 pettini:2 deficiency:1 whether:1 ut:1 inside:1 uv:40 up:1 cases:1 different:7 mtk:1 note:7 ωm:1 spectroscopy:2 distribution:17 value:4 similar:6 called:2 protoclusters:2 separately:1 strongly:7 ac:1 ab:2 associated:8 yagi:2 defined:6 metal:2 abstract:1 describe:1 deep:5 evidence:7 single:1 enable:1 exist:5 our:11 journal:1 babul:2 rees:4 ing:1 distributions:5 happen:1 triangles:3 physical:3 redder:1 again:3 functions:4 avoided:1 discriminate:1 equilibrium:1 no:11 dashed:3 nb:11 when:12 nao:1 graduate:1 field:84 narrowband:3 other:10 role:1 pascarelle:4 spatial:3 toho:1 igm:2 theor:1 hydrodynamical:1 palunas:2 espey:2 consis:1 zheng:4 star:14 superposition:1 gas:7 why:1 searched:1 variation:1 occurred:1 pointings:1 metallicity:1 kaiser:2 5mpc:2 coverage:2 15h:1 astronomy:5 structure:16 exposure:2 building:1 agn:2 younger:4 correlated:2 rr:4 assume:1 requires:1 apertures:1 bottom:2 curve:2 rule:1 enrichment:2 lacey:1 depth:1 mass:29 4k:1 image:7 time:14 baugh:1 l66:1 resolution:2 having:8 normalized:1 |
0704.2239.txt |@word limited:3 similarity:1 luminosities:8 four:2 controversial:1 parameterization:1 poorly:1 increase:11 fronts:2 calculate:8 2lpt:1 suprime:2 γi:10 under:2 summarizes:1 updated:1 πr2:5 void:9 every:4 figs:2 appenzeller:1 affect:9 logarithmically:1 vast:1 spie:3 cianci:1 exaggerate:1 cmb:5 miller:2 consistent:14 estimates:3 direct:1 approximation:3 second:6 qualitatively:2 estimated:3 even:26 errors:8 selected:5 contributed:1 above:9 new:5 increasing:6 coefficient:1 evolving:1 simultaneously:2 sinks:1 whose:1 never:3 residual:2 here:6 ionization:22 fairly:4 active:8 path:3 interpret:1 patches:1 obtained:1 study:11 changed:2 approaches:1 reports:1 ignoring:1 procedure:1 fourier:4 changes:2 der:1 ofsight:1 yamada:1 projection:2 slices:2 explained:1 highly:1 modulated:1 total:4 plot:4 would:26 motivate:1 m1:1 therefore:13 distortions:1 until:2 fractions:3 relax:1 conclusions:6 excellent:1 foregrounds:1 ward:2 hold:1 must:8 abundance:9 ma:2 mm:1 mn:1 erg:11 emitters:87 exceptions:1 hansen:4 springel:7 example:5 give:2 organized:1 indicates:1 degenerate:2 david:1 end:11 minihalos:5 provide:9 feature:3 far:4 significance:7 answer:1 matias:1 modulation:7 lae:93 santos:14 icant:1 law:1 constants:1 marginalize:1 attempt:2 effective:5 hypotheses:1 correlation:29 lensing:1 order:14 wind:20 feedback:1 over:20 vary:1 expects:2 dijkstra:15 xi:79 vastly:1 before:1 satisfied:1 manageable:1 fit:4 imf:2 fix:1 pritchard:2 better:1 production:3 fig:8 weeks:1 totani:3 easier:1 overcome:1 maximal:1 hawthorn:1 affected:4 combination:2 break:6 band:15 effects:9 they:16 represents:3 barton:1 good:2 reasonable:2 each:21 side:7 mean:8 schemes:1 telescope:7 evolve:2 displacement:1 grbs:2 used:15 caustic:2 substantially:3 laboratory:1 contend:1 gridded:1 restricted:1 particles:2 photometrically:1 rb:5 reader:1 millions:1 foundation:2 linear:4 written:1 surveys:60 free:4 standard:4 subtended:1 formation:6 detecting:4 obstructing:1 telescopes:4 nebulae:1 masanori:1 created:4 starts:1 inexpensive:1 cosmic:17 days:1 filter:4 ism:1 signature:5 rybicki:2 speeds:1 moorwood:1 already:5 features:3 nhi:3 primary:1 thereof:1 featured:1 another:3 thick:32 illustrate:1 toy:3 likely:3 similarly:1 top:30 returns:1 approximately:7 needed:1 zeros:1 observations:16 eqn:1 hewitt:2 centered:2 took:1 somewhat:1 peculiar:5 expanding:1 distance:1 target:3 showed:1 tree:1 rate:7 bi:1 matter:3 tion:5 contrasted:1 solely:1 displays:3 entail:1 spectrum:43 attenuation:2 ras:26 seen:6 unaffected:1 tells:1 ray:2 strength:2 responsible:2 indexes:1 oriented:1 fitting:1 calibrated:1 absorbed:4 2006b:3 explanation:3 infalling:1 circles:3 blue:5 though:5 object:1 troughs:1 hui:2 optimized:2 phase:4 mitigate:1 observation:5 upenn:1 calculated:24 flow:1 bracket:1 principle:1 quantifying:1 sum:1 dot:12 incorporate:1 probe:5 infrared:1 implying:3 radii:1 radio:2 d3:2 proposed:1 varied:1 adequate:1 do:19 tiles:1 de:1 stop:1 preferred:1 despite:4 unfortunately:3 fields:6 acknowledgments:1 twice:1 reference:2 sensitivity:8 emergent:1 detection:4 depends:11 radius:13 result:13 sporadic:1 limiting:1 best:1 ichikawa:1 modulate:1 drawn:1 approach:1 sections:1 terms:5 extend:1 nature:5 overestimates:1 weak:2 however:28 wu:1 harvard:3 extent:4 contamination:14 improve:2 essentially:4 lensed:1 uncertainty:6 variance:19 contribution:5 argue:1 timescale:4 targeting:1 radiative:10 three:13 been:17 quickly:3 much:22 interest:1 kodaira:1 fesc:9 suppress:2 concerning:1 argument:1 thommes:3 input:1 contam:1 overdensities:1 employ:3 near:6 suppose:2 launched:1 mistake:1 pessimistic:1 cont:3 ir:1 tions:2 iv:1 ii:17 disfavored:2 conf:1 confirmed:5 constrained:3 perform:4 suggest:6 make:8 cumulative:1 complex:1 potentially:2 dimensionless:2 several:8 independent:17 satellite:1 peaks:3 percolation:2 hand:4 normalization:5 cycle:10 weakly:1 kept:1 programs:3 lidman:1 left:8 mclean:1 just:6 sentence:1 photo:7 newton:2 identify:3 yes:1 yet:1 previous:9 δne:8 had:2 jefferson:1 easy:1 hat:1 opt:1 l85:1 insensitive:1 posed:1 possible:5 collisionally:1 possibly:1 background:1 clustered:3 partridge:2 occurring:3 desire:1 performing:1 isotropy:1 steps:2 arbitrary:1 interestingly:4 webb:2 www:2 right:6 truncated:1 pettini:1 unnecessary:2 escape:3 shapes:1 fov:10 dense:1 popii:2 bottom:24 microwave:1 contributing:1 caustics:1 recombinations:1 post:3 properties:16 proceed:1 limitation:1 haehnelt:2 o:6 plus:1 slightly:8 differencing:1 soc:2 contains:1 presence:4 material:1 bound:2 down:3 refined:1 reducing:1 luminosityweighted:1 often:1 support:1 transform:1 interlopers:6 width:7 influencing:1 fraction:27 astrophysics:4 was:12 subtend:1 medium:3 gaseous:1 form:4 offer:1 forming:1 differences:6 nirspec:8 rauch:1 removed:1 true:5 versions:1 inside:3 detectability:3 maximum:6 discarding:1 simplifying:1 lucile:1 unusually:1 panels:32 emit:2 sight:9 computing:7 abstract:1 statistic:4 evidence:4 exist:1 simulations:16 accounting:2 check:4 physical:1 vista:1 dotted:11 no:8 whereas:13 generally:1 ne:24 imparting:1 reality:4 setting:1 dekel:2 test:4 ns:2 shrink:1 mcquinn:32 peebles:2 models:39 uniformly:2 falloff:1 billion:2 younger:1 happening:3 assume:19 time:8 push:1 nuclei:1 assump:1 slope:2 l17:1 global:2 focus:1 leads:1 computation:4 morphology:9 spaced:1 abundant:1 row:4 certainly:2 depend:7 technique:5 vey:1 2004c:4 2004b:1 2004a:2 keck:2 advantage:3 frequencies:3 choice:2 little:1 exact:5 minute:1 clouds:1 level:5 altering:1 turns:1 anisotropy:1 leave:1 separations:1 upper:3 work:4 trend:2 prediction:2 rhoads:9 spectrograph:3 targets:1 spectral:2 appear:2 uniform:5 current:21 boost:1 satisfy:1 dictates:1 dwarf:1 feng:1 understanding:3 groups:3 along:9 appears:2 change:13 box:30 sausalito:1 thirty:1 shift:1 commonly:1 mosfire:8 poisson:6 resonance:1 deg:8 studies:11 plotted:1 inference:1 extra:1 bolton:2 marked:1 mmin:57 planck:1 predictions:10 scenarios:1 pmpc:13 criteria:1 theoretical:3 anticorrelation:1 outputs:4 apparent:1 absorptions:1 appendix:13 commissioned:1 cases:3 eα:2 easiest:1 parameterize:1 rotational:1 unbiased:1 local:3 reviews:1 labeled:4 hope:1 cam:2 following:1 making:2 trans:1 hibon:1 dedicated:2 figure:95 predict:2 zaldarriaga:11 spt:1 sample:29 weighting:1 priate:1 performed:5 allowed:1 spanning:1 hydrogen:5 mesinger:4 rays:1 fortunately:3 discussion:2 write:2 criterion:3 fourth:1 optimal:4 parameter:5 pint:3 map:3 explorer:1 influenced:1 may:22 use:20 explored:2 lidz:7 data:19 grow:2 correlate:1 sq:12 eng:1 yielding:2 ghz:1 cosmology:7 inform:1 ionized:30 so:2 progressively:1 halos:44 typical:2 wavelengths:2 indeed:1 years:9 ended:1 statistical:2 omitting:1 argued:1 peterson:1 still:2 tendency:1 observational:2 derive:3 group:3 thank:2 how:6 interesting:2 vicinity:2 decreases:5 broadcasts:1 offers:1 ours:1 cuby:2 modestly:1 non:4 matches:2 conversations:1 evolution:28 scaling:6 half:1 discuss:2 halo:38 term:9 equality:1 james:2 appropriate:1 realistic:2 bursts:1 entirely:4 square:4 significantly:18 gaussian:5 snapshots:5 challenges:1 astrophysical:2 year:7 wavelength:1 ev:1 abel:3 shown:5 space:8 furthermore:2 looking:1 suggesting:2 formula:1 dominate:2 correct:4 shows:9 plotting:1 complicates:1 theory:4 jwst:27 million:4 possibility:2 diagnostic:1 statistics:16 complicated:5 org:1 widths:1 place:5 massive:17 first:14 xh:1 spergel:4 shapiro:1 omitted:1 comprised:1 long:5 directly:1 impossible:1 array:3 open:1 angular:11 affords:1 size:13 given:10 ian:1 indicate:2 cooling:2 1e:3 alfred:1 white:10 structures:1 gives:1 deg2:1 hα:2 way:2 twopoint:1 accurately:2 transverse:1 released:1 absorbs:1 eliminated:1 than:81 intrinsically:1 wide:2 l47:1 third:5 favors:4 require:2 future:3 werf:1 were:8 tophat:1 prospect:1 considerably:1 reionization:182 casali:2 locations:1 generalization:1 inhibiting:1 any:5 laes:110 answering:2 isolate:4 note:21 potential:8 take:9 simplifications:2 concern:1 highredshift:3 begin:1 altered:1 trace:1 opposite:4 probed:1 decreasing:5 falls:1 insets:1 intergalactic:3 printed:1 baryons:2 latex:1 especially:1 surprising:2 considered:7 average:31 adopt:2 drive:1 wing:15 larry:1 ohta:1 conservatively:1 typically:10 precise:2 drastically:1 shot:22 show:10 bright:4 threshold:9 aggressive:3 ground:3 xmm:2 astron:2 specifically:1 ratio:13 zahn:7 behind:1 analytic:6 only:25 explicitly:1 black:4 ouchi:5 normalizations:1 windowed:1 soon:1 simplistic:1 unimportant:3 cannot:5 nearly:1 reveal:1 uchicago:1 yield:2 predicted:1 wyithe:5 ignored:2 physically:1 lofar:2 ends:3 bounds:1 relative:7 eliminating:1 uncorrelated:5 wonder:2 detect:10 ways:1 justifies:2 energetics:1 outside:1 morales:2 between:56 justified:2 across:1 notice:1 vertical:3 coms:1 suppresses:1 courbin:2 concentrate:1 virial:7 come:1 outflows:3 many:10 region:21 21cm:3 multipoles:1 expression:2 nearby:2 duty:10 among:1 jeans:1 pole:1 grants:1 anti:3 spans:2 moreover:1 oliver:1 hattori:1 lyman:5 capable:3 suppressed:10 absence:3 sheth:4 damping:15 followup:1 direction:2 thousand:1 photon:4 observe:4 former:2 those:9 case:14 profiles:11 subsample:1 fiducial:6 promising:3 situation:1 salpeter:1 fool:1 dubious:1 middle:20 bias:12 furlanetto:24 different:26 develop:2 same:44 configurable:1 epoch:2 html:1 arguments:1 propose:1 constructed:1 events:1 status:1 investigated:3 boosted:1 constraining:1 investigates:1 changing:1 invariance:1 distribu:1 tracking:1 modes:3 largely:5 motions:1 floor:2 roughly:16 without:4 alleviate:1 fixing:3 model:130 dimension:2 kawai:1 being:6 when:29 ng:2 speed:1 photons:26 seems:1 except:4 improvement:1 instrument:1 unambiguously:1 samples:3 constant:4 real:1 around:5 rules:1 myr:2 amd:1 nircam:3 dark:5 np:5 grid:7 mon:1 using:26 mpc3:2 particle:2 reduces:1 velocities:3 maintained:1 either:2 characterizes:1 inter:1 reduced:6 grouping:9 specifies:1 picture:1 imaged:1 redshifts:14 duration:3 imager:1 provided:4 slice:1 ellis:2 dimensions:4 confirm:4 willis:2 moon:1 evolu:1 decomposition:2 provides:3 refer:1 measuring:2 biased:10 scientific:1 power:42 comparison:8 oh:6 discussed:12 estimator:1 pockets:1 act:3 processor:1 sensitively:2 cambridge:2 redshift:41 landy:2 image:4 accounts:4 ηr:1 determine:3 hep:1 log:2 area:6 assumed:9 there:19 stark:11 dispersion:4 start:2 low:6 stars:6 bubble:21 contiguous:4 assumes:8 combined:1 aoki:1 tight:2 complete:1 enough:5 jun:1 iliev:3 correlated:3 convolving:1 mnras:43 longer:1 raga:1 systematics:2 ωm:3 ωb:3 agree:2 strongly:5 certain:1 describe:2 deep:12 general:4 file:1 lifetime:2 processed:1 again:2 graduate:1 field:51 igm:18 poor:1 pointings:7 a2:4 peak:1 included:6 casts:1 curve:35 knowledges:1 ments:2 dramatic:1 mass:37 adam:1 quantify:5 once:1 resolution:3 represent:11 consider:3 pointing:5 caused:2 lack:2 dollar:2 follow:1 expressions:1 voids:4 causes:3 diffuse:1 tail:1 program:2 sound:1 mpc:68 sitting:1 very:8 induce:2 parry:1 fan:5 fall:6 bubbles:27 difference:6 treating:1 illustrated:1 list:1 damped:1 large:31 adjust:1 small:15 becker:7 employing:1 neighborhood:1 pasj:4 past:1 go:1 zero:8 design:1 enhancement:1 wmap:2 what:6 hernquist:16 sub:2 richard:1 skeptic:1 section:30 ast:1 version:2 sur:1 intersect:1 method:21 contrast:1 edited:2 outgoing:1 full:1 vvir:7 component:3 opteron:1 tage:2 excess:3 directions:1 strong:5 observing:7 allows:2 prior:5 amount:7 pick:1 proportionality:1 narrow:16 brightest:1 via:1 requiring:3 aimed:1 estimate:12 select:2 takes:3 distinct:1 faint:3 strauss:1 comparing:1 taken:2 minor:2 more:49 lowering:1 flaw:1 lemson:2 emission:8 particular:1 largescale:2 evolves:1 none:1 cluster:2 shielded:1 science:4 equation:12 remain:1 paragraph:1 lars:1 history:3 compare:12 challenging:1 cosmological:6 szalay:2 sphere:3 minimum:3 arise:1 sharp:3 axis:2 terrestrial:2 information:8 needs:4 rather:12 maps:6 influences:2 speeding:1 simplicity:2 galactic:8 emulate:1 derived:1 mapping:4 fc:32 fe:39 coming:5 derives:2 short:2 quoted:2 spectra:5 extrapolation:1 parameterizes:1 help:1 mission:5 paper:10 through:11 filters:3 its:21 style:1 rapidly:2 priors:2 fruitful:1 detected:4 systems:2 might:9 alter:1 tentatively:1 incompleteness:3 motivated:2 generously:1 cen:6 gadget:2 sokasian:7 fion:10 framework:1 motivates:2 tchekhovskoy:1 yr:4 easily:1 miralda:4 l95:2 fully:6 presented:3 atacama:1 did:2 radial:3 found:11 likelihoods:2 energy:1 enables:1 reduce:3 osterbrock:2 yoshida:1 expect:1 measurement:4 operation:3 divide:1 since:11 projected:2 denotes:1 sloan:1 induced:4 issue:1 occurs:2 foreground:9 doppler:1 circumstance:1 favored:4 mms:1 difficulty:1 reason:3 imaging:3 put:5 generate:4 pairs:1 unresolved:1 benefits:2 launch:1 conducted:3 leading:1 consequence:1 major:1 probability:7 prevent:1 number:34 linking:1 done:3 construct:2 bland:1 fluxes:1 differ:2 temperature:3 introduction:1 twenty:2 least:9 sargent:1 pinned:1 assumption:3 calculations:17 babich:2 smoothed:1 too:2 parc:1 relationship:1 imprinted:1 immediate:2 sizable:2 part:5 authors:1 king:1 determines:1 determined:2 neufeld:2 motivation:1 strengthen:1 ages:1 randomly:6 substantial:4 quasars:4 orders:1 lie:1 self:2 k3:3 liu:2 build:1 unconstrained:1 kiloparsecs:1 populate:1 rhs:5 reach:1 most:37 significant:10 measured:21 cover:3 km:10 tα:4 optical:3 exp:19 velocity:18 physics:3 particularly:2 cdm:1 scattered:1 evaporation:4 minimizing:1 relation:1 find:16 impact:11 giant:1 parameters:1 merger:2 distributed:1 surveyed:2 factor:27 circle:1 proximity:1 kashikawa:23 his:1 dominant:1 lyα:76 lyβ:2 lyγ:1 dependent:4 kamionkowski:1 imparted:1 cheaper:1 during:19 alexander:2 resolve:2 continuum:1 arxiv:1 investigate:7 obscure:2 bars:8 set:11 signify:1 ser:1 plausible:1 see:20 arc:5 project:1 probable:3 fang:1 distinctive:2 currently:2 woo:2 smallest:7 various:2 probably:7 available:2 catalogs:4 creating:1 missing:1 targeted:1 spectroscopic:10 incident:2 distinguish:15 both:10 prospects:1 evaporated:1 improved:2 sensitive:8 pdm:2 became:1 context:2 pdf:2 finds:5 reside:2 airborne:2 point:1 simple:14 smith:1 corresponds:3 parametrization:1 dimensional:1 simply:1 morphologies:1 throughout:1 expensive:2 pp:7 described:1 raise:1 px:6 due:1 strategy:4 pe:27 ph:11 generating:1 gas:13 covariance:4 briggs:1 determination:1 systematic:1 iye:5 p1:1 uncertain:3 look:1 exponential:2 solid:33 straight:2 budget:1 evaluated:1 while:5 error:8 loop:1 manner:1 approximate:1 averaging:2 apjs:1 rin:1 apjl:6 itself:1 owes:6 vos:2 definitive:1 tasitsiomi:3 shorter:2 randomization:2 resulting:3 relatively:3 horton:2 higher:12 calculation:5 literature:1 attempted:1 uses:6 appreciable:2 robust:2 noll:1 lower:8 analysis:6 edge:3 consistency:2 observed:69 competitive:1 shape:19 atomic:1 questions:1 spatially:2 sxds:12 majority:3 source:41 location:1 sxdf:3 relevance:1 2006a:2 motivating:1 integer:1 helpful:3 shaped:1 follows:3 signal:4 ignore:1 flux:7 yields:5 translated:2 essential:1 pertaining:1 methods:5 some:11 strongest:1 b1:6 b2:7 infall:10 anisotropies:5 scale:23 prox:1 measurements:6 per:1 pen:1 tapken:3 tends:1 proc:1 run:3 processing:1 aj:3 agreement:3 infra:1 step:1 become:3 plots:3 obscured:3 subtract:2 anything:2 constraint:5 simulation:35 range:7 gamma:1 cutoff:1 into:5 within:15 integral:2 nsf:1 subaru:23 shapley:4 primarily:3 proportional:2 clustering:58 uncertainties:2 rows:1 conceivably:1 extremely:2 question:1 fast:1 keating:1 smooths:1 mundane:1 rees:2 adjusting:2 lint:23 sdf:37 properly:1 line:93 raising:1 consist:1 croton:2 uv:2 up:7 us:9 gilmozzi:1 exploration:1 spectroscopy:1 fluctuations:18 schechter:2 similar:17 associated:1 defined:1 metal:1 influence:5 globally:1 single:13 tomography:1 steeper:2 dashed:27 grouped:4 grb:2 mock:23 generates:1 calculating:1 viral:1 fewest:2 msun:4 generated:6 allowing:3 suppression:20 structure:6 suffers:1 algorithm:10 complicating:1 required:2 holes:1 equivalently:1 depth:5 came:1 broad:3 requires:4 having:3 normalized:3 code:7 illustrates:4 results:12 existing:2 steve:1 ionize:1 edu:3 winds:15 conservative:1 worrisome:1 adelberger:1 does:18 unobscured:1 include:3 ionizing:28 random:2 garden:1 wave:1 resonant:5 ending:1 vlt:2 entire:1 transmission:13 positions:1 fewer:2 zm:1 smaller:23 zg:5 cfa:1 imply:2 lmin:7 λcdm:3 disentangle:1 cell:5 consistently:2 body:5 degree:3 respectively:11 gathered:1 spacing:1 objects:5 focused:2 separation:1 extreme:1 dotdashed:1 larger:25 leaving:1 suggests:2 preferentially:2 survey:75 contaminants:1 makes:5 composed:1 scales:19 photometric:24 apj:28 decrease:7 confidence:3 remains:1 next:7 few:9 depicted:1 camera:4 attribute:3 stage:1 upcoming:16 started:1 becomes:3 rarest:1 occurred:2 labelled:1 minihalo:3 rare:2 detects:1 iii:18 account:4 averaged:3 thin:21 meet:1 averages:1 scatter:2 proof:2 weaker:1 escapes:2 process:4 purposes:1 high:27 effectively:1 slit:1 assumptions:6 kosugi:1 weaken:1 invoke:1 sit:7 holds:2 regions:44 located:1 forest:7 instead:9 circular:4 profile:37 specifications:5 evre:1 gardner:4 kneib:1 fits:2 qsos:2 hawk:1 efficiently:2 computations:2 lines:9 correspond:3 allow:3 lα:4 shimasaku:4 bins:6 produces:3 meter:1 produced:3 hii:49 fwhm:8 galaxy:20 contaminated:1 superior:1 le:1 chosen:6 previously:1 degrees:2 instruments:6 clusters:1 greater:1 practice:4 front:3 mcool:4 outlines:1 february:2 university:2 crudely:1 merge:1 magnitude:7 transmitted:2 mode:1 l1:4 crossing:1 references:1 constraints:12 homogeneous:1 constitute:2 frequency:4 measure:6 ous:1 our:42 tenth:1 out:11 matrix:1 mcmahon:1 rev:1 suffices:1 red:3 volker:1 subgrid:1 galaxies:41 diagonal:2 completely:1 likelihood:4 hubble:2 geometry:2 determining:2 could:8 times:12 length:2 produce:2 facilitate:3 south:1 pgg:7 manuscript:1 powerful:1 randomized:1 reached:2 precisely:2 quality:2 biasing:2 taniguchi:6 fair:1 their:16 perfectly:1 ence:1 final:1 dutta:3 uds:3 completed:3 moircs:2 simulate:1 epochs:1 malhotra:7 submitted:3 rarity:1 inversely:1 individual:2 amplitude:5 providing:3 steep:2 distinguished:3 fluctuation:1 unchanged:2 curves:90 need:1 st:1 clearly:1 angle:2 min:4 studying:12 able:10 polarization:2 accuracy:2 patchy:6 unless:2 useful:3 connected:2 overlapping:2 intrinsic:45 why:4 astro:11 subtracted:5 consequences:1 stronger:1 dent:1 proceedings:2 veys:1 artificially:1 constrain:9 fact:5 selection:8 text:2 blueward:2 supported:1 purely:1 debate:1 based:7 should:7 candidates:2 emitting:5 λobs:1 thousands:2 achieve:3 meant:2 cube:1 δxi:2 means:1 quantified:2 ones:6 words:1 spaans:1 lobs:28 areas:1 processes:4 densities:1 course:2 haiman:13 luminosity:105 hydrodynamic:1 contain:4 fixed:13 futuristic:2 view:2 intervening:1 strengthened:1 computed:14 correlations:3 differs:2 enhanced:7 madau:1 luminous:4 closer:2 phases:3 tend:1 state:8 difficulties:1 tens:5 comparable:8 ability:2 importance:6 supernova:1 efficiency:1 reproduces:1 hypothesis:3 key:1 probing:2 emitter:25 limits:2 always:1 taking:3 equal:2 etc:1 estimation:1 detailed:1 relevant:3 cm:2 conclude:1 poissonian:1 ca:1 table:2 escude:4 addition:16 window:5 define:1 contribute:7 corresponding:2 sufficient:2 bulk:1 finished:1 decreased:2 prescription:2 c1:3 present:5 multi:4 unlike:2 appearance:2 value:13 will:61 ultra:1 almost:1 thus:2 surface:1 examined:1 vw:20 sits:2 capture:1 radiation:1 cross:8 matthew:1 unity:7 improves:1 mehlert:1 largest:9 finite:2 infer:1 difficult:12 tighten:1 phh:2 http:3 absorb:1 effect:60 allsky:1 ion:8 v2:1 student:1 dust:5 mcpherson:2 tighter:1 concordance:1 off:4 center:4 modeled:2 well:13 thought:2 sets:4 position:2 arising:1 kauffmann:2 latest:2 spherical:3 newest:1 less:16 increasingly:1 loeb:7 obtain:1 forests:2 sources:40 books:1 predicts:1 rapid:4 density:28 absorption:27 carilli:1 sky:1 capabilities:1 meisenheimer:3 add:2 slits:1 maintaining:1 match:4 identical:1 increased:4 magnify:1 smithsonian:1 increases:5 five:9 press:3 loss:1 displaced:3 necessary:3 like:9 sizes:2 hosts:1 lose:1 δg:16 δe:16 soft:2 page:2 deviation:4 because:35 steidel:1 proper:1 neglecting:1 lead:1 sufficiently:1 demonstrates:1 lean:1 treepm:1 masked:1 assuming:22 demonstrated:1 noise:23 slight:1 selecting:1 stellar:1 pressure:1 host:6 although:1 offset:3 spectroscopically:3 panel:51 a1:8 about:14 actual:1 column:2 universe:25 dependence:7 widefield:4 important:11 discard:1 own:3 owe:5 functional:1 weighted:4 promise:1 van:1 additional:5 transfer:9 justifying:1 smoothing:1 overestimate:1 incurred:1 function:111 hr:3 agrees:1 but:32 volume:32 expected:3 neutral:31 hi:2 made:2 compute:8 packard:1 whether:6 smooth:1 placed:1 below:5 owing:20 limit:6 demonstrate:3 distribution:18 piece:1 heidt:1 int:3 l69:2 tormen:2 periods:2 ing:1 proceeds:1 functions:7 compared:5 percent:1 detail:5 other:17 compares:6 details:2 quantities:1 conclusion:3 repeat:2 star:6 variation:1 astronomy:2 friends:2 vein:1 exposure:1 prevalent:1 starting:1 factors:3 rule:1 portion:2 volumes:4 understand:10 |
0704.2240.txt |@word decelerate:1 represent:1 abundances:2 code:3 sensitive:1 dorband:1 limited:2 caused:1 lack:1 results:7 tested:1 existing:2 per:1 tenuous:1 l7:1 consists:2 disk:6 inspire:1 compact:1 excludes:1 terms:1 calculate:3 xxii:2 segments:3 young:1 passage:1 mwc:27 kα:3 av:2 present:4 text:2 include:1 cm3:1 goodson:3 applied:1 adiabatic:4 periastron:1 downstream:2 evolves:1 very:6 relatively:1 luminosities:1 every:1 nichols:3 stays:2 implausible:1 fur:1 compression:1 difference:7 bringing:1 grevesse:2 cool:2 believed:1 gsfc:1 thiele:2 krasnopolsky:1 presented:2 heasarc:1 shock:7 damped:1 large:3 solved:1 au3:1 phase:2 outburst:1 xmmnewton:1 upper:2 smaller:12 l91:1 ten:2 thin:2 consistent:5 acis:2 japanese:1 pulse:12 steepest:1 morphology:1 second:2 value:7 go:1 further:2 implemented:1 spectral:1 kinetic:4 blobs:3 sum:1 contributed:1 while:4 current:1 axial:1 wolff:1 xvii:3 above:4 values:6 contrast:2 shocks:6 dwarf:6 respectively:7 component:28 understanding:3 ranges:1 reported:4 identifications:1 objects:7 focused:1 compressed:1 separation:2 address:1 active:1 based:1 along:2 strong:5 equations:1 go3:1 great:2 institute:2 study:3 losses:1 allows:1 bow:1 suggests:2 amount:1 periodic:2 resulting:3 suggestion:1 zickgraf:1 conveniently:1 myers:1 changes:1 plotted:1 blackbody:1 xii:1 although:3 nearest:1 apr:1 marginal:1 vii:3 f2:2 highly:2 referee:1 visible:1 decrease:3 cold:1 energies:2 apply:1 counts:1 total:10 camenzind:3 landscape:1 orientation:1 plot:1 use:2 usa:1 faint:1 finally:1 pasj:1 next:2 scenarios:2 few:2 therefore:8 attribute:1 yusef:1 l61:1 today:2 more:11 separated:1 aquarii:2 ejected:6 schroeder:1 conclusions:2 apparent:1 emission:59 payne:2 apec:1 visual:1 warm:9 lehto:1 particular:1 known:2 aligned:1 iii:2 potential:2 origin:4 had:2 logarithm:2 states:2 mg:5 inclinations:1 sutherland:1 integrating:2 equation:1 work:2 modified:1 reproduce:1 makino:1 erg:27 obvious:1 temperatures:19 those:7 making:1 claim:1 compare:2 schmitt:1 f4:1 stated:1 process:1 f9:1 nozzle:3 suggestions:1 confused:1 high:15 sphere:3 assumptions:1 performed:1 allowed:1 spanning:1 made:1 hydrogen:1 occur:1 akinen:2 axis:7 motion:4 rays:11 monitoring:1 varied:1 provide:2 divided:1 holds:1 cygni:2 regions:3 vla:1 hot:16 stuttgart:1 galactic:1 undergoing:1 arcs:2 may:6 after:4 minimum:5 clumps:1 plane:1 fe:16 offset:1 improving:1 data:7 parallel:3 efficiently:1 included:1 ambiguous:1 drop:2 supersoft:2 johnson:1 counter:1 sw:10 correspond:3 rather:1 si:6 ones:1 so:2 progressively:1 media:1 american:1 order:8 outflowing:2 typical:1 wavelengths:1 instabilities:1 pulsed:8 interpretation:1 jordan:1 produces:1 developed:1 over:5 move:1 mainly:1 choose:1 ejecta:1 years:4 produced:3 thermal:8 paper:12 including:6 thesis:1 observational:1 epic:1 existence:4 urset:4 still:1 its:14 galaxy:1 scale:1 exosat:1 style:1 fit:6 maps:7 chosen:2 temporal:1 hypothesize:2 underdense:1 decreases:3 circumstellar:1 better:2 detected:8 complex:7 aped:1 systems:3 covered:1 main:1 might:2 perpendicular:1 archival:3 administration:1 brickhouse:1 non:3 good:1 combination:2 material:8 innermost:2 needed:2 introduce:1 interstellar:2 they:8 feature:2 yr:4 day:15 continuum:4 easily:1 february:2 hereafter:2 oxygen:2 galloway:4 university:1 level:1 alternately:1 identified:1 infer:1 possibilities:2 hollis:7 filling:1 kpc:1 chandra:12 each:12 found:2 zadeh:1 characterized:3 mean:2 heavy:1 significantly:4 series:3 energy:24 hard:9 reduce:2 gaussian:1 used:9 sahai:1 society:1 extended:2 expect:2 measurement:1 laboratory:2 event:1 special:1 out:5 matt:2 fluxes:10 part:1 factors:1 xv:1 furthermore:5 since:16 crucial:1 winglee:2 research:1 f1:2 dominated:1 reader:1 skopal:1 gov:2 supports:2 integrated:1 red:3 shows:5 occurs:1 derived:3 seventh:1 differ:1 carried:1 california:2 proxy:4 estimate:4 phd:1 blob:1 temperature:36 chose:1 interaction:2 created:3 geometry:1 determining:1 could:1 inferred:2 days:10 creates:1 length:1 milliarcseconds:1 ism:2 enough:2 hence:4 onto:1 south:1 first:7 knots:8 carilli:1 already:1 features:8 matthias:2 kafatos:3 number:4 ziegler:2 space:1 stsci:1 another:1 reached:2 clarity:1 electronic:1 angular:2 size:2 given:7 nebulae:1 jet:134 simulated:1 introduction:1 revealed:2 top:7 1990s:1 system:6 adopted:1 their:9 cooling:12 accretion:5 rates:1 observations:20 xiv:1 xix:1 white:6 hundred:2 structures:1 xxiii:2 low:7 shifted:1 grant:1 estimates:1 duration:2 pimms:1 direct:1 nirvana:1 optical:5 cyg:28 too:2 simulate:1 authors:1 asca:3 than:22 vainio:1 distance:8 unsch:3 scenario:1 showed:2 surrounding:1 double:1 approximations:1 programs:1 rate:4 executed:1 matter:2 differently:1 individual:1 germany:1 iron:8 were:9 offer:1 gives:2 tangential:1 pre:1 lowest:1 spectra:18 lines:24 correction:1 spectrum:25 substantial:1 headings:1 seen:7 seem:1 clearly:1 ray:78 acceleration:1 lie:3 estimated:2 angle:1 built:1 depending:1 efficient:1 latter:4 propagation:1 able:4 shocked:3 note:1 ideal:1 internal:5 absorbed:5 predicted:1 xi:1 performance:1 explanation:5 publication:1 ulrich:2 even:2 exactly:1 multiple:3 probed:1 object:1 apj:15 extending:1 eight:1 strongest:1 contrasts:1 cassatella:1 colliding:1 proxies:5 segment:1 mach:1 latex:1 give:2 viii:2 grove:1 calculated:4 later:3 steady:9 drive:1 km:10 typeset:1 heating:2 wind:2 leahy:2 subsequent:1 velocity:20 maxima:6 typically:2 section:1 fact:2 repeatedly:1 slope:2 planetary:1 telescopes:1 phenomenon:1 stute:6 show:14 blended:1 detection:4 probe:1 scattered:1 mnras:3 evolutionary:1 radio:4 hack:4 superimposed:1 fine:2 find:5 schmid:5 xmm:5 giant:4 ratio:9 parameters:3 pressures:1 aeronautics:1 representing:1 explain:7 state:2 should:6 protostellar:1 only:13 rich:2 factor:9 acknowledge:1 emitting:11 partially:1 pointed:1 hope:1 equilibrium:1 do:1 hit:1 template:1 dependent:2 there:1 hetg:1 simplest:1 likely:2 famous:1 ionized:1 new:9 report:1 during:6 interpreted:2 karovska:2 blends:2 unfortunately:1 evolution:3 resolve:1 densities:8 luminosity:27 arxiv:1 tuned:3 whether:1 investigate:2 kallman:2 li:1 common:1 pulses:23 mattei:2 farther:1 characteristics:1 set:5 computed:2 postshock:1 frame:1 up:2 observed:19 see:4 arc:3 radius:3 result:4 enhanced:2 close:5 luminous:1 contour:1 best:1 subject:1 closer:2 lyon:3 detect:1 viotti:2 propulsion:2 away:1 nature:2 propagates:1 solf:2 written:1 determined:2 hipparcos:1 radiated:1 between:25 probably:1 before:1 available:1 variability:1 ix:1 recently:4 opening:1 initially:2 comp:1 emitted:5 jp:2 however:14 js:2 spectroscopic:1 hypothesis:2 ionization:4 hydrogenic:2 demonstrate:1 jets:26 kev:74 overestimated:2 both:17 last:2 limits:1 outflows:2 many:3 region:1 hint:1 equal:1 contract:1 april:2 cylindrical:1 context:1 comm:1 ion:1 magnetosphere:1 whole:1 masses:1 blandford:3 minima:5 adjusted:1 ch:30 extent:1 cm:29 conclude:2 smith:2 ca:3 corresponds:2 pole:1 grants:1 middle:1 modeling:2 constant:4 cp:1 cv:1 considering:1 decline:2 described:4 kinematic:2 instrument:1 addition:1 bode:1 locally:1 radiative:6 three:3 been:15 pc:5 outflow:2 basic:1 expected:2 ph:4 meeting:1 ishida:2 fig:26 engine:3 describe:2 corresponding:4 xxv:2 received:2 gas:11 coincides:1 friedjung:1 1985a:1 observe:2 representative:1 astronomical:1 general:1 explosive:1 suzaku:1 hardness:2 case:4 yso:1 solid:5 defining:1 ejection:8 profiles:1 will:3 seaquist:1 near:3 xiii:2 lx:2 behavior:1 error:1 exist:1 located:3 ljet:4 characterizing:1 unlikely:1 resolved:1 seven:1 changed:1 jpl:1 almost:2 vi:4 simulations:15 thus:12 them:1 apjs:1 iv:31 ii:10 characterize:2 examined:1 piro:1 ambient:4 technology:2 comments:1 binary:2 different:14 cools:1 supported:1 suggest:3 make:2 radiation:2 same:5 varies:3 epoch:1 parts:3 survey:2 several:3 events:4 conflict:1 higher:14 satellite:1 investigated:2 http:1 peaks:1 numerical:7 effect:2 companion:1 average:5 moving:1 hydrodynamics:2 potentials:2 cycle:1 lower:6 emissivities:1 center:1 episodic:1 database:3 makes:1 modeled:1 well:7 increases:1 analysis:1 thought:1 directly:1 without:2 log:6 components:16 sets:1 coordinate:3 accreting:2 model:81 binaries:2 underestimated:1 l107:1 left:1 distances:1 proposed:1 less:4 being:5 photo:1 accurate:2 newton:5 obtain:1 detail:4 sources:2 underlying:1 atomic:3 anders:2 idl:1 scattering:1 previous:1 now:2 preprint:1 timescale:2 density:30 absorption:3 photons:4 slices:1 sky:2 capabilities:1 source:21 atomdb:4 treatment:2 requiring:1 flashing:1 plasma:12 heidelberg:1 funded:1 identical:2 l85:1 explained:2 decided:1 showing:1 spatial:1 term:1 dopita:1 period:7 early:1 kellogg:15 five:1 knot:7 using:12 emergence:7 accepted:5 kaufer:1 01a:1 prominent:5 loss:3 like:3 sizes:1 cooler:2 follows:2 reduces:1 velocities:5 cannot:4 html:1 specific:2 flux:24 xrbs:1 steps:1 either:1 output:1 inter:5 soft:8 reduced:2 cooled:2 therein:1 right:1 methods:1 surrounded:1 plausible:3 downwards:1 some:2 under:1 hartmann:1 trends:1 sight:1 table:5 proper:3 bins:1 provided:1 extinction:2 dense:1 lead:6 bottom:6 tools:1 symbiotic:18 measurements:1 future:4 extensively:1 mukai:4 when:1 does:1 provides:1 assuming:2 hakkila:2 propagating:3 refer:1 core:1 varying:1 disentangle:1 wheatley:2 rosat:2 radial:1 aj:1 agreement:1 expansion:3 stellar:3 pressure:2 step:1 yorke:2 hst:3 become:1 plots:3 emulateapj:1 properties:10 comparison:6 about:28 central:13 would:6 origins:1 most:8 column:1 xviii:1 dependence:4 o:5 range:30 important:1 connected:2 raymond:2 other:7 emissivity:4 thermore:1 significant:2 presence:4 previously:1 into:4 within:5 year:1 ppn:1 due:5 lies:1 appropriate:3 because:4 references:2 national:1 heated:3 proportional:5 anderson:3 telescope:1 uncertainties:1 paresce:4 additional:4 possible:2 area:1 measured:6 initial:2 approximate:1 fast:2 sides:6 width:1 collimated:2 detectable:2 inner:1 stars:13 yrs:1 was:10 function:7 head:2 medium:3 triggered:1 aqr:21 poster:1 differences:3 but:6 sophisticated:1 astro:4 related:2 solar:1 larger:3 lateral:1 helpful:1 line:21 highest:3 he:3 volume:7 sokoloski:5 compute:1 consist:1 default:1 eyres:2 gravitational:1 variations:3 maximum:5 us:2 below:5 astrophysical:4 limit:1 emissions:1 pumped:3 fluctuations:2 distribution:1 define:3 similar:3 emit:2 detailed:1 ohm:2 taylor:4 associated:3 computing:2 defined:1 stronger:1 abstract:2 measure:2 ao:1 evidence:1 images:2 single:5 ar:2 au:12 liedahl:1 our:44 physical:1 nh:2 ni:1 compared:3 dotted:1 no:4 dashed:4 oak:1 ne:14 adequately:1 application:1 pasadena:1 compares:1 papers:1 test:1 heats:1 hydrodynamical:8 optically:1 explaining:3 briefly:2 elements:3 star:3 calculating:1 models:38 sided:1 shown:2 variation:1 includes:1 crosssectional:1 generated:1 coronal:1 peak:1 studied:1 variable:2 reanalyzed:1 n2:1 structure:1 agn:1 implies:1 longer:2 fluorescence:8 practically:1 assume:5 blend:1 age:2 required:1 extraction:1 together:2 itself:1 nasa:4 mass:4 fitted:2 volumes:1 time:26 far:3 nuclei:1 accreted:1 resolution:2 |
0704.2241.txt |@word secondly:1 limited:1 localizes:1 magnetic:9 bonderson:4 desirable:1 four:4 rˆ:3 entropy:2 consists:2 whose:5 calculate:1 under:11 rise:4 every:1 experimentally:2 school:1 cause:1 math:6 guiding:1 indices:2 markov:2 degeneracy:3 force:1 10b:1 consistent:3 direct:3 surrounding:1 second:6 implemented:1 eigenspaces:1 even:2 errors:8 trapping:4 dr1:1 jaeger:2 above:11 resilient:1 new:9 net:3 increasing:1 consisting:1 here:13 atoms:1 pursuit:1 represented:2 path:13 obtained:6 property:4 study:4 changed:1 approaches:1 guide:1 suitable:1 golden:1 elaborated:1 explained:1 highly:5 stern:2 total:6 charge:35 dna:1 would:4 mediate:1 overhead:2 therefore:1 e2:1 type:17 fractions:2 composite:4 reversible:1 hole:1 must:2 schrieffer:3 word:3 ih:1 setup:3 work:3 theories:1 concepts:1 example:12 transition:1 wang:5 indicated:2 give:6 generically:2 fibonacci:9 degenerate:2 times:3 braids:5 how:2 nontrivial:1 answer:3 gate:3 replacing:1 thermodynamic:1 earlier:1 types:11 third:5 chern:2 complexity:1 algorithms:2 order:16 wind:1 operations:13 xj:1 interpretation:2 deform:3 zej:1 over:5 satisfies:2 before:2 fis:1 better:1 strand:1 them:9 combination:4 similar:1 doucot:2 ze2:4 ze3:3 ze1:4 they:13 represents:2 anion:1 invariants:3 classified:1 filling:6 fringes:1 each:18 interfering:1 mean:2 series:5 braiding:25 antiparticle:1 laboratory:1 extract:2 rs:2 gradient:1 restricted:1 particles:31 rf:1 reader:1 interchanging:1 rk:2 linear:2 written:1 free:2 ascending:2 r1:6 r2:4 created:7 starts:1 ath:1 tolerant:2 creates:9 signature:2 onto:1 ℓk:1 already:1 nhc:1 restrict:1 clear:1 another:11 enumerate:1 ℓb:1 thick:1 illustrate:1 similarly:2 cooling:1 approximately:1 perturbations:2 ordered:1 serve:1 zero:6 preparation:2 achieved:2 minus:1 fashion:1 mind:1 spectrum:1 manner:1 emphasizing:1 seen:5 heff:1 strength:1 raussendorf:2 convenient:1 latter:4 isolated:2 oriented:3 causing:1 exactly:2 object:2 spectroscopy:1 involving:3 phase:23 nussinov:2 jx2:1 observation:1 calculated:1 bracket:4 principle:3 section:1 bais:2 labels:2 gauge:12 solutions:1 keywords:1 earth:1 analogue:2 d2:1 d0:2 d1:10 proposed:3 implementation:1 explain:1 topological:35 coefficients:1 rich:2 hamiltonians:2 axiom:1 do:3 dl:1 dj:1 reconstruction:1 localizing:1 anyonic:22 de:1 db:1 fluid:9 da:2 ds:3 runs:1 contributes:1 fields:5 twice:1 kagom:2 emergent:2 observed:4 result:4 best:4 techniques:2 tensor:1 eigenstates:1 symmetric:2 future:1 simplest:1 solenoid:2 discovery:2 triples:1 nature:5 rezayi:1 however:5 unnormalized:1 topology:5 suggested:1 fault:2 against:3 participating:1 faces:1 qubit:11 genus:1 exhibit:1 active:1 polynomial:12 basis:3 observing:1 three:13 been:8 much:3 9jt:1 interest:1 basic:1 expected:1 ann:1 location:2 dots:2 coherent:1 spin:30 manifolds:1 applied:1 employ:1 near:2 neat:1 endpoints:2 qudits:4 procedure:2 jk1:1 jk2:1 need:6 ij:1 cond:3 containing:1 perform:7 algorithmically:1 intersecting:2 complex:7 quant:5 several:10 independent:3 peaks:1 welsh:2 counterparts:2 hand:1 lomonaco:1 fuse:8 kim:2 potentials:2 normalization:1 left:4 protocol:1 just:1 transforms:1 brennen:15 yet:2 depicts:1 jy2:1 oliveira:2 mobility:1 had:2 easy:1 technological:1 iφ:1 iθ:1 advances:2 innsbruck:1 possible:23 spanned:2 possibly:1 fusion:29 background:1 ye1:1 unique:5 apart:2 appearing:1 performing:3 steps:5 arbitrary:3 evolutions:2 valence:1 www:1 right:4 ironically:1 entropic:1 dense:2 normal:1 microwave:3 probed:2 gapless:1 algorithmic:1 illustration:2 rovibrational:1 properties:6 acquire:1 counterclockwise:2 o:4 plus:2 lieb:1 soc:4 presence:7 22g:1 bound:2 down:1 acad:1 degen:1 unambiguous:1 surround:1 support:9 transform:1 class:1 conservation:1 way:9 was:5 form:4 offer:1 encodes:1 enumerating:1 true:1 arrays:1 inside:2 attached:1 separated:1 phil:1 moore:3 computing:15 proven:3 evidence:2 exist:7 commuting:1 dα:2 no:4 wavefunction:4 when:18 codespace:2 reality:1 interested:3 role:1 nr:1 ribbons:2 picture:1 connect:1 models:8 ital:1 variable:2 jones:19 regime:1 assume:1 together:4 time:3 observables:1 neighbors:1 concept:3 global:3 focus:1 obviate:1 leads:1 computation:28 fusing:5 inverse:1 depend:2 graph:4 environment:3 finally:4 analogous:1 string:21 orthogonal:1 frequencies:1 choice:3 exact:2 drag:3 visualized:2 presented:2 irreducible:4 anisotropy:1 proposals:3 solved:2 upper:2 sign:3 spectral:1 appear:1 contracted:1 shares:1 current:6 annals:3 goes:1 filled:3 satisfy:6 supporting:1 alkaline:1 realizations:3 agreement:2 groups:2 address:2 alone:1 ratio:1 along:10 appears:1 change:2 institute:1 commonly:1 trial:1 accomplished:1 resonance:1 kauffman:6 halperin:6 important:3 logical:10 bullock:2 prove:1 quasiparticles:10 going:1 criteria:5 encode:6 theoretical:3 diagrams:1 sharing:1 outputs:1 apparent:1 employed:2 cases:2 fermionic:1 hhc:5 valued:4 deformed:2 avoiding:1 originally:1 modified:1 labeled:1 values:3 following:9 qq1:1 nearest:4 modulation:1 figure:38 sense:1 weighting:1 performed:4 allowed:4 counting:1 distinguishable:1 occur:5 requirements:1 anyon:22 fourth:2 parameter:1 product:8 mat:3 huge:1 may:9 applications:1 produce:3 incompressibility:1 representations:7 natural:1 dynamical:4 sr:2 explicit:1 su:10 so:9 sn:1 jain:4 representation:9 indeed:5 mainly:1 statistical:13 cold:1 braid:15 delgado:2 group:14 interesting:2 coordinates:1 offers:1 main:2 disentangling:1 non:29 stabilizers:3 processes:4 introduce:2 ls2:1 half:4 hall:6 fractionalization:1 possess:1 term:2 temperley:1 e2πi:2 corners:1 possibilities:3 goldstone:1 square:3 ei:1 manifests:1 interferometer:3 gaps:1 wavelength:1 approximated:1 eq:4 shown:8 factors:4 furthermore:1 interference:6 collisions:1 formula:1 dominate:1 correct:1 after:2 theory:21 possibility:3 quite:1 complicated:1 e1:1 care:11 impose:1 motion:1 terhal:2 place:2 massive:1 sarma:4 think:1 first:15 exotic:3 xi:1 symmetry:1 quasiparticle:7 waves:1 xe:3 xz:1 long:2 directly:1 carry:1 ring:1 open:5 angular:2 size:3 wilczek:5 given:10 necessarily:1 anyons:122 crossings:2 anyone:11 indicate:3 returns:1 realization:5 white:1 gives:6 continuous:4 circulated:1 circulates:3 than:3 intrinsically:1 effective:9 require:2 protected:3 were:3 outcome:9 zanardi:2 addressing:1 micheli:2 correction:2 argument:1 winding:1 exchanging:3 recover:1 saw:1 any:13 downwards:1 ideas:2 note:5 sciences:1 potential:3 take:2 green:1 hyperfine:1 begin:2 trace:8 opposite:2 track:2 molecule:1 wire:3 successive:1 pair:9 inequalities:1 considered:3 later:1 typically:1 quantity:1 show:1 encoded:4 ground:29 laughlin:3 behind:1 only:14 explicitly:2 black:3 expectation:2 cannot:2 closure:4 adiabatically:5 fqh:8 d2α:1 outperform:1 yield:1 predicted:1 mapped:2 braidings:4 physically:3 violated:1 j1:4 j2:4 relative:6 inequivalent:3 jz:7 ways:6 subsequent:1 circulating:3 label:1 boundaries:3 enough:2 between:23 geometric:1 notice:1 jx:5 jy:5 vertical:2 qubits:13 comm:2 ji:1 jj:1 jk:1 article:2 come:3 acquiring:1 weaving:1 many:5 region:3 according:3 berry:3 among:1 color:2 overview:1 poly:1 anti:13 spans:2 moreover:2 fruitful:1 considering:2 amer:2 locally:1 wants:1 observe:2 coherently:1 those:1 case:11 single:9 profiles:1 planar:1 orientation:2 endowed:1 yj:1 protein:1 abcdef:3 technology:1 binary:1 different:10 same:4 constructed:1 singapore:1 trivially:1 initialization:1 running:1 edges:12 changing:2 invariance:1 implements:2 charges:1 without:3 model:28 recoupling:6 dimension:14 charged:3 gates:2 2jp:5 being:1 gavin:11 captured:1 leinaas:1 zoller:2 lett:19 contractible:3 fendley:2 momentum:2 real:2 around:21 2u:1 read:6 sums:1 admitting:1 confines:1 vacuum:17 using:10 accepted:1 marzuoli:1 particle:25 identifying:1 collective:2 either:5 reduced:2 preskill:5 twelve:1 supplementary:1 superposition:1 provided:4 dimensions:10 gapped:3 extensively:1 stopo:2 decomposition:1 provides:1 refer:1 measuring:3 eiϕ:1 scientific:1 power:1 equivalent:12 anticlockwise:1 ratios:1 eiφ:1 exciting:3 island:5 discussed:3 generated:3 2j:2 neighbor:3 act:1 mixed:2 cambridge:1 fertile:1 references:2 determine:2 operator:5 accumulated:3 conceptually:1 log:2 prepare:2 area:2 removing:1 strictly:1 there:22 stark:1 low:10 labelling:1 delocalized:2 hard:4 dissipative:1 rolston:2 applying:4 annihilate:2 circulation:4 lukin:2 multiplicity:1 conductance:3 addressability:3 obtains:2 strongly:1 fusions:2 certain:3 cbi:1 moved:1 resultant:1 ap:1 governed:1 controlled:2 moves:1 again:1 field:11 valid:1 spatial:2 mathematics:2 d2g:1 polar:1 perpendicular:2 symbol:4 vertex:16 includes:1 a1:2 commutator:1 a3:1 a2:2 a4:1 d21:1 d20:1 mass:5 decoherence:3 resolution:2 strings:6 external:1 sci:1 consider:5 caused:1 commute:3 generalize:1 follow:1 caveats:1 tv:1 equivalence:3 tr:2 presentation:1 far:2 induce:1 resistance:3 witten:2 reordering:1 difference:1 deformations:3 condition:2 splitter:2 hamiltonian:19 issue:1 list:2 large:6 rj:4 small:3 multiqubit:1 employing:2 ten:1 tex:1 rate:1 perspective:1 further:1 subscripts:1 what:3 abi:3 sum:6 associate:1 version:1 fractional:7 judicious:1 contrast:2 full:1 ranged:1 leeds:2 b2j:1 directions:1 strong:4 equations:4 arena:1 inspired:1 allows:2 yˆ:2 amount:1 periodic:2 action:7 via:2 followed:1 bombin:2 viz:2 establish:2 distinct:2 objectives:1 contains:1 quasi:4 nucl:3 ψm:5 taken:1 more:11 diamond:1 operators:16 corrected:1 site:1 particular:11 known:5 producing:1 quantized:1 science:1 loops:9 indicating:2 evolved:1 beautiful:1 triads:1 states:35 turaev:4 shtengel:6 protects:2 numbers:1 arise:1 exclude:1 species:1 e4πi:1 information:15 rather:2 acts:1 unitaries:5 larsen:3 simplicity:2 intended:1 algebra:4 derived:3 mapping:1 plane:7 coming:1 horizontal:1 geometrical:3 fascinating:1 short:1 resemble:1 register:2 parameterized:1 fundamental:3 farhi:2 parameterizes:1 cross:1 paper:1 through:3 lasers:1 signs:1 existence:1 excitations:19 its:11 rapidly:1 boson:1 actually:1 microscopic:3 systems:15 recombined:1 might:1 deformation:1 yi:1 good:2 return:1 pauli:4 rasetti:1 ye:2 oxford:2 yu:3 easily:4 gets:1 level:2 2d:4 inequality:1 found:5 2n:4 energetically:1 characterized:2 defects:1 constructing:1 generation:3 energy:15 smoothings:1 positioned:2 idea:2 expect:2 measurement:5 quantum:65 operation:9 beyond:1 braided:3 discrete:1 nuovo:1 since:4 research:2 acting:4 schematical:1 denoted:2 induced:3 evaluation:2 belief:1 difficulty:1 reason:2 imagine:1 ask:1 beginning:2 generate:1 pairs:8 leonardo:1 exponentially:3 circuit:3 consequence:2 assign:2 knots:9 major:1 probability:2 encoding:9 relate:1 number:12 linking:1 done:1 least:1 fluxes:1 perturbation:3 temperature:2 introduction:3 leading:2 interact:2 construct:1 molecular:1 smoothed:1 trapped:3 incompressible:1 optical:5 favorable:1 translation:2 determines:2 plateaus:2 annihilation:1 determined:1 pairwise:1 str:1 nonabelian:3 paths:3 constructions:1 depending:2 self:1 k2:2 k1:2 internal:5 generalized:1 ancillary:1 honeycomb:8 added:1 electric:2 goldman:2 most:5 branching:3 kj:1 torus:1 kr:3 electrons:1 exp:1 skein:1 physics:15 lying:1 sector:1 celebrated:1 phenomenon:1 cdi:1 relation:6 networks:1 bravyi:2 preda:1 bfs:4 generators:1 factor:7 abelian:26 triangle:2 dependent:2 recombining:1 combinations:1 lattices:2 freedman:13 alexander:3 arxiv:1 bf1:1 bf0:1 common:2 characteristics:1 set:8 sep:1 grey:1 see:11 individual:1 sec:2 close:1 visualize:1 ibid:1 distinctive:1 dipole:4 various:6 probably:1 recently:2 scalability:1 distinguish:2 both:4 folding:1 connection:5 pdf:1 whole:1 finds:1 experimental:4 reside:3 point:5 simple:4 others:1 corresponds:7 dimensional:9 pr:2 startling:1 fused:13 transformations:2 create:3 due:9 describes:6 anisotropic:3 intensities:1 ph:5 lapan:1 empty:1 generating:1 gas:3 gap:9 understand:1 systematic:2 plants:1 look:1 exponential:1 solid:1 reliable:1 while:5 behavior:11 error:5 evaluates:2 couplings:2 loop:11 unitary:13 approximate:2 rig:1 increased:1 arovas:3 twofold:1 tqc:2 tqo:3 rules:13 emphasize:1 resulting:2 higher:2 calculation:1 used:3 comprehensive:1 levels:2 robust:3 recent:2 lower:1 task:1 analysis:1 picks:1 edge:8 consistency:2 comprise:1 xe1:1 xe2:2 21a:1 reviewed:1 λg:1 atomic:2 questions:1 world:9 alternative:1 conclusions:1 subjects:1 plateau:1 theorem:1 relevance:1 contrary:1 solvable:1 excited:3 demands:1 couple:1 entangled:4 integer:6 bit:2 modifying:1 projects:1 helpful:3 rotate:1 shaped:1 follows:5 adiabatic:5 manifest:1 flux:26 popular:1 disorder:1 topologically:5 spins:9 mathematical:1 sketch:2 creation:4 some:4 emanate:1 understood:2 b1:6 b2:6 b3:4 oscillations:1 ijk:5 scale:1 describing:2 affects:1 measurements:2 per:3 behave:2 connecting:3 tends:1 proc:2 inserting:1 bn:3 processing:4 bi:19 bj:7 restrictive:1 step:2 relating:2 dictated:2 hilbert:2 cnot:1 integers:4 constraint:1 tracing:2 simulation:1 range:2 block:2 therein:1 slingerland:4 computational:1 gutmann:1 into:3 encircling:1 appropriate:6 proportional:1 pentagon:3 statistics:22 span:1 classically:1 specifically:2 bosons:5 properly:1 link:8 ioffe:2 line:1 stumbling:1 up:2 us:2 uk:1 continuously:3 strands:5 called:7 associated:1 defined:7 influence:1 quasiholes:1 nab:3 codes:7 dashed:1 application:1 nat:1 elements:5 generates:1 excitation:3 polynomials:7 prepared:2 meaning:2 structure:3 implies:1 algorithm:9 required:4 holes:1 depth:2 weights:1 walker:2 requires:1 having:2 normalized:1 code:6 illustrates:1 results:4 overly:1 illustrated:1 bohm:6 edu:1 simon:1 concerned:1 stable:1 ionicioiu:2 resources:2 outside:1 engineered:1 wave:2 electron:9 implausible:1 gℓ:1 matrices:8 fidkowski:2 positions:1 notes:1 eigenvalues:2 optics:1 enforce:1 zi:5 zj:2 zk:1 zd:1 ze:4 zx:1 enclosed:1 manipulating:4 dyon:2 odd:1 index:2 plays:1 giving:4 reaching:1 zhang:2 expressed:1 find:1 3j:1 experiment:5 body:5 led:1 degree:1 exchange:4 respectively:2 spacing:1 desired:1 separation:1 making:1 z2:5 ijkℓ:1 involved:3 products:5 implement:1 hexagon:7 makes:3 involves:2 composed:1 abcd:2 scales:1 outcomes:7 austria:1 condensates:1 apply:2 manipulate:1 standing:1 use:2 remains:1 pedagogical:2 next:4 few:2 depicted:7 historically:1 started:1 becomes:2 levin:5 carrying:2 labelled:4 high:1 animals:1 evolution:15 tunnel:1 reproduce:1 stabilizer:2 meet:2 control:1 links:8 process:11 depiction:1 lorentz:1 pachos:14 six:3 spurious:1 varies:1 instead:1 sin:2 dc:1 engineering:1 realized:1 physical:17 bonesteel:1 light:1 lines:6 correspond:8 element:3 lundgren:1 realizes:1 allow:1 subsequently:2 bipartite:1 zℓ:4 produces:1 move:2 produced:1 including:2 outer:1 exclusion:1 zˆ:1 degrees:1 choose:1 criterion:1 dyonic:2 pure:2 richness:1 polarizations:1 camino:2 landau:4 das:4 rotation:3 realize:2 university:2 traced:1 identified:1 sufficiently:3 magnitude:1 trap:1 crossing:4 traces:1 constraints:2 subset:1 related:3 elementary:2 decays:1 measure:5 our:1 special:1 out:3 matrix:8 rev:27 playground:1 lecture:1 suffices:1 red:1 nayak:7 interactions:20 diagonal:2 completely:3 york:1 demler:2 interaction:14 could:6 keep:3 length:1 ortiz:2 hence:9 facilitate:1 staggered:1 precisely:1 aharonov:9 reference:1 condensate:1 ancillae:1 system:20 relations:6 their:18 fermions:7 wrapped:2 final:2 writhe:1 simulate:2 manipulation:2 punctures:1 detection:2 cimento:1 richer:1 inversely:1 appealing:1 amplitude:1 punctured:1 distinguished:1 behaviors:1 unchanged:1 kitaev:12 intertwining:2 demonstration:1 linked:1 viewed:3 depict:1 angle:1 able:9 mechanism:1 instance:1 subject:1 accuracy:2 anticommute:1 connected:2 why:11 laurent:1 neighboring:1 face:16 mechanical:1 fact:3 12n:2 rotating:1 bring:1 trivial:15 debate:1 subtracting:1 inspiring:1 should:20 bases:1 candidates:1 molecules:6 marriage:1 local:21 hopf:1 achieve:1 exchanged:3 means:1 familiar:1 beam:2 ones:1 exchanges:2 quantifies:1 procedures:1 areas:1 qp:1 qs:1 qr:1 tuned:1 qe:3 processed:1 contain:1 generations:1 qn:1 computed:2 exists:3 correlations:1 humans:1 intensity:1 computer:2 terms:5 phases:3 still:4 interacting:2 pattern:1 favor:1 state:51 closed:14 invariant:3 boundary:3 ends:6 implementing:1 configuration:3 taking:2 equal:2 attributed:1 hamma:2 otherwise:1 relevant:1 trajectory:3 quasihole:2 proposal:1 adapting:1 describe:3 corresponding:3 vinci:1 commutes:1 sufficient:3 coherence:1 subspace:5 bull:2 general:4 present:4 encircles:1 laser:1 unlike:1 value:8 choices:1 will:9 layer:1 simons:2 thus:9 surprisingly:1 surface:15 clearly:1 viro:2 duan:2 demanded:1 dual:2 greater:1 φp:1 hubbard:1 began:1 indistinguishable:1 unity:1 parts:1 schematic:3 φh:1 finite:4 φn:1 residing:1 upon:1 effect:10 v1:9 v2:9 infinite:1 identity:6 off:1 nevertheless:2 well:6 thought:2 firstly:1 position:6 arbitrarily:1 less:1 obtain:6 predicts:1 bibliography:2 density:1 jeff:3 wen:9 discuss:1 lattice:26 caltech:1 combine:1 developments:3 adj:1 identical:3 tics:1 definitive:1 five:1 know:1 knot:11 press:1 fradkin:2 necessary:4 like:7 sized:1 martin:2 accessible:1 because:1 classical:9 sequence:5 njk:1 rosenow:2 constructively:1 growth:1 proper:1 transport:1 aesthetically:1 lead:1 manipulations:1 does:3 mutation:1 demonstrated:2 mode:1 biology:2 obey:1 ps:1 described:5 imaginary:1 deriving:1 about:13 freedom:1 briegel:2 carrier:1 introduced:1 fqhe:1 letters:1 artists:1 bosonic:1 additional:2 smoothing:1 inner:2 function:9 brane:1 hv:11 triangular:1 but:17 construction:3 hf:10 hg:1 made:4 compute:2 whether:2 shrunk:1 flip:1 placed:1 below:2 limit:1 problem:5 reconnecting:1 int:1 universal:4 contribute:1 denote:1 interchanged:1 inf:1 happen:1 mutual:2 compared:2 virtual:1 lately:1 other:13 witness:1 theor:1 repeat:1 zhou:2 homologically:1 qφ:1 astronomy:1 coupling:4 starting:2 space:21 rule:6 original:2 4n:1 inset:1 |
0704.2242.txt |@word neighbors:1 positions:5 partial:1 consider:13 springer:3 llr:7 varying:1 results:8 leads:4 ginzburg:1 proposition:12 entropy:22 cooperative:10 go:1 sci:1 instantaneous:1 gj:4 kluwer:1 devoted:1 particles:54 certainly:1 cardinality:1 depend:5 paris:2 speeded:3 eigenvalues:1 deterministic:2 dsl:2 tn:11 common:1 finally:7 critical:1 those:2 under:4 stochastic:3 td:30 norm:1 ingredient:4 restricting:1 case:18 belonging:1 expressing:3 f0n:2 outside:1 very:6 translations:1 connects:3 choice:17 1note:1 additional:3 e2:2 ln:25 difference:3 bringing:3 condition:8 arrange:1 beginning:1 level:1 did:2 irreducible:20 bonds:4 guo:2 solution:9 large:2 discrete:3 settle:1 ǫn:9 small:5 generalize:1 markov:17 ftn:8 originally:3 martingale:4 degeneracy:6 upper:4 strongly:1 smaller:2 neighborhood:2 computation:1 zd:1 estimates:4 direct:1 ornstein:2 filled:1 jump:9 surrounding:1 rate:7 value:3 infimum:1 universit:2 zt:1 further:1 dynamics:12 ρn:1 marginal:3 canonical:1 spectral:20 established:2 what:1 nonlinear:1 filtration:1 stands:1 giving:1 hypercube:5 section:17 celebrated:1 analogously:2 uniform:4 current:1 varadhan:2 version:2 goes:2 flowing:1 suppose:1 construction:1 rd:4 method:13 contrast:1 coefficient:6 supporting:2 evolving:1 exchange:12 respectively:5 hydrodynamical:1 component:4 grey:1 here:9 desired:1 ztn:1 them:6 free:1 address:3 directions:1 path:27 along:3 strong:1 appears:1 change:2 obtained:9 untill:1 remark:4 property:7 restrictive:1 shift:7 study:4 studied:2 allows:4 reason:1 schwarz:4 periodic:1 consists:5 ξ2l:2 usually:1 hospitality:1 quastel:2 postponed:1 sup:35 york:2 uniquely:1 via:8 useful:1 divide:2 classification:1 scales:1 apr:1 requiring:1 vii:1 ls:11 replace:1 brought:1 equals:1 inequality:19 decrease:1 apply:4 establish:1 readily:2 presents:1 use:17 y2:2 proceed:3 would:2 intensively:1 sake:2 positive:12 contains:4 ej:27 negative:1 ψt:1 next:1 few:1 going:3 therefore:5 vi:1 taken:1 generators:1 associated:11 compactly:1 type:1 fr:1 decomposable:1 more:11 introducing:4 equivalence:1 comparison:2 vl:11 glass:2 long:4 reversible:3 particular:1 known:5 cases:1 hold:1 iii:1 analogous:1 must:2 zi:1 evolves:4 account:2 permits:1 recall:6 equation:29 work:2 ρm:1 modified:2 pr:1 macroscopically:1 infinitesimal:1 below:3 ρt:1 determining:1 following:19 2x2:2 landim:16 example:7 proof:31 nearest:10 transition:1 hyperplane:4 nikodym:2 give:2 process:48 arise:1 ηn:5 high:4 minimum:3 bp:1 performed:3 degenerate:18 allowed:15 mail:3 isothermal:1 νn:38 occur:2 guarantee:1 information:1 ef:1 ssep:14 provide:3 verify:1 acts:1 write:5 scale:1 behave:1 pure:1 ritort:1 instead:4 flow:1 looses:1 parameter:2 sin:1 profile:16 simplicity:2 product:12 de:5 blocks:5 etienne:1 algebra:2 may:1 illustrate:1 after:3 derived:1 containing:4 demanding:1 expectation:4 less:1 sepp:2 abuse:1 ainen:2 date:1 end:1 geometrical:1 fl:3 concerns:1 fn:2 goal:1 sabidussi:1 isothermally:1 stress:2 drop:3 natural:2 outline:1 third:2 computations:4 lemmas:1 grant:2 lines:1 correspond:1 st:2 rather:2 yau:2 ones:1 so:4 allow:1 jussieu:2 obvious:1 every:19 order:23 lθ:3 typical:1 restriction:3 tagged:1 holds:11 numbers:1 indeed:2 over:7 move:3 vary:1 satisfied:1 cjn:2 already:4 through:1 statistical:1 spohn:1 y1:1 existence:3 satisfies:6 still:3 avenue:1 its:8 blocked:6 lf:1 γx:1 derive:4 group:2 exclusion:17 τi:6 chosen:2 interesting:1 fix:24 2e1:12 vicinity:1 decreases:2 ds:21 late:1 estimating:1 production:1 microscopic:4 systems:4 lp:36 τy:1 decreased:1 main:8 defining:2 h0:1 overcome:2 split:1 yi:2 non:15 exist:1 janeiro:2 bernoulli:5 processes:6 introduce:7 landau:1 scaling:6 couples:7 radon:2 they:5 cep:2 eµ:1 ys:1 now:14 yt:1 bigger:1 2t:1 easily:2 february:1 several:3 dirac:2 hereafter:1 always:2 presented:5 loosely:1 2y:2 composition:1 2ej:5 theory:1 magnitude:3 l2:6 castorina:2 each:18 2l:13 ηs:5 repeating:1 2h:1 side:2 2j:1 constraints:7 homogeneous:2 domain:3 differential:1 ei:11 independent:2 hard:4 ft:1 idea:6 used:10 operator:3 extended:1 static:1 ex:11 measure:36 a1:6 our:19 transitions:1 eq:1 πs:1 rouen:1 standard:4 clarity:1 closest:1 cnrs:2 space:10 gradient:7 restricted:9 furthermore:4 since:37 u2i:1 u2j:4 denotes:15 diffusive:3 re:3 acting:2 performs:1 reader:2 postpone:1 induced:3 issue:1 occurs:1 math:3 shows:1 ξi0:1 working:1 linear:5 interactions:2 monotone:1 divergence:1 possibility:2 weakly:1 admits:1 difficulty:2 completely:2 complicated:2 term:12 imagine:1 put:4 estimate:24 hand:3 e1:18 e0:5 care:3 definition:16 dirichlet:33 derivation:4 applications:1 argument:1 phrases:1 could:2 impose:2 keep:3 motion:2 appearing:1 kipnis:1 forms:2 consequence:7 a2d:4 configurations:20 facilitate:1 adjoint:2 first:18 origin:2 biroli:1 there:22 probability:15 perturb:1 omitted:1 variables:4 relations:1 cj:3 number:19 restrict:2 clear:2 multiplying:1 least:8 another:2 reached:1 precisely:3 between:6 ηtn:2 size:14 given:19 law:2 checked:1 rewritten:2 their:8 introduction:3 leading:1 hydrodynamics:1 system:19 construct:5 needed:2 rates:40 statement:3 convention:1 speaking:1 inner:3 estrada:2 centered:1 continuous:12 proving:1 telescopic:4 immediate:2 ix:20 2ei:1 x2:2 translation:2 x1:6 than:4 center:1 diffusion:8 distance:19 kind:2 glassy:2 liquid:3 sections:1 stn:4 older:1 slowed:2 ss:1 states:1 editors:1 letters:1 were:4 gives:1 treated:3 minus:1 decompose:2 published:1 hz:5 motivation:1 issn:1 permitted:1 irreducibility:1 rewrite:5 fluctuation:1 ann:1 optimizing:1 dθ2:4 regime:1 say:1 analysis:2 need:6 seen:1 constrained:3 60k35:1 any:17 accurate:1 paths:2 zero:11 depending:2 lim:25 latter:5 takes:2 degenerates:2 τk:3 converges:2 note:13 instance:2 ideal:1 contact:1 square:2 generalized:1 online:1 xi:2 new:2 able:4 unperturbed:1 circles:1 even:1 play:1 cyx:2 fundamental:1 measures:17 molecule:1 clearer:2 most:14 boltzmann:1 involving:1 connected:6 comparing:1 reducible:2 class:8 liggett:1 inequalities:1 hj:3 vazquez:1 observation:2 mobile:19 neighboring:6 torus:4 versa:1 playing:1 χd:1 verlag:3 exp:6 µt:1 communication:1 χn:21 usual:1 physics:3 review:1 fact:14 show:14 chances:1 supported:2 vacancy:3 bring:7 horng:1 solutions:8 sollich:1 rough:1 trivial:1 line:4 fifth:1 occupation:6 completion:1 ytn:5 feng:1 slow:1 ensembles:1 mtn:1 dynamical:1 state:4 should:7 lemma:20 only:10 explicitly:3 black:1 reorganizing:1 factor:3 parabolic:1 circle:1 local:10 γn:4 discuss:1 equilibrium:3 exchanged:1 do:5 dl:3 dlr:6 above:22 notation:14 means:7 express:1 straightforwardly:1 truly:1 pronex:1 aim:1 cannot:2 words:1 exchanges:5 dv:1 during:2 dt:2 du:15 admissible:1 neither:1 dp:20 evolution:2 densities:5 qy:3 qx:3 arxiv:1 laboratoire:1 remove:2 appear:1 investigate:3 paper:1 hydrodynamic:18 contain:3 including:1 fixed:5 inside:2 qn:7 satisfy:4 pµn:2 set:18 exists:11 xlv:1 ωc0:12 uses:1 box:6 bounds:1 relative:9 namely:15 radius:2 result:10 w0:1 close:7 dµ:1 kinetic:1 subject:1 ergodicity:3 lost:1 exploited:1 interacting:5 speed:1 away:2 sites:16 symmetric:4 2ǫn:2 enough:10 µn:24 action:1 simplest:1 invariant:12 boundary:5 before:6 conditions:1 notice:1 dµn:2 terms:4 complementary:1 uj:1 weak:9 however:2 rapidly:1 nρ2:1 le:1 hypothesis:1 key:5 analyzed:1 article:1 configuration:23 distribution:1 topology:2 concentrated:5 both:12 cos:1 cubes:1 last:13 σn:27 limits:2 many:1 region:2 according:6 propagation:1 les:1 context:1 unj:1 mean:2 expression:13 comes:3 considering:5 among:3 relevant:1 cn:20 point:4 simple:14 had:2 corresponds:8 dimensional:11 alone:1 governed:1 respect:21 considers:1 points:5 gratitude:1 destroyed:1 described:3 second:9 basis:2 addition:2 trajectory:2 alves:14 computing:1 due:4 been:8 strategy:2 reduction:1 cesaro:1 slowly:1 basic:1 expected:1 figure:4 empty:3 define:13 wants:1 sfrh:1 ergodic:6 arises:1 corresponding:8 τx:12 gas:1 covariance:1 gap:20 neighbour:2 sobolev:1 univ:1 clusters:4 consecutive:1 c1:1 denote:34 present:1 applied:1 contexts:1 nd:14 empirical:7 profiles:3 choices:2 will:15 while:7 optimization:1 γz:2 compactness:1 behavior:3 x2d:5 situation:1 balance:1 taking:3 manner:1 shortened:1 portugal:1 coupled:1 endowed:3 thus:3 site:14 π0n:1 equal:9 ii:1 cluster:14 saint:1 dual:1 vanish:4 kinetically:3 fy:5 different:3 verified:1 author:2 perform:5 occupied:5 make:7 belong:5 same:17 poincar:1 shifts:1 arguments:7 gibbs:1 modification:1 proved:2 finite:10 showing:2 development:1 evolve:2 literature:4 see:6 percolation:1 i0:5 trajectories:1 phd:1 provided:1 running:1 nk:2 moving:2 purpose:2 bertini:1 reference:4 relies:3 frozen:2 lower:4 correspondent:1 off:1 whose:7 pµ:3 adapted:1 well:5 deal:2 ccr:1 without:1 temperature:1 components:4 sets:3 position:7 model:6 otherwise:2 dimension:4 left:3 distances:1 just:3 theorems:1 being:3 hyperplanes:10 resp:5 obtain:14 rest:2 shape:1 identify:1 thanks:6 using:18 facts:1 macroscopic:5 λn:68 previous:5 adv:1 adding:1 cut:1 uniformity:1 generator:30 density:26 regarded:1 conclude:9 character:2 dνρ:1 lattice:5 add:3 setting:2 nor:6 easy:1 theorem:11 bond:1 eνρ:1 semigroup:2 guarantees:1 remaining:6 take:2 depends:3 represents:1 devised:1 couple:9 decomposed:1 possible:13 ld2:4 boxes:4 eatoires:1 average:1 integer:9 part:7 unique:3 color:1 occurring:1 scaled:1 imposed:1 like:1 particle:41 brasil:2 follows:8 δu:1 porous:13 zerorange:1 gjn:1 communications:1 steps:6 either:1 characterizes:1 orthonormal:1 mode:1 stationary:1 dona:2 replacement:6 mathematical:3 right:3 dordrecht:1 classical:1 sequence:16 absolutely:2 conditional:2 some:14 back:2 towards:1 acad:1 choosing:1 convex:1 proper:7 proofs:4 organizing:1 2d:14 entropic:1 uniqueness:4 describing:1 obtaining:1 umr:3 cσ:1 dropping:1 cρ:3 per:2 conservative:2 rio:2 does:8 decomposition:3 provides:3 minimal:2 refer:3 bd:1 core:3 tdn:28 power:1 slight:1 reach:1 jumps:21 aj:4 agreement:1 bj:11 dξ2:4 toninelli:16 step:7 shifting:1 br:2 putting:1 refers:1 properties:6 guaranteed:2 chapter:2 exposition:3 central:1 carried:2 constraint:4 ψtn:8 prove:14 discussed:2 dependence:1 o:11 πtn:6 range:9 a2:2 plus:6 neighbor:6 uhlenbeck:2 renormalizing:1 introduced:3 slightly:2 block:15 therein:2 perturbed:8 dξ1:4 presence:2 tight:2 into:7 boundaries:1 integral:11 bound:33 ηi:5 three:2 down:3 equality:5 ηt:6 references:3 elementary:5 france:2 performing:3 log:9 her:2 definiteness:1 neighbouring:1 strictly:4 initial:19 transform:1 gases:3 start:3 quadratic:1 low:3 way:6 var:7 analyze:1 was:9 naturally:1 function:14 dνα:3 medium:14 gronwall:1 form:34 reduce:1 sequel:2 sketched:1 but:6 volume:3 hk:3 heat:3 properly:1 hn:10 convergence:2 cauchyschwarz:1 cnpq:1 true:1 ωy:2 commun:1 applying:2 vacancies:1 smooth:6 up:3 us:5 lead:1 considered:1 ωk:1 impa:5 limit:27 pl:1 sum:9 fluctuations:3 problem:3 2πz:1 similar:6 called:2 recalling:1 detailed:2 supreme:2 required:1 constant:14 gonc:14 defined:24 certain:2 abstract:1 describe:1 direction:3 general:4 dξ:2 single:3 dν:1 reservoirs:1 fsn:2 dθ:15 journal:1 dη:22 inf:1 moves:5 physical:4 again:4 functions:9 beyond:2 want:1 no:6 ends:1 when:17 vanishes:3 nx:1 field:2 other:10 role:4 details:2 spatial:1 mathematics:2 jamming:2 fenn:1 cauchy:2 stat:1 repeat:1 separate:3 models:16 remains:1 uniformly:1 variation:1 deriving:1 ξi:1 generated:9 important:1 bounded:13 variable:2 dense:1 implies:4 longer:2 vice:1 starting:3 lebesgue:2 together:11 having:1 mimic:1 inhibited:1 presenting:1 time:18 n2:4 backward:1 requires:1 original:4 restored:1 once:3 |
