text
stringlengths
0
190k
0705.0816.txt |@word riccardi:1 magnetic:3 four:2 increase:4 calculate:2 γp:4 tween:1 under:3 downstream:1 every:1 figs:6 affect:1 tagging:4 solution:16 vector:1 estimates:3 unpolarized:2 kubarovsky:1 second:3 chen:1 estimated:5 even:2 established:1 selected:2 supplied:1 above:12 new:5 behavior:3 never:1 here:13 reported:2 mev:37 brooks:1 logarithmic:1 rescattered:1 obtained:13 items:1 study:3 changed:1 changes:2 instr:3 visible:1 amherst:1 total:3 linearly:1 plot:2 would:3 discrepancies:2 therefore:1 drechsel:2 type:1 until:1 connecticut:3 excellent:1 arndt:4 work:6 suggestive:1 girod:1 example:3 wang:1 give:5 absolute:10 provide:4 g1c:3 very:6 symposium:1 mueller:1 description:1 earlier:2 lab:3 spectrometer:4 summarize:1 disagree:1 third:2 deutsche:1 decreasing:2 g12:1 over:10 fall:1 vary:1 undetected:1 vita:1 before:2 fit:27 fig:30 versus:1 band:1 effects:5 they:3 represents:3 newport:3 reasonable:1 each:28 mean:5 laboratori:1 yvette:1 combining:2 extract:1 crucial:1 george:1 particles:5 laid:1 medicine:1 disagreements:1 foundation:2 arizona:2 standard:6 estimate:8 created:1 incorporated:1 corrections:3 already:1 channels:2 another:1 sober:2 electronic:1 rated:1 geant:1 top:2 approximately:1 needed:1 normalization:18 tool:1 frascati:2 somewhat:1 corresponded:1 positively:1 begins:2 target:12 γπn:2 older:3 zero:3 tion:2 extracting:3 fashion:1 modeldependent:1 paddles:1 spectrum:5 manner:2 seen:13 relatively:3 fitting:1 thoma:1 circles:8 though:3 extending:1 involving:1 germany:1 cummings:1 phase:1 bradford:3 observation:1 calculated:1 doe:2 points:3 calculates:1 signatures:1 nπ:1 attempts:1 gauge:1 availability:1 sanctis:1 just:1 burkert:1 rice:1 bartalini:1 reconstruction:2 klein:2 di:3 de:9 dc:3 yielded:1 christopher:1 despite:1 report:1 reconstruct:1 kyungpook:1 cleanly:1 runs:2 covering:2 irregularities:1 fair:2 detection:6 result:2 incorporating:2 said:25 approach:2 glasgow:2 however:3 wr:13 clues:1 news:2 suggested:2 essentially:1 triggers:1 uncertainty:30 against:1 contribution:5 southeastern:1 con:1 scientifique:1 polynomial:3 proceeded:1 basis:3 union:1 been:20 extraction:4 trigger:18 expected:1 flexible:1 giessen:2 website:1 θc:13 applied:4 publicly:1 near:2 viii:2 possess:1 procedure:2 donnelly:1 phenomenological:1 iv:4 ii:5 lacking:1 perform:2 suggest:1 make:2 several:2 independent:2 peaks:1 schumacher:2 qualifications:1 differing:1 kim:3 tune:1 weakly:1 programs:1 scintillator:1 simulated:1 left:1 quoted:2 distribute:1 assigned:1 via:2 identify:2 scattering:16 yet:1 previous:12 adding:2 hills:1 had:4 wright:1 spread:1 inefficiencies:1 carnahan:1 gave:1 noether:1 mayo:1 disagreement:3 possible:6 atomique:1 possibly:1 background:13 korean:1 steps:3 sezione:1 rebinned:1 yerevan:2 www:2 old:1 extended:2 flux:9 electromagnetic:2 sura:1 contributing:1 unstable:1 disappeared:1 post:1 properties:1 meyer:2 stokes:1 kinematical:1 o:7 constituting:1 slightly:1 duke:1 facility:3 kuznetsov:1 bound:1 orsay:2 existed:1 dytman:1 support:2 initial:2 width:2 fraction:1 was:47 form:4 forming:1 differences:7 failure:1 satisfactorily:1 true:1 absent:1 benchmarks:1 qin:1 check:1 triangles:1 dotted:9 no:5 whereas:1 generally:3 np:1 jenkins:1 ns:1 models:2 preceding:3 variable:1 pion:19 bottom:3 together:2 time:10 observables:1 backward:1 assump:1 varying:1 madison:1 dominguez:1 row:2 certainly:1 bremsstrahlung:3 technique:3 passage:1 finally:1 determinations:5 division:1 geometrical:1 entries:1 presented:4 did:2 guo:1 magnet:1 coincidences:3 dip:1 upper:3 mn:1 trend:1 sign:1 physikalisches:1 adds:1 appear:3 uniform:1 current:3 international:2 falling:1 staff:1 filled:4 multipole:9 french:1 strakovsky:4 smearing:1 address:4 change:2 institute:6 vectors:1 trial:3 g2a:3 resonance:30 plotted:1 useful:1 durham:2 subjectivity:1 schenectady:1 working:1 athens:1 france:2 vineyard:1 hakobyan:1 moriya:1 theoretical:1 smeared:1 apparent:2 validity:4 1µb:1 hanstein:2 cases:3 eγ:18 values:8 9th:1 following:3 deceased:1 dedicated:1 figure:1 sample:1 refine:1 spanning:1 dennis:1 hydrogen:2 occur:1 normalize:1 divided:3 rubin:1 optimal:2 coleman:1 edinburgh:2 explores:1 may:2 explored:2 data:80 compatibility:1 sectors:5 sr:1 nuclth:1 ππn:1 gwdac:1 so:1 representation:1 talk:1 typical:1 tagged:4 canberra:1 nucleon:10 gradual:1 displayed:2 experiments:1 tagger:18 statistical:9 cuts:2 still:1 ular:1 tending:1 group:1 acknowledge:1 maid:8 window:3 inefficiency:8 non:5 ritchie:1 now:1 hall:6 barrow:1 james:1 arrows:1 weighted:3 significantly:3 eg:1 gaussian:5 ex:11 approximated:1 shown:11 napolitano:1 space:1 furthermore:1 looking:2 squares:1 correct:4 shows:9 after:5 fisica:1 possibility:1 quite:1 california:4 org:5 e1:1 e2:3 widths:3 transition:1 turn:1 livingston:1 yun:1 first:2 variables:1 comprised:1 directly:1 array:1 open:6 angular:2 given:13 necessarily:1 gif:1 carson:1 indicate:1 ronchetti:1 structures:1 williams:3 pittsburgh:3 moscow:3 than:9 require:1 future:1 were:32 russia:2 correction:16 dash:7 any:4 exploratory:1 note:7 jefferson:5 deur:1 channel:3 normal:2 track:2 price:1 weller:1 pair:1 america:1 commissariat:1 surprising:1 considered:1 average:4 order:5 conservatively:1 typically:2 precise:2 mainz:2 show:2 troy:1 threshold:4 ratio:6 enough:1 only:11 wood:1 thompson:1 carolina:3 gev:48 get:1 nearly:2 workman:5 yield:13 summary:1 predicted:2 ricco:1 relative:1 college:3 subsequent:1 review:1 nucleaire:1 outside:1 between:16 multiplied:1 vertical:1 tur:1 gratefully:1 jo:1 reaction:23 discernible:1 many:5 region:14 contract:1 gwu:1 multipoles:5 overview:1 period:7 sampling:1 turkey:1 cords:1 mary:1 direction:1 strauch:2 formed:1 photon:43 those:7 single:1 fiducial:2 shafi:1 coupled:2 discrepancy:2 middle:1 motivated:1 technology:1 d15:2 different:5 d13:2 same:6 shifts:1 document:1 events:25 todor:1 investigated:1 closest:1 running:8 arose:1 validate:1 tracking:3 largely:1 minimize:1 roughly:1 without:2 model:4 consisted:1 dickson:1 being:1 when:2 briscoe:3 valuable:1 hint:1 photons:5 parametrization:1 fatemi:1 lett:7 momentum:27 kingdom:2 virginia:12 world:1 adams:1 particle:20 chamber:2 either:3 served:1 reduced:2 existing:1 table:13 matching:3 provided:5 accidental:5 fedotov:1 extensively:1 conservative:4 critical:1 decomposition:1 provides:1 measuring:1 broken:1 guler:1 ratios:1 eiφ:1 graal:4 comparison:12 hicks:1 discussed:2 cambridge:1 ηn:1 determine:6 rossi:1 radiology:1 hep:6 accelerator:4 assumed:1 there:6 los:2 low:2 cebaf:2 survives:1 jun:1 recoil:4 pull:2 datasets:2 eh9:1 agree:1 detailed:1 taylor:2 general:2 reliability:1 lifetime:1 incorrect:1 field:10 implied:1 deviation:8 briefly:1 vertex:1 carnegie:1 includes:3 a1:2 a3:2 important:1 peak:7 coverage:1 included:7 jlab:8 ments:1 mass:30 resolution:1 represent:3 monte:15 consider:1 caused:1 quadrature:2 causes:1 baillie:1 program:1 present:9 th:5 kλ:1 amplitudes:12 worse:1 far:3 dugger:3 polytechnic:2 difference:2 condition:2 norfolk:3 large:4 small:1 rate:2 wmax:2 further:6 what:1 niculescu:2 contributions:10 section:16 brief:2 public:3 version:3 sur:1 fractional:1 method:7 contrast:2 full:9 ranges:1 tracks:1 observing:1 inspired:2 allows:1 prior:2 amount:4 published:2 alexandria:1 vii:2 establish:1 goetz:1 charge:1 comparing:1 nucl:17 archives:1 paterson:1 qcd:2 taken:7 more:7 flat:1 mellon:1 corrected:4 tested:1 particular:1 known:2 endpoint:1 science:2 der:1 protons:9 compare:2 stated:1 states:11 numbers:1 arise:1 information:9 tiator:4 idaho:2 copiously:1 reflect:1 plane:4 horizontal:1 short:3 spectra:4 ito:1 tallahassee:1 developed:2 installed:1 paper:2 through:8 accidentals:2 its:1 rapidly:2 energies:17 d33:2 actually:1 detected:14 strange:1 systems:1 charlottesville:1 alter:1 good:5 avakian:1 cea:1 eugenio:1 association:1 easily:2 always:3 found:10 difficult:1 underconstrained:1 mikhailov:1 weight:1 stepanyan:2 energy:30 wires:1 isospin:6 measurement:3 http:1 beyond:1 event:8 leave:1 genova:2 since:8 research:1 dominated:1 occurs:1 lawrence:1 upon:1 reason:2 generate:1 service:1 rosner:1 hadrons:1 exhibited:1 number:8 least:2 differ:3 termined:1 introduction:1 smoother:1 construct:1 mami:2 assumption:5 expand:1 calculations:2 baryon:3 park:1 part:6 authors:1 polarized:2 pennsylvania:2 determined:20 rensselaer:1 rochester:1 extracted:7 empirically:3 internal:1 added:2 eaire:1 daegu:1 significant:3 undertaken:1 accepting:1 measured:13 branching:2 deviations:1 clear:1 sometimes:1 cover:1 electrons:2 velocity:2 charged:15 physics:8 lying:1 sector:11 thomas:2 particularly:3 extractions:1 scattered:4 find:2 universitaet:1 cell:1 parameters:2 simulation:5 distributed:1 subsection:6 factor:3 notation:3 santoro:1 dependent:1 pions:4 8qq:1 combinations:1 during:2 arxiv:1 hardie:1 dividing:2 bars:1 set:11 see:5 individual:1 migration:5 tkachenko:1 chambers:3 smallest:1 various:5 available:4 korea:1 recently:1 statistically:1 missing:22 initially:2 poorer:1 incident:15 both:10 recherche:1 improved:1 pdg:5 pdf:4 experimental:11 point:1 corresponds:1 proton:24 coincidence:4 simply:1 pp:4 described:16 acceptance:18 due:7 reduction:2 describes:1 ireland:1 nadel:1 tering:1 generating:2 flight:4 elsa:25 gar:1 determination:5 systematic:21 pierce:1 pacs:1 solid:5 reliable:1 calarco:1 empirical:12 while:3 reliably:1 error:8 couplings:8 stoler:1 real:4 concurrently:1 studied:1 encountered:1 italy:2 shaw:1 grant:1 wherein:1 reachable:1 emphasize:1 widely:1 products:1 higher:3 used:14 uses:1 focal:4 recent:8 task:1 database:6 tkabladze:1 analysis:19 morrow:1 consistency:1 centerof:1 cryogenic:6 hypothesized:1 shape:2 intervals:1 using:13 surprises:1 source:1 remaining:1 bin:23 radiator:1 helicity:3 modifications:1 imposed:1 follows:2 collect:1 yields:2 methods:3 some:8 pπ:1 scale:2 resonances:8 measurements:20 efficiencies:1 centroid:1 energie:1 pee:1 breit:2 run:10 s11:4 agreement:10 step:1 plots:1 most:12 clas:77 deserves:1 range:8 extensions:1 f35:2 meson:8 into:6 within:11 predictions:2 guidal:1 uncertainties:11 statistics:1 institut:2 featureless:1 long:6 forward:13 sections:29 atop:1 properly:1 infn:2 zhu:1 up:2 ul:3 kuhn:2 fluctuations:1 similar:2 called:4 associated:15 defined:4 mckinnon:1 influence:2 engineering:1 dashed:2 accounted:1 department:2 excitation:4 problems:1 kamalov:4 william:1 generated:4 structure:5 algorithm:2 required:5 saclay:1 tandem:1 weights:1 berman:1 having:3 gw:3 code:1 partial:2 results:12 gx:1 edu:1 mesons:1 gk:1 ac05:1 marchand:1 excluded:1 include:3 dramatically:1 confirmation:1 implicitly:1 continues:1 wave:1 electron:9 resonant:1 carman:1 entire:1 notes:1 fewer:1 noted:3 84er40150:1 hyde:1 enclosed:1 carlo:15 universities:1 richmond:2 experiment:6 collins:1 body:2 lee:1 respectively:1 separation:1 deduced:1 weinstein:1 raue:1 involved:2 larger:4 suggests:1 resulting:9 shaded:3 private:3 addressed:1 apply:1 lima:1 imaginary:4 usa:1 next:2 few:2 examination:2 egiyan:2 occurred:1 normalized:5 iii:11 high:1 account:4 integrating:1 blacksburg:1 dashdotted:1 averages:1 performed:6 process:5 purposes:1 reconstructed:3 tac:1 united:2 six:2 williamsburg:1 hampshire:2 forest:1 tπn:1 photoproduction:13 collection:1 inst:1 demonstrating:1 fits:25 forschungsgemeinschaft:1 counter:7 lines:7 correspond:2 discussion:2 bins:5 houston:1 wigner:2 produced:1 including:3 facilitates:1 perfect:1 le:1 la:1 chosen:1 masses:2 communication:3 eur:3 acknowledgments:1 greater:2 outlined:1 p11:2 p13:2 subtraction:3 university:29 identified:4 magnitude:4 kph:1 feldman:1 constraints:1 subset:1 map:2 bump:1 krusche:1 protopopescu:1 our:2 meth:4 out:5 matrix:1 res:1 rev:16 asymmetries:1 istituto:1 ref:6 integrated:1 tempe:1 york:2 determining:1 could:4 florida:4 length:2 isotropic:1 south:3 powerful:1 bonner:1 precisely:1 quality:1 publication:1 start:4 revealed:1 histograms:1 πn:5 system:3 their:3 πp:1 intermediate:1 final:6 beard:1 explanation:1 s31:2 simulate:1 july:1 observed:5 liquid:1 amplitude:2 offlight:1 f15:2 fluctuation:1 curves:4 constrained:1 clearly:8 catholic:1 angle:16 physique:2 polarization:2 best:1 detector:5 accuracy:1 serov:1 centre:1 collaboration:21 but:7 preliminary:1 hu:1 subtracted:4 counted:1 artificially:1 fact:1 selection:1 text:2 supported:1 purely:2 planning:1 subtracting:2 nominally:1 based:6 knowledge:1 should:4 ambiguity:1 dodge:1 means:2 mainly:3 overall:6 tbw:2 beam:8 timing:1 procedures:1 rebinning:1 differential:17 crabb:1 processed:3 contain:2 ohio:2 fixed:3 view:1 variations:1 national:5 operated:1 3jz:1 cole:1 nuclear:1 favor:1 state:11 difficulties:1 identification:4 progress:1 industries:1 ability:1 efficiency:18 armenia:1 configuration:1 joo:1 hits:1 limits:2 taking:2 storrs:1 eta:1 passing:1 comment:1 cm:1 cb:25 respect:1 salgado:1 kinematic:16 addition:2 yao:1 bianchi:1 klimenko:1 ignorable:1 contribute:1 corresponding:8 cos:13 angles:12 arisen:1 multi:1 value:13 will:3 texas:1 mecking:2 vi:1 thus:2 examined:1 dual:1 sequentially:1 cross:34 parts:3 largest:1 units:1 huertas:1 ball:2 columbia:1 maximon:1 identity:1 audit:1 center:6 nucleare:1 well:4 sets:8 comparisons:1 arising:1 less:5 kramer:1 obtain:1 sources:2 clinic:1 underlying:1 rapid:2 density:2 absorption:1 smith:3 lattice:1 matched:3 match:1 identical:1 tests:2 increased:1 increases:1 five:1 loss:2 necessary:1 helpful:1 excluding:1 miami:1 mutchler:1 nucleons:1 emmy:1 italian:1 laget:1 does:3 assuming:4 wmin:2 slight:1 drift:5 p33:2 analyses:3 beneath:4 panel:6 about:2 actual:1 extension:2 column:1 certainty:1 dependence:4 angeles:2 dominion:1 tailed:1 introduced:2 massachusetts:4 equally:1 previously:1 tight:1 washington:4 dataset:2 van:1 additional:2 elastic:5 smoothing:1 much:2 applegate:1 function:1 north:1 azimuthal:1 overlapping:1 histogram:3 volume:1 neutral:2 construction:1 highest:1 osipenko:1 made:4 evident:1 whether:3 smooth:2 placed:2 below:8 converted:1 limit:5 distribution:11 display:1 krahn:1 measure:5 nazionali:1 periods:1 nazionale:1 identities:2 functions:4 compared:13 calibration:2 percent:1 detail:4 collimation:1 other:7 compares:2 details:2 quantities:1 conclusion:1 transferring:1 star:2 variation:2 philips:1 coupling:2 factors:1 portion:1
0705.0817.txt |@word replacing:1 represent:1 concept:7 consider:22 limited:2 surrounding:1 skip:3 dynamic:3 results:3 existing:1 four:3 code:2 preface:2 go:1 follow:1 gl:1 saved:6 reasoning:1 issues:2 increase:2 inverse:2 graph:62 subjected:1 similarity:1 g6:2 tp:95 neighbours:19 program:1 present:4 th:2 under:1 nodes:69 include:1 resources:2 inform:2 g7:2 applied:1 updated:2 g4:2 g3:2 string:6 g1:1 very:6 than:17 listed:2 rem:5 connects:2 grid:3 denoted:1 refine:1 worst:5 updates:2 anonymous:2 affect:1 associated:1 difference:3 fractal:4 entire:5 redistribute:2 solves:1 presented:1 did:1 die:1 having:4 list:1 joined:1 t0:5 t1:4 large:1 discrete:1 gd:1 o1:1 small:1 drop:3 intersection:1 round:2 added:2 open:1 slower:1 core:1 temporary:3 edu:3 coefficient:1 discover:1 elegant:1 second:7 pass:4 download:3 further:4 dynamics:3 implemented:4 leakage:1 append:1 even:9 will:106 what:4 abc:2 adds:2 section:18 near:1 shares:1 proprieties:3 current:3 version:8 above:5 new:19 net:4 increasing:3 subcycle:4 public:4 contrast:1 halts:1 body:9 led:1 heavily:1 respectively:2 aggregate:2 never:1 component:1 behaviour:1 met:1 asymmetry:2 test:1 others:4 alone:1 path:4 along:3 table:3 change:17 extreme:7 sending:2 search:3 didn:1 ctp:70 ahead:1 broken:1 receive:8 g19:2 completely:2 queue:2 amount:2 extremes:1 survey:1 procedure:2 published:1 aka:1 suitable:1 changes:3 segments:1 plotted:4 composed:2 useful:3 mobility:1 explained:2 private:1 affected:4 6s:1 decrease:1 send:13 traversing:1 total:4 hoping:1 standing:1 use:7 y2:1 figure:14 working:2 prove:1 sake:1 destination:3 finally:6 distinct:1 few:2 live:5 call:3 therefore:13 memory:8 themselves:1 simpler:1 type:2 until:10 more:18 separated:1 popped:1 hooked:1 knows:2 src:2 started:1 initial:3 marks:1 distribution:3 aware:1 flag:5 bisector:1 particular:1 known:4 cases:5 mounted:1 iii:1 starter:10 must:8 o2:1 none:1 ma:1 extension:3 rights:1 signed:1 achieve:2 modified:3 remain:1 minimum:1 could:1 sent:11 www:1 following:14 unlucky:1 drops:5 example:31 proof:3 control:1 reserved:1 links:13 give:4 process:1 sense:3 share:2 g5:2 high:4 indicates:1 assumptions:1 numbers:1 want:2 allowed:3 phrase:1 g2:2 information:16 respective:1 requirements:2 goal:1 memorize:1 verify:2 divided:1 acts:2 differences:2 range:1 delay:4 far:1 edge:1 pair:2 adapted:1 hop:5 ntk:2 instead:8 those:6 axis:3 parameter:3 wolfram:1 yxz:2 simplicity:2 explores:1 description:3 may:6 quantified:1 after:1 containing:5 substitute:2 upload:10 hence:2 mesh:7 designed:1 cambridge:1 end:5 derives:1 grow:1 bandwith:1 short:2 physical:2 highlights:1 effective:1 whenever:1 backup:1 merged:2 bugs:1 redundant:11 their:4 propriety:1 ones:6 algorithms:2 progressively:1 fundamental:1 enter:1 every:9 operate:3 order:13 worsens:2 recognised:1 operations:1 restriction:1 executed:2 words:6 indeed:6 over:2 soon:1 cpc:1 stability:2 paper:2 through:7 looks:1 caustic:1 differs:1 y3:1 still:4 its:61 before:7 write:4 derive:2 group:7 probability:1 maps:8 lo:1 ll:7 optimisations:2 actually:1 better:2 html:2 choose:2 covered:8 main:2 into:3 split:1 wouldn:1 non:3 usa:1 return:1 adjacent:2 combination:4 yc:2 cay:1 collide:1 finish:1 number:17 srt:1 yz:1 they:11 supposed:2 sorted:3 now:8 register:1 easily:2 february:1 document:9 dabo:2 name:4 always:5 level:5 crypto:2 events:2 disconnection:1 good:2 improvements:1 fitness:1 found:3 uninteresting:15 tracer:27 mean:12 square:1 another:3 map:18 doing:2 series:1 ef:1 idea:2 related:1 solution:2 used:10 measure:1 quantum:3 our:1 operation:1 balance:1 todo:2 event:5 shown:2 fluxes:4 network:40 join:1 space:1 restricted:2 dst:13 since:14 excepting:2 research:1 looking:4 re:6 contained:16 entry:1 com:1 performs:1 internet:3 print:4 py:2 get:2 size:1 occurs:1 red:1 shows:2 foundation:2 differ:2 free:3 isps:1 clarify:2 reason:10 surely:1 org:5 byte:1 measurement:1 generate:4 shortest:2 definition:2 created:2 starts:1 route:100 computers:2 keep:3 filter:4 explored:6 isn:6 atp:9 signature:2 routes:121 facilitate:1 frequent:1 first:33 wiki:1 already:15 saving:2 forwards:11 prevent:1 bouquet:5 xc:2 reflected:4 reaches:4 consequently:1 restrict:1 date:1 xx:1 xy:1 simplified:3 approximately:1 directly:2 simplifying:1 reached:2 forwarding:3 quality:1 spread:1 passes:1 given:5 management:1 exists:1 needed:1 top:1 behaves:1 system:1 least:11 priority:1 indicate:2 attack:1 assumption:2 too:11 decentralised:1 bits:1 mobiles:1 adopts:1 simulates:1 option:1 asymmetric:2 recursively:2 continuous:5 rsa:1 immediate:1 mathworld:1 part:7 copy:1 haven:1 distance:1 scenario:2 cyclic:1 require:1 see:14 packed:1 inversely:1 classes:5 store:2 visited:1 gives:3 abstracts:2 result:6 fashion:1 false:1 survives:1 abcde:1 generation:1 mind:1 generalization:1 needs:1 say:1 substantial:1 manner:1 close:4 need:7 seen:4 null:1 any:23 contents:1 paths:2 min:1 efficient:9 convenient:2 responsible:1 able:5 note:11 majority:3 without:6 build:1 so:8 many:4 worldwide:1 blue:1 sure:3 allow:1 normal:7 knew:1 reach:20 fails:1 falls:1 most:3 awk:6 cyclicity:2 letter:1 successive:3 phase:4 segment:12 class:11 damage:1 exact:2 death:3 constructed:1 observation:1 consequences:1 fills:1 considered:8 later:1 cover:4 vertices:1 graphs:1 points:3 tps:13 fact:3 joining:3 saying:1 signatures:2 simultaneously:1 encrypted:1 supported:1 terminate:4 ending:1 rtt:13 carefully:1 φm:5 uniform:1 find:6 principal:1 access:1 execution:1 q2:23 based:3 simulating:2 copyright:1 hadn:1 hops:3 writes:2 appended:1 distributed:4 should:7 starters:1 only:30 sequential:1 subsection:1 sec:2 distributes:1 local:2 hope:1 costant:1 do:3 gains:1 means:4 dg:1 simplest:1 stop:2 scalable:1 bear:1 da:2 cannot:2 fastest:3 joins:4 reply:1 during:5 conjunction:2 him:1 deductive:1 traverses:1 arxiv:1 remove:2 tuned:1 rfc:3 imposed:1 bilinear:1 traversed:2 common:1 contain:4 release:1 including:1 creates:8 cycles:7 valid:4 view:2 happen:1 ignored:2 traverse:3 set:26 qtp:1 ends:1 packet:42 up:2 pushed:1 y1:1 finiteness:2 injecting:1 us:2 fail:1 contains:14 alternative:1 best:6 techniques:1 closes:3 phases:1 learns:3 capacity:5 nature:1 wikipedia:1 pumo:1 propagates:1 y4:1 symmetric:4 written:1 won:17 various:1 routing:11 closed:3 between:8 exploration:13 reading:1 approach:1 discovery:5 available:1 notice:2 terms:1 creating:1 lg:1 optimal:4 modify:1 however:11 scalability:4 efficiency:19 enters:1 key:3 anonymity:1 problem:3 appending:1 topology:10 retrieves:1 received:37 etp:48 instant:1 reverse:3 license:4 implementing:2 similar:5 infinitely:2 explore:9 april:1 improves:1 receives:18 interesting:23 forall:2 pdf:1 passing:4 whole:3 finds:1 otherwise:3 load:1 among:4 point:10 simple:10 had:3 berkeley:1 authenticity:1 corresponds:4 walk:4 cz:3 cy:1 simply:1 decreases:2 cs:2 moreover:3 considers:9 erased:2 described:8 capable:2 simplification:8 create:2 strings:1 three:1 been:15 quickly:3 much:2 interest:7 recognize:2 expected:1 flexible:1 copied:1 improve:2 empty:5 define:2 website:1 controlled:1 packs:1 sufficient:1 formed:4 neighbour:8 overloading:1 proportional:2 observe:1 understand:1 covers:2 last:4 andrea:1 protocols:1 case:26 highest:2 handling:1 limits:1 unlike:2 gnu:3 straight:2 examine:3 value:6 easier:1 aim:1 while:7 suppose:25 applies:2 situation:2 property:3 loop:3 identical:3 detailed:1 primary:11 ve:11 almost:5 thus:13 them:4 iv:1 ii:1 disjoint:2 daemon:1 vs:3 ave:1 abcdef:2 id:10 different:8 unaffected:2 handled:2 anymore:2 generic:5 disregarded:1 same:27 read:2 parts:2 viewed:1 established:1 several:1 propagate:1 composition:1 consequence:2 higher:1 extended:3 http:7 gw:2 keys:1 permit:1 effect:2 aggregation:1 v1:8 v2:19 levels:1 uses:3 purpose:1 infinite:1 propagated:6 validate:1 totally:1 implement:3 cycle:17 implements:2 lower:3 correspondent:1 kept:3 keeping:2 shared:1 expression:2 random:1 itself:3 analysis:1 obviously:2 costs:1 sets:3 position:2 model:2 usual:1 world:2 stores:1 just:21 less:6 generally:1 paragraph:3 networks:1 obtain:1 actions:1 detail:3 assigned:1 bandwidth:13 stored:2 thanks:1 immediately:3 rest:2 october:1 yet:2 previous:3 oriented:1 rapid:1 secondly:1 integer:3 flood:26 conclude:2 character:1 except:7 5s:1 source:1 verse:1 other:38 extends:1 location:2 input:1 differentiated:1 save:1 useless:1 real:4 tests:1 represents:4 rules:9 evaluate:3 regard:1 unlimited:1 possible:8 forge:1 increases:2 traffic:1 know:15 performance:1 using:3 bit:1 unique:2 synchronization:2 necessary:4 like:7 skips:1 eg1:1 exploit:1 serves:1 noted:1 specific:3 flux:18 parsing:1 continue:7 either:2 become:2 works:1 page:6 poor:1 exceed:2 because:26 old:8 often:2 simulator:4 sends:20 some:8 searching:1 dead:1 polynomial:1 deduce:1 erase:2 b0:3 examples:3 b2:1 escape:1 proper:1 asynchronously:1 happens:2 discarded:1 describing:1 merge:1 avoid:1 opposite:2 per:1 equal:5 dies:3 compute:1 o5:1 o4:1 o3:1 preceding:1 minimal:2 refer:1 considering:3 expires:1 run:1 indicated:1 simultaneous:1 dropped:5 bn:1 each:36 continuing:1 bi:1 how:1 step:4 bw:5 output:3 refers:1 proceed:1 oo:1 comparison:1 about:3 rare:1 would:12 anything:2 simplify:7 attacks:1 ids:1 side:2 remains:1 carries:2 neighbor:1 connected:6 acyclic:6 slightly:2 1gb:1 software:3 warranty:2 exactly:3 own:2 keeps:1 previously:4 xyz:1 implications:1 servers:1 included:1 appropriate:1 en:1 references:1 pivot:5 your:1 forwarded:10 waits:1 aren:5 support:1 there:13 question:2 noticed:1 start:3 describes:2 low:2 way:13 forward:11 overhead:1 slopes:1 analyze:2 was:2 strict:1 opens:1 lowest:2 cryptographic:2 deepened:5 complete:9 form:6 something:1 simplifications:1 erases:1 analyse:5 but:17 back:9 underlined:1 construction:1 link:35 pk:1 don:1 line:3 removed:3 true:1 xac:1 middle:1 improved:4 embedded:1 stanford:2 extremity:1 prevents:1 inside:5 maximum:5 devices:1 mobile:1 below:3 converted:1 limit:9 autonomous:1 minutes:1 called:6 b1:4 multipath:1 preferable:1 wifi:2 ordered:2 ad:1 classic:1 defined:2 packets:16 abstract:1 describe:1 doesn:11 general:16 single:9 simulations:2 mash:1 trip:2 inc:1 ni:2 nk:2 no:1 when:19 portion:1 invalid:3 grouped:3 interested:5 details:1 branch:8 becomes:4 significative:1 eight:1 you:13 ns:1 appends:2 conclusion:1 node:134 generates:3 finite:3 symbol:1 sqp:1 uniformly:1 update:4 generated:2 important:2 authorities:1 gets:3 structure:2 opened:1 building:1 worsened:8 independently:1 algorithm:22 assume:2 requires:2 required:3 pseudo:1 finished:1 rule:7 original:1 depth:3 implied:1 mass:1 time:14 n1:2 starting:5 cpu:2 once:8