0704.2243.txt |@word aided:1 represent:1 partial:3 gr:4 explictly:1 hats:2 global:3 results:3 existing:1 four:2 scalar:2 generalize:1 ga:1 edu:2 go:1 gm:1 contributions:7 centers:4 consider:4 compact:1 whose:2 inverse:1 depend:6 violate:2 indices:6 paris:1 irrelevant:1 equivalence:6 corrections:6 noncompact:1 simplify:3 finally:2 gu0:1 those:8 th:1 under:2 analogous:1 include:3 interchange:2 divergent:1 applied:1 g5:1 p2ij:6 1pn:25 g2:1 straightforward:4 outside:1 far:2 harmonics:1 choice:4 rotational:1 every:1 difficult:1 fall:2 redefinition:4 affect:2 exact:1 yˆa:2 implying:1 dva:1 louis:1 integrating:3 t2:2 t1:4 large:1 differential:1 scalings:3 recall:1 small:3 relation:3 refer:1 infinities:1 application:1 za:2 mn:1 coordinate:3 10m:1 renormalized:3 coefficient:1 direct:1 approximation:4 surrounding:8 second:11 sphere:5 equal:1 further:4 dynamics:1 odd:4 among:1 substitute:2 linear:1 even:3 employ:3 what:1 3x:2 appear:3 brackets:2 displaying:1 section:2 selected:1 contributed:1 near:4 expressed:2 agrees:2 henceforth:1 ˆa:2 version:2 ˆd:2 above:1 values:2 falling:3 ˆk:1 ever:1 method:3 contrast:1 body:79 edited:2 focuses:1 asada:2 multipole:1 respectively:3 aij:4 residual:1 here:3 itoh:2 objects:1 free:1 separation:1 investigating:1 concluding:1 strong:5 equations:30 b2b:2 b2a:1 calculate:2 obtained:1 ponsot:1 ref:1 antisymmetric:2 zone:3 suitably:2 v2j:6 4p:1 study:1 vectors:3 leaving:4 astrophysique:1 p2:17 amount:1 periodic:2 products:2 kopeikin:4 hospitality:1 suitable:4 spacetime:5 cancellation:2 involves:1 being:1 via:1 useful:1 addresses:1 superpotential:1 scales:6 manage:1 replace:1 g6:1 frame:17 redefining:3 total:8 c8:1 clifford:1 derivatives:5 use:7 takes:2 would:3 covariant:1 remainder:2 contains:1 negative:1 generate:1 few:1 mediate:1 m1:51 therefore:7 m3:1 m2:64 taken:1 scope:1 themselves:1 theoretical:1 more:1 separated:1 hoffmann:1 israel:1 definition:6 binding:8 uncancelled:1 corrected:1 keplerian:1 abc:3 appendix:14 everywhere:1 virtue:1 particular:2 known:3 g4:1 ikl:1 3ni:4 iii:5 potential:13 must:11 worst:1 high:1 account:2 balls:1 ma:28 mb:8 science:1 equation:7 work:3 det:1 london:1 theories:3 handle:1 lorentz:3 obvious:1 three:2 astrophys:1 pioneered:1 making:1 ta:3 averages:1 gravitationally:3 control:1 renormalization:4 give:4 calculation:2 expanding:1 identities:1 purposes:1 generically:1 m21:5 states:1 effectively:1 assumptions:4 arise:3 reidel:1 specific:1 spanning:1 rescaling:1 6m2:1 dxa:1 ijkl:5 regularization:1 ib:1 8v:3 g1:3 turn:1 s3:1 s2:2 discussion:3 s0:2 s5:1 regions:2 how:2 nij:1 plus:4 4p2:1 d14:1 product:2 de:1 singular:2 may:3 earlier:1 derived:3 different:1 antisymmetrization:1 reflect:2 hence:1 lay:1 between:2 d10:1 law:1 data:1 jklm:1 stress:1 attempt:1 dynamical:2 effective:2 generalizations:2 grant:1 explicit:1 yielding:2 st:1 greek:1 complexity:1 cannot:1 so:9 sn:1 inspiral:1 things:1 definitions:7 2t1:2 looking:1 order:47 gµν:2 integrated:1 lrr:1 piece:2 indeed:1 over:17 move:1 choose:1 years:1 produced:1 held:1 thermal:1 paper:10 through:3 motions:2 hypersurface:3 satisfies:2 integrands:2 its:5 boosts:1 before:1 perfect:1 style:1 derive:4 group:1 energies:1 masses:12 relativity:5 coordinates:3 actually:1 forms:1 afer:1 absence:1 parts:3 hij:1 systems:2 xc:2 derivative:2 relativ:1 defining:2 setting:1 split:2 symmetrization:1 non:8 h1:2 return:1 combination:1 ya:7 integral:12 practice:1 2nj:1 introduce:1 ppn:1 break:1 framework:1 course:1 effects:5 they:12 instead:2 eµ:1 1b:1 rotation:1 now:9 nos:1 2u:1 february:1 several:1 2p:3 carrying:1 2r:2 2v2:1 quadrangle:4 always:1 university:3 drop:2 2x:1 appropriate:1 expressions:1 orthonormal:1 each:13 found:2 x12:2 taylor:2 s1:4 φi2:1 domain:4 square:1 vanishingly:1 experiment:1 series:3 energy:14 sov:1 idea:1 carry:2 used:7 jkl:2 relativiste:1 measure:3 our:15 beyond:4 eq:30 really:1 living:1 shown:2 space:1 furthermore:1 since:4 vectorial:1 denotes:3 particles:1 similarly:1 conclusions:1 rb:4 reader:1 scaling:9 formula:1 sch:1 illustrate:3 supports:1 correct:3 interchanging:1 foundation:2 after:2 theory:6 interactions:6 variant:1 xib:5 possibility:1 ad3:1 cmw:3 completely:2 blanchet:3 put:2 org:1 beginning:1 cornerstone:1 8u:2 r4:3 parametrized:1 derivation:1 r2:15 r3:12 geometry:1 could:5 impose:1 moment:3 m22:4 motion:29 thing:1 massive:1 δij:1 assumed:1 consequence:1 rudolf:1 eqs:5 first:11 xj:1 xk:1 xi:9 symmetry:3 xm:5 xb:12 relegated:1 variables:2 xa:20 number:5 xd:11 xim:1 restrict:1 spinning:4 2p2:1 done:2 relations:15 directly:1 comprises:1 pulsar:1 precisely:2 angular:2 size:9 1p:2 given:12 cartesian:1 needed:4 introduction:1 leading:3 xij:1 system:9 approximately:1 name:1 1a:1 their:7 assumption:3 1d:1 calculations:2 underlie:1 postulate:1 ranging:1 cited:1 gives:6 baryon:6 completed:1 accurately:1 measurable:1 luckily:1 part:4 x2:9 eliminated:1 x1:4 than:2 written:4 reflection:1 wide:1 kind:2 third:1 showed:2 breuer:2 approximations:1 zero:9 cite:1 matter:5 future:1 were:3 radius:4 dt4:1 8g3:1 rab:6 7b:4 7a:5 correction:2 argument:1 correspond:1 phy:2 say:2 violating:1 manner:3 distorted:1 need:1 seen:1 cumbersome:1 element:1 demonstration:1 any:7 acceleration:9 lie:1 form:12 δma:2 self:17 rudolph:1 gravity:17 mechanism:2 apply:3 note:5 sciences:1 k1:1 internal:18 absorbed:2 take:1 simplified:1 online:1 negligible:1 coincide:1 8m1:1 c7:2 postnewtonian:2 b3:1 sure:1 2ta:1 trace:1 normal:1 track:1 satisfy:2 most:4 involving:7 but:9 formulae:1 pair:1 grateful:1 measured:6 class:1 wex:1 32g:1 bjk:3 characterizes:1 dordrecht:1 calculated:1 stronger:1 kl:3 points:5 focus:1 principle:7 saw:1 velocity:10 physics:3 sum:2 dot:1 quantity:4 2m2:1 thomas:1 currently:1 phenomenon:1 commas:1 show:2 v12:9 random:2 3v:1 rotating:1 purely:2 showing:1 xd3:2 d8:3 d9:2 d6:1 substituting:1 d4:4 d5:2 d2:1 d3:57 d1:2 postulates:1 rev:8 parameters:4 baryonic:11 produces:1 enough:2 should:1 analytic:3 only:21 explicitly:4 black:4 coefficients:2 integrate:3 employed:1 mechanics:1 covariantly:1 local:9 interested:1 substitutions:1 equilibrium:5 continuity:2 do:4 inertial:5 triangle:5 3m2:1 notation:1 means:3 dependent:3 superpotentials:2 fluid:8 preferred:1 v1j:7 v1k:3 xia:6 v1i:5 futamase:2 valuable:1 v1l:2 despite:1 combinations:2 dt:5 averaged:1 procedures:2 combined:3 unfortunately:2 evolution:1 sources:2 fields:4 wang:1 arxiv:1 comprising:1 summary:1 uu:1 qc:1 redefined:1 hydrodynamic:3 contain:1 including:1 nj:10 inside:6 us:3 4g2:1 ignored:2 redefine:1 set:4 modulo:1 term1:2 sep:12 δji:1 violated:1 summed:1 astrometry:1 relative:4 see:14 justification:1 sec:6 result:11 ignores:1 kinetic:3 techniques:2 gravitation:2 tensor:5 xi1:1 gravitomagnetic:2 review:3 eliminate:2 uα:2 diverge:1 symmetric:6 case:2 state:2 various:3 chosen:1 closed:1 example:9 invariant:3 boundary:3 approach:2 preserve:1 multiplied:1 φij:2 latin:1 terms:70 nature:1 attention:1 weak:2 however:3 jr:1 jl:2 ωa:12 no:11 consists:1 jk:24 virial:20 come:1 inertia:3 jb:2 2pn:28 both:2 parentheses:1 freely:3 region:2 offending:1 x2a:1 according:2 4h1:4 called:3 etc:1 involve:3 dated:1 multipoles:1 ωjk:8 expression:2 experimental:1 nearby:2 arbitrarily:2 aa:3 2ni:2 d13:2 timescale:2 point:18 simple:4 xν:1 corresponds:1 except:1 pati:2 ii:6 m12:1 simply:1 math:2 article:1 cancel:6 proved:1 v2i:3 throughout:2 ignoring:1 rac:6 considering:2 described:2 basis:2 addition:1 d15:1 locally:3 ai1:9 detected:1 been:2 ja:1 defined:8 dropping:1 treat:2 interest:2 basic:2 expected:1 deruelle:1 xab:9 jc:1 pn:5 differently:1 v22:4 determinant:1 emphasize:1 quantities:1 subscripts:1 new:1 rescalings:1 bulk:1 xˆj:1 external:4 astron:1 c3:2 c2:1 c1:1 evidence:4 spin:6 c6:2 standard:1 eαˆ:1 4t2:3 multi:1 guarantees:1 laser:2 minkowskian:1 isolated:1 expanded:2 ij:61 aip:2 evaluated:3 transformation:3 will:30 while:5 evaluating:2 many:1 irrespective:1 ωii:1 mitchell:1 couplings:1 procedure:1 kovalevsky:1 va:7 vb:1 studied:1 almost:2 metric:10 2t2:2 thus:8 them:1 surface:2 iv:3 comoving:9 characterize:1 ik:4 itself:2 il:2 exterior:2 turns:1 ia:6 discarded:1 vanish:4 orbits:1 acknowledgments:1 binary:6 containing:1 verified:1 d11:1 d12:2 combining:3 supported:1 powers:9 make:2 renormalize:1 radiation:2 same:9 orders:1 verifies:1 potentially:1 arguments:1 units:1 resulting:2 finite:7 composition:1 neutron:3 higher:2 g3:1 independent:3 material:1 imply:1 closest:1 i1:1 u1:18 upon:1 effect:3 arose:1 companion:1 inhomogeneities:1 v1:38 v2:49 nk:4 hydrodynamics:1 potentials:16 manifestly:1 invariance:6 ab:4 contribution:1 expand:5 built:1 interferometers:1 lower:1 task:1 kept:3 center:12 keeping:1 possibly:1 nevertheless:1 faye:3 stationarity:1 well:6 academic:1 c5:1 mǫ2:1 spectator:1 very:1 position:6 arising:3 latter:1 bodies:35 87a:1 velocities:2 damour:2 cosmologie:1 moments:3 when:4 accurate:1 newton:1 4v1:3 obtain:7 rest:7 4v2:1 infeld:1 proposes:1 c4:1 spherically:4 alternative:3 b5a:1 yet:1 poisson:1 vd3:1 candidate:1 density:6 ease:1 effort:1 had:1 dicke:1 nordtvedt:3 5m:2 source:8 add:1 wep:5 extends:3 lett:2 brumberg:1 violations:2 formal:1 remaining:2 hawking:1 tests:1 evaluation:1 around:1 depends:1 represents:2 evaluate:6 couple:1 papers:1 term:26 harmonic:2 department:1 working:1 boost:1 appendices:1 press:2 using:17 6u:1 unique:1 apart:2 insert:2 yb:1 appearing:1 like:3 shaped:3 splitting:3 qualitative:1 sizes:1 eep:3 sized:3 ai:1 yields:2 either:7 integrals:5 arbitrary:3 leaves:1 accelerations:4 stationary:2 parity:1 www:1 because:8 methods:2 namely:5 people:1 some:6 b4:1 v2k:5 b6:1 examples:1 16u:1 cd:1 kinds:1 gen:1 ijk:6 happens:1 ignore:3 scale:13 lead:1 2xa:1 measurements:1 integration:1 per:1 does:3 lunar:1 provides:1 2xu:1 survive:1 demonstrated:1 ωij:23 obey:1 power:1 bc:1 equivalent:1 l1:1 aj:2 expansion:7 pressure:2 although:1 tidal:6 post:17 2n:2 chapter:1 a1:1 about:7 carried:2 bars:1 extending:1 universe:1 theorems:1 o:13 range:5 r1:4 extensions:1 obeys:2 positive:5 discard:1 consequently:1 other:10 software:3 m2a:1 equally:1 cambridge:3 final:2 presence:1 into:12 within:1 washington:1 bound:3 d7:1 due:4 remarks:1 2v1:2 geophysical:1 national:1 einstein:4 frames:1 proportional:5 next:1 wustl:2 institut:1 additional:3 treated:1 support:2 there:9 question:2 u0:2 long:2 u2:6 accordingly:1 conservation:1 stars:4 gravit:1 was:2 overdots:1 assumes:1 naturally:1 function:5 complete:1 newtonian:32 bµν:2 relaxed:1 jul:1 repeated:1 delta:1 b1b:1 line:1 true:1 brans:1 b1c:1 ji:1 made:5 applying:1 gravitating:7 b5:1 whether:3 characteristic:2 gravitational:22 up:4 rc2:1 4v:7 limit:3 dv:2 demonstrate:1 distribution:2 define:3 similar:2 agree:1 b1:1 detailed:2 sort:1 4u:2 constant:7 ln:3 momentarily:3 4r:2 contribute:1 influence:1 general:6 conserved:3 governed:1 planets:1 gradients:1 appears:1 distributions:1 nab:2 ni:19 functions:3 compared:1 nl:3 nm:1 variety:3 xka:1 generally:1 vanishes:3 field:11 valid:1 details:2 spatial:5 test:5 mcdonnell:1 out:7 hydrodynamical:2 shrink:1 denote:7 provided:1 time:10 ultimately:1 includes:1 deriving:1 generated:3 a2:1 graphically:1 suppression:1 grishchuk:1 included:1 celestial:1 livingreviews:1 structure:9 algebraic:3 implies:1 coupling:1 4x:1 b1a:1 assume:4 requires:1 4t:1 required:3 holes:4 orbit:2 together:2 whereby:1 equivalently:1 implied:1 mass:49 fact:4 4h:2 missouri:1 once:1 4b:2 4a:2 |
0704.2244.txt |@word concept:1 partial:3 consider:13 remarkable:2 equalities:1 global:3 brownian:7 results:4 economics:1 leads:7 proposition:40 grateful:1 edu:2 go:1 denotes:1 payoff:3 compact:3 whose:6 γy:1 inverse:1 zariphopoulou:5 deterministic:1 ξt:2 young:29 including:1 accounting:1 supersolution:7 finally:7 critical:1 those:1 elliptic:1 under:5 stochastic:15 analogous:2 presentation:1 applied:5 random:7 risk:2 straightforward:2 very:1 dollar:1 bulletin:1 corollary:13 wishes:1 every:1 anonymous:1 lecture:1 affect:1 little:1 matrices:1 condition:6 polytechnique:1 exponential:1 solves:8 supports:1 notes:1 solution:61 large:2 admissible:6 recall:5 small:3 markov:3 martingale:6 context:1 unexpected:1 neighborhood:3 maximization:2 measurable:2 zτ:2 jump:1 rate:14 α2t:1 zy:2 infimum:1 concludes:1 zt:13 further:2 dynamics:3 investment:21 theory:3 even:3 aim:1 intersection:1 ˆs:2 vw:2 ˆy:1 sum:2 brief:1 uniform:3 version:1 dominates:1 above:13 referees:1 obvious:2 net:1 increasing:12 hamiltonjacobi:1 consisting:1 seeks:1 coefficient:2 respectively:5 gathered:1 equals:7 here:3 xθ:5 γx:1 than:1 address:2 represented:1 depend:2 along:4 strong:5 respect:12 implicit:2 interpret:1 obtained:2 great:1 suitably:1 items:7 study:1 studied:3 experience:1 yˆ:37 amount:9 resulting:2 nesbitt:1 real:1 complicated:1 changes:1 maker:1 point:8 2007b:1 via:9 useful:3 classification:2 apr:1 distributed:2 merely:3 convexity:4 root:1 specified:2 semester:1 analyzing:1 limm:6 apply:4 establish:1 dct:1 market:4 penalty:2 use:6 wealth:18 consumption:19 prove:21 positive:12 stated:4 chooses:3 next:14 vol:2 program:1 call:1 asset:12 taken:1 indiana:1 zim:4 msc:1 until:2 more:2 exit:1 duality:2 furthermore:1 clearly:2 becomes:1 umich:2 constructs:1 validity:2 parabolic:5 berlin:1 appendix:2 everywhere:1 proceed:3 particular:3 known:2 cases:2 hold:1 iii:4 must:3 ii:12 springer:2 ρb:1 player:1 scholes:3 science:1 equation:22 work:1 mi:2 modified:3 paragraph:1 values:5 lipschitz:8 following:22 strategies:8 original:1 my:6 example:2 proof:62 control:22 claim:4 money:1 lπ:3 give:2 process:25 dxt:1 organized:1 annals:3 bellman:4 high:1 contradicts:5 minimum:22 performed:1 want:2 nonnegative:1 robinson:4 verlag:1 itˆo:5 needs:1 arbor:2 end:2 goal:7 dwt:1 provide:1 s2:2 discussion:1 s0:1 department:2 browne:2 write:6 how:6 crandall:5 criterion:3 fourth:2 optimal:38 parameter:2 dzt:1 fr:1 2my:1 ft:3 algebra:1 replacing:1 db:16 after:6 respective:1 hazard:4 shreve:9 retirement:1 pasting:5 ζt:2 cambridge:3 righthand:1 summarize:1 minimizer:1 purchase:1 natural:1 outline:8 third:2 sets:3 whenever:1 lemmas:1 borrowing:1 yτ:3 parameterized:1 element:3 rather:1 so:5 progressively:2 correlation:2 subsolution:10 invests:6 order:8 g11:1 superscript:1 operations:1 holds:10 feedback:3 indeed:3 over:1 mx2:1 stability:1 paper:8 through:14 motions:5 minα:1 y1:113 y0:48 satisfies:17 y2:14 its:10 depending:1 before:4 τn:6 τm:3 monotonicity:1 interesting:2 τd:9 decreases:1 ds:22 continue:1 choose:3 unbounded:1 jacobi:3 derivative:3 valued:1 volatility:4 fin:1 easier:1 overcome:1 maximal:1 non:17 ym:32 halt:1 thereby:1 2λs:1 outlined:1 introduce:1 yf:2 φˆm:146 hamilton:4 dini:2 they:2 identically:1 yp:1 ys:3 now:10 bounded:11 yt:12 easily:1 stopper:35 yh1:1 equality:4 fully:1 preclude:1 concave:29 intermediary:1 correspondence:1 sufficiently:2 inequality:16 stopped:1 each:7 repeating:1 side:4 mean:2 subset:1 differential:12 financial:7 due:3 series:4 reduce:2 related:9 society:1 ωy1:5 variety:1 our:20 approximated:1 insurance:1 special:1 out:4 krylov:1 shown:3 rw:1 nonlinear:1 space:3 dst:1 since:40 crucial:2 rz:1 research:4 dominated:3 dying:1 term:1 formula:5 get:2 technically:1 cause:1 correct:1 shows:6 foundation:1 earlier:1 turning:1 linear:10 associate:1 limβ:1 discontinuity:1 given:36 free:3 standard:3 surely:2 collection:2 superiore:1 estimate:1 hand:9 remainder:2 hedging:1 definition:8 derivation:2 r2:10 applications:1 omit:1 programming:2 snell:2 times:4 motion:2 turn:3 american:3 place:1 exponentially:2 hence:4 transaction:1 first:28 major:1 initial:2 probability:65 upper:2 relate:1 variables:3 primary:5 reaches:2 multiplying:1 long:1 xp:1 u2:1 open:2 horizontal:1 xt:3 stochastics:1 differ:1 necessarily:1 exists:10 similarly:5 introduction:2 opportunity:1 zφ:2 construct:2 πm:1 their:6 finding:1 too:1 πt:7 convention:1 lions:7 siam:1 variational:1 final:4 jel:1 gives:1 rewards:2 statement:3 relationship:7 tool:1 continuous:19 proving:5 direct:2 assumption:3 part:10 authors:1 zδ:15 off:1 x0:7 sign:1 bρσ:1 coefficients:2 diffusion:7 wide:1 scheme:1 determines:1 showed:4 namely:8 frugal:1 subsequence:2 future:1 contrary:2 williams:2 fˆ:1 were:3 risky:9 motivation:2 generality:2 rewrite:1 ann:2 argument:5 already:4 say:1 close:1 need:2 gronwall:1 lα:5 st:2 cecil:1 relatively:1 mim:1 smallest:1 zero:6 min:10 studying:1 latter:1 converges:8 note:17 z1:10 εn:5 dyt:1 take:3 objective:3 lβ:1 modulus:1 calculus:1 inequalities:1 begin:2 mˆ:2 optimizer:1 though:2 arguing:1 price:3 decreasing:21 viscosity:41 systems:1 bss:1 most:1 regular:10 ht:2 significant:1 representation:1 remarks:1 filtration:1 probabilistic:2 class:1 bsc:1 especially:1 incisive:1 clear:7 later:5 cover:2 points:2 principle:3 exp:1 north:2 section:50 fact:17 gain:1 slope:2 dynamic:2 show:48 definite:1 supported:2 fleming:3 ˆs2:1 minimizing:10 solutions:11 keywords:1 φm:90 find:3 based:3 scuola:1 tchebyshev:1 ruin:58 λt:44 proportion:1 enough:4 controls:5 should:3 terminal:1 lemma:17 only:8 explicitly:1 black:3 specify:1 developed:1 envelope:5 local:2 continuity:4 do:2 his:1 legendre:8 closed:1 notation:1 means:1 dependent:1 michigan:2 sup:18 stop:3 expectation:3 ones:2 negative:2 words:3 new:1 applying:4 dt:50 reprint:1 geometric:2 secondary:2 reveal:1 processes:2 dpp:2 πs2:1 approach:4 arxiv:1 2b2:1 yield:1 summary:1 derive:1 optimally:4 she:1 attained:2 nondecreasing:1 fixed:1 thanks:9 satisfy:5 set:7 constructing:1 fair:1 achieved:1 approximating:1 national:1 saddle:2 up:1 edition:1 depends:1 individual:23 result:18 w0:1 terms:2 best:1 techniques:3 αp:2 αs:3 still:2 αt:6 yty:8 ways:1 arguably:1 user:1 please:3 pisa:1 upgraded:1 arbitrary:3 state:3 difficulties:1 karatzas:13 αg:2 between:3 αi:1 soner:3 boundary:16 conditions:7 souganidis:2 supm:1 available:2 ends:1 recently:1 extend:3 wl:22 actuarial:2 however:3 wv:2 york:1 wt:7 extent:2 referenced:1 martingales:1 optional:1 improve:1 both:7 0p:1 last:3 candidate:1 avoid:1 0z:3 taking:3 equal:3 april:1 games:7 receives:1 pdf:1 argue:2 expression:3 fix:1 otherwise:4 comment:1 among:7 co:1 conclude:14 continuation:4 cf:1 sampling:1 analyzed:1 cy:1 maximize:3 polynomial:1 associated:2 considers:1 ct:8 considering:1 described:3 second:14 addition:1 z0:25 locally:9 three:9 been:1 strategy:18 hitting:6 reduction:1 equicontinuous:1 z2:19 interest:2 cmap:1 expected:2 empty:4 pm:1 firm:1 arises:1 corresponding:10 finishes:1 propositions:12 remark:1 modelling:1 markets:1 policy:3 controller:37 observe:3 optimality:1 mail:2 prices:1 c2:9 c1:6 c0:1 assigning:1 present:2 case:12 exception:1 main:4 unlike:1 turns:3 might:1 value:41 choices:1 will:28 while:1 optimization:5 suppose:12 policies:1 stopping:24 property:6 region:7 bayraktar:23 yi:1 vc:1 existence:1 satisfying:2 almost:3 vi:4 thus:13 surprisingly:1 2βa:1 according:1 helped:1 characterize:1 regularity:39 itself:5 im:18 contradiction:6 dual:11 lifetime:25 motivated:1 cumbersome:1 finance:7 develop:1 handled:1 grant:1 journal:7 pay:1 make:1 problems:21 same:5 any:18 concavity:3 arguments:7 largest:1 filtered:1 proved:2 defines:1 events:1 independent:3 used:9 http:1 imply:3 see:38 functions:28 possible:1 allocation:2 running:8 uses:1 yg:3 bequest:1 normale:1 estimation:1 discounted:2 maximizing:3 minimize:7 ingredients:2 analysis:4 c61:1 pham:4 without:2 lim:8 quantitative:1 reward:9 dimension:5 left:2 λs:11 arbitrarily:1 diffusions:2 λv:2 λu:2 heavily:2 being:1 fˆt:4 resp:2 ishii:3 obtain:12 rest:3 proposes:1 λg:5 λf:11 λe:2 hjb:20 alternative:1 previous:2 letting:1 death:3 vτ:1 integer:1 conclusions:1 characterization:2 except:2 discontinuous:1 other:8 theorem:60 2006a:1 extensive:2 contradict:1 εh:3 identical:2 pair:3 replaced:1 income:2 virginia:16 possibly:3 game:8 inflation:1 know:5 guide:1 press:1 using:19 unique:26 moreover:12 αf:6 δa2:1 review:1 generated:2 loss:2 modifications:1 necessary:1 αb:3 semi:1 university:4 exploiting:1 controllers:1 communications:1 individuals:1 yields:3 either:5 2007a:2 limn:1 page:3 erhan:17 mathematical:6 www:1 right:8 methods:2 classical:19 sequence:14 professorship:1 conditional:1 some:9 choosing:2 self:1 deduce:2 economic:4 evaluated:1 b2:18 convex:31 home:1 proofs:7 library:1 uniqueness:2 decision:1 extensively:1 comments:2 does:4 exposition:1 subjet:2 provides:1 assuming:2 steps:1 minimal:17 refer:3 minimization:2 derivatives:1 uniformly:18 equivalent:1 submartingale:2 immediately:2 bt:1 pressure:1 step:2 substituted:1 although:4 offset:1 riskless:4 super:1 properties:4 simpler:1 chapter:1 comparison:3 would:5 simplify:1 theorems:13 discussed:1 dependence:2 o:6 costs:1 convenient:1 a2:1 vcc:1 augmentation:2 constraints:2 automatically:1 converging:1 david:1 own:2 letters:1 follows:63 pays:1 into:1 ψw:1 lies:2 because:28 references:1 operator:3 reducing:2 your:1 utility:8 rely:1 her:6 strictly:33 there:14 u1:3 transform:8 specifically:4 pages:2 strict:2 touzi:3 editor:1 way:1 analyze:2 sections:3 duffie:6 hara:1 therefore:10 function:48 dbt:2 complete:1 form:4 hs:1 but:6 subjective:1 sde:1 ho:2 convergence:5 line:5 true:3 observation:1 ωy:1 compute:1 rogers:2 selects:1 smooth:18 maximum:6 us:10 um:56 below:2 growth:4 limit:3 verification:7 annuity:1 continuously:2 demonstrate:1 problem:76 define:28 similar:4 detailed:1 required:1 constant:11 moore:2 item:1 defined:13 abstract:1 describe:1 ordering:1 proves:2 exist:4 formulation:1 controlled:7 inf:36 constructed:1 minimizes:1 again:2 mutual:2 compared:1 differentiable:2 integrability:2 no:2 whereas:1 when:17 sudderth:2 application:2 priori:3 papers:1 test:1 mathematics:8 nice:1 equations:7 denote:4 calculating:1 models:1 dies:2 drift:4 propositon:1 deriving:1 meaning:3 important:2 invested:2 additionally:4 variable:2 discretionary:1 sides:3 equicontinuity:1 max:29 correlated:3 implies:11 assets:5 fund:2 assume:17 invest:5 interval:1 together:3 consumes:3 equivalently:2 portion:1 incomplete:1 time:37 far:1 rxt:1 |
0704.2245.txt |@word represent:2 sci:1 consider:1 caused:1 magnetic:26 comparatively:2 results:2 leads:1 york:1 computation:1 skin:9 expressions:6 contributions:3 3m:1 whose:6 depend:2 calculate:4 clarke:1 iii:1 segments:9 disturbances:2 ρs:3 charge:8 does:1 those:5 under:10 include:1 alongside:1 applied:5 belonging:1 amplitudes:2 simmetry:1 very:3 frequencies:9 dq:1 keeping:2 wave:47 electron:26 paraboloid:2 affect:1 difference:3 qv0:3 condition:2 common:1 foo:1 presented:4 transmission:24 cause:4 developing:1 t2:6 solution:1 damped:2 large:1 σxx:3 vector:2 fourier:4 small:10 nizk:1 smaller:7 zh:5 broader:1 renormalized:1 dealing:1 sin2:1 sign:4 approximation:4 zero:2 traveling:3 further:3 odd:2 situated:1 folk:1 goes:1 even:6 will:1 appear:8 3r:1 while:3 expressed:1 thickness:2 current:2 wolff:1 poles:2 above:3 new:2 πc:1 coefficient:18 fiz:8 respectively:5 component:5 equals:2 here:7 quasimomenta:1 met:2 them:1 free:2 represented:1 consideration:2 along:18 strong:4 equations:3 change:2 convert:1 parameters:2 noticeable:1 study:2 larger:1 abrikosov:1 simultaneous:1 resulting:1 poisson:1 usually:1 resonance:8 adopting:2 narrow:1 changes:4 plotted:8 emerge:2 via:1 merely:1 sbe:1 rσ:2 summation:1 δn:1 plot:2 use:3 quasi:1 takes:5 prove:1 remains:2 positive:1 contains:1 negative:5 comparing:2 program:1 therefore:6 typical:1 films:4 type:1 more:3 νs:4 substances:2 becomes:3 acceptable:1 curvature:1 correspondingly:3 everywhere:1 profiles:2 particular:2 known:3 foundations:1 iv:1 producing:1 must:4 account:5 extension:1 mc:1 equation:16 work:8 remain:2 values:11 thin:8 transparency:11 following:9 metal:28 arrive:1 performed:1 f1:3 f2:4 renormalization:1 figure:4 chosen:1 calculation:1 expanding:2 thinner:1 dxs:4 accept:1 lω:2 high:4 collision:2 walsh:1 numbers:2 magnitudes:3 tan:2 occur:5 axis:5 creates:1 carriers:8 provide:3 travel:2 roughness:5 regions:1 located:1 varies:1 specular:3 significance:1 parameter:13 sin:1 circular:5 fp:3 simplicity:1 fs:49 mat:1 may:32 broad:1 earlier:3 reflect:1 plane:5 studies:2 waves:22 factores:1 horizontal:1 fl:6 parallel:3 occurence:1 effective:2 spectra:1 lines:13 correspond:1 neglect:2 extremal:2 rather:5 so:12 predominate:1 order:12 nonequilibrium:1 restriction:2 neighbourhoods:2 help:1 over:8 move:3 vary:2 top:1 experiments:4 through:6 motions:1 signs:1 mentioned:2 excitations:2 its:6 roots:1 before:1 derive:1 longitudinal:7 lc:3 energies:2 interesting:1 actually:1 estimating:1 window:2 complex:2 fig:13 lq:1 puerto:1 main:3 non:1 good:2 greater:8 cadmium:1 landau:1 effects:7 they:1 thanks:1 now:3 yu:2 february:1 finite:1 2s:8 characterizes:2 university:1 possibilities:1 realistic:4 magnitude:4 transmitted:1 mode:18 2m:1 characterized:1 mean:3 schultz:1 en:6 ei:4 significantly:5 collisionless:5 independent:1 series:1 energy:3 sov:5 related:2 eb:2 frequency:38 expect:8 sectional:1 our:2 happen:1 t1:7 eq:10 ep:2 special:2 out:10 shown:8 ying:1 matrix:2 part:1 space:2 σyx:1 rev:9 increase:1 collisions:1 formula:1 electronics:1 ref:3 eksp:5 shows:1 sinh2:1 doppler:6 theory:3 interactions:8 divergence:1 possibility:1 clarify:1 completely:1 dependencies:3 formation:4 term:7 besides:1 usual:2 put:1 estimate:2 chernov:1 e2:2 advance:1 geometry:8 could:9 omit:2 used:2 linearized:2 motion:2 ζs:2 place:1 isotropic:1 corrections:2 teor:5 exhibited:1 first:2 major:2 xn:2 features:1 symmetry:3 πn:1 possessing:1 number:3 restrict:1 xy:1 another:1 reached:6 cups:1 electronic:1 size:12 ωp2:1 given:4 πa:1 asymptotic:2 introduction:1 revealed:1 eqs:1 moderately:1 system:2 relations:1 response:4 their:3 assumption:1 too:1 calculations:2 gives:1 shifted:6 originating:3 grant:2 estimates:2 dissipationless:1 transverse:20 weakly:4 paraboloidal:18 favorable:3 platzman:2 x2:1 stepanenko:1 than:10 reflection:5 relative:2 kind:2 polarized:1 liquid:58 showed:2 accordance:1 ic:1 sections:4 require:1 measured:1 see:8 2ei:1 limiting:3 determined:4 amplitude:1 were:3 enables:1 solely:1 occurences:1 projections:1 gantmakher:2 rewrite:1 occupies:1 spectrum:5 curves:13 dash:3 manuscript:1 7s:1 manner:1 qualitatively:1 any:1 strength:1 angle:1 depending:2 efficient:2 latter:2 mechanism:1 polarization:6 instance:1 take:4 coincide:1 surfaces:6 electric:3 trace:1 normal:2 satisfy:1 falls:1 simplify:1 propagate:2 significant:1 vicinities:7 analytically:3 segment:3 give:2 especially:2 windows:2 soviet:1 clear:1 coincides:2 vertices:3 dod:1 points:7 electrons:42 clean:4 velocity:10 maxima:1 physics:1 dot:3 λs:2 medvedev:2 show:4 absorbing:1 supported:1 bring:3 relation:5 solutions:2 participate:1 substituting:1 d2:1 d3:1 principal:1 iey:1 q0:4 iq:2 q2:8 ratio:2 knowledge:1 ellipsoid:1 conduction:12 inflection:14 iωt:3 written:3 should:1 rico:1 only:3 factor:2 quasimomentum:3 employed:2 constant:1 local:1 oct:1 do:1 intersect:1 notation:1 get:6 occuring:1 displayed:1 da:14 cannot:2 dz:1 nearly:12 dx:11 drawn:1 tungsten:1 penetrate:1 ds:4 xdx:1 qr:8 qv:3 fields:3 arxiv:1 dpz:10 acknowledgments:1 predicted:1 ωp:1 including:2 qm:3 qn:17 kernel:1 computed:1 exists:1 attenuated:2 correlations:3 up:1 observed:2 namely:3 result:3 cyclotron:38 close:4 best:1 conductivity:9 closer:2 axially:4 speed:1 currently:1 µs:3 symmetric:4 case:3 charac:1 various:3 between:4 affecting:1 limit:6 boundary:10 conditions:9 terms:4 creating:1 interfaces:3 weak:2 however:6 incident:5 concentrate:1 4iω:1 less:1 uχ:4 jetp:5 problem:1 originates:1 concentrated:1 both:2 cos:7 providing:1 σn:4 powers:1 region:8 density:6 jn:3 propagation:2 manifestations:2 purely:1 dated:1 contribution:12 whole:2 comes:2 grounds:3 among:2 relevant:4 conclude:2 simple:1 corresponds:7 dimensional:1 directions:1 pole:1 quinn:1 path:2 intersects:1 cq:3 pr:2 extrema:2 described:2 second:1 pz:29 due:9 much:1 slowly:1 damping:7 p2z:1 anomaly:2 define:1 direction:1 arises:1 corresponding:8 deeper:1 observable:1 residue:1 gas:2 t3:1 bulk:1 external:8 derivative:2 catch:1 c2:5 spin:2 diffuse:5 present:6 p2:3 p0:4 singly:1 pacs:1 solid:4 plasma:2 straight:3 originate:1 value:11 employ:2 near:17 helicoidal:2 2ie2:1 promising:1 taking:1 real:3 layer:3 vectors:1 vf:1 phenomenological:1 refs:1 thus:1 propagates:1 surface:26 equal:1 ii:1 cond:1 gumbs:1 vz:1 different:1 predominates:1 author:1 circularly:1 belong:2 cross:5 same:4 selfconsistent:1 unity:1 parts:3 changed:1 arguments:1 schematic:2 figures:1 dimensionless:3 gets:1 difficult:1 meets:1 attenuation:3 infinity:1 hardly:2 ni:1 effect:6 v0:17 conductors:1 recent:1 lower:2 ellipsoidal:2 modes:5 nevertheless:1 expression:15 well:1 analysis:7 academic:1 without:1 solve:1 greatest:1 components:12 coordinate:1 position:1 model:3 magnetohydrodynamic:1 arising:2 possesses:1 left:8 spherical:10 stringent:1 minima:1 obtain:2 rest:1 shape:14 transforms:3 sufficiently:1 σnn:6 scattering:6 task:1 disturbance:3 conclusions:1 5t:2 character:1 iω:1 fermiliquid:1 interested:1 lett:2 silin:4 remaining:5 momentum:2 generalized:2 identical:1 depends:2 holland:1 advances:1 couple:1 possible:5 harmonic:1 increases:2 using:9 emergence:1 follows:5 collective:6 holes:3 alkali:1 integrals:3 always:1 works:2 reasonably:1 replacement:1 right:9 qn2:3 predominance:1 some:6 yudin:1 oscillations:15 extended:1 transport:3 happens:2 provided:5 describing:1 bottom:1 affects:1 romanov:2 inequality:1 provides:1 assuming:9 propagating:5 analyzed:1 limitations:1 considering:2 reach:2 perpendicular:1 pauli:1 plots:1 panel:14 carried:5 proven:1 most:2 certainty:2 anomalous:4 dependence:2 o:1 reduced:1 range:2 connected:1 introduced:2 consequently:1 computational:1 presence:3 omitting:1 maxwell:2 into:10 within:5 integral:2 nsf:1 variable:1 appropriate:6 strip:1 amsterdam:1 binding:1 theoretically:1 impedances:1 terminated:1 area:6 extremely:1 there:4 subdivide:1 transform:1 long:1 dispersion:23 start:3 restricts:1 cosine:1 low:24 way:1 analyze:2 was:9 treat:1 function:13 tight:1 north:1 form:9 enough:1 but:1 taken:4 state:1 russian:1 impedance:2 line:16 δn0:3 directed:2 absent:1 made:3 applying:1 qualitative:1 temp:2 whether:1 mtrl:1 inside:4 smooth:2 maximum:7 us:1 iqr:1 considered:5 below:1 owing:1 fermi:67 ωl:1 suitable:1 observation:1 distribution:4 panels:1 similar:5 calculated:1 strengthens:1 ex:1 strongly:1 diverges:3 associated:4 attenuating:1 cosec:1 certain:1 describe:2 metals:14 general:1 single:1 exist:1 θn:8 film:15 again:1 functions:8 no:2 dashed:2 whereas:1 when:26 depth:3 field:26 other:1 electrical:1 details:1 branch:2 department:1 conclusion:2 integrand:1 nonzero:1 exp:5 separate:2 models:1 time:3 includes:4 lens:3 a0:1 meaning:1 important:1 w911nf:1 included:3 fisher:2 strips:2 cheng:2 dω:1 assume:6 curve:10 orbit:1 mimic:1 fss:8 mass:8 electromagnetic:14 |
0704.2246.txt |@word aoki:1 limited:1 consider:4 chain:1 switched:1 induces:2 magnetic:4 results:7 p01:7 p00:4 computation:1 edu:1 go:1 r1l:2 adjustment:1 contributions:1 bsd:1 terms:5 calculate:1 technique:1 presents:1 finally:7 does:1 present:4 stabilizing:1 sped:1 te:2 concurrences:1 swap:1 sent:2 6p3:1 orthogonal:2 far:1 readout:4 summarized:1 experimentally:6 difference:9 matrices:1 adaptive:1 condition:1 common:2 splitter:3 swapping:7 pbs:4 presented:3 opt:1 ref:1 array:1 solution:1 large:2 discrete:2 small:4 chuang:1 optics:1 round:1 configurations:2 upper:2 smaller:2 consistent:1 pulse:9 sign:1 past:4 consists:1 rate:4 enhancement:2 heralds:3 estimated:2 click:2 established:2 what:2 errors:4 stands:2 section:8 brief:1 find:2 access:2 waiting:2 experiment:2 above:1 shared:1 ground:1 method:1 coefficient:1 full:2 simultaneously:1 1i2:1 never:6 component:5 teleportation:2 here:2 atoms:9 hours:2 reported:4 active:3 ratio:1 along:2 strong:6 appears:1 change:1 deduced:3 obtained:6 sending:1 institute:2 shift:3 elaborate:3 instead:1 ψlr:5 leaving:1 simultaneous:2 resulting:4 cesium:2 resonance:2 demonstrates:1 birefringent:1 studies:1 conditioning:1 via:6 spatially:2 projection:1 apr:1 explained:3 technologies:1 brought:3 addressed:1 turchette:1 counts:2 extinction:1 establish:1 research:1 unit:2 tween:1 use:2 reflected:1 usa:1 prove:3 distinct:1 few:2 sample:2 wood:1 ψl:2 taken:1 heralded:1 type:1 theoretical:2 more:8 separated:5 fellow:1 outputs:3 operators:1 emission:1 visibility:5 controlling:1 investigation:3 particular:2 known:1 cases:1 conditioned:2 iii:4 insights:2 reconstructed:5 account:2 stabilized:2 permits:1 science:3 setup:12 work:1 values:5 ms:4 tracing:1 following:2 meet:2 braje:1 drops:1 spontaneous:2 unconditional:1 performed:2 control:5 ions:1 challenging:1 figure:10 give:2 process:6 preserving:1 organized:1 near:1 nielsen:1 states:11 chin:1 numbers:1 arise:1 occur:1 axis:1 normalize:1 filter:1 needs:5 disruptive:1 noises:1 verify:2 divided:1 validates:1 feature:5 write:18 maps:1 interfere:2 influences:1 significant:1 gate:2 absolute:2 parameter:2 ensemble:15 map:1 product:2 express:1 information:3 filtering:1 ζi:1 sacrifice:1 after:16 ζl:1 lab:1 ζr:1 explored:1 coming:1 improving:1 wave:2 data:3 parallel:2 efficiently:1 waist:2 effective:1 beam:7 light:6 approximation:1 counter:2 correspond:5 su:1 element:1 ones:1 so:1 discussion:1 polyakov:2 acknowledges:2 order:10 typical:1 operations:1 enk:3 office:1 developed:3 over:4 stays:1 satisfied:1 stability:5 paper:3 including:2 lasers:1 cold:1 excitations:2 its:4 before:6 perfect:3 delay:4 group:3 symmetry:1 decay:2 polarizing:1 succeeds:3 pulses:14 wri:2 better:3 wineland:1 detected:4 degrees:3 systems:9 constitutes:1 main:1 definitely:1 setting:1 wavepacket:1 eventually:1 non:2 greater:1 thereby:1 polarizations:3 bound:2 p10:7 records:3 nsf:1 half:3 now:3 discuss:2 inhomogeneously:1 matched:2 term:6 2p:1 2r:5 verifying:1 always:1 θij:1 level:2 successfully:1 establishing:1 capability:1 magnitude:2 transmitted:1 trap:2 2b:1 each:15 2l:5 found:2 higher:4 side:2 characterized:1 schemes:1 retrieve:1 directly:1 weight:1 generation:5 there:1 magneto:2 principles:1 nulling:1 populates:1 interferometer:2 frequency:2 connect:2 measurement:12 quantum:19 laboratory:1 operation:1 transitions:1 eq:2 event:15 out:5 shown:5 matrix:12 since:1 interference:7 projected:1 denotes:1 increase:1 fellowship:1 daniel:1 max:3 denoted:2 current:2 induced:4 cause:1 correct:1 shows:2 foundation:1 fiber:1 linear:2 normalized:1 written:5 monotone:1 diagonal:7 possibility:1 difficulty:1 necessarily:1 california:3 imaging:1 reconfigure:1 imagine:1 van:3 detecting:1 phd:1 generate:3 pairs:18 βr:2 could:1 transition:3 detuned:1 harris:1 period:1 δij:2 assumed:1 βl:2 neglected:2 βi:1 first:11 losses:1 ability:1 already:2 probability:21 striking:2 variables:1 thesis:2 coding:1 number:1 general:1 another:2 improvements:2 thick:1 precisely:1 prohibitively:1 passes:1 given:4 1r:5 xie:1 utilization:1 introduction:1 leading:3 yin:1 system:5 least:2 1a:10 their:1 1b:1 rates:2 observations:1 realization:2 show:1 programmable:3 scheme:4 1l:2 store:1 gives:3 kolchin:1 releases:1 trapped:1 relative:7 continuous:1 hui:1 part:2 kept:2 than:6 center:1 diffusion:1 distance:3 polarized:1 dto:1 fold:1 require:2 zero:5 aims:1 final:2 annihilation:1 matter:5 determined:4 modulators:2 were:2 enables:1 seminal:1 bridge:1 pointed:2 fashion:2 correction:1 roughly:1 unlikely:1 need:1 seen:1 purification:1 demonstration:2 any:5 paths:5 conversion:1 angle:2 built:1 depending:2 efficient:1 polarization:3 instance:2 ideal:6 internal:1 combining:1 detector:8 techniques:1 caltech:2 underestimating:1 d1a:2 raman:2 towards:7 norman:1 kyung:1 price:3 involving:1 connected:3 waveplates:1 pair:19 acknowledgements:1 measured:5 trapping:1 later:2 detectors:6 inferred:1 retrieval:7 curie:1 optical:4 2hz:1 principle:2 gratefully:1 subsequent:1 deng:1 sum:3 fact:1 quantity:1 intensity:2 6s1:1 supported:1 scattered:2 anyway:1 merit:1 relation:1 routinely:1 recording:1 d2:1 networks:2 principal:1 µm:2 based:2 ensembles:57 parameters:1 entangling:1 distributed:2 state:30 should:1 only:5 going:2 factor:3 acknowledge:1 local:1 concurrence:5 achieve:1 directed:2 cryptography:1 king:1 beams:8 de:6 overall:8 scalable:2 processing:1 joint:2 cannot:2 preparing:1 new:1 combinations:2 eme:1 processes:2 fields:31 arxiv:1 european:1 summary:1 investigate:1 architecture:1 mapped:3 through:2 thanks:2 ongoing:1 requirement:8 briegel:1 julien:1 achieved:2 acquired:2 national:1 lett:8 detection:19 namely:3 actively:2 result:5 im:1 close:1 ur:1 fidelity:1 photo:3 subject:1 preparation:2 phases:7 exploited:1 macroscopic:1 nature:4 µs:2 symmetric:1 enough:2 future:1 various:3 between:28 tens:1 reading:6 approach:2 calculates:1 restricting:1 recently:3 creating:1 do:1 corresponding:2 initially:1 arises:1 emitted:2 weak:3 however:3 residual:2 efficiency:6 succeed:1 julsgaard:1 key:1 dlcz:5 analyzed:1 rapidly:1 configuration:7 come:1 both:9 last:1 desired:1 many:1 taking:2 barely:1 equal:4 attributed:1 enabling:1 propagation:3 connection:43 0a:8 logic:3 contribution:1 whole:1 experimental:16 among:1 relevant:2 bell:3 simple:1 overview:1 2i2:10 corresponds:2 2i1:9 directions:1 heralding:4 exhibits:1 sequences:1 constant:2 writing:2 broadens:1 points:1 considering:1 peng:1 longdistance:1 described:2 perspectives:2 second:2 basis:1 union:1 suppressed:1 three:1 been:13 reduction:1 combined:1 collected:1 itano:1 ph:2 fig:7 direction:2 enable:3 controlled:1 deeper:1 θl:2 quantities:2 sufficient:1 coherence:15 photon:36 requires:1 zeilinger:1 coherent:1 determination:3 coherently:1 angles:1 θr:2 improved:1 maximally:2 spin:1 protocols:2 case:10 riedmatten:6 triggers:2 single:22 value:2 spontaneously:1 will:6 while:4 scanned:2 superposed:1 involved:2 revisited:1 eur:1 θi:1 region:1 procedure:1 april:1 real:1 would:8 refs:1 thus:4 them:2 iv:2 ii:2 characterize:2 ij:3 duan:3 technology:2 monroe:1 increased:2 fulfilled:1 different:7 weinfurter:1 fibers:1 perform:1 realizing:1 residuals:1 intrinsic:1 indistinguishable:1 same:3 orders:1 html:1 quant:2 efficiencies:2 finite:5 φl:3 events:11 pan:2 difficult:1 development:1 independent:6 outside:1 used:1 http:1 bali:1 again:1 i1:6 i2:7 upon:4 effect:1 marie:1 hand:1 levels:2 purpose:1 entanglement:58 robust:2 plate:2 lower:5 task:1 off:4 modes:7 p11:6 expression:2 well:4 except:1 d1d:2 theses:1 without:3 comes:3 d1b:2 d1c:2 very:2 model:6 parametric:1 distances:1 stringent:2 protocol:2 proposed:5 less:1 being:2 when:4 photonic:8 sources:1 stored:5 distant:2 atomic:37 predicts:1 stabilization:3 purified:1 scattering:1 underline:2 previous:1 note:1 preprint:1 zoller:5 density:13 photons:3 characterization:1 wen:1 passive:4 visibilities:1 other:3 location:1 samples:1 remaining:11 identical:1 reconstructing:1 aspects:1 around:4 rev:10 exploiting:1 read:22 evaluate:1 absence:2 possible:2 mot:1 entangled:22 vacuum:5 press:1 using:3 projects:2 multiplexing:1 d2b:1 necessary:1 like:1 success:2 follows:2 collective:6 performing:1 clicks:1 communications:2 wooters:1 mhz:1 either:11 arbitrary:1 output:3 ρlr:3 reduced:6 spins:1 function:4 www:1 classical:1 creation:3 back:1 jia:1 deduce:1 meters:2 table:2 neglecting:1 myatt:1 electric:2 2d:2 eiγ:1 scale:1 dense:1 eiη:1 confirm:2 memories:1 measurements:1 recorded:1 overlap:2 eiξ:1 conditionally:1 critical:5 connecting:1 provides:1 bsu:2 steps:1 propagating:3 chains:1 collaboration:1 demonstrated:3 mode:13 measuring:1 kozhekin:1 power:1 equivalent:1 2c:2 how:3 step:2 βij:1 although:1 bs:3 repumper:1 stay:1 stage:3 chapter:1 about:3 polzik:1 actual:2 carried:1 bars:2 choi:1 fringe:1 chance:1 o:4 practical:1 takei:1 must:1 furusawa:1 chou:8 mixed:1 orthogonally:1 financial:1 block:4 cambridge:2 beamsplitter:12 suited:1 presence:2 previously:2 communication:5 into:15 splitters:1 laurat:4 soo:1 univ:1 down:4 phase:28 square:3 references:1 determine:1 parties:1 fruitful:1 significantly:2 unambiguous:1 rely:2 statistics:2 networking:2 interconnects:1 prepare:1 interacted:6 transfer:3 support:2 initial:3 question:1 depicted:1 long:7 start:2 low:5 way:3 prepares:1 delocalized:1 was:1 hz:1 conditional:2 repeater:1 illuminated:1 form:1 adjusting:1 but:4 expected:1 illuminates:1 detect:1 atom:1 line:1 hugues:1 proposal:1 count:5 applying:1 consist:1 lukin:2 inside:3 up:5 us:6 lead:3 below:3 simplifying:1 verification:1 uk:1 demonstrate:4 distribution:3 define:2 similar:2 called:4 detailed:2 storing:1 pij:1 cirac:4 associated:3 a1r:2 defined:3 minutes:1 sketched:2 resultant:1 kimble:7 lived:1 asynchronous:1 our:19 tomography:4 a1l:2 regime:8 high:2 bouwmeester:1 no:4 trials:1 individual:2 storage:2 field:34 pasadena:1 yonezawa:1 details:1 spatial:1 d2a:1 eiθ:1 d2c:2 ns:2 d2d:2 optically:1 elements:7 superposition:1 excitation:25 subspace:1 parenthesis:1 prepared:7 generated:10 important:2 suppression:6 variable:1 repumping:2 network:1 building:4 gao:1 independently:5 correlated:1 remote:2 auxiliary:1 practically:1 assume:1 physics:3 statistical:2 required:2 resolving:1 together:3 having:1 inset:1 leibfried:1 4h:2 time:13 n1:1 decoherence:1 backward:1 starting:1 original:2 once:1 |
0704.2247.txt |@word limited:1 homomorphism:3 similarity:1 rev:46 magnetic:13 dynamic:2 four:1 θr:7 entropy:24 worked:1 localized:1 consider:17 presents:1 under:8 worth:1 conjecture:4 p1:1 figs:2 summarized:3 affect:1 fractal:1 solution:5 frozen:4 unrelated:1 miller:2 consistent:2 direct:1 approximation:3 q1t:1 likely:3 qualitatively:1 implemented:1 haake:3 even:22 established:5 errors:1 complexities:1 above:2 new:9 increasing:8 coefficient:2 agreement:4 kicked:17 notions:1 equals:2 here:12 represented:1 quite:10 logarithmic:1 obtained:5 chaotic:27 rigorously:1 study:8 changed:1 approaches:3 denominator:1 stressed:1 fourier:4 changes:1 golden:1 prints:1 elaborated:1 discontinuous:1 explained:1 highly:1 total:4 propagators:1 unit:19 seligman:10 plot:10 would:9 negative:2 prelovˇsek:1 call:3 therefore:2 type:8 until:1 separated:1 successful:2 solitons:1 odinger:1 berlin:1 interaction:10 excellent:1 hold:1 springer:2 mn:1 suggestive:2 temperatures:9 example:18 renormalization:5 indicated:3 solved:2 organized:1 generically:2 indicates:3 degenerate:1 magnitudes:1 feasible:1 absolute:1 end:2 provide:4 verify:1 feature:1 far:4 nontrivial:1 hartmann:1 gate:2 description:1 arcs:1 transforming:1 thermodynamic:4 after:13 diagram:4 modest:2 law:5 types:1 effective:8 occasions:1 complexity:67 algorithms:1 ultimate:1 correlation:30 order:21 updates:1 interpretation:1 over:16 london:2 fidelity:33 before:5 fit:1 fix:2 exhibits:1 writing:3 better:2 production:1 connes:1 fig:24 easier:1 versus:5 them:2 amenable:2 break:1 effects:1 they:7 p04005:1 represents:4 vidal:4 reasonable:1 each:7 mean:1 series:7 drude:1 conjectures:2 rp:6 unital:2 gradient:2 rz:1 diffusive:4 re:1 vector:4 conjectured:2 smb:4 rj:14 cerruti:1 numerical:43 linear:29 little:1 free:1 standard:4 r0:2 r1:2 r2:2 created:1 chiara:1 iso:1 signature:1 corrections:1 onto:2 separable:1 rand:6 already:1 features:1 synonymous:1 rank:7 another:5 illustrate:3 toy:5 similarly:1 eqs:2 needed:8 perturbations:7 ballistic:7 observations:1 variational:1 ruelle:5 collapse:1 centered:1 serve:1 took:2 guhr:1 somewhat:2 princeton:1 iteration:2 rate:5 final:1 perturbative:2 seminal:1 mind:1 spectrum:8 manner:2 seen:1 seem:1 relatively:1 strength:8 genuine:1 convenient:2 latter:3 isolated:2 oriented:1 weidenm:1 reversed:1 circles:9 shall:20 simulated:1 boltzmann:1 regular:4 echoes:5 phase:10 acknowledgements:1 observation:2 calculated:4 partition:7 points:1 principle:1 presilla:1 sum:4 mejia:4 nπ:1 random:18 thirds:1 d3:1 d1:2 partially:1 finally:1 proposed:3 spite:2 situations:3 summarizing:2 hamiltonians:4 capel:1 continuity:3 do:2 dm:8 dk:1 de:1 zwolak:1 σ1x:3 dx:5 reconstruct:1 dt:5 holland:1 normalizable:4 cleanly:1 twice:2 analytical:4 pioneering:1 reference:2 observes:1 δjk:1 kolmogorov:4 evolving:1 observed:4 depends:2 result:5 discussions:2 best:7 techniques:1 said:1 tensor:2 away:1 yet:4 symmetric:2 unable:1 simplest:1 drawn:1 approach:4 iδm:1 terms:34 extend:5 nature:4 wn:3 restricting:1 weak:2 however:28 topology:4 suggested:3 ranges:1 essentially:5 ill:1 against:8 calabrese:2 uni:1 qubit:9 argue:2 confronted:1 exhibit:2 16j:1 16k:1 2nd:1 σjz:6 σjx:7 σjy:2 applicability:1 polynomial:3 mathieu:1 commutative:1 basis:7 gaspard:2 equations:1 three:12 been:35 much:4 interpret:1 interest:1 basic:3 expected:3 inventiones:1 algebras:4 ann:1 digits:4 ergodic:32 θn:4 deeper:1 θl:2 quantities:4 wish:1 coherent:1 σj2:1 σj3:1 σj0:1 σj1:1 spin:17 applied:6 auxiliary:1 aip:1 transformation:5 aim:1 near:3 abrupt:2 property:6 qudits:3 characterizing:3 schumacher:2 phenomenological:1 iv:2 ii:21 characterize:2 ij:1 cond:1 confirmed:1 perform:2 suggest:4 make:4 complex:6 quant:5 ripoll:1 big:1 dimensionless:2 several:6 grows:4 independent:13 dǫ:21 trajectories:4 counterparts:1 hand:9 slovenia:1 unimodular:1 weakly:3 contact:2 jalabert:3 quantitative:3 left:13 protocol:3 just:5 appropriately:1 rotated:2 σ0x:10 σ0z:1 identify:1 scattering:8 eigenstates:1 functionally:1 previous:2 character:1 easy:1 insensitive:4 iα:1 breaks:1 possible:11 spanned:2 possibly:1 unique:2 apart:1 performing:1 specific:4 steps:2 arbitrary:5 evolutions:1 www:1 right:11 deal:1 people:1 successfully:2 somehow:1 born:3 cnt:2 normal:4 subclass:1 linearly:3 kollath:2 algorithmic:8 oscillating:1 illustration:3 popular:1 jacquod:2 σjα:2 super:11 properties:12 anomalous:3 o:17 constituting:1 melville:1 42q:1 efforts:1 slightly:3 soc:1 statements:1 presence:1 bound:1 bath:8 down:2 lies:2 hermitian:4 amsterdam:1 often:7 rely:1 topologies:3 support:1 initial:43 approximate:3 computable:1 conservation:15 way:7 was:8 m0:5 form:10 converse:1 idealized:2 heat:9 true:3 reset:1 versions:2 prevents:2 inside:3 maximum:1 fermi:2 ψe:1 trotter:3 computing:4 cvitanovic:1 abstract:2 proven:1 evidence:1 peres:2 conserved:3 exist:7 promised:1 simulations:11 loschmidt:9 dε:3 distributions:1 check:1 triangles:4 constructed:4 dotted:1 no:10 liouvillian:2 whereas:8 generally:3 ne:22 ny:1 jona:1 setting:5 investigations:1 fokas:1 test:1 tie:9 picture:4 models:10 dissipation:1 regime:30 longer:3 assume:2 interval:1 pseudo:6 together:1 resonances:4 observables:21 quantity:5 precise:2 measurements:1 chain:32 global:4 truncated:23 guarneri:1 computation:11 remarkably:1 row:1 inverse:7 depend:4 eigenbasis:2 technique:2 environment:11 answered:1 quasi:13 analogous:1 petitjean:1 string:2 advantage:1 orthogonal:3 densitymatrix:1 choice:3 exact:17 partitions:2 presented:1 turns:1 proposals:2 qudit:3 involution:1 upper:3 work:4 slower:5 123a:1 spectral:13 appear:1 uniform:2 current:9 realizations:1 shankar:1 understanding:1 condmat:2 groups:1 address:3 along:3 appears:1 change:4 shift:2 studied:3 commonly:1 poisson:2 usually:5 resonance:3 automaton:1 studies:4 θl1:1 plotted:1 emerge:1 spatially:1 merely:1 giannoni:1 1st:1 planck:4 wang:1 projector:3 working:1 prove:4 perk:1 positive:12 give:4 predictions:1 optimize:1 explicitly:9 opposed:2 criteria:5 theoretical:3 diagrams:1 introducing:1 validity:4 cases:35 logarithm:2 valued:2 reviews:1 labeled:1 values:6 following:20 making:1 trans:1 stimulating:1 nearest:2 figure:24 saito:1 performed:8 allowed:3 conversely:1 occur:1 feiguin:2 verlag:2 s2:11 discussion:2 s0:16 write:10 alicki:1 pure:13 syst:1 extensions:1 parameter:8 map:13 product:16 mat:1 may:15 max:1 needs:1 applications:1 levi:1 osborne:1 data:16 grow:3 stress:2 sx:5 natural:3 dynamical:33 sectors:1 sq:1 explicit:4 yielding:2 ghz:2 st:3 sj:6 si:1 aβ:2 so:18 sn:23 sm:38 sl:10 definitions:3 michel:1 superscript:1 lsd:6 indeed:7 mainly:4 stability:4 course:3 experiments:9 statistical:12 cuts:1 argued:1 still:9 pointer:2 τm:2 group:6 thank:1 how:4 interesting:16 decreases:1 forms:1 constitutes:1 main:3 decades:2 correspondence:2 non:84 gray:1 introduce:2 scaling:20 half:1 bogoliubov:2 sπ:1 discuss:9 possess:1 name:1 arrows:1 possibilities:1 stolze:1 instabilities:1 domain:1 square:4 ek:1 ed:1 σ2x:1 gaussian:3 tracial:3 approximated:1 shown:19 benenti:2 space:25 furthermore:4 squared:1 increase:4 suggesting:1 formula:3 squares:11 correct:2 shows:2 theory:23 possibility:2 mapping:3 unwanted:2 e1:4 e0:2 e3:1 e2:1 derivation:1 βr:4 transition:22 iterative:1 motion:49 turn:2 place:2 βl:4 qn:11 βj:2 first:11 toulouse:1 symmetry:3 variables:4 xx:6 long:2 impossible:1 open:13 size:18 given:11 necessarily:2 1t:3 unitarity:1 indicate:3 1e:8 1d:3 convention:1 white:5 speaking:1 gives:2 exploring:1 continuous:1 braun:1 transverse:14 rightmost:1 representing:3 than:20 coefficients:8 third:1 sinai:1 cardy:1 were:12 pre:1 addressing:1 register:6 dynamically:2 turned:1 saf:1 say:8 lakshminarayan:1 any:17 numerics:1 subsystems:1 computationally:1 efficient:12 pineda:2 ideas:1 note:23 ideal:2 take:6 converged:3 modulus:4 multiple:2 trace:1 opposite:1 fujisaki:2 clearer:1 insets:1 algebraic:1 automorphism:8 pair:4 analytically:1 αt:1 surprising:4 considered:9 average:10 later:5 steady:15 typically:16 laws:16 slope:2 show:8 spaces:5 inconsistent:1 corner:1 ground:3 slow:1 ensembles:4 state:56 relaxes:1 knauf:1 analytic:1 only:15 going:1 closed:1 between:16 expectation:5 aα:12 cannot:7 gen:7 quispel:1 yield:3 mapped:1 discussing:3 rmt:4 physically:3 j1:1 namely:45 college:1 fannes:1 neuman:2 satisfying:2 commutation:1 ways:1 subsequent:1 review:6 functionals:2 enough:6 gases:1 diamonds:7 affecting:1 qubits:2 uj:2 utz:1 jn:6 comm:3 como:1 analyzed:1 article:4 come:1 σj:11 σn:5 σm:2 kicking:1 many:32 according:2 called:4 berry:1 σr:3 among:1 pastawski:3 characterization:2 period:3 translationally:7 werner:2 anti:1 iterations:1 constant:7 actually:4 considering:3 sensible:1 fabricius:2 analogies:1 locally:8 springerverlag:1 combined:1 borders:1 eβj:2 wants:1 direction:1 observe:6 external:5 convergent:1 case:58 σl:17 profiles:1 promising:1 investigating:1 taking:2 maximal:3 coupled:4 characteristics:1 sudden:1 baths:15 supremum:2 cd1:1 different:37 develop:1 paz:2 same:13 shifts:1 physical:7 finish:1 closest:1 kubo:3 entanglement:21 changing:2 invariance:6 cr:5 locality:4 roughly:1 solve:1 components:3 benatti:4 model:47 dimension:7 gates:5 being:7 when:10 σnz:2 rest:1 σny:1 summed:1 touch:1 flavor:2 sampled:2 zoller:1 thinking:1 cl:1 seems:7 except:3 interested:6 treatment:1 extensive:7 real:3 around:1 eigenvalue:10 sums:2 using:13 accepted:1 moreover:1 mod:9 particle:4 chaotically:1 discarded:1 grants:1 either:6 integrals:3 fully:2 inter:1 reduced:9 satisfactory:1 siegmund:2 unraveling:1 eiα:1 provided:3 beginnings:1 confirm:1 conservative:1 critical:3 decomposition:3 provides:2 power:4 equivalent:3 inspect:1 broken:1 comparison:1 central:11 discussed:5 meaning:3 practical:2 mutually:1 stand:1 neighbor:1 mixed:1 ou:1 perturbed:4 cambridge:3 inclusion:1 image:2 numerically:4 garc:1 copies:1 odd:1 references:2 monasterio:4 determine:1 elementary:3 conceptually:2 log:31 seba:2 assumed:1 strictly:4 there:22 start:7 low:5 lot:1 exceptional:1 complete:11 frahm:1 chaitin:1 trying:1 shannon:1 faster:4 h0p:1 robustness:3 agree:1 eigenvector:7 regimes:9 strongly:9 ac:4 cba:5 af:13 certain:9 aj:5 general:10 ar:3 au:1 formulation:1 aα1:2 az:26 sarkar:2 aα0:3 incorrect:1 again:17 ideally:1 commutes:1 nonergodic:1 field:27 valid:1 remarks:1 mathematics:1 briefly:3 fazio:1 time:119 a1:6 a3:1 a2:1 bounded:3 ising:14 suited:1 included:1 conclusive:2 bulk:2 rs:2 curve:4 affer:3 resembles:1 decoherence:11 starting:5 original:2 represent:7 monte:2 sci:1 sch:5 splitting:1 larralde:1 scalar:1 commute:1 follow:2 expressions:1 zinn:1 particles:8 c0:3 remarkable:2 tx:1 tw:1 tt:9 tr:20 acting:1 tq:2 tn:4 tl:12 th:1 tf:1 stochastic:10 norm:2 ta:5 jensen:1 straightforward:2 very:18 mpo:10 lyapunov:8 print:1 ultraviolet:2 mps:1 ln:3 difference:2 condition:2 treating:1 randomness:1 systemenvironment:1 hamiltonian:22 evaluation:1 t2:3 large:7 small:15 titled:1 strunz:1 past:1 integrability:22 displays:3 further:4 canonical:9 what:3 nonlinear:2 sub:3 nbi:1 brackets:1 section:19 version:2 subspaces:1 sup:4 learned:1 method:7 contrast:2 quenched:1 full:16 component:1 behaviour:6 modular:1 ansatz:5 relaxation:13 mul:1 strong:8 observing:1 legend:2 mult:1 search:1 generalizing:2 provably:1 inspired:1 amount:4 periodic:6 stiffness:4 published:1 action:7 options:1 via:1 followed:1 family:2 requiring:2 jadranska:1 analyzing:1 ıa:1 takes:2 nijhoff:1 contains:1 charge:1 comparing:1 partite:2 taken:1 ψc:1 mora:2 more:23 zeitschrift:1 operators:23 site:3 tested:1 tdmrg:15 particular:14 known:4 equation:4 remain:3 indicating:4 evolved:3 tractable:1 compare:3 states:38 numbers:2 sense:1 robinson:1 concept:1 information:8 respective:1 rather:11 breaking:5 eigenenergies:1 maps:2 ensemble:3 ft:1 algebra:14 derived:1 orbits:1 fa:1 ζr:1 faculty:1 response:9 short:4 spectra:4 exhibited:1 generic:8 negligible:1 sect:2 fundamental:3 cs0:2 hierarchy:1 developed:5 thermal:12 paper:10 through:1 berthiaume:1 existence:5 kibble:1 excitations:2 its:15 jacoby:1 bandyopadhyay:1 solving:1 fruitful:2 absence:1 systems:62 might:1 good:4 propose:1 yc:5 yy:1 framework:1 bigger:1 easily:4 2q:1 zotos:1 always:8 level:8 fluctuate:1 labeling:1 2d:4 inequality:1 2l:4 found:12 2n:6 2h:1 notes:2 characterized:6 referred:4 as1:1 as0:1 tilted:2 weight:1 energy:25 hard:1 idea:3 extended:1 expect:3 measurement:3 quantum:242 beyond:2 brandt:1 discrete:3 since:16 research:1 orthonormalized:1 denoted:1 issue:4 voros:1 reason:2 base:2 put:1 asi:1 a4c:2 definition:8 irrespectively:1 exponentially:12 circuit:1 consequence:3 undergo:1 assign:1 major:2 probability:4 perturb:1 relate:2 number:9 enlarged:1 done:1 construct:2 perturbation:22 temperature:15 introduction:3 leading:9 interact:1 least:3 calculations:4 master:2 scheme:1 exponents:6 relationship:1 part:2 jordan:3 norms:2 off:2 translation:1 believe:1 lebowitz:1 kind:3 dth:1 collaborations:1 plateaus:2 determined:3 doubly:3 treated:2 comput:1 randomly:2 confirms:1 orders:13 chirikov:3 lie:1 generalizes:1 zero:4 depending:2 lim:4 speculative:1 lii:1 onset:1 internal:1 useless:1 analogy:1 finding:1 unperturbed:5 towards:1 measures:3 reach:1 kam:1 most:10 eisert:1 experiences:1 significant:4 measured:1 stands:1 h2x:2 h2z:1 clear:6 saturate:1 coincides:1 unreasonable:1 physica:4 traditional:2 3s:1 optical:1 exp:23 posses:2 physics:11 lying:1 r00:1 converge:3 relation:3 fine:1 find:16 indicator:5 simulating:9 parameters:5 failed:1 subsection:3 factor:2 ablowitz:1 integrable:79 circle:10 columns:1 intractable:1 notation:1 dependent:15 zurek:3 famous:1 nonequilibrium:1 closely:2 cd3:1 combinations:1 lattices:5 arxiv:4 factorization:2 investigate:1 common:1 bellet:1 activity:1 obscure:1 scanning:1 set:14 achieved:1 undergoes:1 see:25 individual:1 close:3 analog:1 ergodicity:8 daley:1 uδ:7 positivity:1 various:5 τrel:1 probably:1 conditions:9 available:1 recently:4 statistically:2 complementary:1 initially:1 analogues:1 vanishing:8 phasespace:1 both:15 last:3 sensitive:1 connection:3 context:4 experimental:2 arbitrarily:1 point:6 simple:22 asymptotically:2 corresponds:6 dimensional:9 simply:7 adaptation:1 throughout:2 pr:1 pp:1 pq:1 described:8 perspectives:1 due:12 z1:1 ijσ:1 asymptotics:3 ph:7 z3:2 empty:3 lett:21 sanders:1 generating:4 gap:12 neumann:1 diagonalization:1 understand:3 grabowski:1 δsn:1 intriguing:1 δsm:1 look:1 exponential:18 pacs:1 solid:7 straight:1 expanded:2 while:6 error:5 schultze:2 couplings:2 subsect:1 unitary:14 jpn:1 averaging:2 von:3 unitality:1 reads:2 itself:1 vanish:1 lengths:1 belong:1 resulting:2 subalgebra:1 higher:1 schollw:3 calculation:3 used:10 wilson:1 flows:1 moment:1 purpose:1 robust:5 recent:1 eigenvectors:8 lower:3 task:1 edge:6 stating:2 things:1 poilblanc:1 lde:11 λt:2 reviewed:2 questions:5 useful:3 alternative:1 letting:1 kluwer:1 conclusions:4 signals:1 plateau:3 theorem:5 excited:1 generalized:1 situation:2 evaluate:1 couple:1 entangled:1 integer:3 bit:3 projects:1 formal:1 semi:20 follows:3 interestingly:3 disks:1 e00:4 separately:1 flux:1 continue:2 yields:1 translated:1 essential:3 spins:10 mathematical:2 pertaining:1 methods:8 georgeot:1 mathematicae:1 translational:2 some:31 back:4 understood:3 examples:2 ourselves:1 automorphisms:2 scale:12 describing:1 affects:2 though:3 per:4 behave:1 fishman:1 prog:1 leftmost:1 minimal:4 object:1 run:1 bi:3 bj:1 step:5 plots:2 relating:2 hilbert:7 integers:1 tracing:8 optimized:1 simulation:12 range:2 repulsion:3 consequently:1 block:2 cutoff:7 computational:3 into:4 within:7 suppl:1 appropriate:2 proportional:2 statistics:5 span:1 few:9 mpos:1 question:8 u0:7 fast:1 forward:1 sections:2 propagator:3 opens:2 toeplitz:1 memory:3 hoped:1 link:1 delta:1 line:10 collapses:1 partitioning:1 characteristic:5 implementing:1 up:16 us:24 ur:1 um:1 ul:1 un:1 suitable:3 autocorrelation:1 fluctuations:1 autonomous:3 similar:4 ki:38 entropies:8 jj:6 sometimes:4 ordered:4 defined:8 naef:1 single:2 willey:1 foulkes:1 formalism:1 defines:1 analyticity:1 kr:2 dashed:4 leyvraz:1 application:1 department:1 izergin:1 draw:1 elements:14 excitation:2 sided:2 problems:3 prepared:1 generated:6 allowing:1 vectors:2 structure:6 dimensions:1 correlated:1 implies:2 algorithm:9 practically:4 required:3 notion:2 equivalently:1 implied:1 presenting:1 having:2 code:2 partial:5 illustrates:1 results:30 existing:2 gg:1 eds:3 signatures:1 houches:1 stochastically:3 go:5 compact:1 simon:1 overlapping:3 deterministic:1 uniqueness:1 stable:3 tr0:3 resources:5 bonetto:1 wave:10 groeling:1 putting:1 cellular:1 mixing:18 matrices:20 entire:5 tra:1 positions:1 trc:2 tre:2 try:3 eigenvalues:10 trr:1 mahler:1 dimer:1 configurations:1 zl:1 smaller:2 disordered:1 zc:10 dynamics:52 carlo:3 zq:1 zr:8 index:16 giving:1 d2:2 expressed:2 consistently:2 experiment:1 body:19 lee:1 ibid:3 exchange:1 respectively:10 spacing:1 ock:3 growing:1 explore:2 les:1 z4:6 imperfections:3 z2:1 extreme:1 technical:1 larger:3 leaving:1 suggests:1 products:1 implement:1 makes:2 znidariˇ:5 formulated:1 scales:1 d83:1 limt:1 scaled:8 uger:2 resets:1 use:6 asymptotic:10 commun:1 remains:5 classically:2 estimated:1 themselves:1 noisy:3 bethe:4 formally:3 started:1 benchmark:1 pfo:5 labelled:1 perronfrobenius:1 iii:8 discontinuously:1 ρc:7 crosses:1 challenge:1 averaged:2 infinitesimal:1 thin:1 freedom:2 averages:6 purity:14 process:2 high:7 assumptions:2 varied:2 decaying:1 six:1 slovenian:1 regions:2 trieste:1 ρ2c:1 instead:3 mccoy:1 profile:9 blocks:1 singular:2 philosophy:1 factored:1 ow:1 physik:1 verstraete:1 efficiently:3 realized:1 clarkson:1 computations:1 lines:1 correspond:9 element:6 as11:1 z2n:1 s1:13 fastest:1 vitanyi:1 wigner:3 cd2:1 produces:1 interpreted:8 symbols:5 saturates:2 mentioned:1 longitudinal:3 decay:27 chosen:4 temporal:3 degrees:2 tsx:1 weber:2 eur:2 dam:1 outlined:1 material:2 mention:1 optimal:1 rotation:1 realize:2 dirac:1 university:5 identified:1 sufficiently:7 magnitude:2 l2:2 l0:4 l1:1 traces:2 prosen:20 subset:4 ockmann:3 doing:1 related:9 constitute:1 operator:38 decays:6 static:3 ½c:1 measure:6 our:14 special:4 out:9 maximizes:1 rey:1 matrix:41 rep:3 vcl:1 chaos:86 behaviours:1 performs:1 lecture:2 ref:13 integrated:1 math:12 diagonal:6 completely:12 york:2 weaver:1 backwards:1 could:2 times:5 length:1 hence:5 phrased:1 describes:2 iht:2 echo:5 intuitively:1 adjoint:3 system:40 their:7 intermediate:10 fermions:2 floquet:1 sensitivity:5 stars:4 explanation:1 exactly:11 rajagopal:1 simulate:4 manipulation:1 completes:1 treatise:1 limiting:1 amplitude:2 projections:1 ingenious:1 hz:46 fluctuation:1 curves:8 korepin:1 fail:1 need:1 clearly:9 viewed:1 angle:3 agency:1 able:4 switch:1 instance:1 thirring:1 concerns:2 subject:2 accuracy:1 heisenberg:2 unless:1 allow:1 connected:2 but:18 representation:5 tanaka:2 hu:1 intrinsic:1 class:2 exponent:9 neighboring:1 stronger:1 looked:1 typical:6 fact:5 selection:1 absorbing:2 supported:1 purely:2 trivial:7 agrees:1 principal:2 q1:2 q0:3 based:5 controls:1 should:14 truncation:21 local:52 equilibrium:26 means:1 βh0:1 bear:1 ones:2 words:3 propagated:3 compute:3 portion:1 evolution:50 qr:1 determinants:1 densities:1 tolerance:1 qc:23 europhys:2 overflowing:1 contain:1 fixed:8 qm:1 traceless:2 view:1 multiplying:1 computed:9 exists:3 correlations:3 hδ:2 edition:1 computer:5 truncating:1 conductivity:1 closer:2 interacting:20 ieee:1 written:10 correctly:1 invariant:14 boundary:8 ends:1 interchangeably:1 wj:7 efficiency:9 reproduces:2 derive:2 key:3 problem:17 observable:17 interpretations:2 instant:1 limits:1 coarse:1 invited:1 acknowledge:1 equal:1 dmrg:4 etc:2 grain:1 multiplications:1 otherwise:2 cj:1 relevant:1 conclude:2 cxx:1 environments:1 cd:2 cy:3 cirac:1 maximize:2 sequences:4 cs:1 respect:2 second:2 addition:1 trajectory:1 charts:1 slowly:2 treat:2 rates:1 proposal:1 improve:1 define:8 describe:6 corresponding:8 inspecting:1 truncations:2 sufficient:1 subspace:3 neighbour:1 kicks:1 prescription:1 c1:2 repetition:1 present:3 multi:2 unlike:1 corrigendum:1 value:12 will:11 rotator:2 vc:2 almost:6 refs:3 thus:6 surprisingly:2 hardware:1 casati:5 qd:6 perhaps:10 indistinguishable:1 unity:2 pauli:4 bipartition:1 units:3 finite:36 difficult:1 practice:1 batrouni:1 upon:1 effect:3 infinite:40 grigoryan:1 contribution:1 identity:2 mech:3 schr:1 center:1 nevertheless:4 well:6 position:1 usual:1 magnetization:5 less:5 accurate:3 obtain:1 detail:3 underlying:4 uller:3 macroscopic:1 now:13 density:20 selfsimilar:1 manybody:1 lattice:32 add:1 attractive:1 ljubljana:2 kick:3 saturation:1 spinless:2 increased:1 checking:1 devised:1 increases:1 know:1 press:4 immediately:1 semiclassical:1 tail:1 like:17 success:1 sizes:9 δv:2 alternatively:2 δt:4 fingerprints:1 δp:2 δn:1 become:1 works:1 preclude:1 accessible:1 parity:2 indications:1 classical:49 sequence:8 phenomena:4 self:1 growth:11 choosing:1 convex:1 transport:22 happens:2 orthonormal:2 informationtheoretic:1 literally:1 overlap:1 does:13 assuming:2 chains:8 demonstrated:3 noise:2 obey:1 journal:1 although:3 imaginary:1 cη:1 periodically:2 simpler:4 gained:1 about:9 justin:1 extension:1 universe:1 dependence:4 briegel:2 quasilocal:1 important:4 introduced:2 homogeneous:1 letters:1 h2:2 h0:9 h1:3 fidelities:1 additions:1 van:1 additional:1 transfer:3 imperial:1 quadratic:1 inner:2 crucially:1 nonintegrable:1 gorin:7 suzuki:2 naturally:1 function:27 hx:57 north:1 hr:11 hq:10 ht:3 approximates:1 construction:3 hn:11 hl:2 convergence:1 hc:11 lindblad:3 he:2 tomsovic:1 ½e:1 made:1 wise:1 society:1 whether:4 dangerous:1 smooth:1 flip:1 placed:1 below:1 limit:11 demonstrate:6 distribution:4 display:2 mechanics:14 montangero:2 int:1 universal:1 lasinio:1 denote:2 inf:1 proceeds:1 functions:15 compared:4 variety:1 4l:2 arctan:1 other:18 details:3 branch:1 theor:1 conclusion:2 stat:4 kinds:1 variation:2 signalling:1 coupling:8 4t:2 factors:1 4r:13 rule:1 4n:6 ghose:1 inset:10 4m:2 4j:2 4k:1 4c:1 |
0704.2248.txt |@word sci:1 consider:8 chain:1 focus:1 four:1 mni:2 ge:1 proposition:13 grateful:1 edu:1 follow:1 expressions:3 denotes:4 contributions:1 gi:13 row:1 whose:19 inverse:8 depend:1 subsemigroup:1 γi:17 γn:1 text:1 ven:1 uma:1 division:6 sehgal:2 abelian:10 orthogonal:3 ρj0:1 results:1 corollary:10 sons:1 every:7 reordering:2 entries:2 matrices:6 higman:20 immediately:1 hamiltonian:2 t2:28 item:6 convenience:1 vector:2 upper:1 mn:1 dealing:1 zg:1 direct:8 second:3 gn:1 zs:6 index:7 what:3 abc:1 appear:2 invertible:2 diag:10 section:8 contracted:2 analogously:1 annals:1 wj0:1 above:3 new:1 gl2:2 journal:1 respectively:4 component:8 equals:1 here:1 olica:1 groups:41 others:2 adjoined:1 te1:2 z0:2 z2:8 instituto:1 property:61 items:1 study:2 eiσ:1 contradiction:2 suggests:1 bridson:1 periodic:1 resulting:1 action:1 makes:1 options:1 addresses:1 classification:4 annihilator:2 inverses:2 apply:1 unit:12 clifford:1 use:3 would:1 prove:8 positive:3 contains:5 uniqueness:1 eσ:3 next:2 comparing:1 call:3 therefore:14 usp:3 means:1 type:6 andr:1 definition:4 clearly:11 curvature:1 berlin:1 particular:8 known:2 ok:6 cases:2 hold:1 iii:6 must:2 springer:2 isomorphism:6 recall:4 equation:2 work:1 ρs:3 paragraph:1 obvious:1 following:11 mx:1 proof:17 claim:1 wang:2 give:1 referee:1 allowed:1 suggestions:1 topic:1 ready:1 sense:2 conversely:5 occur:1 information:1 straightforward:2 s3:2 s2:5 s1:5 holds:6 enl:2 orthogonality:1 write:4 embeds:1 nontrivial:1 pure:2 supervised:1 e2i:1 classify:7 sil:2 map:1 product:1 sandwich:1 blocks:2 algebra:44 may:2 wiley:1 consequence:2 multiplication:2 man:1 si1:2 si0:28 natural:1 remember:1 third:2 sp:1 explicit:1 element:19 sk:3 si:39 so:10 sn:5 sm:1 sl:1 representation:1 order:34 acts:2 indeed:1 over:16 soc:1 course:1 paper:1 london:1 thesis:3 left:2 existence:1 its:11 respect:1 ime:3 manuscript:1 maps:1 summands:1 fix:1 absence:2 choose:1 main:3 image:1 semisimple:3 virtually:1 maximal:11 non:33 curtis:1 greater:1 inductively:1 number:3 cev:1 they:3 cep:1 j02:3 souza:6 nov:1 now:6 structural:2 february:1 classified:3 possibilities:2 applied:2 chandra:2 each:12 associative:3 mean:3 em:3 el:8 en:63 ei:25 ek:4 ee:2 series:21 improved:1 society:3 loops:1 operation:6 canada:1 ge1:5 matrix:25 factors:21 although:1 furthermore:5 since:34 sobre:1 research:1 rg:1 ra:2 rational:4 reader:1 denoted:3 occurs:1 math:3 gromov:1 theory:6 diagonal:1 free:19 standard:2 admits:8 atica:2 completely:3 york:1 org:1 subalgebras:1 hand:1 e1:87 e3:13 e2:14 jespers:6 brasil:2 could:1 similarly:5 american:3 hence:29 ej0:2 first:1 indebted:1 xi:1 xl:1 radical:8 conjugacy:1 primary:1 rank:2 multiplying:1 done:3 another:1 ring:14 subring:1 given:3 hyperbolic:72 introduction:2 least:1 indicate:1 quadratic:7 essays:1 m0:11 mostly:1 exactly:1 part:2 zθ:2 x2:1 x0:1 x1:1 than:1 caixa:1 finitely:4 e22:1 cyclic:7 zero:13 submitted:1 determined:1 contrary:1 publ:1 were:1 exhibit:1 generality:1 preston:1 matem:2 say:7 sen:2 disjoint:9 seen:1 idempotents:11 orders:1 depending:1 λ2x:3 jacobson:1 note:3 g0:1 ideal:18 k0:3 converse:6 normal:2 who:2 reach:1 centro:1 gθ:4 algebraic:3 entry:3 dekker:1 acknowledgements:1 pages:1 exponent:4 kg:1 dordrecht:1 clear:3 sf:4 ks:17 federal:1 proceedings:2 hi:2 dos:3 subgroup:5 sum:7 fact:5 aba:1 rings:11 spaces:2 decompositions:1 centralizer:1 centralizes:1 d4:2 trivial:7 principal:18 q1:2 q0:29 copy:1 dividing:4 e11:1 q8:3 e12:2 written:1 sˆ:8 lemma:16 only:18 abs:1 generators:1 factor:16 commensurable:2 preliminaries:1 columns:1 do:2 munn:1 goes:1 notation:2 di:2 dependent:1 de:4 nilpotency:1 words:1 hig:1 secondary:1 qs:65 fields:2 transposition:1 arxiv:2 investigate:1 bab:1 e1l:3 qg:4 contain:2 qi:4 qh:1 fixed:1 qn:2 set:16 exists:14 δjk:1 j0:163 see:5 result:4 qt2:1 best:1 subject:2 γi0:7 µx:6 monoid:1 definite:4 estat:1 αg:2 conditions:3 email:1 λks:1 publishers:1 recently:1 complement:1 however:1 submodule:1 hypothesis:3 key:1 group:60 suggested:1 both:2 last:7 cayley:1 according:2 context:1 filho:6 expression:2 otherwise:3 cn:1 conclude:2 simple:43 ca:1 q12:3 corresponds:2 andar:1 dimensional:17 simply:1 comprehension:1 article:2 moreover:7 throughout:1 torsion:3 semigroups:20 ei0:2 pp:1 described:1 basis:3 addition:2 ue1:1 copies:1 defined:3 basic:3 algebras:15 empty:2 define:3 field:2 direction:1 θi:1 corresponding:2 commutes:1 sufficient:2 subspace:1 remark:9 ekl:2 c3:3 c2:2 surveys:1 those:2 c4:9 case:10 eis:1 µj0:6 nski:1 will:2 ıstica:1 suppose:13 aij:2 indecomposable:1 eij:7 eil:11 ein:1 unitary:4 vol:6 metric:1 thus:20 iv:7 ii:11 ij:1 elsevier:1 qj0:5 ni0:1 id:1 binary:2 different:1 null:14 because:1 author:4 identities:2 make:1 same:2 any:10 paulo:3 zgi:2 unity:1 xj0:1 units:6 finite:62 subalgebra:5 http:1 trivially:1 ni:2 i0:12 sequel:1 phd:3 dimq:8 infinite:8 totally:4 identity:10 subgroups:10 center:1 com:1 idempotent:8 well:1 obviously:3 academic:1 without:2 c5:5 components:2 sets:1 firstly:1 position:1 g1:1 dimension:1 usual:3 λs:5 λx:14 obtain:6 λg:1 using:2 facts:1 λi:5 λm:1 previous:5 letting:1 postal:1 preprint:2 kluwer:1 readers:1 nilpotent:48 except:1 gj0:3 haefliger:1 theorem:41 complements:1 c12:5 semigroup:77 iφ:3 iλ:2 bij:2 hj0:1 inversion:1 integer:2 unique:20 mod:2 epimorphic:1 loss:1 necessary:1 semi:32 follows:12 e21:2 xax:2 eel:10 yields:3 either:8 arbitrary:1 multiplicative:3 terminology:2 mathematical:4 www:1 right:2 some:9 back:1 ideals:6 acad:1 table:2 proper:2 prasad:2 shall:2 providence:1 does:4 decomposition:3 linearly:1 proc:1 tk:2 refer:1 considering:1 longman:1 equivalent:1 rua:1 bi:1 qe1:1 quaternion:5 br:3 santo:1 imaginary:3 properties:1 chapter:2 integers:4 λg0:1 central:18 usa:1 extension:6 most:16 column:1 o:7 union:11 extensions:3 tˆ2:5 consequently:1 subset:1 primitive:3 statements:1 rj0:2 previously:1 into:1 integral:8 isomorphic:15 hyperbolicity:6 ai0:2 square:1 references:1 determine:2 elementary:4 centrality:1 λj0:8 rows:1 whom:1 there:22 u1:1 u2:1 start:1 borel:2 way:4 exceptional:2 was:1 naturally:1 considerably:1 rees:13 complete:1 enough:1 m2:12 triangular:1 ufabc:1 properly:1 he:1 computa:1 annihilate:1 consist:1 gi0:2 characteristic:1 up:4 us:1 below:2 embed:1 more:2 similar:3 called:8 jj:1 ab:2 proved:1 ai:30 abstract:1 condition:1 ao:6 denote:5 enable:1 exist:5 commuting:1 universidade:2 inc:1 again:1 qγ:1 no:3 qθ:1 when:4 ny:1 other:9 details:1 mathematics:4 arithmetic:1 elements:21 sided:4 a1:18 generated:7 a2:7 augmentation:1 structure:5 building:1 implies:5 xbx:2 assume:1 reiner:1 wedderburn:7 c8:8 rep:1 once:1 |
0704.2249.txt |@word aided:1 limited:1 extrapolated:4 four:1 consists:1 under:1 lord:1 worth:1 pastorello:8 conjecture:1 rise:5 amorphous:1 squares:2 progression:1 wooden:2 supports:2 persisted:1 burke:2 straight:2 aeronautics:1 construed:1 miller:2 consistent:4 direct:2 likely:11 qualitatively:2 estimated:1 hucht:1 blue:32 established:2 steiner:2 bipolar:1 above:6 ney:2 new:10 net:2 increasing:2 shocks:8 simultaneously:1 atel:1 never:1 here:7 asymmetry:7 active:1 mex:1 obtained:7 typically:4 approaches:1 astrophysique:1 calculations:2 adopting:1 changes:10 explained:2 highly:1 visible:1 glance:1 total:7 plot:2 swings:1 would:22 negative:1 snrs:1 therefore:5 shed:1 type:15 until:5 berlin:1 aligned:1 must:3 md:1 springer:1 pursue:1 work:1 suggestive:1 erg:2 temperatures:12 example:5 references:2 wang:6 indicated:3 give:2 indicates:1 magnitudes:1 pinto:1 absolute:3 provide:3 feature:8 very:11 hot:17 answer:1 after:14 lris:3 outbursts:2 summarize:1 types:2 elusive:1 recombination:2 green:3 order:4 wind:12 interpretation:4 over:5 before:15 fit:3 somewhere:1 expectations:1 destroyed:2 fig:35 fade:2 weeks:1 overcome:1 affected:1 superposed:3 band:9 effects:4 they:19 nozawa:1 represents:2 brightness:1 classified:1 lucy:4 λfλ:4 explode:2 dwek:8 reasonable:2 each:5 bona:1 side:10 preceded:1 financial:1 monnier:5 bohannan:2 particles:1 conjectured:1 newly:8 ri:1 outburst:9 foundation:1 marang:1 rayet:2 free:1 standard:1 formation:48 estimate:4 telescopes:1 publication:1 silicate:7 created:3 starts:1 days:14 corrections:1 speeds:2 features:4 unfilled:1 quantifies:1 rank:1 implicates:1 another:9 thick:2 sharpest:1 illustrate:1 similarly:3 top:3 approximately:1 needed:1 rates:2 too:3 hypothetical:3 collapse:1 took:2 somewhat:1 shortly:1 peculiar:2 distance:2 erickson:1 episodic:3 showed:5 zero:1 nakano:2 matter:3 pasp:3 hollenbach:3 lbv:33 spectrum:26 blueshifts:1 emphasizing:2 seen:20 seem:4 relatively:9 strength:5 latter:1 responsible:2 causing:2 absorbed:1 davidson:1 circles:1 even:6 though:5 replenished:1 object:5 tcool:3 boltzmann:1 involving:1 phase:10 vazquez:1 observation:1 calculated:1 inferred:2 kashi:2 accounted:1 tech:1 principle:1 gratefully:1 notion:1 came:1 whitelock:2 infrared:2 implying:2 radii:3 subtle:1 just:7 explain:6 rich:17 constant:8 do:4 di:2 blur:1 preferred:1 despite:1 contributes:1 observer:2 zones:1 radius:5 result:7 discussions:1 best:1 techniques:1 draws:1 away:1 propagates:1 continually:2 symmetric:1 unable:1 encounters:1 postshock:2 triplet:5 wc:6 nature:6 wn:7 weak:5 however:11 wr:16 extent:1 clues:3 carbon:3 suggested:2 essentially:2 irregular:3 uncertainty:4 distinction:1 argue:3 disappears:2 presumably:1 exemplary:1 goodrich:3 timescale:3 appeared:2 excess:23 nearir:1 radiative:2 three:4 been:16 quickly:2 much:9 interest:1 progenitor:7 expected:2 retrospect:1 spie:1 reddening:2 exception:1 originate:2 near:30 abrupt:1 overtaking:1 della:1 provocative:1 ir:53 n2e:1 ii:47 cone:1 ic:1 ib:22 cools:2 suggest:3 make:1 cumulative:1 sollerman:2 linked:1 potentially:1 several:5 grows:2 independent:2 emmering:3 hand:2 emissivities:4 scenario:7 programs:1 materials:1 echoes:1 quoted:1 epochs:7 yet:3 previous:3 enters:2 regarded:3 had:12 plasma:1 insensitive:1 bands:4 possible:5 araa:2 background:1 unique:2 occurring:1 appearing:1 cooler:2 specific:1 cooled:4 acad:1 dense:34 bottom:1 normal:3 comments:1 contributing:1 circ:2 christmas:2 core:3 stefan:1 disappeared:5 post:20 properties:3 months:3 o:14 todini:2 slightly:3 obs:2 emissivity:3 considerations:2 presence:2 hallmark:1 coincided:1 down:1 unambiguous:1 support:2 chevalier:3 approximate:1 width:19 l133:1 way:4 wavelengthdependent:1 was:41 medium:1 form:11 offer:1 1961v:2 forming:6 becoming:2 differences:2 soker:2 mysterious:1 heat:3 solar:1 magellanic:2 removed:1 absent:2 strongest:3 unusually:2 later:6 hotter:1 blueshifted:8 steady:1 abstract:1 owocki:6 photoexcitation:2 sometime:3 exist:1 esteban:1 check:1 physical:1 ni:1 dotted:1 no:6 na:1 whereas:2 when:20 ne:1 setting:1 role:2 optically:3 models:9 explosions:1 faster:3 assume:2 normally:2 proposed:2 interval:1 fassia:2 time:54 precedent:1 unshocked:2 datum:1 layers:1 depend:1 zone:30 environment:4 spyromilio:1 suffered:3 keck:7 broadly:1 geometrical:1 stays:1 blast:8 cool:7 presented:3 did:5 dif:1 speculation:1 prevent:1 unexpected:1 slower:1 occurrence:2 trend:1 prediction:3 spectrograph:1 spectral:2 appear:1 assistance:1 thicker:1 reminiscent:2 suspect:3 puckett:1 commensurate:1 filled:1 supporting:2 explosion:5 understanding:2 hillier:2 alone:5 along:1 appears:4 change:6 precursor:1 shift:2 simultaneous:1 usually:2 plotted:6 santa:1 problematic:1 colgan:3 planck:1 undergone:2 positive:1 periastron:3 scope:1 apparent:2 envelope:2 clue:3 visual:3 cases:5 given:2 bouchet:2 car:2 values:4 growing:2 making:4 reflector:1 figure:39 1980k:1 december:6 moffat:2 agent:1 dropped:1 spanning:1 hydrogen:1 occur:1 verlag:1 rays:8 monitoring:1 discussion:1 damineli:2 sne:27 may:29 produce:5 mag:8 date:1 data:5 1993j:3 ss:1 yielding:1 cannot:5 so:16 sn:168 typical:1 wavelengths:13 indeed:1 cygni:3 ended:1 impostors:1 clumping:1 still:6 blocked:1 observational:6 derive:1 thank:1 how:4 interesting:2 decreases:2 forms:2 main:2 happened:1 sooner:1 half:2 now:2 discuss:2 developments:1 stahl:6 january:4 drop:3 bursts:1 instability:3 entirely:1 photometry:11 individually:2 significantly:1 ed:2 manifests:1 challenges:1 doubtful:1 wavelength:10 shown:7 space:1 coincidentally:2 furthermore:1 increase:4 extrapolate:1 suggesting:2 dominate:1 correct:1 shows:18 complicates:1 theory:3 possibility:1 quite:2 california:3 vshock:1 widths:2 transition:3 elmhamdi:5 turn:2 place:1 massive:4 first:15 origin:2 merrill:2 symmetry:1 striking:1 variables:2 danziger:6 simplified:1 fast:1 directly:6 impossible:1 ring:1 size:1 little:3 necessarily:1 occupy:1 rebrightening:2 deimos:2 indicate:4 cooling:8 draft:2 iau:2 structures:1 gives:3 fraction:1 asymmetric:14 l137:1 suntzeff:1 than:24 connections:1 nathan:1 l45:1 hoyle:2 require:3 koenigsberger:6 future:1 were:13 pre:6 lick:5 san:1 remained:1 locations:3 say:1 allen:2 any:9 efficient:1 aside:1 shocked:2 note:2 phillips:2 take:1 tagle:1 strengths:2 modulus:2 begin:1 multiple:1 opposite:1 track:1 compress:1 latex:1 radioactive:1 especially:1 surprising:1 average:1 adopt:3 implications:1 drive:2 typeset:1 link:3 ferrara:2 quantity:1 slope:1 show:11 discovered:1 bright:2 threshold:1 xray:2 slow:1 ratio:9 behind:3 only:16 usov:2 black:3 predict:5 ionized:1 nearly:6 dyk:2 loewenstein:2 summary:1 tuthill:4 predicted:1 characteristic:1 discussing:1 relative:13 namely:1 detect:1 extragalactic:1 ways:1 harvey:1 review:3 enough:7 between:15 affecting:1 geometric:2 multiplied:1 vertical:1 clayton:3 condensing:1 awards:1 originates:1 dates:3 outflows:1 many:2 region:11 bvri:1 matheson:6 among:3 color:1 moreover:1 bizarre:1 better:1 unusual:8 capable:2 mounting:1 mark:1 engine:2 direction:1 thousand:1 formed:27 observe:2 external:1 obscuring:3 evidence:21 hidden:1 those:6 case:15 supernovae:1 profiles:18 refractory:1 characteristics:1 modjaz:1 cluster:2 sudden:1 technology:1 binary:3 different:4 immler:4 same:18 epoch:10 figures:2 document:1 events:4 week:1 defy:1 2006jc:81 companion:4 producers:3 changing:1 cartoon:1 hackwell:2 roughly:9 peculiarities:1 components:1 model:3 binaries:5 l105:1 persistently:1 being:2 relevant:3 aspect:1 speed:2 speculate:1 hint:1 seems:7 mirrored:1 pile:2 struck:1 silverberg:2 1979c:1 lowresolution:1 early:16 department:1 using:6 velocities:5 either:7 fully:1 densest:1 duration:2 provided:2 intensifies:1 stops:1 critical:2 provides:1 moderate:1 porter:1 scientific:1 power:1 linewidths:1 notably:2 ratios:3 emulateapj:1 earlier:6 comparison:2 stone:2 central:4 discussed:9 develops:1 decelerated:1 wolf:2 greatly:1 op:1 carinae:9 burning:3 accumulates:1 rising:2 heated:4 lastly:1 assumed:5 there:9 start:2 died:1 stars:21 slopes:3 regard:1 draine:3 illuminates:2 mnras:7 longer:6 embedded:1 strongly:2 ag:1 aj:11 general:2 ap:1 au:4 again:2 beyond:2 hybrid:1 caltech:1 poor:5 1999em:1 includes:1 important:6 peak:6 included:1 condensation:3 cbet:1 odds:1 curve:6 mass:25 starting:1 represent:1 since:14 sci:1 consider:4 pointing:1 caused:3 lack:1 month:6 ceased:1 systemic:2 follow:1 causes:1 odyssey:1 td:1 far:6 l5:1 interpreting:1 difference:2 plotting:1 large:8 small:8 haas:1 translating:1 rate:8 timescales:1 perspective:1 further:2 steadystate:1 attributable:2 what:3 invoking:1 section:2 brief:4 thickness:2 version:2 learned:1 contrast:2 condensed:1 1987a:3 component:7 ranges:1 compressed:1 berkeley:1 november:1 strong:19 conti:4 prior:2 amount:3 published:1 narrow:6 options:1 extinction:8 takes:1 distinct:1 faint:1 humphreys:1 taken:1 more:23 flat:1 ejected:7 emission:90 leonard:3 basically:1 particular:2 known:9 mounted:1 producing:1 analogous:2 presumed:1 erratum:1 science:1 der:1 sweeps:2 evolved:1 dec:3 2yr:1 collision:1 minimum:1 arise:5 exclude:1 csm:24 respective:1 advantage:2 rather:3 stayed:2 freshly:3 crowther:6 simplicity:1 galactic:1 fe:1 coming:1 short:3 interpolated:2 spectra:32 blueshift:3 extrapolation:1 dispersing:1 remnants:1 help:2 developed:3 fλ:1 soon:1 ejecta:41 mixing:2 paper:29 through:17 filters:1 signs:1 its:21 style:3 rapidly:7 actually:1 late:20 detected:2 systems:3 might:9 return:1 propose:4 transitioning:1 oke:2 sweeping:1 copious:1 yr:10 mystery:1 hereafter:2 always:1 level:3 eruptive:1 radial:1 found:3 jhk:2 referred:1 weight:1 energy:4 idea:2 expect:8 measurement:2 bluer:1 event:9 dominates:1 surrounded:1 research:1 walborn:2 dominated:2 eccentric:2 occurs:2 asp:1 ast:1 reason:1 brightest:1 unresolved:2 retained:1 persists:2 consequence:4 undergo:1 exhibited:1 upper:3 number:1 l97:1 fluxes:12 passes:2 differ:1 temperature:7 introduction:1 leading:4 least:5 assumption:1 passed:2 hundred:4 observations:5 shifted:2 nomoto:1 option:1 exploded:1 part:4 bower:1 differentiate:1 peaked:2 kind:1 observatory:4 double:1 largely:1 contrary:1 toward:4 scarcity:1 substantial:1 headings:1 fading:6 novae:2 carlo:1 severe:2 aa:1 onset:1 extrapolating:1 play:2 eruption:9 singlet:1 most:18 significant:5 colliding:5 measured:4 l103:1 clear:7 sometimes:1 km:10 optical:24 axelrod:1 velocity:4 lbvs:7 ugc:1 blended:1 relation:1 find:5 impact:1 giant:4 spectrographs:1 eruptions:6 factor:2 dominant:2 dependent:3 grew:1 closely:2 during:8 exhibiting:1 continuum:52 transitional:1 arxiv:1 remove:1 common:5 obscure:2 approaching:1 vink:2 declines:1 plausibly:1 plausible:4 gehrz:11 see:21 barb:2 close:1 outward:1 currently:1 various:1 probably:12 conditions:4 recently:2 statistically:1 missing:1 danchi:3 spectroscopic:1 leibundgut:1 selectively:1 invisible:1 abruptly:1 both:12 last:9 reverse:7 barely:1 l23:1 connection:1 became:1 context:1 reside:1 point:3 reasons:5 sweep:1 coincidence:4 simply:7 decline:8 described:4 due:9 annales:1 reduction:1 dropping:1 ph:2 transferring:1 gas:22 gal:2 understand:3 systematic:2 gouiffes:3 intriguing:2 grains:32 solid:2 reliable:1 institute:1 while:11 replaced:1 behavior:6 error:2 guide:1 erupting:1 jpl:1 century:1 herein:1 apjs:2 itself:4 vanish:1 around:14 grant:1 shorter:3 emphasize:1 netzer:2 ray:6 composition:1 higher:4 development:2 used:1 purpose:2 recent:1 lower:4 database:1 cruz:1 leoni:1 calibrated:1 chemistry:3 salvo:1 shape:14 source:2 location:2 input:1 kast:2 showing:2 precipitation:1 wings:1 apj:27 shaped:1 systematically:3 follows:3 flux:28 continue:5 continua:1 sketch:4 faber:2 often:1 some:7 understood:2 trends:1 ejections:1 examples:2 sight:1 mirror:1 curious:1 kirshner:1 pronounced:5 scale:1 chornock:3 stringfellow:2 broadband:2 measurements:2 per:2 ishibashi:1 behave:1 proc:2 foley:7 reach:1 jumps:1 obscures:1 bv:1 lasts:1 obscured:1 piles:1 tracing:1 range:4 block:1 into:8 within:5 indications:1 nsf:1 primarily:3 proportional:2 wn9:2 uncertainties:2 extremely:1 question:1 specifically:2 moseley:3 forward:8 quiescent:1 line:46 considerable:1 fades:3 ut:1 uv:6 paola:1 up:20 faded:8 continuously:3 highlight:2 similar:11 called:3 associated:2 challis:1 influence:3 graham:2 puzzling:1 amounts:2 dashed:4 points:1 nat:1 ferent:1 witteborn:1 elements:1 excitation:1 meaning:1 undulations:1 sides:2 structure:1 ago:2 independently:2 correlated:1 fluorescence:1 required:1 orbit:1 nasa:1 heats:2 requires:2 having:2 issued:1 results:2 existing:4 broader:1 winds:4 contributions:2 young:1 include:2 dramatically:1 indicating:3 continues:2 wave:8 electron:1 telling:1 continued:2 severely:3 staffs:1 shock:45 ryan:1 prototypes:1 ofpe:2 valle:1 noted:14 smaller:3 imply:3 dynamics:1 odd:1 expressed:1 19th:1 lee:3 respectively:6 l21:1 following:4 explore:1 objects:1 bode:3 larger:1 suggests:2 preferentially:1 makes:2 composed:1 photometric:2 scaled:4 decrease:4 administration:1 cloud:2 use:2 feb:1 remains:1 next:2 few:12 cappellaro:2 crab:1 expanding:2 themselves:1 started:2 occurred:5 transient:4 normalized:2 sharply:1 niemela:1 iin:3 iii:3 hints:1 alexei:1 account:4 sightline:1 obvious:3 thin:2 drops:1 weaker:1 process:1 purposes:1 high:11 assumptions:1 chugai:1 evidently:1 regions:1 located:1 varies:1 tenorio:1 instead:8 profile:6 filippenko:18 fits:2 efficiently:2 ambiguous:1 light:17 counter:1 lines:61 correspond:1 1998s:1 allow:1 subsequently:1 astronomical:1 altogether:1 interpreted:2 produced:3 looks:1 fwhm:1 galaxy:2 contaminated:2 ld:2 outer:2 decay:5 temporal:3 hypothesize:1 circumstellar:8 orange:3 defining:1 greater:3 material:10 patat:1 front:1 meikle:2 documented:4 day:42 february:6 university:2 feast:1 identified:1 sufficiently:4 magnitude:3 accompanied:4 upward:1 doing:1 related:4 measure:1 our:27 special:1 out:3 altavilla:1 rep:2 rev:1 asymmetries:1 cause:1 integrated:4 red:46 8b:3 8a:6 galaxies:1 completely:3 shortest:1 interaction:4 geometry:7 determining:1 could:8 obstacle:1 times:20 hence:1 receding:2 evans:3 bars:2 echo:7 reached:3 precisely:2 long:9 nebulae:1 system:3 their:12 nebular:1 intermediate:19 final:1 shell:30 explanation:3 exactly:1 pinwheel:1 observed:25 apss:1 ara:1 submitted:1 rarity:1 individual:1 providing:1 steep:2 exhibit:3 cohen:1 partnership:1 curves:6 unlikely:1 need:1 apparently:2 clearly:3 able:4 mid:7 mechanism:2 hr:1 subject:1 silicates:5 progressively:5 bolometric:5 intrinsic:4 why:3 fair:1 astro:2 consequences:1 bregman:1 neighboring:1 stronger:2 looked:1 constrain:3 obscuration:6 fact:9 impression:1 text:4 2003gd:2 supported:1 anyway:1 rough:1 agrees:1 decade:2 principal:1 µm:5 gilman:2 based:4 ngc:1 should:12 panagia:1 ambiguity:1 postulated:1 emitting:12 tielens:1 ones:1 years:3 collisional:1 symbols:1 evolution:18 densities:9 course:2 luminosity:18 gerardy:4 contain:1 view:1 strengthened:1 shedding:1 national:1 hα:10 enhanced:2 operated:1 herrero:1 luminous:5 creating:2 closer:1 phases:3 interacting:1 nebula:1 tend:1 nucleation:3 favor:1 state:1 unravel:1 graphite:15 kotak:2 tically:1 comparable:2 supernova:6 emitted:2 hypothesis:1 key:3 declining:4 phase1:1 interpretations:1 limits:2 freely:2 acknowledge:1 equal:1 attributed:2 eta:1 grain:15 passing:1 detailed:3 unclear:1 co:2 cm:8 conclude:2 ca:11 contamination:2 environments:1 li:4 wickramasinghe:2 second:2 yam:2 slowly:1 hottest:4 arises:3 corresponding:1 shortward:1 baume:1 sufficient:2 bulk:1 present:16 unlike:3 ejection:1 appearance:1 value:3 will:19 stunning:1 transitioned:1 supply:1 layer:2 almost:3 thus:8 vw:1 perhaps:5 began:3 radiation:2 unity:1 units:1 infer:1 fide:1 difficult:2 turatto:2 absorb:4 upon:1 effect:12 dust:188 expand:1 nevertheless:2 well:11 thought:6 redshifted:4 arising:1 latest:2 spherical:1 less:8 increasingly:1 accurate:1 underlying:3 generous:2 rapid:6 preprint:2 density:7 absorption:4 onward:1 smith:30 add:1 identical:5 increased:2 putative:1 disappearance:1 corresponds:1 increases:2 denser:1 press:3 prominent:3 fransson:2 loss:5 sugerman:2 necessary:1 like:31 excluding:1 alternatively:3 martin:3 setups:1 become:5 preclude:1 warmed:1 because:21 classical:3 sequence:1 wheeler:1 phenomena:1 warmer:1 broad:13 overlap:2 instantaneous:1 does:4 reaching:1 expansion:1 stellar:4 host:1 although:12 swept:16 panel:5 about:7 rare:2 ganeshalingam:2 compatible:2 seeds:1 insufficient:1 constraints:1 equally:1 preexisting:1 interstellar:2 van:3 additional:3 synthesized:4 condense:5 function:3 shane:1 basic:1 but:30 hu:3 volume:3 ho:2 hd:1 he:97 made:2 whether:3 placed:1 below:4 limit:1 ruling:1 distribution:1 radiatively:1 display:1 strengthens:1 deaths:1 contribute:1 persistent:1 proceeds:1 deeper:1 compared:8 calibration:1 percent:2 barth:3 other:17 details:2 wing:1 conclusion:2 francisco:1 star:20 corcoran:2 benetti:1 stay:1 additionally:1 astronomy:1 resolution:1 lasted:3 rule:1 expands:1 eclipsing:1 |
0704.2250.txt |@word essay:1 breadth:1 z2n:1 homomorphism:6 sch:20 remarkable:2 depends:1 osp:7 bull:2 results:4 invent:1 gx:1 four:1 eε:2 helped:1 proposition:39 generalize:2 grateful:2 projective:1 consists:8 partial:11 alt:24 gl:24 imbedding:1 issues:1 consider:27 extra:1 whose:2 depend:4 wω:6 paris:3 equivalence:3 contained:9 including:1 list:5 kα:1 investigation:2 restriction:1 tk:7 th:3 under:9 hermann:4 must:6 riso:13 conjecture:1 supported:1 lboro:2 consequently:1 g1:21 g0:81 very:4 implicitly:1 rise:1 exception:3 geometrical:1 vera:1 every:7 nichols:2 lecture:1 difference:6 exact:1 deformations:1 condition:18 partitions:1 esentations:1 dim:2 basics:1 contemplated:1 russia:2 presented:1 irreducible:29 notes:1 michael:1 solution:1 µp:8 convenience:1 vector:8 science:1 small:5 superalgebras:54 programme:1 zm:2 des:2 x2i:3 hk2:6 mail:2 direct:17 sign:3 sergeev:23 generalisations:1 zero:17 diagrams:1 irreducibility:1 follow:1 xf1:2 odd:4 quite:1 victor:1 bilinear:14 3y:2 lemmas:1 plays:1 appear:1 invertible:2 y1j:1 sum:22 mathematical:3 brief:1 expressed:3 version:3 goes:1 suppose:3 subtracting:2 consisting:7 contrast:1 viii:1 coefficient:1 full:2 simultaneously:1 degree:5 respectively:6 modify:1 equals:2 eλ1:1 perpendicular:1 objects:1 hkn:1 possibility:1 groups:8 others:1 concluding:2 hλn:3 standard:8 equations:1 z2:23 morphisms:9 remark:2 weinstein:2 4we:1 technical:1 involved:2 leaves:1 vectors:2 sbornik:1 x4j:1 le11:2 products:3 x4i:1 permutation:2 action:21 hospitality:1 suitable:2 changes:1 sci:1 quotient:3 uniquely:5 f0:7 schur:2 formulated:1 useful:1 fµ:15 classification:4 f1:14 namely:1 2δn:3 2δi:1 private:2 replace:2 texts:1 2δp:2 transformations:2 apply:3 total:2 univ:1 linearly:6 νp:1 use:7 µn:13 would:2 prove:12 positive:5 supergroups:1 contains:2 eρ:20 negative:3 sµ:5 next:2 ψj:2 comparing:1 linear:20 going:4 call:4 therefore:14 reductive:1 m2:3 taken:1 type:36 reflects:1 more:8 introducing:1 permutations:2 operators:5 ti:3 supergroup:10 pairs:1 eν:6 ebres:3 berlin:2 eλ:17 particular:6 known:2 eδ:2 cases:2 hold:2 eα:18 eγ:2 eβ:2 vp:12 springer:7 isomorphism:9 rα:3 deformed:5 recall:7 equation:4 work:8 modified:1 london:1 labeled:1 obvious:2 xx12:1 following:46 dec:1 root:58 example:6 fulton:2 proof:36 beautiful:1 claim:5 f2:5 degenerate:4 give:4 december:1 preserving:1 pieces:1 numbers:1 hyperplane:6 sense:5 νm:6 exclude:1 orbits:3 conversely:2 µj:6 hλ:1 r20:2 information:1 perspectives:1 dh:8 s3:5 verify:4 orthogonal:1 algorithms:1 write:6 zn2:2 nontrivial:1 exterior:1 ordinary:1 verlag:6 explains:2 map:12 product:8 proc:2 description:10 algebra:33 replacing:1 3tu:2 earlier:1 mapping:1 substitute:1 heckenberger:3 applications:1 multiplication:2 representations:31 fj:6 fl:2 heidelberg:1 types:3 diagonal:1 induction:3 natural:17 imply:4 light:1 parameter:2 sp:6 explicit:5 element:18 lδ:1 sdim:3 used:6 sn:20 fundamental:7 sl:28 representation:30 order:11 talk:1 elie:1 acts:12 interpretation:1 help:1 itep:1 developed:1 over:22 fλ:6 mainly:1 choose:4 interpreted:9 matsumoto:1 course:1 paper:3 through:2 signs:8 mentioned:1 still:1 okounkov:1 its:19 roots:34 before:3 sλ:6 group:57 maps:3 chosen:2 interesting:2 sα:1 affine:6 lj:10 naturality:1 forms:1 integrability:1 absence:1 defintion:1 θt:2 systems:21 derivative:2 main:10 defining:1 image:5 semisimple:13 arguments:3 serre:7 eventually:1 non:19 yj:22 motivated:3 university:5 combination:8 yn:5 finitedimensional:1 introduce:9 functional:1 differential:2 mention:1 they:3 half:3 eµ:7 yp:25 now:21 hall:1 establishes:3 easily:3 term:1 finite:45 equality:2 invariants:9 w2:5 identified:2 tiso:8 good:1 xy:1 each:4 found:4 2n:13 european:1 side:2 associative:2 2k:3 subset:1 domain:1 weyl:42 weight:57 con1:1 stabiliser:2 series:6 related:3 internal:1 books:1 quantum:3 our:13 operation:3 ep:1 special:10 out:2 rt:1 respects:1 shown:2 matrix:1 space:8 rep:1 since:22 denotes:2 may:4 acting:10 groupoids:8 multiply:2 rational:9 denoted:5 formula:12 get:3 subring:13 r10:2 unifying:1 math:16 shows:5 benjamin:1 after:5 reformulation:2 theory:15 reformulated:2 associate:2 comb:1 surveys:1 free:2 enveloping:1 admits:1 difficulty:1 completely:2 base:13 epsrc:1 qh:4 span:2 subalgebras:1 remainder:1 generate:2 definition:22 unique:4 hλ1:3 r0:26 r1:15 r2:3 geometry:2 brown:2 could:1 transition:1 moment:1 nonnegative:1 matrices:1 maximality:1 isotropic:23 hence:4 generalizations:1 think:2 first:23 xj:2 formulas:3 xi:41 xn:20 symmetry:11 xm:5 bijection:2 3the:1 variables:5 xa:1 number:4 rtn:1 restrict:2 multiplying:1 relations:10 directly:1 fi:2 art:1 ring:73 u2:18 xv:1 xw:3 xt:1 illustrate:1 given:11 checked:1 rewritten:2 similarly:2 introduction:5 unknown:1 adjoint:6 system:43 least:1 their:7 identity:9 statement:3 bijections:2 gives:2 square:1 completed:1 immediate:1 part:9 jordan:1 2as:1 supercharacters:18 authors:1 gmodule:1 x3:54 translation:2 x1:88 than:3 coefficients:2 eaires:1 third:1 princeton:1 divisible:6 was:7 older:1 second:6 khudaverdian:3 xi1:1 classes:3 pairwise:2 were:3 identical:9 tion:1 powers:3 distinguished:11 projections:1 kazhdan:2 complexes:1 aln:2 rewrite:1 turned:2 generalization:1 lin:1 already:2 say:1 disjoint:5 seen:1 gradings:1 any:48 contents:1 relatively:1 lie:137 generalizes:1 depending:3 calogero:5 hyperplanes:1 εp:1 note:12 yamane:2 ideal:9 εn:7 εi:52 generalized:19 analogy:1 εj:12 finding:1 so:19 coincide:1 moscow:2 kac:27 even:9 play:3 multiple:2 sm:16 gα:4 english:2 satisfy:1 most:2 automorphism:1 formulae:2 reducible:3 brundan:4 νi:2 acknowledgements:2 class:3 picture:1 laurent:4 z32:3 considered:10 doc:1 partition:1 coincides:5 kn:1 schk:1 curie:1 reflections:2 usual:4 χk:2 section:15 fact:12 enigma:1 2m2:2 hi1:1 mullineux:1 show:4 µq:1 groupoid:36 justifies:1 x2:95 multiplicities:1 relation:6 decompositions:1 d6:2 analogue:3 superalgebra:46 find:1 principal:3 µm:3 believe:1 based:2 proposed:3 explain:2 enough:2 should:3 lemma:18 only:14 explicitly:4 generators:3 reducibility:1 indeed:3 µi:3 constant:4 moser:5 alternation:2 hope:1 abelian:4 his:4 dominant:1 subspaces:3 notation:2 means:16 de:6 repr:1 xx21:1 satisfied:4 famous:1 state:2 aε:1 ϕj:4 combinations:2 subgroupoids:1 amer:3 νp2:2 nicely:1 x21:1 irrational:2 arxiv:1 supp:4 leur:2 common:2 hλ2:5 nα:3 nβ:1 nγ:2 communicated:1 kernel:2 set:33 above:8 exists:7 surjectivity:2 emie:1 2c:1 j1:2 module:41 y1:36 see:40 alg:4 result:8 w1:7 w0:42 recently:2 dµ:1 seems:1 y2:3 learnt:1 tensor:4 away:1 rings:35 consequence:1 symmetric:8 written:4 determined:5 various:2 between:7 invariant:21 geometric:3 λl:1 conditions:19 x23:1 x22:1 terms:6 2m:8 importance:2 component:5 restricting:1 wk:1 veselov:21 jr:2 however:2 york:5 comm:1 here:1 key:2 understanding:1 vinberg:1 improve:1 both:6 essentially:2 last:7 x2k:3 x2j:1 many:1 mrtn:1 according:4 voronov:3 laplace:3 fulfilled:1 characterised:2 admit:1 lusztig:2 context:3 casimir:1 mean:1 whole:2 fix:1 comes:1 otherwise:2 simples:1 among:2 ci:4 ch:3 conclude:3 simple:28 had:3 address:2 cf:2 2nd:1 dimensional:49 represented:3 taylor:3 spans:1 sequences:3 wider:1 respect:19 li:1 ct:1 considering:2 better:1 pp:1 xα:1 described:14 commutative:3 basis:5 union:6 nonisotropic:1 three:1 been:3 defined:26 much:2 change:2 basic:50 algebras:15 abstract:1 empty:3 define:21 surjective:1 determinant:1 describe:4 corresponding:42 serganova:19 mind:1 coherence:1 subspace:2 σi:2 new:7 else:1 andrei:1 axiomatics:1 external:1 τw:1 berezin:2 2n2:2 hµ:9 spin:1 xki:1 present:1 case:63 onishchik:1 p0:26 exponential:2 chap:2 transformation:3 will:19 while:5 replaced:1 april:1 none:1 shift:3 situation:1 property:6 k1:1 maximal:5 cartan:10 vi:4 vj:6 thus:14 them:5 vn:8 equal:3 ii:18 need:6 itself:4 lω:1 contract:1 dual:3 ambient:1 ready:3 ym:18 alone:1 different:7 inc:1 grant:1 journal:1 belong:5 atiyah:2 same:15 dγ:2 complex:7 split:1 congress:1 survey:1 dα:6 subalgebra:12 composition:1 difficult:3 independent:1 chalykh:2 investigated:1 infinity:2 yi:4 trivially:1 i1:1 superanalysis:1 marie:1 hand:2 v0:11 v1:29 v2:17 harris:2 purpose:1 characters:7 infinite:3 changing:9 invariance:1 tradition:1 expand:2 reflection:1 superdimension:1 she:1 well:8 physics:1 components:4 sets:1 dimension:2 subgroup:3 r01:1 λr:1 graded:4 just:2 less:2 being:3 generally:2 young:1 rest:3 oxford:1 automorphisms:1 integer:11 λk:1 λj:1 λi:14 graduate:1 λn:6 λm:16 previous:7 adv:1 εm:16 submodule:1 preprint:1 txi:1 generator:1 sciences:3 point:2 character:6 except:4 macdonald:2 lattice:16 belongs:13 conjugated:1 lett:1 easy:16 theorem:21 solvable:2 remaining:3 take:3 resolved:1 bourbaki:2 cramer:1 vii:1 march:1 dihedral:1 psl:5 characterise:1 decomposed:1 possible:4 spanned:4 nonincreasing:1 press:1 using:6 vλ:3 moody:1 coxeter:1 like:2 semi:5 follows:18 permuting:5 strictly:1 isotropy:2 δp:26 δq:7 separately:7 δm:2 δj:11 either:3 integrals:1 δi:6 reduced:1 acad:2 therein:1 parity:1 shed:1 because:7 methods:1 classical:58 lectures:1 some:18 back:1 2y:2 polynomial:12 deduce:2 repeat:1 analogues:1 b1:3 b2:2 b3:4 extended:2 ourselves:2 tyi:1 δn:15 vol:3 projection:3 dimensions:1 lead:2 comments:1 edition:1 esf:1 does:4 decomposition:9 select:1 assuming:1 deg:1 eε1:1 δk:1 ba:1 power:3 bc:2 june:1 equivalent:11 l1:1 agreement:2 expansion:1 fp6:1 cλ:6 bu:1 bv:1 variation:1 substitution:5 super:19 properties:1 injective:1 proceed:1 integers:4 about:2 eεi:6 intersects:4 extension:1 algebraic:12 commun:2 introduces:1 o:2 pν:2 αx3:3 important:6 nothing:1 2j:1 identify:1 introduced:6 slightly:2 morphism:3 xu:1 supercharacter:20 soc:4 h2:2 communication:2 into:5 h1:2 integral:5 isomorphic:10 usa:1 due:2 down:1 remarks:2 appropriate:1 right:3 references:3 refer:1 wα:4 elementary:1 factor:2 subsets:1 rows:2 van:2 additional:2 support:6 there:11 u1:25 u0:2 u3:15 why:1 start:1 subrings:2 way:6 notices:1 m1:3 exceptional:1 sections:1 recurrent:1 naturally:1 function:7 complete:5 form:30 problems:1 selecta:1 hv:2 hw:1 but:11 hk:30 link:1 functor:2 intern:1 hm:2 clarify:1 highest:31 true:3 saratov:2 partially:1 applying:2 theta:1 understood:1 whether:3 multiplicity:3 verma:1 up:6 us:17 um:5 below:2 ui:15 grothendieck:51 uk:4 ussr:1 xp2:1 problem:3 similar:4 called:12 eigenvector:1 ac:2 ab:2 proved:6 ωf1:1 computing:1 ai:9 certain:2 universal:1 aj:1 history:1 general:3 single:1 proves:3 loughborough:4 av:3 supersymmetric:1 check:13 defines:2 again:3 functions:10 nk:1 nl:2 groupes:3 no:11 when:14 v3:1 kujawa:1 field:1 other:1 role:4 details:2 nat:1 papers:1 department:4 mathematics:5 finis:1 nice:1 category:2 elements:19 denote:1 generates:1 completes:2 categories:1 polynomials:9 includes:1 a1:6 a0:3 generated:26 a2:3 realised:1 variable:1 sider:1 sides:1 structure:5 bases:2 χl:2 implies:10 dω:6 assume:7 values:1 modules:36 orbit:9 rule:2 notion:6 weights:36 reprinted:1 spectral:1 n1:6 n2:3 |
0704.2251.txt |@word concept:1 evidence:1 consider:4 pvlas:2 lagrangian:4 magnetic:1 theoretical:1 results:5 integration:3 leads:1 scalar:15 commute:2 comments:1 computation:1 edu:2 follow:1 expressions:3 contributions:2 gh:1 increase:1 depend:5 calculate:3 estimative:1 acting:4 finally:2 those:1 th:7 under:1 worth:1 p2:6 amplitudes:2 string:2 casadio:3 very:4 wave:4 witten:2 difference:2 exact:1 condition:1 treating:2 four:2 annihilated:1 wetensch:1 level:1 did:1 issue:1 deals:1 discrete:2 small:1 eigenvalues:1 cox:1 equation:2 jhep:4 strongly:1 employing:1 force:22 fout:2 maclaurin:1 sign:4 jump:2 zero:4 further:4 dynamics:1 implemented:1 canonical:1 even:2 what:3 y1i:4 appear:4 diag:1 section:11 favors:1 d3:4 ˆb:2 experiment:1 δfunction:1 above:5 ˆi:4 net:1 contributes:1 preserved:1 satisfy:3 full:1 prescriptions:1 here:3 diagonal:1 canonically:1 objects:1 them:2 separation:6 address:5 represented:1 ratio:2 along:3 strong:2 equations:1 appears:2 change:2 box:2 search:1 antisymmetric:1 study:1 changed:1 allows:1 resulting:1 usually:2 spacetime:4 uniquely:1 via:3 spatially:1 extra:2 problematic:1 f2:2 addressed:1 summation:3 propagators:1 unit:1 standing:1 plot:2 use:6 y2:2 proceed:1 would:6 correc:1 positive:3 flat:1 scenarios:1 few:1 noting:3 therefore:8 distortions:1 taken:4 means:2 type:2 metric:1 more:7 smeared:1 introducing:2 becomes:4 operators:6 derivation:1 dirichlet:2 normalized:1 sharply:2 particular:1 cases:1 hold:2 iii:5 must:3 zi:1 states:3 account:2 gruppuso:3 quantized:1 integrating:1 recall:2 points:1 work:2 theories:6 remain:1 lorentz:2 values:7 cal:1 following:6 making:1 example:6 reviewing:1 f0:10 f1:2 compare:1 give:1 predict:1 moffat:1 high:2 minimum:2 numbers:2 want:1 sense:1 unphysical:1 sharp:1 tions:1 occur:1 axis:1 oliveira:1 needs:4 end:2 rather:2 discussion:1 holds:1 xˆ:1 feature:1 roughness:5 write:1 how:4 fourth:1 instead:1 ordinary:1 parameter:2 sin:2 gordon:1 simplicity:1 product:3 rept:1 description:1 replacing:1 max:1 ladder:3 signature:1 modest:1 plane:8 ff:2 waves:1 cambridge:1 fi:1 data:1 parallel:10 constants:1 bleicher:1 realized:1 short:2 attempt:1 imply:1 classi:1 approximation:1 spectra:1 separations:1 fine:1 so:4 allow:1 hayakawa:1 subsequently:1 acausal:2 dx:3 produces:1 p1i:1 over:6 course:1 paper:1 including:1 mentioned:1 existence:1 still:3 its:2 before:1 perfect:1 revived:1 outer:1 treat:1 located:1 chosen:1 fix:1 coordinates:7 better:1 lw:1 compelling:1 fig:2 inaf:1 derivative:1 might:2 overcome:1 yi:1 non:52 affected:1 bernoulli:1 material:1 reflected:1 mention:1 effects:15 they:2 lint:3 now:8 represents:1 term:5 finite:9 dirac:1 always:2 university:1 hamiltonian:1 f24:1 realistic:1 l4:1 magnitude:1 l2:6 mode:1 positions:1 2l:5 found:2 universit:1 side:2 mean:4 tensor:1 int:1 en:6 ei:2 ek:4 series:1 energy:12 idea:1 used:2 each:2 extended:1 expect:1 quantum:7 our:3 differ:1 eq:14 out:1 large:2 shown:2 dominates:1 space:26 since:6 crucial:1 looking:1 may:2 contained:1 geom:1 formula:1 induced:2 ref:7 shows:2 regards:1 after:1 theory:13 written:2 fisica:1 free:3 standard:4 carried:1 estimate:5 superimpose:1 interaction:7 nπx:1 geometry:3 could:1 impose:1 times:1 length:12 hopeless:1 δij:2 leading:5 corrections:32 noncommutativity:7 assign:1 first:5 xj:1 already:2 variables:1 number:1 b491:1 smaller:3 done:1 least:1 electronic:4 size:3 given:7 perturbation:4 temperature:1 similarly:1 introduction:1 bologna:6 dipartimento:1 πn:2 system:1 relations:3 their:2 assumption:1 seiberg:2 types:2 calculations:3 1i:1 percentage:1 perfectly:4 fuzziness:2 final:2 commutativity:24 a37:1 a36:1 square:2 continuous:4 obtained:2 supplemented:1 lℓ:2 authors:1 x2:2 natural:5 x1:2 than:4 milton:1 nicolini:1 distance:4 unfortunately:1 fundamental:5 require:2 depends:2 modelled:1 annihilation:1 matter:1 amplitude:2 were:2 f12:2 powers:2 f14:1 perturbative:1 generality:1 rewrite:1 electrodynamics:2 correction:10 spectrum:3 tuscaloosa:1 enforces:1 conjugate:1 need:4 seem:1 recover:1 any:3 viewed:1 farina:1 estimated:3 angle:2 lim:3 self:3 mills:1 gravity:1 note:2 instance:1 z1:2 potential:5 absorbed:1 take:3 negligible:2 conductivity:1 accuracy:3 begin:2 sure:1 unless:1 electric:1 shall:10 collaboration:1 took:1 z2:2 most:1 comparing:1 phase:1 measured:1 φk:1 manifested:1 xµ:2 deviations:3 constructed:1 observation:1 consequences:1 considered:4 calculated:4 phil:1 order:17 yang:1 kw:1 exp:3 left:2 physics:1 fact:3 analysed:1 hyper:2 show:4 nπ:2 converge:1 discovered:1 developed:1 spaces:2 fuzzy:3 thickness:3 trivial:4 find:1 subtracting:1 µm:1 based:2 just:1 parameters:1 f22:2 situations:1 explain:1 original:2 outside:2 should:5 only:3 explicitly:2 factor:6 employed:1 constant:3 xˆµ:1 achieve:1 dn:3 do:5 dk:3 klein:1 di:3 express:1 overall:1 da:1 αi:2 ones:2 reversal:1 dp:1 prime:1 geometries:1 fields:3 arxiv:3 recovers:1 common:1 compactification:1 discussing:1 valid:1 view:2 set:2 computed:1 relative:1 y1:2 see:10 smailagic:2 radius:1 result:4 terms:5 momenta:1 poppenhaeger:1 subject:1 surfaces:2 satisfying:2 rizzo:1 commutation:4 placed:1 macroscopic:1 review:4 diverge:1 boundaries:13 pressures:1 state:3 difficulties:1 αd:2 between:24 xˆ1:2 drawn:1 boundary:20 xˆ2:2 approach:10 preserve:1 suppresses:1 recently:1 extend:2 sections:1 ωn:5 p2i:1 however:2 moyal:3 mohideen:1 extent:1 rapidly:1 come:1 irnerio:2 motivations:1 both:6 last:1 similar:3 region:2 density:9 involve:1 unc:1 figures:1 casimir:26 contribution:2 expression:2 finds:2 experimental:2 otherwise:2 among:1 point:5 appeared:2 effective:1 xν:1 rosa:1 dimensional:4 decreases:1 right:1 consideration:1 cancel:1 respect:4 diff:1 branes:1 described:3 commutative:30 second:1 estimating:1 pz:2 px:2 py:2 due:15 been:4 imperfections:3 defined:5 describes:3 damping:4 expected:2 pi:1 define:2 wants:1 xˆi:1 direction:1 θi:11 corresponding:2 remark:1 argument:1 coherent:6 noncommutative:13 covered:1 denote:2 present:2 case:15 k2:1 p0:1 harms:3 look:1 exponential:1 pacs:1 solid:1 defining:2 akad:1 value:2 will:14 euclidean:1 replaced:4 euler:1 evaluating:1 πln:1 property:1 couplings:1 ein:3 studied:1 orientation:1 coupled:1 phenomenological:1 refs:4 thus:3 fin:2 surface:6 iv:2 ii:3 regularity:2 itself:2 interacts:1 increased:1 compactified:1 different:1 italy:3 perhaps:1 media:1 make:1 intrinsic:1 lett:5 same:12 orders:1 complex:1 uncertainty:1 units:3 plates:53 dimensionless:2 several:2 dimension:1 φm:3 φn:4 literature:1 infinity:2 zavattini:1 numerical:1 upon:1 effect:5 levels:1 moving:1 purpose:1 potentials:2 infinite:1 invariance:1 recent:1 off:1 modes:8 scenario:2 changes:1 well:1 without:1 components:1 coordinate:3 position:2 alabama:1 wohlgenannt:1 latter:3 usual:8 surveys:1 proposed:1 being:3 able:1 accurate:1 obtain:2 reviewed:2 sources:2 integer:1 regardless:1 alternative:1 scattering:1 previous:5 heuristic:2 candidate:1 conclusions:2 mostepanenko:1 kon:1 conclude:2 had:1 attractive:2 iω:1 simple:1 other:5 transformed:1 treatment:2 extensive:1 momentum:4 real:4 aspects:1 around:4 rules:1 spatial:3 sums:1 possible:1 makes:1 vacuum:5 using:5 part:2 prominent:1 loss:1 modifications:3 ˆbp:2 necessary:2 follows:1 performing:1 admitted:1 specific:1 ai:2 continue:1 either:1 sezione:1 fully:1 become:1 unperturbed:1 because:4 old:1 neumann:1 affects:1 creation:1 some:2 understood:1 examples:1 b2:2 mirror:1 nonzero:1 scale:2 describing:4 dimensions:3 lead:1 electromagnetic:2 measurements:1 extensively:1 per:1 planck:1 does:1 decomposition:1 snyder:1 proc:2 minimal:2 imposes:1 integrals:1 power:1 location:2 dropped:1 infinitely:2 bo:1 conventional:1 expansion:2 pressure:2 nederl:1 bp:2 although:1 takes:4 comparison:3 conducting:3 usa:1 world:1 universe:1 discussed:1 dependence:2 o:3 a2:6 introduced:2 slightly:1 explicit:1 block:1 exactly:1 soc:1 rev:3 firstly:1 presence:2 into:4 integral:2 functional:1 variable:1 weighted:1 determine:1 operator:1 proportional:4 methods:1 hep:4 fabric:1 area:3 assumed:1 strictly:1 there:6 approximate:1 long:1 much:3 way:2 was:1 propagator:1 naturally:2 function:4 complete:2 form:9 ezp:1 micu:2 brane:1 gaussian:3 volume:16 neutral:1 related:2 larger:1 line:2 infn:1 compute:2 regularized:1 minkowski:3 inside:1 smooth:1 up:3 us:6 eout:1 assume:4 below:1 frequency:1 limit:7 planes:1 problem:3 ua:2 called:1 mechanics:1 separated:1 interval:3 associated:2 computing:1 devise:1 certain:1 universal:1 describe:4 meaningless:1 general:2 exist:1 spallucci:2 commuting:3 physical:3 bordag:1 again:3 functions:4 susskind:1 no:3 dashed:1 whereas:2 when:4 vanishes:1 nam:1 nx:1 field:22 hossenfelder:2 conditions:9 details:1 normal:1 papers:1 department:1 massless:4 briefly:2 plate:7 models:1 toumbas:1 time:30 a1:6 hausdorff:1 generated:1 important:1 vectors:3 included:3 astronomy:1 sides:1 structure:1 regime:1 coupling:8 dω:2 perturbatively:1 factors:3 packets:1 hofmann:1 together:1 gobetti:1 equivalently:1 correspondingly:1 stringy:1 n2:3 n3:2 requires:1 having:2 |
0704.2252.txt |@word monte:2 measurements:1 consider:1 chain:7 rev:11 results:6 four:2 denotes:1 sch:1 looking:1 inverse:1 depend:1 pointing:1 eigenbasis:1 tr:2 intensive:1 versity:1 quasi:1 monotonically:1 tk:17 stochastic:3 analogous:1 indicating:1 p2:1 digit:1 straightforward:2 far:6 p0:2 experimentally:1 matrices:2 level:2 turns:2 solution:2 large:2 adjust:1 filling:1 small:8 ρk:4 lˆ:2 smaller:1 slower:1 consistent:1 direct:3 integrability:1 profiles:2 further:4 dynamics:1 carlo:2 canonical:2 even:2 established:1 nonlinear:1 rate:1 near:1 uniform:5 current:21 goes:1 new:1 increasing:6 method:1 body:1 kicked:1 exchange:1 component:1 here:1 reported:2 focused:1 ansatz:1 relaxation:1 const:2 strong:2 equations:1 appears:1 extreme:1 obtained:1 hbo:1 parameters:1 study:1 studied:2 allows:2 periodic:2 published:1 usually:2 hospitality:1 suitable:1 studies:1 pathological:1 plotted:3 via:1 spatially:1 projection:1 apr:1 semiconductors:2 unif:1 highly:1 scaled:1 limk:1 decrease:1 apply:3 total:2 linearly:1 plot:1 use:1 working:1 probabilities:1 positive:1 peri:1 tl:1 hilbert:2 process:1 prelovˇsek:2 characteristics:1 ψb:1 ψc:3 theoretical:4 more:1 flat:1 conductor:6 started:1 becomes:2 conducting:3 controlling:1 labelled:1 varying:1 known:5 cases:3 hold:1 keeping:1 crosses:1 equation:4 averaged:1 mt:1 values:3 three:3 learn:1 following:1 calcula:1 averages:2 performed:2 compare:3 figure:1 lρ:2 calculation:1 conjecture:1 saito:2 states:4 numbers:3 degenerate:1 exclude:1 tions:1 times:2 conversely:1 ratio:1 information:2 end:1 divided:1 write:1 very:7 pure:4 optimal:1 parameter:3 ensemble:2 profile:4 map:1 product:3 description:2 flip:1 may:2 thermodynamic:3 after:7 ζl:3 lengthy:1 applications:1 ζr:1 designed:1 faculty:1 law:1 response:3 physical:1 dynamical:2 effective:1 sq:1 grant:1 explicit:1 summing:1 generic:1 σ1x:1 so:7 allow:1 decreasing:1 acknowledges:1 order:6 michel:1 reproduced:2 interpretation:1 ith:1 correlation:1 indeed:6 over:2 mainly:1 flips:6 paper:2 statistical:3 affect:1 ffe:5 still:4 its:3 before:2 chemical:1 τk:12 chosen:3 interesting:2 temporal:1 solving:1 decreases:2 writing:2 better:1 strange:1 systems:7 insulator:3 main:1 might:1 eur:1 maximal:2 non:5 propose:1 grand:1 fig:11 asymptotically:1 scaling:2 yz:1 effects:1 they:1 bogoliubov:1 now:2 eigenvalue:5 february:1 several:1 zotos:3 always:4 university:3 hamiltonian:2 sufficiently:1 theory:1 instabilities:1 found:1 2n:6 characterized:1 prosen:2 arxiv:1 σ2z:1 gaussian:1 expect:1 measurement:6 quantum:14 our:5 eq:1 special:1 out:2 shown:1 matrix:8 driving:5 space:3 gradient:6 occupied:1 since:4 interference:1 chaos:1 research:1 increase:2 vector:1 formula:2 ref:3 shows:1 lag:2 linear:5 interactions:3 quite:1 completely:1 put:1 monotonic:1 generate:1 interaction:1 transition:3 feasible:1 turn:1 consequence:1 first:6 initial:2 probability:2 omitted:1 variables:1 number:1 randomized:1 directly:1 precisely:1 open:1 properties:5 checked:1 their:1 observes:1 system:10 least:1 1a:3 indicate:1 1b:3 master:4 fermions:1 calculations:1 perfectly:1 structures:1 final:1 1d:2 mostly:1 explanation:2 exactly:3 next:2 part:1 signaling:1 simulate:1 manifestation:1 µ2l:1 believe:3 representing:1 than:1 coefficients:1 diffusion:1 require:2 namely:8 determined:3 contrary:1 were:3 minus:1 decompose:1 lowest:1 correction:1 measure:1 curves:1 korepin:1 randomly:1 already:1 say:1 close:3 seen:1 border:7 any:3 viewed:1 strength:6 computationally:1 zero:2 depending:1 efficient:4 converges:1 note:4 ideal:6 build:1 interior:4 completed:1 heisenberg:5 begin:1 towards:1 though:2 object:1 most:2 pair:1 analytically:3 probabilistic:2 jx2:1 surprising:1 clear:1 sometimes:1 steady:5 drive:1 points:1 mzvs:1 exp:4 effect:1 maxima:1 physics:4 cannot:2 fact:2 quantity:1 particularly:1 phenomenon:4 show:5 text:1 random:5 scattering:1 decompositions:1 carefully:1 trivial:2 find:11 finally:1 based:1 ensembles:1 dividing:1 situations:1 state:19 should:3 only:12 hope:1 equilibrium:8 above:4 cubic:1 means:4 expectation:2 σ1z:1 ones:1 negative:4 during:2 awaiting:1 hin:3 evolution:5 evident:1 nicely:1 approach:1 differential:4 2b2:1 europhys:1 predicted:1 µ2r:1 analytical:3 fixed:5 explanations:1 borders:1 computed:2 achieved:1 national:1 nus:1 up:10 observed:2 depends:1 full:2 result:4 discussions:1 recently:2 conductivity:7 interacting:6 visiting:1 subsequent:1 review:1 currently:1 µr:14 symmetric:2 µl:17 written:5 various:1 closed:1 between:2 drawn:1 boundary:1 conditions:1 choose:1 terms:4 statistically:1 jz:9 superior:1 qubits:5 however:5 jr:2 jl:2 vanishing:1 concentrate:2 analyzed:1 come:1 distribution:4 essentially:2 realizable:1 last:2 σn:8 many:1 taking:2 hence:1 became:1 variance:1 qubit:11 com:1 experimental:1 cn:3 point:3 simple:5 poissonian:1 σ3z:1 corresponds:1 dimensional:7 instants:2 simply:2 constant:1 factors:1 considering:1 described:5 zeno:1 second:2 basis:1 addition:1 due:3 been:9 strategy:1 pb:11 much:1 treat:1 expected:1 ph:1 define:2 controlled:1 xxz:5 concerning:1 bulk:2 relevance:1 lift:1 external:1 instant:1 c1:3 general:2 spin:29 case:9 intriguing:2 p1:1 jx:6 look:1 exponential:1 pacs:1 expanded:1 value:3 choices:1 while:7 abrupt:1 behavior:7 situation:3 procedure:3 versus:2 unitary:4 coupled:2 almost:4 averaging:1 thus:1 them:1 repeating:1 equal:2 obeying:1 reads:1 casati:1 baths:10 binary:1 different:9 perhaps:1 author:2 perform:2 suggest:1 indistinguishable:1 same:3 complex:1 quant:1 pauli:1 largest:1 finite:4 events:1 castella:1 difficult:1 independent:2 extended:1 see:4 singapore:2 numerical:10 upon:1 ness:8 possible:2 driven:1 slovenia:2 insulating:7 potentials:1 changing:1 contribution:1 recent:1 prescribed:1 spatio:1 well:2 analysis:1 approached:1 materials:2 solve:1 does:1 coordinate:1 model:13 paradigm:1 dimension:1 left:8 gates:1 magnetization:5 just:2 increasingly:1 σnz:5 σnx:1 σny:1 hess:1 macroscopic:3 yet:1 kluwer:1 density:18 seems:2 thermodynamics:1 other:5 treatment:1 ljubljana:2 solvable:1 iτ:1 real:1 spinless:1 around:1 represents:1 couple:1 term:1 increases:1 know:1 press:2 using:2 unique:2 apart:1 insert:1 like:2 particle:1 sizes:4 specific:1 shaper:1 continue:1 steps:2 either:2 arbitrary:2 stationary:1 spins:7 therein:1 right:8 continuous:1 deal:1 sequence:1 conditional:2 some:4 calculated:1 b1:4 b2:1 duration:1 transport:9 provided:3 describing:2 takigawa:1 shall:4 integration:1 prop:1 conditionally:2 behave:1 lattice:1 provides:1 assuming:1 compute:1 chains:2 refer:1 pletely:1 bo:8 chemistry:1 periodically:1 chapter:1 about:2 would:1 anomalous:2 dependence:1 o:2 simulation:9 practical:1 2cn:2 ensure:1 sologubenko:1 cambridge:2 into:1 within:1 numerically:1 bath:10 down:3 nothing:1 references:1 determine:2 operator:1 proportional:1 conceptually:1 theoretically:1 classical:1 extremely:1 support:2 there:1 long:1 lags:4 conservation:1 low:2 analyze:1 was:1 propagator:1 function:6 form:3 oll:1 but:4 anisotropic:1 link:1 filed:1 convergence:2 dissipative:1 collapses:1 applying:2 consist:1 whether:1 characteristic:2 maximum:8 us:1 bethe:1 work:1 below:1 limit:3 critical:1 autonomous:3 ωb:2 similar:1 average:1 eigenvector:2 strongly:3 diverges:1 ordered:1 conserves:1 dp:2 defined:1 describe:1 denote:1 proper:1 reservoirs:3 simulations:8 corresponding:2 exist:1 formalism:1 distributions:1 regime:8 dressel:1 functions:1 compared:1 thermodynamical:1 ideally:3 no:2 index:1 whereas:2 mathematica:1 when:3 vanishes:2 field:19 setting:2 intuitive:1 normal:4 quantities:1 department:1 mathematics:1 izergin:1 conclusion:1 repeat:2 models:1 meaning:2 important:2 coupling:3 practically:2 assume:1 dτ:2 interval:1 curve:1 observe:2 time:14 qualitatively:2 requires:1 lett:8 |