0705.0818.txt |@word ibid:1 limited:1 since:2 sci:2 pointing:1 represent:1 pairing:19 green:2 roc:1 results:7 yellow:1 integration:1 leads:4 yokoya:1 higher:2 controversial:1 research:1 displaying:1 cases:1 gi:2 devoted:1 θc2:2 preserves:2 replacements:1 depend:4 zone:4 re:2 presented:5 29d:1 shanghai:2 29b:1 29c:1 29a:1 simplify:1 charge:6 critical:11 those:5 under:5 γc:3 ren:1 nodes:3 include:1 presentation:1 tc:18 indicating:1 doped:3 consequently:1 g1:10 antiferromagnetism:3 very:5 construction:1 subject:1 wave:16 oxides:1 electron:5 kaminski:1 wider:1 figs:2 bounding:1 experimentally:2 difference:1 exact:1 condition:5 illustrated:2 pre:1 squares:2 hamiltonian:4 proc:1 anisotropy:1 tanh:3 solution:10 large:2 solved:3 vector:1 demonstrated:3 small:5 3b:2 noted:1 configurations:1 smaller:2 says:1 destroys:1 consistent:1 prediction:2 sign:2 past:1 zero:10 θc1:2 evaluated:1 corner:2 manner:1 further:2 dynamics:1 chem:1 goes:1 even:6 will:4 what:2 errors:1 plays:1 appear:1 rate:1 sun:8 section:3 while:6 expressed:2 find:2 consistently:2 experiment:2 fretwell:1 localized:1 cheng:1 destroyed:3 3c:1 new:19 3a:2 increasing:1 method:2 body:4 full:2 christian:1 implying:1 exchange:1 respectively:7 modify:1 here:2 understanding:1 ranges:1 following:7 regimes:1 china:1 groups:2 directions:3 ratio:1 along:3 strong:2 equations:24 appears:1 superconductor:1 obtained:8 arc:6 study:1 larger:2 approaches:3 metal:1 leaving:3 suggests:2 simultaneous:2 resulting:1 published:1 usually:1 narrow:1 changes:1 plotted:2 appropriately:1 regardless:1 projection:1 scales:1 ground:1 summations:2 vii:2 gk:14 replace:2 rx:1 iron:4 sgn:6 circle:1 total:1 wuyts:1 plot:1 permitted:1 expresses:1 takes:2 usa:1 remains:3 positive:1 contains:1 6b:3 finally:2 properties:6 distinct:2 few:2 nucl:1 noting:1 therefore:12 taken:2 dict:1 means:4 type:3 theoretical:3 diagrams:1 more:2 fractions:1 beyond:2 vk:1 wavefunctions:1 started:1 becomes:4 operators:10 apparent:1 due:1 deserve:1 appendix:1 virtue:1 particular:2 known:1 hole:14 detects:1 iii:4 analogous:1 must:3 high:9 lengths:4 defines:2 kanigel:3 permits:2 science:1 equation:2 averaged:11 emerge:2 χk:2 four:2 theories:1 labeled:1 fock:1 values:12 temperatures:12 believed:1 cond:2 interest:3 averages:3 example:4 relative:2 compare:2 renormalization:1 figure:3 give:1 calculation:3 cited:1 preserving:2 organized:1 states:11 assumptions:4 caused:1 numbers:1 employs:1 allowed:1 kamihara:1 made:4 occur:1 calculated:1 yang:1 huge:1 sents:1 g1k:2 goal:1 rather:2 laughlin:1 discussion:1 g0:24 feature:1 write:2 necessary:2 extended:3 adjacent:1 antinodal:2 instead:2 absolute:3 parameter:2 sato:1 simplicity:2 product:4 oxypnictides:1 blocks:2 mat:2 beauty:1 arcs:8 may:11 max:3 philosophy:1 derived:4 different:4 diagram:2 dwave:1 plane:1 waves:1 fits:1 choice:1 data:21 grow:1 types:2 overdoped:3 short:1 physical:1 dynamical:5 effective:2 coupling:2 whenever:1 slightly:1 campuzano:4 explicit:12 su:72 element:1 perhaps:1 ones:1 so:4 fundamental:1 correlation:4 sc:15 definitions:2 integrand:1 order:2 se:1 ding:1 atanh:1 interpretation:2 help:1 seeing:1 chin:2 essence:1 over:7 competing:5 interpreted:1 thermal:1 experiments:10 through:8 tempera:1 motions:1 left:1 differs:3 extensively:1 still:1 its:7 features:1 regions:4 supplemented:1 derive:1 group:1 surviving:1 chatterjee:1 termed:1 chosen:1 interesting:3 solving:2 encompasses:1 decreases:2 li:2 forms:1 pines:2 absence:1 microscopic:3 systems:4 insulator:2 decades:1 h0:3 eur:1 maximal:1 closure:13 non:4 pure:11 entire:2 obtaining:1 moshchalkov:1 practice:1 dai:1 introduce:3 framework:2 resolve:7 preservation:1 they:3 half:3 bogoliubov:1 now:6 transparent:1 represents:3 term:3 several:2 oxygen:1 lies:1 always:1 university:3 level:2 2x:3 identified:1 2d:1 realistic:1 guidry:9 magnitude:2 2a:1 2b:1 each:12 found:4 entirely:1 difficult:1 decreasing:2 side:1 characterized:1 mean:3 qz:3 footing:1 chung:1 challenged:1 energy:18 gaussian:2 related:5 constitute:2 gaps:25 resolving:1 obtains:1 entering:1 measurement:1 quantum:2 our:13 approximated:1 differ:3 eq:16 description:2 emerges:1 shown:3 conceptually:1 matrix:1 space:9 open:8 rep:1 algebra:4 washed:1 cuprate:13 u2k:2 particles:2 rek:2 investigation:1 dominated:3 denoted:1 illustrate:1 ref:21 occurs:1 red:4 commutation:1 earlier:1 theory:4 interactions:5 contain:1 diagonal:1 possibility:2 differing:1 measurable:1 qi:3 completely:7 proportionality:2 corrects:1 demler:1 implication:1 additional:1 straints:1 pairs:5 interaction:7 derivation:1 geometry:2 could:4 transition:10 takenaka:1 keep:1 motion:1 appearing:1 length:1 place:1 isotropic:1 incorporated:1 assumed:2 consequence:2 25a:1 diminishes:1 condensate:1 first:4 origin:2 copper:2 staggered:1 utilizes:1 symmetry:14 ignored:1 quasiparticle:1 number:1 contributions:3 alternatively:1 simplified:4 construct:1 another:1 carry:1 reached:1 xq:5 quality:1 size:3 given:6 temperature:32 likely:1 indicate:2 introduction:1 unknown:1 eqs:10 πi:3 system:2 occupancy:3 ito:1 their:13 underdoped:15 assumption:2 constants:1 calculations:2 πz:2 scheme:1 opening:2 gives:2 kf2:1 fraction:2 relationship:3 centered:3 explanation:1 exactly:2 contribute:1 17b:1 immediate:3 direct:2 hinks:2 part:1 somewhat:1 authors:1 bonds:1 natural:1 rabello:1 than:5 outline:1 approximation:10 kind:1 third:1 double:3 approximations:5 typically:1 second:1 submitted:1 preformed:1 determined:6 mochiku:1 amplitude:2 were:2 identical:2 kf:8 4kb:3 exhibit:1 lowest:1 symmetries:3 generality:1 rewrite:1 lines:4 unchanged:1 conventional:1 measure:2 curves:4 20a:1 already:2 20c:1 20b:1 buried:1 close:1 take:3 constrained:2 clearly:1 complete:1 reaches:1 strength:1 angle:8 discrepancies:1 bruynseraede:1 ideas:1 mechanism:1 propose:1 note:5 fitting:1 potential:1 generalized:2 εk:9 online:3 negligible:1 strengths:8 hightemperature:1 accuracy:1 circles:3 formulas:2 17d:2 gγ:1 allow:1 normal:2 17c:1 measures:1 techniques:1 singlet:5 most:5 nonlinear:1 importantly:1 17a:1 pair:10 centering:1 analytically:1 measured:5 why:1 tensor:1 rosenkranz:1 cosky:3 observation:2 consequences:3 kk:130 arising:1 clear:3 later:2 implications:1 physica:2 takeuchi:1 points:9 electrons:6 principle:1 analogy:1 ky:18 kx:21 physics:10 fact:1 quantity:4 optimal:1 momenta:4 phenomenon:1 show:6 retains:2 probe:1 tures:1 discovered:1 x2:3 relation:2 solutions:16 substituting:1 agrees:1 occupation:1 feng:1 based:6 parameters:3 explain:2 blue:4 written:2 should:4 only:11 explicitly:4 generators:2 rich:1 factor:18 constant:2 hamiltonians:1 g00:3 oct:1 do:12 dominant:1 above:9 notation:1 gik:1 dependent:37 arcwise:1 obtain:5 cannot:1 brillouin:4 despite:1 portions:2 falling:1 takahashi:2 qq:4 portion:1 exhibiting:1 de:1 g0i:2 g0k:9 numerous:1 arxiv:2 suggested:1 summary:2 paper:10 predicted:3 characteristic:1 analytical:5 shi:1 creates:1 fixed:1 inside:1 reveals:1 requirement:1 set:1 exists:3 physically:2 correlations:5 richer:1 observed:2 see:6 individual:2 sec:4 considered:1 capable:2 existence:2 discussions:7 led:1 kadowaki:2 alternative:1 acquires:1 surfaces:2 closes:2 detect:2 interacting:1 compounds:3 γmax:1 knoxville:1 sites:1 materials:1 favor:1 state:11 closed:1 between:6 limit:1 boundary:1 reading:1 approach:1 nernst:1 discovery:1 available:1 adv:1 triplet:4 terms:4 plicitly:1 extend:3 sections:3 importance:1 wk:10 however:4 rapidly:3 wu:11 italic:1 windows:5 key:1 percent:1 tmax:18 suppressed:5 σk:16 observable:1 cos:6 toward:1 scalapino:1 reported:2 many:5 region:8 la:1 equal:3 henley:1 involve:2 improves:1 figures:1 dated:1 ktc:1 focused:1 contribution:1 bond:1 expression:2 experimental:6 con:3 ck:2 among:1 adjusted:1 relevant:4 2kb:3 tong:1 conclude:1 color:3 corresponds:3 represented:2 tennessee:2 anti:1 right:2 v2k:2 doping:39 arsenic:1 actually:2 cu:2 better:1 ensures:2 pq:2 described:6 share:1 basis:1 addition:1 aligning:1 pseudogap:19 curve:7 been:12 quickly:1 describes:2 pg:13 azimuthal:4 basic:1 anisotropic:11 degrees:7 fig:22 6a:4 direction:7 6c:3 corresponding:11 25b:1 quantities:2 formed:1 subspace:3 essentially:1 25d:1 gap:25 coherent:11 tending:1 understand:1 representative:2 bull:1 ozyuzer:1 formfactors:1 worked:1 evidence:2 spin:10 present:6 case:5 heavier:1 exponential:1 pacs:1 solid:5 dopings:5 appearance:2 quadrants:1 value:10 employ:1 deferred:1 near:4 replaced:1 5c:1 behavior:6 situation:2 2k:1 taking:2 20d:1 2uk:1 detailed:1 vd:3 coupled:1 almost:2 vi:4 refs:2 conjugate:1 thus:13 site:1 surface:17 iv:2 ii:3 vq:3 superconducting:13 mott:2 seen:1 illustrates:2 zhang:1 vanish:1 fermion:1 dukelsky:2 orbital:1 intense:1 combining:1 generic:1 suggest:2 make:1 guptasarma:1 same:5 any:1 unity:4 layered:1 angleresolved:1 emphasize:2 established:1 mixtures:1 constructed:1 neutron:1 meaningfully:1 conserved:1 independent:11 used:4 kelvin:1 numerical:1 upon:1 effect:2 randeria:2 hand:2 inhomogeneities:1 compared:3 highly:1 hartree:1 yuan:1 recent:2 lower:1 shaded:6 modes:2 no:8 well:3 remain:2 analysis:1 observations:2 without:2 solve:4 components:2 dashed:3 quantitative:1 model:49 tional:1 photoemission:2 possesses:1 propor:1 subgroup:1 unified:1 magnetization:1 cuprates:7 proposed:4 less:1 being:1 generally:3 superconductors:10 presumably:1 underlying:2 predicts:2 λk:13 taiwan:1 scattering:1 previous:1 vπ:3 onset:1 intersection:1 preprint:1 density:3 point:9 had:1 except:4 discuss:2 lattice:2 add:1 valid:3 extends:1 lett:7 easy:1 natl:1 role:1 guarantees:1 5a:1 momentum:20 5b:1 resolved:1 independently:1 around:3 depends:2 easily:1 evaluate:1 handling:1 possible:5 cruz:1 pseudogaps:3 know:1 background:2 vacuum:1 using:4 accepted:1 souma:1 like:4 loss:1 imposed:1 particle:5 success:1 sizes:1 supercon:1 follows:3 reduces:2 serves:1 communications:1 private:1 imposes:1 steps:1 either:1 arbitrary:1 bi2212:1 become:3 valence:1 collective:7 lerma:1 replacement:1 mathematical:1 tm:1 indications:1 because:15 old:1 often:2 people:1 existing:2 arrows:1 plausible:1 some:8 competition:2 global:1 understood:1 elements:1 acad:1 ordering:1 30a:1 30b:1 norman:2 nonzero:2 provided:2 tave:11 scale:2 describing:1 takigawa:1 lead:1 gapped:2 measurements:3 filling:3 overlap:1 does:2 uchida:1 provides:1 assuming:3 oda:1 chains:1 them:1 minimal:2 inserting:1 formfactor:5 indicated:1 multiple:1 uniformly:1 equivalent:2 2c:1 agreement:1 θk:12 step:2 although:3 impurities:1 hilbert:1 comparison:1 about:1 works:1 extension:5 constraint:6 freedom:7 am:1 od:1 discussed:3 dependence:22 o:2 practical:1 probabilities:1 greatly:2 pockets:1 simplification:2 monotonically:1 islands:1 introduced:3 denote:1 kohno:1 considerations:1 soc:1 rev:12 jiao:1 into:2 within:2 predictions:4 bound:1 three:3 phase:8 appropriate:2 weighted:2 operator:1 proportional:4 next:1 methods:1 straightforward:1 fill:1 ek:6 nodal:13 there:7 question:1 long:1 width:2 anderson:1 window:7 weakly:1 low:4 way:2 was:1 opens:1 function:6 considerably:1 elsewhere:1 form:2 offer:1 phenomena:1 becoming:1 regard:1 removes:1 g01:3 but:16 expected:3 properly:2 pk:2 ex:1 highest:1 true:1 considerable:3 truncation:1 october:1 applying:1 largest:1 whether:2 antiferromagnetic:5 supr:2 welldefined:1 maximum:12 quantitatively:2 until:1 paired:1 below:3 fermi:30 spectroscopy:2 continuously:1 fluctuations:1 problem:3 define:1 similar:5 average:7 nature:7 expect:2 strongly:3 sort:1 result:1 associated:2 reconcile:1 labels:1 af:19 defined:3 certain:2 describe:4 influence:1 mike:1 proven:1 general:5 substantially:1 single:1 exist:3 4p:1 dθ:1 formulation:1 ax:1 formalism:3 triangles:2 regime:8 functions:3 nk:2 us:1 dotted:2 ingredients:1 qθ:2 wavefunction:6 when:4 vanishes:2 scaled:1 field:2 other:7 republic:1 details:1 25c:1 department:3 out:4 shrink:1 θc:15 node:2 picture:2 permitting:1 kinds:2 superconductivity:8 models:1 finite:2 preceding:2 problems:1 generated:1 important:2 restore:1 graphically:1 suppression:1 astronomy:1 structure:8 watanabe:1 building:2 algebraic:1 correlated:2 implies:5 longer:1 tested:1 assume:3 restores:1 required:1 holes:2 governed:1 having:5 arpes:9 restricted:1 qualitatively:1 observables:7 bcs:2 expands:1 original:19 once:1
0705.0819.txt |@word consider:8 ceases:1 lack:1 four:4 computation:2 preface:2 saved:3 gi:1 gr:1 whose:1 tp:18 presents:1 finally:6 under:1 nodes:51 include:1 resources:1 g7:1 belonging:8 global:2 g3:11 g2:15 g1:16 g0:7 very:1 rem:25 every:6 updates:2 anonymous:2 entries:1 locked:1 difference:2 fractal:10 redistribute:1 basics:1 level:84 permits:1 list:3 solution:1 rj:2 recall:1 small:2 round:1 added:1 prevent:1 says:1 second:3 plugins:1 download:1 further:1 dynamics:5 even:4 will:54 what:2 stands:2 giving:1 section:2 near:1 current:2 version:2 above:1 new:15 net:1 public:3 hasn:2 full:1 exchange:1 respectively:1 modify:1 met:2 explore:3 groups:15 active:3 path:2 along:1 respect:1 change:3 wait:1 sending:1 drops:1 ctp:56 receive:2 involved:1 study:1 changed:1 completely:1 queue:1 amount:2 published:1 advantages:1 aka:1 changes:7 composed:4 useful:2 divide:1 modifying:2 ips:2 egress:4 send:13 total:2 gateway:2 use:5 links:10 usa:1 remains:1 contains:18 chooses:2 few:1 duplicate:1 call:3 therefore:2 memory:6 taken:1 tells:1 until:3 reflects:2 more:6 separated:1 flat:5 formally:1 knows:3 becomes:2 marks:2 flag:1 particular:1 known:4 iii:1 must:3 respected:1 account:1 ma:1 rights:1 avoiding:1 itself:2 values:2 sent:12 learn:1 following:7 modifies:1 arrive:1 example:14 initial:1 control:1 computers:2 reserved:1 figure:11 process:1 sense:1 updated:3 high:12 indicates:2 dropped:2 want:1 allowed:1 destination:1 information:15 needs:2 requirements:1 recursive:1 memorize:1 get:1 range:1 write:1 how:5 vital:1 hop:2 ntk:2 instead:3 map:22 continues:1 explores:1 description:1 may:1 reflect:1 consequence:1 membership:2 mesh:1 physical:5 third:1 whenever:1 inform:1 subdivisions:1 so:3 enter:1 definitions:3 operate:1 order:4 operations:1 ingress:4 executed:2 joins:6 over:2 mainly:1 entity:3 radar:6 own:4 through:1 replies:1 still:1 its:50 before:2 perfect:1 delay:1 group:8 maps:5 chosen:1 lo:1 ll:12 inferior:2 writing:2 forms:2 choose:2 might:2 h0:1 them:4 good:1 return:1 combination:1 noticing:1 they:6 now:4 easily:1 february:1 gets:1 name:1 always:2 drop:1 loosely:1 fitness:1 found:1 uninteresting:1 tracer:6 mean:3 domain:1 directly:2 simplicity:2 doing:2 idea:2 numeric:1 connect:2 measure:4 loops:2 our:2 happen:2 avoided:1 out:1 predefined:2 respects:1 accomplish:1 network:35 join:1 restricted:1 since:2 hooked:1 looking:1 re:1 contained:2 performs:1 internet:2 rn:1 receiving:2 ri:1 red:1 bordering:2 foundation:2 working:1 personal:1 free:5 isps:1 clarify:2 reason:2 base:1 surely:1 org:5 byte:2 definition:1 ltp:32 r1:1 created:1 route:20 omit:1 keep:2 creates:5 explored:4 isn:3 routes:6 uses:1 assign:3 first:8 blind:1 already:12 fx:1 forwards:3 symbolic:1 reflected:2 reaches:1 hook:6 another:2 wasn:1 reached:1 forwarding:3 quality:4 given:1 ian:1 their:7 unknown:1 structured:2 least:5 needed:1 too:2 decentralised:1 store:2 low:1 exploring:2 option:1 recursively:2 continuous:1 broadcast:1 part:3 copy:5 than:2 updating:1 kind:1 require:1 computes:2 were:1 wandering:2 launches:2 collecting:1 false:1 unchanged:1 need:3 seen:1 border:2 any:15 contents:1 convenient:1 able:5 ideas:2 note:6 rejects:1 internal:5 instructs:1 build:3 green:2 completed:1 worldwide:1 blue:2 sure:1 normal:2 reach:15 simplify:1 learns:4 connected:1 successive:1 phase:4 measured:1 considered:1 clear:1 later:3 request:2 points:1 tps:2 precise:1 pkt:1 show:1 random:2 rtt:2 bright:2 threshold:1 stores:1 find:2 access:1 giant:1 q2:2 knowledge:1 copyright:1 hops:1 verse:1 distributed:3 should:2 only:19 specify:1 circle:3 hope:1 neighbouring:2 notation:2 means:2 scalable:1 cannot:1 words:3 during:1 crossed:2 having:1 endless:2 regarding:7 floods:3 arxiv:1 rfc:2 traversed:1 contain:1 release:1 view:2 kernel:1 set:1 packet:15 up:1 see:9 computer:1 sec:1 said:1 capacity:2 ways:1 jumped:1 wikipedia:1 pumo:1 propagates:1 symmetric:1 written:1 won:6 various:2 routing:6 correctly:1 between:2 propagated:3 conditions:2 checks:1 available:1 ends:2 terms:1 originated:1 however:1 4gb:1 efficiency:3 interface:1 problem:1 topology:16 received:10 last:4 reverse:2 license:4 taking:1 equal:1 attributed:1 called:1 propagation:2 receives:18 interesting:7 exceeds:1 pdf:1 passing:1 whole:3 otherwise:1 pre:1 relevant:1 point:4 simple:2 corresponds:1 maintained:1 cs:1 moreover:3 considers:1 considering:2 sensible:1 described:1 asks:1 persists:1 create:2 three:2 been:9 homogenous:1 much:1 basic:2 borders:4 wants:1 6a:1 controlled:1 both:2 formed:3 neighbour:1 external:15 improved:1 c1:3 andrea:1 those:1 case:4 limits:1 gnu:3 plain:1 expanded:1 value:6 aim:1 while:4 suppose:13 situation:4 procedure:4 ve:3 ip:16 metric:2 thus:11 contiguity:1 ii:1 ij:1 ave:1 id:18 different:8 generic:1 belong:4 same:23 linked:6 rules:4 html:1 document:8 conflict:1 higher:2 status:1 used:8 http:3 again:1 flooded:7 i0:1 saves:2 v2:7 levels:30 v4:2 purpose:1 v6:2 positives:1 cycle:3 lower:2 kept:1 makes:1 without:5 thought:1 costs:2 sets:3 entry:1 usual:1 gaining:1 just:4 being:1 paragraph:2 isolated:1 bandwidth:1 transforms:1 precisely:1 immediately:3 previous:3 death:3 had:1 add:1 belongs:15 versa:1 input:6 5a:1 march:1 read:1 possible:2 dark:2 five:2 know:5 performance:1 using:2 unique:3 generated:1 necessary:3 like:1 lost:2 loses:4 ignore:1 continue:2 steps:1 either:1 output:2 works:1 circles:1 www:1 because:6 old:1 sends:16 some:7 back:3 bounce:1 repeat:2 examples:1 b2:3 table:2 specific:2 contacts:1 assuming:2 refer:1 run:1 equivalent:1 each:22 continuing:1 broken:2 step:2 bw:1 become:2 periodically:1 deletes:2 about:3 inter:1 would:4 impose:1 tracing:1 completing:1 ids:1 o:3 compatible:1 distinct:3 carries:1 act:1 1gb:1 software:3 warranty:2 cambridge:1 previously:1 into:1 h1:2 servers:1 references:2 determine:2 proportional:1 your:1 forwarded:6 support:1 there:9 subdivide:2 describes:1 ipv4:3 way:7 ipv6:2 forward:2 was:3 considerably:5 complete:1 form:2 forming:1 removes:1 but:7 reiterated:1 link:14 dead:1 delta:1 remote:1 removed:1 directed:1 october:1 embedded:1 inside:6 maximum:5 devices:1 exploration:2 minor:1 autonomous:1 calculated:1 b1:3 detailed:1 website:1 defined:1 abstract:2 describe:4 doesn:4 general:6 single:25 governed:1 file:1 trip:1 inc:1 ni:1 marking:1 dying:1 when:16 flood:4 other:12 details:3 appending:1 you:4 appends:10 conclusion:2 node:85 elements:2 denote:1 nearer:1 1kb:1 update:4 a1:3 dies:3 a2:3 flattened:1 authorities:1 structure:5 independently:1 subdivision:1 algorithm:1 vice:1 established:1 packets:5 rule:8 utilised:1 implied:1 mass:1 time:6 characterising:1 starting:1 cpu:1 once:4
0705.0820.txt |@word limited:1 consider:1 chain:2 hooks:1 activated:1 preface:1 query:3 scp:1 gh:2 referring:1 technique:2 send:7 finally:1 th:1 nodes:9 sent:4 updated:5 string:2 very:2 rc:1 choice:1 worst:1 updates:2 entries:1 telling:1 difference:1 basics:1 level:1 try:2 small:1 possibility:1 prevent:2 approximation:1 second:1 picked:2 follow:1 port:2 substitute:1 even:4 adds:1 overload:2 reply:4 aliases:1 public:4 full:1 hash:39 exchange:1 modify:1 here:1 free:1 others:1 active:5 change:2 wait:1 sending:1 search:1 receive:1 changed:1 completely:2 queue:6 domains:1 changes:1 named:1 private:4 highly:1 ips:4 resolutions:1 total:2 use:4 takes:1 contains:1 readable:1 negative:1 next:2 few:1 call:1 therefore:3 dns:4 memory:1 scope:1 more:3 becomes:2 validity:3 keeping:1 challenge:1 cat:1 values:1 modifying:1 following:1 making:1 example:6 performed:2 nearest:3 share:1 effectively:1 dropped:1 allowed:1 action:1 returned:2 needs:1 redundancy:1 verify:3 feature:2 write:1 how:2 parameter:1 isn:4 may:2 max:1 after:1 tries:1 disable:1 date:1 data:1 register:11 so:1 allow:1 keeps:2 every:5 order:2 rounded:10 indeed:2 symbols:1 replies:1 still:1 its:28 before:4 machine:2 forwards:1 chosen:3 ll:2 choose:2 main:8 non:3 someone:1 return:2 records:10 they:3 stabilise:1 servers:1 association:1 february:1 gets:2 name:5 always:8 each:7 found:1 side:1 domain:4 retrieve:1 directly:2 weight:13 abnormal:2 related:2 exceeded:1 approximated:1 anarchy:2 out:1 ftp:2 network:3 space:1 since:6 re:1 internet:1 denoted:1 occurs:1 associate:3 retrieved:1 pub:2 standard:1 ntk:3 ask:1 org:3 transition:1 days:2 keep:4 place:1 massive:1 signature:2 assign:1 first:5 already:7 features:1 probability:2 number:28 echo:1 hook:2 alternatively:1 another:3 owner:1 array:2 size:1 given:1 management:2 checked:1 service:26 rejects:1 introduction:1 top:1 system:5 wrapper:3 priority:13 their:3 returns:1 too:1 decentralised:2 unreachable:1 hundred:1 bits:1 store:1 gives:1 exactly:1 rsa:1 rejected:1 part:1 hup:1 copy:2 than:2 specify:2 kind:1 optimise:1 double:1 programs:1 see:2 future:1 contrary:2 listen:1 browser:2 counter:11 affirmative:1 randomly:2 manner:1 increment:1 need:1 any:7 zero:6 latter:1 able:3 client:6 note:2 without:1 sure:1 normal:2 expires:3 most:1 services:1 expired:1 considered:1 request:26 principle:1 databases:1 normally:1 fact:2 pkt:3 random:2 scattered:3 registers:5 find:1 priv:1 nearer:1 wraps:1 slow:1 based:1 implementation:1 cache:8 distributed:5 only:6 thousands:1 get:3 db:1 likely:1 famous:1 cannot:1 ssh:1 words:1 new:9 spammers:1 disabled:1 runs:1 resolve:8 arxiv:1 bytes:1 method:1 rfc:7 common:1 queries:2 steal:2 valid:1 caches:1 ignored:1 set:1 exists:2 packet:2 up:1 relative:3 computes:2 result:4 fails:1 probable:1 deactivate:1 wikipedia:1 state:1 won:3 between:1 transfered:1 checks:1 notice:1 however:1 key:9 optional:2 topology:4 last:1 many:1 taking:2 equal:4 etc:5 periodical:1 receives:5 pdf:1 requests:2 whole:1 finds:1 simple:1 corresponds:3 cd:1 simply:1 cs:1 moreover:1 ensures:1 described:1 asks:2 create:1 certify:1 due:1 been:4 strategy:2 wants:2 corresponding:1 attacker:1 general:2 former:1 present:1 case:4 value:2 will:53 while:1 expiration:3 owns:2 ip:30 thus:2 them:2 itself:3 id:1 trusted:1 different:3 perform:1 same:14 proceeds:1 rules:1 verifies:1 avoids:1 document:3 higher:1 used:7 http:5 keys:1 effect:1 existent:1 moment:1 identity:2 lower:1 kept:1 database:6 contact:7 entry:4 latest:1 stores:1 less:1 being:1 generally:1 obtain:1 assigned:1 stored:1 thanks:1 yet:2 web:1 unique:1 passively:1 passive:1 reasons:2 setting:1 rgh:2 heavier:1 warrant:1 resolved:2 format:1 read:1 couple:1 possible:7 know:2 resolves:2 using:2 bit:1 accepted:1 daemon:1 necessary:2 exploiting:1 manual:2 server:1 specific:1 steps:1 fully:1 become:2 page:1 specifies:2 because:1 old:4 sends:7 back:1 cr:10 discarded:1 lead:1 contacts:3 exit:1 mutation:1 assuming:1 chains:1 substitutes:1 deleted:3 equivalent:1 step:2 substituted:2 although:1 periodically:1 chapter:1 about:2 ok:1 anything:1 attacks:1 accepts:1 queued:1 srv:4 backup:1 automatically:3 own:1 into:1 chooses:1 down:1 references:1 registration:22 proportional:1 forwarded:1 transfer:1 there:6 long:1 way:6 usr:1 registered:11 but:3 hierarchical:2 trying:1 true:2 made:1 default:2 inside:5 attached:1 maximum:3 signed:3 record:21 below:1 limit:4 distribution:2 similar:1 called:4 delete:1 storing:1 associated:11 abstract:1 specified:1 doesn:3 denote:2 single:2 associates:3 exist:1 file:2 check:6 nh:2 ni:1 no:1 when:12 invalid:1 website:1 grouped:1 other:2 role:1 you:2 contacting:1 node:66 generates:1 update:5 includes:1 cryptographic:1 practically:2 pseudo:1 utilised:1 portion:1 time:7 resolution:17 original:1
0705.0821.txt |@word sci:2 consider:10 remarkable:1 alg:2 edi:1 truncated:1 results:3 four:4 obstruction:1 generalize:1 computation:3 derf:3 expressions:1 whose:3 corps:1 paris:1 premet:8 description:1 finally:4 th:4 under:2 uchebn:1 zaved:2 xth:1 alternating:1 applied:3 g2:3 straightforward:6 far:1 end:1 multi:9 dokl:2 every:10 exact:13 deformations:34 condition:19 dij:13 hamiltonian:9 zeit:1 turns:2 tre:1 solution:1 vector:4 vuz:1 gabriel:1 indices:3 div:5 dip:1 der:1 says:1 sign:3 groupes:3 second:13 masson:1 zu:1 odd:1 canonical:1 spectral:1 index:20 what:1 sub:1 contemp:1 abh:1 d2:9 section:15 coimbra:1 analogously:1 xτ:51 en:1 above:14 sup:1 ˆi:1 bn:2 coefficient:3 degree:16 respectively:3 even:1 french:1 modular:10 les:1 free:1 groups:13 address:1 quite:1 morphisms:1 obtained:3 remark:1 uspehi:1 drs:26 contradiction:10 rudakov:1 proof:8 makes:1 quotient:1 via:3 divide:1 classification:14 extra:1 namely:1 farnsteiner:2 texts:1 michiel:1 summation:1 univ:1 linearly:1 seligman:1 feb:1 would:1 prove:14 positive:2 contains:1 negative:6 next:3 linear:4 going:3 call:1 therefore:21 characteristics:1 type:14 diagrams:1 more:2 ǫs:2 ecole:1 becomes:2 operators:1 envelope:1 occurred:1 berlin:4 rigid:2 particular:8 known:3 cases:1 iv:2 iii:7 must:6 springer:2 commutatifs:1 frobenius:2 recall:8 equation:1 infinitesimal:27 values:1 determining:1 following:10 trans:1 root:1 example:2 cartan:10 f1:4 f2:4 abelian:2 organized:1 contradicts:2 hilton:1 performed:1 verlag:2 e2p:1 dh:28 ij:2 verify:1 s1:1 s0:3 write:4 very:1 criterion:3 pure:3 es:1 simplifies:2 ordinary:15 divides:1 map:9 npn:1 mat:10 algebra:54 replacing:1 derived:5 par:1 produce:1 coming:1 fi:2 types:2 natural:2 computations:1 sq:30 correspond:3 element:12 si:2 cannot:7 so:1 sn:3 definitions:1 divided:1 bull:2 holds:1 numbers:1 indeed:2 over:15 satisfied:10 interpreted:1 course:1 paper:2 satisfies:5 still:2 its:2 hazewinkel:1 before:3 group:20 maps:1 interesting:1 fix:5 solving:1 squaring:6 choose:2 mail:1 deformation:2 correspondence:1 non:4 dynkin:1 combination:4 factorial:1 introduce:2 sssr:5 vyssh:1 they:2 serre:1 now:4 nor:1 structural:1 kirillov:1 easily:1 term:6 finite:7 2p:1 dhs:2 classified:2 universita:2 ussr:2 each:1 2m:17 monomials:1 characterized:1 homogeneous:1 schemes:4 tuples:1 ergebnisse:1 functor:6 used:3 impossible:1 quantum:2 our:6 operation:4 ring:1 special:6 out:2 category:4 shown:1 unital:2 restricted:83 fu:1 since:17 denotes:1 looking:2 ra:3 izv:8 formula:4 get:6 induction:2 ri:1 math:24 representations:2 theory:2 divergence:2 differ:2 possibility:1 standard:1 small:6 base:8 york:3 put:1 monographs:1 largo:1 definition:14 derivation:21 phrases:1 gerstenhaber:1 βy:1 gruyter:2 appearing:2 place:1 derivations:3 avec:1 hence:1 aca:1 dipartimento:1 first:15 xj:7 xk:7 xh:41 there:13 xn:8 humboldt:1 xb:9 omitted:1 variables:1 xa:104 primary:1 rank:2 will:1 hochschild:11 xr:14 xs:14 xp:27 xq:1 degm:3 xt:1 ser:4 given:18 indicate:2 introduction:1 xik:1 adjoint:8 πi:5 system:1 their:5 assumption:3 daev:1 dik:1 scheme:1 final:1 italy:1 tuple:1 2an:2 akad:5 because:2 x2:6 x0:3 x1:9 than:1 coefficients:2 holland:1 iteration:1 zero:3 classes:3 were:1 sb:4 generality:1 boston:1 ann:6 argument:2 say:1 conjugate:3 any:17 elsewhere:2 lie:87 wilson:6 homological:1 appendice:1 pseudogroups:2 jacobson:6 note:4 ideal:2 without:1 generalized:3 finding:1 kac:3 formulas:2 roma:2 satisfy:1 centro:1 extending:1 germany:1 automorphism:2 preliminary:1 dekker:1 hu:1 class:1 enveloping:3 appear:3 give:1 ebrique:1 exa:2 considered:2 soviet:1 calculated:1 order:2 proceedings:1 bracket:3 usual:4 review:2 fact:3 saying:3 show:1 notations:5 spaces:1 substituting:1 analogue:1 trivial:1 translation:6 d1:17 completion:1 copy:1 representation:9 outside:1 internacional:1 lemma:20 only:5 bases:1 generators:3 local:1 preliminaries:1 dn:5 do:2 dj:27 dk:13 notation:2 exceptional:4 df:1 dg:1 de:7 ones:3 words:3 new:3 during:1 dr:4 ds:5 secondary:1 prime:4 textbooks:1 e1p:1 differential:2 sandwich:1 nauk:7 fixed:2 kernel:3 hθ:2 set:4 modulo:1 computed:1 exists:3 module:5 edition:1 see:23 result:8 terms:1 sem:1 subject:1 αp:1 infinis:1 ways:1 αx:1 away:1 rings:1 2sq:1 symmetric:1 state:1 roots:2 closed:3 between:2 conditions:9 available:4 basis:2 recently:1 extend:1 ju:1 however:4 vanishing:4 hypothesis:7 key:1 distinguish:1 amer:5 ug:6 xˆi:1 both:1 x2i:4 x2h:10 many:1 taking:1 equal:9 hψ:2 und:1 comm:1 expression:4 otherwise:5 co:1 fields:3 point:2 simple:51 cohomology:31 height:1 dimensional:5 simply:1 sequences:1 moreover:3 considering:1 described:1 transformations:1 shafarevich:3 three:4 been:2 quickly:1 ai:17 arxiv:2 basic:1 algebras:78 pn:3 abstract:1 define:4 filippo:8 families:3 finishes:1 sufficient:3 matematika:1 observe:5 determination:1 chevalley:1 hamburg:1 assigning:1 those:2 case:11 explicitly:1 exception:1 unify:1 ǫk:2 ǫj:10 ǫi:41 ǫh:5 harder:1 ǫn:7 aim:1 ǫr:4 suppose:8 freely:1 di:44 maximal:1 iz:1 n2m:1 vol:1 endowed:2 according:3 ii:10 cocycle:5 ebriques:1 vanish:2 ig:8 whitehead:1 different:2 verified:3 belong:3 admit:2 same:2 clearly:3 complex:7 filtered:1 constructed:1 subalgebra:4 independent:1 extended:1 dimf:1 cocycles:3 hand:3 parametrized:1 πii:1 πij:6 infinite:2 uˇ:1 center:1 band:1 hφ:8 well:1 academic:1 contact:6 english:6 model:1 ihrer:1 g1:2 dimension:3 subgroup:1 λq:1 graded:6 monomial:2 toral:2 underlying:2 integer:3 facts:1 λn:1 contradicting:1 preprint:1 family:1 characterization:1 seems:1 reasons:2 interested:1 theorem:16 mod:2 solvable:1 remaining:2 gd1:1 gd2:1 rules:1 showing:3 possible:1 five:2 press:1 using:13 demazure:1 apart:1 loss:1 necessary:3 continus:1 follows:10 interestingly:2 δj:2 either:1 cochains:3 page:1 right:2 classical:15 sequence:14 sends:1 some:7 algebraically:3 deduce:10 examples:1 uspekhi:1 respect:2 proper:1 homf:7 grading:4 ak:1 providence:1 does:3 expressing:1 proc:1 minimal:2 conference:1 power:3 dropped:2 equivalent:1 bi:1 hsq:21 relating:3 repeating:1 simples:1 publishing:1 integers:1 about:1 central:1 usa:1 algebraic:2 dˇ:1 theorems:1 viviani:15 reduced:1 associative:3 introduced:1 slightly:2 tome:1 block:2 vi:2 soc:4 kuznetsov:2 into:3 kostrikin:3 references:1 operator:7 amsterdam:1 reducing:1 institut:1 xpn:2 xpa:7 initial:1 pa:5 inner:16 way:1 jantzen:1 sections:3 grenzgebiete:1 witt:6 north:1 complete:1 hs:2 but:1 nn:2 leonardo:1 matematica:2 russian:12 uniroma3:1 true:1 etrie:1 again:1 xi:50 compute:10 cie:1 whether:1 characteristic:30 inside:1 us:5 assume:1 below:2 un:1 xp2:1 xp1:3 walter:1 called:5 b1:1 ab:1 associated:3 ad:34 ag:1 defined:19 certain:1 universal:1 aj:3 denote:7 chap:1 eom:1 relates:1 corresponding:2 deed:1 exi:2 check:2 defines:1 ni:2 xki:2 integrability:1 no:11 mathematik:2 when:4 vanishes:2 graduate:1 field:10 other:6 details:1 nat:1 mathematics:5 picture:1 expositions:1 elements:20 nonclassical:1 polynomials:1 a1:1 generated:2 important:1 augmentation:2 structure:3 eralit:1 implies:1 dφ:1 space:3 modules:2 together:2 equivalently:2 deg:25 simplicity:1 augmented:1 having:1 semilinear:1