0704.2253.txt |@word limited:3 folklore:1 similarity:3 dynamic:1 yellow:1 four:2 heliocentric:4 oldest:2 whose:2 calculate:3 atzold:1 under:4 updated:1 lack:2 oceans:2 every:3 summarized:1 encounter:6 prize:1 investigator:1 wooden:1 cause:3 scalar:1 vector:1 force:3 faintest:1 consistent:8 estimates:6 direct:1 approximation:1 second:2 chen:2 10p:8 estimated:11 even:9 fgrav:1 brownlee:3 selected:2 above:5 new:9 net:1 increasing:1 particulate:1 simultaneously:1 never:1 here:2 pluto:1 reported:2 asymmetry:3 active:5 path:1 κw:1 interpret:1 patches:3 obtained:4 study:2 california:2 blackbody:2 projection:3 slices:2 explained:3 highly:4 brought:1 visible:12 9p:8 total:20 univ:7 unit:12 jpl:1 plot:3 would:20 discrepancies:1 therefore:6 robertson:1 type:1 until:2 fractions:2 populations:2 giovanni:1 holt:7 crockett:3 award:1 disruption:2 berlin:1 correspondingly:1 excellent:3 aligned:4 must:1 abundance:2 mg:3 ma:1 palomar:1 mm:9 work:7 biosphere:1 emitters:1 ms:2 interaction:1 root:3 example:3 dither:1 bennett:1 indicates:1 magnitudes:5 isothermal:2 absolute:1 recovery:1 provide:5 multiband:2 feature:16 far:5 hot:1 symposium:1 podolak:1 mueller:8 rise:1 description:1 arcs:2 typed:2 after:6 containing:1 diagram:1 lau:1 summarize:1 law:4 meaningful:1 parallel:2 effective:7 maintain:2 green:6 enter:2 order:15 executed:2 extents:1 over:25 expects:1 jorda:1 smithsonian:1 before:7 outgassing:4 fit:1 expectations:1 better:3 production:30 fig:45 versus:12 them:5 affected:2 band:1 repulsive:1 effects:4 they:27 tagliaferri:1 rocky:2 brightness:28 backgrounds:1 reasonable:1 each:27 side:2 mean:31 lifted:2 telescope:7 independent:4 series:2 osip:3 combining:1 laboratory:1 recognizable:1 collector:1 borne:1 burnham:4 centaurs:1 gradient:4 restricted:2 cameras:1 particles:166 reader:1 trajectories:5 linear:9 surveys:2 free:1 ecliptic:3 formation:4 estimate:18 silicate:6 cosmic:1 days:5 dispersal:1 steward:1 filter:1 iso:2 signature:1 corrections:1 onto:3 already:1 features:4 encouraging:1 relations:2 another:1 thick:1 similarly:1 top:1 indeterminate:2 approximately:7 needed:1 perturbations:24 rates:18 too:3 xiv:1 ranging:1 centered:4 tool:1 serve:1 comas:4 deschˆenes:2 somewhat:6 distance:17 showed:3 approximations:2 likely:9 preparation:3 historical:2 feeling:1 solely:1 modern:1 manner:4 seen:7 seem:1 overlays:6 relatively:17 isolated:1 predominantly:1 oriented:1 fitting:1 calibrated:3 forces:10 asher:1 blue:1 faye:5 antisolar:1 object:1 lebofsky:1 rabinowitz:3 22p:1 constancy:2 observation:26 calculated:4 detectors:2 inferred:11 storm:1 poynting:1 nineteenth:1 left:2 fitted:2 planetary:5 probe:1 infrared:33 radii:1 radio:2 keywords:1 earth:12 latent:2 proposed:1 ocn:1 explain:5 minnesota:1 do:7 tiles:1 mixture:1 shopbell:1 df:2 foremost:1 despite:4 report:1 dt:28 saturn:3 dr:1 cleanly:2 runs:2 chronological:1 bar:1 covering:2 fields:1 colas:1 patch:1 fascinating:1 sensitivity:4 detection:11 radius:7 result:4 sporadic:2 best:6 techniques:1 propulsion:1 away:6 rings:1 µm:21 catalogue:2 inset:1 conceptual:1 drawn:1 approach:4 shields:1 discovery:2 accord:1 terms:3 extend:4 nature:12 confusion:1 mcbride:3 weak:1 however:8 extent:7 clues:1 modeling:3 micron:1 received:1 essentially:2 met:2 heating:1 economou:1 contribution:9 behaviors:1 toon:1 wider:4 conference:1 equations:2 three:4 been:16 quickly:1 much:9 basic:2 expected:7 correction:1 life:1 deeper:1 spin:2 exception:1 ishiguro:3 near:15 neat:1 balance:1 delineated:1 played:1 ii:11 characterize:1 damaged:1 miniature:1 apparently:4 make:2 cumulative:4 millis:1 any:1 isocam:1 complex:7 split:3 several:1 evolve:2 satellite:1 numerical:8 monotonic:1 hand:1 cycle:1 neptune:1 shadowed:1 just:2 ephemeral:1 rotated:1 gravity:5 identify:2 thanks:2 scattering:11 previous:13 unique:2 had:18 spread:3 shoemaker:9 plasma:2 iν:15 possible:7 burns:2 advanced:1 zook:1 detections:2 old:4 truncated:1 predominance:1 jupiter:27 separately:1 mosaicking:1 investigations:1 ice:19 contributing:1 circ:1 icy:2 tracker:1 levasseur:1 illustration:1 shifting:1 post:3 super:1 properties:12 months:1 anomalous:1 o:13 ensure:1 slightly:6 demise:1 soc:1 faint:10 presence:2 lien:4 bound:1 ut:2 down:2 lies:1 often:3 support:1 initial:5 inspected:1 class:1 width:14 anderson:2 way:2 was:62 lowest:2 head:1 form:8 campins:1 sagan:1 aperture:1 heat:1 underestimates:1 solar:19 removed:1 true:6 tempel:16 portions:3 maximum:2 tucson:8 stardust:6 panels:1 separated:3 hotter:1 classic:1 covers:2 evidence:5 dθ:15 simulations:7 adversely:1 distributions:2 physical:9 dotted:1 no:15 generally:7 ne:1 narrowband:1 pasadena:2 role:1 test:2 optically:1 models:3 preceding:2 falloff:1 variable:1 makovoz:2 jones:2 younger:1 longer:2 phone:1 dφ:28 pseudo:1 together:5 time:31 nuclei:10 particular:2 roe:1 supplement:1 mukai:1 morphology:1 flyby:1 layers:3 arcsec:1 certainly:2 inverse:2 passage:2 environment:2 determinations:2 analogous:1 vej:5 brown:4 advantage:1 springer:1 cyan:1 little:1 longevity:1 clouds:1 presented:9 did:1 pollack:1 overlaid:1 round:1 upper:10 revolution:11 slower:1 trend:5 trails:79 prediction:1 bombardment:1 appear:3 remain:2 current:5 looking:1 suspect:1 goes:2 falling:2 nakamura:1 supporting:1 explosion:1 understanding:3 water:2 cos2:2 address:1 alone:1 along:20 appears:4 change:4 institute:5 shift:1 studied:4 exemplifies:1 usually:1 noticeably:1 history:5 studies:5 encounters:1 compare:1 planck:1 wealth:1 msx:1 criteria:2 scope:1 apparent:7 visual:3 serendipitously:1 insights:1 collision:1 davies:1 longitude:1 l121:1 vega:2 values:7 following:41 making:1 trans:1 stream:3 ger:2 predict:3 lowry:4 confused:1 sample:8 performed:2 allowed:1 spanning:2 hearn:12 occur:1 rays:1 s2:4 spreads:1 chemical:2 submillimeter:1 rolfe:1 parameter:1 map:1 levy:6 may:21 produce:5 designed:1 date:11 data:13 dynamical:3 johnson:6 sr:24 ueno:1 yielding:6 tale:1 cascade:1 so:16 progressively:1 typical:2 qh2:6 wavelengths:3 correlation:8 indeed:4 years:5 statistical:2 unfavorable:2 still:6 observational:3 derive:1 group:1 monitor:2 how:4 cleanest:1 mantle:1 decreases:5 mail:1 main:3 correspondence:1 non:16 views:1 matches:5 scaling:1 tails:9 half:1 now:6 maintaining:1 inversion:1 coagulation:1 rock:1 photometry:4 weighted:2 significantly:13 gaussian:2 breakthrough:1 owing:1 entering:1 year:4 galactic:1 harker:1 eq:1 adequately:1 ultimately:1 watanabe:1 space:8 coincidentally:1 furthermore:1 generation:1 increase:4 collisions:2 contained:2 nominal:3 gaussians:1 suggesting:8 dominate:3 shows:25 inevitably:1 earlier:2 theory:1 quite:1 complicated:1 remainder:3 e2:2 fixed:1 widths:2 motion:3 place:1 massive:5 neglect:1 frequent:1 first:16 origin:6 comprised:1 specifically:3 directly:1 spectrometer:1 carry:1 impossible:2 array:2 angular:2 size:40 1p:3 given:5 necessarily:2 checked:1 structured:1 indicate:1 cooling:1 iau:1 white:1 structures:5 williams:1 prialnik:2 fraction:6 mostly:5 asymmetric:2 continuous:1 accurately:1 released:2 photographic:1 than:40 coefficients:2 population:10 wide:12 meteors:7 favors:1 require:3 lisse:2 festou:7 were:34 tophat:2 pre:3 san:1 dynamically:3 occupies:1 locations:4 dash:1 distorted:1 hsieh:2 albedo:1 computationally:1 offering:1 note:3 take:1 prevalence:2 l117:1 coincide:1 soter:1 multiple:3 trace:3 opposite:1 track:1 decreasing:2 molecule:2 beta:1 analytically:1 pages:1 latex:1 especially:2 considered:1 average:2 hemisphere:1 bopp:3 nuclear:5 dispersed:4 typically:4 laws:1 slope:1 spaced:2 show:7 discovered:1 osculating:1 bright:21 inconsistent:1 uranus:1 interpretation:2 injection:1 ground:1 astron:3 slow:2 ratio:15 storms:6 behind:7 analytic:4 only:39 black:1 2πa:2 between:19 soon:1 cannot:5 nearly:4 tanigawa:1 ssc:1 prime:1 reveal:1 median:23 attitude:2 summary:1 predicted:6 though:3 mapped:1 fainter:3 ends:1 relative:2 surfaces:1 detect:2 subsequent:1 review:1 outside:1 moons:1 geometric:5 across:4 parent:4 apparition:1 jp:1 jovian:1 coma:20 come:1 pixels:1 dates:1 many:10 region:2 according:1 contract:1 comet:130 nearby:1 among:4 stretches:1 reprocessed:1 characterization:1 color:7 roman:4 period:26 sampling:2 jets:4 anti:6 spans:1 associated:6 combines:1 capable:1 west:4 mark:1 cosine:1 deposited:1 combined:1 reflective:1 peaking:1 direction:12 formed:1 6p:1 dramatic:2 diffuse:2 those:13 case:4 hughes:2 kimura:2 profiles:5 refractory:1 editorial:1 103p:6 yarkovsky:2 zenith:2 coupled:1 bias:6 ephemeris:2 technology:2 levison:4 different:14 revolutions:5 same:14 shifts:1 epoch:2 html:1 coadding:1 streams:10 events:1 extended:5 centuries:1 closest:1 driven:1 devoid:1 running:1 edges:2 changing:1 largely:4 roughly:8 without:5 aphelion:1 components:1 ccd:1 model:12 bodies:3 being:10 when:10 rest:2 ch:1 disperse:1 blow:1 seems:1 except:1 struck:1 momentum:1 around:1 outermost:2 early:2 sekanina:4 grid:1 mol:1 confined:1 using:26 accepted:1 correcting:1 particle:52 velocities:2 either:1 exposed:2 pacific:1 britt:1 table:30 duration:1 trujillo:1 nonzero:2 provided:2 slice:2 toth:1 conservative:1 meteoroids:10 critical:1 lunar:1 greyscale:1 jgr:3 refer:3 biased:1 power:5 notable:1 slaughter:4 ratios:1 akov:3 comparison:5 oh:2 discussed:12 drag:2 stony:1 perturbed:3 cambridge:2 orientation:7 image:43 references:1 determine:3 heated:1 log:1 area:17 assumed:5 strictly:3 there:23 dispersion:1 strict:1 detectable:2 low:10 survives:1 enough:11 mnras:4 marsden:2 pull:1 assume:4 emissions:3 agree:1 detailed:5 celestial:3 af:1 ak:6 aj:2 deep:6 general:6 au:27 planets:5 corresponding:4 az:1 fill:1 bisected:1 discerned:2 roser:1 field:9 fairly:1 caltech:4 spatial:3 poor:1 perpendicular:9 separate:8 fazio:2 drift:1 arcmin:3 important:1 bounded:6 peak:4 buratti:1 included:4 closeby:2 remote:2 l63:1 observe:1 mass:112 cores:1 resolution:1 original:1 monte:6 sci:1 consider:2 pointing:1 caused:2 asteroids:3 splitting:2 spacecraft:11 debris:137 follow:10 content:1 tp:4 tail:39 tj:7 fax:1 straightforward:2 very:28 discrepant:1 focus:1 perihelion:31 fan:4 colwell:1 fall:2 difference:3 worden:1 list:1 t1:1 large:52 small:44 midplane:1 past:2 rate:32 arizona:6 timescales:1 enhancement:2 further:9 gunn:6 what:1 nonlinear:2 sun:14 section:5 crust:2 fractional:1 method:2 contrast:2 full:1 ranged:1 irac:3 component:4 19p:2 ranges:1 cylindrical:1 excess:1 iras:32 strong:5 observing:3 almost:2 arend:4 ahead:1 stretching:2 exceptionally:2 experience:1 prior:6 amount:4 periodic:8 miville:2 mentions:1 narrow:26 elongated:2 imaging:4 via:1 family:14 requiring:3 sensors:1 readily:1 khan:2 distinct:5 contains:3 comparing:1 taken:5 minor:7 more:27 flat:2 hanner:2 ejected:13 jenniskens:5 emission:30 varying:2 known:10 producing:1 none:4 hour:1 science:15 equation:1 protons:1 debated:1 deg:16 f0:4 f2:1 spalding:1 scan:3 sphere:3 minimum:1 arise:4 magenta:1 mn:1 axis:4 information:1 rather:8 jewitt:7 maps:2 acta:1 explains:1 ensemble:1 ft:1 spitzer:35 wiley:1 derived:2 orbits:42 fa:1 plane:15 horizontal:1 derives:1 short:18 spectra:2 parameterized:1 generic:1 extrapolation:1 negligible:3 dispersing:2 passages:2 mission:1 schaller:1 radar:3 thermal:2 paper:18 through:4 existence:4 dithers:1 its:14 quadrupled:1 rapidly:2 actually:4 late:1 detected:26 systems:1 might:3 tentatively:1 lowell:1 impacts:2 tisserand:3 hunten:1 snowball:2 yr:25 easily:2 2p:21 products:1 goldstein:3 always:1 loosely:1 capability:1 2b:1 radial:2 found:11 giese:1 undetectable:1 contiguous:1 reduce:1 expect:1 measurement:2 beyond:4 hartley:7 event:1 really:1 dominates:2 since:9 projected:27 acting:1 dominated:9 occurs:1 belief:1 offsets:1 rieke:2 brightest:2 matthews:2 beginning:3 generate:1 revolutionary:1 ion:1 bumper:1 major:1 yeomans:2 feel:1 contributions:1 traveled:2 fν:2 perturbation:8 temperature:7 jet:1 introduction:1 leading:33 moderately:1 least:9 assumption:1 calculations:3 smoothed:1 recovered:1 observations:38 shifted:3 imperfect:1 passed:5 park:1 part:7 favorable:4 focusing:1 brightnesses:1 believe:1 observatory:5 dtc:2 grey:2 determined:3 aas:1 toward:3 kres:9 derivative:2 ages:12 randomly:1 depleted:1 cometary:43 qpr:4 lie:5 wilson:2 built:1 zero:24 depending:1 liu:2 square:3 build:2 extrapolating:1 index:3 medians:1 measures:2 reach:20 most:17 plan:1 significant:18 britton:1 colliding:1 measured:8 kg:23 clear:8 cover:4 km:36 traditional:1 optical:14 azimuth:1 velocity:41 3v1:1 thomas:5 particularly:3 phenomenon:1 nondetection:1 scattered:2 astrophys:2 fine:1 find:1 impact:7 duncan:4 distributed:1 ebert:1 factor:3 distributes:1 his:4 dominant:1 longest:2 closely:6 combinations:1 during:9 arxiv:1 remove:2 common:7 activity:6 weaver:8 wrote:1 set:10 grain:1 tended:1 gehrz:1 see:2 arc:2 descriptions:1 close:12 mckay:1 project:2 intersected:1 diluted:1 lagache:2 smallest:3 various:1 conditions:3 15th:1 available:1 recently:2 statistically:1 complementary:1 sola:4 distinguish:1 tnos:2 both:14 improved:3 tapered:1 barely:2 sensitive:3 connection:1 dm:16 point:4 simple:3 corresponds:4 dimensional:2 simply:2 experiencing:1 throughout:2 expensive:1 belt:6 pp:11 described:2 enhancements:1 due:45 laplacian:1 reduction:1 describes:1 anisotropic:1 combine:1 ph:1 lived:1 gas:7 convert:2 gap:1 representative:1 systematic:1 extensive:1 elst:2 uncertain:2 grains:10 solid:4 reliable:1 mosaiced:1 while:21 superposed:1 behavior:1 guide:2 fernandez:2 chyba:5 resolved:1 vectors:2 showers:6 century:1 averaging:1 apjs:3 encountered:1 lengths:3 wherein:1 widely:5 modification:1 resulting:3 composition:6 conflict:1 higher:6 development:1 used:2 viewing:13 moving:2 photometer:2 birch:1 mips:5 brussels:1 recent:4 dark:2 lower:27 older:4 analysis:4 edge:14 comae:6 nongravitational:1 distances:2 powering:1 woodward:1 67p:13 shape:5 intervals:1 zodiacal:12 tables:1 cut:1 conclusions:1 diverges:1 guaranteed:3 source:8 polomski:1 location:11 input:3 remaining:2 backscatter:1 qmax:2 showing:1 suffering:1 scaled:1 whitten:1 shaped:4 follows:10 signal:1 impactor:1 shapes:2 flux:6 continue:1 yields:5 howell:6 terminology:1 methods:2 some:11 strongest:1 examples:1 sight:5 mirror:3 gradually:5 scale:5 l14:1 l16:1 measurements:2 integration:1 per:14 l13:2 efficiencies:1 centroid:1 fragments:1 minimal:1 processing:2 agreement:3 subtract:1 russell:5 extending:5 kinoshita:1 simulation:2 range:27 triton:1 computational:1 into:17 within:21 appropriate:1 primarily:2 spending:2 extremely:2 placing:1 gases:1 doubt:1 himself:1 elsewhere:1 memory:1 link:1 line:33 directed:2 rejection:1 consist:1 characteristic:1 up:6 us:1 un:4 spectroscopy:1 planes:1 q24:1 similar:10 called:1 fluence:1 constant:7 defined:2 influence:5 images:37 single:3 associates:1 gru:1 dashed:3 preventing:1 coded:1 department:1 mcdonnell:6 sykes:29 deviate:2 icarus:15 elements:1 lpi:1 sublimation:2 prepared:1 william:2 generated:3 allowing:4 structure:20 ago:5 furthest:2 correlated:2 age:7 required:9 diffraction:1 orbit:85 equivalently:1 depth:8 nasa:2 dot:1 walker:19 requires:2 having:3 evenly:2 gr:4 illustrates:1 issued:1 results:11 eds:9 broader:1 edu:2 gm:3 disintegration:1 cases:1 issues:1 compact:1 young:3 ariz:1 curdt:1 contours:2 stable:4 suite:1 include:3 indicating:4 labels:6 listed:1 neptunian:1 continued:9 entire:3 diverging:2 positions:2 michael:1 colors:1 fewer:1 noted:1 concluded:1 smaller:15 oort:2 133p:2 dynamics:3 carlo:6 hourly:1 labeled:1 expressed:1 consistently:1 experiment:3 volatile:1 bird:2 led:2 degree:1 respectively:3 tsou:1 explore:1 objects:4 separation:20 others:1 suggest:1 whipple:13 great:3 larger:18 shades:1 suggests:4 preferentially:1 survey:23 harrington:1 residents:1 makes:3 composed:5 named:1 clark:8 scales:3 apr:1 kuiper:4 integrations:2 apj:5 aboard:1 decrease:3 apply:2 cloud:8 use:5 figure:18 remains:2 kowal:4 ices:2 few:6 camera:3 themselves:1 panel:5 becomes:1 occurred:1 trail:171 normalized:1 eccentricity:2 testifies:1 iii:3 account:4 balls:1 averaged:1 ρs:1 thin:6 scatter:2 decoupled:1 weaker:2 weissman:3 dependence:3 high:5 effectively:1 assumptions:1 estimating:1 tan:2 regions:3 located:4 instead:5 lamy:3 usui:1 circular:1 profile:5 frad:1 outlier:2 yielded:2 light:14 counter:3 lines:9 correspond:2 gilliland:1 allow:3 subsequently:2 software:1 mjy:37 saturated:1 asteroidal:3 soderblom:2 astronomical:2 insight:1 produced:20 including:7 looks:1 mentioned:1 contaminated:1 outer:5 masses:7 h2:5 degrees:2 inspecting:1 orange:1 covered:3 defining:1 pixel:6 greater:4 material:19 subtraction:1 front:1 rotation:1 day:1 university:1 traced:2 identified:1 crudely:1 magnitude:3 mode:1 prevailing:1 shower:1 variety:1 measure:1 our:18 out:3 sunlight:2 ejecting:1 lecture:1 supports:1 integrated:3 red:1 approached:2 interplanetary:6 completely:2 meech:2 trends:3 van:3 hubble:1 overtake:1 organic:2 geometry:12 sinica:1 could:8 times:1 length:17 hence:1 retain:1 manuscript:2 possessing:1 precisely:14 quality:2 long:15 observer:1 unknown:7 system:8 f1d:12 hale:3 their:36 intermediate:4 final:1 explanation:1 shallow:2 contribute:1 lists:3 constituent:1 updating:1 neck:30 steel:2 observed:58 colleagues:2 ipac:1 splayed:1 submitted:1 individual:8 amplitude:2 providing:1 abstracts:1 distinguished:4 exhibit:1 sp:1 curves:1 unlikely:2 keller:9 need:1 kelley:8 clearly:5 viewed:2 acceleration:1 angle:13 studying:1 able:1 mid:14 mix:1 detector:1 underestimating:1 unless:1 who:1 eight:1 but:39 why:3 delivery:1 subtracted:2 eject:1 32p:5 constrain:1 normally:1 atmosphere:3 selection:3 supported:1 rotating:3 purely:1 convolved:2 rough:3 scotti:2 agrees:1 principal:1 based:10 should:7 jan:1 brighter:2 candidates:1 molecules:1 gradual:1 helios:2 means:3 overall:3 beam:1 ones:2 collisional:2 evolution:12 numerous:1 differential:1 comprising:1 contain:4 cycles:1 gravitational:20 view:6 frame:1 correlations:1 wtr:1 edition:1 intensity:2 geometrically:1 enhanced:2 operated:1 closer:10 placed:1 pattern:1 nebula:1 tend:1 macros:1 schleicher:1 invariant:2 dirty:2 comparable:6 opening:1 emitted:7 efficiency:5 key:1 observable:2 instant:1 limits:4 taking:5 equal:1 beliefs:1 april:1 figures:1 passing:1 temporal:2 strongly:1 relevant:1 co:1 cm:15 ca:2 cf:2 taylor:6 coordinates:2 respect:4 geometries:2 powered:1 addition:1 trajectory:1 gerasimenko:5 genetic:1 outliers:1 anomaly:33 define:1 asymmetrically:1 adopted:1 diversity:2 battrick:1 gustafson:1 cos:1 bulk:2 minneapolis:1 angles:1 ours:1 last:9 present:35 multi:1 atmospheric:1 unlike:1 mazets:2 ejection:23 value:8 promotes:1 will:19 apparitions:1 halley:7 sunward:1 wild:11 comets:166 resident:1 vi:1 thus:6 surprisingly:1 surface:26 meteoroid:14 vs:1 lifetime:1 situ:6 orbital:11 capture:1 complexes:1 perhaps:2 radiation:18 cross:5 unity:2 largest:9 units:2 finite:1 infer:1 difficult:2 practice:1 http:1 again:2 upon:1 effect:9 v1:7 v5:1 dust:63 frequently:2 bhattacharya:1 off:1 center:3 modeled:1 well:12 thought:1 position:7 encke:25 routinely:1 less:8 accurate:4 obtain:1 rapid:2 density:7 absorption:3 sky:15 arrest:1 extends:7 attractive:1 match:3 identical:1 increased:1 myth:1 term:4 zahnle:1 increases:4 five:1 know:2 press:7 immediately:3 prominent:2 loss:28 like:5 excluding:2 sizes:10 loses:1 sized:9 leinert:4 lose:2 become:1 exceed:2 because:8 buitrago:1 sequence:1 kova:1 polynomial:1 warmer:1 planetesimal:1 overlap:1 does:11 esa:1 assuming:13 analyzed:1 demonstrated:2 locate:1 noise:1 inaccurate:1 asteroid:2 expansion:1 pressure:15 pizarro:2 coates:1 although:1 stage:1 iris:1 about:5 actual:5 extension:1 column:2 a3:1 recognized:2 nucleus:84 napier:2 previously:5 interstellar:2 gehrels:5 ridge:3 additional:1 transfer:1 spots:1 smoothing:1 dm3:22 inner:8 lederer:1 suzuki:1 function:3 hr:1 overlapping:2 astro:1 collected:1 hh:2 l61:1 highest:1 he:4 fragmentation:1 made:8 evident:3 whether:2 latitudinal:1 variations:1 record:1 below:5 astrophysical:1 limit:30 demonstrate:2 distribution:24 bearing:1 recognize:1 sectional:1 pid:2 periods:1 wavelength:1 crystals:1 trailing:2 mutual:2 compared:2 calibration:2 mopex:2 detail:4 monitors:1 other:8 details:2 meteor:25 francisco:1 star:1 shown:5 variation:5 astronomy:1 exposure:1 albedos:2 4b:1 factors:1 tork:1 4p:4 portion:6 meteoritic:1 mosaics:3 |
0704.2254.txt |@word gd:1 fi1:1 homomorphism:5 consider:3 electron:1 copy:1 informally:1 results:2 four:3 hαi:1 scalar:4 proposition:41 edu:1 go:1 follow:2 remarkably:1 gl:2 minuscule:58 gi:1 devoted:1 whose:6 aji:2 graph:2 contained:1 preprint:1 finally:2 does:3 γn:1 th:1 under:4 include:2 presentation:1 ingredient:1 applied:1 g2:5 g1:4 very:6 connects:1 choice:1 corollary:1 every:4 fall:1 matrices:1 treating:2 dim:3 school:1 immediately:1 presented:1 did:1 irreducible:16 criterion:1 list:1 sαi:1 d2:1 4j:8 vector:47 dealt:1 quick:1 hesse:4 configurations:2 upper:1 smaller:1 carter:2 submodules:2 consistent:1 direct:2 sign:2 tex:1 consists:4 zero:9 odd:2 linear:10 bilinear:1 intersection:4 plays:1 appear:4 invertible:2 giving:13 trivial:5 sum:1 uniform:1 cell:1 version:1 above:5 judicious:1 suppose:14 contrast:1 satisfy:2 full:6 simultaneously:1 symmetrizable:8 degree:7 αij:2 respectively:21 modify:1 here:2 diagonal:1 explore:1 objects:1 groups:4 meet:1 concluding:2 based:1 enveloping:1 appears:1 box:1 remark:3 vectors:18 allows:1 approaches:2 contradiction:1 later:1 tempting:1 products:1 action:11 symmetrical:1 proof:53 makes:6 involves:2 quotient:2 via:1 term:2 classification:1 extra:2 apr:1 parity:1 namely:1 diagonalizable:1 highly:1 sloane:3 apply:1 establish:1 clifford:1 use:3 additive:1 usa:1 prove:11 remains:2 positive:3 contains:1 humphreys:1 negative:1 next:6 bases:1 call:6 therefore:3 themselves:2 type:39 ψd:3 more:7 billey:1 afford:1 operators:14 lakshmibai:1 appendix:1 observations:1 particular:2 known:13 cases:13 hold:1 iii:12 springer:2 isomorphism:4 join:1 recall:1 equation:3 work:3 paragraph:2 obvious:3 following:8 making:1 root:13 example:5 cartan:13 boulder:1 f4:2 exterior:1 give:3 calculation:1 loci:1 purposes:1 states:2 hilton:1 numbers:2 sense:2 nonnegative:1 occur:1 verlag:2 information:1 end:1 advantage:1 provide:2 hom:1 revisit:1 write:2 how:6 nontrivial:1 pair:3 instead:1 hi:24 explains:1 priori:1 polytopes:27 map:5 product:3 description:1 algebra:53 may:12 after:3 derived:13 orbits:2 fa:12 fb:35 plane:1 representations:47 fj:6 data:1 compatibility:1 types:9 hartshorne:2 short:2 attempt:1 varieties:1 third:3 whenever:1 lines:15 correspond:3 element:9 hypotheses:3 sj:1 si:3 maintain:5 so:3 specifying:1 fundamental:7 representation:17 sa:8 transitivity:1 order:3 operations:2 restriction:1 acts:8 words:2 produces:1 developed:3 over:20 entries:1 satisfied:14 paper:10 including:3 signs:1 differs:1 satisfies:3 its:1 roots:5 before:2 position:1 group:9 singular:1 maps:2 del:9 sα:3 coxeter:7 coordinates:7 edge:1 systems:8 jacobi:1 mail:1 main:3 defining:2 easier:1 fim:1 maximal:1 non:1 good:1 greater:1 combination:2 indexing:1 annihilated:4 introduce:4 bound:2 effects:1 they:5 half:1 formulating:1 now:12 fi2:1 easily:5 2v:14 finite:7 name:2 transitive:1 university:4 each:23 found:3 2n:20 2ea:1 side:2 2j:14 mean:1 subsystem:1 weyl:9 ei:32 directly:4 weight:35 ej:11 hard:3 ea:57 related:1 eb:18 elementary:4 literature:1 measure:1 our:9 recognizable:1 special:2 out:4 rt:1 respects:1 shown:3 matrix:18 space:14 restricted:1 furthermore:2 since:6 induces:1 combinatorial:4 acting:2 reader:1 denoted:3 surprise:1 rn:15 induced:1 occurs:2 math:6 shows:17 theory:7 differ:1 possibility:11 standard:2 reason:1 complicated:3 e8:2 e7:28 e6:14 definition:52 pairs:1 geometry:3 starts:1 omit:1 r8:2 times:3 turn:8 edges:2 place:4 δij:1 consequence:1 retain:1 βn:1 think:1 first:11 already:1 symmetry:2 bijection:2 schubert:1 number:5 done:2 relations:4 another:2 fi:15 carry:1 distributive:1 precisely:3 affords:4 size:2 given:8 checked:2 needed:1 introduction:2 system:60 construct:4 parallel:1 their:4 assumption:1 draft:1 listed:1 calculations:1 realization:1 zeros:1 ordered:1 structures:2 cooperstein:1 gives:1 progr:1 statement:1 mostly:1 explanation:1 exactly:1 proving:2 immediate:3 part:6 labelled:1 x2:2 natural:13 x1:2 than:4 coefficients:3 distance:5 grew:1 edition:1 was:1 require:1 second:5 pairwise:1 were:1 descriptions:2 well:3 argument:22 endomorphism:1 say:2 conjugate:2 need:3 seen:1 recover:1 apparently:1 any:4 elsewhere:1 paths:1 subsystems:3 traditionally:1 convenient:1 latter:4 note:6 ideal:8 k0:5 εi:16 generalized:10 εj:6 green:18 coincide:1 completed:1 kac:14 even:2 converse:1 afli:2 gα:9 track:1 what:1 birkh:1 algebraic:3 satisfying:9 preliminary:1 remarks:2 extremely:1 subspaces:1 constructed:5 observation:2 32d:1 kk:1 clear:1 sometimes:2 vertices:13 typeset:1 bracket:3 link:2 usual:6 physics:1 notion:3 fact:6 precise:1 show:10 spaces:2 relation:2 analogue:2 hypercube:7 agrees:1 subtracting:1 εn:6 ha:28 layout:1 explain:2 nonisomorphic:5 enough:2 completes:5 lemma:44 only:13 explicitly:1 generators:2 equipped:3 dn:15 do:5 establishes:3 notation:14 exceptional:4 embeds:1 routine:1 db:1 inclusion:1 imitating:1 ones:1 actions:1 aforementioned:1 new:5 lattices:1 du:2 places:1 approach:7 transposition:1 arxiv:1 calling:1 qa:1 contain:1 fixed:1 combinatorially:1 coefficient:2 set:19 constructing:2 exists:1 module:49 connections:1 mentioned:1 see:12 rmg:1 corre:1 λj:2 close:1 euclid:1 p28:1 subject:2 surfaces:2 said:5 label:1 symmetric:1 state:2 vkk:1 various:3 closed:1 between:4 αi:12 neither:8 αj:1 conditions:7 checks:2 αn:17 commute:1 multiplied:1 terms:7 extend:1 importance:1 arises:1 restricting:1 points:6 however:5 incident:1 key:2 interchangeable:1 holds:3 regular:1 adapting:4 both:5 essentially:1 polytope:16 according:4 littelmann:1 interesting:1 section:1 passing:2 adapted:1 otherwise:3 affine:14 co:2 cn:8 simple:61 ca:2 corresponds:3 dimensional:24 assertions:6 respect:32 skeletons:1 ei1:1 ei3:1 ei2:1 described:4 transformations:2 basis:24 union:3 skew:5 three:7 been:3 int:1 much:1 basic:1 algebras:53 universal:1 partial:2 define:8 obtained:3 describe:2 families:1 subspace:4 fij:1 observe:1 occurrences:3 pezzo:9 chevalley:1 covered:1 spin:8 present:2 case:35 pitman:1 subsets:4 identifications:1 means:5 value:1 will:8 aii:1 aij:12 property:2 eim:1 serre:2 independent:1 almost:1 vi:24 vj:2 vk:2 thus:3 them:4 surface:7 iv:7 ii:26 exchanging:1 itself:3 dual:3 turns:1 ready:1 result:9 containing:2 formalism:1 author:1 make:1 cross:1 same:13 check:24 rules:1 antisymmetry:1 complex:1 copying:3 resulting:2 proved:3 several:1 subalgebra:6 composition:1 difficult:1 exhaust:1 used:4 eds:1 context:1 lie:84 assignment:1 sequel:1 v0:22 v1:27 v2:23 constructions:2 purpose:1 mentions:1 infinite:2 identity:5 recent:1 lower:1 least:1 reflection:2 changes:2 kashiwara:2 analysis:3 without:1 greatest:1 sets:7 entry:1 schl:2 arising:18 dimension:14 left:3 heaps:5 transitively:2 fαi:1 λu:2 being:1 obtain:2 rest:1 relevant:1 identify:2 using:14 useful:1 λi:14 λn:3 previous:1 letting:1 york:3 submodule:3 europ:1 application:1 vψ:39 auser:1 except:2 boston:1 lattice:2 operator:3 interested:1 easy:10 theorem:13 k7:5 save:1 remaining:1 identical:1 remmert:1 depends:1 fi3:1 checking:1 evaluate:1 showing:1 possible:3 spanned:4 inflation:1 five:1 know:3 background:1 press:3 integer:3 ams:1 unique:5 moody:12 appearing:1 like:2 follows:31 reduces:1 automorphisms:1 either:7 mathematical:1 formulae:1 right:2 methods:1 classical:2 some:16 self:1 ideals:1 examples:8 convex:1 unless:2 proofs:2 reasons:1 nonzero:3 endomorphisms:1 hirzebruch:1 dimensions:4 nonempty:2 models:1 behave:1 decomposition:1 provides:1 proc:1 preceding:1 minimal:1 meanings:1 power:1 multiple:2 kyoto:1 bn:10 pp:1 duke:1 bv:60 although:3 p33:1 relating:2 properties:1 rearranging:1 integers:1 about:6 would:2 most:1 vsi:1 completing:2 meaning:6 recognized:2 assertion:6 distinct:4 involving:3 act:3 referred:1 subset:1 soc:1 cambridge:6 colorado:2 conway:3 into:6 h1:1 h6:2 isomorphic:2 lies:11 appropriate:2 because:7 references:2 restatement:1 bijective:1 val:2 combinatorics:2 support:1 there:14 question:1 lond:1 long:1 start:1 describes:3 way:7 sections:1 naturally:1 lowest:9 stipulating:1 complete:1 form:6 reduce:1 kronecker:1 but:4 hj:2 construction:6 hn:3 heap:2 delta:1 line:1 highest:15 versatile:1 partially:1 directed:1 made:1 consist:1 whether:3 multiplicity:2 verma:2 up:1 us:1 wψ:3 ωi:5 crystal:5 those:1 uk:1 ωn:6 highlight:1 similar:8 called:8 aa:16 definitions:1 associated:5 defined:8 certain:5 abstract:1 combining:1 proves:3 formulation:1 corresponding:21 kl:1 identities:1 campus:1 defines:1 vλ:6 no:6 whereas:1 mathematica:1 field:4 disjoint:3 other:16 role:1 details:5 sponding:1 department:1 mathematics:2 elements:13 keep:1 sided:1 generated:4 a7:1 manivel:2 sides:1 structure:6 connotations:1 implies:9 assume:2 values:3 required:12 modules:35 orbit:1 together:1 eαi:1 weights:8 time:1 requires:1 once:1 |
0704.2255.txt |@word limited:1 monte:2 extrapolated:1 consider:1 ciao:1 magnetic:14 lack:1 results:5 existing:1 four:2 rapid:1 spacecraft:1 debris:5 higher:1 l75:1 disk:6 contributions:1 aliases:1 compact:1 whose:1 depend:1 aug:2 ergs:5 gigu:3 tr:2 young:3 finally:1 does:1 indicate:1 excluded:1 stable:1 l133:1 include:1 cm3:1 yr:1 global:1 amplitudes:1 very:1 continues:1 exception:1 seemingly:1 readout:1 luminosities:1 electron:4 sensitivity:1 month:1 exact:1 prevents:2 entire:1 spie:1 ccos:6 incoherent:2 largeamplitude:1 presented:2 transmission:2 supports:1 z12:8 solution:9 large:5 assignments:1 detected:2 asp:1 small:7 becker:3 shows:1 upper:11 cap:2 10m:1 consistent:2 acis:6 prediction:2 pulse:1 sign:1 surrounding:1 rate:8 camilo:2 timescales:1 chen:3 further:1 estimated:2 carlo:2 gaensler:1 canonical:1 even:3 errors:5 hernquist:1 section:1 dotani:1 near:1 agrees:1 current:1 version:1 twins:1 above:1 new:2 method:3 contrast:1 temperatures:1 full:1 simultaneously:1 caveat:1 degree:1 gathered:1 component:1 residual:2 here:2 objects:1 l25:1 others:1 based:1 strong:3 table:10 digits:1 search:1 study:2 studied:1 allows:1 prior:1 resulting:2 suitable:1 changes:2 york:1 uniquely:1 magnetospheric:1 useful:1 instr:1 apr:1 requiring:1 cylinder:2 highly:1 apj:21 glitch:1 remnant:4 decrease:1 counts:1 eddington:1 clocking:1 intensively:1 next:2 comparing:1 camera:3 archives:1 typical:1 aperture:1 iteratively:1 theoretical:1 marginally:1 more:5 pavlov:10 clearly:1 conclusions:1 under:1 emission:2 validity:1 varying:1 known:1 actual:1 must:1 states:1 account:3 claims:2 grant:1 science:2 torques:1 work:2 theories:1 abundant:1 ere:3 values:1 thin:1 ms:7 making:1 dec:1 root:1 dither:1 history:1 august:1 weaker:1 wang:3 figure:1 december:2 purposes:1 high:1 imaging:2 performed:2 ascension:1 kyr:1 spanning:2 axis:1 provide:2 discussion:1 hot:1 adjacent:2 flow:1 teter:2 parameter:3 sim:1 flanking:1 proc:1 contribute:1 may:10 broad:1 earlier:2 derived:4 caldb:1 mignani:2 date:1 derives:1 data:16 umper:2 mjd:3 natural:1 dynamical:1 pulsations:2 light:2 sensitive:1 lines:8 yielding:3 mereghetti:6 alias:1 si:2 interior:1 so:1 sn:2 fundamental:2 suggest:1 fallback:2 order:5 wind:2 longest:1 decl:1 pulsed:3 remnants:2 produces:1 over:4 fft:2 mission:3 argues:1 combinations:1 thermal:2 through:1 penetrate:1 dilemma:1 accrete:3 still:3 its:16 style:1 position:1 fit:5 τc:5 coordinates:1 actually:1 better:1 absence:3 degrees:1 fig:4 instruments:1 derivative:2 archival:1 woods:2 them:1 affected:1 greater:1 combination:1 press:1 material:1 cover:1 anticipated:1 they:3 half:1 rotation:4 now:3 day:1 matched:1 easily:1 2p:2 oxygen:4 verifying:1 january:3 university:1 level:1 identified:1 did:1 zavlin:10 kpc:2 chandra:11 mode:6 each:3 found:2 difficult:1 award:1 mean:1 individually:1 square:1 significantly:1 ek:2 ed:2 energy:7 stronger:1 ec:1 joined:1 hydrogenic:1 astrophysical:2 measurement:3 obsid:2 laboratory:1 summary:1 special:1 out:1 ktbb:1 furthermore:1 since:2 requires:1 increase:2 investigation:1 ruderman:2 squares:1 cause:1 correct:2 predicted:2 after:5 disputed:1 linear:3 causally:1 mechanisms:2 standard:3 five:1 reason:1 corrects:1 additional:1 r3:2 could:3 days:2 times:2 turn:1 place:1 due:2 ism:1 corrections:1 onto:1 first:4 origin:2 initial:1 features:2 l95:1 fits:1 spinning:4 long:1 another:3 urpin:1 pulsar:13 thick:1 i45:1 open:1 millions:1 given:2 necessarily:1 temperature:1 needed:3 introduction:1 top:1 indeterminate:1 system:1 least:3 their:8 cooling:4 accretion:17 1e:33 observations:25 iau:1 rates:4 recent:1 final:1 buccheri:2 excellent:1 spindown:1 inefficient:1 mostly:1 centered:1 haynes:1 continuous:1 zeroth:1 accurately:1 optical:2 applicability:1 dozen:1 authors:1 july:3 refitted:1 than:10 population:1 wide:1 l41:1 kine:1 determines:1 favors:2 require:4 second:1 submitted:3 matter:1 determined:3 contrary:1 iron:1 were:9 dynamo:1 geometrically:1 distinguished:1 exhibit:1 sao:1 san:1 sw:12 torque:1 spectrum:7 operated:1 headings:1 sas:1 null:1 orders:1 ray:20 strength:5 latter:1 able:3 isolated:5 predominantly:1 narayan:1 liu:2 fitting:2 potential:1 kaplan:1 finding:1 detector:1 sanwal:8 beyond:1 normal:1 barycentric:1 most:3 connected:2 but:4 significant:3 scripts:1 phase:10 measured:2 class:5 latex:1 observation:6 considered:1 average:1 implications:1 typeset:1 ks:1 points:1 funded:1 parenthesis:1 ccb:2 vasisht:1 fitted:1 quantity:1 precise:6 pks:3 spaced:1 12h:1 halpern:8 discovered:1 implying:1 radio:9 interpretation:2 uniform:1 find:2 postulates:1 xmm:18 indicator:2 slow:3 ratio:1 parameters:3 duncan:2 explain:2 jan:2 only:3 factor:1 thompson:2 thousands:1 pointed:1 achieve:2 do:2 invoke:1 accreting:4 secular:1 de:7 hailey:7 obtain:2 ionized:1 listed:3 closely:2 timing:21 during:1 years:2 nearly:1 bar:1 sources:1 luminosity:7 arxiv:1 irregularities:2 roger:2 processed:2 characteristic:4 shi:2 cycles:1 l49:1 lbol:3 intervening:1 arrival:2 set:9 computed:1 seq:1 acquired:1 mori:8 frame:1 turbulent:1 detection:2 see:3 individual:5 radius:1 result:1 cyclotron:6 close:1 best:2 subject:1 nebulae:1 review:1 nebula:1 definite:1 dipole:8 tend:1 xray:2 favor:1 enough:2 between:1 available:2 variability:3 comparable:1 recently:1 kesteven:2 nature:2 importance:1 supernova:5 weak:6 however:4 death:1 key:1 kev:9 both:3 dates:1 discernible:1 last:1 limits:1 uncertainty:4 heating:1 called:1 april:2 became:1 exceeds:2 periodogram:2 nearby:1 among:1 kirsch:2 fields:2 reprocessed:2 cc:4 period:20 environments:1 dimensional:1 twin:1 simply:1 maximize:2 wider:1 observatories:1 throughout:1 chakrabarty:1 uncorrected:1 described:3 helfand:2 piecewise:1 window:1 been:2 extraction:1 magnetized:1 much:3 slowly:2 combined:6 expected:1 ph:2 pn:14 obtained:2 myr:4 partly:1 unavoidable:1 ages:1 photon:5 precision:1 belvedere:1 coherent:6 coherently:1 refutes:1 general:1 spin:25 present:3 case:3 multi:1 unlike:1 reliable:1 empirical:1 value:3 while:4 behavior:1 error:1 rotator:1 leaves:1 procedure:1 program:1 seven:2 larger:2 wherever:1 ir:1 surface:7 quiet:3 00s:1 examined:1 claimed:1 ephemeris:2 helium:1 around:1 binary:1 proto:1 perhaps:3 j1852:4 make:3 same:1 any:2 member:1 epoch:2 several:1 neutron:6 european:1 fairly:1 used:6 columbia:2 comprehensive:1 counterparts:1 companion:1 moment:1 v3:2 uses:1 gotthelf:9 v6:1 v7:1 yuan:1 cycle:1 weakly:1 off:1 center:2 seward:2 wellington:1 analysis:9 cco:4 residuals:4 components:1 sets:2 ccd:1 model:5 comprise:1 latest:1 blackbody:2 background:2 proposed:3 less:2 being:1 when:1 newton:8 neon:1 adjusted:2 propeller:1 atomic:1 moroni:1 previous:4 glitches:1 cut:1 preprint:1 letg:2 ny:1 absorption:7 extra:1 had:2 discuss:1 source:4 valid:1 transformed:1 location:1 grating:2 formal:1 expelled:1 match:1 nasa:2 resolved:1 definitive:1 depends:1 mos:2 showing:1 possible:5 spanned:1 possibly:2 natal:1 grid:1 birth:2 psr:4 using:7 apart:1 unique:1 correcting:1 advanced:1 prominent:1 loss:2 necessary:1 follows:1 signal:1 rpc:1 flux:4 benefit:1 either:2 flickering:1 fully:2 soft:3 page:1 grouped:1 right:1 methods:1 some:1 born:5 bignami:6 mirror:1 bonanno:2 scales:1 provided:1 scale:1 bottom:2 demonstrates:1 measurements:2 magnitude:3 eliminate:1 esa:2 assuming:1 hotter:2 epic:15 yielded:1 luca:7 noise:3 power:4 tdb:1 journal:2 processing:4 agreement:1 symp:1 bp:14 although:3 offset:1 emulateapj:1 properties:3 panel:3 pipeline:1 central:1 would:6 package:1 freedom:1 completing:1 powered:1 meaning:1 range:1 km2:2 signalto:1 bolometric:1 consequently:1 software:2 xu:2 letters:2 letter:1 redshift:1 mysterious:1 image:1 ut:1 down:9 turolla:1 references:1 alpar:2 accumulated:1 nss:1 physical:1 constraint:1 span:5 log:2 area:3 support:1 there:3 knowing:1 reduction:1 specifically:1 start:1 detectable:1 milne:1 low:4 stars:3 astrophysics:1 analyze:1 was:10 assumes:1 therefore:3 lowest:1 speculate:1 faucher:3 becoming:1 jun:3 jul:6 astro:2 taken:1 related:1 basis:1 l61:1 line:4 highest:2 caraveo:3 count:1 made:1 places:1 j2000:2 pulsars:6 gravitational:1 variations:1 up:5 below:1 projecting:1 limit:11 spectroscopy:1 kaspi:3 distribution:1 radiatively:1 similar:1 display:1 penetrating:1 required:3 constant:1 directly:1 defined:2 steady:2 abstract:1 year:1 singly:1 evidence:2 periods:2 our:3 formalism:2 internal:1 regime:2 again:2 compared:1 no:5 zane:1 generally:1 reality:1 field:18 other:2 test:5 you:1 ns:5 revision:2 optically:1 polar:2 francisco:1 star:3 models:1 june:2 variation:1 generated:2 important:1 peak:4 reanalyzed:1 searches:1 independently:1 implies:3 longer:2 starting:1 age:6 interval:1 rather:1 portion:1 declination:1 time:6 accreted:2 resolution:2 original:2 |
0704.2256.txt |@word represent:1 chain:2 switched:1 rev:16 focus:1 leads:14 discreteness:2 eckern:1 consists:1 follow:1 markovi:1 gk:4 localized:1 kuk:1 depend:3 calculate:2 zone:1 concerned:1 charge:10 monotonically:2 present:1 under:2 kσ:5 case:10 takes:1 very:3 frequencies:1 mierzejewski:3 results:7 electron:11 nichols:1 matrices:2 receiving:1 presented:3 solution:1 large:2 solved:1 vector:8 pbc:3 small:1 equation:1 upper:1 work:1 approximation:6 second:1 fits:1 chen:1 will:1 what:3 stands:1 eggert:3 section:5 suggestive:1 expressed:2 current:1 lindhard:1 above:3 new:1 commensurate:2 consisting:2 focuses:1 simultaneously:1 lee:1 respectively:2 modify:1 here:3 atoms:1 2kf:3 concluding:2 consideration:1 strong:2 equations:2 legend:1 xδ:1 obtained:4 institute:1 vectors:3 allows:1 periodic:1 resulting:3 characterizing:1 usually:1 fourier:3 changes:2 helps:1 apr:1 visibly:1 visible:1 color:3 1st:1 summation:1 apply:2 unit:1 sampaio:1 standing:1 use:1 figure:3 would:1 sake:1 contains:1 quasi:1 next:1 filled:1 therefore:2 usp:1 taken:1 panel:2 theoretical:3 more:4 kahng:1 neglected:1 envelope:1 validity:1 particular:4 known:2 off:1 iii:3 silesia:1 discontinuously:1 shinohara:1 account:1 ma:2 science:4 setup:2 internal:1 remain:1 obstacle:1 values:4 following:7 averages:1 nearest:2 indicated:1 give:1 choice:1 organized:1 obc:2 indicates:1 djσ:1 crespi:1 occur:2 simple:1 information:1 schmitteckert:1 end:1 carriers:1 discussion:6 means:2 chemical:4 kri:2 fit:1 instead:1 explains:1 sin:3 simplicity:1 fr:1 mat:1 may:6 derived:2 reflect:1 plane:1 waves:4 wave:16 fl:3 response:3 ambiguous:1 short:1 physical:1 liquid:1 explicit:2 thorne:1 differ:1 green:10 inhomogeneity:1 decreasing:1 representation:2 order:3 terms:1 typical:1 fα:2 holds:1 help:2 produces:1 over:2 insight:2 mainly:1 influence:1 paper:3 through:1 still:1 its:2 diagonalized:1 derive:2 decay:4 energies:1 interesting:1 presence:4 vicinity:2 decreases:1 li:1 microscopic:1 systems:7 non:1 integral:2 investigated:1 significant:1 they:2 half:1 singularity:1 discuss:1 inhomogeneously:2 2t:3 term:1 gets:1 goldstein:1 university:1 hamiltonian:7 krive:2 wong:1 found:1 different:4 energy:3 related:2 applicable:1 inhomogeneous:2 frequency:1 static:1 expect:2 quantum:1 our:3 ev:11 eq:12 out:2 qσ:2 shown:3 matrix:4 space:1 marcin:2 open:1 nuovo:1 since:3 crucial:1 increase:1 posteriori:1 nauk:1 formula:5 get:1 induced:1 ref:1 occurs:2 shows:3 diagonal:3 free:1 standard:2 complicated:2 bal:1 wall:1 interaction:2 ministry:1 geometry:1 creates:2 turn:2 length:4 edges:1 friedel:17 first:1 zan:1 variables:1 number:1 reaches:1 transform:3 clarity:1 electronic:3 stage:1 size:1 brock:1 given:7 temperature:1 similarly:1 introduction:1 eqs:5 smoother:1 system:5 their:1 too:1 difference:1 scheme:1 gives:1 shifted:1 calculations:3 gittins:1 keldysh:5 park:2 accurately:2 believe:1 than:1 wide:2 molecular:1 determines:1 approximations:1 cimento:1 depends:1 determined:9 str:1 bauer:1 tion:1 result:1 cohen:1 curves:1 prj:1 mceuen:1 concentration:1 mantel:1 clearly:1 strength:1 built:1 der:2 lim:1 self:1 isolated:2 mechanism:1 predominantly:1 potential:2 take:2 εk:2 online:3 so:1 formulas:1 exactly:1 allow:3 investigations:3 price:1 correlation:9 impurities:1 most:3 connected:2 remarks:2 luttinger:1 kb:2 kf:4 surprising:2 calculated:5 kp:2 electrons:3 exp:2 χl:3 physics:2 sum:1 fact:1 quantity:3 tron:1 show:1 nπ:1 supported:1 relation:2 indicate:1 occupation:1 slot:1 parameters:4 explain:1 distributed:2 should:3 only:3 explicitly:1 molecules:1 various:1 local:2 equilibrium:4 do:1 distance:1 dekker:1 nanowires:5 differs:1 ones:1 nonequilibrium:5 closely:1 becomes:1 qx:1 arxiv:1 maciej:2 acknowledgments:1 investigate:3 experiments:1 analytical:5 london:2 vincent:1 simplification:1 scanning:1 requirement:1 electrodes:6 correlations:3 maximum:3 see:5 sec:1 us:1 bulka:2 close:1 electrode:3 wire:2 exponent:2 inappropriate:2 bias:10 sites:5 µr:1 µl:1 future:1 enumerated:1 between:9 crude:1 limit:1 boundary:2 approach:1 luo:1 ends:1 recently:2 amplitude:2 nature:2 importance:1 attention:1 weak:1 however:7 jr:1 incommensurate:1 vanishing:2 carbon:1 originates:1 both:3 cos:4 gorczyca:2 many:1 bethell:1 fiz:1 tour:2 retarded:6 expression:1 comes:1 comment:1 reasons:1 asymptotically:1 dimensional:5 moreover:1 confinement:1 lemay:1 kelly:1 described:4 due:3 been:9 describes:1 lr:1 kirczenow:1 sufficiently:1 fig:5 corresponding:1 suppress:1 gas:2 wires:1 hmn:1 katowice:1 last:1 spin:2 those:1 applied:4 solid:1 originate:2 value:2 remaining:2 lesser:2 ǫp:3 replaced:1 situation:2 tunneling:1 richter:1 procedure:1 unitary:1 coupled:4 almost:2 characteristics:1 binding:2 site:6 iv:3 ii:4 middle:1 ij:4 cond:1 vanish:1 currents:2 education:1 grant:1 belong:1 indistinguishable:1 same:3 noninteracting:1 several:1 independent:3 used:1 nanosystem:13 numerical:8 inhomogeneities:2 levels:1 conductors:2 kim:1 potentials:5 brillouin:1 recent:2 distribu:1 lower:1 elec:1 proceed:1 hopping:3 band:1 poland:1 well:6 analysis:3 justified:1 edge:1 experimental:2 justifies:2 model:2 rommer:1 latter:1 left:4 being:1 when:2 vanishes:1 voltage:20 polish:1 momenta:1 macroscopic:10 eigenstates:1 han:1 density:7 seems:2 weiss:2 lattice:4 concerns:1 ska:2 lett:2 easy:1 iσ:10 transformation:3 momentum:1 real:1 analogy:1 read:1 iγ:1 possible:1 test:1 increases:2 using:3 advanced:1 apart:1 necessary:1 particle:1 follows:1 δp:4 δn:1 δm:1 modified:1 niσ:1 beverly:1 become:2 downward:1 because:2 phenomena:5 repeat:1 affects:1 oscillations:26 finite:1 intact:1 transport:8 nonzero:2 lead:1 katarzyna:1 mucciolo:2 specific:1 χr:2 anna:2 equivalent:1 arbitrary:2 agreement:1 step:1 bq:6 although:1 diσ:5 properties:6 nanosystems:6 about:1 actual:1 carried:1 numerator:1 dependence:8 o:1 remains:1 range:1 carrier:2 neighbor:2 el:4 qri:1 into:2 numerically:3 suppl:2 appropriate:1 right:4 accounts:1 difficult:1 proportional:1 reservoirs:1 van:2 additional:1 assumed:3 there:1 approximate:3 fast:2 dispersion:1 anderson:1 much:1 low:2 way:1 hel:3 analyze:2 iˆ:1 function:17 tight:2 form:4 some:1 extended:1 reed:1 dkσ:2 δkp:1 berkovits:2 nanowire:10 line:2 true:1 longer:1 alivisatos:1 2πi:1 nanotube:1 up:1 devices:1 fermi:6 spectroscopy:1 demonstrate:2 distribution:10 similar:1 motion:1 strongly:4 constant:1 describe:1 general:1 single:4 exist:1 collier:1 formalism:1 check:1 regime:1 ni:1 functions:11 nm:1 nn:1 no:2 dashed:1 whereas:3 generally:2 defined:2 application:1 nlσ:1 conditions:2 details:2 spatial:4 department:1 p03b:1 elements:5 meaning:1 important:2 dpσ:2 additionally:1 structure:1 impurity:8 ǫk:9 coupling:11 dω:2 assume:3 4t:2 heath:1 |
0704.2257.txt |@word aoki:1 gt:2 partial:4 consider:2 gp:1 caused:2 magnetic:1 particular:4 results:5 illustrated:1 commute:1 localized:1 gr:1 whose:1 inverse:1 depend:1 groundstate:1 critical:7 helps:1 kδ:1 include:1 tc:1 kσ:5 case:2 supported:1 ckσ:4 without:3 wave:5 electron:4 figs:1 softened:1 experimentally:3 matrices:1 condition:1 hamiltonian:9 solution:15 large:4 solved:3 demonstrated:1 yale:2 small:8 concluded:1 smaller:3 zh:2 occurrence:1 findings:2 renormalized:1 direct:2 alhassid:6 jump:11 second:2 qualitatively:3 dynamics:1 estimated:1 odd:10 linear:1 even:12 fact:2 expressed:1 reminiscent:1 bernhard:1 above:1 new:2 increasing:5 method:1 contrast:2 body:4 full:1 led:1 exchange:32 respectively:1 spacing:5 shankar:2 here:6 ranges:1 mev:3 focused:1 compressed:1 making:1 slater:1 strong:1 equations:3 superconductor:2 obtained:2 solid:2 search:1 increments:1 shift:1 study:4 studied:1 reports:1 couplings:1 trial:1 resulting:1 hospitality:1 narrow:1 makes:1 almost:1 followed:1 projection:2 apr:1 explained:2 prefer:1 altshuler:2 sloane:1 apply:1 rotter:1 total:10 use:2 takes:1 usa:1 remains:1 positive:1 girvin:1 tabulated:1 few:1 nucl:1 monotonically:1 therefore:2 taken:1 theoretical:3 diagrams:6 more:4 separated:1 flat:1 separates:1 vk:3 becomes:1 eν:1 connecticut:1 supercon:1 thouless:3 known:1 hold:1 iii:1 states:2 equation:2 work:5 xing:2 niobium:4 column:2 fock:1 values:17 thin:1 following:1 cond:2 deb:1 trans:1 scatter:1 littlewood:2 compare:3 renormalization:1 give:1 predict:1 neglected:1 high:1 numbers:6 degenerate:1 abrikosov:1 occur:6 portional:1 end:1 holds:1 eigenenergies:1 chemical:3 how:1 flanders:1 pure:1 parameter:5 charging:1 description:1 staircase:4 may:1 fulde:1 diagram:7 plane:8 saxena:1 fg:1 choice:1 fm:14 realized:1 physical:1 neck:1 third:1 lines:4 correspond:2 so:2 correlation:2 sc:14 increase:3 order:3 typical:2 aleiner:2 considerations:1 already:1 through:1 affect:2 argued:1 kinetic:2 still:2 ieee:1 its:2 blocked:4 gµb:22 derive:1 symmetry:1 chandrasekhar:1 la:1 energies:1 exact:13 presence:10 decreases:1 li:1 destroyed:1 yuzbashyan:1 absence:6 distinguishing:1 fig:22 zhou:2 schmidt:2 maximal:2 eventually:1 non:1 good:2 diagonalize:1 propose:1 material:2 band:1 emf:3 equidistant:4 effects:2 they:2 half:1 eµ:6 yu:1 discuss:1 brouwer:2 term:6 finite:5 2s:8 fully:2 university:2 level:7 sufficiently:1 filling:1 magnitude:1 2c:1 found:5 higher:2 mean:23 heavy:1 en:1 financial:1 significantly:1 mesoscopic:5 energy:15 ferromagnetism:5 idea:1 related:1 conductance:2 see:12 expect:1 separating:1 our:2 eq:2 mat:2 shown:12 matrix:1 discrete:1 furthermore:3 since:2 rev:23 research:1 particles:1 surprise:1 ref:8 occurs:3 shows:1 paramagnet:1 theory:5 possibility:1 falci:1 polarize:1 formation:1 estimate:1 e2:1 pairs:5 interaction:18 transition:8 levels:19 place:1 fiz:2 hence:1 teor:2 strictly:1 first:4 there:5 probability:1 occupations:1 omitted:1 number:17 approximately:1 thick:1 ying:1 quality:1 size:8 given:16 interesting:2 introduction:1 leading:1 top:6 system:5 construct:1 intermediate:18 bedell:2 tune:1 variational:1 speaking:1 larkin:1 shifted:2 ratio:1 asymmetric:1 reversed:2 exactly:1 braun:1 larger:9 part:2 haven:1 approximation:9 polarized:8 malhotra:1 effective:1 approximations:1 zero:4 matter:1 determined:6 doubly:7 regions:1 were:3 kf:1 treated:1 exhibit:1 lowest:3 shrinks:2 pro:1 spectrum:8 crossover:3 seen:2 occupied:13 any:1 relatively:2 strength:11 studying:1 latter:1 isolated:1 metallic:8 onset:1 liu:1 potential:5 completed:1 populate:1 though:1 sets:1 diamagnetism:1 impurities:1 most:1 successive:1 pair:1 subset:1 measured:1 volume:1 acknowledges:1 constructed:1 observation:1 gorkov:1 a550:1 average:1 stronger:3 universiteit:1 reflecting:1 electrons:14 physics:4 dot:1 sector:2 stoner:1 ferrell:1 show:4 text:1 random:1 minimizing:2 relation:1 solutions:1 joglekar:1 find:4 ground:17 based:3 parameters:5 than:3 only:4 pairing:45 factor:1 do:2 means:1 dependent:2 de:1 db:1 expectation:1 cannot:2 tallon:1 ˆk:1 approach:2 arxiv:1 tuned:1 investigate:1 experiments:2 predicted:2 rombouts:2 london:3 fixed:7 magneton:1 set:8 exists:3 seniority:3 correlations:24 observed:5 depends:2 radius:2 result:2 enhanced:1 discussions:1 best:1 situation:1 phases:3 row:4 fang:2 placed:1 subsequent:1 ralph:2 tend:1 boundaries:5 favor:2 state:33 µn:1 various:1 rupp:1 closed:1 between:4 fermi:5 boundary:2 paramagnetic:2 across:1 µb:1 terms:3 nature:3 weak:3 focus:1 however:7 js:44 orbitals:2 fluctuations:2 ferromagnet:1 thank:1 suggested:1 both:4 last:1 region:3 τi:1 zeeman:28 chosen:1 grain:33 polarizing:1 disappears:1 experimental:3 con:1 reside:1 eksp:2 solving:2 2no:2 simple:1 corresponds:1 height:1 exhibits:2 maximize:1 respect:3 jetp:2 described:2 tuning:3 pfleiderer:1 three:2 been:1 glazman:1 describes:5 combined:1 empty:4 direction:1 contribute:1 partly:2 sectors:1 sufficient:2 subspace:1 gap:14 bulk:5 clogston:1 observe:4 external:6 maximally:1 spin:88 2ǫi:1 present:3 applied:1 grains:9 pacs:1 ǫk:10 originate:1 value:12 remaining:2 will:1 while:3 exist:1 property:1 gent:2 weakens:1 versus:3 would:2 coupled:2 chaotic:1 vi:1 vj:3 bital:1 thus:5 iv:1 ii:1 characterize:1 superconducting:11 confining:2 fermion:1 dukelsky:1 orbital:1 different:4 twofold:1 grant:1 generic:1 renormalize:1 same:3 pauli:1 dimensionless:1 several:1 difficult:2 independent:1 used:4 closest:3 tinkham:1 effect:4 hand:1 moment:1 compared:3 hartree:1 normalization:1 lower:4 center:2 minimize:2 whole:1 no:14 well:1 roughly:1 analysis:1 bohr:1 materials:1 dashed:3 quantitative:1 model:8 example:3 left:3 magnetization:1 superconductors:1 vanishes:1 bandwidth:2 relevant:1 predicts:2 useful:1 macroscopic:1 eigenstates:4 polarization:8 macdonald:1 9a:1 valid:2 lett:11 mod:1 spin1:1 eigenstate:1 momentum:1 9b:1 insensitive:1 increased:1 rnb:1 breaks:1 coexistence:8 early:1 increases:6 belgium:2 using:4 unique:1 desc:1 like:3 particle:8 qualitative:1 specific:1 unstable:1 either:1 reduced:1 accessible:3 hallmark:1 right:5 kσσ:1 shen:2 creation:2 competition:3 choosing:1 moreover:1 proper:1 cooper:1 truncate:1 bottom:6 affects:1 separate:1 does:4 assuming:1 steps:4 minimal:3 presented:1 sherman:1 scientific:1 rep:1 jumps:15 each:5 agreement:1 expansion:1 step:1 singly:7 ignored:1 von:2 panel:6 comparison:1 stone:1 ferromagnetic:8 coexist:3 discussed:2 dependence:1 costs:1 range:1 plus:2 ψs:4 referred:1 em:2 arcsinh:1 inclusion:2 previously:1 within:5 due:1 down:5 phase:29 because:2 determine:1 sov:2 operator:3 reducing:1 vii:1 ovchinnikov:1 mkf:1 statistics:1 van:3 comparing:1 intrinsic:1 support:2 initial:1 long:2 capacitance:1 appl:2 low:2 was:11 function:8 singleparticle:2 complete:1 form:3 hs:1 but:5 change:1 films:1 staircases:1 hm:1 line:3 partially:5 made:2 applying:1 supr:1 up:1 quantitatively:1 paired:4 note:1 limit:1 uj:2 hemispheric:1 problem:1 panels:4 similar:5 regimes:1 detailed:1 changes:1 gong:1 constant:5 metal:1 universal:3 describe:4 determinant:1 metals:3 general:1 quantum:4 single:8 pˆ:1 laboratory:1 corresponding:4 doe:1 regime:26 functions:3 nk:3 sˆz:1 nm:4 dotted:1 variety:1 na:1 nb:1 when:1 detail:1 field:46 other:1 nr:3 er:1 conclusion:1 zheng:2 denote:2 excitation:1 superconductivity:3 models:1 gas:1 fazio:1 peak:2 describing:1 gets:1 correlated:1 coupling:14 fund:1 required:1 together:2 ensuring:1 came:1 time:2 delft:2 richardson:9 requires:1 having:1 bcs:5 |
0704.2258.txt |@word neighbors:1 represent:1 monte:1 code:37 gs:12 consider:4 caused:1 copy:1 results:24 hawaii:1 four:5 approximable:2 gt:1 ga:7 edu:2 consists:5 sci:2 denotes:10 decisions:1 children:2 scs:1 row:5 whose:1 depend:1 analytic:1 aug:1 graph:42 concerned:1 deterministic:4 young:1 removal:2 finally:2 hardness:28 under:7 stochastic:1 nodes:33 awgn:11 inform:6 applied:1 straightforward:5 returning:1 very:5 rise:1 removing:1 focus:1 corollary:1 worst:2 entries:3 24th:1 matrices:2 condition:2 squares:1 exponential:1 approximability:1 presented:4 transmission:3 proc:1 notes:1 list:1 solution:2 large:3 discrete:1 vector:7 phase:1 min:1 structured:1 section:17 small:14 configurations:6 unsatisfied:4 zm:3 specializes:1 neighborhood:2 zi:2 findings:3 arya:1 parameterization:2 estimates:3 direct:1 past:1 fold:1 rate:3 cost:1 pass:1 rigorous:1 further:1 carlo:1 peredachi:1 linear:13 even:16 established:1 errors:2 trapping:62 cast:1 contributions:1 sum:2 brief:2 decoding:24 current:1 koetter:1 version:1 3n:1 above:7 new:9 construction:5 method:3 body:1 proietti:1 full:3 degree:34 respectively:2 ist:1 equals:1 answers:1 june:3 believed:1 sb:1 objects:2 greedy:3 concluding:1 along:3 strong:2 equations:5 appears:4 change:1 every:6 search:4 incoming:1 suitably:1 root:2 study:1 larger:1 allows:1 suggests:1 resulting:2 carleton:1 wl:1 usually:6 krishnan:1 slope:1 uniquely:1 control:1 via:1 inference:2 ratios:1 family:1 stern:1 apply:2 establish:2 linearly:1 wang:1 use:2 refers:1 additive:1 certificate:1 codewords:7 remains:1 positive:1 contains:6 predictions:1 next:6 few:1 coverings:1 call:5 therefore:5 tahoe:1 vi:12 scope:1 themselves:1 iteratively:1 until:1 more:7 constructed:2 formally:2 outputs:1 stoc:1 factor:3 corrected:1 pairs:1 award:2 vm:1 discussed:1 particular:2 known:16 kulkarni:1 cardinality:10 preserving:2 had:1 chertkov:1 kumar:1 springer:2 include:1 word:2 augment:1 ml:3 work:3 mi:1 measures:1 remain:1 pseudocodewords:2 values:4 achieve:1 following:7 strategies:1 trans:5 specialized:1 example:6 proof:28 conference:1 claim:3 weaker:1 reserved:1 dual:1 figure:7 give:1 process:2 messages:1 decoders:9 organized:1 near:3 high:1 claimed:1 minimum:30 performed:2 arise:1 sought:1 hit:1 mn:1 verlag:1 information:6 ramesh:1 counting:1 end:2 lemma:13 january:2 provide:5 s1:3 means:1 sudden:1 csc:1 machine:1 fpt:8 correctness:1 adjacent:1 optimal:6 parameter:11 belongs:2 product:2 description:3 nl:1 binary:5 may:7 turing:1 stacs:1 after:1 derived:1 different:2 collection:2 restrict:1 tractability:3 applications:2 designed:1 faculty:1 lenstra:1 maj:8 meaningful:1 constants:1 stepanov:1 short:2 dynamical:1 third:2 resemble:1 sr:3 grant:1 lines:3 correspond:3 parameterized:7 element:6 rather:2 complexity:19 algorithms:13 automatically:1 asserts:1 decreasing:1 representation:1 subsequently:1 operate:3 orponen:1 bipartite:10 se:1 operations:1 restriction:3 approx:1 holds:1 poor:1 aided:1 september:1 over:9 flips:1 murali:1 symbols:4 paper:3 through:3 same:6 statistical:1 lattices:1 y1:3 existence:3 y3:2 y2:2 ieee:8 its:5 before:1 remark:1 termed:3 chosen:4 exact:3 pcp:1 solving:2 estimating:5 according:2 algorithmic:2 copies:2 main:2 defining:1 setting:3 texas:1 maximal:2 freeman:1 non:7 good:13 running:4 greater:2 santa:1 arora:1 indexing:2 introduce:2 flipping:2 february:1 they:4 symposium:5 complement:1 milenkovic:2 discuss:1 structural:2 kth:1 represents:4 term:4 finite:1 intractable:1 instances:3 always:2 university:2 tran:1 establishing:1 capability:2 sufficiently:3 iff:15 transmitted:1 editor:1 l0:6 each:23 found:1 2n:4 polynomially:1 locate:1 side:4 characterized:1 referred:3 subset:4 el:2 ei:4 directly:1 weight:11 independent:3 doing:1 series:1 hard:35 gaussian:1 manifests:2 vote:1 see:3 trevisan:1 combining:2 our:11 approximated:1 beyond:1 partial:1 shannon:2 out:3 category:1 ftp:2 shown:8 rp:11 matrix:18 space:2 furthermore:7 urbana:1 research:3 combinatorial:3 investigation:1 reader:2 formula:1 get:1 induced:8 correct:5 weaknesses:1 log2:1 theory:21 easily:1 free:1 standard:1 vazirani:1 aachen:1 included:3 encountering:1 habilitationsschrift:1 org:1 phd:1 likelihood:4 additional:1 definition:10 uiuc:1 cycles:3 r0:6 r1:6 recovering:1 dgs:11 determining:2 transition:1 iterative:16 so:3 times:2 silicon:1 length:10 edges:7 exponentially:1 u4:1 consequence:10 margulis:2 support:2 first:9 xj:1 recall:2 xi:1 xn:1 probability:7 relate:1 variables:2 assumptions:2 number:9 rank:3 channels:1 randomized:1 floors:2 dominating:1 u3:2 another:1 robust:1 carry:1 impossible:2 message:4 clarity:1 electronic:1 xt:1 size:21 given:20 checked:1 zj:1 similarly:3 introduction:1 test:1 urbanke:3 system:2 least:10 their:7 returns:1 assumption:1 rates:1 passed:1 entcs:1 white:1 recent:1 structures:1 final:2 recovered:1 scans:1 exploring:1 paso:2 citeseer:1 inefficient:1 relationship:1 mackay:1 exactly:4 accurately:1 stockmeyer:1 mceliece:1 part:3 signaling:1 peleg:1 x2:2 x3:2 july:2 operates:1 than:9 x4:2 approximation:34 johnson:2 showed:2 bec:8 require:2 iteration:2 second:6 solomon:1 classes:2 berlekamp:1 speaking:1 were:3 ber:3 gives:2 w2:2 exhibit:1 enforced:1 failing:1 false:1 barg:1 generality:3 41st:1 correction:2 measure:1 argument:1 generalization:2 elem:8 zt:2 say:13 manner:2 need:2 elsevier:1 null:1 raz:1 any:26 viewed:1 sa:1 wilson:1 constructions:2 computationally:1 bers:2 zero:8 sj:1 efficient:2 zp:12 latter:3 si:7 thorough:1 note:7 majority:6 subjects:1 simplified:1 finding:11 performance:9 subject:1 channel:15 accuracy:2 circles:1 culminated:1 unless:17 fundamental:1 transactions:1 informatsii:1 incidence:2 systems:3 zigzag:28 most:10 regular:6 connected:13 plus:1 definitions:3 pair:1 future:1 extremely:1 class:14 involving:1 sub:4 prove:3 invoking:2 enumerating:3 especially:1 considered:1 neighboring:1 cover:21 vertices:20 order:1 2nd:1 graphs:15 proceedings:6 hi:2 hamming:1 costello:1 physics:1 microsoft:2 fact:9 precise:2 programming:1 show:14 reductions:4 supported:1 rediscovery:1 reference:1 minimizing:1 solutions:3 determined:1 trivial:1 find:12 decade:1 universitaet:1 impact:1 ni:1 indicator:1 x1:3 based:4 parameters:3 operational:1 failed:2 only:12 going:1 bsc:8 thresholds:1 columns:4 do:1 erasure:4 dominant:2 establishes:1 notation:2 distance:7 champaign:1 vu1:3 assumed:1 processing:1 cannot:4 instance:2 despite:2 report:1 during:1 dt:1 conjunction:1 procedures:4 fe:1 ramanujan:1 hall:1 regarding:2 covering:2 equality:9 arxiv:2 sunil:1 remove:1 consisting:1 twice:1 nκ:1 discs:19 common:1 ensure:2 contain:3 analytical:1 including:2 fixed:11 telatar:1 cole:1 available:3 set:107 thesis:1 exists:17 achieved:1 tree:8 achieves:1 respect:3 zigangirov:2 maximum:8 observed:3 checks:2 depends:1 computer:7 w3:1 result:10 w1:5 fail:3 terms:3 theoretic:1 best:2 techniques:6 babai:1 appear:2 fails:1 still:1 capacity:1 currently:1 equal:1 kann:1 icalp:1 atri:1 behind:2 smallest:14 various:1 between:1 ui:12 approach:3 email:2 hence:7 attention:2 recently:1 august:1 wa:5 sections:1 importance:1 darpa:1 wm:1 punctured:1 analogues:1 however:1 wi:6 regime:1 news:1 suppressed:1 relying:1 improve:1 received:2 instant:1 avoid:1 career:1 many:4 taking:1 annual:2 l2:1 f2n:2 f2m:1 agree:1 april:1 connection:1 improves:1 figures:1 instanton:1 variance:1 passing:4 estimation:3 com:1 finds:1 monograph:1 otherwise:5 comment:1 among:1 ci:3 relevant:1 cn:1 triples:7 characterization:3 within:6 overview:2 ca:1 corresponds:2 height:2 dimensional:7 prone:1 polynomial:28 proved:2 considers:1 society:1 pr:4 consuming:1 described:2 basis:1 addition:3 create:4 computing:6 due:5 been:1 z1:2 hitting:4 mathematics:1 reduction:10 workshop:2 interest:1 certain:1 expected:1 stands:1 empty:1 define:2 graphical:4 corresponding:9 both:2 sweden:1 subspace:2 andrew:1 isit:2 observe:1 c3:1 c2:2 c1:2 denote:2 those:2 c4:1 case:7 subsets:3 comput:2 reliable:1 tractable:4 safra:1 single:1 value:4 will:9 dept:1 while:8 optimization:3 replaced:1 international:1 error:24 stopping:46 di:4 property:3 guide:1 procedure:1 vb:3 vectors:1 mexico:1 memoryless:1 characteristics:1 vj:5 simulations:1 submatrix:1 instantons:3 vn:4 encountered:2 itself:2 im:3 ramifications:1 mcgregor:1 ym:1 vui:1 fellows:4 sequentially:1 capture:1 containing:1 since:14 author:1 lengths:1 alphabet:1 make:1 enumeration:3 campus:1 undirected:1 html:3 arguments:2 widely:1 largest:2 several:3 grows:1 evidence:1 fairly:2 used:14 http:4 assigns:1 solved:2 prohibits:1 mannila:1 appearances:1 upon:2 hand:5 parametrized:2 v1:12 v2:6 codes:53 uses:1 architectures:1 internal:3 pdf:1 frequently:3 gallager:6 focal:1 e1:2 relies:1 compendium:2 newsletter:1 programs:1 nevertheless:1 expression:1 ua:4 floor:10 well:7 roughly:1 analysis:3 without:3 patterns:1 richardson:4 edge:2 sets:48 coordinate:2 position:1 ccf:1 left:8 construct:3 proposed:1 less:2 being:2 accurate:1 dmcs:1 obtain:1 ninth:1 press:1 vardy:4 integer:3 yes:1 bit:2 november:1 fsttcs:1 adding:1 preprint:3 generator:4 density:12 correcting:1 δmax:4 sudan:1 guaranteed:1 lake:1 improvement:1 simple:2 add:5 other:5 treatment:1 theorem:18 input:6 extensive:1 psu:1 remaining:1 identical:2 aspects:1 alternatively:2 showing:3 possible:1 indexed:2 increases:1 know:1 ldpc:28 confined:2 using:2 emergence:1 intersection:1 seattle:1 pinsker:3 mod:1 loss:4 theor:1 sizes:3 δv:2 follows:16 signal:1 israeli:1 consensus:1 steps:1 either:3 sparse:8 arbitrary:2 output:1 δc:7 parity:21 www:4 right:2 methods:5 namely:1 polylog:1 some:19 cs:1 repeat:1 examples:3 specified:3 computers:1 multiple:2 intuition:2 proofs:3 matching:8 intractability:2 provided:3 vol:15 proceeding:1 nondeterministic:1 lead:1 stronger:2 gvc:2 decision:3 does:4 exposition:1 proj:1 provides:1 assuming:1 yields:2 moderate:3 imply:3 augmenting:1 minimal:2 refer:1 optima:1 erased:1 chandran:1 noise:3 run:1 vertex:13 equivalent:1 l1:5 pp:23 illustration:1 step:1 symp:1 convex:1 although:1 inherent:2 approximating:8 includes:1 properties:2 science:4 would:2 constraint:3 column:2 theorems:2 introduces:1 o:20 simulation:3 practical:1 union:1 must:3 subgraph:7 neighbor:1 germany:1 constraints:2 consequently:7 block:5 em:1 computational:3 letters:1 paritycheck:1 pertaining:1 communication:2 codeword:16 bound:3 nsf:2 three:15 remarks:1 odd:8 because:4 references:1 url:1 determine:2 elementary:6 proportional:1 acm:1 approximately:1 often:1 rely:1 rows:4 van:1 log:16 probabilistic:2 strictly:1 there:30 u1:9 approximate:18 long:3 u2:4 ordered:2 start:1 downey:3 low:16 terminates:4 valley:1 was:11 function:2 complete:8 form:8 offer:1 phenomena:2 but:10 volume:1 failure:1 repeated:1 properly:1 reed:1 heuristic:1 decoder:14 russian:1 vl:2 exhaustive:1 observation:1 lncs:1 made:1 compute:1 improved:2 consist:2 garey:2 transmits:2 up:2 us:2 theoretical:3 um:1 ul:2 below:1 limit:2 ballast:21 uk:10 uj:2 computable:1 problem:63 similar:6 called:4 detailed:1 constant:22 yj:2 defined:4 implications:1 abstract:1 describe:2 twenty:1 covers:1 general:3 engineering:1 exist:4 formulation:2 journal:1 families:1 whittle:1 clementi:1 check:37 defines:1 again:1 compared:1 completeness:2 no:34 tuebingen:1 when:10 v3:1 illinois:1 interested:2 electrical:1 special:3 papers:1 np:44 guruswami:1 er:4 conclusion:1 node:19 briefly:3 elements:3 problemy:1 symbol:7 problems:34 precision:1 coding:6 important:2 bounded:7 suited:1 studied:1 variable:8 n2:1 structure:5 searches:2 implies:4 auxiliary:1 algorithm:50 assume:9 tanner:27 factors:1 curve:1 rule:1 notion:7 exhausting:1 equivalently:1 attaining:1 time:30 far:1 failures:2 signalling:2 schechtman:1 original:1 once:1 |
0704.2259.txt |@word limited:2 gu:1 code:5 partial:1 consider:3 chain:1 maximum:1 alf:1 interference:3 trappe:1 osu:1 results:10 four:1 hannel:3 entropy:3 computation:1 edu:3 consists:1 follow:1 remarkably:1 denotes:2 revealed:2 causes:1 restrictions:1 compact:1 amplification:1 depend:2 leung:2 technique:1 vs:1 send:7 presents:1 finally:6 critical:2 under:6 ven:1 stochastic:4 nodes:5 awgn:8 presentation:1 worth:1 resources:2 random:6 damen:1 confidential:9 far:2 zamir:1 focus:2 wiretap:43 equivocation:6 every:1 lecture:1 application:1 difference:3 exact:1 securely:2 illustrated:1 randomness:2 achievability:5 publicly:1 encoding:1 transmission:6 proc:4 notes:1 solution:1 noiseless:13 discrete:11 vector:1 erasures:2 second:1 markov:1 unaware:1 upper:4 smaller:1 degrading:1 liang:2 direct:1 rate:20 perspective:3 rigorous:1 further:2 casual:1 linear:1 even:3 established:4 what:1 errors:1 plays:1 advantageous:1 fact:2 section:9 decoding:5 access:6 version:7 goes:1 sup:5 judicious:1 shared:1 public:21 pioneering:1 full:6 simultaneously:1 notions:1 degree:1 exchange:2 respectively:6 never:1 component:1 equals:2 here:9 agreement:5 following:14 slow:1 free:1 irrespective:1 active:2 along:2 strong:2 observing:1 differential:1 obtained:1 sending:3 balance:1 sender:1 receive:7 study:1 studied:6 allows:1 ignoring:1 suggests:1 resulting:1 special:4 inspires:1 uniquely:1 pxz:1 pxy:1 secure:7 cairns:1 extra:1 apr:4 requiring:1 manage:1 natural:1 private:11 2δt:2 achievable:10 causal:2 narayan:2 jan:1 use:4 additive:17 figure:4 codewords:3 remains:3 positive:7 destination:79 chooses:2 next:2 scenarios:3 memoryless:7 noting:1 opposed:1 odulo:2 type:1 achieving:3 more:12 introducing:1 sharing:3 knows:3 relay:7 organized:1 px1:3 problem:3 aware:1 instrumental:1 particular:3 known:9 cases:7 iv:2 iii:4 bloch:2 must:1 valued:2 sheds:1 korner:1 science:2 challenge:1 work:8 modified:1 oct:3 regions:2 values:1 sent:3 ull:1 learn:1 pioneered:1 trans:21 example:7 proof:8 control:1 rodrigues:2 compare:2 weaker:1 tap:3 challenging:3 stream:1 abelian:1 process:2 sense:2 share:1 purposes:2 tekin:2 effectively:1 assumptions:1 performed:2 allowed:3 calculated:1 information:55 needs:3 seattle:1 csi:1 cryptography:1 provide:1 verify:2 discussion:19 acts:2 workshop:2 delay:1 maps:3 instead:2 ordinary:2 constraints:1 parameter:1 csp:15 mar:2 lai:4 may:9 max:11 after:1 derived:1 elusive:1 constraint:2 applications:1 explored:1 snr:1 choice:3 data:1 gaussian:13 attempt:1 effective:2 light:1 lines:1 departure:2 element:2 rather:1 wishes:2 so:7 allow:1 keeps:2 trellis:1 definitions:3 order:2 typical:1 csf:12 resurgent:1 feedback:86 ith:2 considerations:1 over:32 fλ:4 symbols:1 performance:4 wiener:1 paper:4 through:5 unfavorable:1 existence:3 satisfies:3 still:3 ieee:27 its:9 before:2 perfect:22 superior:1 group:3 render:1 how:1 duplex:17 interesting:1 solving:1 li:1 forms:1 absence:9 offers:1 condition:3 derivative:1 main:21 maximal:1 non:5 crucial:1 motivated:1 propose:1 outlined:1 practice:1 wire:3 fig:4 introduce:3 motivates:1 they:1 half:10 nov:1 now:7 outlines:1 nor:1 possess:1 represents:2 transmitter:2 finite:2 equality:2 2r:1 always:4 university:4 crypto:5 realistic:1 inequality:1 transmitted:8 reasonable:1 each:5 feeds:1 side:2 characterized:3 referred:1 individually:1 el:5 schemes:3 significantly:2 meets:1 generation:1 directions:1 idea:2 used:10 obtains:1 combining:1 our:26 operation:5 summary:1 event:1 shannon:8 out:2 large:2 shown:15 jul:1 matrix:2 solved:1 furthermore:3 since:7 induces:1 research:3 increase:4 re:1 rf:19 adapt:1 denoted:1 rm:5 rn:1 size:6 suffices:1 shows:1 counterpart:1 foundation:1 ece:1 log2:1 theory:30 causally:1 written:2 dmcs:1 cheong:2 possibility:1 quite:2 terminals:3 necessarily:1 complicated:1 term:1 region:5 generate:2 mimo:1 log:6 definition:3 could:2 transition:1 messages:15 creates:1 length:4 place:1 hence:20 dec:2 first:4 feed:5 ntroduction:1 probability:13 zm:1 fading:4 variables:3 coding:10 number:1 channels:23 sept:1 done:1 relations:1 message:11 open:1 gamal:5 take:1 given:7 long:2 leverage:1 privacy:1 unknown:3 sep:1 system:3 least:1 needed:1 assumption:1 draft:21 observations:3 realization:3 rates:2 white:6 perfectly:4 structures:1 naturally:1 gives:1 fraction:2 enhancing:2 behind:1 rsf:3 continuous:4 shitz:1 wisdom:1 broadcast:3 part:8 differentiate:1 authors:1 kept:1 july:2 copy:1 than:8 mclaughlin:2 scheme:32 unfortunately:1 showed:3 princeton:4 taken:1 zero:5 submitted:10 future:2 were:2 y0i:2 sees:2 ignores:4 generality:1 ani:1 generalization:1 randomly:6 outperforms:1 manner:1 need:2 seen:1 any:18 viewed:1 min:1 check:1 studying:1 internat:2 able:2 csisz:5 mechanism:1 note:1 liu:2 potential:1 generalized:2 transmit:7 algorithms:1 coincide:1 being:2 channel:148 allerton:1 play:1 converse:2 unless:1 fundamental:5 transactions:3 systems:1 shaping:1 extending:3 said:2 strikes:1 letter:4 codeword:6 nothing:1 hide:2 maric:2 bsc:17 volume:1 reduces:1 characterizes:2 considered:8 average:1 untrusted:1 dimension:4 necessary:1 points:2 exp:1 notion:3 eliminating:1 multilevel:1 optimal:8 barros:2 show:3 definite:1 supported:1 implying:2 motivate:1 degraded:11 uniform:4 trivial:1 help:1 current:1 x1:52 based:5 parameters:3 implementation:1 distributed:9 negligible:1 should:1 terminal:2 lemma:6 only:13 pointed:1 achieve:9 dn:1 do:3 erasure:5 mixture:1 handle:1 above:3 notation:1 meanwhile:1 overall:2 congruent:1 cannot:1 legitimate:1 words:2 new:2 timing:1 compute:1 enjoys:1 precoding:2 conditions:2 arxiv:1 fixes:1 consisting:1 common:5 ohio:2 vincent:2 approaching:1 revealing:1 set:10 modulo:31 exists:7 achieved:2 national:1 bounds:5 achieves:7 mentioned:1 see:2 computer:3 result:6 wyner:6 y0:7 close:1 theoretic:7 techniques:1 exploited:1 capacity:50 wa:1 erez:1 please:3 symmetric:4 arbitrary:2 state:3 various:1 closed:1 between:7 drawn:1 neither:2 approach:11 luo:1 available:2 recently:1 creating:1 extend:1 adding:1 weak:1 however:3 jr:3 analyzes:1 practicality:1 jointly:1 key:28 analyzed:2 relying:1 both:10 limits:2 reported:1 many:3 taking:1 density:1 equal:5 against:1 enabling:1 chosen:2 receives:2 receiver:3 variance:5 argue:1 arbitrarily:1 forney:3 relevant:1 afterwards:1 point:3 simple:2 corresponds:2 venues:1 eferences:1 dimensional:5 concluding:1 exploit:1 grants:1 maurer:5 ahlswede:1 cs:12 proved:2 throughout:1 entail:1 considering:1 pp:19 described:1 argued:1 lattice:10 addition:4 encryption:14 px:9 py:5 due:3 been:4 strategy:1 instantiations:1 secret:16 yan:2 combined:1 interest:2 basic:1 mean:1 choose:1 adopted:1 corresponding:5 easy:2 confuse:1 received:15 sufficient:1 ensuring:1 equations:2 input:6 denote:6 present:2 case:16 multi:2 novel:4 unlike:1 reliable:1 blahut:1 value:2 choices:1 will:9 technical:2 while:4 error:3 situation:1 property:2 inspired:1 characterizing:1 pessimistic:1 identical:1 larger:2 hoping:1 helper:3 almost:3 vi:2 thus:5 according:1 ii:5 itself:2 converts:1 il:1 conf:1 ready:1 yˆ:5 trusted:1 binary:4 different:4 authenticated:3 perform:1 alphabet:10 orner:1 same:11 clearly:1 pad:1 largest:1 several:3 independent:10 extended:3 mmse:1 keys:2 monticello:1 mutual:1 hand:5 moment:2 levels:1 uses:3 user:1 infinite:1 opportunity:1 outputs:1 lower:3 estimation:1 off:1 scenario:5 yates:3 nevertheless:1 well:2 obviously:1 without:9 sets:3 landmark:1 claims:1 model:14 paradigm:9 loss:1 spend:1 know:5 understand:1 exploits:2 listening:2 proposed:8 less:4 transmitting:1 captures:1 identically:1 yener:2 obtain:6 rest:1 judiciously:1 proposes:1 underlying:1 integer:1 simo:1 incurring:1 previous:3 wiretapper:61 generous:1 poses:1 generator:2 tight:1 bell:2 except:1 signals:2 source:62 interested:1 samples:1 theorem:9 role:5 guarantees:1 remaining:1 specializing:2 real:2 australia:2 aspects:1 increased:1 adversaries:1 easily:3 optimality:1 capacities:1 unlimited:2 possible:2 possibly:1 increases:1 marked:2 burden:1 secrecy:57 using:7 unique:1 moreover:2 mod:16 multiplexing:1 wˆ:2 imposed:1 sizes:1 exploiting:2 interestingly:4 serves:2 loses:1 communications:2 superiority:1 either:1 follows:4 output:7 security:2 works:1 signal:40 cooperation:1 node:1 because:2 classical:1 sequence:1 sends:6 some:7 back:2 understood:3 towards:1 intersymbol:1 respect:2 proper:1 multiple:6 practical:1 confusing:1 nonzero:1 vol:17 proceeding:1 cns:1 dropping:1 decision:1 faction:1 per:5 pen:3 does:10 ucsd:1 assuming:1 chains:1 refer:3 illustrate:1 pr:7 noise:13 algorithmic:1 power:1 june:1 equivalent:10 processing:1 conventional:1 step:1 although:1 renders:1 coset:2 finding:2 noisy:32 comparison:1 about:4 prove:1 carried:1 extension:2 simplify:1 eavesdropper:4 freedom:1 intensively:1 discussed:3 chance:1 o:1 hinge:1 pz:3 wolf:4 insufficient:1 introduced:4 slightly:1 other:7 exactly:1 computational:1 significant:1 communication:5 into:1 bound:2 sphere:1 remarks:1 appropriate:1 caire:1 primarily:1 destroys:1 additional:3 few:1 assumed:5 there:9 specifically:5 describes:1 way:1 forward:4 was:15 cancel:1 therefore:2 function:5 receiving:2 form:2 enough:1 believe:1 sequel:3 but:7 encoder:3 wireless:4 strike:1 link:2 gain:2 encoded:1 line:1 he:5 dmc:6 wise:1 whether:1 up:2 theoretical:1 boldface:1 ωn:4 observation:1 distribution:10 similar:4 clear:1 strongly:1 later:1 hellman:2 computing:1 defined:3 certain:4 abstract:1 decrypt:1 general:6 engineering:4 ar:5 periods:1 journal:2 diversity:1 spends:3 adelaide:1 tedious:1 again:2 functions:1 codes:3 encrypt:2 relaxing:1 no:1 eedback:2 when:6 detail:1 virtual:1 calligraphic:1 field:1 setting:7 electrical:4 details:1 papers:1 department:4 approximated:1 offered:1 conclusion:1 poor:5 symposium:2 briefly:1 generates:5 completes:2 separate:3 symbol:4 uniformly:9 deriving:1 generated:3 important:2 bounded:1 variable:6 structure:6 independently:1 correlated:6 implies:1 assume:2 tradeoff:2 observe:4 mass:1 presenting:1 time:17 n0:5 n1:26 n2:20 requires:1 original:2 |
0704.2260.txt |@word replacing:1 code:2 consider:2 similarity:1 caused:1 equalities:1 bull:1 results:9 leads:8 unmixed:7 mild:1 proposition:8 latter:1 per:1 consists:1 issues:1 qbc:2 relationships:2 whose:1 simon:2 later:2 calculate:1 zone:3 concerned:1 technique:1 acting:1 finally:2 uniquely:1 those:4 under:12 analogous:3 heterogeneity:3 symmetry:1 ta:1 applied:1 fax:1 random:2 r12:6 presently:1 without:1 very:3 frequencies:29 hirsch:1 assuming:1 discordance:1 choice:1 reconstructions:1 jack:1 anonymous:1 stays:2 mixing:14 associated:2 difference:4 exact:4 vast:1 partitions:2 illustrated:1 beginning:1 doesn:1 presented:5 transmission:1 issue:1 t4:4 t5:4 t2:10 t3:4 terminating:1 t1:14 large:5 discrete:3 convenience:1 vector:7 min:3 ml:2 small:6 noted:1 proof:7 cfn:2 upper:1 supp:1 neighborhood:1 occurrence:1 findings:1 guaranteed:1 d3:2 direct:2 across:9 imply:6 perspective:1 infimum:1 substituting:2 genomic:1 further:1 bacterial:1 linear:2 even:8 mammalian:1 what:4 lemmas:1 appear:4 invertible:1 clock:1 specification:2 lawrence:1 labeled:3 expressed:2 debate:3 makes:1 toric:1 reconstruction:15 sup:1 new:3 forming:1 method:3 contrast:1 satisfy:17 philippe:3 full:1 led:1 excludes:1 respectively:2 genes:9 genet:4 here:11 understanding:3 ranges:2 q14:9 q13:9 aid:1 ratio:3 along:1 quite:1 equations:10 implicit:1 change:1 intersect:1 nontrivial:3 dividing:1 division:4 identifiable:5 study:1 larger:2 completely:1 commonly:1 controversy:1 amount:1 resulting:17 christchurch:1 pick:1 action:2 chang:3 gene:7 mix:9 pathological:3 biases:1 criticism:1 emerge:1 showing:3 formulated:1 inference:1 projection:1 rosenberg:2 jukes:2 quartets:3 substitution:6 private:1 highly:1 tools:1 select:1 horizontal:2 use:4 dna:2 indicated:1 working:3 lemma:11 probabilities:6 positive:13 continuous:6 stated:3 chooses:2 their:4 vol:1 ψi:4 call:3 therefore:10 criteria:5 ψb:2 ψc:2 themselves:2 rearranging:1 selects:1 historically:2 diagrams:2 more:8 sort:1 main:4 bρ:1 initiated:1 relevant:3 becomes:3 ti:9 problem:1 concatenation:2 phone:1 s3:4 appendix:2 generically:1 particular:7 known:6 cases:2 aligned:1 qabcd:1 potential:1 must:9 kumar:2 springer:2 ma:1 cluster:1 recall:2 equation:10 work:6 reproduce:1 m24:2 remain:1 itself:1 values:3 codimension:1 evolved:3 following:7 making:1 example:11 history:1 claim:1 relabeling:3 wang:2 figure:11 telling:1 process:3 distributions:3 carroll:1 r14:7 accept:1 reconstructed:3 minimum:1 numbers:1 write:1 sought:1 identifiability:10 dennis:1 r23:6 occur:4 absolute:1 information:2 needs:1 r24:8 klein:3 renumbering:3 rather:2 s2:6 s1:8 holds:3 moves:1 s5:4 species:2 regions:1 how:7 varies:1 misleading:1 criterion:3 adjacent:4 syst:4 answer:1 ensure:1 widespread:1 happens:1 parameter:13 simplicity:1 product:3 express:1 blocks:1 may:16 peeling:1 advice:1 after:7 derived:4 depiction:1 collection:1 diagram:2 applications:1 wrong:2 produce:2 coming:2 fits:1 minimizes:1 data:40 concerns:1 types:1 shortcomings:1 short:6 branches:2 varieties:1 four:7 light:1 sit:1 lines:1 correspond:1 assign:1 mislead:1 perform:1 si:7 interior:2 algorithms:5 expression:1 definitions:1 first:17 order:8 insight:1 substitutions:1 evolutionary:5 rounded:2 indeed:1 over:4 q34:8 encounter:1 satisfied:9 interpreted:1 held:1 paper:5 through:2 indicating:1 moulton:2 fidelity:7 still:1 its:2 before:1 phillips:3 derive:2 group:5 thank:1 fit:3 qad:1 susceptible:1 bringing:1 lateral:1 franke:1 rubio:2 actually:2 forms:1 attraction:1 absence:1 semple:5 choose:4 secondary:1 might:2 split:4 fool:1 them:2 good:1 return:2 greater:4 thereby:1 entire:1 practice:1 processes:2 slicing:1 framework:1 they:8 oxford:4 magic:1 now:12 allowable:1 lineage:1 easily:1 term:1 mcmc:2 wenk:1 invariants:27 university:3 level:1 via:2 k42:2 grows:1 sufficiently:3 inequality:3 reasonable:1 each:7 found:2 entirely:1 side:5 qab:3 constraints:1 homogeneous:1 weighted:1 directly:2 weight:6 evolve:2 doing:2 ed:1 reduce:1 stronger:1 related:1 inhomogeneous:1 disappears:1 expect:2 loops:2 our:5 summary:1 r13:8 out:3 shown:11 funding:1 matrix:1 analytic:1 space:12 open:2 furthermore:6 trivially:1 bad:1 research:1 combinatorial:1 contained:1 reader:1 denoted:1 lecture:1 get:1 cause:1 correct:2 math:4 shows:7 provide:2 theory:2 written:5 hull:1 divergence:2 given:17 free:1 standard:3 indices:1 approaches:1 pitfalls:1 pendant:26 trends:3 element:1 put:1 sheet:3 detecting:1 likelihood:12 generate:1 definition:3 pairs:3 derivation:1 hulls:1 geometry:2 could:2 transition:1 so:9 david:1 length:29 levels:1 canterbury:1 transfer:1 kingdom:1 strictly:3 quartet:18 4ac:3 already:1 features:1 probability:13 martin:1 variables:3 number:7 intuitively:1 ℓi:1 multiplying:3 m34:1 biol:15 another:5 carry:1 impossible:2 precisely:2 extra:1 summarize:1 maple:1 differ:3 checked:1 reference:1 biomathematics:1 similarly:2 leading:3 top:2 system:1 least:2 1a:1 indicate:1 returns:2 assumption:3 rates:7 tell:1 calculations:1 wildly:1 molecular:4 r34:6 williams:1 gives:8 fraction:1 reversed:1 exactly:9 part:2 authors:1 natural:1 believe:1 than:21 specify:1 steel:18 distance:1 perfectly:2 third:2 roles:1 favors:1 require:2 tree:94 second:9 submitted:1 reconstructing:1 states:2 determined:2 pairwise:1 assume:7 represents:1 were:2 rate:1 distinguished:1 inferring:1 collecting:1 motivation:1 plos:1 false:1 generality:1 quantitative:1 concludes:1 argument:2 subvarieties:1 outperforms:1 baldauf:3 substantial:1 unlikely:1 close:4 need:3 seen:1 constrained:1 any:13 relatively:1 lie:1 wilson:1 generic:1 smallest:1 zero:10 k32:2 describe:2 translate:1 thornton:4 able:1 complexity:1 mechanism:1 k3:23 k2:23 k1:27 internal:11 take:2 k5:7 k4:24 finding:2 performance:2 mis:3 subject:1 text:5 nigro:1 formulas:2 pagel:2 sure:1 though:3 who:1 mimics:3 simplify:1 detect:1 eukaryotes:1 formulae:1 pair:3 subset:3 segment:1 class:2 inconsistency:1 zealand:2 kb:2 ka:2 give:1 observation:1 characterizes:1 considered:1 neighboring:4 ki:11 sometimes:1 frederick:2 dimension:5 simplex:3 points:6 qbd:2 error:1 exp:4 sorts:1 hellwig:1 typically:4 sum:1 fact:10 precise:1 qcd:2 selection:2 phenomenon:2 show:9 v12:4 v13:4 detection:1 labels:2 bmc:1 12s:2 supplied:1 keywords:1 subtle:1 d4:2 parsimony:3 d2:2 find:4 d1:2 based:6 knowledge:1 parameters:2 hope:1 enough:1 should:6 terminal:1 taxa:11 only:4 bases:1 black:2 positively:1 molecules:1 factor:1 matsen:4 discuss:1 continuity:1 do:2 mixture:51 above:14 notation:4 di:1 vary:2 incongruent:1 designated:1 assumed:1 trees:32 likely:2 among:2 cannot:1 nearly:1 invariant:7 symmetries:1 quantifies:1 geometric:4 holland:1 gray:1 evolution:14 course:1 allman:3 arxiv:2 sturmfels:3 characterizable:1 qa:2 bag:1 investigate:2 roger:4 common:5 contain:1 qi:3 including:2 fixed:2 mcintosh:1 set:27 farris:1 exists:7 achieved:2 ancestral:1 testing:1 up:6 observed:4 see:4 individual:1 geometrically:1 result:3 reviewer:1 fail:1 terms:12 forthcoming:1 satisfies:2 best:1 gmail:1 closer:2 satisfying:9 inequalities:6 pattern:32 nature:4 convex:2 sites:6 label:3 symmetric:10 state:12 score:1 closed:1 between:14 progress:1 hold:1 conditions:2 email:1 aρ2:1 felsenstein:2 recently:3 right:2 complementary:1 component:1 however:8 groisman:1 cut:1 hypothesis:1 article:1 meaningful:1 distribution:5 topology:67 both:3 prospects:1 improved:1 subinterval:1 many:5 region:3 correctly:2 according:3 sullivant:3 assure:1 leibler:2 figures:1 interesting:3 exceeds:1 ernst:1 estimation:2 com:1 fix:2 arbitrarily:5 detailed:1 alternate:1 triples:1 point:4 simple:9 quality:1 q12:9 strategy:1 inf:3 cd:2 dimensional:4 exploit:1 mossel:8 simply:4 m14:2 mitochondrial:1 sequences:5 polynomial:1 table:3 considering:3 described:5 simplification:3 three:1 been:6 appears:1 pmin:6 genetic:1 much:2 combined:2 goes:1 pe:2 expected:6 jc:1 phylogenies:3 define:2 field:1 mike:1 penny:3 corresponding:13 restrictions:1 θb:1 going:1 propositions:1 andrew:1 uncommon:2 seeks:1 implied:1 deep:1 systematic:1 stems:2 bayesian:1 last:1 general:5 extensive:2 present:2 reverse:1 case:10 kimura:2 splits:1 comput:4 means:2 s4:4 empirical:1 value:2 ugly:1 will:31 pace:1 while:6 bounds:2 behavior:1 rhodes:3 situation:2 property:1 taking:3 procedure:1 versus:1 seven:1 vectors:4 existence:3 compact:3 almost:1 averaging:1 thus:6 site:29 equal:7 characterize:1 bias:1 ambient:3 evol:9 protein:2 vanish:2 pill:1 binary:1 different:22 perhaps:4 since:1 author:1 lengths:63 acknowledgments:1 make:7 indistinguishable:1 same:23 clearly:1 coalescent:1 stimulated:1 complex:2 arguments:2 qac:3 mixtures:26 come:1 products:1 finite:1 infer:2 difficult:3 development:1 independent:2 calculation:5 used:4 closest:1 paths:1 upon:1 effect:2 hand:4 subvariety:12 average:2 running:1 edges:7 kim:2 infinite:1 changing:2 identity:1 recent:1 numbered:1 lower:4 fourier:15 delivers:1 programs:1 k22:2 changes:1 sits:1 well:3 analysis:3 non:4 thought:1 patterns:1 edge:20 components:4 sets:30 exponentials:1 position:2 model:40 simplified:1 spencer:3 usual:1 distances:1 just:2 less:7 being:7 generally:1 numbering:1 rest:2 underlying:9 transforms:6 questions:2 ribosomal:2 useful:1 alternative:1 previous:1 adv:1 note:14 rapid:1 majority:2 phylogenetics:6 character:1 except:2 sinauer:1 mathematically:1 pillars:1 sullivan:2 setting:7 versa:1 theorem:3 input:1 fares:2 transformation:2 match:1 identical:1 bio:2 tests:1 explained:2 loss:1 characters:2 biologists:1 rna:2 implications:1 possible:10 corresponds:2 possibly:1 increases:1 rrna:1 phylogeny:4 pages:1 mol:8 press:3 using:11 intersection:1 k2p:1 insert:3 sorting:1 necessary:3 like:4 lost:1 alternatively:1 reduces:1 zool:1 m13:2 remind:1 m12:1 2007b:1 either:7 2007a:7 rearrangement:1 output:1 ψa:2 gaining:1 shed:1 because:8 methods:12 sequence:7 some:12 back:1 lineages:1 ideals:1 understood:1 sunderland:1 towards:1 q24:10 examples:12 specified:1 classes:1 nonzero:3 provided:3 scale:4 lead:4 bottom:1 demonstrates:2 centre:2 extensively:1 comments:1 meade:2 does:1 connecting:1 mutation:1 innovation:1 steps:1 demonstrated:1 inserting:1 mimicking:3 equivalent:17 arbitrary:1 simplifications:1 stem:1 wong:1 pathologies:1 although:3 become:2 hadamard:6 refers:1 subtract:1 properties:1 science:2 about:3 simplest:1 rare:1 would:6 most:2 brinkmann:2 anomalous:2 taxon:4 o:2 simulation:2 practical:1 distinct:5 involving:1 repulsion:15 greatly:1 mixed:23 generalization:1 mean:1 consequently:1 block:1 considerations:1 statements:1 presence:2 into:8 within:3 bound:2 due:1 fidelities:8 phase:1 appropriate:1 ecology:1 references:1 primarily:1 heated:1 conceptually:1 often:1 k12:2 log:7 topologies:3 support:1 there:14 question:6 transform:15 long:7 why:1 exchanging:1 appl:1 structure:2 way:3 series:1 bryant:1 was:5 neyman:1 function:2 kc:2 head:1 elsewhere:1 form:3 concatenated:3 δkl:18 differences:2 jun:1 but:4 allan:1 volume:1 hn:2 gain:1 line:9 trying:1 true:5 considerable:1 outside:1 again:2 pi:3 applying:1 compositional:1 robustness:1 maximum:9 us:2 theoretical:1 record:1 below:1 q23:9 simplifying:4 leaves:2 heterogeneous:6 demonstrate:1 intersects:5 similar:6 called:3 clear:1 regimes:2 strongly:1 ab:2 proved:1 worthwhile:1 classic:1 defined:1 certain:3 abstract:1 phylogenetic:49 proven:1 evidence:1 globally:1 single:8 θi:7 exist:8 together:1 simulations:3 follows:1 biosci:2 messy:1 identities:2 check:3 regime:3 incorrect:1 high:1 functions:1 proofs:3 akaike:1 no:6 fixing:1 whereas:1 when:24 substitutional:1 application:1 disjoint:1 other:13 genome:4 branch:106 θc:2 mathematics:2 kullback:2 conclusion:1 poor:1 explaining:1 m23:2 apparent:1 denote:4 elephant:1 zhou:1 separate:1 models:16 problems:1 convention:1 generated:4 bounded:1 additionally:1 scores:1 variable:1 vigoda:10 correlated:1 implies:8 longer:2 vice:1 cantor:2 virtually:1 required:2 resolving:1 rule:1 mimic:10 king:1 weights:4 time:3 far:1 θa:3 section:4 original:2 |
0704.2262.txt |@word homomorphism:3 consider:6 results:2 proposition:3 computation:1 gl:2 inverse:1 tq:2 quasi:16 th:3 under:2 applied:1 g2:2 zhang:3 p0:16 splitting:2 corollary:2 every:3 formula:4 zµ:1 zeit:1 irreducible:36 upq:6 direct:2 sign:1 second:1 odd:17 canonical:2 even:2 index:6 64b:3 dept:1 section:13 xτ:1 above:3 t2q:2 new:1 gl2:4 consisting:1 exercise:1 degree:2 respectively:8 lem:1 here:2 china:1 groups:2 studied:1 products:1 action:1 ducible:1 quotient:1 followed:1 projection:1 apr:1 summations:1 replace:1 apply:1 univ:1 unit:1 use:1 positive:1 next:5 linear:1 bases:1 call:1 means:1 vpq:4 conductor:1 particular:1 known:2 cases:6 must:4 springer:1 isomorphism:4 gℓ:2 recall:2 ρj:36 det:6 values:2 following:6 trans:1 root:1 proof:4 beijing:1 f2:2 numbers:7 unramified:6 4j:1 verlag:1 gcd:7 acts:1 write:4 maps:1 extensions:1 sin:14 simplicity:1 product:1 frobenious:5 may:2 kaist:1 ζk:4 ζp:17 ζq:30 abuse:1 representations:38 summarize:1 ρej:2 lifting:2 z2s:1 correspond:1 element:5 so:24 sect:3 representation:19 order:3 over:8 mainly:2 soc:1 paper:2 roots:1 before:1 mod2:2 mod4:2 fix:1 gtm:2 choose:1 lq:3 weber:1 maximal:1 non:3 primary:5 oke:3 tsinghua:1 they:4 das:1 serre:1 now:9 2t:1 modq:7 2v:2 equality:3 2q:12 2s:22 always:6 2z:14 2d:5 l2:4 each:3 monomials:1 2i:4 2j:8 qz:2 cyclotomic:20 map:2 our:1 happen:1 eq:2 matrix:2 space:1 furthermore:4 since:19 induces:1 qb:1 rational:1 ramified:12 induced:5 math:6 theory:2 free:1 standard:2 completely:3 york:1 ρij:47 put:2 e1:1 e2:1 definition:1 dirichlet:3 r2:2 introduction:2 first:5 yong:1 number:13 rank:1 relations:3 ring:2 given:5 dedekind:2 similarly:3 zτ:1 yin:5 construct:3 assumption:1 gives:1 b22:4 lℓ:13 x2:1 showed:1 cyclic:1 double:2 namely:5 preparation:1 determined:3 modern:1 say:1 conjugate:1 need:2 any:7 constructions:1 sciences:1 ideal:5 residue:1 begin:2 normal:1 algebraic:1 2tv:2 gauss:1 automorphism:2 class:3 lfunctions:1 indg:1 sum:3 fact:4 show:1 trivial:1 principal:1 aπ:1 q2:1 state:1 lemma:2 only:19 explicitly:2 generators:4 local:6 abelian:11 dj:1 notation:1 get:7 dz:3 words:1 prime:21 qp:3 runs:1 fields:15 arxiv:1 summary:1 bae:1 contain:1 qj:1 kernel:1 set:6 modulo:3 computed:1 relative:2 see:12 result:2 σqq:1 µs:2 written:1 notice:1 korea:1 nature:2 jp:1 daejeon:1 group:10 amer:1 inertia:6 jb:1 last:5 σn:1 freely:1 iℓ:18 σq:52 σp:38 otherwise:4 v2q:1 dimensional:12 ρijk:10 σq2:11 proved:1 zeta:2 considering:3 pq:7 described:2 basis:4 pz:1 three:4 sl2:2 uπ:1 springerverlag:1 frq:2 4q1:1 ireland:1 basic:1 define:8 surjective:1 congruence:1 commutes:2 gal:3 c3:4 c2:4 those:1 case:34 exception:1 splits:4 will:1 fr2:16 2fℓ:1 iq:6 thus:13 them:1 ij:13 vt:2 containing:1 jb2:4 same:2 clearly:1 liftings:2 finite:1 used:2 trivially:2 i2:6 nj:2 hand:1 v2:25 characters:2 identity:2 well:2 dimension:17 subgroup:16 being:1 rosen:1 resp:4 qℓ:3 uℓ:3 facts:2 useful:1 preprint:2 character:1 except:1 easy:4 theorem:2 solvable:3 february:1 know:2 integer:1 unique:3 mod:4 follows:1 separately:2 arbitrary:1 works:1 methods:2 classical:1 some:3 ideals:1 b2:17 b3:10 2qj:1 happens:3 cosets:1 prop:1 decomposition:4 minimal:2 run:1 power:1 equivalent:2 bq:1 artin:10 integers:2 ok:3 extension:4 generated:9 addition:3 aℓ:12 plus:1 act:1 gamma:1 duke:1 primitive:1 integral:1 isomorphic:3 due:1 square:4 references:1 determine:14 σp2:15 matrixes:1 log:3 there:3 u2:1 anderson:1 quadratic:5 way:2 m1:6 function:2 complete:1 form:8 epsilon:1 kronecker:1 but:2 hu:2 compute:9 uq:4 up:2 us:2 bijectively:1 coverings:2 called:2 associated:7 computing:1 defined:15 abstract:1 describe:1 denote:3 aq:4 ap:1 chap:1 check:2 inc:1 again:1 functions:12 fℓ:6 galois:3 when:20 detail:2 field:10 other:6 details:2 bℓ:43 department:1 mathematics:1 nt:1 arithmetic:3 elements:4 symbol:1 a3:6 a2:8 structure:5 implies:1 assume:15 factors:6 4q:2 ramification:1 n0:1 rep:1 |
0704.2263.txt |@word gv:1 consider:4 gp:2 caused:2 particular:1 dynamic:1 results:2 leads:1 gb:2 lewenstein:1 whitlock:1 poorly:1 depend:1 calculate:1 violation:1 quasi:4 tj:1 shenoy:1 th:4 under:1 nodes:1 include:1 dramatically:1 ta:2 p2:2 yr:1 supported:1 orthogonal:2 very:1 witthaut:1 p0:4 wave:21 every:1 stays:1 experimentally:1 elena:1 condition:2 four:5 school:1 groth:1 hamiltonian:1 large:1 excellence:1 small:6 enhance:1 optics:1 degeneracy:5 employing:1 direct:1 approximation:1 burger:1 second:2 imprinting:1 populating:1 chen:1 manipulating:1 dynamics:6 chem:1 odd:1 theory:4 even:3 employ:1 what:1 nonlinear:42 trapping:7 rate:5 assisted:18 notches:2 version:1 collins:1 sidorov:1 method:1 contrast:3 3d:1 satisfy:1 condensed:4 lee:5 degree:1 exchange:3 respectively:3 khaykovich:1 here:4 atoms:8 behaviour:1 reported:1 explore:2 relaxation:1 strong:1 equations:1 appears:2 obtained:2 tunneling:33 antisymmetric:3 splitting:1 zener:2 resulting:2 resonance:1 shaded:2 studies:1 involves:1 composed:1 spatially:1 projection:1 clark:2 castin:1 private:1 highly:2 brought:1 uger:1 condensates:8 total:7 shlyapnikov:1 use:1 schumm:1 remains:2 albiez:1 comparing:1 therefore:1 australian:2 type:3 hulet:1 more:2 separated:1 oberthaler:2 populations:2 solitons:23 zozulya:1 varying:2 cases:1 must:2 states:21 bagnato:1 science:2 equation:5 work:1 mk:1 remain:1 values:4 choi:2 following:1 akin:1 saba:1 smerzi:1 stimulating:1 control:1 council:1 figure:7 give:1 process:8 involve:1 collision:1 numbers:2 degenerate:2 tal:1 sharp:1 keep:1 occur:1 junctions:1 schmiedmayer:1 pritchard:2 six:2 chemical:2 nontrivial:1 gati:2 place:1 shortens:1 parameter:2 obeys:2 de:2 description:1 our:4 db:1 after:4 dx2:1 diagram:1 explored:3 waves:1 agosta:1 graefe:1 ou:1 natural:1 dynamical:1 effective:17 recombination:3 schneider:1 correspond:3 sk:1 negligible:2 decreasing:3 sg:1 order:3 doublewell:1 canberra:1 leanhardt:1 developed:3 over:1 satisfied:1 interpreted:2 paper:1 including:1 tunnelling:1 kinetic:2 still:2 excitations:6 before:2 phillips:2 ld:2 longitudinal:1 manuscript:1 la:1 ln:2 lm:2 varies:1 decreases:2 absence:1 degrees:1 fig:10 into:5 versus:1 non:4 affected:1 gray:1 washington:1 processes:1 landau:2 break:1 framework:1 repulsive:6 effects:1 sweeping:1 ys:2 now:1 φj:10 develops:1 φk:1 characterizes:1 university:2 2d:1 sufficiently:3 trap:6 each:1 crossing:4 2m:1 reconfigured:1 mean:8 em:1 differential:1 significantly:1 independent:7 generation:3 series:1 energy:5 ea:1 gaussian:1 group:1 interferometer:15 frequency:6 measure:2 quantum:32 aids:1 operation:1 avoided:2 nonlinearities:1 ep:1 mat:2 ketterle:2 shown:1 dominates:1 furthermore:1 since:1 interference:2 research:2 particles:2 collisions:5 engels:2 rg:1 dominated:1 denoted:1 induced:1 supports:1 occurs:1 shows:1 christensen:1 linear:11 barrier:19 interactions:9 carr:2 mechanisms:1 possibility:1 completely:1 formation:4 yuri:1 eigenvalues:1 lisak:1 interaction:6 could:1 bistability:1 kivshar:3 times:1 turn:1 length:3 period:1 massive:1 barriers:1 configurations:1 onto:2 condensate:11 first:19 there:3 probability:8 cj:6 number:18 fast:1 damski:1 given:1 likely:1 similarly:1 introduction:1 top:1 system:16 approximately:2 hofferberth:1 their:2 cooling:1 ostrovskaya:2 1d:5 national:1 sengstock:1 relationship:1 trapped:5 serve:1 transverse:4 manipulation:1 x2:3 peculiar:1 coefficients:1 population:21 hannaford:1 bec:10 andersson:1 see:4 submitted:1 final:1 preparation:1 matter:18 appealing:1 determined:2 amplitude:1 sr:1 wildermuth:1 decompose:1 san:1 unchanged:3 bourdel:1 wannier:3 ke:1 any:1 viewed:2 strength:4 zero:1 zp:1 self:1 responsible:1 mechanism:2 note:1 sciences:1 high:3 potential:33 ramped:1 ramping:3 so:6 brand:1 strecker:1 added:1 multiple:7 centre:2 sl:2 wells:5 most:1 involving:1 thank:1 significant:5 phase:9 intrinsic:2 denschlag:1 sub:2 soliton:1 observation:2 nonlinearity:33 kk:1 neighboring:1 chosen:1 kr:1 ferrari:1 principle:2 exp:1 usual:1 physics:1 spatiotemporal:2 drastically:1 show:4 absorbing:1 timedependent:2 authors:1 d2ω:1 bright:1 becs:2 d2:3 find:2 ground:17 slow:1 based:3 parameters:3 observe:2 only:1 cubizolles:2 indeed:1 integrate:1 joseph:1 fu:2 oscillate:1 oct:1 hall:2 dl:1 means:1 dependent:6 µj:2 quantified:1 generalise:1 liu:2 ones:2 preparing:1 dx:3 during:1 dt:1 becomes:4 alexander:1 adiabatically:2 evolution:11 bar:1 pasquini:2 arxiv:2 garcia:1 investigate:1 cf:2 yukalova:1 double:14 shi:2 ql:3 pitaevskii:1 salomon:1 set:2 sensitivity:1 evolving:1 plateaus:1 differs:2 depends:4 arc:2 result:2 discussions:1 close:2 techniques:2 instance:1 satisfying:1 αt:1 hagley:1 presilla:1 symmetric:6 state:23 various:1 between:23 boundary:1 conditions:1 across:1 reinhardt:2 wd:2 herrero:1 cristiani:1 nature:4 initially:3 weak:1 however:3 rapidly:1 wu:2 loading:1 jh:1 wr:1 key:1 wp:1 bose:3 ja:1 originates:1 suggested:1 both:2 always:3 region:1 conclusions:1 equal:3 sensitive:3 merging:4 jo:1 whole:1 experimental:2 ck:2 minima:1 ca:1 harmonic:6 height:10 dimensional:1 exhibits:2 giovanazzi:1 je:1 normalisation:1 cw:2 bongs:1 described:1 tuning:1 basis:1 quantisation:1 due:7 been:2 ai:1 reduction:1 slowly:2 pj:5 utilizing:1 pn:1 dynamically:1 systems:5 interparticle:4 corresponding:4 coherence:1 gao:2 coherent:1 confinement:1 external:2 those:1 case:3 p3:2 multi:1 p1:2 josephson:3 pacs:1 solid:2 engineering:1 value:2 transformation:1 will:4 behavior:2 korsch:1 di:1 balance:1 procedure:1 aa:1 henkel:1 coupled:7 almost:2 vi:1 thus:1 vm:1 according:1 dettmer:1 vs:1 cond:2 junction:2 different:18 hubbard:1 schreck:1 zakrzewski:1 radiation:1 cross:1 stimulated:1 complex:1 schematic:1 units:1 dimensionless:2 several:1 evolve:2 used:1 peaks:1 numerical:4 effect:1 counterparts:2 v0:4 moment:2 levels:2 moving:1 potentials:4 niu:2 interferometers:5 modes:3 hopping:1 fully:6 nevertheless:1 changes:2 well:28 thought:1 academic:1 edge:1 feshbach:1 quantitative:1 model:4 recombine:1 left:4 ae:1 splitters:1 being:1 sanpera:1 obtain:1 press:1 shape:2 atomic:3 partridge:1 scattering:4 eigenstates:37 captured:1 hai:2 inelastic:1 preprint:1 density:8 seems:1 confirmed:1 e0l:1 internal:1 transformed:1 attractive:1 theorem:1 input:1 excited:27 take:1 opt:3 australia:1 rev:19 corresponds:3 dark:17 increases:1 mol:3 confined:1 integer:1 fantoni:1 modifications:1 submission:1 follows:2 collective:3 adiabatic:6 harmonically:1 turitsyn:1 confinements:1 evolutions:2 inter:1 stationary:6 reduced:1 exceed:1 right:4 methods:1 classical:2 successfully:1 ertmer:1 growth:1 b0:5 choosing:1 oscillations:1 michinel:1 peter:1 gross:1 gradually:2 scale:1 feder:1 lead:3 bottom:2 though:1 extensively:1 overlap:3 instantaneous:1 decomposition:1 ptot:3 mode:9 dcl:1 truscott:1 obey:1 arbitrary:1 oscillating:1 bi:1 broken:1 bv:1 found:1 cattani:1 about:1 freedom:1 dependence:2 probabilities:8 yukalov:1 ensure:1 greatly:1 modal:1 act:1 helmerson:1 other:3 localised:6 chu:1 h2:1 communication:1 h0:3 numerically:1 lb:1 down:3 references:1 simsarian:1 determine:1 einstein:1 operator:1 binding:1 rows:1 additional:1 normalised:1 transfer:8 initial:10 populated:1 transform:1 long:1 dispersion:1 width:2 anderson:2 conservation:1 low:2 was:2 interferometry:2 lowest:4 tight:1 atherton:1 form:4 adjusting:2 hj:1 expected:1 atom:4 line:2 highest:6 rolston:2 zhu:1 qualitative:1 up:1 devices:1 considered:2 below:2 projecting:1 distribution:3 sacha:1 strongly:1 associated:1 ag:1 defined:1 abstract:1 deep:4 single:10 exist:1 simulations:3 perez:1 gradients:2 distributions:3 ew:1 physical:1 diego:1 no:4 wavefunction:1 when:2 detail:1 invalid:1 field:9 valid:1 spatial:1 kosloff:1 shin:1 picture:5 formed:3 superposition:6 excitation:3 pronounced:1 berman:1 prepared:1 generated:7 peak:1 realised:2 feasible:1 coupling:4 assume:2 deng:1 utilised:1 neighbouring:2 mass:1 time:23 lett:11 once:1 |
0704.2264.txt |@word consider:3 pte:1 particular:3 results:1 computation:1 edu:1 whose:3 graph:17 removal:2 presents:1 neighbours:1 presentation:1 conjecture:8 straightforward:1 reader:1 coloured:4 uwa:1 condition:4 school:1 hamiltonian:8 discrete:1 science:1 small:4 inspection:1 smaller:2 teo:2 literature:2 sign:3 second:3 evaluated:2 odd:9 what:2 section:1 version:1 obvious:1 net:1 contributes:2 satisfy:1 degree:1 respectively:2 behaviour:1 path:2 along:1 obtained:5 study:1 larger:1 colourings:5 leaving:1 suggests:2 survey:1 suitable:1 useful:1 toughness:2 family:5 apr:1 requiring:1 hindsight:1 counts:2 total:1 use:1 would:1 prove:3 remains:2 positive:2 negative:3 therefore:5 type:4 more:4 hackensack:1 labelled:1 varying:1 known:3 ser:1 recall:2 work:2 thomassen:7 values:1 following:6 root:13 example:3 proof:3 claim:1 weaker:1 figure:7 stated:1 purposes:1 high:1 cutsets:2 exclude:1 information:2 advantage:1 fortunately:1 feature:1 how:1 blocks:1 algebra:1 replacing:1 connectivity:1 value:2 types:3 natural:2 maybe:1 lines:1 rather:2 so:5 fundamental:1 decreasing:1 order:5 produced:1 paper:3 through:1 existence:1 its:4 roots:22 interesting:1 choose:1 derivative:5 main:1 non:8 chromatic:51 they:5 false:2 now:2 discuss:1 represents:1 february:1 university:1 possibilities:2 sufficiently:1 each:1 found:1 subset:1 significantly:1 related:1 extended:2 our:4 conjectures:4 shown:3 jackson:10 factors:1 electronic:1 denotes:1 geom:1 conjectured:3 math:2 theory:1 koh:8 free:5 completely:1 complicated:1 r1:1 r2:1 omit:1 place:1 gordon:2 ltd:1 hence:2 probab:2 first:2 symbolic:1 number:9 least:2 dong:8 open:2 maple:1 size:4 passes:1 given:1 necessarily:1 similarly:1 introduction:1 approximately:1 zeros:3 siam:1 cycle:1 final:2 gives:2 relationship:1 exactly:1 immediate:1 x8:1 part:1 western:1 somewhat:1 authors:1 x2:1 x3:1 x6:1 x7:1 x4:1 x5:1 showed:1 backgound:1 zero:6 classes:4 were:3 providing:1 symmetries:1 need:2 any:1 paths:1 isolated:1 k3:1 ideal:1 combin:3 though:1 who:1 connected:12 considered:1 calculated:1 flow:1 vertices:10 bipartite:15 graphs:29 sum:2 joining:1 show:1 attempts:1 substituting:1 knowledge:1 outside:1 than:10 lemma:2 only:5 explicitly:1 intrinsically:1 continuity:2 do:1 overall:1 cannot:1 differentiating:2 arxiv:1 common:1 including:1 cycles:1 set:1 questions:2 see:2 computer:1 result:4 close:3 concern:1 palette:1 said:1 extend:1 colours:3 enough:1 smallest:3 various:1 between:1 conditions:1 terms:7 wa:1 however:8 clues:1 distribution:1 received:1 last:1 equal:1 contribution:2 expression:1 comes:1 arbitrarily:2 co:2 conclude:1 consideration:1 polynomial:15 table:4 considering:1 described:1 raise:1 addition:1 three:3 been:1 much:3 combined:1 interest:1 arises:1 families:1 both:8 sufficient:1 neighbour:1 general:2 chromaticity:1 present:1 case:1 look:1 comput:2 engineering:1 royle:1 choices:3 aim:1 replaced:1 situation:1 property:1 leaves:2 computed:1 unsatisfactory:1 vi:3 thus:3 them:1 vn:1 itself:1 counterexamples:1 different:2 perform:1 make:2 member:1 complex:1 arguments:1 largest:1 independent:4 used:1 comprehensive:1 possible:1 v0:6 v1:9 v2:5 v3:6 v4:6 colouring:5 infinite:3 recent:3 well:1 analysis:1 edge:1 components:5 sets:4 just:1 aspect:1 world:1 tough:3 alternative:1 previous:1 adding:1 had:1 book:1 location:1 theorem:7 extensive:1 remaining:1 real:5 australia:2 easily:1 term:1 five:3 immediately:1 excluding:1 follows:2 separately:1 either:1 decimal:2 because:2 namely:1 some:4 back:1 understood:1 deduce:1 examples:2 respect:1 happens:1 ignore:1 confirm:1 asking:1 refer:1 scientific:1 problems:1 although:1 properties:1 publishing:1 about:1 actual:2 anything:3 package:1 distinct:1 software:1 computational:1 previously:1 due:1 references:2 elementary:1 combinatorics:1 there:6 question:6 describes:1 was:2 loopless:1 function:1 complete:2 form:1 but:1 line:1 considerable:2 raising:1 made:1 places:2 whether:2 multiplicity:3 us:1 demonstrate:1 problem:1 similar:2 clear:2 detailed:1 strengthening:1 constant:1 certain:1 abstract:1 contribute:2 evidence:1 single:1 au:1 tedious:1 nj:1 no:12 when:5 other:5 briefly:2 vertex:2 polynomials:5 important:1 interval:10 resolving:1 portion:2 having:1 |
0704.2265.txt |@word extrapolated:4 consider:2 chain:35 rev:7 magnetic:4 excellent:1 brownian:1 results:21 pearce:2 b540:1 per:1 computation:1 gn:2 expressions:3 cases:5 causes:1 equivalences:3 calculate:1 subjected:1 equivalence:1 behaviours:1 intensive:1 charge:15 critical:5 th:20 under:1 include:4 hill:1 alternating:2 amplitudes:1 string:3 g1:5 zhang:1 very:2 nichols:2 onsager:2 difference:2 exact:7 condition:5 squares:1 magic:1 presented:4 positions:1 anisotropy:1 having:2 vertex:5 solution:15 bajnok:2 large:5 solved:1 fourier:5 indices:1 eigenvalues:2 anal:1 noted:1 upper:1 strongly:2 l97:1 inevitably:1 maclaurin:4 mussardo:1 cosh:10 approximation:1 zero:3 masson:1 growing:1 further:9 bose:1 ρn:38 odd:30 situated:1 fonction:1 linear:2 even:28 aim:1 nonlinear:1 appear:2 morse:1 giving:2 section:15 iωλ:2 henceforth:2 eckel:1 paragraph:1 issues:1 above:10 hamer:3 contributes:2 method:3 contrast:1 satisfy:1 condensed:1 umper:3 respectively:11 here:11 behaviour:3 desired:2 explore:2 objects:1 ansatz:18 sinh:23 others:1 woynarovich:4 resemblance:1 along:1 sine:9 equations:10 change:2 b663:1 box:1 generalizing:1 b631:1 study:2 studied:5 experience:1 periodic:1 loop:1 ρtotal:2 suitable:1 studies:1 4a1:2 family:1 extra:11 explained:1 private:1 a23:1 sgn:2 summation:2 redefining:1 total:1 during:1 imaginary:2 bound:1 wang:1 tricritical:1 use:5 henri:1 usa:1 recalling:1 beginning:1 whittaker:1 contains:1 finally:3 next:3 few:1 nucl:13 approach:3 m1:2 therefore:2 m2:2 compactly:1 bethe:24 more:7 successful:1 becomes:1 surprisingly:1 derivation:3 interaction:2 particular:1 known:3 hole:25 given:8 must:1 extrapolations:1 topic:1 account:1 ma:2 erratum:1 ashkin:2 equation:6 work:2 theories:3 nlie:3 vega:5 values:20 ruiz:1 den:1 following:18 making:1 root:7 example:1 nearest:1 compare:1 omit:1 challenging:2 give:3 calculation:5 b504:1 suggestions:1 baseilhac:1 ann:1 hexagons:1 states:26 reviewing:2 palla:1 tan:1 counting:6 g2:8 b594:1 rather:3 discussion:3 holds:1 feature:1 arrangement:2 write:1 located:4 pure:1 tak:2 parameter:5 sin:12 derivations:2 mat:3 algebra:4 may:2 thermodynamic:1 advice:1 earlier:1 derived:5 feshbach:1 corrections:12 plane:1 representations:1 fl:1 parallel:1 changes:1 short:2 natural:1 outline:1 third:2 resemble:1 computations:2 spectra:1 explicit:1 st:1 extrapolation:1 so:1 sn:4 enter:1 representation:2 subsequently:1 order:5 six:1 closely:1 schwartz:7 hierarchy:1 indeed:1 over:5 vary:1 soon:1 years:1 course:2 wiener:2 statistical:1 signs:1 mentioned:2 excitations:12 its:5 roots:44 before:3 thank:1 curly:1 la:1 ln:2 matrices:2 solving:4 destri:1 boson:2 resorting:1 resort:1 complex:1 meissner:1 choose:1 van:1 defining:1 cef:17 non:3 fourth:1 numerically:7 questions:1 anticipated:1 cosh4:1 framework:1 effects:6 they:1 half:1 now:4 teller:2 continuum:1 2u:6 term:2 temperley:2 2s:1 fully:1 university:3 hamiltonian:4 2e:1 2a:20 each:7 found:12 2n:21 defects:1 baxter:1 int:1 en:7 financial:1 directly:1 broeck:7 energy:50 hard:2 related:4 conventions:1 operator:2 arrives:1 poincare:1 quantum:12 our:11 special:4 out:3 batchelor:4 shown:3 accomplish:1 impurity:1 since:3 crucial:3 denotes:1 content:1 extrapolate:3 pyatov:1 favours:1 suggesting:1 formula:4 rn:4 illustrate:1 supports:1 math:1 shows:1 sinh2:1 after:3 theory:9 interactions:1 diagonal:13 free:4 standard:1 approaches:3 carried:1 york:1 nightingale:1 region:2 e1:12 e0:3 e2:8 dirichlet:12 r1:4 r2:8 applications:2 determining:2 could:2 conformally:2 motion:1 b595:1 length:3 explored:1 gordon:9 hence:12 barber:2 b453:1 first:5 origin:1 already:1 utilizes:1 peculiar:1 jhep:1 omitted:2 number:28 nested:2 restrict:2 utilized:1 2a2:1 least:1 another:1 2a1:1 open:17 size:19 differ:1 long:1 introduction:1 leading:1 system:2 adopted:2 b622:1 needed:2 nepomechie:14 zeros:3 calculations:1 siam:1 potts:2 exponents:1 gives:1 shifted:1 a30:1 a37:2 a36:1 reversed:1 employ:4 part:3 manipulation:1 elusive:1 than:4 effective:5 sections:1 depends:1 matter:1 cardy:2 determined:1 yang:3 fˆ:2 onedimensional:1 function:2 bootstrap:1 footnote:2 appreciate:1 correction:16 zamolodchikov:1 mind:1 spectrum:4 seen:1 seem:1 constrained:1 any:3 complete:3 lie:1 issue:1 gier:2 sch:1 lin:1 ruegg:1 able:1 note:7 potential:1 generalized:5 new:4 alcaraz:1 heisenberg:4 spectral:2 begin:4 multiple:1 shall:4 twodimensional:1 sequence:1 extending:1 attempt:1 involving:3 definitions:1 alez:1 future:1 especially:1 considered:2 calculated:1 later:1 upset:1 z3:1 g12:1 z5:1 bracket:2 physics:5 sum:8 lying:11 ghoshal:1 sector:6 nπ:4 sklyanin:1 nh2:1 dependant:2 12n:10 notations:2 relation:1 solutions:7 algorithms:1 find:3 ground:16 q1:17 nearer:1 q2:13 based:6 knowledge:1 parameters:11 inozemtsev:1 explain:2 written:3 sˆ:2 analytic:3 only:5 version:1 integrable:10 circle:1 hopf:2 hope:1 his:1 dh:1 get:1 de:8 watson:1 ones:2 words:1 invariant:3 ahn:4 applying:2 ds:2 quispel:2 resolve:1 densities:1 fields:7 arxiv:1 modern:1 2b1:1 acknowledgments:1 qa:10 ˆn:1 contain:1 analytical:8 shi:4 nβ:1 qn:4 set:1 computed:2 exists:1 seas:4 summed:3 namely:6 radius:1 result:5 sea:26 terms:20 contour:1 capacity:1 subsequent:1 review:1 sites:4 boundaries:8 state:38 µn:2 various:3 closed:2 between:6 progress:1 boundary:54 λl:25 conditions:6 notice:4 recently:2 however:7 cao:1 article:1 affleck:2 both:8 cos:3 last:1 σn:4 limits:2 ˆa2:2 many:2 vanden:6 density:2 equal:1 quantization:1 figures:1 casimir:7 contribution:2 expression:4 cosech:2 among:1 conclude:1 address:2 corresponds:1 dimensional:2 oshikawa:1 dependance:1 table:4 considers:1 proceeded:1 transformations:1 second:2 addition:2 due:9 been:12 expressed:1 l189:1 logarithmic:1 interest:1 expected:2 utilizing:1 algebras:1 anomaly:2 universal:2 systems:2 obtained:2 direction:2 relations:3 corresponding:3 received:1 xxz:31 iµ:1 bulk:8 denote:2 spin:26 former:1 present:7 cot:1 case:17 explicitly:1 multi:4 practicality:1 look:1 unlike:1 tanh:1 contexts:1 koizumi:1 value:1 will:7 near:1 momentum:1 exist:1 conformal:18 taking:2 b633:1 a20:4 a21:2 reverse:1 a24:1 henkel:1 a26:2 eventually:1 a28:1 von:1 thus:2 them:2 surface:2 ii:1 pressing:1 cond:3 turns:1 rittenberg:3 compactified:1 different:2 recover:1 make:3 same:5 check:1 unity:8 parts:1 arguments:2 pauli:1 largest:9 finite:29 otte:1 hermiticity:1 independent:3 used:3 see:6 numerical:10 upon:1 effect:1 uses:2 infinite:3 invariance:5 ebulk:3 scaling:4 task:2 shortly:1 scenario:2 charges:1 makes:1 well:3 fusion:1 analysis:9 without:3 solve:3 induced:1 firstly:1 position:2 model:27 dimension:1 usual:2 cosh2:2 proposed:2 σnz:1 obtain:2 σnx:1 σny:1 transforms:1 predicts:2 integer:2 λk:37 λj:38 previous:2 site:1 heuristic:2 urged:1 readers:1 point:2 favouring:1 iω:3 lattice:5 belongs:1 transformed:1 lett:7 versa:2 iπ:3 solvable:1 excited:21 euler:4 take:1 real:6 universality:1 ravanini:3 criticality:1 read:1 increases:2 press:1 using:14 saleur:4 mod:1 like:3 excitation:2 b676:1 miami:2 follows:1 twisted:1 ignore:1 gehlen:1 yields:7 either:1 arbitrary:3 invaluable:1 mode:2 spins:10 right:7 methods:2 lectures:1 some:16 a17:1 mech:6 gaudin:1 b1:1 b2:4 nondiagonal:17 gables:1 provided:1 dimensions:10 obtaining:3 confirm:2 onde:1 signifying:1 integration:3 comments:1 does:1 steps:1 chains:13 refer:2 obey:1 bl:1 a19:3 bn:1 agreement:1 although:1 mcgraw:1 relating:1 refers:2 dictated:1 properties:2 simpler:1 about:1 central:16 would:2 extension:2 constraint:2 coral:1 o:1 acs:2 remains:1 range:2 a2:9 ensure:1 rule:3 addendum:3 introduced:2 lieb:2 cambridge:1 presence:6 iµa:1 communication:1 h0:2 within:2 integral:4 functional:2 three:1 down:2 lies:1 square:1 references:1 determine:3 strip:1 elementary:1 bosonic:1 neumann:6 forth:1 hep:20 area:1 completing:1 support:4 there:7 question:2 transform:2 signifies:1 accordingly:1 low:11 forward:1 was:2 suzuki:1 lowest:21 elsewhere:1 form:6 restrictions:1 triangular:1 but:4 rajan:1 volume:2 anisotropic:1 true:6 made:1 compute:8 ig1:4 leclair:1 antiferromagnetic:4 dω:2 up:1 theoretical:1 below:4 2πr:1 limit:6 uj:17 utz:1 distribution:2 similar:15 nµ:5 mechanics:1 constant:1 defined:1 certain:2 abstract:1 contribute:1 upsets:1 general:6 single:1 pˆ:1 dλ:18 supersymmetric:1 kl:3 dγ:7 gonz:1 nh:10 again:5 functions:9 completeness:1 no:3 whereas:1 when:1 treatment:1 rewriting:1 field:7 other:7 details:4 department:2 really:1 presenting:1 a14:1 stat:8 calculating:2 models:19 gas:1 remarked:1 problems:2 a1:13 important:1 a9:1 a4:1 variable:1 strips:1 structure:1 matrix:1 neighbour:1 implies:1 coupling:1 algorithm:5 vice:2 assume:1 holes:24 4s:1 together:1 strings:2 4n:1 fact:4 resembles:1 n1:2 n2:4 original:1 |
0704.2266.txt |@word apr:1 ak:1 xf:25 cd:1 λk:1 cy:1 y0:2 ay:1 xs:3 dt:1 ct:3 lc:4 uº:1 ln:1 uf:20 acl2:1 nf:1 3t:1 tn:2 pe:8 tf:45 log10:3 sin:2 wµ:4 sin2:8 xº:2 a0:9 a2:9 cosh2:2 eµ:5 ys:3 aº:2 dr:1 ky:1 pw:8 cos:7 2w:1 arcosh:2 tanh:2 sech:1 arxiv:1 x0:2 ωt:1 2πn:4 2d:1 3f:1 cº:1 2n:1 nlin:1 |
0704.2267.txt |@word neighbors:1 iǫ2:1 code:1 sci:1 consider:1 caused:9 global:1 results:7 integration:1 eds:1 ǫa0:1 broader:1 edu:1 4e2:1 contributions:2 reichmann:1 localized:1 simon:1 terms:3 calculate:1 zone:2 monaco:1 eα:3 technique:1 containing:1 supported:2 contract:1 charge:4 does:1 under:1 anharmonic:22 include:2 silicon:1 ta:1 case:1 begemann:1 breathing:5 2γj:1 g0:5 far:5 rise:1 amorphous:1 induce:1 wave:3 electron:1 putting:1 figs:3 dispersions:1 summarized:1 resonant:1 specific:1 4er:1 evaporation:1 exact:3 rα:2 northwestern:1 vibrational:6 hamiltonian:1 turns:1 solution:2 large:4 solved:1 vector:2 pba:1 disagreements:1 small:5 eigenvalues:1 originally:1 configurations:2 χn2:1 fabian:1 approximately:1 force:3 disordered:6 coefficient:4 direct:1 approximation:1 zero:1 orthogonal:1 value:3 further:4 crystallography:1 quite:2 linear:3 even:1 index:1 developed:1 sun:1 section:1 kantor:1 while:7 supplied:1 thickness:1 cell:3 experiment:5 causes:1 above:4 new:3 contributes:1 method:2 slabs:1 fe3:2 body:4 condensed:1 full:2 respectively:4 presence:1 component:1 equals:1 here:1 understanding:1 reported:1 decay:2 brα:1 address:1 active:1 depend:2 along:2 strong:3 respect:1 appears:1 change:1 obtained:2 almost:1 ac02:1 χn:1 geophys:1 shift:4 study:2 larger:1 shoulders:2 metry:1 resulting:1 procedure:3 usually:1 resonance:2 conveniently:1 suitable:1 makes:1 eˆ:1 followed:1 projection:1 extrapolations:1 apr:1 replace:1 visible:1 iron:2 vc:2 analyzing:1 issue:1 total:1 univ:1 planck:1 unit:1 derivatives:1 use:6 remains:1 feo:6 contains:4 suppl:1 next:1 comparing:1 program:1 estimated:1 therefore:1 taken:2 associated:1 iteratively:2 type:1 jacobsen:4 fex:13 more:3 accuracy:1 becomes:1 company:1 tested:1 fixed:1 rigid:5 discrepancy:1 cases:2 meneses:1 iii:3 eγ:2 must:1 c44:3 states:4 mg:7 room:4 rβ:2 rγ:2 mm:3 science:5 equation:3 averaged:4 oscillator:2 mt:1 oxide:3 infinitesimal:1 vibronic:1 thin:1 following:2 trans:2 wedge:1 reasonably:1 figure:1 chosen:1 calculation:2 pieces:1 sample:7 indicates:1 numbers:2 sense:1 unphysical:1 tao:1 qj2:2 salts:1 information:1 soc:1 carriers:1 rather:2 s2:6 s1:5 acts:2 feature:3 write:1 very:2 pure:24 opt:1 parameter:2 kung:1 description:1 may:4 after:1 them:1 applications:1 fe:21 mag:2 fits:1 computation:1 data:14 response:2 constants:4 times:2 short:2 dα:2 dynamical:1 effective:6 pertubation:1 consequently:1 spectra:10 correspond:1 brun:1 s3:6 green:4 insofar:1 order:10 bins:2 typical:1 help:1 office:1 constituents:1 over:9 refractive:1 mainly:1 choose:3 symbols:1 thermal:2 paper:4 including:3 omitting:1 still:2 its:9 operative:1 perfect:2 regions:1 treat:2 fit:3 la:1 energies:5 lo:1 295k:4 brook:1 extract:1 better:2 detected:1 parts:1 microscopic:1 fig:12 bin:1 main:1 into:2 revcolevschi:1 non:2 good:2 adjacent:1 combination:1 ωto:13 press:1 polarizations:1 material:1 investigated:1 repulsive:1 effects:7 they:3 focus:2 mao:1 ecv:1 now:1 elliott:1 dielectric:25 susceptibility:5 february:1 finite:3 name:1 goncharov:2 ifs:1 university:3 spectro:1 homes:1 vibrations:2 l2:4 mode:11 reasonable:1 each:6 found:1 identifies:2 difficult:2 side:1 lorentzian:1 fairly:1 ed:1 energy:21 reduce:1 displacement:3 used:7 frequency:36 static:1 lowestorder:1 proportional:1 quantum:1 our:6 ev:13 eq:4 mat:1 shown:9 divide:1 impurity:3 space:1 res:2 rep:1 since:2 interference:2 denotes:5 replacing:1 contained:1 conclusions:1 jolla:1 denoted:1 formula:2 ref:4 occurs:1 red:1 shows:1 provide:1 hofmeister:3 theory:5 interactions:6 free:1 standard:1 clarify:1 completely:1 perturbation:2 california:1 york:3 philip:1 definition:1 interaction:8 r0:3 r3:1 widths:1 could:1 transition:3 moment:1 david:1 motion:1 isotropic:3 transfer:1 corrections:1 ionic:1 neglect:1 first:3 origin:2 major:1 features:6 symmetry:1 stoneham:2 third:2 number:4 system:1 restrict:1 smaller:2 done:1 defects:1 directly:2 carry:1 impossible:1 electronic:5 appl:2 size:3 dispersion:2 necessarily:1 temperature:9 their:4 introduction:1 cambridge:2 eqs:2 gpa:4 construct:2 mutschke:1 indicate:1 halide:1 2ωj:1 listed:1 calculations:1 scheme:2 98ch10886:1 final:1 gives:2 shell:32 discussion:1 exactly:1 part:16 simulate:2 authors:1 branches:1 than:4 specify:1 population:1 wide:2 gγδ:2 fe2:4 approximations:2 measured:11 matter:2 determined:2 magnesium:4 amplitude:1 identical:1 treated:4 exhibit:1 lowest:2 san:1 angel:1 unchanged:1 spectrum:3 curves:3 summing:1 randomly:1 gale:1 progr:1 analysis:4 allen:2 concentration:5 clearly:1 relatively:1 strength:4 angle:1 built:1 depending:2 anharmonicity:9 self:23 mid:2 sciences:1 high:6 potential:5 gσ:1 label:3 converged:1 negligible:2 strengths:1 unperturbed:1 kahan:1 prevot:1 electric:2 normal:1 bruce:1 incidence:1 impurities:1 most:3 struzhkin:3 propagate:1 significant:1 comparisons:1 phase:1 hu:1 intrinsic:1 chap:1 kc:1 give:2 mineral:2 surprising:1 calculated:8 phil:3 stronger:1 questioned:1 km:1 typeset:1 kr:1 optical:4 reflections:1 exp:15 brookhaven:1 physics:4 sum:1 fitted:4 underestimates:1 planetary:1 show:3 doped:8 scattered:1 infrared:16 mg2:4 mg1:13 relation:1 expressed:1 sunysb:1 astrophys:1 earth:4 uβ:3 find:1 astron:2 ear:1 causality:1 parameters:7 conduction:2 explain:1 distributed:1 written:1 should:2 only:9 won:1 black:1 coefficients:1 factor:3 hennion:1 leastsquares:1 equilibrium:1 ser:1 do:4 dominant:1 get:2 dependent:1 de:1 mgo:26 christopher:1 brillouin:2 report:1 holland:1 liu:1 evolution:1 spikes:1 intrinsically:1 krumhansl:1 arxiv:1 zαβ:2 remove:1 acknowledgments:1 experiments:2 predicted:1 ωp:5 nα:1 qj:9 grad:1 cells:3 ignored:2 set:1 computed:3 reference:1 national:1 j1:3 j2:4 relative:1 isotope:3 radius:2 result:1 close:2 observed:1 conductivity:5 surfaces:1 ωj2:4 timusk:1 tensor:1 phonons:5 uδ:1 uα:1 dipole:2 uγ:1 materials:6 boundaries:1 sites:2 state:5 converted:1 various:1 jth:2 correctly:1 between:3 approach:3 across:1 spectrometers:1 tsun:1 recently:1 statistically:1 nature:2 modify:1 weak:2 however:7 modeling:1 atoms:1 tensors:1 both:8 piece:1 many:2 region:5 vibration:1 attributed:1 sγ:1 grain:1 dated:1 retarded:1 0j:20 contribution:1 cowley:3 whole:3 experimental:15 kugel:1 among:1 relevant:1 cm:42 ca:1 harmonic:8 2nd:1 alone:1 homogeneously:1 bose:1 doping:6 points:2 considering:1 broadening:3 configuration:1 described:2 yagi:1 basis:4 addition:3 keppel:1 radiative:2 due:7 been:12 much:1 complicated:1 combined:1 interest:1 maradudin:1 monotonic:1 tetrahedron:1 ls:27 dots:2 direction:3 relations:1 corresponding:8 kronig:3 am:1 sufficient:1 6k:7 photon:1 kramers:3 ensuring:1 iπ:1 worked:1 denote:4 spin:5 those:6 eiq:4 extracted:1 ǫa:1 infared:1 pacs:1 solid:7 bruker:1 empirical:1 evaluated:1 rectangular:1 will:7 near:7 optimization:1 reliably:1 leaves:1 loop:1 reflectance:19 uncertainty:3 iq:1 averaging:2 ir:1 thus:7 site:2 surface:1 iv:1 ii:11 examined:1 cond:1 il:1 ambient:1 qj1:5 convection:1 faraday:1 situ:1 greater:1 different:1 sensitive:2 estimate:1 distributions:1 make:1 radiation:1 lett:1 same:11 any:1 complex:4 split:1 largest:1 units:2 figures:1 dimensionless:1 several:1 horton:1 iγ:2 higher:4 independent:2 extended:1 peaks:1 calculating:1 cubic:1 effect:1 sym:1 hand:1 ion:1 insulating:2 compared:6 uses:1 potentials:3 totally:1 expand:1 eigenvectors:3 lower:3 leath:1 modes:5 keeping:1 jcs:1 well:5 wedged:1 without:2 thought:1 solids:2 edge:1 sets:1 position:1 model:37 lin:1 mon:1 wedging:1 less:3 when:1 accurate:2 obtain:1 seen:1 sources:1 underlying:1 atomic:3 mineralogical:1 differentiation:1 alkali:1 scattering:20 eigenstates:1 based:2 upton:1 absorption:5 photons:5 extra:3 seems:1 except:2 evanston:1 lattice:3 treatment:1 samples:6 diagonalization:1 c12:3 c11:1 guarantees:1 plasma:2 guyot:1 take:1 real:7 rev:5 represents:1 evaluate:1 couple:2 term:1 corresponds:6 increases:5 nvc:4 know:1 hemley:1 average:1 using:3 burns:1 mod:1 shoulder:4 like:1 semi:1 adiabatic:1 dos:3 separately:1 eβ:1 either:2 become:1 inter:2 disorder:24 reduced:2 susceptibilities:1 methods:1 classical:1 dorschner:1 spring:1 successfully:1 back:1 born:3 b2:1 table:8 transport:1 nonzero:1 ignore:2 vol:1 dimensions:1 confirm:1 resonances:1 avoid:1 measurements:2 inside:1 fringes:2 linearly:1 propagating:1 smyth:1 o2:3 l3:4 digitized:1 core:3 sherman:1 reaching:1 equivalent:3 agreement:3 pressure:2 wong:1 revtex:1 although:2 eiω:2 imaginary:13 refers:1 super:3 properties:10 publishing:1 comparison:2 about:6 central:1 dependence:1 o:25 range:8 neighbor:1 chow:1 concentrations:1 introduced:1 slightly:1 stony:1 equally:1 computational:2 mantle:2 eˆα:2 dyson:1 nsf:1 pair:1 right:1 determine:3 steven:1 sized:1 reducing:1 utility:1 uncertainties:1 rows:1 elastic:2 artifacts:1 assumed:6 speck:1 ωp2:1 width:5 quadratic:1 henning:2 low:4 way:2 was:5 synthesis:1 function:20 north:1 complete:2 differences:2 but:4 histogram:2 volume:1 buckingham:1 heat:5 properly:1 related:2 atom:4 line:6 highest:1 sdj:1 especially:1 calc:12 compute:2 disordering:2 ωpd:2 whether:2 mtrl:1 vacancies:1 smooth:1 theoretical:2 nearest:3 crystal:17 below:3 ωj:3 limit:1 diagrams:1 how:1 define:2 similar:2 clear:2 distance:1 detailed:1 constant:3 labels:2 defined:4 abstract:1 measurement:1 influence:8 life:2 general:4 single:2 laboratory:1 crystals:4 work:1 dβ:1 check:1 physical:3 tedious:1 diego:1 functions:3 transitions:4 mccammon:1 no:5 dashed:2 hybrid:1 phonon:19 field:1 other:2 details:3 branch:1 department:5 out:1 picture:1 repeat:1 star:1 ballistically:1 separate:1 models:4 time:3 vertex:1 chem:1 includes:1 a3:8 important:3 peak:2 a6:1 included:1 tendency:1 astronomy:1 needed:2 neighbour:1 independently:1 coulomb:2 assume:1 values:6 together:1 depth:1 mass:3 resembles:1 inaccuracy:1 n1:3 n2:2 gαβ:3 once:1 |