0705.0822.txt |@word represent:1 partial:2 consider:1 remarkable:1 similarity:1 vilk:1 roc:1 unique:1 results:6 leads:1 rapid:2 generalize:1 expressions:1 adjustment:1 displaying:1 gi:1 depend:2 zone:2 description:3 shanghai:2 shall:2 finally:2 present:2 under:1 include:1 tc:14 indicating:1 global:2 antiferromagnetism:2 very:1 differently:1 wave:9 electron:1 figs:1 exact:1 partitions:1 illustrated:1 level:1 issue:1 anisotropy:1 applicable:1 correct:1 labels:1 vector:1 indices:1 upper:1 averaged:1 antinodes:1 consistent:5 direct:2 sign:1 zero:5 evaluated:1 qualitatively:1 linear:2 spectral:1 bruynseraede:1 nazarenko:1 overdoped:1 completely:1 sun:7 near:6 expressed:1 consistently:2 above:4 fractional:2 new:1 occupation:1 filled:1 dagotto:4 full:7 christian:1 lee:1 respectively:2 here:1 understanding:4 china:1 groups:1 address:1 directions:2 along:3 strong:8 equations:4 implicit:1 superconductor:3 obtained:1 generalizing:1 exemplified:1 precursor:1 larger:2 reason:1 leaving:1 suggests:4 narrow:1 segments:1 uniquely:1 adjustable:1 followed:1 projection:1 scales:1 forbid:1 explained:1 gk:3 highly:1 scaled:4 sgk:3 decrease:3 removal:3 unit:1 plot:1 usa:1 furukawa:1 charge:2 calculation:1 ungapped:1 therefore:1 taken:1 survive:2 theoretical:3 more:5 flat:2 becomes:1 operators:2 curvature:1 virtue:1 varying:1 hole:9 graphical:2 fermionic:1 schrieffer:2 account:1 wuyts:1 kanigel:3 indicates:1 science:1 equation:1 work:2 theories:3 reproduce:1 fock:1 temperatures:3 believed:1 cond:2 drops:1 example:3 heart:1 renormalization:1 figure:1 give:2 predict:1 introduces:1 states:9 pushed:1 numbers:1 absolute:1 influenced:1 destroying:1 s2:1 discussion:2 g0:4 regions:5 pair:4 pure:1 instead:2 mysteries:1 parameter:1 product:1 mat:2 arcs:17 may:7 max:1 earlier:2 diagram:1 takenaka:1 hussain:1 fits:1 horizontal:2 data:19 drop:2 physical:1 effective:1 lines:7 correspond:1 su:25 hypotheses:1 si:2 ultimate:1 correlation:10 sc:5 order:1 ito:1 produces:1 over:3 top:1 displayed:1 years:1 thermal:9 staggered:1 including:2 argued:1 its:3 kbt:2 derive:1 group:1 symmetry:4 termed:1 energies:1 solving:2 decreases:1 li:2 mcelroy:1 systems:1 insulator:2 decreased:2 maximal:1 closure:2 violating:1 fourth:1 moshchalkov:1 dai:2 discriminating:1 scaling:3 they:3 half:2 bogoliubov:1 now:2 outlines:1 nor:1 mystery:1 february:1 university:3 hamiltonian:1 loosely:1 appropriate:1 realistic:2 guidry:8 magnitude:1 bonn:1 each:3 identifies:1 constraints:3 tensor:1 significantly:1 chung:2 energy:21 reduce:1 related:1 solution:6 gaps:3 interplay:1 quantum:2 our:12 beyond:1 eq:8 special:1 out:1 shown:2 opened:1 space:4 restricted:1 rep:2 since:1 rev:20 cuprate:6 particles:1 müller:1 dominated:1 ref:7 viable:2 red:1 theory:9 interactions:1 mechanisms:1 weakly:1 approaches:1 pairs:9 interaction:1 geometry:1 damascelli:1 transition:4 length:12 place:2 isotropic:2 hence:1 liquids:2 ture:1 condensate:1 first:2 origin:3 there:5 surviving:3 pines:1 number:2 contributions:1 smaller:1 approximately:1 carry:1 luchini:1 electronic:1 given:4 bracket:1 temperature:29 indicate:3 ordering:1 interact:1 πi:2 system:1 occupancy:2 their:3 underdoped:6 salmhofer:1 percentage:1 variational:1 recovered:1 kf2:2 fraction:1 centered:1 explanation:3 prediction:1 part:1 somewhat:1 tempera:2 representing:1 than:3 third:1 double:2 imply:2 preformed:1 determined:2 assumes:1 takeshi:1 were:3 toward:1 engelbrecht:1 perturbative:1 exhibit:2 explicit:1 curves:4 neel:1 takigawa:1 oda:1 constrained:2 occupied:1 dition:1 viewed:1 invite:1 lie:1 strength:1 angle:5 self:2 mechanism:2 note:1 high:10 generalized:1 εk:2 online:3 finding:4 extrapolating:2 singh:1 strengths:2 hightemperature:1 blue:2 norman:4 opposite:1 decreasing:3 phases:1 singlet:8 algebraic:1 boltzmann:1 statt:1 importantly:1 significant:4 phase:1 measured:2 probes:1 kb:7 cosky:1 kf:14 kk:32 average:1 implications:1 inferred:1 physica:1 yang:1 diagonals:1 kt:1 ky:8 kx:9 χk:2 lying:1 incorporate:2 show:3 agreed:1 doped:2 tures:1 discovered:1 gauge:1 solutions:4 ground:2 removed:1 ratio:1 just:1 parameters:3 outside:1 should:1 only:8 generators:4 factor:2 employed:1 constant:4 rice:1 oct:1 do:2 dominant:1 cheng:1 means:1 dependent:4 liquid:1 between:5 pengcheng:1 enters:2 brillouin:1 reversal:1 competing:1 report:2 interpreted:2 bardeen:2 qq:2 gray:3 evolution:1 exhibiting:1 arxiv:3 expansions:1 calling:1 optimally:1 experiments:1 nayak:1 qi:2 through:3 fixed:4 inside:1 black:2 set:2 exists:3 correlations:10 observed:1 see:4 arc:26 descriptions:1 forthcoming:1 points:6 surfaces:6 closes:3 fails:1 timusk:1 interacting:2 compounds:1 away:1 knoxville:1 boundaries:1 state:7 inset:5 closed:2 simplest:1 comparable:1 triplet:3 terms:1 reproduced:1 nature:5 weak:1 attention:1 focus:1 however:4 wu:9 conjugates:1 key:1 rapidly:2 thank:1 received:1 cos:1 limits:1 region:6 equal:1 dated:1 exceeds:1 attributes:1 argue:1 experimental:1 con:2 ck:2 detailed:1 adjusted:1 tong:1 point:2 color:3 wen:1 tennessee:2 doping:27 uchida:1 ensures:1 pq:5 described:1 second:1 addition:1 pseudogap:12 been:2 mex:1 varma:1 int:1 pg:18 expected:2 utilizing:1 meeting:1 fig:29 dots:3 mike:1 corresponding:2 both:2 sufficient:1 essentially:1 gap:8 coherent:3 angles:1 spin:3 those:3 case:2 solid:4 value:1 invoking:1 while:2 abrupt:1 behavior:5 error:1 versus:4 almost:4 refs:2 thus:6 surface:35 superconducting:2 vs:1 mott:2 illustrates:1 vanish:2 fermion:2 result:2 different:5 az:1 campuzano:1 lengths:5 suggest:2 make:1 same:2 any:1 widely:1 finite:3 putikka:1 independent:5 extended:1 comprehensive:1 upon:1 differing:1 randeria:1 possible:1 viewing:1 compared:1 uses:1 aggregate:1 hartree:1 yuan:1 lower:4 shaded:1 largely:2 no:9 well:2 analysis:1 evolves:1 without:1 components:3 quantitative:4 model:10 photoemission:1 left:1 unified:1 magnetization:1 cuprates:2 proposed:1 among:1 compound:2 superconductors:4 obtain:1 predicts:1 summed:1 taiwan:1 yet:1 adv:1 renewed:1 generator:1 density:1 conclude:1 seems:1 except:1 lattice:2 lett:7 relevance:1 extensive:1 mod:3 momentum:7 resolved:1 insensitive:1 depends:1 term:1 test:1 increases:1 pseudogaps:2 vacuum:1 accepted:2 occurring:1 loss:3 particle:1 either:2 bi2212:2 reduced:1 therein:1 because:2 deal:1 people:1 shen:1 arrows:1 some:1 algebraically:1 strongest:1 bednorz:1 balents:1 scale:6 cooper:3 zhou:1 gapped:1 normal:4 filling:1 critical:3 connecting:1 linearly:1 assuming:2 prog:2 intersections:2 demonstrated:1 δk:3 formfactor:3 equivalent:1 egami:1 agreement:4 shifting:1 although:1 properties:7 simpler:1 central:1 constraint:2 anomalous:1 dependence:13 o:1 must:1 important:1 mean:1 contours:1 jiao:1 previously:1 into:3 predictions:1 speculates:1 lies:1 hermitian:1 right:2 accounts:1 primarily:1 fisher:1 operator:1 nodal:16 support:2 pairing:7 specifically:2 low:2 italic:1 flatter:1 biggest:1 opens:1 function:2 complete:1 form:2 offer:1 but:5 anisotropic:6 lowered:1 line:1 highest:1 zhu:1 whether:1 supr:1 maximum:4 quantitatively:2 below:4 fermi:64 spectroscopy:1 fluctuations:7 problem:1 define:1 similar:1 strongly:1 rvb:1 associated:4 af:18 defined:3 curve:8 universal:1 describe:3 néel:1 direction:2 general:1 single:1 antinodal:10 formulation:1 formalism:3 proceeds:1 defines:2 functions:1 nk:4 entirely:1 dotted:1 variety:1 dashed:6 when:2 vanishes:2 field:1 other:1 republic:1 details:2 papers:1 department:3 shrink:1 node:1 picture:2 excitation:1 superconductivity:6 models:3 uniformly:1 variation:1 generated:1 gapping:3 graphically:2 describing:1 astronomy:1 structure:1 watanabe:1 ago:1 individual:1 coupling:2 physics:3 holes:1 having:2 arpes:5 time:1 observables:1 requires:1 original:2 bcs:5
0705.0823.txt |@word proposition:1 externally:1 concept:1 transitions:1 consider:2 maximum:1 global:2 desirable:1 results:9 soften:5 leads:3 roy:1 avalanche:4 softer:2 consists:2 sci:2 phonons:1 contributions:7 issues:1 content:1 aligned:3 zone:24 transferred:1 paris:2 subjected:1 vs:1 containing:1 granular:1 quasi:10 those:2 under:2 γc:4 tg:1 γa:1 heterogeneity:1 incompressible:1 random:1 deforming:1 straightforward:1 sitting:1 very:4 dynamic:3 implicitly:1 rise:3 amorphous:7 focus:1 falk:4 softened:1 summarized:1 ui:11 difference:1 illustrated:1 dominate:1 immediately:1 presented:1 diverging:1 supports:1 eigenmodes:1 criterion:1 lequeux:3 decreasing:1 t1:1 large:10 avalanches:7 vector:1 form:1 math:1 succession:2 small:19 eigenvalues:1 drop:1 inspection:5 configurations:4 upper:1 abbreviated:1 smaller:3 force:1 disordered:5 consistent:4 prediction:1 sign:2 past:1 surrounding:1 rate:3 directionality:1 further:1 dynamics:3 correspond:2 maloney:4 quite:1 theory:2 reproduce:1 sub:1 trivial:1 section:5 near:8 ajdari:2 quadrupole:2 localized:4 above:7 blur:1 increasing:7 journal:1 advected:1 coefficient:2 quenched:2 evolving:1 full:1 simultaneously:2 whose:1 respectively:2 gathered:1 negative:1 component:2 here:4 atoms:1 ranges:2 growing:2 explore:1 tangent:6 address:1 active:6 schrøder:1 along:2 strong:3 respect:2 appears:6 interpret:4 suggest:1 dry:1 remark:2 trans:1 increments:1 exemplified:1 noticeable:1 shift:4 study:4 studied:1 step:2 commonly:1 leaving:1 suggests:3 recently:2 simultaneous:1 resulting:5 constitutive:1 stressed:1 barely:1 noticeably:2 studies:2 hump:4 involves:1 plotted:1 emerge:1 via:3 spatially:2 projection:3 scales:1 discontinuous:2 quadrupoles:1 sgr:3 highly:1 logarithmic:1 visible:5 sizeable:1 decrease:1 quenching:1 circumvent:1 landscape:1 qs:1 plot:3 use:3 figure:25 would:2 intensively:1 remains:6 termed:1 tail:10 france:2 few:5 cascade:1 approach:3 ψn:1 lennard:1 survive:1 themselves:1 rearranging:1 type:1 until:1 corners:1 more:11 becomes:1 limitation:1 visibility:1 mixes:1 instrumental:1 glass:6 spinodal:6 reversible:1 everywhere:1 normalized:2 excellent:1 cases:3 given:2 iii:2 analogous:1 dyi:1 must:2 md:1 account:1 ser:1 cluster:1 dep:8 recall:1 equation:2 work:1 fast:1 strain:20 suter:1 debated:1 infinitesimal:2 values:7 thin:3 following:3 making:2 drops:3 root:3 dee:5 numbers:1 claim:1 eshelby:5 indicated:2 give:3 process:1 attribute:1 organized:1 pieces:1 sample:1 indicates:2 assumptions:1 performed:1 particles:3 constituting:2 occur:1 information:6 respective:1 lacks:1 eng:2 dγ:3 write:1 get:1 xˆ:1 renew:1 revisit:1 regions:5 located:1 models:5 softens:2 significance:1 answer:1 acta:1 explains:2 displacements:14 sequentially:1 blocks:1 mat:2 undergoing:1 may:2 signature:3 minimum:3 minimized:1 reflect:1 consequence:1 γee:3 share:1 horizontal:1 data:7 response:7 types:2 gaussian:4 stress:11 short:3 branches:3 dynamical:3 effective:3 light:3 approximation:1 lines:7 interrupted:2 rather:2 ones:5 so:10 demkowicz:1 correlation:3 representation:4 opinion:1 order:8 triggering:2 typical:3 feed:1 interpretation:2 indeed:8 over:8 toward:2 displayed:2 flips:12 interpreted:1 course:1 thermal:2 saturates:3 london:1 jakobsen:1 motions:1 mentioned:1 existence:3 still:1 its:15 before:5 strikingly:1 supplemented:1 longitudinal:1 decompose:2 la:1 picard:4 lateral:1 affine:28 lj:8 exhibits:5 doliwa:3 caroli:1 permanent:2 microscopic:1 systems:7 convective:1 total:4 clusters:2 main:1 decades:1 deformation:3 shear:28 yip:1 focussed:1 non:33 good:1 schematic:2 dyre:1 reveal:1 propose:2 evolution:9 number:1 scaling:1 walls:1 tails:2 effects:1 they:16 grows:2 now:9 developments:1 structural:4 develops:1 easily:1 february:1 several:1 hereafter:1 intuitively:1 goldstein:2 parameter:1 traced:2 identified:3 alter:1 ensemble:4 2d:7 into:7 fig:11 mode:6 arrow:1 each:7 crossing:1 instability:3 universit:1 out:2 soft:8 characterized:1 glasses:3 homogeneous:7 el:11 sawtooth:1 square:3 directly:2 weight:3 ee:1 series:1 energy:5 displacement:4 related:1 constitute:1 harrowell:3 frequency:3 static:3 expect:3 accumulated:1 jagged:1 our:18 beyond:3 extract:2 event:5 description:2 try:1 shown:6 dominates:1 matrix:1 rs:1 gradient:1 since:3 rev:10 interspersed:1 diffusive:2 transforming:2 acting:1 investigation:1 dominated:1 rl:1 induced:6 ref:4 occurs:1 independence:1 shows:5 trajectories:2 linear:1 fluctuates:1 localization:1 simulation:2 divergence:3 little:1 free:1 like:6 qualify:1 put:1 region:2 rises:1 speculation:1 temperature:2 inhomogeneities:1 rearrangements:3 overtake:1 r2:1 geometry:1 rule:1 just:1 phy:1 times:2 motion:9 appearing:1 length:4 segments:1 due:2 navier:1 hence:4 retain:3 neglected:1 rheol:1 think:2 first:3 origin:1 already:2 features:4 champs:1 u1:11 flipping:3 raise:1 clear:4 glassy:2 simplified:1 approximately:1 another:3 carry:1 illustrating:1 thick:2 precisely:2 loaded:2 biasing:1 size:20 lemaˆıtre:5 cartesian:1 yia:5 asymptotic:3 likely:1 occupy:2 introduction:1 leading:1 top:1 system:29 least:2 plastic:54 their:25 modes:2 advection:3 observations:3 rates:1 structures:11 speaking:1 gives:1 back:4 collapse:2 centered:1 reversed:1 continuous:1 transverse:13 argon:7 weakly:1 surviving:1 somewhat:1 authors:1 wittmer:1 foams:2 than:6 positively:1 center:2 diffusion:8 relative:2 kind:1 critically:1 sectors:1 second:2 grained:1 matter:1 quasistatic:1 absence:1 heuer:3 amplitude:9 were:2 negatively:1 enables:1 stz:6 projections:1 exhibit:2 function:1 formulated:1 consistence:1 ana:1 transformable:1 quench:1 unchanged:2 mind:1 measure:1 curves:1 rai:1 randomly:1 substantiates:1 mater:1 width:1 compression:2 increment:3 conjugate:1 need:1 seen:2 confirms:1 clearly:9 viewed:2 relatively:1 chem:2 built:1 roux:1 depending:1 lim:4 lin:1 responsible:1 able:5 simul:1 mechanism:1 onset:1 mix:1 high:3 internal:1 take:1 bailey:1 essential:1 accuracy:1 circles:1 cnrs:1 towards:1 elastically:4 bands:3 though:2 parallel:1 reach:1 z2:1 most:4 involving:2 connected:1 phase:1 bocquet:2 marie:1 measured:1 class:1 conspicuous:1 appear:5 demand:1 episode:1 observation:1 average:9 later:2 flow:7 drive:1 takeuchi:1 curie:1 elucidating:1 part:3 error:1 pattern:2 sequence:2 notion:1 fact:3 laws:1 slope:1 emerging:1 particularly:1 show:4 text:1 mott:1 labels:1 foregoing:1 purely:7 radii:1 threshold:7 corner:1 present:1 fine:1 find:4 d0:5 principal:1 believe:1 based:2 proposed:2 irreversible:4 delays:1 distributed:1 state:2 topological:1 should:5 only:7 explicitly:3 candidates:1 bottom:1 pursuing:1 various:1 constant:7 population:2 local:5 thresholds:1 checked:1 sur:1 characterization:1 do:1 mixture:1 dominant:2 means:2 dependent:5 de:1 uiα:1 next:1 widmer:3 cannot:2 nearly:3 during:5 speculative:1 target:1 adiabatically:1 processes:2 continuum:2 invaded:1 dpp:8 nicely:1 fields:7 arxiv:1 comprising:1 yield:1 investigate:1 underlying:1 contain:2 distant:2 fixed:1 approaching:2 reveals:2 moduli:2 computed:2 supporting:1 generally:1 frame:1 correlations:3 condensed:1 up:2 observed:2 namely:7 individual:1 result:4 versus:2 close:4 forthcoming:1 uncorrelated:1 clarifies:1 closer:1 fails:1 invoked:3 αpl:9 plasticity:5 inappropriate:1 particule:1 subsequent:1 review:5 finally:2 label:1 γpp:6 enough:3 future:1 identification:1 between:7 progress:1 boundary:1 conditions:2 across:1 blow:1 notice:1 pushing:1 terms:6 extend:2 nature:5 importance:1 however:5 concentrate:1 distinguish:1 article:2 understanding:1 come:2 alters:1 bulatov:3 improve:1 both:8 collaborators:1 discernible:1 last:1 rightward:1 coarse:1 many:1 taking:1 hint:1 equal:1 barrat:2 agree:1 sensitive:2 σy:2 inclusions:1 figures:3 dated:1 concentrates:1 variance:2 contribution:8 mean:1 whole:1 comes:1 ago:1 strongly:3 necessary:1 space:1 conclude:2 simple:2 relaxation:1 way:1 corresponds:4 sampling:1 directions:1 written:1 jammed:4 decreases:2 multistable:1 prominent:2 factors:1 deng:1 ensures:1 described:2 transformations:3 basis:3 addition:1 glotzer:1 markedly:1 been:4 z1:1 much:3 slowly:2 change:1 interest:2 basic:3 expected:1 combine:2 originates:1 pl:2 choose:1 slips:1 direction:2 arises:2 corresponding:7 observable:1 concerning:2 essentially:4 proportional:1 observe:3 understand:4 external:5 derivative:1 careful:1 standard:2 case:2 multi:2 exponential:5 frames:1 solid:6 defining:1 appearance:1 empirical:1 value:9 remaining:1 will:4 while:8 behavior:12 involved:2 property:1 couplings:10 unlikely:1 yi:6 larger:4 orientation:1 coupled:4 phenomenological:2 characteristics:1 thus:10 them:6 iv:2 ii:8 characterize:3 sudden:4 cond:2 flipped:1 disappear:1 grown:1 binary:1 different:2 verified:1 perform:1 media:6 make:1 disappearance:2 cross:2 same:2 any:2 sastry:1 shifts:3 hessian:1 coworkers:1 phenomenology:6 units:2 proved:1 finite:9 events:40 difficult:1 independent:1 instances:1 see:13 maeda:1 numerical:4 upon:4 effect:4 flows:1 driven:1 nonaffine:1 moment:1 levels:1 purpose:1 student:1 heterogeneities:1 frequently:1 discernable:1 identity:2 recent:3 lower:1 mech:1 traps:2 immaterial:1 disappears:3 substantially:1 ingredients:1 well:5 roughly:5 analysis:6 patterns:3 solids:3 without:1 components:3 dashed:2 position:2 model:4 equilibrium:1 stating:1 left:1 confirm:1 pairs:1 stringent:1 protocol:1 softening:2 less:1 true:1 when:3 resp:2 vanishes:2 amount:1 shape:4 intervals:8 identify:1 atomic:2 questions:1 merge:2 previous:1 site:1 note:3 loading:4 signal:1 density:1 rigid:1 point:4 signals:5 source:1 other:3 extends:2 lett:5 samples:2 inducing:1 relevance:2 eur:1 extensive:5 occurring:2 convected:1 transformation:4 varying:1 resolved:1 evaluation:1 2u:1 evaluate:3 decomposed:1 term:2 decorrelate:2 possibly:1 increases:8 philos:1 know:1 background:4 insert:1 confined:1 using:3 emergence:2 unique:1 sheared:1 vertically:2 imposed:3 helpful:1 particle:16 sizes:8 follows:3 schematized:2 identifying:2 loses:1 discarded:1 collect:1 episodes:5 unstable:1 either:2 fully:3 rearrangement:1 works:1 disorder:6 qualitative:1 shed:2 right:4 smoothly:1 affects:1 some:3 pierre:1 self:2 deduce:1 growth:1 approximant:1 autocatalytic:1 moreover:5 gradually:5 scale:6 colloidal:1 trace:1 lead:1 umr:1 broad:2 opposite:1 vortex:3 instantaneous:3 pioneer:1 critical:5 decomposition:5 kobayashi:1 provides:1 moderate:2 proc:1 measuring:1 core:1 particular:2 noise:9 deflation:1 elucidate:1 jumps:5 agreement:3 rue:1 likewise:1 athermal:1 departures:1 although:1 acoustic:1 propensity:2 entirely:1 after:3 noisy:1 explicited:1 about:10 inter:3 bars:1 stationary:1 dependence:2 o:2 langer:4 emerges:1 range:13 ensure:2 transients:2 cos:1 upward:1 slightly:1 cates:1 soc:2 letters:2 decreased:1 inclusion:1 previously:1 zones:35 within:4 jβ:1 three:6 remarks:1 because:1 accounts:1 primarily:3 elementary:7 cascades:4 precritical:1 physical:7 significantly:1 remain:2 statistics:1 institut:1 log:6 elastic:54 renewal:2 crystallization:1 support:1 initial:7 question:2 lond:1 long:3 u2:4 quadrupolar:10 compliant:1 jcp:1 low:3 fraction:8 analyze:3 was:2 combined:1 lowest:5 jones:1 medium:2 aqs:4 but:3 lemaitre:1 volume:4 strictly:1 connecting:1 convergence:1 sollich:3 line:7 level:4 dissipative:4 exhaustive:1 middle:1 consist:2 characteristic:4 marne:1 variations:1 flip:10 us:7 entails:2 below:2 limit:4 embedded:1 phenomenologies:1 heterogeneous:1 fluctuations:2 distribution:9 similar:2 called:1 disappeared:1 detailed:2 hiα:1 changes:1 diverges:1 associated:13 play:1 defined:4 stronger:1 abstract:1 describe:1 akin:1 generating:1 rightwards:1 general:2 separating:2 single:5 governed:1 simulations:6 diversity:1 reflecting:1 distributions:3 proceeds:1 four:1 regime:8 physics:1 again:1 functions:1 compared:3 nl:1 lees:1 dotted:1 no:3 amounts:2 eq:1 edwards:1 tanguy:6 detail:1 rheology:1 field:20 points:1 role:1 details:2 branch:2 spatial:2 ns:1 sufficient:2 life:1 picture:3 stat:1 met:1 separate:1 christiane:1 αel:3 modelization:1 generated:4 important:1 peak:3 cores:1 variable:2 cooper:3 structure:6 building:1 correlated:4 coupling:2 algorithm:1 controlled:1 resolution:1 statistical:3 interval:7 curve:6 persistent:1 together:3 bulletin:1 equivalently:1 phonon:1 transient:2 lying:1 time:4 qualitatively:1 plastically:2 starting:2 initiating:1
0705.0824.txt |@word dωde:9 limited:1 positions:1 code:2 partial:2 systematic:1 represent:1 caused:2 magnetic:2 orientationally:5 dynamic:6 results:1 leads:4 gf:5 gd:1 thermalisation:1 overlap:1 broader:1 edu:2 consists:1 milo:1 friedrich:2 gi:8 phenomenon:1 whose:1 certainly:1 depend:1 system:7 aug:1 re:1 technique:1 environment:1 finally:2 behave:2 those:1 th:1 under:2 td:1 include:1 applied:1 keenan:3 images:1 translations:1 choice:1 orientations:2 experimentally:2 sublattices:1 difference:3 condition:1 tetrahedrons:1 timely:1 four:3 incoherent:11 vibrational:6 hamiltonian:4 irreducible:1 integrating:1 t2:6 solution:1 t1:7 large:6 solid:44 differential:1 small:2 eigenvalues:1 ups:1 methane:41 still:1 upper:1 population:1 5mev:1 disordered:3 periodicity:1 foundation:1 probabilities:2 hindered:21 consistent:1 direct:2 cosh:3 approximation:4 zero:2 evaluated:2 chen:1 further:3 dynamics:1 20mev:1 linear:3 even:6 ˆr:12 43m:1 stands:2 section:49 axes:1 while:1 cell:2 consistently:1 experiment:1 dominates:1 lovesey:1 ch4:13 occupation:1 method:1 3d:4 coefficient:1 dep:2 condensed:2 degree:4 vi:1 respectively:4 27k:1 component:2 vol:1 here:2 atoms:8 mev:25 possibility:2 separation:1 address:1 directions:1 consideration:1 strong:3 table:1 appears:2 change:2 calculate:3 obtained:1 search:1 tunneling:14 canadian:1 shift:1 larger:2 completely:1 commonly:1 approaches:1 heidemann:1 amount:2 resulting:1 within:1 permutation:2 usually:1 symmetrical:1 narrow:1 makes:2 reactors:1 foresee:1 convolution:2 explained:1 integrations:1 neutrons:15 vc:2 decrease:1 translational:6 apply:2 total:20 unit:4 plot:3 use:1 start:1 would:2 distinct:1 contains:3 mcnp:1 kataoka:3 few:2 explicitly:1 estimated:1 therefore:7 knoll:1 taken:4 indiana:4 associated:1 type:2 theoretical:7 more:8 tolerated:1 ambiguity:1 initiated:1 becomes:3 stable:1 emission:1 warm:2 rigid:1 surface:1 particular:2 ozaki:7 cases:2 iii:2 must:3 high:5 springer:2 rotational:49 defines:1 room:1 sphere:1 tunnel:1 nω0:1 work:5 protons:7 prager:2 fli:3 mw:1 minimum:1 obvious:4 temperatures:8 eigenstates:1 following:1 drops:1 example:1 decoupled:1 performed:2 calculation:9 thermally:1 suggestions:1 states:23 collision:3 way:2 thus:2 numbers:1 hydrogen:6 verlag:1 needs:1 gs:2 straightforward:1 fortunately:1 divided:1 six:1 sudden:1 ultracold:2 chemical:7 located:1 get:1 answer:1 optimal:1 off:2 parameter:2 sin:1 orientational:7 product:3 kroll:2 gammas:2 description:2 hydrogens:1 may:4 thermodynamic:1 after:3 confirmed:1 diagram:2 applications:1 ortho:1 fc:3 studies:2 improving:2 fi:9 wave:10 data:3 response:1 types:2 curve:1 pocket:3 diagonal:1 short:1 physical:5 effective:3 spectra:4 downscattering:1 summing:1 element:3 rather:1 cannot:2 so:5 expression:1 allow:1 suggest:1 dz:1 operate:1 order:3 pulsed:1 wigner:1 help:1 diagonalizes:1 developed:2 over:6 insight:1 mainly:3 flips:1 spallation:3 produced:1 course:1 thermal:4 paper:2 through:7 motions:5 mentioned:2 cold:10 1mev:1 excitations:1 its:8 superthermal:1 before:1 transitions:4 group:6 probability:1 general:1 energies:14 interesting:1 hq2:1 constant:1 complex:1 exhibits:1 forms:2 absence:1 production:1 degrees:3 fig:22 pergamon:1 decreased:1 setting:1 them:2 good:1 affected:1 thereby:1 infrequent:1 rotations:5 practice:2 operator:2 framework:1 effects:4 they:2 symposium:1 oxford:1 rotation:9 inelastic:12 yu:1 possess:5 easily:1 term:2 finite:1 brightness:2 james:3 university:3 classified:1 sufficiently:1 vibrations:3 mode:19 reasonable:1 each:15 notated:1 2m:10 organized:1 interpolation:1 side:1 2k:2 baxter:1 en:6 ei:10 primarily:2 accelerator:1 populated:1 ee:3 house:1 energy:54 ef:8 reduce:2 principles:2 related:3 speculated:1 frequency:27 expect:1 reached:1 quantum:1 our:7 approximated:3 harker:8 eq:11 special:1 out:1 ultimately:1 reducing:1 matrix:6 space:17 furthermore:1 since:3 interference:1 100b:1 denotes:8 increase:5 collisions:8 mediated:1 dominated:1 socalled:1 rn:5 induced:1 evaluation:1 occurs:1 red:2 shows:6 inevitably:1 8h:1 theory:8 written:3 turned:1 maintains:1 material:1 given:3 free:34 standard:1 release:1 reason:1 abnormally:1 brightest:1 van:1 monographs:2 iucf:3 definition:1 interaction:9 starts:1 could:3 transition:8 david:1 motion:7 ordering:2 conducted:1 isotropic:2 transfer:8 consequence:1 oscillator:2 neglected:1 undergo:2 first:7 there:8 features:1 symmetry:18 third:1 number:8 reaches:1 libration:1 employing:1 long:2 another:2 wasn:1 carry:1 pulsar:1 electronic:1 intermolecular:1 interchange:1 little:1 law:1 temperature:10 their:3 introduction:1 equilibria:1 vibrate:1 needed:2 cooling:7 assumption:1 chem:1 too:2 ordered:6 especially:1 final:6 listed:1 inefficient:1 para:1 using:9 centered:3 explanation:1 oscillates:1 part:4 1ev:2 attempt:1 than:6 center:3 begins:1 past:1 kind:1 molecular:12 target:2 was:18 rate:1 matter:2 compensation:1 electrostatic:1 reference:2 represents:4 providing:1 treated:1 iωt:1 behaviors:1 lowest:2 vector:1 ev:1 unchanged:1 modern:1 7k:1 spectrum:22 generalization:1 operated:1 qualitatively:1 need:2 rotors:6 20k:24 orders:1 rotor:9 strength:3 angle:1 depending:2 efficient:1 latter:1 responsible:2 snow:1 polarization:1 extracted:2 empirically:1 potential:5 take:1 converged:1 new:1 switching:1 accuracy:1 spectral:2 multiple:2 normal:3 collaboration:1 