0704.2268.txt |@word partial:1 consider:13 remarkable:1 rev:1 magnetic:3 global:1 people:1 results:4 existing:1 leads:1 proposition:23 grateful:1 kato:1 consists:2 follow:1 denotes:1 devoted:1 isometric:3 inverse:7 depend:6 calculate:1 combinatorial:5 graph:45 segments:1 tu:1 canonical:1 editors:2 diamagnetic:1 tn:16 finally:3 th:10 under:5 kuchment:8 analogous:1 x00:1 norm:11 case:10 random:3 straightforward:3 outside:2 very:1 calkin:1 p0:3 roe:1 corollary:1 valued:10 every:30 lecture:1 difference:7 matrices:2 condition:7 visualized:1 ve2:1 immediately:1 hamiltonian:5 turns:1 notes:2 vertex:2 t1:4 discrete:43 indices:3 eigenvalues:7 anal:1 referred:2 noted:1 zn:184 employing:1 sturm:1 periodicity:1 conca:1 direct:1 located:3 imply:1 infimum:1 pass:1 further:2 reine:1 chem:2 linear:8 spectral:17 index:2 what:2 nano:6 diag:3 section:12 localization:1 mechanics:1 ktα:1 uniform:3 above:1 sup:16 illustrations:1 expresses:1 t2:4 method:3 satisfy:3 compact:5 implying:1 respectively:3 even:1 certainly:1 here:4 behaviour:1 objects:1 cos2:2 represented:1 consideration:2 equations:3 mex:1 z2:3 obtained:4 instituto:1 technical:1 shift:5 study:6 vectors:3 steffen:1 contradiction:1 periodic:56 products:1 akl:5 action:15 fourier:2 makes:5 sci:1 york:4 uniquely:1 boundedness:3 via:7 useful:2 lobanov:2 family:1 ix:24 apr:1 prefer:1 marked:1 inverses:2 apply:2 weierstrass:1 univ:1 jan:1 use:4 takes:1 physics:5 distinct:1 positive:3 contains:1 chl:3 only:14 reflexivity:1 properties:12 zig:3 closedness:1 call:5 therefore:2 atα:3 taken:2 vj:1 more:3 subcases:1 becomes:2 operators:126 ti:1 odinger:34 berlin:3 particular:2 known:4 cases:4 iii:1 account:2 isomorphism:7 vladimir:2 ih:1 recall:3 loops:1 det:2 london:1 ij:14 obvious:2 three:3 following:22 affiliated:1 root:1 example:10 proof:6 memoirs:1 figure:4 give:1 calculation:2 organized:1 saito:1 states:2 assumptions:2 numbers:2 sense:3 occur:1 verlag:2 information:1 soc:6 winter:1 szeged:1 provide:1 verify:1 acts:8 evidently:1 write:7 maps:2 vital:1 criterion:3 adjacent:1 instead:2 polit:1 description:3 algebra:32 angew:1 max:3 wiley:1 orbits:5 reflect:1 applications:7 wrong:1 plane:2 lax:1 waves:2 multiplication:4 fj:1 goal:2 cokernel:1 short:1 natural:3 dynamical:1 effective:1 whenever:2 sp:54 explicit:2 electron:1 redundant:1 element:2 so:6 automatically:1 fundamental:4 representation:3 order:3 oper:4 holds:6 ith:1 indeed:2 over:2 satisfied:2 years:1 russian:1 course:1 wiener:13 paper:3 including:1 enumeration:1 banach:22 mentioned:1 satisfies:1 poincar:1 june:1 its:12 constituted:1 tending:7 derive:2 group:19 decay:1 chosen:1 interesting:1 fix:1 lh:1 gen:1 forms:2 absence:1 complex:4 systems:2 lp:78 lq:1 jacobi:1 mail:2 main:2 image:1 non:3 good:1 material:1 introduce:7 functional:2 band:44 they:1 acta:2 now:2 transparent:1 possess:3 easily:4 term:1 dirac:2 presented:1 identified:1 sufficiently:1 inequality:2 roch:10 each:14 found:1 universit:1 λja:6 side:1 mean:2 heavy:2 darmstadt:3 domain:4 differential:2 ei:4 fairly:1 series:1 harris:1 w12:13 related:5 pauling:1 equivalence:1 3b:1 quantum:14 our:6 mapping:8 eq:2 special:3 out:3 respects:1 shown:3 matrix:11 space:30 since:5 induces:4 research:1 particles:2 attracted:1 acting:4 dominated:25 ra:17 denoted:1 formula:7 rn:3 induced:1 issue:1 occurs:1 math:27 shows:1 foundation:1 theory:13 associate:2 interscience:1 contain:1 diagonal:4 free:5 standard:1 clarify:1 completely:2 perturbation:2 subsequences:1 convolutions:1 cmv:1 estimate:2 e1:3 e2:3 definition:4 pairs:1 interaction:1 r1:2 r2:2 agree:1 geometry:1 determining:1 ath:3 motion:2 thing:1 technische:1 georgescu:2 place:2 gordon:2 hence:15 βn:2 onto:2 βj:2 first:1 xj:15 already:2 xn:8 reflexive:1 finiteness:1 isometrical:1 bijection:1 zag:3 number:7 dinger:1 another:2 precisely:2 overlapping:1 illustrate:1 given:7 necessarily:1 introduction:1 deift:1 adjoint:7 construct:1 their:13 assumption:1 too:1 floquet:1 structures:4 shifted:1 rabinovich:10 lot:1 tool:3 continuous:3 immediate:1 authors:2 norms:5 x3:1 x0:7 x1:16 uhlmann:1 than:1 coefficients:7 finitely:4 distance:2 determines:1 sections:2 depends:3 project:1 subsequence:5 determined:2 pairwise:2 were:1 college:1 providing:1 distinguished:1 w2:11 bhk:3 spectra:15 few:1 ann:1 modern:3 spectrum:44 curves:9 say:3 disjoint:2 seen:3 hexagonal:3 mint:2 clearly:8 smallest:1 min:2 describe:2 lim:12 latter:5 ideas:1 maxt:2 lp0:3 note:10 instance:1 ideal:1 potential:11 2g:1 generalized:1 xi:10 new:5 coincide:1 gmail:1 caltech:1 honeycomb:2 cl:5 formulas:2 electric:2 abdullaev:1 zigzag:8 birkh:1 most:1 said:1 connected:5 plan:1 subset:1 class:5 exico:1 dresselhaus:2 ka:12 invertible:8 considered:5 clear:1 later:1 tβ:1 vertices:9 tα:6 countable:2 graphs:21 points:16 usual:2 germany:1 bdo:2 fact:2 allows:1 show:4 german:1 supported:1 converge:2 notations:2 x2:12 spaces:15 relation:4 vogelius:1 ve1:1 eiϕ1:2 eiϕ2:2 based:1 basel:1 assertion:3 should:2 values:1 theme:1 stand:2 specify:1 constant:5 hamiltonians:4 local:1 carlson:1 do:4 biblio:1 klein:2 means:5 de:1 aα:9 v1h:8 made:1 words:1 invariant:5 wise:2 admissible:1 3a:1 closure:2 mattis:1 bolzano:1 approach:4 arxiv:6 yield:1 calling:1 sum:1 intervals:5 compactification:1 through:1 ecnico:1 kernel:1 set:21 exists:7 observes:1 imposing:1 hγ:30 operates:2 λk:7 see:9 radius:1 result:5 w1:8 forthcoming:1 techniques:1 hilbert:3 satisfying:2 eigenfunctions:1 mogilner:1 justifies:1 fulling:1 tend:1 symmetric:1 unions:1 classes:2 closed:4 between:6 ui:4 geometric:1 αj:2 conditions:4 checks:1 terms:1 h12:7 importance:2 attention:1 wj:6 inclusions:2 fredholmness:5 distinguish:1 carbon:5 amer:6 ker:1 both:3 collaborators:1 shubin:1 last:2 2n:2 limits:2 cayley:4 freely:5 σa:10 equal:1 laplace:2 propagation:1 σah:1 context:3 highlights:1 comm:3 passing:1 com:1 masses:1 monograph:1 otherwise:1 unitarily:3 cj:12 kirsch:1 cn:61 point:4 simple:2 yafaev:1 dimensional:1 simply:1 coordinates:1 lattices:1 sequences:2 respect:14 throughout:1 coker:1 ensures:1 korotyaev:2 second:1 basis:1 union:5 locally:2 due:3 been:2 ai:3 belongs:1 slowly:14 asymptotics:1 basic:4 expected:1 conjugated:1 ph:4 algebras:9 empty:2 define:1 generating:7 aj:2 corresponding:1 commutes:1 going:1 sufficient:2 subspace:1 argument:3 finds:1 func:1 c2:1 albeverio:2 denote:8 present:1 applied:3 multi:1 splits:1 subsets:1 ap:23 solid:1 crossed:1 examine:2 will:2 contemp:2 proves:1 suppose:3 viii:1 behavior:1 many:3 exist:3 ending:1 property:7 leaves:2 identical:1 settles:1 ve:2 mexico:1 vh:1 vi:6 metric:28 thus:13 ii:2 need:1 ik:1 itself:1 avh:1 vu:1 reports:1 cycon:1 orthogonal:2 vainberg:1 binary:2 different:2 develop:1 grant:1 media:2 belong:3 same:3 any:2 shifts:2 parts:1 emphasize:1 proved:1 finite:10 subalgebra:3 consequence:4 difficult:1 independent:3 ball:2 infinity:18 embedding:1 comprehensive:1 upon:1 hand:1 berkolaiko:1 v1:15 v2:15 edges:3 arrived:1 auser:1 potentials:4 infinite:2 identity:4 suitable:2 schr:35 center:1 mention:2 well:7 analysis:6 without:1 academic:2 edge:1 sets:1 position:1 model:1 chemistry:1 soviet:1 self:7 left:4 isometry:3 stores:1 just:1 heavily:1 being:1 obtain:1 isolated:1 torus:1 body:1 underlying:1 identify:2 integer:2 facts:1 λj:2 λi:2 scattering:2 previous:2 adv:2 preprint:1 infinitely:1 conclude:3 had:1 exclusively:1 nacional:1 possibly:1 lattice:7 cantor:3 conacyt:1 location:3 theorem:24 guarantees:1 heidelberg:2 real:10 opp:6 around:2 represents:1 ipn:1 possible:2 boundedly:1 vα:5 vβ:1 press:4 equality:3 prominent:1 loss:1 modifications:1 necessary:1 particle:7 δy:1 follows:11 reduces:1 html:1 collect:1 yields:2 either:1 arbitrary:2 edu:1 anti:2 pointwise:1 essential:33 terminology:1 anisotropy:1 mathematical:4 www:1 old:1 methods:3 sequence:20 some:12 springer:2 certain:2 understood:1 describes:1 hunziker:1 examples:6 moreover:4 reasons:1 provided:2 v2h:8 dense:1 2e:1 electromagnetic:2 isometrically:1 providence:5 does:5 provides:1 tends:4 l2:7 preceding:2 refer:3 run:1 indicated:1 problems:7 equivalent:5 l1:4 oscillating:14 amrein:1 bj:2 bk:5 likewise:1 br:1 post:1 possesses:1 notation:1 edif:1 simpler:2 weighted:1 algebraic:1 theorems:1 http:1 o:2 reduced:1 convenient:1 whence:2 fredholm:21 act:1 nucleus:1 observation:2 consequently:3 block:1 op:10 rieman:1 therein:3 perturbed:3 cambridge:2 inclusion:1 h2:6 into:4 h1:5 integral:3 isomorphic:1 negative:1 lies:1 hermitian:2 square:1 references:4 laplacian:8 operator:112 next:2 physical:1 often:2 schrodinger:1 van:1 springerverlag:1 support:1 there:21 u1:2 transform:3 imperial:1 dispersion:1 much:1 editor:1 way:7 was:4 function:28 complete:2 form:15 converse:1 but:4 hu:1 hj:3 hh:1 state:1 reed:2 nanotubes:1 convergence:3 lectures:1 line:1 ha:3 true:1 hg:4 he:1 coset:1 applying:1 embedded:3 multiplicity:1 nanotube:1 liouville:1 un:2 limit:43 uj:5 continuously:1 problem:4 similar:3 called:14 strongly:2 froese:1 sometimes:1 associated:1 ag:6 defined:7 ah:29 abstract:1 pseudodifferential:3 general:3 multiparticle:2 single:3 invertibility:3 au:17 av:1 ax:1 inf:10 check:1 four:1 defines:4 silbermann:3 again:6 functions:17 courant:1 no:2 mathematik:1 whereas:5 aromatic:1 field:1 other:6 electrical:1 details:1 papers:3 concerning:1 nice:1 elements:8 models:1 symbol:3 setting:1 uniformly:2 polynomials:1 generated:2 important:3 bounded:13 gap:3 structure:12 network:1 simon:4 independently:1 implies:11 auxiliary:1 assume:3 tubes:2 interval:5 orbit:3 together:4 equivalently:1 appl:3 nuclei:1 starting:1 |
0704.2269.txt |@word limited:1 partial:2 consider:3 interference:1 particular:8 dynamic:1 results:3 leads:4 computation:1 edu:1 consists:1 follow:1 expressions:2 faster:2 gj:11 gi:3 whose:4 aligned:1 depend:3 calculate:1 iii:1 concerned:1 γw:1 γv:1 γu:1 γt:10 environment:2 finally:2 flopping:1 present:3 under:3 analogous:4 include:1 adiabatic:2 r12:36 g2:11 straightforward:1 g0:5 very:4 frequencies:9 rise:2 differently:1 choice:5 every:2 orientations:1 chuang:1 resonant:1 difference:4 exact:1 condition:2 look:1 milburn:1 illustrated:1 school:1 level:20 positions:10 guo:1 solution:3 t0:1 damped:2 large:3 discrete:4 vector:30 succession:1 small:2 eigenvalues:1 shows:8 optics:1 equation:19 leibfried:1 upper:6 smaller:1 slower:1 antinodes:10 qubit:1 trend:1 sin4:1 sin2:3 direct:4 approximation:3 slowed:1 tana:1 dynamics:12 substitute:1 even:2 what:1 plays:1 appear:8 section:1 localization:6 remain:3 charac:1 poles:2 localized:3 above:3 new:6 maioli:1 occupation:1 apply:1 acknowledgments:1 contrast:1 satisfy:1 quenched:4 processing:1 degree:4 exchange:1 respectively:3 never:3 component:2 here:6 atoms:107 ranges:1 met:1 selective:1 decay:2 inversion:6 separation:5 address:1 active:1 along:2 strong:1 equations:8 z1:1 change:1 obtained:4 sending:1 turchette:1 involved:3 study:3 vectors:1 allows:2 reason:2 experience:1 eberly:2 suggests:1 amount:2 periodic:1 resulting:1 pictorial:1 action:1 resonance:4 studies:2 involves:2 plotted:2 composed:1 useful:1 apr:1 explained:1 while:1 scaled:1 modulated:1 suffered:1 decrease:1 traversing:1 establish:1 readily:3 standing:17 tn:3 use:4 2g02:3 takes:2 would:2 probabilities:1 give:2 examined:1 periodically:5 wood:1 call:2 therefore:3 associated:1 raimond:1 creates:1 reflects:1 unequally:1 separated:1 lowering:1 populations:3 becomes:4 operators:5 mismatch:1 emission:3 surprisingly:1 transient:10 varying:2 known:1 cases:1 iv:2 antinode:13 nodes:5 ρa:1 couples:1 none:1 distributes:1 locked:1 sphere:3 science:1 challenge:1 work:1 ρs:9 itself:1 obvious:1 publications:1 ficek:5 following:3 modifies:1 coherences:4 spontaneous:4 example:3 numbers:1 minima:1 ions:1 modulation:1 wang:1 figure:3 mirrors:1 process:4 sinusoidally:1 neglected:1 haroche:1 nielsen:1 states:3 effectively:3 performed:1 council:1 2γt:1 tan:1 domokos:1 occur:3 axis:4 information:3 g1:12 rather:3 siz:2 holds:1 feature:2 far:1 varies:7 criterion:1 akram:1 pure:6 answer:1 optimal:1 absolute:2 parameter:4 sin:7 oscillatory:2 product:2 description:1 fx:1 max:3 after:1 3rd:1 produce:1 wave:18 unentangled:3 parallel:1 constants:17 changes:2 short:2 waist:1 third:2 whenever:2 ρnm:1 correspond:1 think:1 sj:19 si:6 so:7 increasing:2 allow:1 representation:1 words:4 order:2 restricted:1 help:3 2sj:1 produces:1 over:4 insight:1 vary:3 satisfied:2 produced:1 course:1 paper:1 through:12 cold:1 still:1 excitations:1 its:13 before:1 τn:1 controllable:1 derive:2 lc:1 located:13 interesting:9 temporal:2 complex:1 exhibits:5 actually:4 wineland:2 absence:1 according:2 itano:2 choose:2 rabi:3 main:1 emphasize:1 versus:2 mathis:1 them:1 good:1 nonideal:1 pauli:1 thereby:2 delocalization:1 obtaining:1 practice:2 fig:11 introduce:1 reflected:1 modification:1 precess:1 precession:3 effects:1 they:2 now:2 yu:1 represents:6 february:1 regularly:2 fully:3 university:2 traced:1 huelga:1 2d:2 sufficiently:1 magnitude:2 mode:67 fields:1 found:5 quarter:1 singlequbit:1 schemes:2 ei:1 significantly:2 populated:2 there:7 energy:29 hard:1 gilligan:1 related:1 inverted:2 elementary:1 frequency:13 measure:2 quantum:13 our:4 happen:1 trf:1 eq:11 special:1 out:5 shown:4 chap:1 matrix:8 driving:3 space:2 δra:11 quantify:1 rep:1 since:6 rev:22 bad:1 research:1 increase:1 may:18 hill:1 formula:1 electronics:1 induced:7 forth:1 ri:1 rj:3 predicted:2 occurs:6 wiley:2 theory:1 interactions:2 bertet:1 diagonal:3 possibility:1 standard:1 difficulty:1 completely:9 included:1 term:11 asj:1 e1:4 generate:1 shortest:1 e2:5 v0:16 interaction:24 r1:2 r2:2 created:1 happens:1 could:2 transition:7 times:27 motion:4 turn:3 plane:1 place:1 transfer:1 consequence:6 eqs:4 south:2 first:7 origin:2 already:2 features:4 rydberg:1 relate:1 number:6 reaches:3 progresses:2 alternatively:1 done:1 long:5 another:1 knight:1 reached:1 precisely:5 electronic:1 engineer:3 dispersive:2 given:12 closest:1 exists:1 introduction:1 leading:2 interact:1 behaves:1 system:48 least:2 intense:1 their:2 cooling:1 master:15 influence:2 scheme:2 sensitivity:1 gives:2 shifted:2 imperfect:7 trapped:4 centered:2 distribution:2 relative:3 continuous:4 leaking:1 motionless:1 motivates:1 optical:8 ith:1 x2:1 off:1 representing:1 than:11 population:13 begins:1 distance:4 wootters:3 determines:7 nath:1 rate:6 kraus:1 preparation:5 determined:1 amplitude:5 enables:1 w2:1 exhibit:1 raman:1 pointed:2 generality:1 locations:10 curves:1 achieves:5 2t0:1 seen:7 any:2 relatively:1 lie:1 angle:6 uncertainty:2 zero:4 depending:1 mechanism:2 note:4 sciences:1 concerns:1 absorbed:3 zou:1 analogy:4 coincide:1 strengths:4 eichmann:1 exactly:6 unless:1 electric:1 opposite:1 reach:3 z2:1 most:7 involving:1 significant:1 successive:3 phase:2 spin:1 measured:1 why:2 manifested:2 αt:12 unequal:5 observation:2 consequences:2 considered:1 average:1 later:1 bergquist:1 qualitative:1 part:1 principle:2 exp:2 kz:1 oscillates:4 physics:4 naively:1 fact:4 ritsch:1 particularly:1 phenomenon:3 show:4 nπ:7 random:1 visualized:2 relation:6 solutions:7 king:1 australian:1 inequality:1 find:9 ground:1 aρ:1 slow:1 knowledge:3 parameters:3 explain:2 dynamical:1 enough:1 should:4 being:1 only:10 explicitly:2 captures:1 circle:1 oscillate:1 concurrence:39 achieve:6 equilibrium:1 exchanged:4 serafini:1 intersect:1 notation:1 means:2 dependent:5 familiar:1 db:1 degradation:1 beam:1 cannot:1 closely:1 despite:1 dv:1 during:2 dt:2 procedures:1 reveal:1 evolution:23 dρs:1 conditions:11 arxiv:1 summary:1 twice:3 investigate:1 experiments:2 common:1 analytical:2 including:1 qk:1 fixed:2 valid:2 locating:2 set:2 reference:2 achieved:2 variations:2 frame:2 lett:11 detection:1 edition:1 depends:4 bare:1 result:5 eliminating:1 w0:16 close:3 optimum:17 satisfies:1 analog:3 points:2 annihilation:1 exploited:1 interacting:3 pattern:6 dipole:26 initially:12 state:20 various:2 jth:2 between:45 graphically:1 approach:3 wide:2 multiplied:1 terms:16 creating:2 opening:1 qubits:3 illustrate:1 however:7 w02:1 vanishing:3 separately:1 suppressed:1 ωc:2 both:1 cos:14 always:5 many:1 region:3 la:1 equal:13 display:1 sensitive:2 σy:5 plenio:1 dated:1 ωji:1 passing:1 experimental:2 otherwise:1 reside:1 among:2 afterwards:1 point:2 simple:7 effective:2 narrower:2 corresponds:5 imperfection:1 dimensional:1 represented:1 pole:5 written:2 simply:2 decreases:1 keitel:1 bose:2 moreover:1 li:1 second:3 described:2 cavities:1 basis:1 observing:1 create:3 auffeves:1 radiative:2 due:6 been:5 appears:3 detuning:11 much:3 slowly:3 damping:9 interest:1 basic:1 ph:1 treatment:1 sjz:1 generating:1 arises:2 corresponding:4 quantities:1 coherence:8 photon:6 essentially:2 argument:1 coherent:8 dramatic:1 understand:1 maximally:2 importance:1 those:1 case:28 extracted:1 multi:1 laser:1 processes:2 unlike:1 pacs:1 solid:4 appearance:1 examine:3 value:13 will:7 near:1 encountered:1 behavior:3 shift:8 situation:3 property:2 procedure:2 maximal:1 detailed:1 larger:1 satisfying:1 osnaghi:1 coupled:11 linked:1 vi:1 refs:2 thus:9 non:2 natali:1 ii:1 superconducting:1 arrangements:1 duan:1 cone:1 allen:1 vanish:1 monroe:1 greater:2 different:16 bollinger:1 supported:1 plotting:1 cosine:4 locking:2 cross:2 same:2 clearly:1 shifts:4 unity:3 parts:2 quant:1 split:1 widely:2 largest:2 units:1 dimensionless:1 regime:1 privileged:1 difficult:1 development:2 independent:4 used:5 see:5 effect:8 driven:8 moment:1 levels:22 moving:1 entanglement:85 contribution:1 zheng:1 early:1 lower:7 task:2 kept:1 modes:2 makes:5 modeled:1 well:2 analysis:1 evolves:3 more:7 without:2 solve:2 components:5 sets:2 coordinate:2 position:17 model:3 oscillation:5 maxima:2 distances:3 returns:2 proposed:1 less:3 brisbane:1 storage:1 observed:3 obtain:4 rest:1 tδ:1 intervals:2 distant:6 atomic:17 immediately:2 λi:1 rotates:3 previous:2 york:3 intersection:1 zoller:2 density:11 nutation:1 photons:1 bell:1 dicke:1 other:7 location:10 easy:5 zeros:3 wiseman:1 excited:1 uw:1 take:1 identical:3 australia:1 aspects:2 around:1 easily:3 possible:2 harmonic:1 dark:1 increases:3 entangled:14 press:1 using:1 accepted:2 apart:1 loss:1 modifications:1 pertinent:1 like:2 shaped:1 follows:5 collective:3 performing:1 raizen:1 noted:1 specific:1 goldstein:1 imposes:1 yariv:1 arbitrary:3 popular:1 become:1 stationary:1 essential:2 cooled:1 because:6 affects:1 creation:12 some:5 back:2 certain:1 understood:2 elements:7 respect:1 complementarity:2 brune:1 translates:1 neglecting:1 matching:1 myatt:1 nonzero:2 provided:2 scale:6 cavity:88 resonances:1 2nπ:2 microwave:2 does:4 eliminate:1 provides:1 tends:1 demonstrated:3 ωij:6 lowest:2 obey:1 detuned:9 plot:1 equivalent:8 δi:6 oscillating:4 perpendicular:1 how:2 evolve:1 shifting:1 reduces:1 imaginary:1 properties:4 proceed:1 twolevel:3 about:9 polzik:1 central:1 increasingly:1 tracing:1 discussed:2 dependence:1 reduced:6 practical:3 remains:1 range:4 interpret:1 beige:1 introduced:2 consequently:6 bloch:29 peak:1 xu:1 equally:2 cambridge:2 nonequivalent:3 presence:3 previously:1 into:5 within:3 auxiliary:1 attains:1 three:4 swain:2 variable:1 determine:2 operator:5 real:1 area:1 assumed:4 springer:1 initial:19 question:2 u0:15 stark:4 u2:1 surprising:1 width:2 describes:2 way:2 delocalized:1 was:2 assumes:1 function:18 north:3 complete:2 form:7 denoting:1 gerry:1 but:5 idealized:4 gain:1 atom:51 elimination:1 line:10 dissipative:1 utilizing:1 raising:1 longer:5 inverse:1 gi2:1 evident:1 whether:1 characteristic:1 inside:15 uq:1 maximum:1 us:5 limit:9 evers:1 problem:3 ωb:12 similar:1 clear:1 strongly:3 cirac:3 constant:13 worthwhile:1 introducing:1 defined:1 recognize:2 specified:1 moved:1 direction:1 general:2 oscillations:5 single:16 lived:1 au:1 wavelength:1 journal:1 accounting:1 physical:1 functions:2 transitions:1 nm:1 dotted:2 no:10 dashed:5 whereas:6 when:20 vanishes:5 field:29 interested:2 role:1 details:1 spatial:9 department:1 node:4 picture:5 permitting:1 superposition:4 excitation:5 separate:1 handicap:1 variation:10 prepared:6 important:1 cos2:7 queensland:1 structure:6 independently:1 implies:1 coupling:34 assume:4 values:5 diffraction:13 quite:2 mancini:2 tradeoff:2 investigated:2 observe:1 time:55 meystre:1 having:2 |
0704.2270.txt |@word schlegel:1 magnetic:1 four:4 facilities:1 whose:2 calculate:2 aug:5 presents:2 under:6 every:6 classifications:4 school:4 humidity:5 enhance:1 consistent:1 direct:5 second:2 tangential:1 estimated:1 even:2 errors:3 contributed:1 lights:1 above:7 new:3 med:7 residual:4 here:5 reported:1 protection:1 active:5 obtained:7 study:1 symmetrical:2 changes:3 blackbody:11 diameter:5 divide:1 classification:4 9b:1 highly:1 total:4 kobayashi:7 would:3 negative:1 tabulated:2 therefore:9 type:5 until:1 successful:3 curvature:4 hole:6 must:1 room:2 err:5 mm:10 work:2 roof:1 pinholes:1 temperatures:4 transparency:1 give:3 indicates:2 want:1 times:1 attract:1 machine:2 very:5 classify:2 sato:1 lan:1 after:7 movable:1 diagram:8 parallel:3 types:9 attempt:1 effective:1 correlation:1 vapor:3 order:8 wind:2 executed:1 office:1 over:20 vary:1 japan:16 before:4 fit:1 better:1 fig:16 cref:3 versus:1 them:4 affected:3 combination:2 safe:1 band:9 effects:1 they:6 brightness:9 classified:3 reasonable:1 each:16 side:1 mean:6 telescope:16 combining:1 laboratory:1 rs:1 restricted:3 gradation:1 particles:1 newly:1 size:5 turning:3 linear:5 little:2 free:1 standard:18 proportionality:1 estimate:1 telescopes:2 r0:6 exposing:2 motohara:1 corrections:1 onto:1 purpose:1 primary:15 channels:2 another:1 categorize:1 thick:6 electronic:1 similarly:1 top:11 rates:2 observations:18 percentage:3 ceiling:1 somewhat:1 distance:1 target:1 zero:1 tref:4 project:3 pasp:3 acquisition:8 sees:2 raw:5 seen:8 contents:1 relatively:2 convenient:2 latter:1 recommended:1 academy:1 transmit:1 magnum:20 circles:1 though:3 object:1 extending:1 optimized:5 regular:1 bradford:1 doi:1 observation:20 calculated:4 points:1 fitted:4 stephens:2 rayleigh:1 infrared:32 integrate:1 oct:5 rectangle:1 plate:9 mixture:1 stop:1 dc:1 degradation:2 baffle:1 dz:2 despite:1 dr:2 bar:1 fields:1 bad:1 automatic:2 decides:2 reference:8 observes:1 sensitivity:7 detection:3 depends:1 radius:1 result:1 best:2 subject:1 said:1 capacity:1 away:1 µm:12 drawn:1 approach:1 preserve:1 extend:1 however:12 extent:1 improve:2 suggested:1 triggers:1 cox:2 against:3 0b:1 coe:1 logic:1 asked:1 lenses:2 widen:1 height:1 shiromizu:1 strong:1 three:2 been:15 quickly:1 much:3 basic:2 expected:1 dry:3 quantities:1 concerning:1 chile:4 spie:4 catch:1 worked:1 applied:2 microns:2 aip:1 air:2 near:9 aid:1 procedure:1 cone:4 ic:1 containing:2 make:2 plated:2 plates:1 several:19 fairly:1 numerical:1 rain:29 hand:2 osawa:2 tune:1 emissivities:2 thn:8 left:4 seasonal:2 just:1 hongo:2 scattering:2 kanagawa:1 regarded:2 spread:2 board:3 easy:2 5b:1 sagamihara:1 elevation:4 possible:2 possibly:1 rny:6 background:16 shadow:3 advanced:1 sparse:1 night:9 cooled:1 www:1 right:4 deal:1 people:1 successfully:2 proportionally:1 bottom:7 daytime:2 okada:1 cnc:1 shamir:2 manufacturing:1 permitted:1 aerosols:1 months:8 o:8 costs:1 cirrus:2 automatically:2 primitive:1 faint:1 facility:1 down:3 methods:1 altitude:6 initial:1 sunlight:2 gif:1 way:2 was:16 medium:8 form:1 manufacturers:1 taken:1 hemisphere:1 prevents:1 attached:1 devices:1 mtk:1 millimeter:1 sapphire:1 emis:1 emit:1 originating:1 abstract:1 proves:1 exist:1 dλ:2 dθ:2 check:2 triangles:2 physical:2 nm:1 dotted:1 no:9 when:19 setting:1 digital:11 test:2 node:2 models:2 describe:1 miscellaneous:1 θmin:2 longer:1 interval:1 daily:1 time:8 serious:2 nuclei:2 remarkable:1 particular:2 focus:1 manager:1 grateful:1 depend:1 zone:2 environment:4 finally:4 protective:2 advantage:1 frequencies:1 trouble:1 minute:1 clouds:33 presented:2 did:1 dig:1 hawaii:6 cloudy:11 quick:1 upper:2 revolution:1 trend:3 cost:2 dried:1 targets:2 appear:1 current:2 template:4 filled:3 supporting:1 water:3 apache:1 along:6 change:2 ndata:3 institute:3 throughput:2 usually:1 studies:1 plotted:1 regardless:1 rarely:1 planck:1 working:3 visit:1 sports:1 selects:1 theoretical:1 diagrams:1 rainfall:3 outputs:4 apparent:6 degrade:1 tokyo:11 deformed:1 avoiding:1 originally:2 labeled:1 printing:1 values:4 following:4 figure:23 mirrors:6 december:1 allowed:1 nmsu:1 monitoring:5 winter:3 divided:2 chemical:1 map:4 mar:5 may:6 spot:2 needs:1 4th:1 mag:3 data:31 liquid:1 cosmology:1 bunkyo:2 so:7 emissivity:22 typical:2 wavelengths:1 shield:1 displayed:1 years:10 stability:1 ended:1 thinner:1 nitrogen:1 ttl:3 cold:2 still:2 observational:3 monitor:40 how:1 coordinates:3 window:2 mail:1 main:5 non:1 records:1 half:3 nov:5 now:7 discuss:1 execute:3 january:5 240k:1 entirely:4 photometry:2 individually:1 el:1 kband:1 significantly:2 ed:3 bradley:3 owing:3 year:5 wavelength:14 avoided:1 eq:1 shown:6 container:1 space:2 furthermore:1 increase:2 nominal:2 internet:1 squares:4 sensor:9 shows:11 hull:2 org:1 advance:1 ministry:1 place:1 φout:2 frequent:1 first:3 origin:3 rms:4 directly:2 comprises:1 impossible:1 array:3 open:1 engineer:1 city:1 given:4 anyone:1 cooling:2 moisture:5 white:3 bits:1 national:2 gives:1 mostly:1 season:2 continuous:1 than:17 were:7 resistivity:1 correction:1 locations:1 allen:1 any:2 14µm:2 note:9 take:3 thermometer:1 interior:2 performance:4 channel:1 sure:2 decreasing:2 falls:1 detect:7 skinner:1 latex:1 average:13 precise:3 show:2 cheap:1 migrations:1 bright:1 ground:5 upgrade:1 ratio:8 enough:6 only:10 going:1 black:2 lapse:1 cannot:2 bolometer:3 secondary:12 aluminum:5 vision:1 ignored:1 blurred:1 relative:3 masahiro:1 surfaces:1 fails:1 satisfying:1 sites:3 outside:1 between:13 august:3 vertical:2 aberration:2 jp:1 dome:8 jr:1 come:1 pixels:5 originates:3 parentheses:1 many:10 region:1 according:7 multicolor:1 comes:1 afterwards:1 overview:1 period:2 sampling:1 anti:1 moreover:4 deposited:2 combined:7 reflective:1 direction:2 restrictions:1 mauna:5 former:2 those:3 case:1 operational:1 squeezes:1 ongoing:1 clr:8 situation:1 zenith:11 characteristics:2 unit:3 bias:2 ambient:3 technology:1 different:5 develop:1 same:3 html:1 status:2 wires:1 meteorological:1 driver:1 delicate:2 totally:1 uncooled:6 without:4 components:6 dashed:1 coordinate:1 ccd:1 model:10 summer:2 outdoor:10 being:10 generally:3 cease:1 speed:1 seems:1 except:6 instrument:1 real:4 around:5 psf:3 dark:3 scheduler:1 world:2 vertically:1 server:1 shutter:11 either:1 fully:1 output:7 reduced:3 respect:2 images:23 imager:36 finkbeiner:1 recorded:1 conservative:1 critical:1 refer:1 measuring:1 airmass:4 scientific:1 power:4 seconds:2 equivalent:4 naoj:1 island:3 discussed:2 practical:2 os:1 sensitively:1 amber:6 cautions:1 instruments:1 image:35 numerically:1 references:1 determine:8 heated:1 operator:1 accumulated:3 prepare:1 area:22 refinements:1 strictly:2 there:13 start:1 low:2 stars:4 complete:1 jun:5 jul:5 fabricate:1 strongly:1 ac:1 celestial:1 certain:3 aj:1 6b:1 watches:1 watcher:1 reliability:2 together:1 nickel:2 az:1 field:22 spatial:3 deviation:3 polar:1 separate:1 vertex:4 includes:6 computerized:1 important:2 flattened:1 coverage:12 brass:1 remote:4 controlled:1 nagano:1 waveband:7 resolution:2 original:11 since:3 sci:1 consider:1 pointing:1 caused:2 month:4 follow:1 safety:1 tc:5 worse:1 straightforward:1 far:3 condition:32 large:7 small:5 10µm:4 ten:2 rate:8 design:6 pass:1 further:1 gunn:1 what:3 sub:25 sun:1 section:6 thickness:3 method:1 compilation:1 component:5 ranges:1 operating:2 compressed:2 directions:2 commercially:2 observing:7 allows:2 amount:3 narrow:1 hogg:2 aimed:1 extinction:9 sensors:5 select:1 nemiroff:2 archived:1 eye:2 distinct:1 contains:2 comparing:1 aperture:4 takeo:1 achieving:2 more:12 flat:10 diamond:3 erode:1 thus:1 company:2 corrected:4 emission:3 instrumental:1 controlling:1 varying:1 weighed:1 science:6 equation:1 remain:2 dec:6 deg:1 cosmological:1 share:1 autumn:1 exclude:1 axis:6 information:1 respective:2 rather:2 breaking:1 srinivasan:6 maps:10 centimeters:1 galactic:2 tried:1 advice:1 derived:2 reflect:1 panoramic:3 plane:2 coming:1 plank:1 imagers:4 fundamental:1 help:1 developed:8 soon:1 installed:2 thermal:30 paper:1 through:5 its:20 rapidly:1 late:2 systems:7 might:2 deformation:2 good:2 number:4 easily:3 hereafter:1 always:2 level:8 siegmund:1 raytheon:1 micro:2 stopped:1 ifa:1 radial:2 found:4 referred:2 heavy:1 colder:1 fish:2 hard:2 reduce:3 idea:3 operation:9 beyond:1 missed:1 surrounded:2 projected:2 research:4 dominated:1 sloan:1 sagittal:1 evaluation:1 guess:1 base:1 imaging:1 put:2 onsite:1 circuit:4 unmanned:6 probability:2 reflected:2 done:5 construct:1 fluxes:1 differ:1 temperature:21 introduction:1 reflectivity:1 scheme:1 banana:1 listed:3 relationship:1 selector:1 part:5 favorable:1 center:10 kind:1 observatory:21 headers:1 determined:1 aas:2 toward:1 risky:1 beforehand:2 defect:1 headings:1 quasars:1 mountain:1 nights:10 built:1 internal:2 electric:1 warnings:1 reach:1 most:4 significant:2 extremely:1 deviations:1 tsutomu:1 clear:28 sometimes:4 cover:1 km:1 optical:10 ku:2 azimuth:1 particularly:2 gold:4 converge:1 relation:1 degraded:2 fine:1 cdy:6 northern:2 less:4 subsection:1 factor:1 circle:1 columns:1 goes:1 dependent:2 during:6 catches:1 arxiv:1 bytes:1 scanning:2 bars:1 achieved:3 culture:1 see:10 individual:1 sec:1 sea:3 close:4 analog:6 various:6 acidic:1 conditions:30 available:3 recently:2 synchronizing:1 incident:3 rapid:1 interface:2 both:10 improved:13 mega:1 annual:1 sensitive:3 objective:1 whole:73 point:4 simple:1 corresponds:2 header:1 simply:1 linux:3 observatories:3 throughout:1 bλ:4 decline:1 described:3 monthly:5 due:3 aspherical:7 pc:6 reduction:3 maintenance:6 ph:1 meeting:1 partly:1 wavebands:3 convert:2 determination:1 representative:1 systematic:1 cassegrain:6 uncertain:1 look:3 solid:2 expanded:1 empirical:2 evaluated:8 while:7 error:1 evaluates:2 itself:1 grant:1 shorter:2 products:1 ray:1 higher:1 development:2 used:8 alert:1 levels:1 photometer:1 fabrication:1 focal:2 early:4 lower:4 percentages:2 analysis:6 edge:4 shape:5 using:13 alignment:6 conclusions:1 bolometers:1 signals:16 remaining:1 photometric:11 format:1 evaluate:2 aerospace:1 bit:5 like:7 tangentially:1 shaped:3 signal:17 separately:1 flux:8 often:2 spring:1 some:15 trends:3 sight:2 mirror:39 facing:1 scale:4 measurements:1 integration:3 per:4 proc:4 agreement:1 become:1 subtract:3 range:1 block:1 seeing:2 into:18 within:2 frames:2 inspects:1 statistics:5 measured:9 long:1 analyze:1 sections:1 opens:1 considerably:1 hawaiian:2 properly:1 line:8 directed:1 up:3 us:3 exploration:1 kuhn:1 fluctuations:2 similar:9 constant:3 defined:1 single:4 warning:1 rainy:9 fixing:1 nao:1 preventing:1 electrical:3 department:1 elements:1 calculating:1 prepared:1 lens:8 structure:1 independently:1 correlated:2 algorithm:1 required:3 subsections:1 depth:4 requires:2 once:3 illustrates:1 results:1 cobalt:1 illustrated:1 edu:2 moon:1 compact:1 concerned:1 stably:1 send:1 suits:1 intensive:1 helps:1 stable:2 weather:14 include:1 dramatically:1 continued:2 entire:3 optics:20 noted:1 smaller:1 compensated:2 compensates:1 incidentally:1 apparatus:1 access:1 3a:1 degree:2 respectively:4 objects:6 consideration:1 widening:3 great:1 parameters:4 technical:1 larger:4 survey:1 apr:6 extinctions:1 decrease:1 apo:1 cloud:97 standing:1 use:11 feb:5 remains:1 nagoya:1 next:7 few:6 camera:17 themselves:3 panel:1 started:1 becomes:4 visibility:1 central:2 detects:2 challenge:1 averaged:1 thin:11 fulfill:1 drops:5 scatter:2 proof:2 control:1 do:3 process:1 thermally:1 proportions:3 dripping:1 high:12 slit:4 kosugi:1 tan:2 roughness:1 regions:1 located:2 θmax:5 instead:1 sin:2 circular:2 specifications:7 rays:1 fits:1 platt:2 light:2 lines:1 correspond:1 alloy:1 discussion:1 produces:1 astronomical:7 produced:2 including:6 converting:1 outer:1 degrees:9 resistively:1 covered:2 pixel:4 kiso:4 material:1 subtraction:1 hands:1 satellites:1 transparent:3 warned:1 university:6 traced:1 magnitude:1 illuminate:1 related:1 inverted:2 frequency:2 calibrate:1 measure:3 relates:2 out:5 respects:1 fundamentally:1 minezaki:2 cause:1 integrated:4 8b:1 maintains:1 galaxies:3 completely:4 york:1 could:4 feasible:1 length:1 assumed:1 powerful:1 improvements:1 quality:3 salient:1 deceptive:1 sep:5 system:39 adopted:2 their:13 yoshinodai:1 transistor:2 environmental:1 reflecting:10 too:1 july:3 observed:4 colleagues:1 roberts:1 compensation:1 collecting:1 hz:2 need:1 instrumentation:1 angle:14 agency:1 mie:1 mechanism:1 detector:7 subtracted:3 pipe:3 snapshot:1 fact:1 atmosphere:8 indoor:1 subtracting:1 based:5 controls:1 should:13 jan:6 atmos:1 micron:1 molecules:1 achieve:1 photographs:1 means:8 astigmatism:2 mainly:7 norio:1 ones:1 words:1 areas:9 gray:2 differential:3 processed:4 grab:1 cycles:1 view:12 requirement:1 statistical:2 exists:1 acquired:6 frame:9 okayama:2 intensity:1 closes:1 pattern:6 haleakala:20 macros:1 converted:1 closed:1 tens:1 comparable:1 opening:1 kea:5 efficiency:3 key:2 psfs:1 configuration:1 distribution:5 thank:2 observable:5 commands:1 etc:1 figures:1 otherwise:1 adjusted:1 co:1 cm:2 environments:3 decreases:1 table:21 addition:1 copies:3 compensating:1 senses:2 corresponding:1 controller:1 expenditure:1 angles:1 ours:1 present:2 hiroyuki:1 align:1 appearance:2 value:13 rectangular:1 will:1 maui:3 cvd:1 ultra:2 fielding:4 vignetting:3 barely:1 almost:7 coating:4 site:10 surface:26 hardware:8 suganuma:2 vs:2 supported:3 began:1 radiation:5 parts:3 schematic:2 units:2 atacama:4 difficult:3 http:3 effect:1 v5:1 robotic:5 dust:1 frequently:2 reflection:2 well:7 sets:2 position:1 sensing:1 spherical:1 restore:1 heavily:1 obtain:1 germanium:3 clocks:1 distant:1 adu:1 preprint:1 absorption:2 sky:98 day:2 attractive:1 wet:2 increased:1 government:1 mitaka:2 mitake:1 increases:1 five:5 press:1 immediately:4 necessary:1 helpful:1 success:1 loses:1 regulated:1 works:1 opacity:1 because:20 convex:3 demonstrates:1 does:3 assuming:1 sdss:1 noise:6 coated:1 analysed:1 offset:7 noisy:1 about:17 actual:1 carried:2 getting:1 column:4 universe:1 dependence:5 shipping:1 carries:1 introduced:5 software:8 washington:1 weighted:1 housing:5 yoshii:5 spots:1 inner:1 upwards:1 miyashita:1 function:9 triggered:2 triangular:1 but:9 astro:1 construction:1 automated:14 partially:1 made:3 converter:2 whether:8 placed:2 below:3 astrophysical:1 limit:2 takami:1 problem:1 minutes:4 mask:1 universal:1 contribute:1 meaningless:1 pix:5 our:41 crystals:1 education:1 inc:1 functions:1 compared:1 calibration:8 percent:1 detail:1 virtual:1 other:14 details:1 star:4 radially:4 variation:3 astronomy:3 exposure:2 coat:2 ranks:3 4a:1 |
0704.2271.txt |@word arcminutes:2 parkes:2 remnants:8 whiting:3 lhcp:4 astronomical:1 atca:1 displayed:1 results:2 valuable:1 discovered:3 eds:1 bandwidth:1 radio:1 edu:1 keywords:1 macquarie:1 taken:1 x000000000000000x:1 indicator:2 thank:1 density:1 produces:1 help:1 james:1 magnetic:3 program:1 fig:1 sydney:1 excited:1 over:1 australia:1 beam:1 mcdonnell:2 using:4 new:3 continuum:1 produced:1 clouds:4 densities:2 fields:3 university:1 arxiv:1 identified:1 yield:1 large:2 flux:4 mhz:23 radial:1 small:2 found:2 beamsize:1 circular:2 csiro:1 caswell:5 seventeen:1 right:2 rhcp:4 people:1 slysh:1 braiding:1 used:1 observed:3 see:1 astrophysical:1 equivalent:1 expected:1 table:2 further:1 transitions:3 gridded:1 assistance:2 sites:2 per:1 identification:1 ra:1 remain:1 between:2 international:1 nsw:1 email:1 jy:3 degree:1 interactions:1 l111:1 respectively:2 supernova:8 weak:1 analysed:1 like:1 mnras:2 formation:1 brightest:1 stacy:1 observing:3 both:1 search:1 interaction:2 multibeam:2 column:2 kylafis:2 uncertainty:1 http:1 duchamp:2 zeeman:1 addition:1 conducted:2 survey:2 matthew:1 ism:1 receiver:2 other:1 peak:4 size:1 wardle:4 already:1 apr:1 catherine:1 www:1 environments:1 channels:1 remnant:1 square:1 references:1 approximately:4 pairs:1 total:1 cloud:1 vaughan:2 unambiguous:1 polarisations:2 would:1 width:1 union:1 three:1 been:3 mark:1 their:1 reduction:1 recognised:1 therefore:1 calculations:2 iau:2 ph:1 molecular:2 was:3 scans:1 direction:1 baan:1 forming:2 emission:5 alan:1 astro:1 indicators:1 cubes:1 observations:1 excellent:1 known:1 magellanic:2 line:4 than:1 present:2 absent:1 mg:3 solid:1 oh:11 likely:1 atnf:1 while:3 mq:1 splittings:1 were:4 dec:1 minutes:1 discoveries:1 mader:1 weaker:1 associated:2 figure:1 almost:1 well:1 abstract:1 goss:1 them:1 proven:2 ii:1 dashed:1 au:2 km:6 coincident:1 ascension:1 analysis:2 any:1 maser:9 containing:1 no:2 suggest:2 apj:2 regions:3 field:2 methanol:2 calibrated:1 potentially:1 masers:11 frail:2 department:1 symposium:2 channel:2 higher:2 satellite:1 towards:3 star:2 peaks:2 excitation:1 multiple:1 may:2 searched:1 southern:1 hand:1 helping:1 stars:1 allowing:1 preliminary:3 acknowledgements:1 data:4 recent:1 doi:1 subtracted:1 programs:1 resolution:1 calculated:1 spectra:1 lines:2 chapman:1 ghz:2 proceedings:2 declination:1 time:1 velocity:3 physics:2 left:1 |
0704.2272.txt |@word represent:1 gu:1 managed:1 chinese:1 capaccioli:1 caused:4 activated:1 results:4 although:1 disk:3 centers:1 issues:1 arcsec:1 inverse:1 seyferts:4 alamos:1 young:2 interactions:1 finally:2 program:2 present:3 include:1 2mass:1 activities:5 ınguez:1 supported:2 mpa:1 very:4 kewley:11 hst:1 drexel:1 dispersions:1 summarized:1 affect:3 difference:13 akritas:1 large:5 yale:1 small:2 concluded:1 upper:4 heckman:2 smaller:2 l93:1 kim1:1 guidelines:1 estimates:2 japanese:1 progenitors:2 rate:1 pasp:1 profiles:1 estimated:2 spectral:2 reviews:1 what:2 errors:3 hernquist:1 sub:2 chicago:1 section:1 selected:6 dr5:6 current:1 version:3 causes:1 new:5 method:5 led:1 dwarf:1 degree:2 stages:1 understanding:1 ranges:5 objects:2 adelman:1 apache:1 ratio:3 along:1 strong:1 change:1 great:1 naval:1 institute:7 study:8 studied:2 monbukagakusho:1 survey:4 fermilab:1 adopting:2 studies:3 imaging:1 named:1 secure:1 family:1 photometric:1 engineering:2 apj:16 lenticular:1 univ:1 planck:3 select:3 use:1 links:1 prove:1 probabilities:1 negative:1 guideline:1 criteria:3 aperture:1 robertson:2 panel:4 type:79 theoretical:2 toomre:2 more:2 populations:3 line:14 pipeline:3 lehnert:1 babu:1 bisector:2 known:1 cases:1 iii:5 vp:5 science:3 der:1 work:1 tanvir:1 reproduce:1 groves:5 bias:1 obvious:3 starbursts:1 springel:1 example:1 history:1 compare:2 cosmological:2 process:2 loci:1 tecza:1 weinberg:1 sample:13 council:1 sense:1 axis:1 information:1 provide:1 tilt:7 discussion:2 american:1 how:1 varies:1 larsen:1 criterion:5 fps:1 elliptical:4 answer:1 ordinary:1 kias:2 snellen:3 fp:43 seoul:3 may:13 max:3 after:3 diagram:8 catalog:4 plane:4 cambridge:1 empirical:5 data:8 parallel:1 types:1 trevena:1 short:2 physical:2 outline:1 effective:3 joint:1 light:1 l57:1 lines:2 liner:14 cosmology:2 so:1 fundamental:13 acknowledges:1 martini:1 typical:1 katz:1 evolutionary:5 interpretation:1 produces:1 laboratory:1 funneled:1 produced:1 experiments:1 through:1 existence:1 its:1 galaxy:12 observational:3 phillips:1 style:1 fittings:1 interesting:2 late:3 continue:1 fig:8 searle:2 lira:1 main:1 might:6 versus:4 non:3 good:1 affected:1 similar:1 safe:1 finish:1 band:1 circumnuclear:1 effects:2 they:7 structural:1 february:2 brightness:2 parameter:2 university:14 infer:1 magnitude:3 classify:2 each:11 found:5 higher:1 constraints:1 domain:1 differential:1 tilted:2 telescope:1 ed:1 energy:1 abnormal:9 related:1 group:2 society:1 investigated:1 combining:1 our:14 shown:5 rp:6 space:11 gradient:5 furthermore:1 since:6 research:3 re:2 sloan:3 l39:1 correct:1 r90:1 shows:2 foundation:4 fiber:1 marel:1 offsets:1 ultraluminous:1 dressler:2 galaxies:169 guess:1 formation:12 york:3 org:2 estimate:1 anchez:2 times:1 conducted:5 snu:4 massive:2 yun:1 davis:2 museum:1 first:2 origin:4 major:2 already:1 aeronautics:1 primary:1 fluxes:1 sutherland:1 size:4 given:2 introduction:1 revmexaa:1 adopted:2 their:13 returns:2 intermediate:1 draft:2 observations:1 alfred:1 capetti:2 structures:1 consistent:7 too:1 deg2:2 relationship:3 pittsburgh:1 academy:1 exactly:1 park:4 lynden:1 part:1 western:1 apjs:2 natural:1 than:7 dynamical:1 urry:1 observatory:2 target:1 showed:2 princeton:1 petrosian:2 resampled:1 preparation:1 incompleteness:1 classes:19 busarello:2 were:5 toward:1 distinguished:1 mpia:1 portsmouth:1 modern:1 randomly:1 longo:1 headings:1 emission:2 distorted:1 need:1 concentration:1 fading:1 contents:3 hydrodynamic:1 rigopoulou:1 self:1 menanteau:2 consortium:1 mechanism:2 sciences:1 ideal:1 causing:1 davies:1 korean:1 blue:2 dimming:1 added:1 normal:42 ugriz:1 who:1 giavalisco:2 letter:4 measured:2 class:9 latex:1 lee:5 genzel:1 dom:1 considered:2 calculated:1 adopt:1 cover:2 inferred:1 km:13 typeset:1 kr:6 points:2 joon:1 velocity:6 abraham:3 physics:1 institutions:3 ho:1 slope:22 selection:2 show:3 glazebrook:1 random:3 infrared:1 colors:1 relation:1 corner:1 find:1 homology:3 based:1 parameters:5 merger:2 explain:2 basel:1 woo:3 haven:1 only:3 micron:1 rich:3 identification:2 burkert:1 do:2 stoughton:2 kosef:1 agns:3 state:2 closely:1 drawn:1 earl:1 gray:2 evolution:5 franx:2 fields:1 arxiv:1 blanton:2 investigate:3 scientist:1 common:1 activity:2 release:1 ohio:1 finishing:4 fixed:1 mergers:3 set:2 fair:1 hβ:5 national:4 hα:5 connections:2 see:1 radius:4 result:1 japan:1 close:1 subject:1 tenreiro:1 nuclear:1 boundaries:1 initially:1 outside:1 various:4 between:21 limit:2 boundary:1 email:1 available:1 korea:5 recently:2 extend:1 mcintosh:1 targeted:1 however:9 spectroscopic:4 clues:1 distinguish:1 virial:2 distribution:4 suggested:3 both:1 panels:3 limits:1 cox:3 region:2 conclusions:1 according:1 tinsley:1 participating:3 sensitive:1 connection:7 artal:1 kavli:1 estimation:4 hwang:1 σv:17 nearby:1 reside:3 among:8 tacconi:2 point:1 color:10 cd:1 active:3 observatories:1 throughout:1 considering:2 addition:3 three:1 been:2 describes:1 combined:1 basic:1 expected:1 figure:2 ph:1 define:1 direction:1 easy:1 quantities:1 formed:4 gas:11 schilizzi:1 systematic:2 djorgovski:2 those:9 case:1 resulting:1 unlike:1 aiz:1 solid:3 dissipational:1 reliable:1 estimations:1 cbp:2 value:1 will:1 while:4 diverse:1 error:6 balmaverde:2 larger:2 mexico:2 site:1 surface:2 ii:3 middle:1 dongdaemun:1 vs:2 absurd:1 different:16 grant:1 lamost:1 belong:1 administration:1 merging:13 same:10 zinn:2 parts:1 products:1 several:5 events:2 difficult:2 evolve:6 used:9 http:2 numerical:1 effect:6 hand:1 constraining:1 fabian:1 tremonti:2 kjærgaard:1 vogeley:1 recent:1 dark:1 lower:4 center:1 scenario:7 minimize:1 changes:1 feigelson:1 analysis:4 without:1 position:1 model:1 kauffmann:7 left:1 r01:1 responsible:1 accretion:1 starforming:2 less:2 segregate:1 lutz:1 baldwin:3 previous:3 web:1 cut:1 preprint:1 classification:5 hint:1 bell:4 sky:3 dissipationless:1 samples:1 theorem:1 terlevich:2 match:1 heisler:1 tests:2 bernardi:5 march:1 dekel:2 bands:1 capozziello:1 possible:5 early:76 possibly:3 makes:1 press:1 using:11 sampling:5 advanced:2 serna:1 necessary:1 particle:1 sizes:1 follows:4 signal:1 faber:1 flux:2 seyfert:16 bpt:4 become:1 works:1 differentially:1 interestingly:1 www:2 right:2 methods:1 sequence:3 flatter:1 some:4 cosmos:1 ols:1 table:3 trujillo:2 mccarthy:1 provided:2 ellis:2 myung:1 does:1 provides:1 sdss:19 participation:1 isobe:2 noise:1 stellar:2 host:17 ratios:1 tidal:1 post:1 emulateapj:1 properties:2 seong:1 comparison:2 about:3 goods:1 central:1 origins:1 hopkins:2 choi:6 o:10 acs:1 range:3 slightly:1 obs:1 own:2 significant:1 redshift:4 johns:1 into:7 within:2 washington:1 because:3 references:1 england:1 significantly:1 van:1 l29:1 artifacts:1 support:1 there:4 question:1 approximate:1 long:4 jørgensen:2 dispersion:5 los:1 much:2 fraction:2 astrophysics:3 slopes:10 was:9 maza:1 triggered:1 forming:30 differences:4 jun:1 forever:1 but:3 astro:4 repeated:1 hierarchical:1 segregation:3 automated:1 mnras:7 r50:1 variations:1 us:2 tell:1 astrophysical:3 ωm:1 spectroscopy:1 planes:2 2003b:3 problem:1 2003a:2 subclasses:3 clear:1 puddu:1 ac:4 earlytype:5 defined:1 stronger:1 abstract:1 aj:5 deep:1 evidence:1 single:1 reliability:1 simulations:2 gradients:1 education:1 distributions:2 steeper:1 compared:1 completeness:1 dotted:1 dopita:4 dashed:5 whereas:1 when:2 bremer:1 other:2 potsdam:1 ulirgs:2 digital:2 department:2 conclusion:3 poor:1 star:39 corrected:4 june:1 liners:4 variation:2 includes:1 important:3 nucleus:1 dissipation:1 funding:2 astronomy:4 structure:1 agn:30 implies:1 lee1:2 assume:1 values:1 baker:1 mass:1 time:1 nuclei:1 reserve:1 |
0704.2273.txt |@word consider:12 illustrates:1 lagrangian:11 global:3 splitting:4 leads:8 roy:1 scalar:26 follow:1 whose:2 sahni:1 caldwell:1 hochberg:1 finally:1 critical:1 th:1 under:10 sorkin:1 brown:1 very:7 mpl:2 rise:2 choice:2 mixing:1 experimentally:1 difference:1 exact:2 condition:8 treating:1 entire:1 level:3 die:1 solution:15 large:9 adjust:1 small:12 eigenvalues:2 der:1 jhep:1 smaller:1 garnavich:1 riess:2 joglekar:1 zero:8 displays:6 further:1 theories:1 what:2 fine:3 section:8 current:3 3h:4 cheng:4 new:4 method:2 contrast:1 satisfy:2 full:1 respectively:2 never:1 here:11 possibility:2 address:1 along:2 quite:2 equations:5 appears:1 obtained:1 canadian:2 study:1 larger:1 suggests:1 resulting:3 pick:1 action:22 suitable:1 9h:1 useful:1 padmanabhan:1 scales:1 explained:1 apj:5 addressed:1 demir:1 total:1 planck:9 dζi:1 would:1 covariant:1 predictions:2 next:7 classically:1 nucl:2 call:3 therefore:2 m2:17 taken:1 associated:1 today:1 more:1 introducing:1 tsujikawa:1 india:1 acceptable:1 primarily:1 particular:1 known:2 cases:2 parameterize:1 quartic:2 mb:1 equation:6 fµν:5 modified:2 salam:1 remain:1 minimum:2 values:1 era:2 ρv:2 making:1 trans:1 spontaneous:3 example:1 decoupled:1 cosmological:24 give:2 expanding:1 allowed:2 neglected:1 weinberg:2 high:2 lorentz:2 pawlowski:1 want:1 arise:1 copeland:1 needs:1 provide:3 breaking:16 write:2 far:7 instead:2 parameter:11 sin:11 alternative:2 may:19 ζi:5 earlier:5 φr:1 hence:17 explored:1 summarize:1 law:1 data:1 four:3 higgs:4 light:1 βi:1 rather:1 maintain:1 negligible:4 jain:1 order:20 talk:1 produces:1 indeed:1 over:1 displayed:1 satisfied:3 including:2 argued:1 existence:1 satisfies:1 still:2 its:6 before:1 group:2 thank:1 interesting:2 masses:6 solving:1 boson:5 absence:3 complex:8 choose:4 derivative:4 eventually:1 non:2 teitelboim:3 diagonalize:1 dam:1 eiθ0:2 gauging:2 introduce:1 break:1 they:1 foot:1 rotation:3 now:5 easily:3 term:17 daughton:1 sufficiently:6 magnitude:3 mode:1 turns:1 found:5 ann:1 differential:1 directly:1 energy:29 applicable:1 literature:1 expect:1 quantum:16 our:6 happen:1 eq:3 out:6 canada:1 cosmologically:6 shown:2 dominates:3 matrix:3 space:3 furthermore:2 since:5 squared:2 research:1 content:1 vector:2 dominated:2 rel:1 print:1 postpone:1 ref:2 math:2 theory:22 free:1 standard:7 approaches:1 besides:2 van:2 estimate:3 generate:5 hubble:5 waterloo:1 impose:4 motion:8 turk:1 massive:1 corrections:2 neglect:1 first:1 kanpur:1 symmetry:34 reaches:1 restrict:1 fast:1 another:4 illustrate:1 given:1 toy:4 publication:1 introduction:1 leading:4 5th:1 approximately:2 quadratic:1 observations:1 townsend:1 gives:6 explanation:1 exactly:2 eliminates:3 part:1 eliminated:4 than:4 intrinsically:1 wide:3 require:2 second:3 modelled:1 matter:2 states:2 future:2 tonry:1 anomalous:2 treated:1 perturbative:1 lowest:1 symmetries:12 rewrite:1 dynamically:1 spectrum:6 generalization:1 gentle:1 need:6 seen:1 turner:1 dragon:1 orders:3 relatively:1 prohibits:2 generalizes:1 strength:1 angle:2 ratra:1 self:1 able:1 gravity:2 mechanism:4 violates:1 mix:1 internal:1 generalized:3 kaplan:1 so:12 mit:1 accuracy:1 towards:2 fundamental:5 iφ2:1 shall:3 volkas:1 consistency:1 kao:3 significant:1 acknowledgements:1 extremely:1 why:2 consequences:1 considered:5 clear:3 later:1 implications:1 physica:1 exp:2 dηi:3 physics:6 fact:1 precise:2 phenomenon:3 show:3 2g:1 gauge:18 astrophys:1 substituting:2 d4:6 d2:3 find:15 ground:3 astron:2 slow:11 parameters:1 state:6 only:7 wood:2 factor:1 perlmutter:1 adiabaticity:1 dn:1 do:5 dominant:1 gev:1 get:2 dependent:5 aα:1 cannot:1 dt:7 gen:1 λb:1 fields:12 arxiv:1 borrow:1 4πg:1 through:1 fixed:3 view:1 ignored:1 set:2 ricci:1 acquired:1 undergoes:1 observed:6 depends:4 sundrum:1 discussions:1 dµ:1 kinetic:1 tensor:1 review:1 symmetric:1 written:3 determined:5 simplest:1 invariant:9 diagonalized:1 conditions:2 terms:9 focus:1 however:9 louko:1 both:6 cos:11 last:1 many:1 conclusions:1 equal:6 called:1 involve:1 contribution:4 argue:2 arbitrarily:1 relativity:1 point:4 simple:1 period:1 dimensional:1 simply:3 starobinsky:1 bν:1 conference:1 described:2 tuning:3 due:1 been:1 dropping:1 frw:1 basic:1 expected:1 ph:2 correction:3 define:2 life:1 corresponding:1 observable:1 wheeler:1 dave:1 demand:1 irrelevant:1 present:1 case:10 replaces:1 papini:2 aurilia:1 value:12 remaining:1 will:13 procedure:2 identical:1 coupled:2 almost:1 metric:2 ii:1 itself:2 different:6 plunien:1 suggest:1 make:3 same:3 any:5 unity:2 parts:3 split:2 widely:1 dimensionless:1 gets:1 higher:2 breakdown:3 independent:4 used:2 see:1 published:1 effect:1 purpose:2 invariance:28 expand:3 early:1 weakly:1 modes:3 well:3 analysis:1 kobakhidze:1 solve:1 does:2 sets:3 coordinate:5 model:17 construct:3 buchmuller:1 guided:1 rotated:1 actions:1 bµ:5 λa:1 identify:3 predicts:2 untested:1 preprint:1 rajpoot:1 density:7 alternate:1 potential:8 lett:7 nicolai:1 mod:4 mitra:1 transformation:6 take:1 real:2 bij:1 around:5 henneaux:2 breaks:2 papers:1 results:1 possible:1 dark:13 background:8 vacuum:13 press:1 using:1 ruled:1 acute:1 necessary:1 particle:8 ignore:1 collect:1 either:1 regulated:1 essential:2 nishino:1 because:1 classical:22 choosing:1 oscillations:1 ourselves:1 nonzero:2 provided:1 scale:31 ellis:1 dimensions:7 lead:7 realistic:1 eiθ:4 eiξ:2 pankaj:1 assuming:3 particles:4 barris:1 varying:1 obey:1 rep:1 expansion:4 broken:14 although:1 imaginary:1 transformations:8 universe:6 discussed:4 dependence:2 remains:1 range:4 introduced:1 soc:1 rev:7 steinhardt:1 presence:2 into:3 ηi:10 three:1 rolling:8 references:1 determine:3 einstein:1 proportional:4 relativistic:1 hep:3 additional:1 dimensionful:1 question:1 lond:1 long:3 much:1 astrophysics:1 slowly:9 sections:2 naturally:1 function:2 complete:1 form:2 adjusting:1 jun:1 but:2 regularization:1 construction:4 aµ:3 true:3 gravitational:6 generating:3 up:1 us:3 sami:1 perturbatively:3 below:2 fαβ:1 fluctuations:3 problem:6 display:3 phil:1 constant:20 int:2 abstract:1 refered:1 general:11 dβ:1 check:3 dα:2 again:3 compared:1 detail:1 ng:1 field:47 other:2 role:1 becomes:2 department:1 massless:1 roll:10 peebles:1 separate:1 models:1 problems:1 important:2 included:1 implies:1 coupling:6 assume:10 required:2 pseudo:19 rule:1 mass:37 time:11 serious:1 requires:1 original:3 4a:1 |
0704.2274.txt |@word represent:1 customary:1 consider:10 magnetic:2 global:1 results:8 leads:2 eds:1 mild:1 edu:2 follow:1 optical:1 compact:1 inverse:26 depend:1 uniqueness:4 tm:3 those:2 elliptic:2 under:3 analogous:2 te:4 inhomogeneity:1 sound:8 orthogonal:1 frequencies:1 vt:2 continues:1 translations:2 wave:29 corollary:4 lecture:1 exact:1 condition:10 school:1 beginning:1 notes:1 solution:19 large:4 discrete:4 small:1 eigenvalues:1 anal:1 cox:1 upper:2 neighborhood:1 periodicity:3 direct:2 limǫ:2 second:2 rigorous:1 hdx:1 ode:1 schiffer:1 theory:4 spectral:1 plays:1 bdc:3 brackets:1 section:2 near:2 polygonal:1 above:5 new:2 method:1 slabs:1 raton:1 satisfy:2 outgoing:15 respectively:3 component:1 here:9 boca:1 equations:5 change:1 obtained:5 incoming:8 study:1 studied:2 guide:4 periodic:4 suitable:1 studies:1 uniquely:5 acoustically:2 via:1 family:1 apr:1 replace:1 apply:2 approximating:1 use:5 proceed:2 prove:4 positive:4 contains:1 ψw:9 approach:3 call:2 therefore:1 more:1 odinger:1 berlin:1 particular:1 known:3 cases:1 hold:1 springer:1 valued:1 r2:5 tokyo:2 equation:2 work:1 ms:1 following:5 making:1 def:1 proof:10 control:1 theorems:1 indicated:1 give:2 cited:1 purposes:1 assumptions:1 want:1 sense:1 chapman:1 iωµ0:1 kurylev:2 influenced:1 lemma:10 exceptional:2 off:1 occur:1 write:1 maps:2 nontrivial:2 hαk:1 permitivity:2 axis:2 map:11 product:1 may:2 earlier:1 dx2:1 dx1:7 plane:28 designed:1 waves:24 representations:1 choice:2 data:21 grow:1 imply:1 hα0:1 hα2:2 correspond:1 st:9 hypotheses:1 so:4 allow:2 definitions:4 integrand:2 order:1 holds:1 words:3 thresholds:5 move:1 ahluwalia:1 paper:3 y1:5 satisfies:1 y2:6 roots:1 before:1 underwater:1 disconnect:1 chosen:6 solving:3 complex:1 lv:1 continuations:2 absence:1 lu:5 choose:2 unbounded:1 mail:3 main:1 defining:2 setting:1 polarizations:3 kkl:4 they:6 half:2 now:3 hall:1 dielectric:7 reconstruction:1 articles:1 term:1 equality:1 james:1 university:1 sufficiently:3 l2:8 l0:2 l1:3 acoustic:2 traces:1 2i:2 mean:1 homogeneous:2 domain:3 square:7 ei:8 primarily:1 weight:1 series:1 energy:3 hard:1 reduce:2 conventions:1 elementary:1 ey:2 combining:1 eu:1 our:5 out:1 shown:1 since:18 replacing:1 contained:4 formula:1 current:1 math:4 shows:2 linear:1 region:2 e1:4 e2:3 dirichlet:21 r1:1 recovering:2 determining:2 impose:1 turn:1 exponentially:1 hence:7 conductors:6 support:8 speeds:1 first:2 initial:3 variables:1 eskin:5 philadelphia:1 done:1 directly:1 carry:1 sturm:1 open:2 xu:3 given:9 necessarily:1 marine:1 asymptotic:1 hyperbolic:11 introduction:1 arch:1 adjoint:2 analog:3 their:2 manifolds:1 statement:1 gilbert:3 structures:3 gives:3 continuous:3 transverse:2 reflecting:2 x2:107 x3:4 translation:2 x1:85 completes:2 coefficients:5 undefined:1 iωt:2 mclaughlin:2 determines:4 showed:1 fundamental:8 computes:1 limiting:3 lim:3 determined:6 stratified:1 were:1 dielectrics:1 topics:1 argument:2 ordinarily:1 rat:1 distorted:26 need:2 sees:1 recover:2 any:2 e2πiα:1 zero:2 convenient:1 self:1 note:7 k2:5 k0:2 take:2 objective:1 unperturbed:2 begin:2 unless:1 electric:3 friedman:1 liouville:1 metrics:1 extending:1 connected:2 representation:4 analytically:2 intrinsic:1 parametrize:1 observation:2 considered:1 rellich:1 part:1 verlag:1 exp:12 physics:3 sum:1 show:9 supported:3 scattered:5 dy1:1 dy2:1 iǫ:7 solutions:4 substituting:1 d2:1 δx2:2 d0:14 symmetric:1 knowledge:1 distributed:1 state:2 should:3 analytic:12 only:4 stated:1 integrable:6 over:1 do:3 dm:3 dk:1 get:1 ralston:2 dx:10 dy:2 settings:1 fields:2 arxiv:2 contain:1 bao:2 fixed:6 coefficient:4 set:20 exists:1 smooth:3 hα:2 observed:1 see:4 result:1 masahiro:1 best:1 surfaces:1 satisfying:6 eigenfunctions:2 speed:4 siam:1 µp:1 µm:25 outside:2 µn:8 identification:1 invariant:2 boundary:16 conditions:12 checks:1 x22:1 knowing:1 basis:1 extend:2 comp:2 complement:1 jp:1 however:4 continuously:1 incident:1 inclusions:1 dx21:1 restrictions:1 c20:8 last:1 many:1 taking:2 propagation:2 layered:1 comes:1 arbitrarily:1 kirsch:2 harari:1 point:2 cc:1 continuation:3 corresponds:2 environments:1 r45:1 simply:3 respect:1 throughout:1 geil:1 lw:2 union:1 ucla:4 been:1 reduction:1 petit:1 ak:1 define:2 corresponding:2 both:4 grating:2 coincides:1 modelling:1 determination:3 c2:5 c0:4 present:2 case:14 value:3 choices:1 will:20 while:1 suppose:1 applies:1 situation:1 eil:8 dobson:1 keller:1 thus:8 vtt:2 surface:2 ii:4 im:16 il:4 exterior:1 vanish:3 currents:1 make:2 belong:2 eigenvalue:1 same:2 parts:1 arguments:3 finite:1 φm:12 φn:6 independent:1 used:1 infinity:2 i0:16 inhomogeneities:1 uses:1 identity:2 recent:1 buchanan:1 fourier:2 schr:1 modes:23 charges:1 acoustics:3 obstacles:1 well:1 ocean:2 without:1 sets:1 model:1 bodies:1 less:1 gdx:6 resp:2 obtain:1 rest:1 immediately:2 yamamoto:2 scattering:25 guides:15 λm:10 letting:3 polarization:1 cut:1 kluwer:1 sciences:1 absorption:3 conclude:3 simple:1 gmx:2 extends:3 easy:1 theorem:14 generalized:18 real:8 eigenfunction:4 easily:2 big:1 harmonic:1 finding:1 know:1 using:6 unique:2 mod:1 modifications:2 dµm:1 follows:8 δt:9 δr:1 either:3 soft:1 reduced:1 permittivity:1 mathematical:3 neumann:17 some:4 back:1 mech:1 deduce:1 choosing:1 moreover:2 provided:2 dense:3 lead:1 electromagnetic:1 does:2 decomposition:1 assuming:1 propagating:23 bf:2 bc:1 bm:5 equivalent:1 each:3 expansion:1 step:2 shifting:1 imaginary:1 properties:1 simpler:1 λh:7 conducting:1 extension:3 gratings:16 discussed:1 o:4 compatible:1 stand:1 gregory:1 cutoff:1 soc:1 previously:2 maxwell:2 into:4 boundaries:3 bound:1 conjugates:1 appropriate:1 references:1 determine:15 operator:11 methods:1 span:2 strictly:2 there:6 transform:1 long:1 inner:1 ed:1 was:1 function:2 complete:1 form:6 enough:1 lassas:2 hk:2 construction:4 line:4 true:3 embedded:3 2πi:1 wish:1 variations:1 h0k:1 below:1 limit:3 utt:1 ix2:7 problem:16 ix1:1 laplace:1 ac:1 constant:2 defined:8 likewise:2 abstract:1 citation:1 am:12 denote:4 ap:2 single:1 exist:2 moves:2 eigensystem:1 again:3 functions:4 amounts:1 commutes:1 when:16 graduate:1 field:1 other:3 role:1 branch:2 papers:2 department:2 mathematics:2 conclusion:1 separate:2 preceding:3 problems:16 bounded:3 variable:1 needed:1 implies:2 assume:4 interval:2 holes:1 depth:1 time:1 requires:1 |
0704.2275.txt |@word precise:2 operations:1 homomorphism:1 proposed:1 rings:3 pointed:1 unique:1 obtain:1 notations:1 contemporary:1 proposition:4 evissage:1 integer:1 sci:1 poincar:1 its:1 perfect:1 write:1 claim:2 group:4 generator:2 maps:1 notice:1 true:4 sheaf:1 simple:1 tr:2 assertion:5 discuss:2 forms:2 lemma:9 only:6 k0:4 corollaries:2 categories:2 theorem:15 teaching:1 main:7 local:9 spec:4 semisimple:1 continuity:1 finitely:1 conjecture:16 nat:1 notation:1 get:6 fabrice:1 results:1 comparing:1 isomorphic:1 famous:1 corollary:6 isomorphism:4 serre:1 using:2 now:3 exact:5 him:3 condition:1 mod:1 prime:3 well:2 identity:1 adams:1 semi:1 follows:1 notes:3 arxiv:1 factorization:1 discrete:1 theory:8 multiplicities:1 diagram:2 minimal:2 each:3 references:1 valuation:1 pe11:1 ann:1 www:1 set:3 gersten:13 weight:2 sequence:7 series:1 edu:1 some:2 back:1 module:3 thomason:1 colim:6 zero:8 result:4 combining:1 mochizuki:2 uiuc:1 theories:2 zariski:1 xp:2 canonical:5 category:4 vol:2 satisfying:1 perf:3 space:1 define:2 section:1 since:5 induces:3 version:1 closed:2 between:1 formula:6 induced:3 induction:1 deformation:1 math:7 grothendieck:2 available:1 representations:3 historical:1 derived:1 equivalent:1 ufd:1 proc:1 here:1 vanishing:2 r0:2 groups:3 ρx:5 put:4 article:1 ord:1 inductive:1 improve:1 integers:1 about:1 shuji:1 usa:1 algebra:1 complexes:2 levine:1 p2:3 aut:1 approach:1 chow:1 hence:3 lax:5 scheme:1 acyclic:1 bloch:2 grounds:1 xi:9 statements:1 trobaugh:1 inclusion:6 apr:1 explained:1 encouraging:1 thankful:1 acad:1 non:2 sequences:2 associated:2 ring:6 cw:1 coker:1 pr:3 lect:3 commutative:10 changing:1 prove:11 introduction:2 monographs:1 strictly:1 there:2 negative:2 relations:2 next:2 perr:1 reduction:3 assumption:1 therefore:4 statement:1 codim:6 pi:3 universal:2 more:1 equivalence:2 schemes:1 duality:1 definition:3 hp:1 nakayama:1 proving:1 remark:1 part:1 known:2 implies:2 injection:1 iii:5 retraction:2 morphism:1 case:1 presheaf:1 p1:3 defines:1 springer:4 cyclic:2 supp:1 propositions:1 points:1 mi:1 see:3 axiom:1 will:8 mp:45 takeshi:1 learn:2 following:18 making:1 property:2 declare:1 stimulating:1 proof:11 kazuhiko:1 f1:25 ach:1 proved:2 cite:1 codimension:1 defined:1 certain:2 abstract:1 sense:1 argument:9 auslander:1 saito:2 ii:5 ap:5 numbers:1 fibration:1 need:1 obviously:1 identities:1 any:18 contents:1 absolute:2 noetherian:1 satoshi:1 author:1 theoretic:1 divided:1 isomorphisms:2 check:5 note:1 application:1 ideal:1 kp:2 quillen:3 dim:5 mathematics:1 finite:1 composition:1 higher:5 fp:34 map:12 elements:1 http:1 shall:6 easily:2 assignment:1 sherman:4 variant:1 equidimensional:1 applications:3 generated:3 regular:17 connected:1 purpose:2 frequently:1 lifting:1 algebraic:5 short:2 natural:1 ke:1 acknowledgement:1 lemmas:1 strict:1 modules:6 kn:24 morphisms:2 element:3 sh:6 so:2 principle:1 kt:1 representation:2 first:2 resolution:3 buchsbaum:1 fact:1 |
0704.2276.txt |@word limited:1 l169:1 lagrangian:7 magnetic:3 isotropically:1 contino:2 yellow:1 four:6 entropy:3 consists:1 looking:5 violate:1 attracted:1 contained:1 mediated:1 under:6 cm3:1 worth:2 divergent:4 bτ:1 connects:1 raffelt:3 every:3 figs:2 experimentally:2 logarithmically:1 vast:2 school:7 basics:1 cmb:8 viable:3 vector:2 math:1 relics:2 indices:1 generalize:1 glued:1 degeneracy:1 jhep:7 bill:1 force:7 consistent:4 estimates:1 direct:14 approximation:7 likely:4 follow:1 spontaneously:1 zino:1 quite:11 agashe:2 even:36 established:5 errors:1 dr0:3 dr2:1 reheating:3 above:7 new:34 ever:2 petra:1 told:2 coefficient:1 agreement:3 whose:4 divergence:2 hera:1 never:1 here:20 atoms:6 reported:2 asymmetry:3 mev:12 jcap:2 tevatron:1 logarithmic:1 calculate:5 obtained:3 singapore:1 study:15 changed:3 drn:1 buckley:2 slc:1 spacetime:2 cancellation:6 9h:1 fantastic:1 yamada:1 gluons:2 highly:2 neutrons:5 visible:2 b347:1 org:1 neutrino:11 total:6 linearly:2 derivatives:1 would:22 negative:5 riv:1 m1:2 therefore:30 m3:6 m2:14 type:1 until:1 composite:5 naive:1 tf:4 correspondingly:3 midst:1 must:9 me:13 schrieffer:1 mf:1 ma:2 mb:2 thaler:1 work:10 mh:11 theories:3 mu:1 mt:5 suggestive:1 treelevel:1 mp:27 ms:17 my:7 example:7 mz:2 renormalization:1 give:4 relativistic:7 preserving:1 generically:1 reviewing:1 want:4 isothermal:2 keep:4 guarantee:1 end:6 hoc:1 thing:2 verify:1 how:13 hot:10 answer:2 symposium:1 ordinary:3 derivations:1 fourdimensional:1 description:1 replacing:1 francis:1 after:11 diagram:8 bernardeau:1 cft:1 law:4 constants:2 third:5 nussinov:1 things:2 order:20 updates:1 exotic:1 over:11 choose:1 ibanez:1 θqcd:1 japan:1 satisfies:2 before:2 asymptotes:1 kofman:1 fiz:1 better:6 production:4 fig:49 renormalizable:3 donors:1 them:21 weakness:1 bang:12 effects:10 they:32 schools:1 represents:1 2πr0:4 brightness:2 giddings:1 backgrounds:1 hepth:3 rocks:2 faraway:1 victory:1 reasonable:3 each:12 acoustic:1 went:1 side:2 s1:2 telescope:6 series:1 displacement:1 haber:1 antiparticle:1 literature:1 combining:1 laboratory:7 extract:2 buscher:1 rt:2 rp:4 rs:29 particles:32 re:7 daniel:1 gersdorff:1 rc:28 got:2 rn:3 millions:1 rh:6 mτ:1 mχ:40 linear:4 associate:1 little:6 free:3 standard:94 formation:2 estimate:14 telescopes:2 r4:2 ate:1 r0:34 chiral:12 r2:18 created:1 starts:2 ds4:2 cosmic:18 ds3:3 ds1:2 isn:1 tempting:1 corrections:3 moving:3 cooperating:1 mellier:1 already:13 features:1 champs:3 reintroduced:1 spinning:1 warped:5 another:9 vainshtein:2 radiate:1 electronic:1 rewritten:1 similarly:2 top:7 approximately:4 needed:2 confirming:2 perturbations:2 too:13 hypothetical:1 percentage:1 murayama:47 urban:1 geneva:1 tool:1 serve:1 took:3 barbieri:1 weakly:3 somewhat:1 tsukamoto:1 peculiar:2 distance:31 last:6 showed:4 approximations:1 tree:2 second:6 preparation:1 matter:136 historical:2 tion:1 feeling:1 powers:1 perturbative:3 fashion:1 ev:10 objects:8 mind:1 spectrum:10 talking:2 veldhuis:1 seen:15 seem:4 tells:1 contents:1 relatively:5 forced:1 quadrature:1 strength:2 realm:1 convenient:1 latter:1 responsible:1 causing:3 absorbed:1 forces:1 blue:2 acquire:1 though:15 denominator:1 simplify:2 boltzmann:12 phase:2 transverse:2 don:16 observation:2 calculated:3 inferred:1 passes:2 points:8 principle:6 left:7 notion:1 incomplete:1 probe:1 nχ:8 gauge:18 solutions:3 fuzzy:1 keywords:1 earth:3 analogue:2 d2:12 tremaine:2 d1:11 pick:2 proposed:1 superparticles:4 explain:1 theme:1 coannihilation:2 rich:2 integrate:1 axion:26 dn:1 do:27 mixture:1 dj:2 cheng:5 klein:7 di:2 sup:1 stop:4 perceive:1 preferred:2 machos:14 reversal:1 dy:2 dt:12 dφ2:1 dr:13 dp:1 runs:2 paczynski:2 fields:5 lavalle:1 4πg:1 twice:1 bad:1 eventually:7 jakobs:1 explanations:1 traverse:1 fair:1 ltp:1 sensitivity:4 testing:1 axinos:1 detection:17 naturalness:1 depends:3 radius:10 result:7 discussions:7 dµ:3 best:2 subject:3 said:2 tensor:1 away:6 supergravity:1 artificial:1 symmetric:2 hopefully:2 conceptual:1 drawn:1 approach:5 discovery:3 terms:4 positron:10 nature:14 confusion:1 were:6 weak:7 however:15 bose:1 improve:1 cos:12 ilc:3 lensed:1 ill:1 uncertainty:4 shouldn:2 against:1 zakharov:2 protection:1 receives:3 distinction:1 contribution:9 burdman:1 asked:1 inflaton:1 appeared:1 nmssm:1 applicability:1 mχχ:1 ease:1 mssm:2 nomura:3 triviality:2 observing:1 chirality:1 three:15 been:6 quickly:2 much:27 interest:1 basic:2 expected:7 correction:12 tini:1 dots:1 life:3 supersymmetric:10 deeper:2 quantities:1 arkani:7 agrawal:1 confinement:1 ρhalo:1 worked:1 spin:7 applied:2 microns:1 tête:1 tanh:2 remaining:2 aim:1 near:1 polon:1 mistake:1 seven:1 settles:2 phenomenological:3 λqcd:1 ii:2 ik:1 ij:2 superpartner:4 ig:1 constrained:1 perform:1 suggest:3 make:10 speculating:1 complex:2 split:1 phenomenology:4 avoids:1 dimensionless:1 several:2 iγ:2 european:1 independent:4 satellite:1 numerical:6 hand:16 antoniadis:1 fuse:1 kim:1 nir:1 pioneers:1 opportunity:1 tune:1 fourier:4 changes:1 humble:1 mother:2 quantitative:1 paradigm:4 technicolor:7 unified:3 stringent:2 just:23 slosar:1 newton:2 ideas:1 identify:2 thanks:1 spherically:1 facts:2 axions:1 rotates:1 scattering:7 yet:10 previous:9 adding:2 enters:2 rosenberg:1 candidate:13 infinitely:1 1sec:1 furry:1 regarded:3 had:6 iω:1 belongs:1 sterile:1 easy:5 nlsp:2 5d:2 plasma:2 gave:1 yukawa:1 breaks:2 possible:14 possibly:1 fusion:4 counterintuitive:1 unification:2 background:8 poses:3 apart:1 excitation:5 patience:1 obvious:1 unnecessary:1 luminous:1 specific:1 remind:1 misled:1 n1:5 steps:1 contradict:1 evolutions:1 interestingly:1 warping:1 www:1 right:10 honored:1 deal:1 people:10 somehow:2 deflection:11 born:1 yotsuyanagi:1 jupiter:1 indirect:5 confusing:1 cooper:2 bottom:2 electromagnetic:1 quarks:11 microwave:5 contributing:1 everything:1 asking:1 unit:1 core:2 plot:1 molecule:1 gaitskell:1 oscillating:1 illustration:1 leptons:5 hsu:1 emits:3 limitation:2 months:1 o:8 horizon:2 connected:3 slightly:3 obs:2 automatically:1 considerations:1 raised:1 presence:1 trotta:1 maxwell:1 sergio:2 bound:7 bath:3 accommodate:1 lies:2 sov:1 old:2 fischler:2 methods:1 rely:2 fabric:1 mcdonald:2 support:2 flying:1 transform:2 stuck:5 anderson:2 conservation:2 physicists:2 way:22 resulted:1 call:2 was:33 annals:1 form:3 offer:1 differences:1 removes:1 aperture:7 heat:3 hear:1 solar:6 radiative:1 magellanic:2 true:5 absent:1 2r02:2 versions:3 inside:4 maximum:1 tell:4 fermi:1 gould:1 stages:1 damps:2 emit:1 recalling:1 hotter:1 classic:2 upset:1 evidence:7 conserved:1 exist:5 fashioned:1 dη:1 floating:1 check:1 physical:3 no:9 zand:1 when:29 vanishes:2 handed:2 ny:2 setting:1 papers:3 test:3 roll:1 models:20 kitano:1 gouvea:1 variable:2 seeing:1 billion:1 radioactivity:1 longer:5 pion:1 assume:7 deflector:1 together:4 warm:1 χi:1 time:21 observables:2 nuclei:3 n3:2 n4:1 ibid:1 particular:1 focus:3 mandic:1 leads:3 roy:1 hole:2 devoted:1 amplification:6 depend:1 technique:1 cm2:2 finally:2 okada:1 determinations:1 macho:15 abundance:26 lrc:1 string:6 md:1 frequencies:1 allsman:1 choice:1 prog:2 stays:1 cook:1 trouble:2 exact:3 cool:1 annihilated:1 impressive:2 solves:1 level:8 did:9 turns:6 anisotropy:1 nucl:15 leave:2 solved:3 annihilates:1 recall:2 quick:2 equation:20 upper:7 revolution:3 says:2 oscillation:2 dealing:1 discover:1 atl:1 sign:5 spanos:2 hagmann:1 y3:2 appear:4 mw:1 agrees:3 current:8 mv:1 suspect:1 ksvz:3 goes:11 international:1 filled:2 era:2 dwarf:1 steigman:1 understanding:6 water:2 contemplate:3 maldacena:1 xν:1 alone:2 along:8 appears:8 change:4 wait:2 accomplishes:1 shift:1 studied:5 wherever:1 g2f:1 resonance:2 studies:2 emerge:1 useful:6 extra:30 planck:6 wang:2 additive:1 baer:1 covariant:1 positive:1 scan:1 predictions:2 live:2 going:4 theoretical:11 diagrams:9 introducing:1 apparent:1 clue:1 eν:1 appendix:12 olive:2 cases:1 tokyo:1 gregoire:1 local:2 originally:1 ms4:1 oscillator:1 gundlach:1 reviews:1 regions:1 values:3 believed:4 making:4 modifies:1 gravitationally:1 heart:1 dedicated:1 degenerate:3 figure:1 predict:2 expanding:3 arise:2 smirnov:1 topic:3 dropped:1 allowed:5 hydrogen:5 occur:2 roszkowski:1 rays:1 monitoring:2 fortunately:2 s2:6 discussion:3 s0:4 s4:3 write:4 pure:1 radio:2 parameter:13 map:1 astroph:2 mar:1 huge:1 may:39 produce:3 data:13 natural:6 remember:3 correlate:1 higgs:47 ss:1 maybe:4 su:9 cosmology:12 so:35 deposit:3 taking:1 representation:1 acausal:1 talk:7 typical:4 nhalo:1 tagged:1 correlation:1 indeed:10 pointed:2 lsm:1 soc:1 years:4 stability:1 course:8 experiments:24 bernabei:1 statistical:1 argued:1 cold:7 still:4 b306:1 observational:1 group:7 thank:2 interesting:12 jim:1 amazing:1 decreases:2 window:2 dwarfs:2 tors:1 main:3 decades:4 perpendicular:1 τp:1 happened:1 correspondence:1 non:15 evolution:3 introduce:5 scaling:1 prunet:1 hamilton:2 msugra:1 half:2 n04:1 now:18 n01:1 discuss:13 nor:2 n02:1 down:13 term:9 holographic:1 equality:1 name:1 servant:3 didn:3 r2π:1 possibilities:3 realistic:1 moroi:3 spinor:1 square:4 significantly:1 ej:1 gaussian:2 asztalos:1 bradley:1 astrophysical:2 ex:1 proportional:7 wavelength:1 happen:1 avoided:1 eq:19 er:1 shown:9 5kpc:1 space:14 squared:2 cancels:1 increase:1 sabino:2 seriously:2 formula:2 dominate:2 correct:8 shows:9 rlm:5 earlier:8 mνi:2 theory:27 carr:2 singularities:1 million:1 mechanisms:1 ors:1 possibility:7 quark:6 california:1 lma:3 lmc:4 forbids:1 e2:6 hamed:7 recon:1 collapsing:1 transition:4 motion:4 turn:3 place:4 massive:5 think:7 colliders:2 first:21 origin:1 simplifies:1 symmetry:23 striking:1 reductionist:1 variables:2 xf:25 georgi:2 temporarily:1 directly:5 carry:1 impossible:1 size:19 squashed:1 given:21 necessarily:2 sheet:1 width:1 unitarity:1 subatomic:1 white:1 gives:13 fraction:4 mostly:1 schwarzschild:3 eliminates:1 electroweak:8 astrophysics:1 ridiculous:1 x2:5 x3:3 x0:3 than:31 e3:1 wide:3 hepph:17 unfortunately:1 hoyle:1 require:3 future:5 aesthetic:5 phy:1 austri:1 prospect:1 generality:1 mundane:3 topics:1 turned:2 argument:6 say:2 distorted:5 flatness:1 recover:1 any:12 aside:1 mr2:1 zoo:1 note:8 ideal:2 potential:10 take:7 observationally:1 spergel:1 concern:1 channel:1 hyperfine:3 ironically:1 sure:3 multiple:2 normal:2 track:1 enter:1 neutrinos:21 beta:3 importantly:2 pair:4 baryons:2 analytically:1 gρσ:2 pages:3 xµ:1 forever:1 especially:10 considered:2 average:1 later:10 l21:1 feynman:6 arguably:1 typically:5 quantity:3 precise:2 drastically:3 show:1 friction:3 longitudinal:1 discovered:6 threshold:10 aggressive:1 ground:2 feng:2 upgrade:1 ratio:1 weisskopf:3 teyssier:1 written:1 collapses:1 analytic:5 only:38 explicitly:6 black:6 sensitivities:1 legendre:2 gev:43 get:17 rept:4 weiglein:1 expectation:3 cannot:13 nearly:6 lighter:1 progress:2 hooper:1 bardeen:1 reveal:2 heckel:1 grojean:4 yield:3 worried:1 ignored:4 vx2:2 imposing:2 starkman:2 pbhs:3 bounds:3 relative:3 namely:19 cim:1 y0:10 violates:1 wonder:2 detect:2 ways:2 review:7 sites:2 enough:8 kilometer:1 between:8 complications:1 geometric:1 reading:1 across:1 verification:1 dvali:2 vertical:2 uj:1 jovian:1 4r0:2 coma:1 virial:1 come:4 originates:2 acquiring:1 fit:3 resides:1 many:27 region:5 correctly:1 contract:1 mont:1 σp:2 expression:2 σv:2 comes:5 nearby:1 among:2 cmssm:1 afterwards:1 color:1 donoghue:1 period:1 jets:2 pole:1 anti:6 article:2 cancel:2 constant:19 branes:1 considering:2 sensible:1 collider:3 tuning:6 suppressed:3 selfenergy:1 insensitive:1 b429:1 combined:1 prototype:1 imt:5 direction:2 formed:3 photon:7 observers:1 observe:2 coherently:1 careful:1 diffuse:1 those:1 case:14 trick:1 invoking:1 σb:1 cancelled:1 situation:1 conformal:1 σa:3 dθ:3 coupled:4 determination:1 metric:4 couples:2 canceled:1 sudden:1 perez:1 peskin:1 technology:1 mpc:2 different:11 verified:1 pay:2 virialized:1 same:15 shifts:2 html:1 arguments:5 events:6 assigns:1 closest:3 trivially:1 kelvin:1 siegel:1 doublets:1 changing:3 invariance:2 tradition:1 electromagnetism:3 modes:5 macro:1 nuclide:1 d1d:2 without:9 solve:7 components:4 coordinate:4 model:119 σt:1 dimension:13 charged:6 summer:3 b192:1 r02:11 ishii:1 superconductors:1 rest:1 violent:1 cease:1 aspect:2 flavor:2 speed:9 captured:1 blow:1 death:1 helioseismology:1 thinking:3 photons:5 conclude:1 seems:2 except:1 lets:2 interested:1 lett:26 complements:1 heavier:2 momentum:5 ross:1 real:4 mystery:1 aspects:1 around:10 spectacular:2 read:2 sums:1 early:9 inflation:2 5h2:1 mon:1 vacuum:10 using:18 mod:6 vertically:1 76sf00098:1 particle:49 reduces:2 velocities:1 technibaryon:1 either:5 always:4 tower:1 stationary:1 reduced:1 erase:1 moreover:1 images:7 root:2 nanometer:1 matching:1 gross:1 slice:1 ellis:3 dimensions:29 confirm:1 cavity:4 footing:1 stops:2 mesons:1 critical:1 provides:1 v2l:1 transmutation:1 majorana:1 measuring:1 scientific:3 power:6 broken:2 2m:1 exciting:3 hadron:1 central:1 oh:1 discussed:9 factors:1 tremendous:1 stand:1 mixed:1 enhancement:1 burning:1 redshift:1 image:11 numerically:2 pisarski:1 references:2 determine:6 einstein:8 elementary:9 accumulated:1 your:2 theoretically:2 baltz:1 hep:40 log:3 prepare:1 area:2 aren:1 assumed:1 there:51 dimopoulos:6 dispersion:1 start:2 low:5 lot:4 gravitinos:3 slopes:1 bubble:1 burgess:1 assumes:2 survives:1 relic:2 complete:1 bµν:1 regard:2 jun:1 jul:1 curiously:1 yad:1 promote:1 outskirts:1 anomalously:2 applying:1 coulomb:10 embedded:4 ωs:1 fπ2:1 dφ:2 shifman:2 ωm:6 ωb:4 agree:2 obtains:1 strongly:5 gone:2 ab:1 ad:1 certain:4 describe:3 am:2 deep:3 general:4 loops:1 planets:2 yanagida:2 lifetime:2 horse:2 again:5 mathematica:1 depth:4 graduate:1 field:37 valid:2 spatial:1 you:61 massless:1 deviation:1 briefly:2 separate:2 a0:2 a3:3 important:17 nucleus:4 serious:4 n2:3 tricky:1 casts:1 curve:3 mass:71 2mχ:1 resembles:1 resolution:2 original:3 abundances:2 consider:8 forbidden:1 splitting:3 scalar:8 mp2:4 partial:2 expressions:1 disk:1 causes:2 content:5 quiros:1 undistorted:2 tr:4 former:1 program:1 th:2 kλ:1 worse:1 sitting:1 very:47 b189:1 b188:1 puzzles:4 witten:2 neutralinos:1 ln:5 difference:2 n03:2 condition:2 broeils:1 induced:1 eds:1 list:5 applicable:4 t0:5 large:16 collect:1 4πgn:4 small:18 ten:4 foundation:1 yaffe:1 ratz:1 past:4 zero:3 perspective:2 pass:2 further:1 ter:1 tev:27 wmap:1 gunn:2 what:37 sub:3 sun:4 section:37 version:2 waals:2 learned:2 method:1 multitude:1 edited:2 full:1 christophe:2 adelberger:1 component:6 answers:2 squeezed:1 tracks:1 anticipation:1 berkeley:5 directions:1 strong:18 equations:3 search:5 allows:4 experience:1 amount:5 periodic:3 published:3 action:1 mpbh:4 higgsless:1 via:1 followed:1 requiring:1 put:1 detecting:1 csaki:3 ekin:1 matarrese:2 takes:2 gravitino:14 seckel:2 revelation:1 magnification:1 sitter:1 ψn:6 qcd:8 taken:6 veltman:2 achieving:1 more:33 flat:8 elliptic:1 ejected:1 operators:2 corrected:1 emission:1 tested:7 domination:1 basically:3 varying:1 known:5 factories:1 producing:1 dobrescu:1 cluster:5 shielded:1 science:2 der:2 protons:5 remain:1 excursion:1 history:5 beautiful:1 santoso:2 cosmological:6 brown:2 ds2:4 superparticle:1 ann:1 states:11 contradicts:1 minimum:6 protects:1 numbers:5 sense:3 mn:1 species:4 information:2 needs:1 simps:5 polchinski:1 rather:5 breaking:8 cline:1 acta:1 galactic:15 tried:1 inflationary:1 derived:4 fa:9 plane:7 coming:1 2t:2 horizontal:1 short:3 lhc:8 yχ:2 fundamental:12 farhi:1 baryogenesis:1 help:1 hierarchy:15 developed:1 cosh:4 soon:1 distortion:2 resonant:1 thermal:10 paper:4 through:10 existence:3 kinetic:2 suffer:1 excitations:2 its:33 eros:3 freezeout:1 energies:5 solving:1 boson:37 actually:13 detected:1 microscopic:2 jacobi:2 duffy:1 supersymmetry:17 misalignment:4 wouldn:1 good:5 motivated:1 seeking:1 tisserand:1 underground:3 walls:1 accumulate:1 yu:1 bigger:3 chromodynamics:1 easily:4 finite:8 2s:1 fully:3 philosophical:4 micro:1 2g:1 stopped:2 sundrum:1 found:6 errata:1 heavy:13 cyburt:1 tilted:1 idei:1 accelerator:8 generation:2 energy:55 hard:1 idea:8 terning:2 expect:5 quantum:19 beyond:51 event:3 really:5 nuovo:1 since:10 bibber:1 dominated:4 hill:1 py:1 tf2:1 issue:2 foreground:1 doppler:2 lawrence:1 asy:1 unexplained:1 labs:1 difficulty:1 reason:5 imagine:3 mme:1 randall:1 rises:1 generate:2 definition:3 pairs:1 cdms:3 terrible:1 accumulation:1 exponentially:1 twenty:1 consequence:4 exhibited:1 integrand:1 indebted:1 major:1 probability:1 feel:3 radical:1 number:22 talked:2 done:1 blanc:1 y02:2 tev2:4 story:1 perturbation:1 heads:1 temperature:14 srednicki:2 introduction:3 leading:4 5th:2 tata:1 least:3 identity:1 calculations:4 molecular:1 store:1 listed:1 shifted:1 statement:1 behind:1 baryon:11 park:1 larly:1 sn1987a:1 part:11 consult:1 focusing:1 believe:2 postulate:1 kind:5 hundred:1 determines:4 kindly:1 giudice:1 collaborations:1 gotten:1 annihilation:17 determined:4 marriage:1 supposed:1 milky:2 motivation:4 raby:1 electrodynamics:3 wµν:1 roughly:1 randomly:1 substantial:1 quasars:1 concentration:2 orders:4 lie:1 depending:3 alcock:2 self:16 lit:1 empirically:1 finding:1 towards:6 electric:3 dθ2:1 measures:1 reach:4 singlet:1 most:19 significant:1 nothing:6 1au:1 extremely:1 kg:2 kk:4 h2t:3 clear:3 calling:1 km:8 optical:3 electrons:5 clean:2 velocity:2 subgroup:2 physics:87 naively:3 lying:1 sector:1 particularly:1 phenomenon:1 carefully:1 fine:11 find:21 impact:4 causality:1 parameters:10 trh:1 ies:1 overclose:1 19th:1 3h:6 pretty:1 factor:1 circle:4 giants:1 his:2 hit:1 notation:3 meanwhile:1 dependent:2 express:1 famous:4 feels:1 closely:1 alexander:1 σann:21 cry:1 common:3 cre:2 switzerland:1 doubles:1 baroque:1 doublet:2 approaching:1 scanning:1 set:4 art:1 edoardo:1 see:38 bare:6 sea:1 ρmatter:1 accelerators:3 close:4 spindependent:1 ritz:1 halved:1 binds:1 begeman:1 currently:1 dipole:1 various:9 probably:2 neubert:1 dilutes:1 numerous:1 knowing:1 tristan:1 creating:1 missing:3 attention:4 hitoshi:2 invisible:3 tmax:1 4gn:5 relying:1 m23:1 both:7 improved:2 neutralino:3 sensitive:2 connection:3 became:2 context:1 forgotten:1 focused:1 interactive:1 whole:2 finds:3 experimental:4 sinh:1 point:15 simple:17 corresponds:2 proton:14 coincidence:8 dimensional:9 simply:1 throughout:1 complication:1 described:1 pt:1 create:1 varieties:1 due:14 describes:1 superconductor:3 muons:1 ph:50 extreme:1 annihilating:2 firm:2 compositeness:4 generating:1 lived:3 partly:1 gas:8 precision:4 else:2 whatever:2 understand:7 demand:1 p2:3 look:8 exponential:1 solid:3 straight:3 expanded:2 empirical:7 evaluated:1 technical:1 while:20 microlensing:13 pilo:2 behavior:3 fun:2 evaluates:1 couplings:2 loop:6 pack:1 dominantly:2 century:2 vol:1 von:1 itself:6 triple:2 beautifully:1 rid:1 vanish:1 fermion:8 manton:1 vy2:2 gs2:2 italy:1 grant:1 shorter:12 thermalized:1 carone:1 emphasize:3 grand:3 products:2 ray:4 composition:2 neutron:6 higher:6 development:2 calculation:1 used:3 pospelov:2 assignment:2 yannick:1 moment:4 zwicky:1 uses:2 purpose:3 implementation:1 dine:4 ptolemy:1 recent:5 dark:124 lower:1 2gs:1 elem:1 analysis:5 obviously:4 concrete:1 edge:2 castano:1 chemistry:2 lin:1 2gn:1 know:27 distances:5 simp:1 hypothesized:1 observed:1 ldr:3 atomic:6 questions:2 world:4 love:1 letting:1 signal:2 conclusions:2 ins:1 griest:1 signals:2 source:2 m4h:1 location:1 theorem:1 excited:2 irges:1 darkmatter:1 big:17 couple:2 integrations:1 smallness:1 helicity:1 bit:1 projects:1 helpful:1 rotate:1 imposed:1 success:1 obser:1 adiabatic:2 holes:4 translates:2 ignore:1 flux:1 popular:8 weiner:1 spins:1 faber:1 often:4 some:24 back:12 understood:2 added:2 b0:2 examples:4 sight:9 mirror:5 curious:1 ourselves:1 hannestad:1 scale:67 schmaltz:2 resonances:1 oscillates:2 measurements:3 pep:1 integration:3 per:1 tends:3 photino:1 minimal:11 object:1 patient:1 use:9 msusy:2 nucleons:1 être:1 anything:2 constraint:3 sake:1 range:6 gamma:2 cutoff:1 exhaustively:1 into:19 within:9 integral:1 lensing:12 primarily:2 ǫijk:1 ellipse:1 acknowledgements:1 dimensionful:2 question:5 long:6 u2:2 bosons:5 forward:3 adam:1 sections:4 disallowed:1 mountains:1 pastor:2 atom:1 line:24 themselves:1 inverse:4 middle:1 up:14 us:25 2πr:3 ui:1 today:1 spectroscopy:3 sum:1 2πx:1 similar:5 called:23 saturate:1 associated:1 defined:5 redshifts:1 doesn:1 vertices:2 fujii:1 duration:4 single:1 initial:2 friedmann:1 objection:1 invalid:1 b12:1 department:2 deviate:1 nice:2 explaining:2 draw:2 elements:1 accidental:1 temperatures:4 problems:7 lens:5 suppression:1 emergence:1 sides:1 structure:7 ago:1 suffers:1 implies:2 practically:3 zooming:1 age:2 required:4 speculations:1 orbit:2 phonon:1 came:3 far:9 requires:6 having:3 once:11 katz:2 gs:1 jedamzik:1 results:1 gg:1 gf:2 ge:1 squarks:2 houches:2 edu:2 go:8 gn:11 conservative:5 contributions:3 issues:1 2r0:1 compact:3 copernicus:1 simon:1 3ht:2 ac03:1 weyl:1 contours:2 excluded:5 stable:7 atlas:2 details:3 ev2:2 include:2 lkp:5 outside:1 ρc:4 lc:1 wave:6 tritium:1 electron:37 putting:2 mixing:1 2rr:6 arrange:1 entire:3 fewer:2 try:6 assignments:2 eigenvalues:1 refer:4 optics:1 smaller:6 ued:3 lightest:8 peccei:1 astrophys:4 dynamics:2 l2z:2 odd:8 λcdm:1 index:1 invisibly:3 rate:8 opaque:1 senjanovic:1 d3:1 waiting:3 experiment:4 8πgn:2 3b:1 body:1 led:3 chose:1 desires:1 exchange:3 gilles:1 lep:3 desired:1 explore:1 les:2 admx:1 lev:1 others:1 4r02:10 z2:8 z3:2 great:4 cern:3 involved:1 larger:5 suggests:2 resulting:2 opinion:1 makes:6 involves:1 kachru:1 scales:11 apr:1 win:1 crazy:1 messengers:4 scaled:1 volt:1 decrease:1 names:3 anomalies:2 apply:2 orderings:1 m2χ:2 m2π:1 causal:1 cloud:2 confidence:2 refers:2 asymptotic:4 usa:2 remains:2 pedagogical:1 next:11 few:9 depicted:2 doubt:1 estimated:2 tanh2:2 doubling:3 historically:1 clever:1 started:1 becomes:7 takayama:2 m2ν:1 account:2 balls:1 integrating:1 averaged:1 higgsino:1 infinitesimal:1 crossed:3 splittings:1 universe:44 meet:3 drops:4 escapes:1 process:8 thermally:1 pieces:1 high:16 effectively:2 assumptions:1 something:8 triangle:1 tan:1 mix:1 erratum:1 memorize:1 sit:1 lepton:2 trieste:1 varies:1 elliptical:1 instead:5 intelligent:2 sin:4 circular:1 tension:3 de:5 singular:1 watch:1 fluid:1 realized:1 decaying:1 22nd:1 light:26 lines:5 element:2 s3:2 gravitons:1 allow:4 shirman:2 divided:1 gµν:4 organizers:1 dx:6 produces:1 astronomical:4 despite:1 produced:7 including:3 looks:3 mentioned:5 yamaguchi:3 galaxy:17 chemical:3 eui:1 exclusion:2 decay:16 chosen:1 masses:9 relativity:2 li:2 2λv:1 primordial:3 degrees:7 ls:1 covered:1 lz:3 fourth:1 violating:1 gaugino:2 greater:1 lzp:1 material:1 federico:1 mention:4 rotation:15 day:1 articles:1 dirac:3 university:1 identified:2 sufficiently:1 magnitude:10 l2:9 mode:4 electrically:2 crossing:3 traces:1 constraints:3 homogeneous:2 arxiv:69 doing:1 related:9 decays:4 eisenstein:1 measure:5 our:20 witness:2 out:39 matt:2 m2t:2 rev:41 m2s:3 geometry:1 mate:1 m2h:1 superkamiokande:1 romain:1 lecture:1 cause:2 integrated:1 red:2 quinn:1 interactions:4 discontinuity:1 galaxies:11 completely:4 kribs:1 hubble:4 interaction:12 her:1 napoli:1 dubbed:1 could:8 hypercharges:1 times:2 4th:1 wrote:2 hence:39 quadratically:1 repeats:2 manuscript:1 reaches:1 spiral:3 barr:1 reached:2 blows:1 precisely:6 unknown:2 condensate:3 system:7 πr:4 their:13 fermions:8 normalization:1 nelson:4 final:4 ictp:2 shell:2 stars:15 completed:1 exactly:9 bino:3 biggest:1 constituent:1 dynamical:4 epair:2 epochs:5 boring:1 distinguishes:1 richer:1 limiting:1 claim:1 whenever:1 amplitude:1 sec:12 iωt:1 symmetries:2 fluctuation:7 cohen:2 curves:2 kepler:1 unlikely:3 need:15 st:1 apparently:2 clearly:2 she:2 wacker:1 angle:10 hamaguchi:1 studying:2 nucleosynthesis:4 able:2 gravity:10 mechanism:5 instance:2 concerns:1 kaplan:3 detector:4 reproducing:1 lecturer:1 lectures:11 unless:1 collaboration:10 who:1 propagate:1 but:43 device:3 why:28 astro:13 appelquist:1 32g:1 radiating:1 resonantly:1 stronger:3 deuterium:2 looked:3 proceedings:3 lθ:2 mechanical:1 constrain:1 superscript:1 normally:3 fact:8 supported:3 anyway:1 longevity:2 bring:1 superimposed:2 trivial:2 debate:1 decade:1 subtracting:1 µm:1 based:8 knowledge:2 baryonic:7 nucleon:2 should:13 brighter:1 simmons:1 candidates:12 ethan:1 molecules:3 constituents:1 kaluza:7 thresholds:2 hope:5 equilibrium:7 meant:1 3m2:1 means:1 convert:1 simplest:1 overall:4 lucky:1 seljak:1 ones:1 words:7 penetrate:1 halo:23 annihilate:1 processes:1 densities:4 conditions:2 tuned:1 processed:1 contain:1 fixed:4 generations:2 view:4 predictive:1 requirement:2 omission:1 lsp:8 exists:2 particu:1 national:2 davoudiasl:1 freeze:3 enhanced:1 recently:1 2me:2 ikv:6 interacting:3 nuclear:8 tend:2 eboli:1 state:12 identification:1 closed:1 crude:1 invariant:1 boundary:2 ends:3 orbifold:4 prediction:1 embarrassment:1 job:2 hypothesis:2 kev:2 p2y:1 distribution:4 monitor:1 eichler:1 limits:6 freely:1 invited:1 mixings:2 b436:1 etc:7 manifestations:1 passing:1 ll:1 otherwise:2 detailed:5 relevant:6 cm:36 cl:1 wall:1 ca:2 harmonic:1 taylor:3 coordinates:1 table:3 cp:4 harnik:1 bbn:4 kolda:2 powered:1 addition:12 yao:1 slowly:1 hawking:1 kapner:1 meissner:1 anomaly:3 define:1 arises:1 corresponding:1 scalars:1 astrop:1 sufficient:1 bulk:5 angles:1 astron:2 c2:10 repetition:1 present:6 novel:1 splits:1 value:9 will:28 tait:1 profumo:1 layer:2 ve:7 almost:3 refs:1 squid:1 surprisingly:1 surface:1 mizuta:1 raison:1 partner:1 generic:1 divergences:1 radiation:8 cross:27 unity:1 strange:3 pauli:2 units:1 glaring:1 solution:7 infer:2 difficult:4 http:3 igv:1 effect:5 matchev:2 kohri:1 v2:2 student:1 pdf:1 expand:4 off:8 center:11 com:1 well:16 patterns:1 sets:2 usual:6 spherical:2 jupiters:1 excessive:2 26e:1 less:4 xdx:1 obtain:11 underlying:2 predicts:1 protecting:1 untested:1 macroscopic:1 adv:1 4m2:1 rapid:1 ads:1 density:23 bell:1 smith:3 hall:6 reasons:5 add:2 extends:1 attractive:8 wimps:18 kick:2 incarnations:1 spinless:3 historic:1 five:4 community:1 swanson:1 immediately:1 loss:1 like:24 lost:1 sized:1 martin:1 become:2 works:3 kawasaki:1 parity:14 battaglia:1 because:56 qed:1 classical:5 immortal:1 stau:3 scatters:1 proper:1 kinds:1 zeppenfeld:1 neglecting:1 happens:2 lead:3 avoid:5 superconductivity:2 does:18 assuming:9 dfsz:2 sdss:1 demonstrated:1 l3:2 biology:1 reaching:1 selecting:1 zhitnitsky:1 expansion:9 stellar:2 offset:2 analyses:3 about:51 actual:1 carried:1 extension:1 getting:2 freedom:7 dependence:4 compatible:2 a2:2 introduced:2 equally:1 own:3 keeps:1 h2:12 transparencies:1 h0:2 chemists:1 weather:1 champ:1 tiny:2 pomarol:2 bosonic:1 mere:1 van:3 additional:3 elastic:3 populated:1 condense:1 wimp:17 spread:3 sin2:5 quadratic:1 µev:1 hadronic:1 sleptons:1 naturally:3 function:6 rajaraman:2 kpc:5 brane:7 ht:1 volume:1 reminds:1 neutral:5 convergence:1 hc:1 he:5 made:9 compute:1 places:2 rc4:4 dangerous:1 gravitational:13 smooth:1 flip:1 rc2:4 tan2:2 below:8 frequency:2 limit:22 problem:37 piece:2 minutes:1 mechanics:4 superpartners:3 iny:1 sanders:1 int:5 recognize:1 universal:2 year:8 upsets:1 combine:1 ink:1 functions:2 compared:2 susskind:1 nonetheless:2 percent:2 detail:2 virtual:1 arctan:1 other:52 special:4 theor:3 conclusion:1 repeat:2 star:12 buchmuller:1 dama:1 variation:1 stay:1 chance:3 astronomy:1 friends:1 howie:1 searches:4 coupling:15 baker:1 100h:2 searched:1 4g:1 4d:1 |
0704.2277.txt |@word monte:2 sch:1 results:11 four:4 scalar:6 consists:1 expressions:2 contributions:1 compact:1 equivalence:5 presents:1 finally:1 does:2 those:2 case:3 straightforward:1 very:3 rise:3 conditions:4 splitting:3 klaus:1 every:1 figs:1 fall:2 exact:10 condition:1 treating:1 turns:1 solution:1 large:1 discrete:1 convenience:1 vector:1 sexton:2 indices:1 eigenvalues:2 configurations:3 findings:1 dealing:2 plaquette:4 sign:2 second:1 cost:1 corner:1 odd:5 approached:1 even:5 what:1 stands:1 rate:1 giving:1 sum:3 selected:1 while:1 expressed:1 wolff:5 above:3 new:5 contributes:1 method:2 full:1 christian:1 reliably:1 error:2 neveu:11 here:10 erhard:1 explore:1 directions:4 path:2 strong:4 appears:1 change:1 obtained:2 remark:2 shift:1 study:2 larger:4 allows:4 completely:1 experience:1 trial:3 periodic:3 usually:2 advantages:1 therein:1 fourier:3 changes:1 cancellation:1 apr:1 search:1 compare:5 austria:1 decrease:3 total:3 flavors:2 derivatives:2 use:9 andreas:1 would:1 positive:5 suppl:3 next:1 comparing:1 nucl:12 type:1 more:2 separated:1 introducing:1 ir:1 formally:1 becomes:1 enormous:1 site:1 geophysics:1 particular:1 known:1 cases:1 selfavoiding:1 iii:1 fermionic:4 couples:1 springer:1 valued:1 language:1 integrating:2 pursue:1 avoiding:3 work:1 sweeps:2 theories:3 leder:3 remain:1 values:3 strategies:3 example:2 numbers:7 f1:6 f2:10 links:3 give:2 minimum:2 performed:5 want:1 pinto:1 kenna:2 regularization:1 advantage:2 discussion:1 far:1 behave:1 optimal:1 parameter:1 product:1 may:4 thermodynamic:2 derived:1 needs:1 fb:1 explored:1 physik:2 lat:2 representations:6 data:6 heidelberg:1 types:2 stress:2 jiang:1 ss:4 algorithms:1 expression:1 allow:1 representation:16 sf:3 wind:1 help:2 over:6 symbols:2 course:1 paper:1 through:2 statistical:2 signs:4 still:1 its:5 perfect:2 rapidly:1 symmetry:1 fit:2 how:1 ln:3 logarithmically:2 reweighting:3 degrees:1 fig:8 non:2 introduce:1 landau:1 effects:6 they:1 now:2 discuss:2 nor:1 susceptibility:4 several:1 dirac:1 corners:2 university:1 alternately:1 magnitude:2 reasonable:1 each:9 found:4 universit:1 difficult:1 mean:2 lat2006:1 spinor:1 eo:7 lat2005:3 another:1 weight:6 ee:11 there:1 energy:3 gaussian:1 related:1 measure:1 quantum:4 our:9 mapping:1 avoided:1 eq:1 special:1 out:3 living:1 shown:2 matrix:2 space:2 restricted:1 furthermore:1 since:5 rev:6 denotes:1 increase:2 gaussians:1 denoted:1 formula:1 illustrate:1 issue:1 integrated:2 red:9 shows:3 reformulation:1 theory:4 interactions:3 free:3 standard:11 small:4 reason:1 complicated:1 hep:2 generate:1 pairs:2 interaction:1 chiral:8 r2:1 could:5 transition:1 tries:1 removing:1 top:1 first:2 already:2 probability:1 afer:1 jackknife:1 number:10 theoretische:1 directly:2 reached:1 quality:1 size:4 given:4 rewritten:1 indicate:1 introduction:1 condensate:4 system:2 their:2 fermions:6 salmhofer:2 gives:2 exploring:1 exactly:2 serve:1 rejected:1 environmental:1 wenger:1 part:1 simulate:5 eliminated:1 believe:1 than:2 double:1 zero:1 correlators:2 classes:4 doubly:1 were:4 f12:1 visited:1 outcome:1 treated:1 minus:1 behavior:1 alongside:1 generalization:2 winding:2 conjugate:1 need:2 seen:2 seem:1 occupied:2 linked:1 relatively:1 wilson:1 exploratory:1 depending:1 carlo:2 self:3 able:1 incentive:1 violates:1 oriented:3 sciences:1 internal:1 finding:1 so:1 blue:9 begin:2 quote:2 measures:1 systems:3 regular:1 germany:1 letter:1 phase:1 analytically:1 appear:3 kk:1 calculated:1 partition:6 repeated:1 order:1 traditional:1 points:3 exp:1 typically:1 section:1 sector:1 show:1 purely:1 colors:4 gauge:3 earth:1 d2:3 find:1 occupation:8 topological:1 should:1 analytic:2 only:7 going:1 factor:4 windings:3 local:5 do:1 plaquettes:1 notation:1 de:1 overall:1 cannot:2 2f12:5 lattices:1 neither:1 differentiating:1 graz:2 increasing:3 determinants:1 continuum:1 settings:1 fields:7 karsch:1 arxiv:2 acknowledgments:1 strouthos:1 mapped:1 fixed:1 discussing:1 bars:1 set:1 computed:3 exists:1 principal:1 testing:1 maximum:1 see:6 individual:2 result:7 discussions:1 close:2 flavor:4 techniques:1 phases:2 capacity:1 visiting:1 currently:1 sites:4 f22:2 written:1 various:1 closed:5 between:2 conceptual:1 fermi:4 boundary:6 approach:13 terms:4 notoriously:1 however:5 efficiency:1 fluctuations:1 analyzed:3 configuration:7 come:1 distribution:1 improve:1 both:7 essentially:1 limits:1 always:1 many:1 according:1 etc:1 contribution:1 disappears:1 finds:1 otherwise:1 minima:1 point:7 simple:2 sweep:2 dimensional:3 anti:1 respect:2 cv:1 source:1 due:3 been:2 quickly:1 int:2 empty:3 lett:2 determinant:7 corresponding:1 prospects:1 curves:2 reference:1 gausterer:2 equilibration:1 present:2 applied:1 replaces:1 pacs:1 value:1 spontaneously:1 will:2 euclidean:2 near:2 evaluating:1 promising:1 situation:2 richter:1 loop:32 vectors:1 costly:1 almost:2 simulations:4 thus:6 them:1 discrepancy:5 iv:1 ii:1 cluster:1 reads:2 mod:2 vanish:1 fermion:15 different:7 hubbard:1 make:1 belong:1 cross:2 same:2 orders:2 complex:3 arguments:1 pauli:2 largest:2 avoids:1 finite:7 higher:4 independent:1 used:7 trivially:1 grassmann:1 numerical:14 upon:2 effect:1 action:2 plot:3 forcrand:1 changing:1 normalization:1 modes:1 hopping:1 markus:1 obstacles:1 well:4 without:2 sets:6 model:16 nearby:1 latter:1 chandrasekharan:5 moments:1 hybrid:1 aspect:1 immediately:1 touch:1 alternative:4 stratonovich:1 like:1 schnetz:1 exclusively:1 improvement:1 lattice:19 treatment:1 guarantees:1 transformation:4 real:2 around:1 big:1 possible:3 munich:2 pos:4 department:1 background:3 using:12 accepted:1 color:1 prominent:1 adams:1 sizes:1 signal:1 performing:1 addressed:1 knechtli:2 either:3 arbitrary:5 become:1 works:1 accessible:2 because:1 methods:3 formulas:2 seiler:1 successfully:1 some:1 understood:2 thies:1 gross:11 scale:2 dimensions:4 lead:1 measurements:1 cχ:7 thank:1 2g:2 proc:3 refer:1 limitations:2 metropolis:2 run:1 power:2 slight:1 huber:1 equivalent:1 agreement:1 expansion:1 broken:1 binder:1 although:2 2n:2 oo:7 comparison:3 freedom:1 discussed:1 o:1 simulation:15 involving:1 mixed:1 introduced:3 cutoff:2 into:3 within:1 integral:2 three:2 assess:2 remarks:1 references:1 inverting:1 rossi:1 often:1 spinors:1 statistics:2 institut:1 2dimensional:1 pc:1 transfer:1 strictly:1 initial:1 question:1 way:1 was:6 function:9 considerably:2 annals:1 form:1 gattringer:2 denoting:1 but:4 volume:10 heat:1 philipp:1 gain:1 ha:1 considerable:1 compute:1 algorithm:3 assessment:2 smooth:1 up:2 ur:1 discretized:1 below:1 limit:4 autocorrelation:1 demonstrate:3 problem:4 similar:2 clear:1 diverges:1 worthwhile:1 defined:3 certain:1 direction:1 singly:1 loops:28 formulation:7 again:1 functions:2 no:2 dressed:1 when:7 vanishes:1 schwinger:1 field:10 other:4 spatial:1 test:2 mass:1 massless:1 christof:1 wiese:1 update:5 helpful:1 generated:2 important:4 observables:4 lang:3 suffers:1 coupling:6 dψ:1 physics:1 factors:2 curve:1 weights:1 volumes:5 time:2 n0:7 n1:9 n2:3 dϕ:1 having:1 |
0704.2278.txt |@word consider:7 gupta:2 results:5 expressions:1 adjustment:1 analytic:1 tr:1 uniqueness:1 monotonically:2 those:1 under:5 γg:1 applied:1 conjecture:1 labels:1 comm:1 orthogonal:1 far:1 every:1 fall:1 difference:2 matrices:5 encounter:1 school:1 level:7 evaluation:1 t2:2 solution:1 standards:1 large:16 small:7 eigenvalues:42 dis:1 upper:2 smaller:5 approximation:18 second:3 further:1 estimated:2 even:6 aim:1 what:1 g22:2 diag:9 section:9 above:3 sup:1 new:5 principal:5 bn:2 make:4 multivariate:7 convergences:1 respectively:2 never:1 component:3 equals:1 desired:2 test:6 q11:1 others:1 ratio:4 extreme:4 difficulty:1 study:2 larger:3 glg:2 suggests:1 usually:2 california:1 appropriately:1 inference:5 apr:1 requiring:1 put:1 limi:1 apply:1 fbn:1 select:1 derivatives:1 confidence:7 asymptotic:22 prove:1 positive:3 comparing:1 asser:1 therefore:4 type:4 until:1 more:4 populations:1 stable:1 normalized:4 excellent:1 known:1 cases:2 tokyo:1 science:2 examined:1 determining:1 following:3 root:1 example:2 proof:2 f1:3 compare:1 give:7 calculation:2 purposes:1 sample:21 indicates:1 numbers:4 sense:2 guarantee:1 information:1 needs:1 varied:1 minimax:1 di:12 how:2 methodology:1 criterion:3 significance:3 sij:1 absolute:1 parameter:1 deviated:1 may:2 use:4 applications:4 improving:1 evaluations:1 meaningful:1 majorization:1 natural:2 third:1 explicit:1 correspond:1 parameterized:1 st:1 so:1 decreasing:1 fan:1 order:4 g11:2 closely:1 ith:1 developed:1 vary:1 satisfied:1 course:1 paper:6 including:1 statistical:4 its:3 roots:1 derive:2 group:3 exact:4 lm:17 li:13 better:5 degrees:1 lp:5 covered:1 might:2 h0:11 within:3 return:1 finance:1 yo:1 propose:1 framework:1 they:3 das:2 now:4 eigenvalue:13 term:2 finite:2 equality:5 hereafter:1 university:2 hermitian:1 sufficiently:4 inequality:1 l2:10 reasonable:1 l1:24 found:1 mean:2 lie:1 significantly:1 ed:1 positioned:1 w11:5 used:2 expect:1 measurement:1 our:2 operation:1 beyond:1 out:2 precisely:1 matrix:12 3rd:1 factors:1 res:1 furthermore:1 since:9 conjectured:1 get:1 supports:1 math:4 shows:2 wiley:2 theory:9 limβ:1 diagonal:2 standard:1 olkin:2 surely:1 york:1 χ2n:2 estimate:1 likelihood:2 phrases:1 could:1 similarly:2 times:1 american:1 hence:2 βi:3 first:3 xi:5 probability:4 rank:2 bartlett:1 approximately:2 another:1 xp:1 tributed:1 summarize:2 size:3 given:14 indicate:3 introduction:3 unknown:1 least:1 their:1 percentage:2 gives:10 exactly:1 rejected:2 part:3 favorable:1 authors:1 x1:1 than:12 population:27 kind:1 approximations:3 zero:8 tion:1 naturally:1 deciding:1 minj:1 shrinks:1 ann:3 modern:1 already:2 say:2 need:5 null:3 any:3 nλ1:1 traditionally:1 lim:3 note:1 wishart:11 generalized:1 performance:1 coincide:1 accuracy:1 spectral:2 normal:4 most:1 significant:1 preliminary:1 inequalities:1 doi:1 especially:1 considered:1 sometimes:1 traditional:1 points:8 pλ:7 exp:11 dispersed:5 fact:2 show:4 random:1 notations:3 solutions:1 decompositions:2 portfolio:2 d2:6 find:2 d1:13 based:7 simulating:1 parameters:2 sphericity:2 distributed:5 enough:2 lemma:5 only:1 explicitly:1 subsection:1 thompson:4 employed:1 zγ:2 dm:10 goes:5 notation:2 means:3 between:3 variate:1 words:1 wise:8 dp:7 volatility:2 increasing:1 arxiv:1 expansions:2 statist:4 analytical:1 ohio:1 fixed:2 require:1 view:3 set:1 constructing:1 exists:1 testing:18 maximum:1 see:7 decided:1 sec:1 result:9 close:3 theoretic:1 alternative:2 degree:2 away:1 below:1 tend:1 symmetric:1 state:1 smallest:8 various:1 simplest:1 αi:3 approach:1 notice:2 terms:1 wm:3 however:2 hypothesis:9 key:1 wp:4 monotonicity:1 problem:7 both:7 last:2 refinement:1 many:1 σa:1 according:2 against:2 april:1 interesting:1 variance:4 estimation:12 jersey:1 among:2 ch:1 point:9 asymptotically:1 corresponds:1 dimensional:1 sequences:1 respect:3 hayakawa:1 three:2 been:1 much:4 takemura:13 asymptotics:7 basic:1 pi:1 generating:1 θi:11 samples:6 sufficient:1 natl:1 covariance:8 systematic:3 c1:2 denote:3 present:3 case:7 semidefinite:1 value:5 easier:1 will:1 while:4 suppose:3 error:4 situation:3 property:1 margin:1 region:4 economics:1 almost:1 ip:4 equal:2 good:6 im:2 technology:1 different:1 muirhead:3 journal:2 divergences:1 complex:1 largest:6 several:1 independent:2 literature:1 trivially:1 comprehensive:1 numerical:1 hand:2 moment:1 infinite:7 robust:3 normalization:2 eigenvectors:2 lower:2 off:1 possibly:1 well:2 analysis:7 academic:1 components:4 simulated:1 very:1 organization:1 model:1 dimension:3 λp:15 less:1 being:1 generally:2 accurate:1 identically:1 biometrika:1 λi:8 λm:8 previous:1 sugiura:2 cut:1 infinitely:6 seems:1 interested:1 treatment:1 easy:2 theorem:12 extensive:1 tests:1 aspects:1 represents:1 possible:1 department:1 press:2 using:3 accepted:2 shinshu:1 follows:4 serves:1 specific:2 pillai:2 2007b:5 2007a:2 become:1 works:1 blockwise:1 deviation:2 because:2 methods:2 classical:1 some:7 q21:1 q22:1 table:4 intractability:1 happens:1 ignore:1 decision:1 critical:13 decomposition:1 unit:1 yields:1 moderate:1 refer:1 columbus:1 bold:2 power:1 equivalent:2 each:2 conventional:1 expansion:5 percentile:2 comparison:1 carried:2 freedom:3 generated:1 o:6 simulation:3 practical:4 consequently:1 block:8 marshall:2 h1:3 1lp:1 appropriate:3 references:1 often:2 log:1 there:3 u1:10 approximate:5 u2:10 dispersion:10 anderson:6 handbook:1 way:1 was:1 gij:1 asset:1 function:3 form:1 bur:1 repeatedly:1 convergence:3 made:1 rejection:3 consist:1 characteristic:1 up:3 theoretical:1 mth:3 distribution:23 similar:1 required:2 constant:1 abstract:1 statistic:1 general:1 ap:1 arises:3 distributions:3 approximated:2 again:1 functions:1 no:2 when:14 vanishes:1 graduate:2 application:1 other:3 papers:1 np:1 poor:1 elements:1 ξp:5 sided:5 problems:7 a1:1 ξi:7 ξj:1 important:2 bounded:1 ξm:5 coverage:1 variable:1 needed:1 structure:1 independently:1 assets:2 practically:2 interval:20 w22:5 n1:2 starting:1 having:1 once:1 |
0704.2279.txt |@word replacing:1 limited:1 code:1 consider:1 similarity:1 caused:5 truncated:1 results:4 four:2 claret:4 edu:3 follow:1 expressions:5 abundant:1 rot:31 θp:10 causes:1 layers:1 copernicus:1 certainly:1 depend:7 calculate:1 δv:5 indicate:1 helps:1 γm:2 pamyatnykh:5 differing:1 include:2 applied:1 moreover:2 amplitudes:27 straightforward:2 far:2 frequencies:5 rise:1 harmonics:1 focus:1 figs:5 rm:7 affect:1 difference:3 condition:1 look:1 pulsators:1 leads:2 p4:1 cmi:1 presented:1 cause:1 solution:1 daszy:7 large:5 vector:3 small:7 refer:2 noted:2 sectorial:1 upper:1 employing:2 force:4 coordinate:1 oscillation:9 consistent:2 sin2:4 cosi:2 sign:3 approximation:7 photospheric:4 qualitatively:1 odd:3 gm:1 quite:2 linear:6 even:6 disk:5 plays:1 rate:9 contributions:3 section:6 selected:10 expressed:1 uniform:2 pulsating:1 boundary:2 increasing:5 connected:1 method:4 contrast:1 revealing:1 focuses:1 lee:6 degree:6 whose:1 respectively:4 component:2 here:3 ranges:2 bildsten:3 address:1 alone:3 ratio:1 standard:2 equations:4 z1:2 change:4 essentials:1 obtained:4 propagative:1 great:1 antisymmetric:1 institute:1 study:3 losses:1 allows:1 experience:1 ignoring:2 significantly:1 p2:1 simultaneous:1 bol:3 domains:1 symmetrical:2 adopting:3 changes:7 plotted:1 hint:1 subtracts:1 apr:1 photometric:9 arccos:2 visible:4 decrease:1 plots:5 limb:6 total:5 pulsational:5 unit:2 horizontal:2 derivatives:4 use:6 asymptotic:1 would:1 p7:3 remains:2 1x:1 process:1 depicted:1 call:1 therefore:2 m2:1 taken:2 type:4 diagrams:4 more:8 separated:1 ujazdowskie:1 becomes:2 envelope:1 emission:1 visibility:7 appendix:4 normalized:1 particular:3 known:1 cases:6 must:1 account:5 rotational:4 rβ:1 recall:1 inertial:1 work:2 centrifugal:3 debated:1 values:6 following:6 eri:1 reasonably:1 indicated:1 give:2 calculation:2 table:4 high:4 ℓx:2 assumptions:1 numbers:3 employs:1 arise:1 dominant:3 spb:2 prograde:4 axis:2 information:1 end:1 predictors:1 provide:1 s0:2 feature:1 regions:1 hough:9 hot:1 vrot:9 instead:2 those:2 parameter:4 sin:39 profile:1 product:1 modulation:1 after:1 derived:2 constraint:1 applications:1 plane:2 mag:2 cancellations:1 summarize:1 law:3 revealed:1 parallel:2 goal:1 introduced:1 branches:4 remember:1 third:1 interpolated:1 light:21 spectra:4 explicit:2 correspond:3 likewise:1 element:3 rather:2 ones:1 so:2 specifying:2 allow:1 enter:1 imθ:3 order:11 least:3 interpretation:1 help:1 indeed:1 astronomical:1 mainly:2 distortion:7 thermal:1 paper:1 through:2 still:3 its:5 write:4 rapidly:1 how:3 ln:10 temporal:1 varies:1 decreases:2 ds:7 better:1 detected:2 distinguishing:1 choose:2 mail:3 main:7 might:1 lx:2 gives:2 them:2 integral:1 outlined:2 fig:26 bartycka:1 band:3 effects:5 they:4 rotation:35 now:2 easily:5 term:6 profound:1 always:1 university:1 b3:3 blanketed:1 sufficiently:2 mode:43 2b:5 radial:32 crossing:1 found:1 photometry:3 uniwersytet:1 2i:1 characterized:1 mean:5 balona:2 square:1 determine:2 instability:2 bump:1 series:2 displacement:2 related:1 seismic:1 logg:1 frequency:11 static:1 expect:2 quantum:1 our:15 differ:1 eq:18 nonmonotonic:1 shown:7 furthermore:1 since:1 lagrangian:1 projected:1 cancels:1 increase:2 may:24 acting:1 formula:3 evaluation:1 mθ:1 i2:1 theory:1 localization:1 mψ:10 possibility:1 diagnostic:3 mϕ:1 reason:1 dependencies:2 complicated:1 intermediate:1 detecting:2 temperature:6 r2:1 geometry:5 could:2 leading:1 hence:2 2005a:4 2005b:6 first:3 already:2 symmetry:3 variables:1 number:2 ℓj:1 unexpected:1 done:2 adopted:3 carry:1 fluxes:1 angular:12 illustrate:1 given:17 perturbation:8 smaller:1 observer:4 likely:2 similarly:2 introduction:1 data:17 eqs:6 system:3 approximately:1 their:2 perturbations:1 rates:3 observations:1 calculations:3 convention:1 final:2 townsend:15 listed:2 way:2 geneva:4 difficult:2 moscow:1 p8:1 part:5 somewhat:1 representing:1 than:4 coefficients:4 center:1 relative:1 observatory:1 determines:1 unfortunately:1 showed:1 iωr:1 was:4 approximations:2 zero:2 determined:6 amplitude:21 were:1 toward:3 pulsation:3 russia:1 rad:8 derivative:1 rewrite:2 unchanged:1 spectrum:2 generalization:3 departure:3 axk:4 z0:3 manner:1 distorted:1 need:4 seen:5 clearly:1 warsaw:3 acceleration:1 strength:1 angle:6 δns:2 min:2 distinguished:1 latter:3 mid:2 mechanism:1 εr:2 note:1 fitting:1 potential:2 absorbed:1 take:5 finding:1 negligible:1 accuracy:2 spectral:1 play:1 opposite:4 any:1 twodimensional:1 who:2 z2:12 most:10 nonlinear:3 instytut:1 significant:3 formulae:2 phase:7 adds:1 acknowledgements:1 measured:1 why:1 αt:1 equatorial:11 considered:2 calculated:10 adopt:3 metal:1 km:46 traditional:6 hints:1 exp:3 dor:4 velocity:41 typically:1 specification:1 fact:1 quantity:1 atmosphere:7 selection:1 show:4 chances:5 supported:1 rotating:7 reference:1 solutions:2 astrophys:10 find:3 ground:1 impact:1 slow:7 based:5 parameters:11 reflection:1 less:2 written:3 should:2 only:11 specify:1 rich:3 factor:1 various:4 adequate:2 population:1 local:1 over:9 equilibrium:1 pℓ:2 his:3 legendre:2 correctly:1 means:1 dependent:2 nobs:7 cannot:2 nearly:1 passband:3 despite:1 dt:1 averaged:4 him:1 secondary:2 disentangling:1 evolution:2 conditions:1 arxiv:1 summary:1 though:2 analytical:3 including:1 require:1 view:2 monochromatic:1 exists:1 p03d:1 variations:5 respect:4 ωt:3 detection:6 see:18 decided:1 darkening:6 wroc:1 dµ:2 best:2 phases:4 suffer:1 eigenfunctions:2 saio:5 pattern:1 dipole:1 symmetric:1 enough:1 identification:11 envelopes:1 between:11 justified:1 approach:2 across:2 variability:4 comparable:2 wd:1 terms:8 str:1 vertical:1 baade:2 attention:1 however:11 vrad:16 meridional:1 outer:1 improve:1 observable:6 prospects:5 panels:6 improved:1 cot:3 many:3 conclusions:1 equal:1 laplace:1 l145:1 multicolor:1 harvard:1 retrograde:5 uni:1 contribution:9 whole:2 nonadiabatic:8 simple:2 effective:1 period:1 antisymmetrical:2 dimensional:1 pole:1 coordinates:1 modeling:1 associated:2 multiband:1 considering:3 unusual:1 strong:1 described:8 contributors:1 kinematic:1 addition:1 discrimination:10 radiative:4 three:5 been:7 reduction:3 much:4 slowly:2 combined:1 azimuthal:6 oθ:7 expected:3 ph:2 deduced:1 pl:3 define:1 passbands:4 direction:1 arises:3 corresponding:3 easy:2 both:1 quantities:1 sufficient:1 essentially:1 θz:5 confinement:4 determination:2 representative:2 angles:1 astron:5 oϕ:7 spin:4 present:5 case:15 p3:1 p1:1 atmospheric:1 nska:7 unlike:1 p5:1 reliable:1 p9:1 single:2 value:5 remaining:1 will:4 rests:1 near:1 situation:1 procedure:1 layer:2 equator:3 averaging:3 thus:6 non:4 surface:15 savonije:2 different:3 moves:1 grant:1 suggest:1 same:11 orders:2 complex:6 dhx:4 resulting:5 relatively:1 prerequisite:1 higher:2 independent:1 used:7 http:1 peaks:1 αg:1 numerical:5 upon:3 effect:12 counterparts:1 constraining:1 moment:1 uses:1 frequently:1 normalization:4 recent:1 relies:1 lower:4 modes:88 framework:1 expression:11 poland:3 nonetheless:1 well:5 increases:3 analysis:1 without:1 patterns:1 edge:1 components:2 relied:1 very:4 entry:1 model:15 mnisw:1 left:2 spherical:5 decreasing:1 νobs:1 obtain:3 gravity:5 shape:1 identify:2 aspect:17 spherically:1 polish:1 yielding:1 yet:1 application:1 axisymmetric:1 regarded:3 except:1 astrouw:1 combine:1 impairs:1 excited:3 mmag:11 real:2 explained:2 aspects:2 eigenfunction:1 depends:4 eigenvalue:1 bands:1 possible:5 harmonic:3 suffering:1 average:2 using:3 unique:3 oph:1 occurring:1 atmospheres:1 table1:1 like:3 semi:2 cooler:1 follows:4 velocities:4 flux:5 benefit:1 unstable:9 integrals:5 arbitrary:4 δf:4 become:4 unperturbed:1 coriolis:1 essential:1 parity:3 because:5 often:2 grids:1 sequence:5 do:1 arrows:1 some:3 begin:1 b4:1 understood:1 b6:1 growth:2 advective:1 examples:2 b2:1 specified:3 oscillations:1 extended:1 b8:1 b9:1 daszkiewicz:7 nonzero:1 scale:1 describing:1 calculating:1 lead:1 affects:1 normal:2 integration:8 contributing:1 does:2 cutler:1 αxt:6 assuming:2 yields:1 2a:1 reasonable:1 minimization:1 equivalent:1 each:5 expansion:2 stellar:12 ratios:8 δg:1 tidal:1 properties:5 proceed:1 comparison:1 about:4 actual:1 carried:2 extension:2 extending:1 discussed:2 dependence:27 o:1 reduced:2 range:3 a2:2 ushomirsky:1 mixed:4 bolometric:1 constraints:3 obs:1 perturbed:7 letters:2 measurements:2 h3:1 into:7 within:1 numerically:2 due:1 b7:1 right:4 references:1 primarily:2 proportional:4 inclination:6 teff:8 unambiguous:1 uncertainties:1 rely:1 log:10 area:2 intrinsic:1 there:12 fast:5 occupy:1 detectable:1 low:8 stars:13 sections:3 naturally:1 function:8 hx:25 interest:1 form:7 differences:5 but:16 astro:3 hemisphere:3 mnras:8 line:4 highest:1 true:1 hd:3 castelli:2 directed:2 kurucz:3 b5:1 whether:1 latitudinal:3 ωr:1 detectability:1 up:2 us:4 ul:2 zβ:13 limit:1 spectroscopy:2 2003b:6 problem:3 2003a:3 similar:2 called:2 puls:4 b1:3 strongly:1 constant:3 rossby:1 defined:1 certain:1 abstract:1 describe:1 life:1 cotθ:1 dξ:1 examine:2 exist:1 periods:2 dθ:12 av:11 formalism:3 identities:1 check:1 jerzykiewicz:2 chance:1 camk:1 functions:14 thermodynamical:1 no:5 cos:15 individual:2 when:1 detail:2 field:3 other:3 role:4 branch:1 dipolar:1 additional:1 dziembowski:6 opacity:1 polar:1 briefly:1 star:11 excitation:2 separate:1 models:7 ξr:1 p6:1 variation:13 includes:1 a1:2 a3:2 important:10 observables:2 included:2 au:1 astronomy:1 l77:1 structure:1 observers:1 implies:1 longer:2 dψ:14 imprecise:2 together:1 depth:1 time:2 walker:6 luminosity:2 dϕ:1 requires:2 once:2 |