correlation:5 molecule:18 singlet:1 most:2 optimized:1 fcc:1 eight:2 overlapping:2 significant:1 representation:3 phase:49 measured:3 refrigerator:1 kb:5 vapor:1 kf:9 url:1 clear:4 later:1 physica:1 face:2 waller:2 kr:5 proceedings:1 lowered:2 principle:3 exp:22 velocity:6 treats:1 typically:3 sum:1 fact:1 q2:10 σinel:1 reactor:1 intensity:2 show:4 iqα:2 causes:1 supported:1 discussion:1 dipole:2 moderator:6 ki:14 bright:1 octopole:4 relation:2 label:1 d2:9 find:2 ground:7 iq:4 slow:2 based:3 ensembles:1 parameters:1 directly:1 edited:1 blue:2 state:20 alternative:1 should:1 values:2 liberation:1 only:11 indistinguishable:2 black:2 central:1 molecules:15 factor:5 σel:1 circle:1 partially:2 equilibrium:3 predict:1 dk:1 meanwhile:1 dependent:1 overall:3 cd4:3 feels:1 ones:1 christopher:1 librates:1 shared:1 report:2 dt:1 averaged:1 procedures:1 coth:1 liu:1 processes:1 bar:2 densities:1 fields:3 arxiv:2 acknowledgments:1 twice:1 okada:1 predicted:1 though:1 double:2 analytical:1 including:2 fixed:2 16th:1 doublet:1 atomic:2 set:3 exists:1 higher:8 10mev:3 catastrophic:1 frame:2 module:6 freeze:1 depends:4 individual:2 intramolecular:3 considered:2 multiplet:1 cyclotron:1 close:1 kinetic:5 barn:1 et2:1 phases:1 rotates:1 computer:1 interacting:1 phonons:2 nuclear:5 review:2 definite:1 sites:3 tend:1 symmetric:3 pressures:1 enough:1 determined:4 between:10 approach:3 across:1 available:1 comparable:1 terms:1 august:1 rotating:1 importance:1 modify:2 were:2 weak:5 however:6 jl:1 efficiency:1 incident:3 carbon:1 suppressed:1 problem:1 improve:1 librate:1 reaction:1 essentially:1 improved:1 discusses:2 many:3 region:3 vibration:5 agree:2 etc:1 hω:12 figures:1 dated:1 retarded:1 lavelle:1 coh:2 regimes:1 adapted:1 messiah:1 comes:1 load:1 minima:4 ch:6 sinh:3 conclude:1 reasons:1 relaxation:2 corresponds:1 dimensional:4 cz:1 remeasured:1 tracts:1 simply:1 decreases:3 anisotropically:1 ucn:1 crystalline:3 factors:2 hω0:1 destroyed:1 µev:1 second:2 source:5 addition:3 simplification:1 due:5 been:10 strategy:1 describes:2 tetrahedra:1 interest:1 microscopic:2 ph:1 pi:6 meeting:1 concentrated:1 mike:1 corresponding:4 going:1 concerning:2 6k:1 cos:1 defect:1 moderation:6 external:2 folklore:1 despite:1 denote:1 spin:14 dmr:1 present:3 case:7 multi:7 sampson:1 pacs:1 indefinitely:1 tetrahedron:3 engineering:1 value:1 excited:1 will:1 near:3 replaced:2 match:1 behavior:1 situation:1 property:1 guide:1 procedure:1 real:1 aa:1 losses:1 orientation:1 almost:2 characteristics:1 simulations:1 binding:2 site:2 additional:2 iv:2 ii:25 vq:6 itself:1 im:1 triple:1 seen:1 df:3 alone:1 increased:2 result:1 capture:1 different:15 decoupling:1 inc:4 combination:1 caprio:1 grant:1 perform:1 media:3 make:1 radiation:1 cross:51 same:2 any:1 parts:3 changed:1 pauli:2 several:1 events:1 neutron:78 planned:1 development:1 independent:2 used:5 http:1 peaks:1 cubic:3 numerical:1 upon:1 series:2 average:1 moment:1 levels:7 liquids:1 delicate:2 infinite:1 changing:1 validate:1 identity:2 amplitude:1 lower:4 integral:1 modes:16 whole:1 possessed:1 degeneracy:1 well:5 analysis:1 academic:1 solids:2 materials:1 experimental:2 components:1 speculations:1 model:26 chemistry:1 magnon:1 possesses:1 oscillation:1 subgroup:1 spherical:1 agency:1 just:1 among:4 obtain:2 rest:2 sources:5 stored:1 librations:2 integer:2 uller:4 momenta:1 yamamoto:6 scattering:71 yet:1 now:2 density:11 absorption:3 point:7 fitting:1 simple:4 other:8 treatment:1 5k:1 diagonalization:2 structural:2 transformation:1 momentum:5 gave:1 identical:1 around:7 loss:1 25mev:1 multiplets:2 possible:3 harmonic:2 hove:1 2w:6 press:8 damage:1 accepted:1 advanced:1 ga:1 melting:1 rotate:2 necessary:1 like:2 particle:2 follows:2 collective:1 performing:1 flux:2 yields:1 either:1 arbitrary:1 anti:1 conrad:2 disorder:3 essential:3 cooled:1 www:1 because:4 nm2:1 namely:1 sequence:3 creation:2 some:6 self:2 calculated:4 b2:1 respect:1 proper:1 extended:1 superposition:2 2l:4 communications:1 measurements:6 per:4 conservative:1 quickly:1 magnitude:2 lattice:6 conclusions:1 tends:1 particles:2 bessel:2 core:1 process:1 scientific:1 power:2 jl2:4 multiphonon:1 reach:1 journal:8 expansion:2 pressure:1 although:5 plots:3 imaginary:1 properties:4 chapter:1 a1:2 about:5 42m:1 usa:1 oh:6 column:3 freedom:7 basis:3 ejk:2 o:6 reduced:1 practical:1 remains:1 range:6 important:2 greatly:1 mixed:1 observation:1 slightly:2 peak:3 librational:7 considerations:1 rev:1 22k:8 200b:1 followed:1 facility:1 h2:2 h3:2 into:5 h1:2 splitting:2 bound:2 h4:4 three:9 bravais:1 right:1 moderating:8 determine:1 elementary:3 proportional:1 tetrahedral:6 ridge:1 compression:8 elastic:7 area:1 assumed:2 initial:6 approximate:2 fast:2 dispersion:1 width:2 conservation:2 low:9 fraction:2 triplets:1 bloomington:1 analyze:1 sections:6 treat:2 function:39 medium:18 complete:4 form:2 ea:1 removes:1 but:6 heat:1 hi:1 gain:1 atom:5 implies:1 line:6 level:3 active:2 he:1 made:3 applying:1 places:1 eiωτ:1 characteristic:1 gravitational:1 up:3 quantitatively:1 ωi:2 crystal:7 below:6 meta:1 limit:3 thermalization:1 σtot:2 distribution:5 called:6 obtains:1 detailed:1 shin:3 debye:4 defined:3 certain:3 abstract:1 measurement:1 dσ:1 oscillations:1 single:2 exist:1 wavelength:1 ind:2 crystals:1 moves:1 distributions:1 constructed:1 2kb:3 again:1 functions:6 compared:6 dotted:2 no:6 dashed:2 nc:1 when:3 vanishes:1 sublattice:2 nx:2 field:5 interested:2 role:1 details:1 better:1 department:1 correlates:1 d2d:5 4k:30 discrepancy:1 elements:2 3h:2 excitation:15 separate:1 time:2 distance:1 shown:5 lens:3 generated:7 a2:2 allowing:1 vectors:1 dissipation:1 generalized:2 structure:20 national:1 severe:1 lane:1 correlated:1 regime:2 coupling:1 uncoupled:1 dω:3 assume:1 physics:15 dτ:1 required:2 diffraction:1 coherent:4 dr:1 phonon:24 mass:4 presenting:1 4h:1 remarked:1 international:4 nuclei:3 once:1
0705.0825.txt |@word limited:1 leighton:1 gr:35 remarkable:3 represent:1 doubts:1 results:1 leads:3 scalar:5 microwave:1 controversial:1 follow:1 gm:2 contributions:2 reasoning:1 causes:1 consider:6 particles:10 certainly:1 calculate:2 producing:1 equivalence:1 quasi:1 rg:1 aut:1 th:2 under:1 gopal:1 include:1 worth:1 subtleties:5 case:7 confirmation:2 rαβ:1 mpc:1 far:5 than:2 rise:1 p1:1 interpreting:2 got:3 trouble:4 little:1 exact:1 galaxies:1 cmi:2 ρc2:13 issue:1 consequences:2 solution:1 correct:2 try:1 vector:5 excellence:1 recall:1 small:3 noted:8 attracting:1 still:2 unexpected:4 force:9 disordered:2 insignificant:1 protons:1 sin2:1 prediction:5 sign:1 approximation:1 surrounding:1 zero:3 cost:1 narlikar:3 enclosed:2 substitute:1 belief:2 even:4 what:3 adds:1 appear:2 giving:1 specification:1 celebrated:2 current:1 experiment:3 suspect:1 precisions:1 above:7 new:3 net:2 contributes:2 consisting:1 seeks:1 paradoxical:2 supporting:1 bazin:1 respectively:1 component:2 here:4 perpendicular:1 behaviour:2 objects:1 address:1 xβ:1 xα:3 equations:9 appears:5 interpret:1 ordinary:1 stresses:3 convert:1 balance:1 dividing:1 wesley:1 receive:1 leaves:1 quiescent:1 mx:1 p2:1 amount:2 resulting:4 action:3 symmetrical:1 suitable:1 spacetime:3 examining:1 extra:1 highly:1 brought:1 decrease:2 total:7 univ:1 crisis:2 unit:2 derivatives:3 use:5 takes:1 would:10 covariant:3 positive:6 contains:3 negative:3 next:1 process:1 circumstances:1 noting:1 examination:2 δgµν:1 those:2 vi:1 mysterious:2 type:1 theoretical:2 more:1 flat:1 successful:1 thus:1 dxµ:3 diagonal:2 keplerian:1 clue:1 eν:3 tested:3 carrying:1 everywhere:1 virtue:1 eλ:1 known:2 cases:2 iii:1 must:1 states:1 account:2 mc:1 indicates:1 science:2 equation:22 work:5 mi:4 theories:4 remain:1 mv:1 obvious:2 following:12 root:1 example:9 randomizing:1 cosmological:2 chosen:4 predict:1 relativistic:16 high:4 sphere:5 posing:1 magnitudes:2 honest:1 decipher:1 ones:1 vanish:4 validity:1 provide:3 holds:1 feature:4 write:2 how:2 correctness:1 thermodynamics:1 opposite:1 mysteries:2 alternative:1 cosmic:4 may:11 after:1 derived:3 collection:1 corrections:1 rays:2 g11:1 law:4 revealed:1 stress:14 purely:1 collision:4 light:1 lost:2 element:15 their:4 rather:1 accelerated:1 maintain:1 so:9 increasing:1 fundamental:3 increase:5 order:5 gµν:6 typical:1 interpretation:3 dx:4 developed:1 over:2 despite:1 soon:2 interpreted:1 presence:8 dv:2 including:1 daniel:1 motions:2 mentioned:7 converting:2 kinetic:9 suffer:2 its:16 earlier:1 perfect:7 derive:1 rapidly:1 ln:1 inward:1 temporal:1 relativity:6 hot:1 coordinates:5 actually:2 attraction:1 absence:4 permanent:1 choose:1 inconsistencies:4 clusters:1 hidden:1 shear:1 freeman:1 dxν:2 combination:1 bernoulli:1 dxβ:1 dxα:3 number:1 framework:2 walls:1 compelled:1 effects:1 they:1 half:1 front:1 rotation:1 now:5 realize:2 nor:1 mystery:1 term:18 profound:1 publication:1 always:3 university:1 realistic:3 magnitude:3 truth:1 each:1 crossing:1 side:1 mean:2 square:1 ei:2 another:1 energy:89 related:2 cmb:5 static:3 expect:2 measure:2 quantum:1 our:4 differ:1 shearing:2 neighbourhood:4 out:3 container:8 space:1 gradient:2 since:1 content:2 cobe:1 acting:1 mate:1 dominated:2 hill:1 produced:1 dsi:1 surprise:1 cause:3 originally:2 common:1 imported:2 theory:18 argument:1 divergence:2 attempt:1 possibility:1 standard:3 reason:1 york:1 imagine:1 put:1 onoma:1 estimate:1 hand:1 compression:1 ds2i:1 definition:1 unique:2 derivation:3 r2:1 dubbed:1 could:1 similarly:1 ds2:2 success:1 local:3 motion:1 length:2 universidad:1 hence:8 speeds:2 first:1 origin:8 intuition:1 already:2 symmetry:1 enhances:1 zac:1 rank:1 philosophical:1 done:6 relations:1 directly:2 carry:1 pulsar:1 electronic:1 angular:1 given:2 exists:1 needed:1 introduction:3 unknown:1 system:7 least:1 indicate:1 observations:8 hypothetical:1 realization:1 dt2:1 frame:4 gives:3 stars:3 explanation:2 realized:1 wisdom:1 galilei:1 x2:1 x3:1 x0:1 x1:1 peculiar:2 character:3 distance:2 kind:1 accordance:1 double:1 second:3 matter:21 contrary:1 sr:1 outcome:1 tangential:2 humble:1 ev:1 remained:1 footnote:1 well:1 ram:1 dθ2:1 generalization:1 ultra:1 formula:3 kepler:1 seem:1 cosmology:3 orders:1 collapse:3 acceleration:1 form:2 responsible:3 gravity:8 note:3 ideal:2 potential:1 schiffer:1 forces:4 interior:1 negligible:2 mis:1 wmap:1 lectures:1 added:1 ray:1 allow:1 centre:1 molecule:3 most:4 propagate:1 significant:1 phase:4 plays:1 colliding:1 measured:4 pages:2 inconsistency:1 unidad:1 astro:1 especially:1 surprising:1 failure:1 considered:2 clear:3 face:3 feynman:2 accounted:1 principle:4 mechanical:2 velocity:4 physics:4 section:2 fact:7 laws:3 precise:2 emerging:1 3p:2 violation:1 random:2 anyway:1 rotating:1 implying:2 radio:1 constituent:2 astrophys:1 analogue:1 trivial:1 find:5 paradoxes:9 resisting:1 parameters:1 situations:3 explain:2 state:1 should:10 surroundings:3 only:8 going:1 molecules:5 factor:2 tune:1 g00:5 equilibrium:4 do:2 his:1 get:1 spurious:2 dg:1 de:2 fluid:46 famous:1 cannot:6 dz:1 words:1 dy:2 timing:1 carries:5 dt:7 dr:5 ds:13 dp:2 reveal:1 resolve:2 4πr:1 course:1 fields:1 arxiv:4 qc:2 exercise:1 though:10 through:6 movement:1 explanations:1 inside:3 view:1 reveals:5 requirement:1 erroneous:1 questions:1 observer:8 physically:1 exerted:3 observed:1 argued:1 see:9 individual:2 radius:1 result:2 eliminating:1 close:2 outward:2 subject:1 gravitation:10 tensor:22 nuclear:1 symmetric:1 enough:1 between:2 infrastructure:1 terms:8 ability:1 right:1 nature:2 zacatecas:2 weak:1 however:17 tolman:9 blame:1 vanishing:2 cut:3 key:1 inertia:1 comparably:1 pull:1 faced:1 many:3 according:3 attributed:1 ehlers:1 vishwakarma:1 supplies:2 context:1 quite:1 contribution:4 expense:1 disappears:3 photons:1 experimental:1 otherwise:2 mechanics:1 solving:1 point:3 wall:6 aticas:1 others:1 directions:2 non:6 exhibits:1 respect:1 cp:1 cv:1 points:1 ct:1 considering:1 finally:1 described:2 ozsvath:1 capable:1 addition:2 create:1 locally:5 due:4 been:6 dux:3 momentarily:1 magnetized:1 bianchi:1 wherein:1 basic:1 ph:1 empty:1 direction:7 contribute:1 thousand:1 wheeler:1 gas:8 matem:1 2g12:1 dramatic:1 understand:2 stems:1 c2:14 careful:1 present:3 applied:1 p3:1 p0:1 novel:3 inertial:8 look:2 pacs:1 appearance:1 single:1 value:1 will:3 while:2 euler:1 situation:3 property:1 mexico:1 analyses:1 characteristics:1 metric:2 binding:1 violating:4 iv:1 ii:1 vx:2 hydrostatic:3 galileo:1 disappear:2 different:1 starlight:1 etc:1 make:2 formulations:1 radiation:9 cross:1 same:6 any:11 thermalized:1 pressureless:1 conventional:2 several:2 events:1 neutron:4 used:2 temporary:1 receives:2 bonus:1 defy:1 effect:7 noticing:1 average:2 moving:2 aℓ:1 reference:3 recent:2 early:2 concordance:1 off:4 mention:1 expression:1 failing:1 bounces:1 bang:1 analysis:2 thorn:1 without:2 comes:1 components:6 coordinate:6 repulsive:3 model:5 arising:1 researchers:1 usual:2 spherical:2 just:2 generally:6 obtain:1 rest:7 dφ2:1 sources:1 identify:1 plagued:1 aspect:2 spherically:2 differentiation:1 untested:1 speed:6 enters:1 preprint:3 candidate:1 density:39 satellites:1 regarded:2 seems:6 except:2 signals:1 source:11 internal:2 attractive:1 interprets:1 transformation:1 momentum:4 identical:1 makes:2 tests:2 aspects:2 around:1 defies:1 big:1 disagreement:1 possible:2 dark:9 know:2 background:1 press:2 using:1 poses:1 vague:1 loss:1 modifications:1 appearing:2 like:5 particle:5 follows:1 reduces:4 accelerating:1 yields:1 either:1 become:2 replacement:1 mathematical:1 satisfactory:1 acad:1 theorists:1 classical:2 polar:1 some:8 somehow:2 authority:1 algebraically:1 einsteinian:2 towards:2 choosing:1 proper:8 creep:1 happens:1 vol:1 describing:1 dimensions:2 avoid:1 shall:3 2c2:1 whole:1 does:9 provides:2 assuming:3 measuring:1 power:1 reaching:1 equivalent:3 agreement:1 expansion:1 pressure:66 confrontation:1 although:2 notorious:1 post:1 refuge:1 about:3 carried:1 mcgraw:1 universe:6 penetration:1 mutually:1 whence:1 extensions:1 introduced:1 consequently:1 therein:1 cambridge:1 inclusion:1 into:6 within:1 balances:1 lies:1 because:1 accounts:1 primarily:1 einstein:7 additional:7 elastic:1 whom:1 there:6 noticed:1 conservation:9 way:3 misner:1 assumes:2 therefore:1 questionable:1 himself:1 complete:1 newtonian:11 energies:1 phenomena:1 removes:1 but:7 volume:4 taken:5 contradictory:1 gain:1 becomes:1 true:2 oxford:1 longer:1 absent:2 made:2 uy:1 ux:2 adler:1 uz:1 pulsars:2 gravitational:10 variations:1 us:2 limit:2 critical:1 sum:1 sands:1 problem:2 called:1 recalling:1 strongly:1 tsui:1 constant:1 exerting:1 devise:1 abstract:1 describe:1 am:1 avoiding:1 general:11 examine:2 exist:4 predictions:1 formulation:1 identities:1 physical:2 vrms:1 compared:1 paradox:13 nm:1 no:2 whereas:1 percent:1 reality:1 field:7 other:3 role:2 special:2 normal:1 spatial:2 test:4 really:3 company:2 conclusion:1 area:1 apparent:1 star:6 generates:1 why:1 includes:1 important:2 curvature:1 additionally:1 vi2:4 happening:1 calls:1 values:1 dτ:7 required:2 pseudo:1 orbit:1 mass:23 time:8 serious:1 quantity:7 requires:1
0705.0826.txt |@word gt:4 sci:2 results:1 gd:3 consists:1 centers:14 devoted:1 calculate:1 lammers:1 tm:6 tb:1 ın:1 johri:1 zhang:2 very:9 mn1:1 tends:1 lumin:8 formula:1 difference:7 10µs:1 level:1 small:1 optics:1 der:2 smaller:1 miller:1 direct:20 pulse:62 rate:2 pozna:3 insertion:1 chen:1 dynamics:1 chem:2 even:1 established:1 abe:1 sum:1 bergman:2 experiment:1 above:1 acknowledgments:1 condensed:1 lee:1 respectively:1 neves:1 here:1 reported:1 excess:2 florez:2 appears:2 change:1 obtained:5 great:3 electroluminescence:4 allows:2 products:1 chang:1 plotted:2 instr:1 explained:2 total:3 use:1 er3:1 cavalli:1 program:1 therefore:1 taken:1 until:1 semilogarithmic:1 emission:1 cases:1 sekiguchi:1 iii:1 account:3 sa:3 equation:9 mn:2 dn1:3 thin:5 dn2:1 hansen:1 petersen:2 example:2 wang:2 figure:3 give:1 process:1 cited:1 numbers:1 end:20 decaying:1 busse:1 di:2 jacquier:1 acta:1 faulty:2 explains:1 product:1 description:3 may:1 after:20 derived:1 treatments:1 faculty:1 photoluminescence:1 data:2 short:15 light:15 gilliland:1 zns:4 sect:1 subsequently:1 order:1 sd:3 produces:1 merz:1 produced:4 paper:3 pulses:6 kinetic:5 its:4 before:1 decay:2 ln:3 decreases:1 better:1 meissner:1 fig:16 τt:4 yi:1 good:3 murakami:1 attains:4 now:1 n01:3 february:1 university:2 2d:1 each:1 found:1 investigators:1 chung:1 generation:2 energy:21 100µs:1 used:2 eq:3 es:1 shown:2 rev:8 research:1 increase:1 got:3 integrated:15 shows:1 mechanisms:5 reason:2 put:1 rises:1 silicon:1 length:1 gordon:1 transfer:21 first:5 initial:2 features:1 researches:1 number:5 another:1 electronic:1 given:2 width:3 introduction:1 relations:1 theis:1 john:1 bowen:1 nobody:1 park:1 part:5 than:2 lucas:1 begins:2 kind:1 depends:2 matter:1 contrary:3 were:3 krasnov:1 curves:1 seen:4 any:1 lie:1 lim:1 mechanism:3 fitting:1 gτ:4 k5:1 singh:2 spectral:2 centre:2 gallagher:1 device:1 why:3 zeitler:1 sometimes:2 ramirez:1 points:1 schulz:1 physics:2 show:2 tb3:1 supported:1 dependences:1 infrared:1 relation:3 keywords:1 d3:1 based:1 explain:1 inflection:2 only:1 going:6 emitting:2 dn:6 dominant:1 get:1 lobe:1 de:12 aim:1 during:13 dt:7 superlatt:2 arxiv:1 analytical:1 lifetimes:1 up:1 relative:1 intensity:11 leslie:1 powder:1 seo:1 roura:2 αt:2 crystal:1 µs:7 luminescent:3 between:5 probably:1 bhargava:1 αn:2 however:3 wu:1 huang:1 analyzed:1 both:7 last:2 many:1 region:1 equal:1 figures:2 dated:1 exceeds:1 disappears:3 experimental:4 point:3 address:1 pol:1 exhibits:1 cr:1 described:8 due:2 been:1 mart:1 describes:3 pl:1 benoit:1 transferring:7 determination:2 baus:1 case:5 exponential:1 pacs:1 solid:1 straight:1 value:1 rectangular:12 will:1 technical:1 behavior:2 taking:2 procedure:1 electrochem:1 iv:1 ii:6 allen:3 ia:2 technology:2 id:2 hong:1 lengths:1 same:2 parts:2 several:1 powell:1 investigated:3 infinity:1 i0:4 upon:1 rigby:1 harris:1 kim:1 poznan:1 costa:1 luminescence:70 center:3 expression:1 poland:1 well:5 quantitative:1 recombine:1 nd:1 obtain:2 voltage:1 using:1 ohmori:1 lett:2 excited:13 meas:1 increases:2 kash:2 immediately:2 microstruct:2 mathematical:1 often:1 formulas:1 some:3 growth:1 duration:3 scale:1 describing:1 measurements:3 katsumata:1 assuming:2 prog:1 moreno:1 agreement:1 bw:1 exciting:35 stage:2 tm0:6 comparison:1 discussed:1 dependence:21 o:1 soc:1 into:4 obtaining:1 sol:5 determine:1 proportional:2 theoretically:1 van:3 additional:1 assumed:3 there:4 long:2 start:1 appl:4 was:3 m0:1 function:2 considerably:2 αn0:1 form:2 gauss:1 films:1 line:1 absent:1 characteristic:1 cells:1 maximum:6 devices:1 ul:1 below:1 joubert:1 similar:2 strongly:1 saturate:1 shin:1 resolving:1 describe:3 aizawa:1 lifetime:5 work:1 film:2 constructed:1 functions:1 us:1 when:7 elemental:2 valid:1 investigations:3 papers:1 conclusion:1 stat:5 permitting:1 excitation:27 kapoor:1 technol:1 correlated:1 longer:4 practically:3 assume:4 morikawa:1 curve:5 time:43 n0:2 n1:1 n2:1
0705.0827.txt |@word represent:1 ijklmn:2 consider:1 induces:1 lack:1 results:4 perelman:11 leads:1 scalar:4 signatures:1 grateful:1 follow:1 research:1 indefinite:1 compact:1 whose:3 certainly:1 hold:1 violate:1 technique:1 charge:5 monotonically:3 those:2 th:2 under:2 alberta:2 details:1 nodes:1 include:2 divergent:1 mpg:1 global:2 string:1 2ri:3 very:2 rise:1 choice:2 jack:1 nontrivially:1 condition:2 2rp:1 harmonicity:1 school:1 solves:1 notes:1 solution:1 ri:7 large:13 vector:7 rj:3 subscript:1 small:1 provided:2 rk:1 straight:1 mn:1 pragmatic:1 sign:6 second:20 linear:1 even:3 reviews:1 gibbons:1 nonlinear:1 giving:1 section:9 selected:1 brief:1 expressed:1 find:1 current:1 above:3 new:2 solitonic:1 preserved:3 coefficient:1 completion:1 evolving:1 full:3 led:1 here:5 desired:1 tangent:1 address:2 along:18 standard:1 appears:2 change:2 knowledge:1 obtained:3 rdv:2 institute:2 study:1 studied:2 drt:1 suggests:1 resulting:1 action:29 hospitality:1 suitable:1 makes:1 vic:1 via:1 diffeomorphisms:1 extra:2 outcomes:2 addressed:1 decrease:1 org:1 planck:1 rkj:1 integrates:1 derivatives:6 use:2 proceed:1 would:7 d75:1 remains:2 positive:10 contains:2 negative:2 next:4 nucl:6 opposed:1 brunswick:2 assessment:1 more:2 flat:1 ferus:1 clearly:2 becomes:5 apparent:1 odinger:3 curvature:15 berlin:2 particular:3 known:9 iv:18 iii:17 circumstances:3 logarithm:2 springer:2 valued:1 integrating:1 klm:10 equation:2 work:7 modified:1 mj:2 reproduce:1 making:1 example:1 stimulating:1 claim:2 compare:2 renormalization:4 give:1 process:1 expanding:1 arise:2 neglected:1 reconstructed:1 indicates:2 dm:2 dxk:1 want:1 sense:2 conversely:1 occur:2 presently:1 monash:1 dilaton:6 discussion:4 holds:4 off:2 write:1 perry:1 dg:1 sij:1 flow:60 parameter:6 b406:1 product:1 express:1 contribute:2 may:6 max:1 after:2 wrong:1 explored:1 fi:3 fj:1 minimizer:4 data:1 grow:1 constants:9 arkady:1 natural:2 imply:1 whenever:3 explicit:1 element:1 diffeomorphism:1 rather:1 so:15 sl:1 friedan:1 definitions:1 integrand:2 order:55 superscript:1 e2ϕ:2 words:1 indeed:4 over:2 vary:2 argues:1 course:2 paper:2 including:1 statistical:2 during:1 satisfies:2 its:6 group:3 thank:1 directional:3 chosen:1 lm:1 coordinates:1 choose:2 van:1 derivative:17 might:2 formulæ:1 eventually:3 non:1 greater:3 combination:1 break:2 βkl:5 now:3 ordinary:1 represents:1 term:14 equality:2 verifying:1 always:3 university:5 establishing:1 sufficiently:2 iff:1 magnitude:2 found:2 organized:1 difficult:1 decreasing:2 side:1 homogeneous:1 differential:1 series:6 energy:1 gary:1 related:1 contracting:1 extended:1 obtains:1 todd:1 quantum:1 our:1 happen:1 beyond:4 special:1 out:2 canada:4 pullback:1 shown:1 dominates:3 space:17 gradient:27 furthermore:1 since:6 squared:1 denotes:1 increase:2 rg:24 reader:1 rl:1 formula:11 induced:1 issue:3 occurs:2 math:3 shows:3 theory:9 monotone:1 divergence:1 differ:1 free:1 quite:4 admits:1 institut:1 estimate:2 beginning:1 generate:1 jkl:2 perform:1 geometry:1 starts:1 keep:1 turn:1 length:1 place:1 invitation:1 corrections:1 parallel:1 onto:1 first:15 initial:1 ril:4 symmetry:1 third:1 number:2 enlarged:1 another:2 calculational:1 precisely:2 size:1 given:5 perturbation:14 checked:1 gpi:1 strict:1 introduction:2 leading:9 jki:1 behaves:1 least:2 gjk:2 their:2 manifolds:9 calculations:1 convention:1 draft:1 variational:5 gives:3 lot:1 albert:2 required:1 part:1 contracted:2 attempt:1 x0:1 than:3 coefficients:1 begins:1 target:7 ew:1 was:1 require:2 namely:1 were:3 contribution:1 minus:1 truncating:1 lowest:3 motivation:1 ann:2 zamolodchikov:4 measure:3 say:1 close:2 curved:1 orders:3 nλ2:1 zero:2 gravity:2 mechanism:1 λgij:1 note:1 sciences:4 potential:4 take:4 timelike:1 woolgar:2 lectures:1 trace:1 though:1 vnl:1 metrics:4 beta:1 germany:1 significant:1 nothing:1 class:8 soliton:1 deviations:2 reduces:1 surprising:1 kj:1 clear:1 sometimes:1 curvatures:6 γjk:1 kl:4 points:2 rev:1 principle:1 unzle:1 sigma:8 fact:3 quantity:1 atmosphere:1 celebrated:1 show:1 b363:1 supported:1 converge:2 solutions:1 b194:1 analogue:1 longer:3 july:1 ualberta:1 gravitationsphysik:1 partially:1 finally:1 based:2 just:3 notice:1 situations:1 enough:4 untruncated:2 should:1 only:4 explicitly:4 geometric:1 integrate:1 invokes:1 constant:4 truncation:6 local:1 oct:1 hope:1 do:1 his:2 dominant:1 absent:1 dependent:1 familiar:1 de:1 overall:1 expectation:1 cannot:4 nearly:1 closely:1 dv:32 compute:2 dt:8 ds:23 reveal:1 b308:1 fields:1 arxiv:3 fixes:1 yield:1 summary:1 schematically:1 mapped:1 qj:1 grad:3 view:3 riemannian:4 set:1 computed:1 exists:1 ricci:11 unpublished:1 reiterate:1 up:1 see:6 result:6 fail:6 recently:2 seh:1 fails:2 nonderivative:1 tensor:5 worldsheet:4 ways:1 review:1 definite:10 symmetric:1 written:1 vkl:6 closed:3 between:1 boundary:1 approach:3 available:1 comparable:3 uhlenberg:1 terms:11 initially:2 combining:1 however:3 jl:11 council:1 oliynyk:3 spoil:1 multiplier:4 monotonicity:26 jetp:1 distribution:1 comparably:1 both:1 essentially:1 parentheses:1 improved:1 onofri:1 dxi:3 taking:1 equal:1 unb:1 context:2 passing:1 perturbative:1 expression:1 grounds:1 arbitrarily:1 ch:1 point:1 appeared:1 ca:2 jk:5 cg:1 harmonic:7 dimensional:6 simply:1 routine:1 lagrange:4 wider:1 respect:7 throughout:2 pp:1 described:2 submanifold:4 ishes:1 inclusive:1 due:2 been:1 bianchi:2 judging:1 expected:2 enlarging:1 uik:1 empty:1 define:1 direction:2 arises:1 corresponding:1 truncations:2 cotangent:1 generalizing:1 last:3 c0:6 present:2 case:6 tracefree:1 look:1 ujk:1 reliable:2 will:13 dept:4 while:2 replaced:2 bounds:1 evaluating:1 error:1 aie:1 situation:2 property:1 couplings:2 loop:1 va:1 klebanov:1 unitary:1 spacelike:1 coupled:1 vi:1 metric:33 ir:1 thus:3 according:1 ii:35 b322:1 ik:16 ij:41 rij:9 il:2 exterior:1 seen:1 vanish:1 ric:6 eigenfunction:2 acknowledgments:1 2g1:2 confirmed:1 grant:1 perhaps:1 suggest:1 divergences:1 belong:1 any:2 parts:3 products:1 finite:3 higher:4 breakdown:1 independent:1 literature:2 mohammedi:1 upon:3 monotonic:3 flows:2 hand:1 inhomogeneities:2 usually:2 purpose:1 infinite:2 tli:1 identity:3 lower:1 argue:1 schr:3 scenario:1 well:2 analysis:2 obviously:2 thought:1 easily:2 model:7 otherwise:1 arising:1 dimension:1 left:1 ny:1 manifold:4 proposed:3 γijk:1 being:3 5a3:1 obtain:3 vanishes:1 front:1 using:6 hess:4 rijkl:5 preprint:1 candidate:1 readers:1 parametrization:1 b278:1 other:1 extends:1 lett:2 theorem:2 guarantees:1 fateev:1 gkl:2 australia:1 around:1 depends:1 eigenvalue:3 read:2 breaks:3 spatial:1 sums:1 possible:3 cf:1 possibly:1 appearing:1 bit:1 replace:1 edmonton:2 necessary:1 like:2 semi:6 follows:3 signal:1 serves:1 gjl:6 yields:2 either:2 integrals:2 arbitrary:2 become:6 works:1 interestingly:1 mathematical:3 because:3 truncated:4 steady:1 some:4 glk:1 neglecting:1 umj:1 happens:1 riem:11 scale:2 describing:1 confirm:2 opposite:1 integration:1 comments:1 does:7 assuming:2 refer:1 workshop:1 obey:3 june:1 expansion:2 b294:1 βij:7 hilbert:3 about:3 callan:1 central:5 extension:1 discussed:1 o:19 must:3 plus:1 obeys:1 act:1 discard:1 osborn:2 bourguignon:1 therein:1 own:1 integral:1 functional:8 down:5 qrs:1 references:2 einstein:9 operator:3 lastly:1 statistics:2 hep:2 log:1 there:4 question:3 long:2 extremizing:2 expanders:1 inner:1 way:1 ed:1 gil:5 gik:2 gij:24 therefore:1 function:12 form:4 but:7 volume:1 failure:1 construction:4 skip:1 larger:1 unreliable:1 rjl:4 rjk:1 proposal:4 raising:1 he:2 shrinkers:1 applying:1 whether:4 smooth:2 particle:1 us:1 ur:1 tseytlin:14 besse:1 problem:4 called:2 aa:2 ab:4 associated:1 computing:1 defined:4 certain:1 abstract:1 uij:6 am:1 general:1 dirac:1 engineering:1 gradients:1 check:1 again:1 functions:6 no:4 index:2 nb:1 wavefunction:1 when:6 detail:2 field:5 valid:1 potsdam:1 solitons:4 test:2 mathematics:4 appends:1 deviate:1 wishing:1 generates:4 emerges:1 models:1 problems:1 variation:4 generated:3 important:1 validity:1 generalized:2 t6g:2 jones:1 implies:1 coupling:9 restores:1 interval:1 governed:1 equivalently:1 e3b:1 time:3 original:1 once:1