0704.2280.txt |@word represent:1 partial:1 consider:3 rev:12 kielpinski:1 results:5 leads:1 gf:3 scalar:3 generalize:1 consists:1 sci:2 eτ:3 localized:2 row:1 devoted:1 whose:1 inverse:2 aug:1 mihalache:1 deterministic:1 nonlocal:1 containing:1 presents:1 those:1 dressing:9 ingredient:1 applied:1 amplitudes:3 g2:2 straightforward:1 g0:2 far:1 bilinear:1 springer:1 wave:11 fortier:1 shin:1 sidebands:1 entries:1 mixing:1 difference:3 exact:4 condition:4 ieda:4 four:2 school:1 riemann:1 presented:1 experiencing:1 solution:29 t0:1 large:2 discrete:1 vector:3 excellence:1 math:6 small:1 eigenvalues:1 ueda:1 optics:1 noted:1 employing:1 illustrating:1 det:1 sin2:1 weiping:1 cosh:4 approximation:2 zero:1 concludes:1 qualitatively:1 dynamics:7 situated:1 linear:8 spectral:9 will:4 nonlinear:16 diag:3 section:3 eiαj:1 d3:4 dχ0:1 above:1 new:6 net:1 d1:4 method:8 textures:1 full:7 fiz:2 respectively:2 component:7 q3:2 here:7 atoms:2 growing:1 galilean:1 sinh:2 address:1 directions:1 sine:1 equations:10 obtained:4 institute:1 study:1 changed:1 allows:1 experience:1 mx:1 p2:1 minsk:1 products:1 published:1 domains:1 chang:1 changes:1 elongated:1 york:1 spatially:1 projection:3 ipl:2 modulated:1 decrease:1 condensates:3 total:1 establish:1 linearly:2 use:2 projector:7 remains:2 dnl:2 contains:1 negative:1 tightly:1 hilbert:1 m4:1 m1:3 therefore:2 m3:3 m2:1 taken:2 australian:2 type:1 more:5 pencil:1 sharing:1 definition:1 solitons:5 stable:2 odinger:2 cycles:1 proceed:1 known:4 iii:2 r1:3 account:1 mf:1 equation:14 mn:1 mi:12 ibe:6 mj:2 reviews:1 simplify:1 bureau:1 values:2 novikov:1 following:4 under:2 nlin:1 example:2 performed:2 control:1 ma2:1 calculation:2 organized:1 2i:2 numbers:1 degenerate:1 sense:1 miyakawa:2 dress:1 axis:2 hoc:1 darboux:2 ie:2 zhang:2 feature:2 chemical:1 forest:1 instead:2 parameter:3 sin:24 exponentially:1 profile:1 description:1 inherent:1 modulation:3 after:3 derived:1 orbits:2 applications:1 produce:1 lax:2 dj0:2 waves:7 evgeny:1 d10:4 choice:1 revealed:1 types:1 kurn:2 schober:1 dynamical:1 effective:2 explicit:1 correspond:3 dragon:1 rather:1 si:1 ones:1 so:2 fundamental:3 decreasing:2 representation:2 subsequently:1 order:2 bas:1 ulam:1 words:2 canberra:1 produces:1 leanhardt:1 indeed:2 over:3 insight:1 choose:2 stability:3 paper:5 pulses:1 existence:2 avenue:1 its:4 write:1 derive:1 decay:2 chosen:1 interesting:1 temporal:1 lm:1 coordinates:1 li:3 complex:11 degrees:2 systems:3 main:2 maclaughlin:1 belarus:1 reveal:2 numerically:1 outlined:1 fig:3 martikainen:1 framework:1 they:2 now:2 yu:1 hall:1 yv:1 represents:2 term:2 several:1 2k:1 always:1 university:2 identified:1 sufficiently:1 mode:2 instabilities:2 instability:14 soc:5 d40:4 side:1 mean:1 homogeneous:1 spinor:8 differential:1 ej:3 reduce:2 used:3 applicable:1 bra:1 frequency:1 interplay:1 entering:1 quantum:2 our:4 beyond:2 nonlinearities:1 πs:4 special:2 out:1 ketterle:3 shown:2 matrix:28 space:3 since:1 crucial:1 chaos:2 research:1 may:1 stud:2 machida:2 ref:5 rj:2 matrices:1 theory:6 interactions:1 contain:1 differ:1 free:1 standard:1 completely:2 formation:1 yuri:1 dx:1 e4:3 e1:3 generate:2 e3:2 e2:3 r4:2 incorporates:1 interaction:1 derivation:1 r2:1 r3:2 could:1 impose:1 kivshar:1 linearized:1 manakov:1 length:1 explored:1 period:4 gordon:1 incorporated:1 hence:9 sauer:1 teor:2 pitaevskii:2 eqs:5 first:2 2p1:1 there:2 features:1 spoken:1 relate:1 faculty:1 number:3 rank:7 isoshima:1 ik0:2 lengthy:1 2a0:1 zh:1 electronic:1 size:1 given:4 perturbation:2 indicate:1 introduction:2 cambridge:2 condensate:9 system:8 their:1 returns:1 melnikov:2 zeros:5 constants:2 faddeev:1 siam:1 floquet:12 structures:2 exponents:4 recovered:1 gives:2 kulagin:1 behind:1 tool:1 exactly:1 serve:1 plane:7 transverse:1 larger:1 optical:1 authors:1 x2:3 than:2 coefficients:1 population:1 kind:1 determines:2 accordance:2 bec:13 ohmi:2 sth:1 second:2 normalizing:1 matter:1 determined:2 contrary:2 speaking:1 amplitude:3 treated:1 exhibit:1 jpn:5 akhmediev:2 spectrum:6 chapman:2 seed:8 4k0:1 bigelow:1 chikkatur:2 seek:1 any:1 elsewhere:1 built:1 depending:1 trapped:2 mechanism:1 note:5 sciences:2 k1:7 potential:3 ostrovskaya:1 take:1 finding:1 channel:1 hyperfine:3 trillo:1 formulas:2 modulationally:2 continuous:7 multiple:3 centre:2 wabnitz:1 phases:1 algebraic:2 phase:8 analytically:1 class:1 soliton:3 especially:1 dordrecht:1 ks:19 regards:1 exp:8 µt:2 vassilis:1 typical:2 physics:3 fact:2 ho:1 nls:13 show:2 herbst:2 notations:2 bright:1 relation:1 solutions:19 αjl:1 d4:4 d2:4 find:2 ground:3 q1:3 q0:2 indicator:1 q2:1 based:4 q4:2 parameters:8 state:4 should:4 analytic:2 only:3 explicitly:4 factor:5 integrable:15 circle:1 pointed:1 do:2 dj:2 means:3 dependent:1 beams:1 mclaughlin:1 uchiyama:2 2mc:1 liu:1 cannot:1 φo:1 reversal:4 combinations:1 arranged:1 qq:1 produced:1 evolution:13 transversal:1 densities:1 conditions:2 coalescence:1 arxiv:1 hyperbolic:1 saturates:1 double:18 analytical:2 london:1 fixed:4 view:1 thessaloniki:2 set:1 exists:1 national:1 up:2 observed:1 see:3 sec:2 result:4 greece:1 terms:3 points:16 et0:1 spindependent:1 eigenfunctions:1 scattering:5 definite:1 label:1 boundaries:1 enough:1 various:2 between:6 fermi:1 αj:1 approach:5 αl:1 law:1 available:1 notice:1 recently:1 2m:2 modify:1 muraki:1 weak:1 however:1 modulational:8 extent:1 analyzed:1 bose:4 understanding:1 wright:2 barrett:1 both:1 essentially:1 many:1 region:1 etc:1 admit:1 figures:1 context:1 expression:1 andrews:1 among:2 imj:1 co:1 periodic:7 simple:1 homoclinic:25 pop:1 dimensional:3 distinguish:1 written:3 d30:4 constant:7 ae:6 ps:7 pp:1 ket:1 described:4 persistence:1 trajectory:2 px:8 three:6 been:4 describes:5 asymptotics:1 expected:1 pritchard:1 define:1 direction:1 corresponding:2 formed:1 cos:15 iρ:3 pxe:7 confinement:1 determination:1 2ik:3 systematic:1 c2:7 c0:6 spin:18 present:3 case:7 p1:4 exponential:7 pacs:1 consultant:1 single:1 evaluated:1 stenger:2 aim:1 technical:1 while:2 suppose:1 du0:1 property:7 procedure:2 opt:1 studied:2 coupled:1 chaotic:2 refs:2 iv:2 ii:3 ik:4 good:1 ia:2 eberly:1 technology:1 2g0:1 qx:1 different:2 twofold:1 lengths:1 fractals:1 demands:1 locking:1 lett:8 same:4 parts:1 dimensionless:1 finite:2 raghavan:1 higher:3 development:7 independent:2 extended:1 eds:1 numerical:2 hand:1 v0:2 usually:1 infinite:2 invariance:1 interested:2 ablowitz:3 schr:2 modes:3 band:1 nevertheless:1 ingredients:1 well:3 analysis:6 components:10 dressed:1 coordinate:1 model:18 parametric:1 possesses:1 surveys:1 manifold:1 proposed:1 inouye:2 being:3 obtain:7 press:1 transforms:2 predicts:1 ps2:1 macroscopic:1 robins:1 begin:1 conclusions:1 zakharov:1 point:6 jost:1 iψ:2 valid:2 attractive:1 diagonalization:2 suominen:1 transformation:2 real:5 australia:1 easily:2 koashi:1 breaks:1 corresponds:2 dark:1 qj:2 know:1 background:2 confined:1 using:1 emergence:1 unique:2 imposed:2 shaped:1 follows:2 δs:1 serves:1 specific:1 imposes:1 unstable:3 either:1 reduced:3 terminology:1 salle:1 methods:2 classical:1 2qq:1 some:1 play:1 summation:1 growth:6 b0:2 b2:9 oscillations:1 gross:1 threecomponent:2 describing:2 realistic:1 demonstrates:2 integration:1 2c2:1 2g2:1 does:1 unit:2 provides:1 tends:2 pattern:1 demonstrated:1 process:1 assembly:1 obey:1 each:1 eiρ:1 step:1 found:3 pasta:1 eiψ:1 imaginary:2 refers:2 properties:2 clarkson:1 stage:4 about:1 ferromagnetic:3 constraint:5 column:1 freedom:2 pu:1 dependence:1 o:2 essential:1 obeys:1 2iψ:2 act:1 constraints:2 projectors:4 miesner:2 perturbed:1 computational:1 ikλ:1 into:5 within:3 obtaining:2 due:2 determine:2 einstein:4 next:2 iµt:23 theoretically:1 arranging:1 k12:1 hamley:1 transfer:5 strictly:1 initial:5 u0:5 long:8 stamper:2 start:1 accordingly:1 quadratic:1 way:2 perform:1 malomed:1 analyze:1 was:6 function:2 complete:3 form:9 phenomena:1 collin:1 but:5 stepanov:1 construction:1 ankiewicz:1 related:1 yang:1 atom:2 truncation:1 bloch:7 applying:2 arrays:1 multiplicity:3 mat:1 maximum:1 us:1 limit:1 demonstrate:1 problem:12 similar:1 called:2 regimes:2 ab:2 associated:3 ad:1 af:3 univ:1 describe:2 deep:1 general:2 separating:1 engineering:1 exist:1 periods:1 aristotle:1 accounting:1 ing:1 physical:2 ulation:1 functions:2 nl:2 integrability:2 no:1 eq:9 when:5 rs:3 multipliers:3 field:1 other:3 role:1 spatial:2 department:1 mathematics:1 you:1 deviation:1 polar:2 denote:1 pronounced:1 models:1 wadati:7 a2:14 vectors:7 structure:1 nonintegrable:1 regime:3 coupling:2 d20:4 interval:2 orbit:8 rule:1 reproduce:1 mass:1 lying:1 time:18 appl:4 original:1 tsuchida:2 |
0704.2281.txt |@word ambiguities:1 consider:1 lagrangian:1 qdq:1 focus:1 leads:1 roy:1 generalize:2 computation:3 contributions:3 localized:1 whose:1 certainly:1 ver:1 isobar:1 γw:3 those:1 stable:1 include:2 presentation:2 b147:1 amplitudes:1 g2:1 straightforward:1 orthogonal:2 very:2 decreases:2 m2k:3 seemingly:1 results:6 witten:2 summarized:1 difference:6 matrices:1 condition:1 solves:2 hamiltonian:2 did:1 turns:1 solution:4 d2:1 herbert:1 large:13 integro:1 convenience:1 praszalowicz:4 small:3 exhibits:1 jhep:1 squared:1 grateful:1 ten:1 sin2:1 prediction:2 rra:7 tex:1 second:4 further:1 20mev:1 odd:1 substitute:1 mπ:6 even:1 what:2 diag:1 exactly:1 find:1 current:4 axial:3 experiment:1 goeke:2 above:3 ˆi:1 ground:1 acknowledgments:1 coefficient:1 outgoing:1 full:1 simultaneously:1 malized:1 respectively:1 component:1 here:3 xλ:6 xθ:11 mev:9 address:1 along:1 strong:1 equations:1 obtained:2 remark:1 shift:18 study:2 drr:2 allows:1 commonly:1 suggests:2 resulting:1 action:6 resonance:17 fourier:1 changes:1 cancellation:1 criticism:1 emerge:2 via:2 scales:1 apr:1 tr:4 merely:1 highly:1 visible:1 anomalies:1 meson:10 m2π:6 b223:1 unit:1 readily:1 standing:1 eiωt:1 d70:1 would:3 positive:1 contains:3 negative:1 scenarios:1 nucl:10 therefore:1 decuplet:2 qcd:1 ψb:1 techniques:1 type:1 more:3 introducing:1 becomes:3 operators:3 under:1 odinger:1 rigid:1 particular:2 known:1 b202:1 must:4 account:1 rotational:3 rβ:3 integrating:1 equation:7 hicks:1 modified:2 mk:20 labeled:1 values:2 canonically:1 example:1 decoupled:1 omit:1 degenerate:1 figure:5 give:1 expanding:1 pieces:1 states:4 indicates:1 caused:1 want:1 arise:1 tan:1 rescaling:1 calculated:1 gev:5 information:1 counting:1 end:1 verify:1 breaking:4 differences:1 carries:1 orthogonality:1 aλb:1 pure:1 acta:2 ordinary:1 parameter:2 sin:1 simplicity:1 b72:1 may:6 after:1 reflect:2 physik:2 fk:1 constants:1 stress:1 effective:1 b160:1 su:9 element:2 switch:1 maintain:1 so:3 reduced:1 representation:2 order:1 hedgehog:1 separable:2 nucleon:6 indeed:5 over:1 mainly:1 satisfied:1 formalism:2 argued:1 still:1 excitations:7 its:3 ηb:1 decay:11 energies:1 interesting:2 coordinates:2 actually:3 shifts:5 absence:1 degrees:5 fig:3 total:1 mail:1 into:4 cls:1 non:5 motivated:1 dab:2 matches:1 numerically:1 introduce:1 functional:1 scaling:1 modification:1 skyrme:7 effects:2 they:2 identically:1 rotation:1 now:1 represents:2 term:7 finite:1 always:2 university:1 classified:1 identified:1 fπ:7 theory:1 mode:3 fields:1 weigel:12 characterized:1 mean:1 spinor:1 differential:1 significantly:1 hadronic:6 series:1 energy:3 kopeliovich:1 decays:3 isospin:2 expect:2 substantially:1 our:4 eq:16 out:1 emerges:1 shown:3 matrix:11 2m2k:1 factors:1 furthermore:1 since:2 crucial:1 contained:2 conclusions:1 ra:1 reader:1 print:1 ref:6 earlier:1 disputed:1 linear:3 b35:1 b36:1 given:1 free:1 standard:3 indices:1 approaches:1 dependencies:1 proportionality:1 put:1 estimate:1 definition:1 interaction:7 chiral:10 widths:5 transition:1 motion:5 turn:1 length:1 iso:1 incorporated:1 invitation:1 hence:1 hadrons:1 first:4 exotic:1 major:1 xi:1 symmetry:5 nc0:1 wave:7 number:2 lond:1 exact:1 smaller:1 approximately:1 differ:1 perturbation:1 b301:1 introduction:1 adjoint:1 system:1 adopted:1 statement:2 realization:1 dwell:2 veff:1 recovered:1 gives:1 a31:1 calculations:1 baryon:8 convention:1 contribute:1 artifact:1 sizable:1 simply:1 somewhat:1 consult:1 x2:1 schr:1 than:2 quantitative:1 unfortunately:1 double:1 zero:3 isovector:1 annihilation:1 matter:2 future:1 contrary:2 solely:1 perturbative:1 lowest:1 sb:1 cohen:1 argument:1 winding:1 parameterized:1 seen:1 seem:1 constrained:1 any:2 angle:3 convenient:1 latter:1 note:4 extracted:1 empirically:1 potential:6 generalized:1 unconstrained:1 concern:1 channel:4 acquire:1 though:2 collaboration:1 reach:1 resonates:1 most:3 petrov:1 germany:1 definitions:1 phase:21 baryons:3 intrinsic:3 bsa:4 soliton:22 unequal:1 surprising:1 clear:1 adopt:1 kn:6 typeset:1 proceedings:1 accounted:1 principle:2 exp:5 a260:1 physics:1 satisfies:1 lying:1 sector:1 show:2 solutions:1 participate:1 threshold:1 d4:2 d5:1 trivial:1 d3:3 occupation:1 based:3 behind:1 appreciated:1 only:3 version:2 generators:1 factor:1 constant:3 local:1 do:3 ˆf:1 notation:1 means:1 de:1 straightforwardly:1 famous:2 cannot:1 despite:1 dr:5 subscript:1 processes:1 continuum:1 conditions:2 arxiv:5 yield:1 twice:1 estimates:1 yθ:2 predicted:2 contain:1 yabu:1 gell:1 omission:1 pentaquark:10 computed:4 frame:3 φsol:5 differs:1 see:1 result:4 biedenharn:1 rmk:1 alternative:1 quantizing:1 subject:4 detect:1 40mev:1 review:1 exchange:3 functionals:3 symmetric:3 state:10 unable:1 various:1 between:5 invariant:1 boundary:1 approach:7 terms:5 reproduced:1 however:2 key:1 fluctuations:8 distinguish:1 wz:1 suggested:1 both:1 2θk:1 reverse:1 schat:1 powers:1 taking:1 hint:5 according:2 previously:1 quantization:2 etc:1 uni:1 contribution:1 argue:1 mann:1 otherwise:1 among:1 afterwards:1 point:1 color:1 corresponds:1 dimensional:2 pole:2 anti:3 conjugation:1 respect:2 pseudoscalar:2 described:3 itzhaki:1 induces:1 three:3 wess:2 inertia:1 int:1 reduction:1 describes:1 complicated:1 hornbostel:1 b581:1 ph:5 anomaly:1 define:1 θk:2 direction:2 arises:1 corresponding:1 scoccola:1 kaon:12 subspace:1 hayashi:1 pentaquarks:2 ensuring:1 systematic:1 stems:1 spin:1 present:1 case:4 bφ:1 karliner:1 reliable:1 premature:2 will:2 walliser:4 match:1 behavior:1 rotator:1 situation:3 eur:3 klebanov:3 larger:1 orientation:1 thus:5 partner:1 mod:1 vanish:2 acquires:1 different:3 az:1 verified:1 generic:1 lett:3 elevated:1 φa:2 8nc:1 parts:1 split:1 avoids:1 dimensionless:2 constructed:1 zumino:2 literature:1 upon:1 siegen:3 moment:1 levels:1 kim:1 genuine:1 off:2 modes:2 scenario:1 nevertheless:1 b256:1 without:1 solve:1 experimental:1 components:1 consistency:1 coordinate:2 position:2 model:16 left:3 just:1 being:2 skyrmion:1 λa:3 summed:1 augments:1 flavor:15 scattering:5 eigenstates:1 previous:1 k3:1 application:1 conclude:1 hyperons:1 add:1 treatment:2 heavier:1 remaining:1 momentum:8 polon:2 identical:4 iλ:1 yukawa:4 eigenvalue:1 multiplets:1 background:3 using:1 prominent:1 rotate:1 particle:1 follows:1 collective:14 δr:1 serves:1 shaper:1 yields:2 arbitrary:1 underestimation:1 become:1 callan:2 topologically:1 because:4 methods:1 classical:4 creation:1 some:1 understood:1 deduce:1 towards:1 pφ:2 γsk:2 γsb:3 provided:1 scale:1 ellis:2 lead:2 resonances:4 best:1 mesons:2 does:2 provides:1 proc:1 d72:1 diakonov:2 workshop:1 canonical:1 polyakov:1 radial:4 ando:1 expansion:3 stem:1 d42:1 properties:2 panel:3 comparison:1 about:5 central:1 constraint:2 freedom:5 discussed:5 dependence:2 o:7 essential:1 range:1 ensure:1 importantly:1 reproducing:1 skyrmions:1 kaons:2 organizers:1 duke:1 soc:1 rev:3 flavor:1 strangeness:8 inclusion:1 h2:3 puzzle:1 a359:1 rotations:1 bound:8 due:1 appropriate:1 right:3 references:1 chemtob:1 operator:1 proportional:1 quickly:1 mere:1 unambiguous:1 hep:5 additional:2 treated:1 there:4 u0:6 long:1 dγα:2 width:16 quadratic:2 gobbi:1 hooft:1 was:2 function:12 form:1 lint:1 but:1 taken:1 repeated:1 yang:1 true:1 hyperon:1 compute:1 qualitative:1 embedded:1 ωq:4 hardly:1 dω:1 up:1 ωk:10 frequency:1 limit:7 static:1 problem:4 piece:1 called:2 associated:1 defined:1 ωmk:2 describe:3 am:1 model5:1 resultant:1 single:2 exist:1 laboratory:3 moves:2 inc:1 again:2 functions:4 no:2 extract:1 nc:52 when:1 vanishes:1 invalid:1 field:2 interested:1 details:1 test:3 theor:1 conclusion:1 elements:5 a11:1 generates:1 excitation:2 models:11 generated:2 variable:1 ξa:1 cherman:1 structure:4 b262:1 implies:1 coupling:4 pion:2 fπ2:3 space:1 quite:1 observe:1 mass:6 fachbereich:1 requires:2 having:1 |
0704.2282.txt |@word represent:8 concept:3 dist:9 consider:1 funct:1 alternatives:1 resistance:4 four:6 generalize:1 computation:4 edu:1 consists:11 gn:3 gr:1 relationships:1 21st:1 combinatorial:1 graph:115 segments:1 simplify:1 send:1 removal:1 presents:1 finally:1 program:1 present:3 stable:2 nodes:58 undirected:2 sent:5 alternating:36 p2:4 conjecture:1 reality:1 preserved:3 schrieffer:1 linked:6 could:1 pages:1 rise:1 results:3 electron:2 every:43 get:3 decide:1 fall:1 difference:4 lefthand:1 special:1 leads:3 subsets:3 level:1 turns:2 proposals:1 applicable:1 t1:2 large:1 assignments:20 vector:5 harry:1 small:2 equation:1 configurations:3 smaller:2 says:2 carter:1 abstracted:1 elusive:1 requirements:1 direct:2 dimensional:1 zero:1 diagrams:1 design:2 rigorous:1 implemented:1 odd:29 port:85 quite:1 theory:19 even:32 index:2 what:2 diam:4 adds:1 stands:1 frameworks:1 section:22 shares:1 find:5 cell:80 version:1 com:1 goes:1 new:7 contributes:2 consisting:1 satisfy:1 full:1 degree:18 respectively:4 modify:3 equals:1 here:10 atoms:8 behaviour:12 test:4 wechselwirkung:1 groups:2 represented:2 path:18 along:1 strong:1 equations:4 change:2 extreme:1 obtained:10 sending:6 search:1 endpoints:1 rassat:1 division:2 transition:1 institute:1 shift:1 study:1 studied:1 allows:1 reason:1 contradiction:2 anchor:1 suggests:1 helv:1 resulting:1 usually:4 resonance:7 conveniently:1 hexagon:3 changes:1 foundations:1 diameter:9 via:6 useful:2 classification:5 sri:1 merely:1 vii:2 prefer:2 vio:10 logical:2 highly:1 boolean:2 viz:1 apply:3 total:1 linearly:4 use:12 additive:1 figure:2 would:6 prove:3 distinct:7 e1:5 contains:19 neighbours:1 induction:3 next:3 depicted:9 redox:2 memory:3 taken:1 doubling:1 simpler:1 spaces:1 theoretical:3 possible:5 more:10 flat:1 preserving:1 relax:1 clearly:5 conclusions:2 operators:1 conducting:1 aware:1 binary:1 berlin:1 cycles:8 particular:1 known:2 central:2 cases:4 disabling:1 easiest:1 must:11 states:67 springer:1 endpoint:1 bits:1 science:3 der:9 work:1 london:2 paragraph:1 values:1 concepts:3 following:9 meet:1 atome:1 arrive:3 example:12 proof:19 claim:1 impose:1 indicated:3 give:2 role:1 sense:6 organized:1 hexagons:4 high:2 performed:1 want:2 allowed:4 spanning:1 hydrogen:4 occur:3 junctions:2 weaken:1 influenced:1 needs:1 answer:1 end:3 straightforward:1 provide:2 verify:5 write:9 bonds:20 chemical:8 how:4 failures:1 influences:1 simplifies:1 symposium:1 ordinary:1 happens:1 inputs:3 abstraction:6 description:1 algebra:1 may:14 max:1 sp2:1 confirmed:1 diagram:2 connectivity:5 demonstrating:1 share:2 multiplication:2 righthand:3 horizontal:1 data:1 flexible:22 types:1 man:1 realized:4 introduced:2 branches:1 lemmas:2 corollary:9 su:1 element:14 rather:2 switch:5 so:14 specifying:1 allow:1 enter:1 definitions:2 subsequently:1 sg:3 order:6 travel:1 operations:4 restriction:4 acts:1 interpretation:2 feedback:1 developed:1 over:22 mainly:1 choose:7 interpreted:1 stability:3 combinations:1 attitude:1 paper:6 including:1 enumeration:1 thesis:2 mentioned:1 existence:3 satisfies:5 still:1 ieee:1 its:24 before:3 perfect:6 controllable:1 style:1 position:1 group:5 treat:1 interesting:4 doubleton:1 encompasses:1 conjugation:5 better:1 absence:2 continue:1 degrees:5 systems:7 annual:1 reachable:2 might:1 weber:1 heitler:1 correspondence:2 flex:14 them:4 motivated:1 pentagons:2 dim:2 introduce:2 primary:1 yields:3 effects:1 they:5 acta:1 own:1 nov:1 now:11 day:1 above:5 groningen:3 restrict:1 february:1 netherlands:2 indeed:3 name:3 2r:3 invariants:5 university:3 presented:3 identified:2 possibilities:3 2e:1 2a:1 each:4 found:3 2n:1 pow:36 ports:96 associative:1 bond:8 subset:10 weighted:2 matchings:2 formulate:2 energy:3 semiempirical:1 reduce:1 idea:4 related:1 solution:4 bijective:1 conductance:1 used:7 remove:1 measure:1 quantum:9 our:9 naming:1 beyond:1 yet:2 out:2 principles:1 leave:1 shown:5 opened:1 space:7 open:31 useless:1 since:44 rev:3 research:1 transforming:1 contained:5 investigation:1 socalled:2 reader:2 electronics:2 suffices:2 stringer:1 shows:4 model:4 linear:12 associate:1 asz:1 yale:1 differ:1 possibility:1 standard:1 vazirani:1 indices:2 terminals:2 complicated:1 term:2 usual:1 put:1 hand:2 remainder:5 finite:3 e2:5 a4:1 definition:1 pairs:1 interaction:1 organic:1 language:1 applications:2 just:4 abstractions:1 feasible:1 length:3 edges:39 signature:6 hence:4 view:3 neglect:1 first:11 origin:4 initial:10 symmetry:4 kernel:2 radical:1 nach:1 dynkin:1 number:28 reaches:1 u0:6 channels:34 wees:1 devices:1 general:1 done:2 construct:3 another:2 type:3 ring:1 precisely:16 electronic:5 several:4 size:1 given:16 rightmost:1 fascinating:1 table:2 their:4 introduction:1 leading:2 system:10 least:5 parallel:3 characterize:1 needed:2 intermediate:1 chem:5 observations:1 postulate:1 molecular:16 structures:9 speaking:1 gives:2 e0:4 shell:5 kekul:182 addition:3 serve:3 part:4 natural:1 translation:6 than:4 linking:2 distance:5 scheme:1 roles:1 cyclic:1 double:19 distinguishes:1 tree:10 depends:1 project:1 matter:1 classes:3 supposed:1 represents:1 toward:1 polaron:2 unintended:1 derivative:1 ann:1 conventional:1 mind:1 argument:1 curves:6 incidentally:1 connectors:1 angew:1 current:3 need:8 st:1 any:16 solitons:4 she:1 paths:10 depict:1 realm:1 subgraph:20 depending:1 efficient:3 speculative:1 therewith:1 ideas:2 note:7 k2:3 k1:11 internal:23 generalized:2 k5:5 k4:2 interior:1 algorithms:3 subject:1 switching:9 channel:51 play:1 regard:1 multiple:2 fundamental:1 investigations:2 reckon:1 who:1 molecule:13 most:2 wire:1 connected:21 gauss:1 accordance:1 scripts:1 pair:11 homogeneous:3 class:1 soliton:9 cause:1 observation:2 dijk:1 considered:2 bowden:1 request:1 vertices:1 drawing:1 χg:3 graphs:35 hom:1 points:2 electrons:5 principle:1 hamming:5 mechanical:7 left:4 sequence:1 sum:4 fact:2 laws:1 precise:2 emerging:1 heptagons:1 gold:1 show:6 violation:1 lewis:1 probe:4 anyway:1 notations:2 bring:1 determine:5 multiplicities:2 disconnectedness:1 solutions:4 participate:1 calvert:1 dimension:6 d2:2 indicate:2 descriptors:1 d1:2 impact:1 hesselink:2 removed:1 based:4 alluded:1 extending:1 assertion:3 topological:2 should:5 terminal:1 lemma:8 only:36 smallest:2 transfer:1 molecules:12 constituents:1 equivalents:1 circle:1 interested:1 hope:1 storage:1 do:4 triangle:1 therefore:28 notation:2 means:9 dekker:1 simplest:4 likely:2 heeger:1 words:2 invariant:1 report:1 disadvantage:1 conjunction:4 combined:1 requirement:1 areas:1 closure:1 hybridized:1 coulson:1 arxiv:1 yield:1 twice:4 investigate:3 common:3 contain:8 through:6 implication:1 fixed:3 mayor:1 require:1 crystal:1 hydrocarbons:15 preserve:2 pvs:4 set:54 exists:3 physically:1 generally:3 respect:2 unsaturated:3 arrives:1 maximum:2 observed:1 see:11 computer:2 result:13 w1:2 w0:9 close:2 nitzan:1 hydrocarbon:2 conductivity:1 closes:1 said:1 potential:2 compounds:1 purpose:2 rings:4 sites:1 rod:1 materials:1 symmetric:2 state:80 determined:4 various:2 closed:11 between:30 drawn:2 boundary:2 reading:3 approach:3 available:4 terms:1 august:1 missing:1 initially:3 component:2 attention:1 however:3 shankar:1 incident:7 concentrate:1 orbitals:1 recent:1 subgroup:1 carbon:9 configuration:2 suppressed:2 naphthalene:1 recall:2 requires:1 reaction:1 circumference:1 repeated:2 wel:1 always:7 many:2 taking:3 density:2 equal:2 agree:2 etc:2 merging:2 figures:1 context:3 logic:4 inspired:1 veen:7 prescribe:1 adapted:1 comes:1 sci:1 ci:5 relevant:1 point:7 simple:12 overview:2 specification:1 cf:1 cd:1 subgraphs:4 article:1 cs:2 proved:2 delocalisation:1 kp:20 considering:1 forms:1 described:3 commutative:3 basis:6 tremendous:2 come:1 three:8 been:1 attaching:2 int:1 describes:1 pg:10 basic:7 corollaries:1 proposal:2 pi:2 pn:2 empty:9 define:19 direction:3 describe:1 controlled:2 versa:2 both:9 am:1 sufficient:2 subspace:1 remark:6 neighbour:3 schrijver:1 external:1 input:14 consecutive:1 c0:4 those:2 case:11 p0:14 p1:9 disconnected:1 formalization:2 isolated:2 quantenmechanik:1 prover:2 transformation:2 will:3 technical:2 while:4 optimization:1 replaced:4 leaves:2 situation:1 property:2 remains:2 loop:1 maximal:1 planar:1 vectors:1 pahs:1 geometric:1 almost:1 vi:1 von:1 non:3 marcel:1 iv:3 ii:3 middle:3 csl:1 itself:2 commonly:1 return:1 mod:13 k0:17 ig:10 orbital:1 capture:1 different:11 verified:2 synthesis:1 perform:1 realizing:1 belong:5 connection:3 same:11 toggling:4 add:1 parts:1 potentially:1 split:1 und:1 dealt:1 start:3 consequence:1 difficult:1 development:1 independent:5 wires:1 http:1 affairs:1 assignment:31 numerical:3 upon:2 effect:2 phd:2 esch:1 levels:2 solubility:1 student:1 beckmann:1 entanglement:1 build:2 cr:3 six:2 reference:1 cycle:5 lower:2 postponed:1 kept:1 splitter:1 charges:1 studies:1 modeled:1 well:2 roughly:1 without:5 thought:1 patterns:1 de:3 edge:35 polyacetylene:1 components:3 sets:2 very:3 quantitative:2 signalled:8 chemistry:9 self:2 charged:1 proposed:6 less:1 being:2 captures:1 obtain:3 aside:2 oxford:1 identify:1 showed:2 integer:2 alternative:1 ng:7 eigenstates:1 adv:2 k3:3 unique:9 candidate:1 field:4 regarded:3 seems:2 except:1 vb:1 discuss:1 signals:1 operator:3 belongs:1 conjugated:11 lett:1 easy:11 theorem:31 relevance:2 functionality:1 formal:1 remaining:2 take:5 real:1 aspects:1 around:2 myth:1 easily:4 read:5 polycyclic:12 topology:1 corresponds:3 possibly:1 quest:1 five:3 guide:2 press:1 using:2 bit:1 intersection:3 advanced:1 debatable:1 melting:1 necessary:3 like:4 semi:18 identifying:1 follows:25 qualitative:2 serves:2 translates:2 specific:1 roth:1 transform:1 steps:2 either:4 arbitrary:7 completely:3 become:1 valence:5 signal:4 terminology:1 mathematical:6 polymers:1 sketch:2 right:4 often:1 exposed:1 some:15 back:1 complexity:2 trends:1 mat:1 acad:1 examples:4 moreover:3 proper:2 kinds:1 extended:1 archetype:1 matching:5 transport:2 electric:1 nonzero:2 pronounced:1 bottom:1 nonempty:1 though:1 whole:2 otschel:1 does:2 exit:1 eliminate:1 summand:1 tends:1 ped:1 indication:1 leftmost:1 power:1 hsk:20 equivalent:3 electrically:1 rug:2 constructive:2 translated:2 step:1 although:1 output:20 renders:1 fused:1 finding:1 properties:7 proceed:1 chapter:2 integers:1 about:2 actual:4 socket:14 oh:1 theorems:2 discussed:2 o:4 page:1 union:3 whence:1 a2:3 plus:1 act:1 violating:1 eight:1 referred:1 consequently:1 optoelectronic:1 op:11 benzene:5 soc:1 computational:3 letters:1 into:6 within:3 splitting:2 functional:7 remarks:1 because:3 references:1 primarily:1 contributor:1 pentagon:1 positive:1 van:11 additional:2 switches:3 area:1 removing:2 there:34 question:3 handles:2 long:1 u2:13 fully:1 strict:1 much:1 lov:1 low:4 way:19 forward:1 was:4 opens:3 opposed:2 function:2 complete:2 form:10 enough:2 micali:1 converse:1 reichert:1 independently:1 but:15 transformed:1 neutral:3 chim:1 atom:2 elimination:1 line:1 highest:1 a1:3 longer:1 reset:1 applying:2 algorithm:2 consist:5 inhomogeneous:2 whether:5 characteristic:2 cells:24 vice:2 attached:4 up:5 us:1 until:2 paired:1 below:6 retaining:1 verification:1 uk:1 soldering:1 demonstrate:1 problem:2 similar:2 called:30 say:3 interplay:1 bearing:2 ac:1 ab:3 associated:2 contributors:1 computing:2 defined:12 certain:6 abstract:2 sketched:1 condition:6 denote:7 loops:1 single:13 proves:5 exist:4 rule:1 jonkman:4 corresponding:4 conversely:10 moves:1 operation:7 triangles:1 physical:5 again:1 functions:3 transitions:1 nl:2 no:13 objection:2 whereas:2 eastern:1 when:9 aromatic:4 zernike:1 application:7 disjoint:7 other:15 electrical:4 details:1 becomes:2 formalize:3 mathematics:5 you:1 really:1 nw:2 node:35 picture:1 briefly:2 elements:32 star:2 superposition:3 models:2 symbol:3 fowler:1 problems:1 ratner:2 subtraction:1 includes:1 replace:3 important:1 bullets:1 pathways:3 a6:1 fisher:1 kivelson:1 n2:2 structure:11 connotations:1 algebraic:1 implies:12 auxiliary:1 bullet:1 u1:13 assume:15 physics:1 required:1 curve:21 together:2 notion:1 4n:1 jong:1 speculations:1 neighbouring:2 weights:1 time:2 far:1 serious:1 signalling:5 starting:5 having:1 |
0704.2283.txt |@word sci:1 consider:1 rev:13 global:3 brownian:2 focus:1 leads:1 entropy:1 follow:2 lee:1 weakly:1 causes:2 particles:3 certainly:1 const:1 calculate:2 stacked:1 subjected:2 deterministic:1 tinoco:2 quasi:1 compensate:1 under:4 stochastic:1 provides:1 advantage:1 hatano:1 very:1 results:1 manipulated:1 every:1 experimentally:6 difference:1 exact:4 rotating:2 modulator:1 presented:1 cosine:1 tietz:1 small:11 optics:1 equation:1 smaller:2 force:16 speck:4 periodicity:1 measurable:3 sign:2 second:3 video:1 displays:1 anggi:1 further:1 petrosyan:1 tweezers:2 linear:10 established:1 what:1 nonlinear:1 trapping:1 rate:1 sum:1 contributed:1 expressed:1 current:4 linke:1 experiment:3 expresses:1 net:1 increasing:1 contrast:1 coefficient:6 den:1 respectively:1 error:1 here:1 understanding:1 searles:1 path:1 along:11 strong:1 observing:1 implicit:1 change:5 obtained:1 involved:2 study:1 larger:2 allows:1 periodic:7 resulting:1 shaded:1 changes:1 involves:1 diameter:2 via:1 followed:1 mobility:9 apr:1 highly:1 modulated:1 wang:1 plot:1 decorrelation:1 would:2 gallavotti:1 remains:1 positive:1 bechinger:2 escapes:1 negative:2 tightly:1 next:1 therefore:3 averaging:1 taken:1 type:1 theoretical:5 today:1 more:2 introducing:1 grier:1 becomes:2 tested:2 berlin:1 everywhere:1 known:2 actual:3 iv:1 iii:1 must:3 states:1 springer:1 integrating:1 science:1 setup:1 work:4 minimum:1 values:2 ms:2 following:1 collin:1 performed:2 compare:1 challenging:1 synchronized:1 mirrors:1 toroid:1 sample:1 effectively:1 seifert:5 numbers:1 occur:1 verlag:1 helden:1 provide:2 holds:1 how:1 ritort:4 ensemble:1 circular:1 oscillatory:1 product:2 mat:1 modulation:1 oscillators:1 after:1 derived:1 different:6 physik:1 data:2 response:10 attempt:1 effective:1 beam:2 description:2 so:1 correlation:1 definitions:1 order:1 typical:1 indeed:1 over:4 insight:1 choose:1 report:1 thermal:3 experiments:1 through:3 statistical:1 still:3 its:5 evans:2 fit:1 decay:1 temporal:1 gen:1 better:1 production:1 systems:7 van:1 suspension:2 focussed:1 non:14 good:1 affected:1 introduce:1 framework:1 exponentially:1 they:1 rotation:1 balances:1 2t:1 term:7 electro:1 overdamped:1 micro:1 magnitude:2 transmitted:1 trap:6 toroidal:1 universit:2 side:2 characterized:1 mean:15 subset:1 tilted:3 telescope:1 broeck:1 ed:1 energy:2 displacement:1 toda:1 frequency:2 measure:3 substantially:1 our:8 beyond:4 eq:13 out:1 shown:4 dominates:1 fundamentally:1 driving:12 quantify:1 since:6 crucial:3 denotes:1 diffusive:1 acting:1 adapt:1 100x:1 integrated:1 math:1 lutz:2 theory:5 written:1 free:1 quite:1 intermediate:1 derivation:1 created:1 determining:1 could:1 transition:1 keep:1 motion:7 period:1 due:3 hence:2 first:4 mittag:1 probability:6 ignored:1 crisanti:1 theoretische:1 revolution:2 approximately:1 directly:2 open:1 angular:3 passes:3 given:3 temperature:2 together:1 observes:1 system:3 relations:3 their:4 assumption:1 show:1 white:1 circulate:1 trapped:1 relative:2 optical:2 biomolecules:1 authors:1 focusing:1 than:2 coefficients:1 diffusion:12 distance:1 determines:1 third:1 depends:2 future:2 schuler:1 distinguished:1 decompose:1 hz:1 fluctuation:2 ann:1 generalization:1 randomly:1 close:1 clearly:1 estimated:1 zero:1 depending:1 convenient:1 responsible:2 able:2 liphardt:3 ideal:1 causing:1 generalized:3 forces:7 objective:1 negligible:1 twolevel:1 most:1 involving:3 jarzynski:5 letter:1 representation:1 pair:1 measured:5 libchaber:1 kb:8 deviations:1 considered:2 average:3 steady:7 dent:1 part:2 exp:1 mechanical:1 velocity:23 physics:2 dragged:1 fact:2 intensity:5 rayleigh:1 violation:19 friction:3 superimposes:1 discovered:1 x2:1 relation:20 subtracting:1 cell:1 finally:1 knowledge:1 parameters:1 morriss:1 state:7 only:1 circle:1 local:8 indepen:1 equilibrium:22 do:1 his:1 dependent:4 dd:1 fluid:1 famous:1 cannot:2 dx:2 3b:1 bead:4 during:1 quantifies:2 3a:2 gray:2 extract:1 resolve:1 bar:2 approach:1 arxiv:1 microscopy:1 microscope:1 europhys:3 cf:1 scanning:1 bars:2 set:2 achieved:1 benard:1 violated:1 correlations:2 up:3 observed:1 see:2 result:2 terms:2 uncorrelated:1 subject:1 mechanically:1 interacting:1 erez:1 arguably:1 nature:2 diluted:1 µm:3 colloids:1 enough:1 determined:5 various:1 between:4 limit:1 conditions:3 recently:1 complementary:1 importance:1 however:2 jr:1 js:4 kicking:1 faithful:1 probing:1 hashitsume:1 both:6 last:1 bustamante:4 freely:1 region:1 equal:1 stuttgart:4 connection:1 passing:1 expression:1 experimental:7 relevant:1 point:1 simple:2 corresponds:1 sampling:1 dimensional:2 ps:6 described:2 trajectory:3 three:1 been:1 much:2 yag:1 pn:2 cohen:2 fig:12 direction:1 quantities:3 sufficient:1 natl:1 rubi:1 hayashi:1 offers:1 understand:1 external:1 systematic:1 irrelevant:2 diffuse:1 present:3 replaces:1 laser:7 exponential:1 pacs:1 solid:3 value:2 will:2 while:1 replaced:1 behavior:3 blickle:2 balance:2 ein:1 versus:1 coupled:1 characteristics:1 thus:4 according:1 ii:4 vs:13 cond:1 maximal:1 convection:1 containing:1 stein:1 same:3 reconstructed:2 emphasize:1 ciliberto:2 finite:1 events:1 difficult:1 breakdown:1 used:1 comprehensive:2 trajectories:4 upon:1 monotonic:1 hand:2 driven:8 kubo:1 moving:2 potentials:1 invariance:1 recent:2 deflects:1 mech:1 traps:2 sevick:1 well:2 spent:1 analysis:1 obviously:1 lim:1 coordinate:2 position:3 paradigm:1 arising:1 dimension:1 comprise:1 maxima:1 less:1 when:1 obtain:1 vanishes:3 speed:1 previous:1 numerical:1 density:1 regarded:1 scales:2 smith:2 reimann:1 source:1 potential:15 lett:13 theorem:2 input:1 kick:1 fluctuating:2 around:1 lacking:1 digital:1 confines:1 increases:1 five:1 confined:1 using:3 2nd:1 imposed:2 helpful:1 particle:23 aqueous:1 follows:1 reduces:1 velocities:3 separately:1 flux:1 arbitrary:1 become:2 stationary:2 sketch:1 right:2 classical:1 madrid:1 understood:1 acad:1 oscillations:1 neglecting:1 colloidal:7 measurements:2 langevin:1 integration:1 conservative:1 does:2 connecting:2 embodies:1 proc:1 2a:1 limitations:1 noise:2 reasonable:1 indicated:1 broadening:1 crooks:2 equivalent:1 agreement:1 illustration:1 step:1 offset:2 dumont:1 comparison:1 central:1 extension:2 extending:1 discussed:1 dependence:2 extensions:1 germany:2 hatched:1 slightly:1 equally:1 markovian:1 previously:1 into:3 integral:7 bath:2 because:2 determine:1 einstein:13 paradigmatic:1 france:1 institut:2 additional:1 there:1 transform:1 stark:1 start:1 describes:1 viscous:1 function:9 form:1 adjusting:1 memory:1 reichert:1 but:2 histogram:1 heat:2 pfaffenwaldring:2 line:5 highest:1 versions:1 access:2 maximum:2 us:1 ur:1 below:2 2πr:3 physikalisches:1 fluctuations:2 distribution:4 torus:5 regimes:1 detailed:2 constant:12 universal:1 sketched:1 deep:2 dashed:2 single:7 proves:1 eom:3 moves:2 regime:7 again:1 functions:1 nm:3 na:1 nd:1 detail:3 field:1 valid:2 spatial:2 test:4 sasa:2 forcing:1 optically:1 stat:1 elements:2 p6:1 drift:5 wrachtrup:1 variation:2 important:1 additionally:1 laroche:1 dissipation:1 independently:1 implies:1 starting:1 dτ:1 resolving:1 governed:1 correlates:1 time:8 silica:3 resolution:1 original:1 |
0704.2284.txt |@word gr:4 remarkable:1 ali:2 rev:11 separates:1 desirable:1 focus:1 illustrated:1 obstruction:1 scalar:11 entropy:1 tuba:1 edu:1 inflating:44 remarkably:1 manipulations:1 contributions:1 hole:2 consider:11 kh:1 whose:6 amplification:2 depend:1 patches:2 indices:1 turkish:1 assumptions:2 concerned:1 tr:1 young:1 containing:1 finally:2 behave:1 award:1 th:4 late:2 visualizing:1 include:1 tc:15 indicating:1 overlaps:1 supported:2 amplitudes:2 straightforward:1 kτ:1 very:3 wave:12 size:1 bubbles:6 difference:1 exact:2 danielsson:1 condition:1 four:2 differentiated:1 induced:4 exits:1 presented:2 turns:5 anisotropy:1 henri:1 t2:1 cmb:4 t0:8 ri:1 large:2 solved:4 vector:5 small:5 provided:2 optics:1 equation:16 bases:1 smaller:5 htc:4 findings:1 summarizing:2 consistent:5 trodden:1 b23:4 b22:2 pulse:5 b20:3 feasibility:1 surrounding:2 second:4 reality:1 equal:4 further:3 dynamics:8 amplified:3 canonical:3 even:6 aim:2 gibbons:1 brackets:1 section:17 worldline:5 while:1 expressed:2 uniform:1 current:1 birkhoff:1 reheating:1 3h:1 above:8 flowing:2 2r0:5 acknowledgments:1 filled:1 paradoxical:1 satisfy:3 crunch:1 integrated:1 degree:1 relates:1 respectively:5 modify:1 amounts:1 here:3 understanding:2 growing:3 objects:1 tangent:3 sinh:9 others:2 represented:1 ignore:1 along:3 equations:15 appears:4 change:2 knowledge:2 obtained:4 incoming:3 institute:1 leaves:1 larger:7 allows:1 completely:1 leaving:1 spheres:2 usually:2 decouple:1 suitable:6 spacetime:10 involves:2 plotted:1 uniquely:2 via:1 spatially:1 scales:2 discontinuous:2 rendall:1 explained:1 sign:8 addressed:1 gordon:3 semiclassical:1 planck:1 unit:1 derivatives:1 use:3 ht:4 figure:9 would:6 prove:1 covariant:1 positive:5 contains:1 direction:1 negative:4 next:5 scenarios:1 comparing:3 sitter:26 therefore:17 expanding:2 taken:7 robertson:2 associated:1 until:1 today:1 more:4 separated:1 flat:16 setup:1 effectively:1 successful:1 initial:11 naive:1 israel:1 occurred:1 curvature:3 comoving:20 appendix:8 normalized:3 particular:3 known:7 cases:2 iv:5 iii:3 origin:1 must:1 obeying:3 account:1 room:1 pushed:1 shielded:2 recall:2 past:3 work:1 oscillator:12 detaches:1 occurs:1 trajectories:1 ij:1 thin:12 freedom:1 following:4 drops:1 example:4 address:1 history:2 claim:1 gravity:2 transition:1 cosmological:16 bubble:23 process:1 ds2:5 choice:1 neglected:3 purposes:1 respective:1 states:2 glued:3 detaching:1 minimum:1 taking:1 arise:1 keep:2 recollapse:1 occur:1 calculated:1 normalize:1 huge:1 ones:1 rays:2 end:2 sphere:1 rather:1 verify:1 means:2 feature:3 freezes:3 regions:15 how:5 nontrivial:1 trusted:1 pure:1 instead:2 ordinary:1 parameter:1 b15:2 isotropic:3 rept:1 oy:1 information:4 inflationary:14 stop:1 oscillators:1 after:8 derived:2 dx2:3 exactly:2 complicated:1 produce:3 waves:1 mah:1 law:1 constants:2 curve:1 dω22:3 shortcomings:1 short:3 natural:3 dynamical:1 effective:2 geb:1 spherically:3 approximation:7 nicest:1 lines:2 yielding:1 cosmology:4 switch:1 ertan:1 negligible:3 asserts:1 enter:7 increase:1 imply:2 order:10 eikx:5 typical:2 wavelengths:10 commutator:1 acts:1 played:1 considerations:1 hierarchy:2 indeed:7 pointed:5 mainly:1 satisfied:2 gram:1 stability:2 paper:5 through:1 same:8 ursey:1 differs:1 existence:1 still:4 excitations:1 its:6 tendency:3 boun:1 sciences:1 rh:5 rapidly:1 symmetry:2 singular:1 chosen:3 interesting:2 fix:1 solving:1 turok:1 coordinates:14 actually:3 forms:1 previously:1 absence:1 offers:1 fig:8 derivative:3 hidden:1 main:6 might:1 alter:2 eventually:2 non:1 junction:4 anticipated:1 differential:1 units:2 bang:6 detachment:3 effects:2 they:11 sij:4 nov:1 now:7 smoothness:1 nor:1 matched:1 2t:2 easily:2 february:1 gets:1 overdamped:4 always:3 university:1 investigator:1 b3:4 identified:2 academy:1 realistic:2 magnitude:3 transmitted:2 mode:19 radial:4 crossing:7 found:3 difficult:1 side:7 characterized:1 2k:13 homogeneous:3 square:1 ei:1 eh:1 superhorizon:7 independent:3 generation:2 energy:9 einstein:3 inflates:1 gaussian:2 related:4 solution:18 poincare:1 books:1 intrinsic:1 expect:3 entering:2 measure:3 quantum:12 our:11 avoided:2 event:1 special:4 out:31 try:1 dominates:1 rr:1 space:55 furthermore:1 since:22 crucial:2 denotes:4 content:1 obstructions:1 sissa:1 dominated:9 aligned:1 dominate:1 issue:4 subhorizon:4 shows:3 inevitably:2 foam:1 turning:1 theory:2 causally:4 written:6 discontinuity:2 free:7 standard:5 difficulty:1 reason:3 perturbation:11 formation:3 term:9 element:1 blau:1 b17:1 inevitable:1 wall:1 r4:1 definition:1 hubble:12 r0:27 derivation:1 r2:9 created:7 starts:1 kij:1 cosmic:7 success:1 times:1 motion:1 turn:1 plane:2 place:2 exponentially:6 leading:2 corrections:2 uses:1 guendelman:1 assign:1 first:10 exotic:1 already:2 features:1 probability:4 xf:3 reflected:1 reaches:1 b19:1 restrict:1 ihk:1 multiplying:1 2a2:2 construct:2 another:1 impossible:4 thick:2 precisely:1 open:1 long:2 illustrate:3 b9:4 interchange:1 given:8 necessarily:2 temperature:4 likely:1 indicate:5 introduction:1 unknown:2 extrinsic:3 system:3 least:1 unruh:1 their:5 perturbations:27 too:1 nν:2 dt2:4 white:1 expanded:3 smoothed:2 gives:6 bebek:1 shell:10 becomes:5 sin2:1 reversed:1 acquire:4 realized:2 required:1 kθθ:7 part:2 needed:1 b21:3 cosh:5 φtr:4 than:16 reflection:3 observed:3 supposes:1 third:1 αr0:2 penrose:2 horizons:1 was:2 cimento:1 namely:1 hypersurfaces:3 annihilation:1 matter:1 oppose:1 future:1 amplitude:8 were:1 powers:1 ktc:1 pre:1 false:9 generality:1 nuovo:1 fluctuation:2 pro:1 modern:1 spectrum:17 curves:1 correspond:1 randomly:1 say:1 2t0:2 conjugate:1 flatness:1 seen:9 sees:1 null:10 any:6 viewed:1 collapse:1 acceleration:1 robertsonwalker:1 minimally:1 depending:1 studying:1 able:1 isolated:3 mechanism:4 tkachev:1 note:12 instance:4 di:2 potential:2 take:3 timelike:4 simplifications:1 interior:13 asymptotics:1 carroll:1 linde:2 continuous:2 unless:1 components:2 though:2 quote:1 denominator:1 reach:3 hollands:1 metrics:1 most:2 involving:1 propagate:2 plan:1 phase:5 analytically:1 precludes:1 why:1 tensor:4 kφφ:1 give:1 surprising:1 considered:5 clear:3 later:2 flow:1 points:1 quadratic:1 left:6 physics:4 width:1 wavenumber:7 laws:1 precise:1 think:2 show:4 imagines:1 scattered:1 friction:1 radii:1 spaces:3 relation:3 solutions:6 subtle:1 d2:1 find:2 ground:5 component:3 boundaries:1 touches:1 causality:4 just:1 parameters:2 explain:3 specified:2 outside:12 should:19 only:5 explicitly:1 black:5 geodesics:2 ambiguity:1 factor:1 oscillate:1 local:17 over:9 continuity:3 do:2 loss:1 klein:2 distance:5 dependent:7 simplified:2 de:26 overall:2 obtain:6 define:1 remedy:1 cannot:7 dz:3 nearly:2 reversal:1 dy:3 safer:1 during:3 hij:3 dr:1 geometric:1 freedman:1 prime:4 adiabatically:2 evolution:6 resolve:1 roles:1 indicated:1 nicely:1 fields:3 arxiv:1 suggested:1 yield:2 patch:12 crc:1 qc:4 common:1 minkowski:2 analytical:1 fixed:6 valid:1 view:3 whole:2 ignored:3 set:4 art:1 observer:13 achieved:2 imposing:1 hypersurface:11 comparable:1 lett:2 freeze:3 plausible:1 argued:2 see:28 radius:11 result:1 dimensionfull:1 terms:5 dµ:1 gmail:1 singularity:2 commutation:1 superk:1 review:2 malized:1 φref:2 artificial:1 symmetric:3 state:6 αe:1 closed:3 between:6 invariant:3 boundary:25 conditions:14 across:1 pictured:2 choose:2 observational:1 ends:3 recently:1 ability:1 ikt:1 initially:1 confusion:1 spoiled:1 however:14 killing:1 2αg:1 piran:1 key:1 invisible:1 configuration:1 suppressed:2 problem:6 originates:1 motivations:1 both:11 parentheses:1 last:1 limits:4 successes:1 region:45 conclusions:4 according:3 nµ:9 a5:2 propagation:4 involve:1 figures:1 dated:1 embedding:5 expand:1 hσ:1 passing:2 argue:1 com:1 finds:2 comes:1 wald:3 among:1 ci:1 hold:2 point:11 simple:2 seems:2 each:5 vachaspati:1 period:2 lake:3 dimensional:2 simply:3 starobinsky:1 moreover:6 throughout:2 factors:1 considers:1 appeared:2 turkey:2 better:1 complication:2 jetp:1 described:1 submanifold:1 source:5 trajectory:1 create:1 arbitrary:2 due:3 been:5 annales:1 defined:3 much:8 foliated:1 damping:1 interest:1 basic:2 dr2:1 gazi:1 σk:2 generating:1 arises:1 corresponding:10 mazenko:1 sufficient:1 formed:1 ik:1 argument:10 observe:2 understand:2 vµ:1 transplanckian:1 berezin:1 denote:1 dh:1 present:1 case:7 k2:1 disconnected:3 exponential:3 frozen:1 gravitational:1 originate:1 examine:1 spontaneously:3 will:7 near:1 dν:1 match:1 behavior:4 irrespective:1 eik:5 property:1 conformal:2 study:2 supply:1 studied:2 coupled:2 chaotic:2 ip:1 metric:10 formulation:2 thus:12 discrepancy:1 encountered:1 ii:5 need:1 reads:1 itself:3 exterior:13 ambient:4 claimed:1 hyperbola:1 φin:2 worry:1 inserted:1 different:3 verified:1 sov:1 sensitive:1 generic:2 vintage:1 make:5 radiation:12 cross:1 penetrate:1 read:1 unity:2 arguments:1 underdamped:2 φk:10 grows:1 conflict:1 freeness:1 2kr:1 evolve:3 used:3 context:3 maeda:1 paths:1 disagreement:1 numerical:1 effect:2 hand:10 inhomogeneities:2 action:1 moving:8 potentials:1 interested:1 spreads:1 contribution:4 normalization:4 separations:1 lower:1 fourier:1 modes:13 scenario:2 band:1 settled:1 corresponds:1 inflate:1 well:5 objection:1 observations:2 without:5 solve:5 toy:3 coordinate:1 salient:1 model:9 paradigm:2 dh2:1 justify:1 spherical:15 comment:2 λp:6 enormously:1 proposed:3 being:1 when:10 identically:1 starting:1 homogeneity:2 profoundly:1 identify:2 kaya:1 using:12 differentiation:4 useful:1 alternative:1 glue:1 yet:1 previous:6 contradicting:1 looks:2 enters:3 preprint:1 density:6 aguirre:1 photons:1 conclude:1 sky:1 except:1 realize:1 guth:1 thermodynamics:1 homogenous:1 spread:6 attractive:1 easy:2 theorem:3 b12:4 pointing:1 bifurcating:1 momentum:5 b13:1 real:2 asymptotically:1 b10:4 depends:3 wavelenght:1 situation:1 big:7 b11:3 results:4 possible:11 harmonic:6 early:2 possibly:1 inflation:38 five:2 background:3 vacuum:15 press:1 immediately:3 unique:1 calculate:2 vertically:1 imposed:1 like:5 particle:3 sizes:1 contradict:1 da:6 isotropy:4 accelerating:1 specific:1 yields:5 either:2 follows:3 become:4 works:1 τs:2 imprints:1 wonders:1 sketch:2 because:1 classical:3 picture:4 creation:1 some:13 somehow:1 driving:1 hair:1 born:3 b6:1 sure:3 pφ:2 examples:1 b2:2 respect:4 proper:8 curious:1 b8:1 matching:5 exists:1 happens:2 canonically:1 scale:20 describing:4 disconnection:1 avoid:2 opposite:1 integration:1 microwave:1 causal:8 does:8 seeding:1 assuming:1 unstable:1 propagating:3 bessel:1 refer:1 considering:1 obey:1 power:12 location:1 equivalent:4 bo:1 oscillating:1 expansion:8 pressure:4 although:13 instability:1 drawn:1 properties:3 asymptotic:2 chapter:1 harmful:1 about:2 actual:1 origins:1 extending:3 universe:17 discussed:1 dependence:7 o:2 2i:1 range:2 a2:8 obeys:2 horizon:13 stress:1 connected:1 mean:1 consequently:1 explicit:4 road:1 seeing:2 raised:2 φ2k:8 a7:1 presence:1 h2:3 into:22 a6:1 radiate:1 three:1 nothing:1 appropriate:1 right:9 raises:1 determine:10 a8:1 operator:2 proportional:2 sufficiently:1 eht:2 hep:5 shells:2 assumed:4 there:19 approximate:2 signifies:1 start:3 conservation:3 kuzmin:1 inner:1 way:4 conceivable:1 sections:3 assumes:2 naturally:1 function:5 guide:1 complete:2 form:3 enough:5 hr:1 phenomena:1 denoting:1 berera:1 but:5 lemaitre:1 properly:3 delta:1 line:3 algebraically:1 true:3 ph:1 partially:1 b4:2 b5:1 whether:4 characteristic:1 inside:3 up:5 us:11 b7:2 limit:5 critical:1 signs:1 fluctuations:4 distribution:1 monopole:1 called:1 b1:1 detailed:1 goldwirth:1 interval:3 constant:18 choosing:1 ln:10 ai:4 curvatures:1 ak:3 describe:1 influence:1 expands:1 general:14 separating:2 single:5 ar:7 reenter:2 predictions:2 wavelength:18 correlation:1 check:2 physical:8 again:1 functions:4 compared:4 istanbul:2 no:4 universes:2 determining:1 wavefunction:1 generally:3 vanishes:2 quantization:3 b16:4 field:13 b14:2 other:8 dt:8 details:1 normal:4 spatial:1 department:1 isotropization:1 nr:2 massless:1 nt:2 operators:1 b18:1 conclusion:1 johnson:1 explaining:2 briefly:1 may:11 superposition:1 excitation:2 emerges:1 models:10 problems:1 variation:1 a1:2 push:1 a3:2 important:3 flattened:1 a4:2 suppression:1 vectors:1 variable:2 complications:1 sides:1 structure:6 relativity:4 algebraic:1 kx:2 implies:10 faster:2 assume:13 thermalization:3 dτ:1 lot:2 holes:4 together:1 original:2 final:1 portion:2 fact:1 4h:8 time:26 walker:2 requires:2 having:3 |
0704.2285.txt |@word limited:1 code:1 illustrates:1 results:3 bc:3 garching:1 computation:1 revealed:2 ebeling:2 editors:1 environment:1 those:1 mpc:16 difference:1 steeper:1 level:4 large:4 small:2 upper:1 work:6 consistent:2 direct:1 second:1 street:1 further:1 canonical:1 even:1 errors:3 briel:2 selected:6 near:2 version:1 nep:6 3d:1 spectroscopical:1 full:1 lef:1 respectively:2 here:2 objects:1 active:1 strong:1 obtained:5 dividing:1 institute:3 study:1 larger:1 allows:1 survey:8 shaded:3 makes:1 plotted:1 via:2 scales:6 apr:1 gioia:2 dennison:1 highly:1 apj:6 names:1 apm:1 planck:1 confidence:2 usa:2 positive:1 vol:1 therefore:1 taken:1 type:1 reflects:1 more:2 thus:1 known:1 central:2 must:1 sample:5 account:2 cluster:13 averaged:1 resents:1 infinitesimal:1 values:1 henry:4 following:1 making:1 deg:2 figure:1 szalay:3 high:2 performed:3 arise:2 exclude:2 hereinafter:1 information:2 needs:1 arbor:1 discussion:1 s0:5 regions:1 galactic:1 max:1 southern:1 physik:1 law:6 δva:2 δvc:2 natural:2 joint:1 separations:5 element:2 allow:3 correlation:18 order:2 typical:1 schuecker:1 elia:1 over:1 years:1 overdensity:4 paper:1 scott:1 still:1 galaxy:7 blake:2 derive:1 efstathiou:1 fit:7 ruderman:2 detected:4 fig:2 inaf:1 clusters:23 good:2 effects:1 they:3 now:1 bigger:1 easily:1 university:3 presented:2 identified:1 cowie:1 found:4 spectroscopically:2 mean:1 differential:1 significantly:2 series:1 expect:1 measurement:4 our:10 operation:1 space:5 rep:1 since:3 increase:1 investigation:1 dominated:1 istituto:1 shows:2 asp:1 galaxies:11 given:2 free:3 ecliptic:1 completely:1 threedimensional:1 california:2 rises:1 likelihood:2 anchez:4 length:3 facilitate:1 first:3 major:1 mag:1 probability:2 number:3 smaller:1 relations:1 another:1 sutherland:1 angular:1 biasing:3 surveys:2 publication:1 introduction:1 bologna:1 behaves:1 least:1 their:2 observations:3 final:1 shallowness:1 deg2:1 way:1 part:1 honolulu:1 authors:1 than:3 observed:1 showed:1 imply:1 aims:1 matter:2 amplitude:1 were:5 motivation:1 fluctuation:1 ann:1 measure:2 randomly:2 any:3 ray:16 strength:1 zero:1 studying:1 majority:1 fitting:1 correlating:1 investigations:1 overdensities:10 extending:1 germany:1 significant:5 conspicuous:1 astro:1 especially:1 considered:1 average:2 drive:1 yang:3 physics:1 fact:1 slope:2 shot:1 pope:1 show:1 detection:1 ss0:1 georgakakis:1 data:6 find:2 gilli:2 ratio:3 quoted:2 parameters:2 title:1 distributed:1 only:1 postfach:1 factor:5 identification:1 fanti:2 mobasher:1 tracers:2 di:1 michigan:1 agns:22 cannot:2 becomes:1 densities:1 fields:2 arxiv:1 median:1 43p:1 though:1 fixed:1 bars:1 computed:1 extraterrestrische:1 dadina:1 maximum:2 relative:6 see:1 crosscorrelation:1 best:3 detect:2 maddox:2 bias:4 cappi:4 between:7 progress:1 recently:1 targeted:1 restricting:1 however:2 spectroscopic:1 concentrate:1 come:1 last:1 ohringer:4 region:6 uncertainty:2 improves:1 cappelluti:6 adapted:1 point:1 ca:3 environments:1 dimensional:3 pole:1 church:1 respect:1 conference:1 bbg:4 three:2 much:1 expected:1 ph:1 reflex:1 huchra:1 define:1 precision:1 observe:2 deep:1 mail:1 present:3 exception:2 uncertain:1 limits:1 value:3 will:1 while:1 error:2 taking:1 real:2 almost:3 tions:1 surface:3 comoving:3 characterize:1 lambas:1 incompleteness:1 voges:1 technology:1 different:1 italy:1 perform:1 suggest:1 cross:11 same:1 check:1 unity:1 mullis:3 several:2 difficult:1 used:4 barger:1 palumbo:1 lower:1 off:1 center:4 analysis:1 dashed:1 drawing:1 left:1 distances:1 plionis:1 basilakos:2 less:1 paragraph:1 obtain:1 sources:3 shape:1 distant:1 using:1 previous:2 sampled:1 cut:1 hawai:1 density:3 cdfn:2 conclude:2 had:1 woodlawn:1 source:3 cdfs:1 5h:1 samples:1 resolved:1 aspects:1 around:8 l81:1 clasxs:1 dark:1 test:1 increases:1 mushotzky:1 radioastronomia:1 necessary:1 like:1 lost:1 signal:2 specific:1 become:1 works:1 soft:5 therein:2 right:2 classical:1 redshifts:1 indirect:1 scale:3 dense:1 l14:1 measurements:1 does:2 meaningful:1 noise:1 ba:2 power:6 disentangle:1 rosat:3 bj:1 broken:1 properties:2 h70:6 panel:2 comparison:1 about:2 rare:1 would:2 extension:1 most:1 universe:1 discussed:1 factors:1 angeles:1 range:2 estimator:1 plus:1 redshift:6 landy:3 into:1 within:1 because:1 references:3 proportional:1 clustering:10 uncertainties:1 statistics:1 approximate:1 los:1 low:1 fraction:1 was:3 opposed:1 function:12 north:1 complete:5 georgantopoulos:1 but:1 volume:3 hi:1 mnras:4 loveday:1 line:1 up:2 anel:2 ur:1 limit:1 autocorrelation:1 distribution:2 similar:2 distance:5 constant:1 defined:1 abstract:1 year:1 covers:1 evidence:3 single:1 bg:2 archive:1 physical:1 functions:1 compared:6 no:3 na:2 nc:2 when:4 ξcg:3 field:1 pasadena:1 spatial:5 department:2 conclusion:2 draw:1 calculating:1 malaguti:1 important:1 astronomy:3 deprojecting:1 structure:2 agn:9 implies:2 outskirts:1 interval:1 nuclei:1 gobetti:1 |
0704.2286.txt |@word consider:3 brownian:2 results:3 saar:1 four:2 eds:1 supplement:2 entropy:2 sol:1 go:1 issues:1 depend:1 paris:5 dickey:1 presents:1 finally:1 present:3 lra:2 chajnantor:2 amplitudes:1 melott:1 vla:5 focus:1 summarized:1 difference:1 fractal:4 vast:1 morceaux:1 stanimirovic:1 clouds:4 alma:17 notes:1 frozen:1 vector:4 bally:1 radio:1 servation:1 configurations:9 upper:5 oscillation:1 ted:1 direct:2 threshold:2 design:1 dynamics:1 gaensler:1 even:3 sud:1 giving:2 section:6 wavelike:1 uniform:1 current:1 experiment:1 above:4 fractional:2 shandarin:1 unsurprisingly:1 notions:1 never:1 here:2 hours:1 tracks:1 address:1 along:4 observing:3 appears:2 obtained:2 increments:12 shift:1 elaborate:1 studied:1 allows:2 amount:4 extremes:1 survey:1 fourier:16 studies:1 plotted:1 griffiths:1 apr:1 highly:1 apj:6 decrease:1 pdfs:1 total:1 tools:2 unit:1 use:2 proceed:1 uniformity:1 prove:1 remains:1 positive:2 next:1 few:1 therefore:3 taken:2 inner:1 type:1 theoretical:3 more:6 separated:2 optimizing:1 pads:1 becomes:1 antennae:2 normalized:1 particular:1 burkert:1 pouquet:1 largescale:1 high:2 springer:1 science:1 work:1 ere:1 values:2 hope:1 concepts:1 following:1 field:12 scherrer:2 repre:1 example:1 control:1 dedicated:1 tap:1 give:1 ence:1 sample:2 minimum:2 performed:4 sought:1 keep:1 guarantee:1 information:8 needs:1 end:3 decaying:1 s0:2 maps:2 ens:4 pair:2 axis:1 parameter:1 fr:3 galactic:1 description:1 may:6 lag:4 derived:1 par:1 millimeter:1 plane:2 deviates:1 date:2 law:1 data:2 miesch:1 supersonic:1 radiometry:1 short:2 dynamical:1 effective:1 elmegreen:1 polynˆomes:1 dot:1 spectra:1 lines:2 departure:1 cosmology:1 so:3 allow:3 correlation:1 vapor:3 bins:2 six:1 hierarchy:1 indeed:1 over:2 vary:1 stability:1 through:1 statistical:5 avenue:1 its:5 galaxy:1 before:1 manuscript:1 located:1 ln:2 edith:2 temporal:1 inclusion:1 decreases:1 actually:1 better:1 detected:2 fig:15 mail:3 decades:1 into:1 than:2 practice:1 primary:1 scaling:1 they:1 nor:1 structural:1 represents:4 brightness:10 applied:1 visibilities:2 each:4 found:2 universit:1 characterized:1 coles:1 significantly:1 series:2 reduce:1 idea:1 related:1 aide:1 interferometer:1 used:6 interplay:2 measure:6 our:1 thick:1 martinez:2 out:1 gonzalez:1 shown:1 space:4 rep:1 since:5 squared:1 lecture:1 correct:1 shows:6 franc:2 after:2 southern:1 free:1 estimate:1 times:1 turn:1 kohno:1 edges:1 ism:2 signature:1 lay:2 origin:1 probability:2 prevent:1 wave:1 number:4 reaches:1 done:1 directly:1 crit:1 array:3 bensch:1 size:1 given:5 needed:1 introduction:1 twenty:2 top:1 histograms:2 their:1 observations:2 perfectly:1 structures:4 final:1 gives:1 correlations:2 collapse:1 deconvolution:1 tool:1 larger:1 sents:1 undoubtedly:1 regridding:1 observed:4 molecular:3 require:1 see:1 future:1 contrary:1 tion:1 distinguished:1 fluctuation:1 correction:1 spectrum:7 curves:2 say:1 substantial:1 seen:1 recover:3 any:2 instrumentation:1 convenient:1 self:1 sakamoto:1 able:3 phillips:1 ideal:1 eles:1 finding:1 green:1 memo:1 channel:1 observatoire:2 spectral:1 multiple:2 shall:1 track:2 measures:2 fails:1 most:2 optimized:1 nonlinear:1 significant:3 phase:63 inserted:1 doi:1 observation:2 considered:1 prevails:1 mcclure:1 dimension:1 points:1 tech:1 radford:1 velocity:1 kx:1 typically:1 lying:2 quantity:9 structureless:1 show:3 random:6 bring:2 relation:1 lhomond:2 keywords:1 earth:1 o:2 based:2 implementation:1 delays:1 distributed:1 outside:1 topological:1 should:7 only:1 black:2 factor:1 falgarone:6 achieve:1 do:2 get:1 de:8 assumed:1 beam:1 reveal:1 evolution:7 fields:3 arxiv:1 yield:1 whether:2 contain:1 fixed:1 rms:2 computed:1 fair:2 achieved:1 kolmogorov:2 turbulent:4 grey:2 detection:5 depends:2 individual:1 radius:1 result:1 uncorrelated:1 heithausen:1 definitely:1 phases:10 detect:5 boundaries:1 enough:1 various:1 between:3 approach:1 terms:1 ability:3 receivers:1 importance:1 combining:1 however:2 contamination:1 configuration:10 distribution:11 assess:1 suggested:1 received:1 minutes:2 hint:1 equal:1 planned:1 context:1 pdf:3 estimation:1 whole:2 pdb:1 point:1 simple:2 corresponds:2 dimensional:2 exploit:1 coordinates:1 considering:1 described:2 perspectives:2 kinematic:1 instrument:4 would:3 west:1 dub:1 due:2 been:1 ph:3 fbms:1 direction:1 both:1 quantities:2 locations:1 understand:1 covered:1 fl:1 those:2 case:5 atmospheric:9 look:1 solid:5 wellknown:1 value:5 will:4 while:2 procedure:1 layer:1 vectors:1 zenith:1 characteristics:1 according:1 ossenkopf:1 mod:1 different:1 baseline:4 thesis:1 indistinguishable:1 same:6 another:2 complex:1 geographical:1 finite:2 attenuation:1 numerical:3 flows:1 levels:1 uses:1 comet:1 ois:2 refractivity:2 interferometers:2 weakly:1 antenna:2 largely:1 motions:3 calibration:1 well:1 analysis:7 thought:1 without:1 components:2 quantitative:3 model:5 drawing:1 less:2 being:1 woodward:1 obtain:1 valuable:1 underlying:1 using:8 rotates:1 yet:1 previous:1 radiometers:1 density:3 conclude:2 source:3 plateau:3 input:1 east:1 real:2 elevation:1 easily:1 possible:3 increases:3 turbulence:3 accepted:1 apart:1 like:2 follows:1 sized:1 yields:1 become:1 essential:1 making:1 accessible:1 methods:2 namely:1 simulator:1 spring:1 some:2 understood:1 election:1 sight:1 specified:1 extended:1 specific:1 bottom:1 measurements:1 integration:12 per:1 does:1 fbm:1 francois:2 porter:2 bure:3 noise:10 power:6 rue:2 although:1 output:1 transported:1 comparison:1 about:3 actual:2 carried:1 extension:1 column:1 discussed:2 recognized:1 simulation:1 practical:1 range:2 ensure:1 obspm:1 insufficient:2 ou:1 introduced:1 consequently:1 sheets:1 presence:4 image:3 numerically:1 interstellar:3 three:2 down:1 lies:2 stutzki:1 references:1 france:1 statistics:2 measured:14 there:1 question:1 transform:1 long:2 editor:1 astrophysics:2 interferometry:2 function:5 medium:1 complete:1 compressible:1 simplifications:1 but:5 histogram:2 astro:1 butler:1 cedex:2 solar:1 delta:1 line:10 fragmentation:1 made:1 compute:1 hartmann:1 arrays:3 la:1 detectability:1 maximum:1 verlag:1 below:2 un:1 limit:5 fluctuations:1 problem:1 similar:1 ex:2 associated:1 curve:1 abstract:1 measurement:2 influence:1 single:2 reliability:1 formalism:1 distributions:5 viallefond:4 assessing:1 akaike:1 dotted:3 no:3 dashed:2 water:3 detail:1 application:1 other:4 spatial:3 hydrodynamical:1 conclusion:1 diagnosis:1 uniformly:1 interferometric:2 coverage:1 wind:1 astronomy:2 structure:32 correlated:1 longer:1 physics:1 required:1 mask:2 mass:1 fact:1 boone:2 time:14 walker:1 resolution:1 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.