0705.0829.txt |@word gs:4 consider:1 yasuhiro:1 gupta:1 magnetic:5 results:6 leads:2 parameterization:1 consists:1 remarkably:2 2l1:1 causes:3 swave:2 diffusive:1 calculate:1 tx:1 re:1 technique:1 tr:1 tn:5 quasi:1 does:3 those:3 under:1 andreev:2 crest:1 tc:1 kashiwaya:6 case:5 very:1 rise:1 connects:1 wave:23 electron:1 figs:2 resonant:2 difference:2 matrices:2 condition:4 induced:1 level:1 transmission:1 knight:2 pacs:1 proposals:1 large:2 vector:2 τˆi:1 small:2 dip:7 smaller:1 yukio:1 cosh:1 zero:13 compensates:1 enhancement:4 qualitatively:1 odd:11 even:1 what:2 superlattices:1 usadel:6 contributions:2 expressed:1 current:10 experiment:3 localized:1 above:1 new:2 increasing:1 method:2 contrast:4 satisfy:1 condensed:1 midgap:2 degree:1 respectively:4 never:1 urhge:1 here:1 l21:1 cos2:2 address:1 directions:1 path:1 along:1 strong:2 z0:4 superconductor:21 tunneling:3 institute:1 shift:2 studied:1 suggests:1 usually:1 resonance:1 suitable:1 cancellation:1 plotted:1 composed:1 useful:1 washes:1 explained:1 highly:1 apply:2 sch:1 unit:1 use:1 would:1 positive:1 nagoya:2 next:1 program:1 therefore:3 theoretical:1 reflects:1 flat:1 becomes:2 yokoyama:1 spoils:1 uge2:1 everywhere:1 thouless:1 cases:2 states:4 science:3 equation:6 spinsinglet:2 modified:1 ρn:3 itself:1 temperatures:1 following:2 im:1 modifies:2 point:2 f1:7 f2:6 weaker:1 challenging:1 give:1 calculation:1 discussed:2 topic:1 numbers:1 allowed:1 junctions:31 axis:1 rather:1 discussion:2 feature:5 hot:1 pure:1 flow:1 explains:1 sin:4 fr:2 fs:5 ft:5 mat:2 may:4 fy:1 different:1 2rb:7 dwave:1 saxena:1 faculty:1 drastic:2 horizontal:2 fl:2 mal:1 ruo4:3 short:1 quasiclassical:1 third:1 spectra:11 en0:1 green:2 imθ:2 order:1 stoof:1 interpreted:1 symbols:1 thermal:1 experiments:4 through:2 japan:4 satisfies:1 sapporo:1 supplemented:1 derive:1 probability:1 2e2:1 interesting:1 fix:2 zaitsev:2 decreases:3 detected:1 fig:18 goennenwein:1 junction:5 pauli:2 propose:2 dǫ:1 material:1 break:1 kleinsasser:1 penetration:1 effects:2 cosh2:1 half:1 rotation:1 yu:3 discuss:2 nor:1 2t:2 susceptibility:1 february:1 netherlands:1 2r:4 always:4 university:3 classified:1 bergeret:1 microstructures:1 realistic:1 2g:1 l2:9 l1:10 efetov:1 side:1 characterized:1 differential:7 detect:1 series:1 energy:7 related:1 conductance:42 frequency:10 measurement:1 keizer:1 beyond:1 eq:11 out:2 shown:8 impurity:1 factors:1 gˆr:3 since:1 rev:18 research:1 increase:2 gˆk:2 socalled:1 rb:2 dutch:1 rn:11 gˆa:2 issue:2 shows:2 takayanagi:1 microfabrication:2 completely:1 complicated:1 pairs:12 chiral:6 ministry:1 geometry:1 minigap:1 impose:1 exponentially:1 first:2 industrial:1 symmetry:31 quasiparticle:6 powerful:1 bhat:1 defects:1 robust:2 quality:3 summarize:1 interchange:1 given:3 temperature:3 data:1 eqs:1 approximately:1 indicate:1 assumption:1 twente:1 structures:1 listed:1 tool:2 keldysh:3 serve:2 realized:1 part:4 authors:1 undesired:1 sign:1 undoubtedly:1 than:2 diffusion:2 observed:1 bruder:1 require:1 second:1 matter:1 classes:1 amplitude:2 aoki:1 resistivity:1 symmetries:1 generality:1 unchanged:2 any:1 strength:1 angle:4 depending:2 latter:1 instance:1 potential:1 online:3 detector:1 transparent:1 exactly:1 multiple:1 electric:2 opposite:2 singlet:12 jst:1 most:1 involving:2 connected:2 pair:5 intrinsic:1 deˆ:1 cause:1 kf:1 clear:4 metal:24 physica:1 points:1 electrons:3 dos:7 usual:3 physics:4 fact:3 phenomenon:1 show:6 supported:1 relation:3 hokkaido:1 find:2 decade:1 finally:2 explain:2 maeno:1 state:2 should:1 analytic:1 only:5 candidates:1 factor:2 quasiparticles:1 di:7 de:1 ones:1 negative:2 dx:2 dv:7 penetrate:2 dt:4 alexander:1 volkov:3 arxiv:1 yield:2 greene:1 bad:1 paper:2 enhances:1 electrodes:1 national:1 detection:1 culture:1 depends:3 result:1 existence:2 conductivity:1 phases:1 wire:1 compounds:1 nuclear:1 away:1 currently:2 tend:1 outside:1 between:2 limit:2 boundary:4 conditions:1 across:1 triplet:26 spintriplet:1 jt:2 weak:1 however:4 incident:1 2iǫ:1 interface:6 cos:10 last:1 according:1 powerless:1 sensitive:2 involve:2 figures:1 dated:1 retarded:1 distinction:1 eth:5 expression:1 belzig:1 experimental:4 con:1 unclear:2 conclude:3 color:3 height:1 dimensional:2 cancel:1 respect:2 basis:3 addition:3 observing:1 due:3 been:1 describes:1 change:1 mars:4 expected:2 proposal:1 anomaly:5 suppress:1 sufficient:1 formed:1 resistance:2 bulk:1 observe:2 external:1 angles:1 spin:44 former:1 present:5 aid:1 applied:4 novel:1 josephson:2 tanh:3 value:2 choices:2 will:3 near:1 behavior:2 promising:1 irrespective:1 property:1 procedure:1 orientation:4 jpn:1 almost:1 thus:7 xiao:1 surface:1 superconducting:2 bias:13 cond:2 technology:3 ig:2 orbital:2 confirmed:1 education:1 grant:3 make:1 cross:2 klapwijk:2 wilhelm:1 damages:1 schematic:1 several:5 asano:4 difficult:1 independent:2 used:2 unconventional:2 assist:1 effect:19 hand:3 moment:1 compared:1 purpose:1 potentials:1 satoshi:1 contribution:2 disappears:1 well:1 analysis:1 materials:1 solve:2 ae:1 milliken:1 hˆ:1 miao:1 enschede:1 muon:1 proposed:2 being:2 subgap:1 proximity:20 golubov:3 superconductors:11 identify:1 voltage:1 scattering:2 previous:1 cut:2 density:1 z02:1 mathematically:2 signals:1 reasons:2 other:5 advantages:2 lett:13 real:2 insensitive:2 around:4 easily:1 nazarov:3 possible:1 department:2 increases:1 advanced:1 mod:2 zbcp:10 necessary:1 fined:1 shaped:10 follows:4 signal:1 extremely:1 specific:1 characterizes:3 become:1 accessible:1 parity:3 because:13 methods:2 phenomena:2 calculated:1 transport:5 gradually:1 cooper:11 dimensions:1 lead:1 normal:24 integration:1 sr2:3 critical:2 fom:1 scientific:1 power:1 each:1 although:1 imaginary:1 about:1 ferromagnetic:2 acquire:1 anomalous:1 dependence:1 obeys:1 slightly:1 soc:1 into:5 within:2 three:1 tanaka:8 fσ:4 sports:1 terminated:1 statistics:1 synthesized:1 measured:2 support:1 pairing:8 width:3 conservation:1 low:4 way:2 mesoscopic:1 analyze:1 was:1 function:5 form:2 but:1 hu:1 heat:1 implies:1 technologies:1 partially:1 absent:2 fabricate:1 characteristic:2 supr:1 robustness:2 mackenzie:1 us:2 work:1 below:1 decays:2 fermi:5 spectroscopy:2 distribution:1 similar:2 called:1 nature:3 detailed:1 penetrating:1 constant:1 resolving:1 contribute:1 influence:2 tb:6 right:1 formalism:1 dγ:2 ni:2 ev:14 discriminate:1 no:1 whereas:1 percent:1 vanishes:1 field:3 valid:2 branch:1 test:4 ns:6 realize:1 conclusion:4 superconductivity:12 important:1 peak:5 suppression:1 tsukuba:1 structure:10 remote:4 coupling:1 assume:1 typically:1 kinetics:1 orbit:1 requires:1 original:1
0705.0830.txt |@word concept:2 partial:1 consider:1 magnetic:2 illustrated:2 scalar:2 microwave:1 edu:2 consists:1 expressions:1 research:1 issues:1 fellowship:2 vacuous:2 presents:1 under:1 td:3 wave:7 refractive:14 difference:3 four:2 school:1 transmission:8 evaluation:1 solution:3 occurs:1 solved:2 vector:4 optics:2 zl:7 upper:1 sin2:1 pulse:8 morphology:1 second:1 chen:4 cfw:16 amplified:1 zr:3 blue:1 index:14 specification:1 optoelectronics:1 foregoing:1 expressed:3 thickness:3 replaced:1 method:2 filled:1 full:1 chose:1 respectively:1 component:3 here:1 reported:1 active:6 consideration:1 along:3 z0:1 implicit:1 deduced:2 obtained:1 noticeable:1 institute:1 study:2 controversy:3 conveniently:1 fourier:2 studies:1 plotted:1 emerge:1 reflectance:4 substitution:1 phasors:3 viz:1 unit:2 usa:4 commun:1 positive:3 negative:5 next:1 occupying:1 taken:1 associated:1 theoretical:2 more:1 xiao:1 appendix:2 normalized:1 iii:1 must:2 valued:3 obliquely:1 science:2 equation:3 work:1 values:2 thin:1 following:1 root:4 mackay:2 wang:2 figure:5 calculation:1 states:2 indicates:2 application:1 performed:1 exclude:1 iωµ0:1 axis:2 stemmed:1 delay:1 beams:1 opt:5 parameter:2 sin:18 edinburgh:3 fs:2 inherent:1 may:3 plane:16 waves:6 representations:1 choice:1 data:1 parallel:3 constants:1 waist:3 iii1:1 light:2 so:2 representation:1 order:3 superscript:1 restriction:1 pulsed:4 over:6 fft:1 stability:1 through:2 argued:1 avenue:1 its:3 roots:1 position:1 group:1 thank:1 chosen:2 zˆ:1 solving:3 writing:1 absence:1 complex:1 fig:8 covered:1 refracting:1 them:1 thereby:2 matches:1 components:4 material:2 reflected:8 half:9 now:2 hall:1 dielectric:9 easily:1 dirac:1 hereafter:1 university:4 possibilities:2 did:1 transmitted:8 arrow:2 found:7 cliffs:1 side:1 characterized:1 mean:6 domain:26 arxiv:1 ei:14 ed:1 energy:3 gaussian:5 related:2 inverted:2 society:1 frequency:15 our:2 avoided:1 er:3 rt:6 emerges:1 shown:3 literature:1 matrix:8 space:14 furthermore:1 urbana:2 rev:6 denotes:1 re:3 issue:1 correct:2 red:4 shows:1 disputed:1 linear:1 free:8 uiuc:1 determining:1 could:1 turn:2 length:1 isotropic:1 onto:2 first:1 origin:1 fischer:4 number:1 approximate:1 xz:2 least:1 another:1 comprises:1 clarity:1 angular:3 given:4 phasor:3 introduction:1 top:1 adopted:1 their:1 calculations:2 tom:1 relations:1 unboundedly:1 centered:1 continuous:1 park:1 part:5 coefficients:8 iωt:2 polarized:3 require:1 determined:3 contrary:2 were:5 negatively:2 skaar:2 rad:3 occupies:1 spectrum:1 eqn:6 further:1 null:2 slab:17 sandwiched:1 angle:8 latter:1 indexes:1 note:1 sciences:1 materials:1 schematically:1 green:1 spectral:1 begin:1 electric:7 normal:3 incidence:5 most:1 importantly:1 strikes:1 claims:2 phase:1 acknowledgements:1 intrinsic:1 lakhtakia:5 considered:3 calculated:2 flow:1 messier:1 exp:13 physics:1 ˆz:3 fact:2 quantity:2 ambiguities:1 spatiotemporal:1 bellingham:1 supported:3 spaces:2 postdoctoral:1 keywords:1 substituting:1 delivers:1 postulates:2 causality:1 parameters:1 explicitly:2 ambiguity:1 factor:2 oblique:1 invoke:2 champaign:1 straightforwardly:1 beam:22 grew:1 closely:1 compute:1 dt:2 neither:2 evolution:1 resolve:1 fields:1 differential:3 comprising:1 mapped:1 fixed:1 pertains:1 view:1 ik0:10 computed:3 undergoes:1 relative:8 w0:4 discussions:1 3jz:1 λo:7 µm:5 state:2 invokes:1 between:3 boundary:4 conditions:1 email:3 terms:2 wa:1 interfaces:2 transpose:1 however:1 incident:16 premise:1 distinguish:1 problem:5 both:4 cos:26 region:1 beckman:2 against:1 deduction:1 propagation:2 context:1 refraction:4 grounds:1 point:1 royal:1 represented:2 twin:1 scottish:1 respect:2 tgm:1 described:1 basis:1 equations:5 been:2 geddes:3 pa:1 prentice:1 utilizing:1 lett:8 direction:3 θi:22 corresponding:4 concerning:1 determination:1 spie:1 c0:3 solid:3 value:3 while:1 suppose:2 eik:3 procedure:2 resolved:2 planar:2 thus:1 herein:1 ii:3 vs:1 im:6 il:1 technology:1 since:1 author:1 make:1 wherein:1 parts:2 arguments:1 finite:3 grows:2 used:3 accentuate:1 numerical:1 upon:2 nj:1 concluding:1 recent:4 reflection:8 pennsylvania:1 analysis:4 without:1 solve:1 mathews:1 sets:1 coordinate:1 undertaken:1 interface:1 possesses:2 bending:1 being:2 executive:1 resolution:1 bandwidth:4 alternative:1 speed:1 polarization:4 density:2 wei:1 conclude:1 had:1 passive:3 source:1 k0:4 transformed:1 nor:1 mod:1 real:4 haus:1 leapfrog:1 vacuum:3 press:1 using:4 advanced:1 psu:1 englewood:1 imposed:1 helpful:1 visible:1 alternatively:1 steps:2 either:1 follows:1 permittivity:10 refracted:1 right:1 methods:1 deflection:2 duration:1 2d:2 bottom:1 electromagnetic:2 recorded:1 per:1 does:2 propagating:3 scientific:1 power:1 martin:1 perpendicular:2 step:1 references:1 eiφ:1 plots:2 imaginary:3 about:1 algebraic:2 column:3 dependence:1 o:1 carrier:1 introduced:1 computational:1 maxwell:3 into:4 numerically:1 remarks:1 square:4 accounts:1 tiny:1 transfer:1 support:1 there:2 question:1 transform:1 fast:1 width:2 accordingly:1 joseph:1 fraction:1 series:1 was:9 function:6 medium:18 north:1 elsewhere:1 form:2 but:1 films:1 ramakrishna:3 delta:1 impedance:2 line:1 reflectances:2 wise:4 whether:1 ut:3 maximum:1 us:1 eh9:1 discretized:2 limit:1 uk:2 ωc:3 similar:1 clear:1 mechanics:1 ac:1 constant:1 defined:3 certain:1 abstract:1 engineering:1 wavelength:4 curl:2 permeability:1 physical:3 functions:2 nm:15 dotted:2 dashed:4 when:2 illinois:1 field:10 other:2 details:1 spatial:1 department:1 mathematics:1 out:1 conclusion:1 technol:1 evanescence:1 algorithm:3 normally:2 time:15 n2:1 nonmagnetic:2 dϑ:3
0705.0831.txt |@word represent:2 lognormal:2 code:1 consider:3 caused:1 magnetic:8 results:4 produce:1 leads:1 ciudad:2 comments:1 disk:26 localized:1 overplotted:1 compact:1 maller:2 fronts:1 depend:1 including:1 preprint:1 ıa:1 quasi:1 aut:2 determinations:2 under:1 fountain:1 starbursts:1 sound:4 supported:1 very:4 deviates:1 assuming:3 induce:1 focus:1 dispersions:1 fall:2 difference:1 exact:1 cool:2 clouds:27 level:4 turns:1 explosions:1 shock:3 cloudy:1 occurs:4 large:3 discrete:1 small:4 midplane:4 configurations:2 upper:3 smaller:3 force:3 consistent:2 blitz:2 likely:1 populating:1 dynamics:2 maloney:2 gazol:2 even:3 power:3 reaching:1 m33:1 m31:1 uniform:3 current:1 new:2 net:1 fiducial:3 mee:2 condensed:1 respectively:6 component:5 here:1 reported:3 explore:1 compressed:1 directions:1 accretion:17 along:6 standard:1 equations:1 logarithmic:1 extreme:1 box:2 instituto:1 drops:1 zones:1 northern:1 larger:2 hydrostatic:1 amount:1 periodic:1 resulting:2 milky:3 complicated:1 studies:1 heiles:4 parravano:2 being:4 useful:1 scales:4 marked:1 bullock:2 scaled:1 decrease:1 apply:1 raymond:2 total:6 cloud:2 environment:2 refers:1 asymptotic:1 would:1 levine:3 contains:1 predictions:1 next:1 few:2 magnification:1 kinematics:1 taken:2 panel:1 theoretical:1 minor:1 more:1 started:1 stone:3 warm:7 clumpy:5 labelled:1 varying:1 known:1 rare:1 producing:1 clumps:2 sample:1 account:3 crosses:1 characterize:1 der:2 work:2 semadeni:4 cant:1 reviews:1 l121:2 erg:3 values:8 temperatures:1 mr:2 following:1 perturbs:1 mx:3 displayed:1 compare:1 challenging:1 figure:1 thermally:1 high:6 indicates:1 performed:1 arise:1 isothermal:5 rodr:1 firmly:1 azquez:4 information:1 end:1 goal:1 rather:3 discussion:2 regions:3 how:4 varies:3 instead:1 axis:3 parameter:1 massive:1 profile:6 tension:1 galactic:14 substructure:2 spitzer:6 may:6 after:2 derived:1 consequence:2 plane:3 value:6 multiphase:1 waves:1 fits:1 horizontal:5 choice:1 revealed:1 parallel:2 varied:1 gaussian:3 accrete:1 physical:4 t0:1 elmegreen:4 ss:1 salcedo:9 sp:4 martos:1 departure:1 maintain:2 so:3 partly:1 ivcs:1 order:5 remnants:1 feedback:3 oblique:2 insight:1 vary:2 interpreted:1 thermal:9 saturates:1 through:4 statistical:2 cuts:3 existence:1 cold:2 still:2 its:3 galaxy:5 observational:1 derive:2 rapidly:1 probability:2 fit:1 maps:1 interesting:1 hot:1 decreases:2 absence:1 fig:7 latitude:1 main:1 might:2 h0:9 heating:1 them:1 within:2 material:1 hunter:3 evolution:3 number:2 effects:3 they:3 half:3 yr:3 halo:1 structural:1 represents:1 hereafter:1 brightness:3 by2:1 model1:1 events:1 2d:2 astronom:1 good:1 kpc:17 2b:1 radial:4 crossing:1 found:5 energetically:1 anisotropy:1 mean:1 em:1 domain:6 square:1 ei:1 significantly:2 fairly:1 ed:1 energy:7 hard:1 displacement:1 used:1 dib:4 our:16 beyond:1 out:4 shown:5 network:1 driving:4 space:1 since:2 vcl:8 increase:1 collisions:2 shull:1 sustain:1 gaussians:1 l39:1 integrated:1 predicted:1 benjamin:2 southern:1 mechanisms:2 possibility:1 quite:1 cut:1 completely:1 threedimensional:1 formation:4 flows:3 onoma:2 r0:2 anchez:10 widths:3 could:4 but:4 times:5 length:1 explored:1 isotropic:1 ism:7 universidad:2 hence:2 onto:2 top:1 frequent:1 first:2 origin:2 initial:3 symmetry:2 shapiro:2 opez:3 disregarded:1 reaches:1 dilute:1 approximately:1 thick:1 heights:1 open:1 size:2 city:2 given:2 cartesian:1 checked:1 temperature:2 introduction:1 data:1 interact:2 hvcs:4 adopted:4 response:1 their:2 cooling:1 intermediate:1 rates:2 observations:4 calculations:1 hundred:1 structures:1 sensitivity:1 inflow:1 exploring:1 shell:1 elasticity:1 fraction:1 mostly:1 zeus:1 braun:2 assumption:2 optical:3 ncl:7 too:1 simulate:2 injected:3 off:2 than:3 oscillate:1 distance:4 kpc2:2 double:1 rate:10 matter:1 determined:1 stratified:1 aas:1 were:7 hollenbach:1 galactocentric:5 enhancement:1 fashion:1 betancort:2 unchanged:1 ram:1 spectrum:4 randomly:2 1992a:2 1992b:1 headings:1 need:1 seem:1 any:1 relatively:1 strength:1 aj:1 depending:1 efficient:1 self:1 1d:1 able:1 gravity:1 mechanism:1 note:4 mix:1 ideal:1 potential:2 take:1 finding:1 negligible:1 infalling:7 patchy:1 continuous:2 norman:3 though:1 measures:1 reach:1 falls:1 most:1 intergalactic:2 gallagher:1 an1:1 letter:1 preliminary:1 phase:4 cap:1 extremely:1 exico:2 volume:3 subtracted:3 considered:1 l105:1 calculated:1 flow:5 drive:1 km:39 face:1 bracket:1 magnetorotational:1 mechanical:1 velocity:17 constrain:1 physics:1 fact:2 gyr:11 magnetohydrostatic:1 αz:1 spaced:1 apj:16 show:2 lewis:2 detection:1 random:3 implying:1 radii:1 scarce:1 asymmetry:1 injection:6 impact:1 halves:1 ratio:2 ıguez:1 parameters:3 ngc:1 shostak:2 distributed:1 should:3 4πr02:1 only:10 kruit:2 factor:9 corredoira:3 emitting:1 burkert:3 partially:1 local:1 equilibrium:3 do:1 dl:1 spurious:1 compiled:1 de:6 fluid:1 cannot:1 instance:2 nearly:1 n2e:1 during:1 averaged:2 nordlund:2 processes:1 densities:2 arxiv:1 median:1 patch:1 investigate:1 experiments:4 hydrodynamic:1 excesses:1 fixed:1 cells:1 mergers:2 view:1 rms:2 set:1 motions:7 reference:1 frame:1 hα:3 turbulent:8 up:1 observed:11 depends:5 computer:1 radius:5 result:2 kinetic:3 subject:3 c2s:1 phases:2 interacting:1 αx:1 nature:1 symmetric:1 case:5 behind:1 various:1 between:11 αi:1 probably:1 boundary:3 conditions:7 law:1 side:1 notice:1 vertical:8 sections:1 initially:3 supernova:3 however:1 efficiency:2 condensing:1 amez:1 outer:9 configuration:3 suppressed:1 thank:1 both:3 σi:1 cox:3 region:2 conclusions:1 beckman:3 equal:1 rijo:2 σz:2 σx:1 faces:1 pdf:2 contribution:2 σw:11 otherwise:1 detailed:1 macros:1 uniformity:1 afterwards:1 cm:4 bell:3 color:1 ca:1 each:5 corresponds:1 height:1 dimensional:1 active:1 right:1 universitaria:2 cs:21 table:4 dissipated:1 broadening:5 described:1 second:2 addition:2 radiative:1 due:3 been:11 pc:10 much:1 far:2 azimuthal:1 basic:1 expected:4 ph:1 abstract:1 walter:3 obtained:1 direction:2 contribute:1 corresponding:3 thousand:1 formed:1 gas:30 external:4 padoan:2 general:1 diffuse:2 present:2 scaleheight:8 uncertain:4 exponential:1 solid:1 permit:2 empirical:2 profiles:3 supersonically:1 will:4 while:2 compressions:2 situation:1 balance:1 exponent:1 layer:3 find:2 mexico:4 t1:2 thus:6 surface:7 according:1 middle:1 unit:1 itself:1 vortical:1 ambient:4 vx:1 vz:1 selected:1 neutral:1 around:2 capture:1 different:4 develop:1 grant:1 suggest:2 intended:1 pepe:1 same:4 parts:4 units:2 dimensionless:1 several:2 infer:1 difficult:1 independent:1 satellite:1 extended:4 galaxies:7 slightly:2 see:9 kelvin:1 numerical:2 rain:2 hand:1 driven:4 moving:1 hydrodynamics:1 kim:1 identity:1 lower:1 korpi:2 center:2 scenario:1 nevertheless:1 whole:1 well:2 edge:4 allow:1 components:2 dashed:1 alfredo:1 grid:1 model:9 magnetohydrodynamic:1 arising:1 ferguson:2 distances:3 velocities:2 appropriately:1 moments:1 relevant:1 identify:1 shocked:3 using:3 speed:3 previous:1 accreting:2 transonic:1 timescale:1 density:16 fitting:2 nacional:2 apjs:3 source:1 internal:1 inner:1 plumes:1 input:2 blok:3 remaining:1 momentum:1 nasa:1 identical:1 rescaled:1 increased:2 ample:1 iα:2 caps:2 increases:4 five:1 turbulence:13 naturally:1 bistable:1 bottom:1 follows:1 mhd:4 disks:6 zoom:1 specific:1 remind:1 either:1 lose:1 wyse:1 dilution:1 therein:2 because:6 zcl:4 arrows:1 some:4 back:1 examples:1 sight:1 specified:1 images:1 infall:4 separately:1 scale:3 describing:1 l19:1 flux:2 scalo:1 avoid:1 thilker:4 per:6 does:1 linearly:1 provides:1 tends:1 restoring:1 run:10 repository:1 bc:4 equivalent:2 instabilities:2 continuing:2 stellar:2 pressure:7 evolve:1 instability:2 prepared:1 properties:2 franco:2 comparison:1 about:5 central:2 carried:2 extension:2 column:1 discussed:1 dependence:2 o:1 simulation:4 range:2 impacting:1 plus:2 consequently:1 computational:2 presence:2 into:3 putman:5 stratification:1 interstellar:1 three:3 assess:1 included:1 weighted:3 references:3 castro:1 hidalgo:1 undertaken:1 van:2 compression:1 shells:1 astroscu:3 there:5 dispersion:5 width:3 trigger:1 low:4 way:3 was:5 assumes:1 unam:5 function:2 underestimated:1 medium:4 gaseous:2 form:1 latex:1 compressible:1 phenomena:1 amongst:1 principles:1 astro:1 heat:1 quiescent:1 gain:1 mnras:3 line:8 hf:2 infers:1 longer:1 pull:1 infinity:2 circulation:1 gravitational:4 maximum:2 quantitatively:1 placed:2 those:1 continuously:1 distribution:3 panels:1 similar:4 display:1 strongly:1 constant:4 defined:3 certain:2 universal:1 myr:2 deep:1 evidence:2 ap:1 referee:1 exist:2 simulations:6 lifetime:1 thronson:1 proceeds:1 regime:1 again:2 functions:1 compared:1 us:1 no:3 amounts:1 neglecting:1 whereas:3 brandenburg:2 when:5 nx:1 field:5 other:4 dgapa:1 coupling:1 forcing:1 hydrodynamical:1 elements:1 star:4 ballistically:2 models:6 ultimately:1 variation:2 emission:1 runs:3 push:1 important:1 dissipation:1 astronomy:1 structure:2 jones:2 stirred:1 implies:1 outskirts:1 bcd:1 bce:1 v5:1 interval:1 bca:7 bcb:4 bcc:3 depth:1 rcl:10 mass:15 time:4 n0:3 everywhere:1 accreted:2 resolution:2 once:1
0705.0832.txt |@word dualizing:1 gu:1 brunn:1 sci:2 consider:5 maximum:1 skip:1 isotropically:6 brownian:1 results:2 invent:1 2c1:7 leads:3 scalar:1 generalize:1 edu:1 partial:1 remarkably:1 denotes:1 analiz:1 devoted:1 whose:8 pj:2 depend:1 analytic:1 paris:3 technique:2 presents:1 finally:2 does:3 restriction:2 elias:1 under:9 stochastic:1 norm:3 eliminate:2 conjecture:6 random:39 orthogonal:2 far:3 frequencies:1 koldobsky:2 dokl:4 choice:6 brenier:2 corollary:29 valued:2 klartag:3 specific:1 sssr:2 convexity:12 explanatory:1 tracts:1 obvious:1 did:1 noordhoff:1 notes:5 t2:3 applicable:2 t0:90 prob:1 large:4 discrete:1 convenience:1 vector:20 cϕ:1 small:9 eigenvalues:4 markov:1 equation:1 application:2 zn:3 employing:1 neighborhood:1 lecture:6 estimates:11 measurable:5 sign:2 approximation:6 elegant:1 zero:15 normed:1 tangential:1 infimum:2 barthe:1 further:2 requiring:1 substitute:2 linear:3 even:11 established:2 zinn:3 ct0:1 sub:2 ct2:1 fubini:4 section:22 axes:1 uniform:3 version:1 absolute:1 3n:2 above:2 sup:12 deal:2 replaced:4 learned:1 increasing:1 method:1 slabs:1 body:21 compact:1 bi:20 transportation:5 dunod:1 respectively:1 error:1 here:2 lichnerowicz:2 lack:1 desired:3 inversion:1 alone:1 const:1 principle:5 respect:4 z1:3 change:1 κs:1 obtained:1 remark:3 property:3 technical:1 study:1 vectors:3 allows:1 contradiction:1 amount:1 products:1 x4i:1 poisson:1 published:1 domains:5 cˆ4:1 fourier:1 changes:1 york:1 control:1 via:1 useful:2 projection:1 bounds:4 marginal:2 merely:1 explained:1 mech:2 replace:1 logconcave:1 feller:1 rσ:1 apply:11 des:1 establish:1 unit:5 readily:1 derivatives:4 use:9 4u:1 figure:2 would:2 prove:14 remains:2 e1:2 continuous:7 contains:1 negative:6 next:10 vol:6 ψi:4 call:1 therefore:12 bochner:1 associated:1 compactly:3 type:5 entails:3 minor:1 more:6 israel:5 zonoids:1 comparison:1 clearly:4 conclusions:2 validity:1 monotonicity:2 payne:3 appendix:2 everywhere:3 normalized:7 particular:5 known:10 actual:1 hold:4 iii:5 must:2 high:2 springer:5 balls:4 viewed:1 completion:1 recall:3 setup:1 work:2 rθ:1 regularity:2 reproduce:1 values:4 thin:7 learn:1 following:12 arrive:2 ekopa:3 example:3 unconditional:32 proof:42 f0:2 f1:4 f2:5 weaker:3 zeros:1 pushes:2 maxt:2 calculation:1 referee:1 suggestions:2 ann:1 states:2 sphere:2 assumptions:6 o:20 dxi:2 lov:1 sharp:2 distributions:2 guarantee:1 information:2 fn:5 chebyshev:2 rather:2 verify:2 purpose:1 holds:6 american:1 write:18 very:4 hot:3 pure:1 optimal:8 considering:1 map:8 product:1 de:1 petersburg:1 algebra:2 may:26 rm:2 after:1 variant:1 hdµ:1 dx1:5 constraint:1 consequence:2 volberg:2 fits:1 fi:19 sasha:2 arch:2 types:1 goal:1 short:1 convolution:1 sets:5 whenever:3 consequently:12 δi:2 explicit:1 abs:2 element:1 emanuel:1 sj:4 sons:1 so:5 s2:5 integrand:2 order:4 c2:10 typical:3 brehm:2 help:1 ith:4 correlation:2 over:8 dy:2 vary:1 outer:1 stability:1 conclusion:3 already:1 through:2 statistical:1 signs:4 weitzenb:1 existence:3 satisfies:6 poincar:1 milman:5 its:8 before:2 position:1 group:1 symmetry:3 maps:1 fix:12 sη:1 coordinates:4 actually:3 better:3 estimating:1 absence:1 parts:1 condition:2 lp:1 mail:1 hidden:1 main:1 setting:1 highdimensional:1 non:23 good:1 greater:1 integral:7 eitξ:2 runs:1 introduce:1 attains:1 differential:1 2p:6 they:1 acta:1 now:2 wiley:1 densities:4 eigenvalue:17 term:5 finite:4 equality:5 university:3 concave:25 appropriate:2 orthonormal:3 sufficiently:5 inequality:28 l2:6 each:1 done:2 entirely:2 side:3 referred:1 perimeter:1 domain:8 en:2 ei:3 meets:1 gaussian:5 related:8 solution:1 elementary:3 isoperimetry:1 used:6 ey:3 expect:1 measure:19 funct:4 our:10 kannan:2 ep:2 es:2 out:2 category:1 shown:1 matrix:3 space:6 tribute:1 characteristic:1 robert:2 since:24 crucial:2 research:1 looking:1 optim:1 acting:1 rei:2 weighted:1 socalled:1 rational:2 reader:4 denoted:2 formula:2 rn:98 suffices:4 math:25 shows:3 wojtaszczyk:2 provide:2 log2:2 theory:8 localization:1 monotone:1 possibility:1 standard:10 complicated:1 collection:1 org:2 estimate:10 beginning:1 anal:7 log:23 definition:3 dirichlet:4 r2:5 applications:2 geometry:3 cube:3 omit:2 nonnegative:1 length:1 place:2 isotropic:4 hence:21 retain:1 probab:1 onto:1 first:17 origin:3 indebted:1 intuition:1 xi:56 xn:41 graduate:1 probability:6 variables:9 ℓp:1 restrict:1 smaller:6 simplified:1 least:2 another:2 fleury:1 impossible:2 smoothing:1 open:1 appl:1 passes:1 given:5 necessarily:3 reference:1 similarly:1 introduction:3 leading:1 πi:7 system:1 approximately:1 assumption:4 manifolds:1 constants:7 statement:2 tom:1 wasserstein:1 john:1 relations:1 gives:1 free:1 shell:7 sternberg:2 relationship:1 centered:1 recursively:1 exactly:3 eliminates:1 var:1 x8:1 part:3 because:1 dilates:1 x2:3 x0:15 x1:53 than:9 coefficients:2 distance:1 kind:1 desvillettes:1 showed:1 princeton:5 sections:2 second:3 normalizing:1 xi2:9 xi4:2 speaking:1 were:2 rate:1 integer:1 w2:11 conjectural:1 symmetries:3 entail:1 generality:2 membranes:1 topics:2 occupies:1 argument:7 generalization:1 say:7 progr:1 2t0:1 need:4 concentration:7 st:1 any:45 hessian:2 extremal:1 dµ:6 cε2:13 depending:5 general:4 lim:6 latter:3 internat:1 able:2 ideas:1 taylor:3 note:13 instance:5 potential:2 εh:1 interior:2 new:1 nadirashvili:4 subject:1 esaim:1 kac:1 spectral:2 begin:6 towards:1 altered:1 normal:2 vibration:1 4u2:1 who:1 birkh:1 helffer:4 centroid:1 connected:2 edric:1 claims:1 remarks:1 segment:3 pages:1 inequalities:4 workshop:1 deviations:3 especially:1 consequences:1 considered:1 soviet:2 witnessed:1 curvatures:1 exi:3 lpn:1 points:1 reflections:1 exp:13 2ar:1 yann:1 orlicz:2 er:1 quantity:1 precise:2 show:6 decomposition:1 supported:5 russian:3 minimizing:1 relation:2 esseen:7 exploits:1 dimension:3 trivial:2 translation:3 principal:1 q1:7 symmetric:10 ock:1 based:1 schwartz:2 eigenspace:2 distributed:18 enough:4 completes:3 lemma:55 only:8 going:3 factor:1 integrable:1 mechanics:1 ematiques:1 centrally:1 6c1:1 do:2 dm:1 notation:4 means:2 ϕu:1 express:2 expectation:2 yielded:1 dxn:3 joint:2 cannot:3 legitimate:1 dx:15 probably:2 ϕd:2 dt:12 ds:7 regarding:6 qt:1 conditions:1 arxiv:3 yield:2 nκ:1 nauk:2 convolve:1 statist:1 minkowski:1 qi:5 london:2 fixed:1 explanations:1 valid:3 2u:1 λf:1 riemannian:2 satisfy:2 requirement:3 set:10 ser:1 exists:7 banach:1 lnp:1 flip:1 observed:2 mentioned:1 see:26 radius:1 result:6 japan:1 discussions:2 terms:1 ark:6 analog:1 techniques:2 appear:1 hilbert:1 eigenfunctions:9 8a2:1 currently:2 definite:3 functionals:2 tend:2 xvi:4 behind:1 various:2 closed:1 between:6 invariant:1 boundary:18 fields:1 approach:2 law:1 available:4 adv:2 cλ1:1 complementary:1 uϕ:1 attention:1 combining:2 however:5 comm:1 eλ1:11 2pi:8 article:1 amer:3 problem:5 concentrated:2 both:1 σi:10 figured:1 last:1 pisier:1 dario:1 solely:1 taking:1 readers:1 according:21 meckes:1 laplace:1 etc:1 connection:1 geom:4 sudakov:2 berry:7 context:2 variance:1 expression:1 otherwise:6 among:1 english:4 author:1 point:4 simple:4 seems:1 eξ:3 ce:5 dimensional:6 connectivity:1 digression:1 simply:1 cs:2 moreover:4 levine:1 throughout:2 ct:2 pr:4 described:2 transformations:1 basis:5 addition:1 equations:1 θi2:14 laplacian:9 inertia:1 ai:7 belongs:2 logarithmic:1 kronecker:1 expected:1 marginals:1 pi:8 pn:2 abstract:1 empty:2 define:6 suggested:1 direction:4 θi:38 corresponding:10 sydney:1 groupes:1 sufficient:1 subspace:1 cos:10 cambridge:4 else:1 implied:1 observe:4 ormander:4 univ:1 derivative:2 x2i:3 c1:9 denote:26 present:3 case:19 dξ:6 p1:1 simonovits:1 cnα:1 akad:2 value:4 choices:1 will:9 euclidean:3 proves:2 suppose:17 shall:2 many:1 endpoints:1 couplings:3 exponent:1 zumbrun:2 geometric:6 almost:2 thus:14 equal:1 ii:22 reads:1 pajor:1 maximal:1 aspects:5 seem:2 around:1 spaces:1 xj:3 different:1 verified:1 grant:1 finitedimensional:1 suggest:1 iξ:3 admit:1 same:8 orders:2 concavity:3 4c1:11 arguments:1 bernoulli:4 plates:1 proved:3 several:1 dµε:2 higher:1 erausquin:3 independent:12 ball:10 http:2 trivially:1 leonid:2 i1:5 i3:5 i2:7 upon:1 effect:1 hand:3 steps:1 scale:1 a2i:8 sodin:4 cross:2 normalization:2 lower:1 weakly:1 cδ1:6 acknowledgement:1 studies:2 min:3 well:9 analysis:7 without:2 relied:1 coordinate:7 quantitative:1 arising:1 spencer:1 bodies:20 know:2 spherical:4 manifold:1 voigt:2 quoted:1 being:5 accurate:1 λx:1 obtain:2 valuable:1 cˆ:3 abbreviation:1 thanks:1 λd:3 λk:2 spatially:1 comput:1 pγ:1 previous:2 letting:1 rs:3 intersection:1 lebesgue:3 density:30 cε:5 indust:1 auser:1 conclude:9 iϕ:1 exceed:2 improvement:1 iψ:2 other:1 combine:2 advanced:1 easy:2 theorem:42 dµ1:1 ought:1 generalized:1 identical:1 vii:1 2p2:1 eigenfunction:16 stein:1 easily:1 rules:1 nazarov:6 sums:1 tβ:1 describe:1 test:1 preference:1 background:2 press:3 using:2 unique:1 maurey:2 leindler:3 loss:1 like:4 semi:2 follows:9 serves:1 δn:2 cx:1 yields:3 either:1 clay:1 rearrangement:1 works:1 therein:2 sketch:1 right:3 functional:5 neumann:23 classical:7 loosely:1 some:12 back:3 oln:3 self:1 understood:1 deduce:12 acad:2 b1:3 convex:55 elastically:1 treatments:1 proofs:2 provided:1 cp:4 recently:1 dimensions:2 lead:1 cσ:1 demonstrates:1 opposite:1 integration:1 comments:1 manipulations:1 everything:1 magnitude:1 exposition:1 select:1 statements:1 tends:1 borel:6 content:1 proc:2 bobkov:6 minimal:3 refer:2 gratitude:1 biased:1 measures:4 ba:1 strongly:1 intimate:1 uniformly:17 equivalent:1 bo:1 vitali:1 ellipsoids:1 notably:1 how:2 step:4 cξ:3 found:2 villani:4 subtract:1 properties:1 injective:1 guaranteed:1 chapter:5 stokes:3 about:2 ol:1 central:14 usa:1 extension:1 most:6 theorems:3 asz:1 folland:2 stand:3 mccann:2 positive:13 permission:1 mean:1 slightly:1 book:2 functions:5 mathematical:1 soc:6 eφ:2 letters:1 publishing:1 previously:1 boundaries:1 obtaining:1 bound:22 nsf:1 nothing:1 odd:4 square:2 references:3 returning:1 operator:3 additional:3 real:2 few:2 assumed:1 strictly:3 there:12 beitr:1 transform:1 spots:3 u2:3 width:2 much:6 lions:1 way:1 forward:2 analyze:1 was:6 strict:4 asymptotics:1 function:37 isoperimetric:1 complete:9 form:2 simplifications:1 identities:1 3t:1 but:1 idea:3 volume:5 taken:1 illuminating:1 rauch:1 delta:1 convergence:1 line:5 role:1 observation:1 burdzy:3 again:1 ji:5 calc:1 builds:1 society:1 multiplicity:4 smooth:20 up:2 us:3 4v:1 below:2 limit:14 distribution:10 similar:5 called:2 detailed:1 his:3 required:1 constant:30 czechoslovak:1 defined:5 certain:2 universal:25 aj:2 schechtman:3 proven:10 fellow:1 chebychev:1 single:1 ar:15 exist:2 eom:1 θn:8 inf:8 az:1 ostrand:4 dγ:5 computational:1 inc:1 ni:3 nj:2 differentiable:1 seminar:5 no:22 index:2 when:13 vanishes:7 eo:2 power:1 tight:1 interested:1 weinberger:4 details:3 department:1 mathematics:3 trans:1 absurd:1 polar:1 korn:1 etrie:1 models:1 class:1 jerison:2 problems:3 polynomials:1 a1:2 a2:1 bounded:6 chavel:1 nuelos:1 variable:13 proceeding:1 gap:1 max:4 implies:10 coupling:4 dψ:1 assume:21 cauchy:2 age:1 interval:8 quite:1 aε2:14 equivalently:4 cordero:3 mass:4 travaux:1 recherches:1 international:1 n2:1 transports:4 furthermore:2 once:1
0705.0834.txt |@word represent:1 syzygies:1 homomorphism:15 consider:3 results:12 invent:3 four:15 obstruction:1 proposition:1 generalize:1 edu:1 consists:1 follow:1 primes:1 gl:9 contributions:1 equivalences:5 whose:8 heller:2 inverse:1 paris:2 equivalence:9 auslander:7 rightmost:1 th:6 stable:23 syzygy:2 spec:3 applied:1 belonging:3 deforming:1 string:1 very:2 algebr:1 induce:1 splitting:2 corollary:6 every:6 lecture:2 exact:19 deformations:2 condition:2 erdmann:3 irreducible:7 notes:2 t2:2 discrete:1 vector:1 bleher:14 shows:1 smaller:1 oort:2 direct:6 second:3 further:1 odd:3 residue:3 index:1 giving:1 xσ:9 sum:3 xτ:1 above:1 new:3 mazur:1 satisfy:1 edited:1 full:1 led:1 degree:4 respectively:2 component:5 here:1 modular:6 groups:31 others:1 represented:1 strong:1 respect:1 morphisms:5 obtained:1 remark:14 oxford:2 study:1 vectors:5 profinite:2 mx:2 resulting:2 permutation:4 action:2 studies:1 brauer:3 sci:2 quotient:4 schur:1 via:2 useful:2 projection:1 classification:3 replace:2 apply:2 univ:1 use:3 would:2 prove:7 distinct:3 positive:2 contains:2 eσ:6 next:2 almost:16 therefore:1 reciprocity:1 butler:2 associated:2 type:6 more:5 2la:1 under:1 surjection:2 glass:1 berlin:4 particular:9 known:1 projective:5 must:2 keeping:1 isomorphism:18 ma:1 ρd:1 frobenius:2 recall:1 cap:1 stabilizer:1 following:8 primitive:1 trans:2 root:1 example:7 def:2 proof:14 quiver:5 stated:1 arise:1 organized:1 kcg:1 ann:4 involve:1 numbers:2 sense:2 unramified:2 verlag:4 information:1 notation:1 provide:3 acts:2 s4:6 how:2 answer:2 instead:1 ordinary:6 divides:1 map:3 product:1 blocks:17 description:4 fv:3 algebra:11 ζi:1 earlier:2 derived:3 orbits:3 diagram:3 consequence:2 ω2n:2 cambridge:3 representations:8 fm:2 lifting:2 short:19 natural:6 imply:1 whenever:1 lemmas:2 counter:1 explicit:1 fraction:3 green:1 2u:2 representation:9 order:7 restriction:5 over:59 fλ:3 satisfied:1 paper:3 including:1 mentioned:1 satisfies:1 y2:3 its:2 before:1 group:40 thank:2 ext1:2 la:2 summands:3 matrices:1 forms:1 ls:2 radical:2 bouw:1 ωki:1 main:3 deformation:48 maximal:3 them:1 iowa:2 inductively:1 number:3 band:1 kki:3 they:1 h98230:1 nov:1 now:6 discuss:2 2t:2 easily:1 term:5 tensoring:4 homomorphisms:2 always:2 university:3 classified:2 2d:17 each:3 simplified:1 2n:4 few:1 lifted:1 series:2 idea:1 functor:3 elementary:4 literature:1 expect:1 our:2 mat:1 conjectures:2 respects:1 shown:5 space:1 restricted:2 since:27 induces:1 cornelissen:2 denotes:2 rd:6 reformulate:1 rg:2 chinburg:5 rational:1 denoted:1 formula:1 get:1 induced:1 induction:5 math:15 nν:3 fiber:1 theory:9 reformulated:1 free:15 frans:1 completely:1 york:3 ask:2 definition:2 applications:1 phrases:1 sextic:1 turn:2 length:1 hence:14 onto:1 first:4 xi:1 relate:1 conjugacy:2 primary:1 rank:5 restrict:1 lenstra:1 morita:8 least:3 another:2 ring:44 precisely:6 city:1 given:12 table:3 introduction:3 construct:2 their:3 statement:1 structures:1 gives:1 grant:2 completed:1 continuous:4 zν:3 part:5 lehr:1 x2:3 x1:3 completes:1 finitely:17 showed:1 cyclic:4 sections:1 tree:1 namely:2 classes:6 pairwise:5 monomorphism:1 represents:1 descriptions:1 motivation:1 rend:1 involution:1 boston:1 pro:1 defect:13 curves:1 endomorphism:14 say:1 ringel:2 need:3 confirms:1 any:1 viewed:3 studying:1 latter:3 answering:1 note:4 k2:4 k1:2 lifts:10 best:1 so:2 coincide:1 calculus:1 play:1 exactly:2 cosets:2 gν:3 object:3 rickard:1 algebraic:2 pair:4 class:5 tensor:1 kc:8 kg:26 kd:139 considered:1 ki:1 later:1 indd:2 χd:12 χc:12 χb:1 χa:1 section:1 fact:3 saying:1 show:7 supported:1 ending:8 notations:1 d8:3 centralizer:1 flach:1 trivial:56 find:1 principal:1 aσ:12 aτ:12 alperin:3 nonisomorphic:1 basel:1 αc:2 topological:1 should:1 lemma:25 only:6 corresponds:3 local:10 preliminaries:1 abelian:3 klein:4 means:5 de:1 manuscripta:1 fν:9 words:3 progress:1 mgx:1 aν:117 secondary:1 closure:2 runs:3 fields:4 arxiv:1 coproduct:1 nλ:18 she:1 pointed:1 through:3 fixed:1 shapiro:1 set:6 modulo:2 exists:5 module:73 relative:1 y1:3 see:9 sylow:1 result:6 resc:3 discussions:1 sem:1 evenaz:5 theoretic:2 subquotient:2 subject:1 uν:4 said:1 give:1 rings:35 representatives:1 symmetric:2 outside:1 various:2 closed:7 between:4 ωm:1 terms:2 vertical:1 2m:14 were:1 points:2 stably:4 surjects:1 comm:1 key:1 endf:3 endk:1 amer:2 ker:5 endo:44 restrictions:4 cor:1 last:1 many:5 equal:1 inclusions:1 context:1 hσ:3 characterization:1 simple:13 character:10 ca:1 berkeley:1 cg:2 rad:4 dimensional:5 na:2 sequences:5 moreover:10 torsion:2 considering:2 pp:2 described:3 commutative:4 basis:1 three:1 been:3 ai:1 workshop:1 algebras:7 universal:45 define:5 surjective:5 arises:1 general:1 concerning:2 locations:1 maps:1 lift:20 understand:1 mail:1 rephrased:1 evidence:1 case:12 splits:1 originate:1 will:2 proves:2 suppose:14 indecomposable:15 cτ:5 yi:1 studied:1 vd:1 brou:2 carlson:6 thus:5 non:16 n2d:11 ii:20 middle:4 itself:3 dual:2 ia:1 noetherian:3 bν:27 containing:2 idempotents:1 author:2 generic:1 same:2 puig:6 unity:1 vℓ:2 split:23 finite:19 composition:1 φn:1 used:2 dimf:5 trivially:1 dimk:5 hand:1 v0:5 uses:1 auser:1 characters:10 infinite:6 totally:1 identity:1 subgroups:7 off:1 center:1 dade:1 onedimensional:1 well:1 thm:5 components:1 sets:1 arising:1 dimension:3 left:3 obtain:10 sources:1 underlying:2 questions:1 linckelmann:5 homkg:1 resd:16 previous:2 intersection:5 infinitely:3 nilpotent:12 had:1 lattice:1 belongs:1 location:2 easy:1 theorem:14 heidelberg:2 real:2 dihedral:20 isomorphisms:3 possible:2 caps:3 inflation:1 background:1 press:3 using:10 unique:10 poset:1 advanced:1 helpful:1 like:2 follows:28 pries:1 automorphisms:1 either:1 arbitrary:5 smit:1 because:2 classical:1 sequence:37 sends:1 some:13 springer:4 algebraically:7 examples:1 homk:2 homf:3 proofs:1 zariski:1 homc:1 vol:2 dimensions:2 cσ:7 comments:1 prop:3 does:3 summand:3 intersections:4 o0:1 power:1 equivalent:3 cλ:1 uiowa:1 cors:1 fermat:1 relating:1 birkh:1 properties:1 injective:2 quotients:1 integers:1 about:1 extension:5 od:1 covariant:1 a2:1 extensions:4 eτ:6 endotrivial:1 introduced:1 other:3 block:15 morphism:3 soc:17 own:1 inclusion:1 previously:1 nsa:1 into:1 h1:2 gunther:1 isomorphic:32 nsf:1 due:1 lies:3 acad:2 references:1 raises:1 determine:5 operator:2 category:3 comparing:2 there:28 question:8 socle:1 tame:3 quadratic:2 way:2 analyze:2 was:6 naturally:1 witt:5 complete:14 form:15 enough:1 converse:1 construction:1 related:1 true:1 padova:1 applying:1 places:1 whether:3 characteristic:12 welldefined:1 up:8 reiten:6 limit:1 problem:1 similar:2 called:6 proved:3 defined:4 abstract:1 describe:2 deep:1 denote:2 referee:1 exist:1 corresponding:6 oℓ:1 defines:1 no:2 galois:7 whereas:1 when:11 ng:3 field:15 valid:1 role:1 department:1 mathematics:5 sufficient:1 arithmetic:4 rt:1 elements:1 problems:2 a1:1 generated:22 important:1 additionally:1 krause:1 structure:7 source:2 building:1 eν:9 implies:11 address:1 assume:1 factors:1 modules:65 orbit:1 together:2 gal:1 image:1 res:1 n2:13 having:2
0705.0836.txt |@word four:1 sci:2 localized:1 whose:7 feeding:1 ℜe:12 manifolds:1 under:6 conjecture:4 regional:2 every:19 encounter:2 thiele:1 solution:17 convenience:3 vector:1 estimates:24 direct:3 second:16 tangential:9 estimated:1 even:8 established:5 errors:1 hide:4 christ:4 iterating:1 above:17 new:3 contributes:1 coefficient:12 mea:1 mem:2 error:8 equals:10 here:16 diagonal:1 refinement:1 celebration:1 obtained:13 delle:1 elaborate:1 suitable:1 diameter:1 schur:1 replace:10 univ:6 unit:1 derivatives:4 would:2 negative:3 therefore:18 m2:1 indiana:2 type:8 tk:4 warn:1 hofmann:46 correspondingly:1 hold:13 must:3 springer:2 word:1 mc:2 pursue:1 work:3 mq:1 lipschitz:12 root:9 example:2 defer:5 give:2 organized:1 involve:1 indicates:1 advancing:1 absolute:5 end:13 verify:7 significance:1 after:3 salsa:2 arch:1 constants:26 third:1 summing:2 hypotheses:12 green:5 first:39 order:14 restriction:1 over:11 auscher:42 london:1 satisfies:23 before:3 fis:1 fix:15 destroyed:1 hidden:2 maximal:10 them:1 elementary:1 often:2 they:2 each:18 side:24 mean:4 series:4 journ:2 combining:4 rt:55 xq:3 rp:1 rq:2 gradient:4 content:1 erateur:1 reader:6 rn:343 ri:2 independence:13 rk:5 foundation:1 turning:1 linear:3 surveys:1 standard:36 ian:1 estimate:47 publ:3 r0:6 r1:2 r2:27 antecedents:1 already:5 primary:1 restrict:1 caloric:1 similarly:9 perturbations:7 observations:2 variational:1 2an:2 realization:2 serve:1 somewhat:1 finitely:1 distance:2 last:28 roles:2 princeton:6 approximations:1 likely:1 matter:4 fashion:1 mind:1 mitrea:6 seen:2 seem:1 seek:1 forced:1 convenient:2 latter:13 fourier:4 indexed:1 shall:39 denominator:1 involving:2 iterate:1 acknowledgements:1 maria:1 observation:6 partition:1 points:1 notion:1 lewis:1 solutions:21 substituting:1 analogue:3 d2:21 explain:1 integrate:1 constant:20 continuity:10 do:2 dj:1 establishes:1 dh:3 di:18 fractional:3 db:9 dc:2 dz:3 dx:31 dy:40 dt:77 ds:37 dp:3 dq:4 runs:4 bar:3 twice:1 mathematicum:1 transforms:1 riemannian:1 kolmogorov:1 observed:1 depends:2 radius:3 result:13 w0:2 best:1 techniques:1 capacity:3 exponent:5 away:1 supε:1 symmetric:23 c2k:2 approach:4 c2m:2 terms:14 extend:5 mcintosh:3 weak:19 however:2 wt:3 ellipticity:21 extent:1 dualize:1 topology:1 0s:1 essentially:5 conclusions:1 against:2 colloquium:1 contribution:9 con:1 had:3 16t:1 16q:1 conference:5 union:1 three:1 been:10 much:1 ann:5 concerning:6 θr:1 θt:82 applied:6 fubini:1 suppose:63 property:2 procedure:1 jk1:8 jk2:2 iv:27 ii:78 ih:6 ik:2 im:15 cone:4 exterior:4 containing:2 make:2 complex:22 split:5 several:2 fεk:3 european:1 independent:17 unboundedness:1 i1:18 i0:2 i3:3 i2:9 hand:20 kim:35 potentials:77 a2m:4 prescribed:1 weakly:5 giorgi:9 quantitative:5 left:11 just:5 appropriately:1 solvability:22 identify:1 thanks:1 facts:2 previous:8 5q:6 belongs:2 corollaries:1 board:2 easy:11 iτ:3 designate:1 iξ:3 plancherel:5 iε:2 possible:2 possibly:1 boxes:3 unique:6 specific:1 steps:1 schwarz:9 arbitrary:2 gη:3 www:1 right:6 deal:2 truncated:1 cnrs:1 born:1 dense:5 icm:1 umr:1 hodge:4 multipli:1 boll:1 properties:4 meyer:3 chapter:1 numerator:1 o:8 plus:5 slightly:2 duke:2 soc:6 statements:1 bound:64 hermitian:3 refined:1 reducing:1 neumann:7 accretive:1 sup0:2 support:7 subdivide:1 transform:1 editor:1 way:3 austral:2 was:5 form:12 heat:3 true:2 supp:6 supt:19 bounds:16 b1:5 proved:6 fattened:1 convergent:1 proves:2 exist:4 a1n:2 a1i:2 check:1 nj:2 nk:2 integrability:1 no:26 whereas:1 when:7 vanishes:5 interested:1 test:1 nq:1 picture:1 a11:1 cotlar:3 truncate:1 a12:1 ξr:2 uniformly:18 tribution:1 ξn:1 variable:10 lemmata:1 jones:2 assume:4 dτ:6 pseudo:1 dσ:2 together:1 time:1 n2:18 precise:3 global:2 invent:1 dsdt:5 depend:8 efinit:1 graph:2 finally:5 elliptic:31 analogous:7 multilinear:2 supported:11 broadly:1 choice:2 entries:2 solves:7 presented:1 did:1 leave:3 item:1 annihilates:1 recall:14 div:64 upper:8 says:1 dealing:1 measurable:1 riesz:2 sign:1 appear:2 uniform:5 annals:4 satisfy:29 zygmund:9 address:5 along:3 appears:2 change:6 sobolev:3 poisson:3 domains:8 t20:1 deg:2 studies:2 useful:3 convolution:2 extra:1 problematic:1 merely:1 escorial:2 inverses:1 handled:11 working:1 prove:37 sake:3 positive:1 france:1 compactly:2 duality:4 acceptable:1 appendix:3 cases:2 valued:3 tokyo:2 values:1 following:23 making:2 heart:2 4t0:5 allowed:1 verlag:1 regularization:3 s2:2 s1:1 s0:2 berlin:2 orthogonality:1 kenig:21 write:17 criterion:1 fourth:3 optimal:1 allowable:1 parameter:1 product:1 mat:6 may:71 max:1 residues:1 applications:2 cbms:2 divx:11 data:5 2l2:2 natural:1 whenever:17 lemmas:7 yielding:1 su:1 st:1 so:34 definitions:2 sg:2 se:1 canberra:2 indeed:18 stability:1 course:7 differs:1 still:3 group:1 curly:2 sγ:1 interesting:1 toro:2 mail:5 main:10 non:24 conversations:1 introduce:1 half:19 now:66 discuss:8 term:59 drop:1 establishing:1 el:2 domain:6 square:24 gaussian:3 conventions:1 owing:1 shown:2 space:27 furthermore:3 contained:3 rational:1 suggesting:2 formula:3 dominate:2 100r:2 shows:1 reformulation:1 theory:11 state:2 divergence:11 care:2 hc1:1 turn:12 place:3 βm:8 βk:6 origin:1 xi:2 xn:3 symmetry:2 omitted:2 variables:4 approximate:9 soci:1 directly:2 bijectivity:1 open:1 1q:6 given:20 necessarily:1 indicate:1 1b:2 convention:1 continuous:3 proving:4 transverse:2 x2:1 x0:84 x1:1 than:6 coefficients:36 require:3 were:3 decompose:3 topics:3 argument:24 anu:1 say:4 any:6 converges:6 note:20 sciences:2 potential:14 take:5 interior:1 modulus:2 begin:8 sure:1 rellich:1 trace:3 normal:4 arguing:1 1rn:3 falls:2 formulae:4 remarks:1 wc1:3 average:2 later:3 cεn:1 quantity:1 dualizing:1 show:17 spaces:2 aσ:3 enough:35 analytic:4 only:33 explicitly:1 parabolic:4 embeds:1 manuscripta:1 5in:1 aε:6 justified:1 closure:2 regarding:1 pascal:2 yield:3 ut:15 kernel:25 imposing:1 differentiable:1 concern:1 fails:1 satisfying:13 review:1 outside:2 geometric:1 across:2 jt:2 jr:1 jn:2 comm:1 parentheses:1 many:1 region:1 expression:6 among:3 exploit:3 moreover:27 considering:1 better:1 locally:1 dtds:1 combined:3 dtdx:1 caffarelli:4 direction:2 pseudodifferential:1 bmo:1 6q:3 observe:16 former:4 those:4 case:65 trick:1 situation:3 σa:1 middle:2 regularity:6 supremum:4 technology:2 1c2:2 develop:1 author:3 distributions:2 granted:3 same:26 poincar:3 verifies:1 arguments:3 extended:1 trivially:1 delicate:2 invariance:1 tradition:1 d1t:1 coifman:4 definiton:1 without:5 solve:1 coordinate:1 dimension:12 justify:1 eitξ:4 nd:1 resp:3 rest:1 differentiation:1 lebesgue:1 cl:1 seems:2 except:3 smoothness:4 setting:15 treatment:1 extensive:1 real:25 np:1 grid:4 using:18 fabes:6 eitτ:3 either:2 integrals:11 grouping:1 madrid:1 gaffney:1 deduce:8 respect:3 duration:1 2xi:1 provided:4 dimensions:3 eiξ:2 decomposition:5 provides:2 refer:1 radial:1 found:2 tdt:6 ok:7 theorems:9 discussed:1 mutually:1 ξk:1 act:1 op:22 references:2 inverting:1 strip:1 bijective:3 area:1 h01:3 there:16 assumes:2 complete:4 implies:9 pull:3 applying:5 ωt:4 quantitatively:1 3t0:2 define:18 strongly:1 taylor:1 momentarily:5 certain:5 am:4 deep:3 general:7 aq:2 littlewood:5 invertibility:16 au:1 formulation:2 ay:3 controlled:2 gradients:1 ℑm:2 again:13 mathematica:1 valid:2 d2n:3 mathematics:4 briefly:2 symbol:5 a1:21 a0:16 important:1 bounded:20 sulla:1 cauchyschwarz:1 curve:1 having:2 wr:3 missouri:2 original:1 dist:2 consider:30 splitting:4 follow:6 mutatis:1 equivalence:1 tr:9 spirit:1 kα:9 tm:29 tj:1 preserved:1 th:1 ti:1 tf:1 te:10 tb:2 norm:7 straightforward:1 very:1 denoted:4 corollary:9 difference:1 condition:7 t2:60 t3:1 t0:153 t1:95 large:4 small:24 anal:2 neighborhood:1 edu:4 zero:1 pass:1 further:6 diam:1 sub:4 brackets:3 section:22 version:8 sur:1 sup:73 method:6 full:2 b2q:9 strong:4 equations:11 published:2 action:1 specialize:1 via:13 2we:1 family:7 dxdτ:7 establish:15 readily:10 proceed:3 contains:1 ψt:8 subsumed:1 taken:3 minor:1 more:7 operators:37 ital:1 particular:19 known:10 seminorm:1 science:1 equation:4 remain:1 history:2 f0:3 f1:6 f2:4 stated:2 sense:20 dydt:1 respective:2 dyds:13 rather:8 dydx:4 dydz:1 acta:3 simplicity:2 fr:1 fs:2 ft:5 ζi:1 variant:4 mapping:4 fg:1 horizontal:2 fk:2 nonsmooth:4 short:1 departure:1 extrapolation:2 courbes:1 fundamental:10 fδ:9 fε:4 fη:20 held:1 paper:10 ahlt:2 existence:5 concentric:2 cc2:1 its:5 solving:4 actually:2 systems:6 lacey:2 yi:1 good:15 return:3 yn:1 permissible:1 yt:12 2t:80 wloc:1 2q:8 2r:20 2s:3 always:2 inequality:31 2b:3 2c:2 2m:14 2n:3 2j:5 2k:95 reduce:9 idea:3 finish:3 obtains:1 really:1 since:62 induces:1 denotes:16 acting:7 dominated:12 dxdy:1 dxdt:26 induced:1 issue:1 dxds:8 lebesque:1 reformulated:1 ast:1 mmt:4 like:4 difficulty:1 reason:1 calder:10 maths:1 muscalu:1 definition:12 omit:11 nonnegative:1 american:2 consequence:6 cc12:3 indebted:1 2kα:2 number:2 dini:2 done:1 construct:4 differ:1 perturbation:8 introduction:1 least:2 obtainable:1 assumption:4 statement:2 relies:1 st2:2 immediate:3 part:6 consult:1 norms:1 off:3 translation:1 albeit:1 john:1 critically:1 double:4 aah:2 yang:1 fˆ:1 accad:1 treated:5 motivation:1 roughly:1 conjugate:1 jour:1 depending:14 lim:11 self:9 centered:5 k1:2 k0:5 generalized:2 jacobian:1 measures:3 reach:1 most:3 tξ:13 ct2:2 tη:22 clear:2 sometimes:3 km:4 kr:2 ext:5 kp:12 exp:3 kt:25 authors:1 relation:3 find:1 completion:1 cr1:2 parameters:6 fefferman:4 being:1 factor:2 moser:8 triangle:1 invoke:2 ϕt:7 ϕq:20 trees:1 ϕk:17 arxiv:1 remove:2 set:40 unpublished:1 sez:1 collectively:1 see:24 close:2 forthcoming:2 unione:1 uθ:3 uε:8 uη:4 various:1 conditions:3 recently:1 missing:1 complement:1 attention:3 analogues:2 differentiability:1 both:2 cubes:6 improved:2 previously:2 connection:1 context:3 pde:3 point:9 simple:2 corresponds:1 dimensional:4 throughout:3 simpler:1 kernels:4 pp:10 described:1 pt:74 due:3 laplacian:1 strategy:1 ph:1 whitney:4 p2:1 exponential:1 ǫi:3 ǫn:1 deferred:1 while:4 replaced:2 behavior:3 ǫt:1 vol:3 averaging:3 itself:2 triple:3 ready:1 ric:1 emphasize:1 modification:1 development:1 used:27 usually:1 moment:3 uses:2 purpose:1 koch:2 lxi:1 lower:14 older:4 analysis:8 λr:5 λt:10 cǫ0:64 letting:2 cut:2 k2:2 m4q:1 egrale:1 theorem:61 solvable:2 remaining:4 stein:5 showing:2 matters:5 integer:8 bit:1 formal:1 modifications:1 δx:1 semi:1 follows:63 separately:2 continue:1 yields:8 pointwise:1 essential:1 terminology:1 mathematical:4 sketch:1 methods:2 some:35 back:5 b4:2 examples:1 b2:4 b3:2 scale:1 rℓ:1 integration:4 providence:2 proc:2 minimal:1 annular:1 bk:1 bt:1 step:9 bq:19 br:11 integers:2 sharper:3 pε:4 beijing:3 extensions:1 consequently:7 block:3 into:12 integral:17 appropriate:4 ψext:4 degli:1 few:1 u0:29 specifically:1 sections:6 arise:1 gauss:1 properly:1 l2loc:1 us:12 un:1 carleson:13 uk:7 sum:2 continuously:1 4r0:1 similar:15 laplace:2 associated:15 defined:23 specified:1 problem1:1 single:12 analyticity:31 amounts:3 fixing:2 rewriting:1 application:2 priori:5 nat:3 grk:1 nice:4 elements:3 axelsson:33 sided:1 problems:14 utterly:1 gr2:2 gr1:2 required:1 equivalently:1 weights:1 b1q:7 nash:10 requires:2 avoid:1 once:4 gt:8 partial:1 gr:3 funct:1 results:17 steve:1 kato:12 issues:1 compact:2 disposal:4 uniqueness:15 stable:3 ingredient:1 g1:3 continues:1 matrices:6 categories:1 notes:2 noted:1 cfk:2 hk2:4 l2n:3 jump:8 imply:2 concludes:4 zt:10 invertible:4 3r:1 3q:1 analogously:1 3t:1 3m:3 capital:1 3b:1 3a:1 degree:1 respectively:10 desired:13 les:1 implicit:2 deduced:2 remark:5 technical:3 larger:3 resulting:1 ctm:1 makes:1 boundedness:19 named:3 ii1:7 ii3:2 ii2:7 limr:1 limt:1 ϕ2k:13 hardy:2 apply:6 tchamitchian:3 use:21 andreas:1 usa:1 remains:14 next:13 classically:1 hiding:2 dxt:1 becomes:1 normalized:1 iii:45 balls:1 integrating:6 pour:1 ch2:3 proof:89 control:5 dn:67 lσ:5 pieces:1 assumptions:22 pulling:1 tao:1 notation:10 pure:1 holds:14 paley:4 de:12 singular:17 conormal:4 counter:1 correspond:1 element:1 lε:5 spain:1 lγ:1 allow:7 hardylittlewood:1 discussion:2 vmo:1 torino:1 produces:1 altogether:1 interpreted:7 including:2 mentioned:1 mod0:1 kp2:5 outer:1 decay:2 chosen:4 ll:1 dispose:1 lw:1 lu:22 ls:1 derivative:5 lx:1 greater:1 mention:1 dirac:3 university:3 identified:1 sufficiently:13 l2:211 l0:23 l1:64 traces:2 constraints:1 homogeneous:2 erisque:1 apologize:1 related:2 operator:36 factorization:1 measure:13 our:45 special:5 category:1 matrix:28 m2q:8 stud:1 m2k:3 lecture:2 suffices:12 integrated:1 math:33 limη:1 ψdx:1 completely:1 8t:1 dirichlet:7 could:1 times:1 length:7 hence:8 manuscript:1 iht:1 precisely:3 publication:1 adjoint:17 system:2 relations:2 their:4 final:1 reversed:2 exactly:2 july:1 completes:1 cmcm:4 limiting:2 claim:22 ss:1 subsequence:1 collecting:2 curves:1 harnack:1 need:9 clearly:2 viewed:1 mappings:1 min:9 pursued:1 mechanism:1 εk:1 calculus:2 lectures:4 unless:3 centre:1 but:29 preliminary:1 device:2 class:7 fjk:10 consequences:2 stronger:2 proceedings:2 fact:23 12k:5 12q:2 rough:1 pipher:8 principal:1 based:1 knowledge:1 should:2 lemma:175 local:8 preliminaries:1 cube:17 handle:11 means:1 familiar:3 dyadically:1 qt:16 differential:3 expansions:1 contain:1 cℓ:10 fixed:9 view:1 modulo:9 constructing:1 exists:12 notational:3 national:1 dyadic:7 fatou:2 nature:3 written:1 identification:1 routine:1 invariant:1 boundary:27 perfect:1 transpose:1 w01:9 hypothesis:9 key:1 amer:5 lu0:1 hits:1 limits:4 taking:9 equal:1 etc:2 otherwise:4 ck:6 cj:1 ch:3 co:3 cn:14 cm:19 conclude:5 harmonic:14 cr:7 cq:1 ct:28 addition:11 ai:14 cauchy:19 treat:14 choose:5 corresponding:19 sufficient:1 subspace:1 bull:1 c2:30 c1:4 c0:51 present:12 hmc:3 splits:1 ap:1 value:14 will:32 layer:91 almost:1 vi:8 thus:49 vt:7 dual:2 claimed:1 φt:4 generic:2 cross:1 unity:1 parts:9 adjointness:1 fkp:5 cjs:1 finite:2 ball:4 http:1 4ct:1 upon:7 identity:14 mech:1 recourse:1 center:1 well:10 sets:1 arising:1 usual:11 obtain:55 underlying:1 adv:1 preprint:3 density:4 semmes:2 c13:1 semigroup:1 adj:16 identical:3 dahlberg:2 five:1 press:5 immediately:6 tl:1 necessary:2 helpful:1 c1m:1 alternatively:2 δm:3 works:1 italian:1 because:1 classical:5 smoothly:1 polynomial:1 growth:2 choosing:4 proofs:2 cψ:3 cρ:1 cφ:1 manipulations:1 does:3 summand:4 assuming:1 psud:1 ensures:1 although:5 cβ:2 cη:7 cε:6 cδ:4 about:1 extension:3 dependence:1 angeles:1 a2:2 introduced:2 converging:1 letters:1 h2:2 h3:2 washington:2 functional:4 en:7 appl:2 inner:1 function:17 hr:10 sequel:7 ht:5 volume:1 hk:2 construction:5 convergence:19 truncation:1 wise:1 society:2 whether:2 wish:1 smooth:8 below:4 limit:6 problem:19 bearing:1 int:1 denote:30 inf:1 identities:2 functions:12 ematique:1 other:10 details:11 mass:1 conclusion:11 star:2 jerison:7 caccioppoli:14 rule:2 4k:1
0705.0837.txt |@word transitions:1 angles:1 lagrangian:1 magnetic:2 lack:2 focus:1 four:1 scalar:2 edu:1 contributions:1 consider:1 γx:1 behave:1 tk:1 fermionic:2 case:5 amplitudes:2 straightforward:1 very:5 differently:1 wave:2 m2d:2 electron:21 wavy:1 summarized:1 experimentally:1 converge:1 nio:1 feeble:1 cheung:1 accompanying:1 evaluation:1 vector:12 enjoy:1 upper:1 smaller:1 unpolarized:2 sign:1 past:1 zero:1 unparticle:29 further:1 odd:1 tev:13 subscripts:1 aim:1 what:2 appear:1 d3:1 current:2 axial:3 above:1 fractional:1 3c:1 new:5 contrast:1 body:4 simultaneously:1 respectively:3 here:2 hundreds:2 ranges:1 reported:1 china:1 study:1 studied:2 prior:1 resonance:1 narrow:1 makes:5 ratios:2 scales:4 ecp:1 total:1 conventional:1 projector:1 working:1 remains:1 few:4 nucl:1 m2:1 theoretical:3 diagrams:1 more:3 operators:1 normalized:1 known:1 must:4 md:10 work:3 cancellations:1 theories:2 obvious:1 following:4 weaker:1 challenging:2 figure:1 high:5 lorentz:1 numbers:1 allowed:1 occur:1 goal:1 rather:1 how:3 nontrivial:1 instead:1 ordinary:6 sin:5 simplicity:3 may:2 br:6 explored:1 data:2 attempt:1 effective:8 lines:1 cannot:1 so:4 banks:1 gµν:1 origin:1 remnants:1 move:1 mainly:1 years:1 experiments:1 through:1 argued:2 its:1 symmetry:1 decay:10 energies:1 interesting:1 boson:1 systems:2 might:4 yi:1 them:2 combination:1 orthopositronium:3 polarizations:2 investigated:1 scaling:6 mention:1 effects:4 they:6 now:3 channels:1 university:1 evade:1 2d:11 found:4 mean:1 em:1 differential:2 energy:16 hard:1 idea:3 decays:15 entering:1 measurement:1 our:5 avoided:1 eq:1 out:1 shown:1 space:1 tianjin:1 clade:1 since:3 interference:1 particles:5 mediated:1 rb:1 denoted:1 ref:11 integrated:1 i2:3 theory:4 eca:1 interactions:5 divergence:1 standard:3 ecs:1 imagine:1 finishing:2 interaction:2 dubbed:1 could:2 times:1 corrections:2 assign:1 exotic:8 peculiar:1 gabrielse:1 number:2 restrict:1 georgi:6 directly:1 precisely:4 angular:2 checked:1 exists:1 πd:5 similarly:1 unitarity:1 unknown:1 interact:4 phenomenologically:2 system:1 least:1 their:3 assumption:1 rates:4 calculations:1 final:2 recovered:1 gives:1 shell:4 continuous:1 transverse:3 constituent:1 than:4 badertscher:1 double:1 rate:3 matter:6 states:1 determined:1 contrary:1 were:2 contrasted:1 symmetries:1 explicit:1 spectrum:1 seen:1 any:2 depending:1 latter:2 responsible:2 note:3 instance:1 fitting:1 potential:1 generalized:1 even:2 though:1 most:6 involving:1 phase:1 intrinsic:1 branching:2 deviations:1 observation:1 surprising:1 considered:2 clear:1 later:1 implications:3 electrons:1 γup:2 constrain:2 physics:5 momenta:1 particularly:1 confront:1 probe:1 infrared:2 iǫ:1 λp:3 relation:1 keywords:1 d4:4 fine:1 find:1 ground:1 based:1 elucidated:1 should:2 only:5 dominant:1 familiar:1 perceive:1 ones:1 dx:2 processes:3 fields:3 arxiv:5 common:1 qk:1 fixed:2 transversality:1 monochromatic:1 set:2 computed:2 fascinating:1 sep:1 up:6 detection:3 differs:1 see:1 result:3 recently:3 λi:1 phases:1 interacting:1 distinctive:2 definite:1 state:6 between:1 tens:3 invariant:2 luo:1 preserve:1 terms:1 positron:1 missing:1 however:1 positronium:13 invisible:12 atoms:1 suggested:4 observable:1 last:2 limits:1 region:2 uncertainty:1 against:1 sensitive:1 exceeds:1 passing:1 comes:1 among:1 relevant:2 cn:1 point:1 appeared:1 ca:2 cs:8 cp:4 cv:5 pseudoscalar:1 ps:24 unusual:1 collider:1 kinematic:1 due:5 been:3 much:1 ph:5 fig:3 describe:1 corresponding:2 quantities:3 photon:7 coincides:1 systematic:1 demand:1 c2:2 general:1 spin:3 former:1 those:2 p2:16 p0:5 p1:5 conception:1 look:1 pacs:1 solid:2 ǫj:1 ǫi:2 evaluated:1 will:7 while:7 behavior:1 couplings:4 loop:2 phenomenological:2 thus:4 ia:10 limit:3 orbital:1 funny:1 different:1 lett:7 same:1 arguments:1 several:1 higher:1 independent:2 used:3 imply:1 numerical:2 upon:2 counterparts:1 parametrized:1 moment:2 changing:1 invariance:1 yuan:1 identity:1 recent:1 lower:2 weakly:1 scenario:1 pµ:1 well:2 analysis:2 patterns:1 experimental:2 consistency:1 dimension:6 λs:4 muon:2 stringent:5 λv:3 b196:1 being:2 when:1 λa:2 underlying:1 world:1 flavor:1 nonintegral:2 polarization:3 density:4 photons:2 nonrelativistic:1 signals:2 reasons:1 setting:1 combine:1 attractive:1 input:1 remaining:1 momentum:4 take:1 real:2 depends:1 phenomenology:1 couple:1 results:1 possible:1 increases:1 descending:1 know:2 using:3 necessary:1 like:3 particle:6 exploiting:1 yields:1 integrals:1 follows:1 become:1 δa:1 exceed:1 because:1 qed:4 some:3 ourselves:1 provided:1 scale:6 dimensions:1 normal:1 integration:3 does:1 demonstrated:1 illustration:1 step:1 odom:1 although:2 accommodated:1 described:1 properties:2 asai:1 about:2 zaks:1 constraint:5 kinoshita:1 anomalous:1 dependence:1 o:16 pν:1 range:3 plus:1 stand:1 constraints:2 considerations:1 rev:9 previously:1 into:2 22d:5 bound:6 three:2 eqs:2 appropriate:1 references:1 determine:2 proportional:1 bosonic:1 mere:1 rely:1 hep:5 measured:7 there:2 h06:3 restricts:1 detectable:1 low:3 was:1 propagator:2 function:2 attempted:1 lint:1 keung:1 but:3 sophisticated:1 pµν:1 neutral:2 delta:1 removed:1 he:2 zhu:1 whether:2 uv:7 attached:1 bounds:9 us:2 assume:3 below:2 accustomed:1 ua:2 aa:4 constant:1 ad:16 certain:1 abstract:1 contribute:2 denote:1 ap:4 single:2 nankai:2 av:6 identities:1 dγ:4 physical:1 again:2 functions:2 beyond:2 weakened:1 no:5 dashed:1 generally:2 field:2 other:5 details:1 papers:1 department:1 compete:1 massless:1 separate:2 parities:2 structure:1 ago:1 implies:1 unparticles:22 dω:1 dφ:1 kˆj:1 factors:1 together:1 4m:3 mass:7 time:3 far:5 4d:1
0705.0838.txt |@word limited:1 gs:2 angles:1 global:10 rod:1 results:3 leads:1 roy:2 ge:1 hennig:1 entropy:2 ga:2 go:1 sci:1 contributions:1 voter:2 depend:2 perature:1 g2:1 very:4 activation:11 ǫa:8 electron:1 every:1 difference:1 exact:1 vibrational:1 level:1 ref:1 large:4 small:5 reliable:1 configurations:1 strongly:2 smaller:3 neighborhood:2 tem:1 foundation:1 miller:1 approximation:6 likely:5 christensen:1 qualitatively:1 dynamics:7 chem:7 linear:4 blue:1 rate:2 morse:5 giving:1 selected:1 contributed:1 current:1 experiment:1 diaz:1 goes:2 values:4 increasing:1 method:2 contrast:1 led:1 notions:2 arb:2 respectively:1 here:1 atoms:10 directions:1 path:3 along:4 strong:1 obtained:2 hansen:1 parameters:1 study:3 larger:2 resulting:1 plotted:1 followed:1 scales:1 visible:1 santini:1 surmount:1 total:1 unit:2 plot:2 visit:1 negative:1 call:1 therefore:2 lennard:8 taken:1 jacobsen:2 more:16 started:1 brings:1 curvature:4 everywhere:1 particular:1 cases:2 md:20 crosses:1 cluster:12 science:2 originally:1 averaged:2 crossed:1 following:2 making:1 trans:3 averages:2 scatter:2 figure:2 calculation:1 dahl:3 high:8 minimum:31 sense:2 distinguishable:1 jensen:1 axis:1 needs:1 end:2 eng:1 holds:2 negation:1 chemical:4 how:1 varies:1 instead:1 product:2 de:1 may:1 after:2 derived:1 different:1 connects:1 barriers:3 physik:1 cambridge:2 drastic:1 computation:1 data:3 constants:1 imply:1 lines:2 green:1 fundamental:1 correlation:4 subsequently:2 order:2 bins:1 over:6 already:1 london:1 statistical:1 hypersurface:1 kinetic:6 its:2 before:6 onsson:1 kress:2 rapidly:2 thank:1 la:1 energies:10 decreases:1 actually:1 better:2 attraction:13 fig:33 derivative:1 might:1 versus:2 them:1 good:3 university:1 parabola:3 practice:1 runs:3 functional:1 wiley:1 easily:3 reasonably:1 realistic:2 magnitude:1 stopped:1 each:2 crossing:1 found:7 universit:1 energetically:2 bond:1 reactions:1 schemes:2 financial:1 significantly:1 energy:63 ea:4 approximates:1 eb:4 connect:1 entering:1 quantum:2 our:8 approximated:1 summary:1 out:1 shown:2 matrix:1 driving:1 since:3 rev:6 research:1 increase:1 internet:1 catal:2 xu:1 evaluation:1 red:1 shows:4 foreground:2 numerical:1 theory:1 barrier:6 interactions:4 discontinuity:1 free:7 base:1 complicated:1 york:2 nørskov:3 put:1 shortest:1 pairs:1 interaction:1 derivation:1 geometry:3 starts:1 transition:4 times:1 silicon:3 introduction:1 length:1 hence:1 first:2 initial:3 mousseau:2 evans:9 number:15 reaches:1 done:1 least:1 another:3 force:4 size:2 given:2 publication:1 start:1 goedecker:4 dft:1 crossings:4 system:5 relations:1 heights:1 their:1 too:1 calculations:1 molecular:8 final:2 gives:3 shifted:1 exploring:1 hypothetical:1 centered:4 released:1 argon:1 part:2 believe:1 than:12 relative:1 scheme:3 rugged:1 see:2 states:1 determined:1 yang:1 were:6 visited:11 bep:9 umrigar:1 delley:1 alonso:1 mater:1 unlikely:1 seen:3 orders:1 hessian:1 lie:1 zero:1 check:1 responsible:1 k2:2 k1:2 potential:15 take:1 forces:1 finding:1 even:1 any:1 who:2 reach:1 coordinate:4 pair:1 hu:1 extremely:1 kb:2 considered:1 kj:1 calculated:3 partition:2 implications:1 counted:1 traditional:1 points:10 principle:30 exp:2 mechanical:2 physics:1 fact:3 precise:1 doye:4 show:3 random:1 kwon:1 attempts:1 relation:7 find:1 des:1 based:1 dividing:2 basel:2 state:7 only:4 going:2 molecules:1 local:32 pointed:1 achieve:1 do:1 notation:1 distance:1 landscapes:1 simplest:1 foremost:1 new:3 richards:1 liu:1 qs:3 consisting:1 arxiv:1 gbi:3 qa:1 switzerland:1 fixed:4 set:1 ser:1 national:1 lett:3 chemisorption:1 observed:2 namely:3 computer:1 hammer:2 wonder:1 probable:1 subsequent:1 surmounted:1 consequence:2 importance:1 behind:1 various:1 between:11 approach:1 bromberg:1 terms:1 initially:2 comp:1 steepest:1 however:2 article:1 bulatov:1 reaction:14 many:2 region:4 density:1 chosen:1 context:4 minima:33 point:2 basins:6 harmonic:1 height:1 dimensional:2 simply:1 wider:1 faraday:3 considering:1 described:1 union:1 trajectory:12 due:2 been:2 hellmann:3 much:3 treat:1 expected:1 ph:1 systems:4 direction:1 partly:1 normand:1 both:5 sufficient:1 subspace:1 modelling:1 gai:5 clusters:6 wales:5 denote:1 present:3 exception:1 solid:3 straight:1 value:2 will:7 optimization:6 replaced:3 property:2 ekin:15 thus:3 surface:13 middle:1 containing:1 bollinger:1 verified:1 descent:1 perform:1 things:1 make:1 cross:5 same:2 mole:1 shorter:1 catalysis:1 several:1 higher:1 extended:3 swiss:1 closest:1 trajectories:14 hand:1 kim:1 potentials:1 lower:1 weakly:1 modes:1 hopping:2 well:2 without:1 components:1 gsi:3 quantitative:2 chemistry:2 left:1 velocities:1 just:1 decreasing:1 accurate:1 actions:1 parabolas:8 atomic:1 succeeding:1 accepted:1 tight:5 wei:1 16k:1 reasons:1 valid:6 treatment:1 adn:1 gave:1 optimizations:1 marcus:4 combination:1 background:3 mol:2 press:1 using:5 intersection:3 adams:1 melting:1 mhm:6 like:1 success:1 performing:1 steps:1 dissociative:1 served:1 downward:1 inter:2 stationary:1 reduced:1 right:1 often:1 classical:1 escape:2 lead:5 demonstrates:2 recorded:1 does:1 connecting:1 proc:1 says:1 jumps:1 stefan:1 agreement:1 become:1 plots:4 bahn:1 central:1 saddle:6 simul:1 simplification:1 henkelman:1 soc:4 computational:2 into:14 within:4 numerically:1 bound:1 getting:1 proportional:1 binding:5 statistics:1 institut:1 support:1 there:3 strict:1 quadratic:1 low:19 way:4 forward:1 slopes:1 was:8 function:4 considerably:1 form:1 epsilon:2 but:7 histogram:1 lowered:1 barkema:1 delta:2 true:2 basin:13 whether:2 up:1 us:2 ur:1 below:1 limit:1 neighboring:1 continuously:1 similar:1 average:3 expect:1 bell:7 dill:1 constant:1 certain:2 moved:1 general:1 examine:1 journal:1 moves:1 proceeds:1 no:1 edwards:1 when:3 field:4 other:2 becomes:1 energetic:1 garland:1 models:1 exothermic:1 time:3 visits:3 generated:1 important:1 validity:2 jones:8 implies:2 requires:1 interval:1 together:2 having:2 lying:1 searched:1 starting:2 original:2 once:1
0705.0839.txt |@word gt:4 sci:2 consider:4 funct:1 global:1 results:5 steve:1 generalize:2 kato:7 depend:1 analytic:1 providence:1 graph:2 tn:8 finally:4 ℜe:2 tk:1 elliptic:17 under:1 analogous:2 norm:1 conjecture:1 straightforward:1 regional:1 corollary:2 condition:2 solves:2 t2:7 solution:10 t0:3 ri:1 vector:4 math:12 science:1 small:9 div:3 edu:2 estimates:2 jump:1 imply:1 tangential:4 bilinear:9 employ:1 hide:2 appear:1 ct2:1 section:6 uniform:1 annals:2 sur:1 above:3 sup:28 new:2 method:2 exercise:1 satisfy:2 full:2 mem:2 respectively:1 modify:1 equals:1 here:3 l21:3 desired:2 les:1 address:1 equations:8 implicit:1 change:3 obtained:2 remark:2 sobolev:2 technical:1 larger:2 poisson:4 disposal:1 domains:3 boundedness:3 family:1 extra:1 limt:1 hardy:1 escorial:1 tchamitchian:2 establish:1 unit:2 derivatives:1 use:10 handled:1 usa:1 prove:5 remains:1 uniqueness:1 next:2 therefore:4 associated:2 compactly:1 type:1 more:2 sort:1 formally:1 becomes:1 operators:10 parabolic:1 hofmann:14 virtue:1 known:3 hold:2 iii:3 seminorm:1 valued:3 mc:2 integrating:1 recall:4 equation:2 work:1 pour:1 infinitesimal:2 www:1 lipschitz:4 following:6 posing:1 root:3 proof:6 continuity:2 organized:1 pulling:1 allowed:1 asociated:1 end:1 dyds:1 int:1 torino:1 american:1 kenig:4 write:2 acta:2 product:1 mat:3 singular:3 may:7 maz:1 variant:1 mapping:1 consequence:1 cbms:1 divx:2 summarize:1 data:3 mal:1 constants:2 nonsmooth:1 conormal:1 slightly:1 departure:1 hypotheses:7 extrapolation:1 so:4 fundamental:2 definitions:1 order:6 dx:18 indeed:1 vary:1 stability:1 held:1 auscher:4 paper:1 london:1 satisfies:11 dt:14 fis:1 sγ:1 42b20:1 42b25:1 parts:3 cǫ0:4 derivative:1 main:4 lacey:2 maximal:3 non:4 yn:1 ya:1 washington:1 half:1 now:5 discuss:1 2t:23 term:8 finite:1 2r:3 identified:1 d3n:1 sufficiently:4 inequality:8 l2:28 l0:1 each:3 found:1 side:6 mean:2 homogeneous:1 el:1 domain:4 square:4 series:1 gaussian:1 t3:1 society:1 measure:1 our:6 special:4 rt:6 precisely:1 matrix:7 space:5 gradient:2 since:2 denotes:5 acting:3 dominated:2 erateur:1 reader:1 dxdt:8 rn:76 suffices:1 integrated:1 independence:3 foundation:1 turning:1 theory:2 divergence:9 given:2 standard:4 estimate:8 publ:2 anal:1 r4:1 definition:2 dirichlet:4 r2:4 omit:2 times:1 length:2 hence:2 first:7 xn:2 kim:2 kernel:4 bijection:1 variables:1 iv3:2 u0:3 another:1 bijectivity:3 several:1 inapplicable:1 perturbation:1 adjoint:4 indicate:2 manifolds:1 convention:2 continuous:1 coifman:1 x0:6 than:2 coefficients:9 showed:1 double:2 require:3 drift:1 depends:1 accad:1 ann:1 mind:1 argument:1 meyer:1 conjugate:1 seen:1 any:1 viewed:1 generalizes:1 depending:2 lim:3 latter:5 converges:3 note:3 instance:1 potential:3 courbes:1 techniques:1 even:2 unless:1 rellich:1 shall:8 multipli:1 measures:1 systems:1 2tk:6 representation:3 nothing:1 acknowledgements:1 considered:1 proceedings:1 kt:4 usual:3 precise:3 show:3 lewis:1 supported:2 spain:1 spaces:1 solutions:7 analogue:2 3t:2 d2:5 july:1 pipher:2 completion:1 dividing:1 enough:4 fefferman:2 lemma:15 only:5 corresponds:1 factor:1 integrate:1 dn:2 do:1 notation:2 de:4 dc:1 manuscripta:1 solvability:1 aforementioned:2 dy:4 hermitian:4 ds:2 arxiv:1 fixed:5 riemannian:1 coefficient:6 set:4 modulo:1 exists:3 smooth:2 national:1 see:4 result:11 terms:4 subject:1 satisfying:1 fatou:2 its:1 symmetric:4 state:1 boundary:10 across:1 recently:2 mcintosh:2 transpose:1 analogues:1 densely:1 ellipticity:4 amer:3 both:1 cubes:2 last:8 context:1 pde:1 expression:1 otherwise:1 cn:3 cl:1 ca:1 harmonic:5 dimensional:2 moreover:4 second:3 semigroups:1 pp:2 described:1 pt:3 basis:2 addition:1 locally:1 laplacian:1 strategy:1 defined:8 lu:8 treat:1 define:3 direction:2 corresponding:2 concerning:4 observe:2 whitney:2 mail:1 c0:1 present:2 case:10 mitrea:2 harder:1 value:3 will:3 suppose:15 delle:1 layer:11 vol:1 thus:6 vn:6 iv:3 ii:4 middle:1 regularity:3 cone:1 exterior:1 author:2 generic:1 problems:3 same:1 poincar:1 complex:10 split:1 proved:1 wloc:3 independent:4 used:5 http:1 i1:1 published:1 upon:2 hand:3 uses:1 iv1:3 iv2:2 potentials:8 tradition:1 identity:3 lower:1 weakly:1 giorgi:3 older:1 well:3 definiton:1 analysis:2 dimension:3 left:3 obtain:6 underlying:1 thanks:1 facts:2 previous:1 preprint:1 classification:1 generator:5 sciences:1 seems:1 egrale:1 maxi:1 board:1 theorem:33 semigroup:5 adj:2 real:4 stein:3 isomorphisms:1 dahlberg:12 boxes:2 using:4 bit:1 unique:4 like:1 follows:3 continue:1 yields:1 schwarz:2 integrals:1 conclusion:1 terminology:1 italian:1 mathematical:2 sketch:1 right:1 classical:1 shen:1 some:6 back:1 born:1 deduce:3 choosing:1 respect:1 dimensions:1 opposite:1 hodge:1 efinit:1 assuming:1 proc:1 refer:1 conference:3 tdn:1 uniformly:3 step:4 tdt:2 about:1 extension:1 theorems:2 whence:1 plus:2 2k:16 consequently:2 block:1 op:1 soc:3 statements:1 into:2 integral:2 bound:4 sulla:1 appropriate:1 en:7 lieu:1 operator:7 degli:1 there:4 question:1 approximate:1 cauchy:4 inner:1 way:1 was:2 combined:1 function:4 form:11 sequel:1 but:1 heat:2 construction:1 he:1 made:1 applying:1 supt:2 bounds:2 differentiable:1 momentarily:1 un:1 carleson:3 problem:10 laplace:1 strongly:1 bearing:1 taylor:1 constant:4 af:2 ai:2 deep:1 general:1 littlewood:1 single:3 invertibility:3 dδ:1 again:1 functions:3 analyticity:2 us:1 no:8 mathematica:1 when:1 green:1 application:1 setting:3 details:3 nat:1 d2n:3 mathematics:2 nice:1 briefly:1 denote:5 axelsson:1 symbol:2 vertex:1 includes:1 a0:5 bounded:2 variable:7 structure:1 independently:1 implies:1 caccioppoli:5 established:1 having:1 missouri:2 nash:3 original:1
0705.0840.txt |@word neighbors:3 dist:1 consider:12 gq:20 jǫ:3 splitting:2 steve:1 proposition:7 edu:1 follow:1 children:16 whose:2 depend:2 tr:80 finally:2 ℜe:2 those:1 elliptic:2 analogous:1 tb:1 dxdy:2 case:7 implicitly:1 regional:1 every:10 difference:3 condition:5 leads:1 thiele:1 12q:1 suffices:3 tokyo:2 t1:1 leave:1 discrete:9 convenience:1 bq1:65 small:2 1r:4 martingale:2 neighborhood:2 dealing:1 estimates:4 direct:1 zero:2 nonhomogeneous:1 concludes:3 further:2 canonical:2 established:2 christ:5 sum:7 abk:6 enjoyed:1 abq:1 version:5 3n:3 above:6 sup:5 suppose:10 contrast:1 satisfy:5 respectively:1 applies:1 equals:1 b2q:19 desired:6 zygmund:19 address:1 along:1 ntv:2 observing:1 appears:1 box:1 remark:2 technical:3 leaves:1 larger:1 allows:1 ekb:12 p2:1 amount:1 published:1 studies:2 cancellation:1 boundedness:4 schur:2 via:3 useful:2 mail:1 family:2 claim:1 namely:3 replace:1 hardy:1 summation:1 apply:2 establish:4 readily:2 use:4 proceed:2 working:1 lemma:43 recalling:1 contains:2 next:6 linear:1 therefore:10 associated:4 cδ:4 more:7 duality:1 operators:22 hofmann:15 particular:2 known:4 hold:1 iii:11 must:1 rδ:3 mg:3 mb:5 science:1 ch2:2 mq:1 lipschitz:1 following:11 averages:1 example:1 proof:36 control:4 defer:2 f2:4 theorems:3 triple:1 give:4 sense:2 tao:1 absolute:1 end:6 dh:1 verify:4 holds:5 dydx:1 regions:2 need:3 paley:1 adjacent:1 acta:1 allowable:1 ancestor:1 parameter:1 either:1 simplicity:1 fs:3 mat:1 singular:5 may:13 earlier:1 variant:2 mapping:1 collection:3 dc:1 hence:4 cbms:1 volberg:1 fj:5 constants:3 2l2:3 third:1 whenever:1 combining:3 dilate:1 summing:5 st:2 hypotheses:4 perform:1 extrapolation:1 so:18 transposes:1 representation:1 indeed:3 over:13 altogether:1 satisfied:1 auscher:4 enumeration:1 satisfies:7 cc2:6 its:5 before:2 perfect:6 write:5 chosen:3 fix:5 absence:1 trick:1 lr:1 systems:1 lp:1 lq:1 covered:1 main:2 lx:1 maximal:2 non:6 good:11 return:2 washington:1 runs:6 introduce:2 jα:2 13q:1 tails:2 they:1 yq:3 now:33 discuss:2 nor:1 rµ:1 term:24 2p:4 2q:17 verifying:1 university:2 2d:13 sufficiently:1 inequality:6 l2:55 l1:3 found:1 2n:2 side:6 2j:4 2k:2 subset:1 domain:1 square:3 another:1 ek:83 generation:1 series:1 related:2 society:1 extended:1 measure:2 our:13 extract:1 large:1 rp:6 rq:3 furthermore:4 since:27 denotes:4 contained:2 dominated:3 adapt:1 reader:1 formula:1 rn:14 supports:1 ri:1 math:7 foundation:1 lebesque:2 theory:2 localization:1 upon:1 divergence:2 standard:18 calder:9 estimate:15 muscalu:1 definition:23 hg:1 ζq:17 omit:5 mathematicum:1 turn:5 length:2 consequence:1 adjoint:1 first:9 symmetry:1 omitted:1 variables:1 1q2:1 number:2 2p2:1 done:1 calderon:11 enumerate:1 ring:1 precisely:3 1q:89 1p:6 given:7 qµ:3 exists:3 similarly:5 top:1 system:1 least:6 1a:1 their:1 1b:2 listed:1 convention:2 normalization:2 assign:2 treil:1 relationship:1 continuous:1 measurable:1 part:2 completes:3 coefficients:2 bek:1 princeton:3 double:3 second:4 matter:1 elementary:1 future:1 publ:1 treated:1 decompose:3 fashion:3 entail:1 unchanged:1 argument:5 curves:1 say:3 disjoint:1 seen:1 apparently:1 any:5 min:1 general:2 convenient:2 self:1 embarking:1 note:6 sciences:1 take:2 reproducing:1 lectures:2 begin:3 unless:1 shall:12 buffer:11 measures:1 plugging:1 involving:2 renormalizing:1 overlapping:3 remarks:1 whence:2 sub:3 kg:1 considered:2 later:1 yang:2 left:2 3q:9 fact:3 dbk:8 show:12 12i:1 supported:8 purely:2 spaces:2 dbq:7 analogue:1 find:2 q1:66 q2:30 based:1 parameters:2 fefferman:3 analytic:2 only:12 annals:2 factor:2 local:15 do:4 cube:11 handle:1 dk:22 notation:3 familiar:2 ϕq:5 expectation:2 trees:1 solvability:1 dz:8 dx:3 dy:4 dv:3 applying:1 dyadically:3 lloc:2 arxiv:1 missouri:1 whether:1 bad:5 qb:1 cℓ:4 fixed:7 qm:4 valid:1 remains:5 kernel:15 set:7 modulo:1 reference:1 notational:2 national:1 relative:1 differentiation:2 see:3 result:4 dyadic:33 concentric:3 appear:1 satisfying:2 capacity:2 inequalities:1 enough:5 enumerated:1 routine:3 lxi:1 boundary:1 conditions:2 choose:3 terms:2 nature:2 initially:1 weak:1 attention:1 transpose:1 however:1 subdividing:1 hypothesis:12 here:4 amer:1 observer:1 topology:1 both:2 essentially:2 cubes:10 last:15 region:5 according:1 connection:1 colloquium:1 expand:1 contribution:5 adapted:2 otherwise:1 arbitrarily:1 qℓ:1 ch:4 p2i:19 cm:2 point:1 ca:1 harmonic:3 dimensional:2 ab:1 simply:1 moreover:10 16q:1 pr:1 kernels:3 complication:1 strong:1 described:1 mb1:1 addition:1 equations:1 been:1 momentarily:3 cauchy:6 treat:5 pj:4 topics:1 define:9 rp2:2 corresponding:1 gist:1 sawtooth:7 bmo:1 6q:2 observe:4 whitney:1 child:19 c2:19 c0:6 present:7 applied:2 splits:1 ǫn:1 value:2 will:6 replaced:4 error:6 stopping:1 situation:1 property:3 taking:1 exponent:1 layer:2 iq:3 thus:23 them:1 iv:5 ii:18 middle:2 reads:1 dual:5 claimed:1 supremum:1 φq:3 handled:2 author:1 generic:1 granted:1 belong:2 cc0:2 same:6 clearly:1 benign:1 complex:1 split:2 cjs:2 proved:3 several:1 independent:2 used:21 tops:1 hand:2 1q1:11 delicate:1 kim:1 potentials:2 recall:4 pde:1 identity:1 coifman:4 off:1 center:1 cδ2:3 older:2 expression:5 depending:4 well:6 analysis:3 dψa:16 without:1 lim:4 position:1 dimension:2 usual:1 λq:1 just:1 being:1 generally:2 adjustments:2 obtain:14 rest:1 facts:1 alternative:1 previous:1 cut:1 preprint:2 except:2 semmes:1 belongs:2 extends:1 treatment:7 easy:1 theorem:39 remaining:1 generalized:1 around:1 stein:5 iα:5 big:1 nazarov:1 decomposed:1 sums:1 grid:1 know:1 press:3 using:3 identifying:1 follows:12 qualitative:1 separately:1 expository:1 steps:1 schwarz:4 integrals:3 arbitrary:2 c1q:6 terminology:1 mathematical:2 right:2 classical:1 conditional:1 some:18 deduce:1 b1:117 choosing:1 respect:2 proofs:1 happens:1 scale:1 univ:1 providence:1 does:1 decomposition:1 assuming:1 yields:4 moderate:1 refer:1 conference:2 each:12 bj:3 bk:11 step:6 bp:2 bq:14 although:1 properties:2 meyer:3 usa:1 extension:2 prove:4 o:2 2i:7 beijing:1 sake:1 carries:1 plus:2 obeys:1 introduced:1 consequently:8 duke:1 soc:1 ψq:2 presence:1 into:3 integral:4 bound:8 latter:2 because:3 operator:8 reducing:1 accretive:4 telescoping:2 suffice:1 there:6 long:1 board:1 editor:1 was:2 function:5 form:2 sequel:3 but:10 volume:1 construction:1 convergence:1 enumerating:1 doubling:1 truncation:1 wise:1 versions:1 supp:6 supq:1 smooth:1 bounds:2 us:2 below:1 carleson:7 rq2:3 similar:1 called:1 supreme:1 partition:1 constant:7 b2:151 rq1:6 defined:2 certain:1 describe:1 denote:9 littlewood:2 proves:1 exist:2 ay:2 controlled:1 distributions:1 check:1 again:3 functions:1 analyticity:1 qδ:1 no:6 when:1 finish:2 setting:3 details:4 test:1 mathematics:2 conclusion:4 axelsson:1 time:1 problems:1 bounded:4 jones:1 implies:1 longer:1 assume:1 american:1 pseudo:3 b1p:5 b1q:11 having:2 once:3
0705.0842.txt |@word aided:1 integrated:6 pairs:1 xin:1 sensitive:1 convolute:1 less:1 npart:2 over:3 probe:2 results:2 valuable:1 shape:2 underlying:1 through:1 statistical:2 edu:1 suffer:1 contributions:1 find:1 suppressed:3 subtracting:2 pt:23 ratio:1 decay:9 jin:1 photons:7 unity:2 adler:3 better:1 tail:1 production:1 black:5 systems:2 factor:3 mail:1 pythia:1 remaining:1 momentum:1 ideal:1 do:1 non:1 gev:1 rev:3 get:1 decomposed:1 term:3 cf:5 early:1 indication:1 working:1 subtraction:2 background:6 shown:1 variables:1 unique:1 moreover:1 rhic:3 above:1 g31:1 modifications:2 measures:3 quantitatively:1 particle:6 unchanged:1 university:1 arxiv:1 list:1 make:1 yield:20 correct:2 large:4 pout:8 yields:16 each:1 small:2 found:1 higher:1 decreasing:1 side:36 constraints:1 heavy:1 bars:2 performing:1 agreement:1 what:1 hadronic:2 there:1 consistent:8 correlations:14 some:1 direct:16 around:1 modified:1 relative:1 zero:4 decays:3 ex:2 measurement:5 close:1 7gev:1 extract:2 event:3 independently:1 sum:1 trig:1 employ:1 transverse:2 dense:2 nuclear:2 away:22 measurements:3 precision:1 while:1 per:14 uniform:1 collisions:9 experiment:1 identification:1 use:1 between:3 new:1 induced:1 method:3 red:5 shows:9 observed:2 pqcd:1 biased:1 full:1 plot:1 component:1 were:1 weak:1 however:2 perpendicular:1 efficiency:1 complicated:1 york:1 although:1 excess:1 jets:4 along:1 strong:1 come:1 properties:1 hadron:38 obtained:1 both:3 interpretations:1 central:5 usa:1 created:1 widths:3 study:3 conclusions:1 allows:1 dijet:1 phenix:17 raa:4 suggestion:1 mixed:2 contribution:1 hadrons:2 first:3 via:1 useful:1 significant:1 into:1 within:1 obtaining:1 number:4 arms:1 channels:1 modulated:1 weighted:1 done:1 construct:1 energies:1 respect:1 cu:22 xe:3 broadening:1 most:2 additional:1 jet:12 comparing:2 introduction:1 subtract:1 acceptance:2 iaa:13 due:2 been:1 indicate:2 nucl:2 trigger:22 kinematics:1 therefore:2 azimuthal:6 expected:1 trend:3 energy:1 possible:1 fig:9 function:10 direction:3 medium:9 jia:1 statement:1 mostly:2 comparison:3 finally:1 dijets:1 photon:29 cos:1 gaussian:5 volume:1 observe:3 systematic:1 authors:1 increasing:1 when:1 than:1 present:1 especially:2 applied:1 extracted:1 asso:2 made:2 qualitative:1 collaborations:1 double:1 triggers:2 see:4 us:1 peripheral:1 near:14 bias:2 divided:1 error:2 distribution:7 more:1 similar:1 region:4 enhancement:1 cleaner:1 references:1 would:1 associated:5 wang:1 figure:3 inclusive:6 defined:1 stronger:1 abstract:1 awayside:1 thus:2 surface:2 high:12 indicates:2 single:2 substantial:1 au:20 seen:2 standard:1 simulation:1 distributions:1 their:1 constructed:2 normalize:1 feeddown:1 compared:2 baseline:1 calibration:1 provide:3 studying:1 whereas:4 radiation:1 expect:1 same:2 data:1 lett:3 ny:1 hot:2 other:1 modification:10 fragmentation:1 sin:1 difficult:1 blue:4 used:2 columbia:2 peaks:1 may:1 collaboration:1 after:1 derived:2 effect:1 difference:1 ion:1 v2:4 important:1 peak:1 suppression:5 pair:5 spectrometer:1 colliding:1 acknowledgements:1 measured:6 relies:1 lower:1 nian:1 coupling:1 using:2 starting:1 calculated:1 no:2 flow:1 extraction:1 order:1 fact:1 appendix:1 weights:1 sn:1 components:1 correlation:2 quantitative:2 5gev:1 once:1 physics:1 width:4 fitted:1 quantity:1
0705.0843.txt |@word monte:4 chain:1 lack:1 desirable:1 results:9 bhatt:1 entropy:2 per:3 computation:6 edu:1 oster:1 compact:1 white:1 tr:1 nakajima:1 hirshfeld:1 critical:11 those:4 under:6 analogous:1 dramatically:1 applied:2 updated:1 md:2 very:1 focus:1 print:1 every:1 ma:2 ending:1 exact:3 condition:3 entire:1 exponential:2 t0:1 large:5 discrete:2 hukushima:1 small:2 biological:1 configurations:2 upper:1 smaller:3 force:1 trebst:1 consistent:1 direct:3 modified:5 second:1 cost:1 further:1 dynamics:3 estimated:14 carlo:4 ues:1 canonical:3 errors:7 chem:13 advantageous:2 brackets:1 zig:2 while:1 expressed:1 uniform:1 above:4 new:4 increasing:1 method:17 filled:1 3d:7 troyer:1 simultaneously:1 lee:4 ibid:3 respectively:8 here:6 hours:1 desired:2 address:1 strong:1 table:4 change:3 simulating:1 box:1 increments:2 clarendon:1 study:3 larger:7 adopt:1 periodic:1 rosenbluth:2 drn:1 implement:1 fitting:2 via:3 followed:1 marked:1 scaled:1 energies:3 total:2 linearly:1 use:1 takes:1 usa:2 commun:1 probabilities:1 visit:1 next:6 few:1 sample:1 poulain:1 therefore:3 lennard:3 associated:1 panel:2 type:3 until:2 more:8 separated:1 flat:2 optimizing:1 conformational:1 βu:2 tested:2 correspondingly:1 particular:1 known:3 cases:1 effort:1 circle:1 must:1 states:8 ρc:4 defines:1 mc:8 setup:1 work:1 sweeps:5 tc:7 values:6 temperatures:15 following:1 bioengineering:1 example:2 numbers:1 ma1:1 wang:5 accept:1 high:1 indicates:1 performed:4 allowed:1 lation:1 information:1 tuckerman:1 end:2 recursive:1 divided:1 zhang:1 csa:2 feature:2 regions:1 instead:3 ferdinand:2 ensemble:5 profile:1 mat:2 thermodynamic:2 after:2 derived:1 diagram:1 applications:1 tries:1 law:3 data:1 parallel:1 types:3 ferrenberg:2 liquid:6 ghz:1 annealing:2 cannot:1 negligible:2 sn:1 allow:1 enter:1 vapor:5 order:1 houston:2 ith:1 indeed:1 over:7 move:15 soc:1 years:1 held:1 paper:2 through:4 statistical:5 peterson:1 its:1 before:1 chosen:3 fix:3 vicinity:1 coordinates:1 better:1 accurately:1 window:2 offers:1 systems:5 decreased:3 texas:2 versus:1 eventually:1 non:1 practice:1 beads:1 introduce:1 landau:4 scaling:1 framework:2 they:1 half:1 accumulate:1 multidimensional:1 now:1 realize:1 teller:2 nos:2 easily:1 february:1 university:1 proteins:2 2d:3 baylor:2 magnitude:1 each:20 inherent:1 repeating:1 wβ:7 square:2 directly:1 there:2 energy:36 hard:1 related:2 frequency:4 expect:2 accumulated:1 our:4 transitions:2 eq:3 out:1 shown:6 space:4 since:4 rev:18 dsn:1 studying:2 extrapolate:1 flattening:2 medicine:1 rn:1 shows:4 state:9 free:7 keyes:1 approaches:1 advantages:2 beginning:1 faller:1 advance:5 nemoto:1 transition:7 βe:2 length:1 gordon:1 hence:2 βi:4 frequent:1 first:4 mackie:1 histograms:2 probability:10 attractions:1 number:14 clear:1 another:1 pablo:4 electronic:1 size:1 given:1 temperature:56 unknown:2 sep:1 system:13 their:1 intermediate:1 zeros:1 listed:1 calculations:1 percentage:1 scheme:3 shell:1 liang:1 favorably:1 continuous:1 took:1 lists:1 part:3 than:3 updating:2 wide:1 molecular:4 rugged:2 third:1 require:1 see:1 inversely:1 determined:2 were:22 lowest:2 comput:1 fibonacci:1 fluctuation:3 dynamically:1 generalization:1 nakamura:1 randomly:1 stillinger:1 increment:7 any:2 viewed:1 relatively:1 implemented:1 min:1 efficient:4 convenient:3 latter:1 able:1 oriented:1 ideal:1 potential:3 packed:1 finding:1 so:3 accuracy:3 circles:1 hoover:2 multiple:1 reach:1 falls:2 insets:1 zv:5 phase:2 class:1 acknowledges:1 especially:2 windows:1 neighboring:1 average:1 partition:24 berg:3 spend:1 traditional:1 bracket:1 principle:1 exp:6 dos:5 typically:1 violation:2 random:1 merit:1 converge:1 relation:1 algorithms:2 find:3 ground:14 q0:1 based:5 ensembles:3 parameters:2 distributed:4 outside:2 should:4 black:4 factor:2 helmholtz:1 rice:1 merged:1 do:1 panagiotopoulos:1 cheng:1 notation:1 strands:1 de:5 fluid:1 define:1 ones:3 rejection:2 klein:1 irb:1 runs:1 densities:2 conditions:2 arxiv:2 summary:1 xeon:1 europhys:1 contrast:1 qi:3 velyaminov:1 fixed:6 set:5 computed:1 achieved:2 straub:2 unpublished:1 relative:6 computes:1 college:1 close:1 forthcoming:1 contour:1 incorporating:1 points:1 biology:1 capacity:11 exponent:2 erez:1 written:1 vorontsov:1 various:3 between:1 consecutive:1 boundary:2 approach:2 multiplied:1 terms:1 initially:1 wl:7 deliver:1 however:3 dellago:1 efficiency:7 fluctuations:1 configuration:1 improve:2 both:2 hansmann:1 panels:1 improved:1 landscapes:1 region:2 equal:1 ln:25 bachmann:1 dated:1 receives:1 passing:1 expense:1 whole:3 aa:1 point:2 simple:4 coexistence:3 sampling:22 dimensional:3 ab:3 sequences:1 moreover:1 throughout:1 cv:6 expensive:3 ensures:1 pv:1 okabe:1 acceptance:5 due:2 tiny:1 quickly:1 yan:2 interest:2 pj:2 flexible:3 pi:1 empty:1 fig:9 obtained:1 corresponding:2 arkin:1 quantities:1 sufficient:1 gas:1 finished:1 clusters:1 last:3 spin:3 present:4 case:6 handling:2 macromolecules:1 reciprocal:1 pacs:1 solid:2 expanded:1 swendsen:4 value:3 will:3 zhang1:1 near:1 replaced:1 many:1 balance:2 taking:1 procedure:2 changed:1 jpn:1 thus:2 them:1 iv:1 ii:6 cluster:3 cond:2 protein:4 different:7 grant:2 parisi:1 lett:10 same:2 unity:1 complex:1 gibbs:2 modification:1 several:2 independent:1 nih:1 used:15 equalizing:1 possible:1 running:1 paving:1 kim:2 infinite:1 frequently:1 totally:1 contribution:1 recent:1 newman:1 lower:2 mech:1 kept:1 expression:1 well:1 roughly:4 simulated:2 position:1 model:14 precalculated:1 left:1 mclean:1 simu:1 minima:1 oxford:1 immediately:1 alternative:2 macroscopic:2 sampled:1 density:9 except:1 lattice:1 priori:1 location:1 easy:1 elp:2 bin:1 around:5 represents:1 term:1 topology:1 know:1 mol:1 press:1 using:6 intel:1 particle:3 performing:1 microcanonical:4 steps:5 janke:2 reduced:3 because:3 methods:3 exposed:1 welch:1 choosing:2 specified:1 proper:1 extended:1 huse:1 gradually:1 scale:1 martyna:1 sufficiently:2 avoid:1 overlap:1 does:3 landscape:2 assuming:1 three:1 demonstrated:1 metropolis:4 nonuniform:1 power:3 equivalent:1 pressure:2 step:2 variation:1 refers:1 tempering:2 baumann:1 stage:13 acc:1 comparison:1 about:3 carried:1 ack:1 plaza:1 discussed:1 celik:1 o:1 simulation:22 range:6 neuhaus:1 processor:1 automatically:1 cutoff:1 raised:1 subrange:2 thermostat:1 into:2 within:1 bath:1 pair:1 been:2 determine:2 fisher:2 proportional:2 additional:1 val:1 comparing:1 support:1 initial:1 nucl:1 long:1 accordingly:1 inner:1 way:2 series:1 was:23 purposely:1 function:24 head:1 form:1 enough:1 but:1 histogram:8 volume:5 heat:12 lowered:2 barkema:1 convergence:2 line:1 subtracted:1 compute:2 partitioned:1 inside:1 maximum:2 below:2 continuously:1 demonstrate:4 problem:1 stages:3 similar:2 calculated:5 detailed:2 debenedetti:1 required:1 constant:2 computing:1 certain:3 general:2 single:3 simulations:9 truncation:1 moves:7 distributions:1 constructed:1 functions:3 compared:1 no:5 biochemistry:1 whereas:2 when:1 other:2 department:2 stat:1 zhou:1 models:5 uniformly:1 entropic:1 visits:3 folding:1 important:1 katzgraber:1 ising:9 variable:3 multicanonical:1 jones:3 bcm:2 suffers:1 factorized:1 algorithm:15 physics:1 interval:1 curve:3 tmc:1 volumes:1 time:1 requires:1
0705.0844.txt |@word gw:2 gv:10 outlining:1 homomorphism:3 consider:12 chain:2 pth:1 bull:1 results:14 invent:1 extends:13 four:22 ge:6 commute:1 computation:13 c2:5 consists:2 partial:1 expressions:2 kgk:3 skeleton:4 compact:3 whose:6 preserves:4 segment:3 number:10 calculate:4 reported:3 graph:5 segments:2 equivalence:13 γv:2 noncompact:1 containing:2 simplify:1 finally:12 c5:1 under:3 geom:2 presentation:4 tessellations:4 conjecture:3 g2:7 g1:7 far:4 implicitly:1 rise:1 removing:1 splitting:7 corollary:13 endpoint:2 every:11 size:1 cellular:9 fall:1 exact:7 condition:1 splits:1 entire:2 squares:1 obvious:2 irreducible:3 notes:2 evc:15 list:11 joined:7 fewer:1 discrete:2 proposition:4 reich:1 math:17 indices:1 semidirect:1 concluded:1 gg1:1 grateful:1 gg2:1 zd:1 lecture:1 zf:4 zg:13 direct:5 unable:2 imply:1 zy:1 picked:1 follow:1 further:1 zw:2 zq:9 substitute:1 canonical:5 spectral:19 established:6 what:1 appear:8 giving:6 d2:93 section:62 localization:1 entries:2 uniform:7 cell:7 bass:17 tail:1 above:23 nine:4 row:1 consisting:6 contrast:1 satisfy:2 relationships:2 outgoing:1 full:2 commensurability:1 notions:1 stabγ:9 respectively:1 presence:1 dimf2:7 isometric:2 here:2 understanding:2 canonically:1 identifications:1 z8:1 groups:191 situation:4 directions:1 ignore:2 along:1 observing:4 tetrahedra:2 amalgamation:1 obtained:11 sending:1 endpoints:1 lafont:20 forum:1 study:1 allows:2 sbornik:1 tschantz:2 periodic:8 resulting:2 procedure:5 zd4:5 action:12 implement:1 specialize:2 head:2 quotient:6 via:2 projection:6 family:9 claim:14 merely:2 explained:4 conjugated:3 equivariant:2 apply:1 zd2:10 establish:6 quotients:1 readily:1 use:5 covolume:1 proceed:9 would:4 recalling:2 uniqueness:1 reflexivity:1 next:12 few:2 depicted:1 call:5 m2:4 taken:1 themselves:1 care:1 type:44 diagrams:4 more:1 untwisted:1 introducing:1 said:1 r5:3 clearly:1 curvature:1 surjection:1 appendix:3 observations:3 particular:12 known:9 applying:3 cases:9 iii:5 must:4 leary:1 involve:1 isomorphism:14 ma:2 ser:1 middle:1 recall:14 work:13 mh:2 wh:2 equivariantly:2 labeled:2 paragraph:3 stabilizes:2 stabilizer:39 containment:4 following:28 im:9 trans:1 example:3 proof:4 control:1 cokernels:14 f2:37 f3:2 f5:6 figure:7 give:5 arise:3 purposes:1 states:1 sphere:2 numbers:1 hyperplane:2 sense:2 dennis:1 conversely:2 occur:5 axis:1 information:3 respective:1 hhh:1 end:3 notation:4 srs:2 provide:2 verify:2 discussion:3 holds:2 s4:15 write:2 how:4 adjacent:1 4k:1 divides:2 classify:3 map:36 product:4 regional:1 algebra:11 may:1 fran:1 earlier:4 orbits:3 collection:19 algebr:2 diagram:11 consequence:1 horospheres:2 coming:5 cambridge:1 representations:3 summarize:3 subsection:1 types:4 harmon:2 cokernel:4 elusive:1 outline:1 third:3 sets:3 computations:9 grant:1 explicit:6 descends:1 element:5 pushouts:1 so:15 contributes:1 allow:1 s2:2 intersect:1 representation:3 crystallographic:7 transitivity:1 ghi:1 restriction:2 six:13 help:1 developed:1 over:4 move:1 find:5 py:29 grunewald:1 produced:1 abstractly:1 paper:6 through:7 mentioned:5 existence:4 satisfies:2 its:2 polyhedron:3 before:6 sciences:1 group:109 thank:1 maps:9 lo:15 fix:3 coxeter:47 conjugation:3 actually:3 lw:5 except:1 copies:11 h3:27 mail:2 main:2 image:1 consult:1 maximal:24 cusp:8 non:51 h1:5 return:1 stabilizers:37 primary:1 yz:2 equidistant:1 hyperbolicity:1 they:4 focus:2 serre:6 now:40 wiley:2 pz:27 easily:4 term:5 several:4 simplices:3 picard:1 stabilize:3 always:6 university:2 identified:8 labeling:3 establishing:2 dirichlet:1 connolly:1 each:33 simplified:1 2n:1 referred:1 subset:1 inserts:4 domain:25 square:7 cocompact:16 classifying:6 z12:1 osaka:1 ef:46 reduce:1 functor:1 elementary:5 literature:2 obtains:2 sectional:1 our:32 mapping:1 modules:2 ep:6 special:18 out:15 w2:2 respects:1 shown:4 space:12 furthermore:9 since:24 induces:2 denotes:4 looking:10 acting:3 zdn:1 verbatim:1 rational:1 reader:13 denoted:1 formula:16 rn:1 induced:10 induction:2 burke:1 shows:14 benjamin:1 franc:17 after:3 theory:65 associate:1 free:9 quite:2 small:2 cartesian:5 last:2 york:3 pw:30 e1:2 generate:3 wall:1 juan:1 r4:2 definition:5 r6:1 fixed:1 r2:3 r3:2 geometry:2 determining:1 could:1 similarly:2 r8:1 r9:1 nonconjugate:2 turn:1 american:1 adic:4 pure:1 assumed:3 hence:30 onto:1 first:21 xj:8 xk:1 xi:11 finiteness:1 kernel:1 bijection:1 relate:1 conjugacy:19 geodesic:20 rank:8 nested:1 xz:2 xy:2 done:2 fi:1 zh:5 ring:5 precisely:23 f1:3 carter:11 passes:1 given:15 ian:1 reference:1 likely:1 hyperbolic:59 introduction:1 leading:1 surjectivity:1 system:3 relations:2 wy:2 their:1 listed:12 statement:4 tom:1 ordered:1 subgroups:83 final:1 gives:12 e0:9 calculations:1 centered:2 johnson:2 addition:1 exactly:3 immediate:3 reflecting:1 univ:1 authors:13 focusing:3 natural:3 copy:3 completes:1 coefficients:1 zγ:4 finitely:4 kindly:1 showed:2 cyclic:22 split:2 require:2 zero:17 normalizing:2 project:4 lim:1 classes:16 pairwise:3 monomorphism:1 were:6 identical:1 tion:1 counting:3 truncating:7 sees:5 behavior:1 sw:1 ann:2 argument:2 sv:12 already:3 say:1 manner:1 conjugate:4 disjoint:9 seen:3 decide:2 any:14 indeed:9 lie:3 mij:3 angle:4 smallest:1 general:1 pineda:2 self:2 hyperplanes:11 converges:1 note:32 k2:4 ideal:31 ghg:1 generalized:4 hgh:2 interior:3 new:5 coincide:1 mayer:8 efe:3 even:1 begin:1 relatively:3 fundamental:26 cois:1 opposite:1 bruce:1 who:1 techniques:1 z2:75 extending:3 involving:1 eight:2 encodes:1 automorphism:1 pair:11 intrinsic:1 model:10 pushout:4 ki:12 antipodal:2 coincides:2 kn:12 z3:19 order:13 nonarithmetic:1 z5:1 kq:8 hi:7 reflections:3 kt:1 kz:26 left:5 sum:5 fact:7 joining:2 spherical:5 hyper:5 particularly:3 supported:1 purely:1 spaces:2 relation:15 d6:92 substituting:2 d4:67 d5:94 trivial:34 d3:30 strengthening:1 subsections:2 homology:15 q2:2 q5:3 q4:1 ratcliffe:2 q8:1 explain:2 nonisomorphic:1 considerable:1 values:3 lemma:3 only:22 explicitly:5 generators:9 geodesics:35 equipped:1 parabolic:7 g07:2 local:2 columns:1 dn:7 abelian:1 his:1 triangle:1 dk:2 viewpoint:3 get:5 xγ:4 il1:17 retraction:3 zr:3 blank:1 subcomplexes:1 ones:5 negative:3 words:1 expresses:1 boils:2 lattices:9 represented:1 boundary:5 layout:1 prime:2 well:5 pearson:5 norms:1 arxiv:2 fixes:1 doubled:1 acknowledgments:1 twice:24 qg:1 forces:5 including:1 nγ:17 inside:10 view:3 riemannian:1 preserve:2 set:11 modulo:2 computed:8 exists:3 achieved:1 peripheral:1 hα:21 module:6 relative:17 see:81 result:6 triples:2 waldhausen:10 acts:5 points:6 instance:2 satisfying:4 exponent:1 subsequent:1 rings:5 representatives:9 label:5 symmetric:1 state:2 projecting:1 various:5 permutes:1 closed:1 between:4 milnor:1 geometric:3 approach:2 knowing:1 ends:1 never:2 terms:26 extend:1 sections:4 arises:1 isom:2 equals:1 incident:1 inclusions:3 comm:2 analyzed:1 preprint:2 dress:2 configuration:1 come:4 ker:1 vinberg:2 wx:2 needs:3 both:10 linear:1 x2i:1 reverse:1 desired:1 many:8 invited:1 ve:2 according:1 previously:1 called:1 vanish:6 present:1 embedding:1 faces:6 contribution:2 summarizing:1 adapted:12 finds:3 comes:3 comment:1 ci:1 relevant:1 lists:1 point:4 simple:2 address:2 corresponds:1 walk:1 dimensional:30 z4:11 ab:2 simply:1 quinn:10 sequences:3 occuring:1 table:41 writing:1 cw:5 z6:5 torsion:8 considering:9 ensures:1 amer:5 described:2 commutative:1 second:7 triviality:2 union:5 px:30 locally:2 three:26 been:1 whom:1 bianchi:1 combined:1 goes:1 recognize:1 pj:5 pk:1 entered:1 pi:7 define:4 ranicki:1 generating:2 contribute:2 corresponding:29 concerning:2 degenerates:2 countably:2 fund:1 observe:10 understand:3 angles:6 graphics:1 incoming:1 c1:4 denote:8 subdiagram:1 gab:2 those:4 case:15 exception:3 cofinite:2 bimodule:1 swan:3 will:61 while:6 miyata:1 replaced:3 safely:1 cannot:1 applies:2 associating:1 property:9 taking:1 unlabelled:2 london:3 correspondence:1 vc:18 horoballs:1 equator:6 vi:21 vj:6 thus:1 them:2 equal:2 ii:8 need:13 ij:1 equality:1 triple:2 ambient:1 curtis:2 4w:1 vietoris:6 k0:55 different:1 whitehead:7 complexes:4 d10:57 author:1 perform:1 make:3 same:5 tells:8 x2:2 complex:16 potentially:2 virtually:20 largest:1 units:1 finite:38 isometries:1 independent:1 used:8 infinity:6 countable:3 nil:19 hand:5 edges:26 uses:1 purpose:2 characters:1 infinite:24 ois:17 recent:3 lower:46 σp:9 off:9 reflection:30 tessellation:16 expression:3 itself:1 davis:1 analysis:2 thought:1 edge:33 reflect:3 projective:2 studying:1 very:1 claims:3 jean:18 arising:6 dimension:2 subgroup:36 isometry:2 neighborhood:1 manifold:2 just:3 being:1 able:4 modular:1 identically:2 obtain:18 actions:2 vanishes:7 oxford:1 cocompactly:3 identify:12 topol:2 immediately:14 previous:11 contradicting:1 tables:7 intersection:4 helping:1 classification:3 generator:2 infinitely:5 ease:1 conclude:3 k1:41 lattice:3 other:4 combine:2 board:1 easy:6 theorem:16 extensive:1 occurring:1 remaining:10 take:3 real:2 available:1 marco:1 dihedral:13 isomorphisms:5 read:9 showing:3 sums:3 possible:4 topology:2 possibly:3 2w:3 five:2 know:11 press:1 using:10 part:2 unique:4 projects:2 like:1 injectivity:1 rotate:1 appearing:17 helpful:1 semi:1 miami:1 follows:9 reduces:1 isotropy:3 specific:4 remind:2 steps:1 either:10 edu:2 pointwise:1 page:2 mathematical:2 right:2 spans:1 namely:5 sequence:35 do:4 unsuccessful:1 some:15 oh:2 examples:5 b2:1 proper:1 gave:1 ourselves:1 provided:1 vol:2 amongst:5 dimensions:1 uck:6 normal:1 comments:1 everything:1 does:5 unit:1 summand:4 r7:1 yields:10 content:1 proc:3 refer:7 conference:2 columbus:1 assembly:13 nonuniform:1 bi:5 likewise:2 step:2 oliver:1 simplex:53 found:15 relating:1 properties:5 injective:6 stage:1 chapter:2 integers:1 about:2 works:1 a1:5 algebraic:57 column:2 completing:1 discussed:2 factors:3 o:8 reduced:1 distinct:4 a2:12 connected:1 introduced:1 automatically:4 plan:1 soc:8 farrell:16 inclusion:11 h2:5 unbounded:1 into:8 within:5 integral:7 isomorphic:28 nsf:1 due:3 down:2 lies:4 ussr:1 references:1 determine:2 ohio:2 bijective:2 tetrahedral:2 forget:1 methods:2 statistics:1 span:1 additional:2 m4:1 ggg:1 ortiz:22 there:31 subdivide:1 transform:1 class:6 start:8 appl:2 series:1 exceptional:1 analyze:2 was:4 naturally:2 r10:1 shall:1 subdiagrams:1 complete:11 form:3 vanishing:6 hp:2 hq:29 but:21 volume:2 hk:2 construction:1 hn:8 encoded:1 injection:1 trying:1 true:3 collapses:4 providence:1 partially:1 compute:13 consist:3 society:1 whether:3 represent:1 cells:23 up:21 us:38 bijectively:2 ranks:3 below:5 dms:1 limit:2 reflects:3 reiner:4 a4:1 clear:3 correspond:1 sometimes:1 associated:13 computing:5 defined:6 certain:2 abstract:1 congruence:1 remove:1 proven:1 vertices:31 single:3 proves:2 exist:2 orders:1 families:2 truncation:4 face:1 combining:2 triangles:2 again:7 no:17 index:4 when:2 detail:2 bartels:2 sk1:9 d2k:1 interested:7 details:2 department:2 mathematics:3 most:2 mutually:1 arithmetic:1 nice:1 conjectures:1 briefly:2 elements:8 morphisms:4 calculating:1 vertex:53 conjugates:1 replace:1 generated:14 important:1 a5:63 allowing:1 additionally:1 sides:1 structure:5 jones:8 implies:10 il0:17 provides:1 assume:3 hnh:1 interval:2 curve:1 original:4 portion:1 carrying:1 lying:1 hnv:2 f77:2 joins:1 having:1
0705.0845.txt |@word represent:1 concept:1 gr:1 remarkable:1 illustrates:1 skip:1 dynamic:1 leads:6 broader:1 go:1 research:1 consider:2 kowalski:3 gab:1 under:5 stabilizing:1 case:4 g4:1 deforming:4 string:4 advantage:1 outside:1 very:4 translations:5 ηij:1 choice:1 interpreting:1 summarized:1 experimentally:1 bringing:1 deformations:6 themes:1 level:2 p5:1 large:2 admissible:1 vector:4 indices:1 configurations:1 zm:2 zn:2 says:1 verifiable:1 ten:1 prediction:1 zb:4 likely:2 perspective:8 further:8 cft:1 implemented:2 theory:12 established:1 what:6 giving:1 deeply:1 current:1 version:1 above:4 new:10 contrast:1 3d:2 edited:1 respectively:1 gener:1 component:1 here:8 κc:3 explore:1 galilean:8 xν:1 represented:1 consideration:1 along:5 strong:1 respect:1 contraction:1 obtained:3 study:1 vectors:2 approaches:2 suggests:1 pˆµ:5 suggestion:1 usually:1 spacetime:3 sticking:1 stabilization:5 extra:5 apr:1 jrn:1 jrm:1 modifying:1 jrs:1 logically:1 translational:1 establish:1 planck:20 linearly:1 d73:1 kinematics:1 next:2 aharony:1 explicitly:2 estimated:1 taken:1 scope:1 means:1 type:1 theoretical:4 more:5 sort:2 introducing:1 basically:3 particular:1 known:1 topic:1 account:1 deformed:2 recall:1 challenge:1 work:2 theories:1 lorentz:3 concepts:1 following:1 chryssomalakos:2 example:1 numbers:1 renormalization:2 cosmological:1 give:6 introduces:1 high:2 assumptions:1 something:3 want:2 standard:2 g2:2 bousso:1 rather:9 divided:1 six:8 feature:1 s5:1 write:1 how:2 pure:1 instead:2 parameter:2 inputs:1 description:9 mendes:1 algebra:10 may:10 philosophy:1 hence:5 produce:3 preferred:1 coming:1 representations:1 summarize:1 parallel:2 constants:1 realized:2 natural:3 effective:1 light:1 grant:1 explicit:1 correspond:1 element:1 so:40 expression:1 fundamental:7 definitions:2 discussion:1 forced:1 breaking:1 interpretation:2 developed:1 over:1 kong:2 xi:1 through:8 looks:1 hypersurface:5 existence:1 satisfies:1 still:5 its:1 boosts:2 before:1 group:5 interesting:3 relativity:34 coordinates:6 li:1 better:1 according:1 microscopic:2 differently:1 deformation:15 correspondence:1 them:1 good:1 introduce:1 za:6 framework:3 they:3 half:1 formulating:1 rotation:1 discuss:1 bigger:1 matched:1 easily:2 term:1 holographic:1 invariants:1 university:2 presented:1 identified:2 establishing:1 magnitude:1 breach:1 lorentzian:5 pˆν:2 domain:1 chung:1 energy:9 idea:4 related:1 breakthrough:1 extended:1 quantum:52 our:7 beyond:6 eq:2 special:3 really:1 shown:1 matrix:1 ators:1 space:22 rep:1 since:2 rev:8 denotes:1 re:1 seriously:1 denoted:1 ref:9 correct:1 linear:3 quite:2 admits:2 completely:1 york:1 put:1 intermediate:1 teach:1 wanted:1 definition:1 geometry:18 starts:2 ds5:1 days:1 times:1 counterpart:1 thing:1 length:15 iso:11 gordon:1 signature:2 consequence:1 generalizations:1 think:6 first:3 origin:1 snyder:2 xn:6 features:1 symmetry:30 xm:8 radical:4 xa:1 number:1 done:2 adopted:2 another:2 open:1 given:5 introduction:3 observes:1 tata:1 system:1 least:1 confirming:1 assumption:1 kµ:2 realization:3 scheme:1 frame:4 gives:8 terminates:1 exactly:3 ncu:1 direct:2 part:7 somewhat:1 authors:2 translation:1 believe:2 x6:1 than:3 x4:7 x5:7 require:1 zero:3 limiting:2 supposed:1 fˆ:5 behaviors:1 symmetries:3 mind:1 locations:1 generalization:2 say:3 need:1 seen:1 sees:1 apparently:1 dynamics:6 sitting:1 lie:2 mij:1 form:2 essentially:3 latter:8 mills:3 gravity:4 note:6 instance:2 fitting:1 take:2 heisenberg:1 though:2 probed:1 most:2 satisfying:1 connected:2 letter:5 preliminary:1 nothing:1 µy:2 acknowledgements:1 class:1 xµ:6 observation:1 considered:8 clear:1 adopt:1 yang:4 principle:2 velocity:1 pˆλ:1 usual:1 physics:20 notion:3 fact:4 quantity:2 phenomenon:1 show:1 jµ:1 supported:1 infrared:1 bring:1 nowak:2 fifth:1 q5:2 o:2 based:2 parameters:1 title:1 j45:3 commutators:1 enough:3 should:5 jan:1 only:4 going:3 generators:4 zµ:1 indeed:1 partially:1 jab:1 oct:1 hope:1 do:6 notation:2 get:4 familiar:2 bear:1 cannot:3 legitimate:1 closely:1 interpreted:1 neither:2 arxiv:1 grav:1 qa:2 qc:4 compactification:1 glikman:3 qm:1 qn:1 set:3 presuming:1 reference:4 achieved:1 imposing:3 national:1 ursey:3 emergent:1 plausible:1 namely:1 result:5 violet:2 discussions:1 subject:2 suffer:1 qµ:1 arguably:1 importance:1 behind:2 identification:2 conceptual:2 invariant:12 geometric:2 approach:6 ends:1 terms:2 nature:2 originated:1 attention:1 however:3 js:2 implementing:1 jµ5:3 debt:1 suggested:3 both:3 dates:1 last:2 jm:6 many:2 taking:3 ir3:1 ir4:1 ir5:1 against:1 quantization:2 mµν:7 connection:3 poincar:4 inspired:1 whole:1 finds:1 experimental:3 otherwise:3 magueijo:1 d13:1 point:2 simple:3 dimensional:2 superstring:1 simply:1 z5:2 constant:1 actually:2 sensible:1 described:1 transformations:2 dub:1 three:4 been:7 pb:1 whom:1 oν:1 much:2 interest:1 basic:1 proposal:2 pi:1 pn:2 location:2 arena:1 corresponding:2 quantities:1 concerning:1 precision:1 noncommutative:5 external:1 input:1 c2:7 former:1 present:5 c4:2 applied:1 look:3 p4:1 pacs:1 solid:1 will:3 while:3 replaced:1 ultra:2 conformal:10 leaves:1 procedure:3 century:1 triply:1 iv:1 itself:1 cone:1 dual:1 different:1 author:1 suggest:1 lett:2 same:5 any:3 complex:1 otto:1 dimensionless:1 finite:2 four:2 independent:5 literature:1 see:3 ni:2 hand:2 parametrized:1 infinite:1 build:2 invariance:1 tradition:1 recent:1 scaling:4 lower:1 center:1 pµ:7 studies:1 extending:1 well:2 analysis:2 obviously:2 without:1 comes:1 components:1 sets:1 coordinate:7 model:1 justify:1 just:1 being:5 das:1 obtain:1 rest:1 identify:1 questions:1 useful:1 taiwan:2 speed:1 ads:1 generator:3 readers:1 thinking:2 scales:1 mathematically:2 setting:4 nor:2 relevance:1 5d:4 oµ:2 transformation:5 momentum:5 generalized:2 aspects:1 depends:1 represents:2 big:1 admitting:2 early:1 five:4 know:2 press:1 world:12 moreover:2 mod:5 imposed:1 like:5 particle:1 follows:1 ηac:1 ηab:5 audience:1 unstable:4 either:1 popular:1 works:1 essential:1 beltrami:1 mathematical:3 right:3 theorists:4 methods:1 classical:13 tells:1 some:7 back:2 table:5 proper:1 nonzero:1 scale:16 describing:1 dimensions:3 illustrated:2 broad:1 unavoidable:1 does:2 assuming:1 minimal:3 bc:2 equivalent:1 evolutions:1 worthy:1 stage:1 about:11 ηbd:1 central:2 incline:1 extension:2 getting:2 universe:3 camelia:1 discussed:4 ob:1 oa:2 deserves:1 range:1 plus:1 characterized:2 d67:1 introduced:2 nsc:1 accessible:1 cambridge:1 ηm:3 within:5 bound:5 m0i:1 variable:1 because:1 ηs:2 einstein:6 elementary:1 old:1 lesson:1 technically:1 hep:1 stabilizations:1 u4:1 there:5 question:2 transform:1 start:1 accordingly:1 pa:3 physicists:2 way:3 resulted:3 call:1 was:2 assumes:1 naturally:1 complete:1 newtonian:1 offer:1 smolin:2 sequel:1 but:7 line:2 trying:1 true:1 adler:1 jµν:1 challenges:1 minkowski:6 inside:1 bounds:1 us:3 below:1 limit:6 ηmn:2 refs:1 pm:3 similar:1 called:2 detailed:1 changes:1 ab:1 associated:1 int:4 abstract:1 describe:2 evidence:1 formulation:4 amelino:1 6d:1 check:1 metric:3 regime:1 again:3 nj:1 no:7 other:3 role:1 details:1 spatial:2 department:1 mathematics:2 you:1 conclusion:1 conclude:1 picture:4 briefly:1 ads5:15 resembles:1 chance:1 important:3 included:1 structure:4 independently:1 starting:1 together:2 naively:1 mass:8 time:22 4d:14 requires:2 having:3
0705.0846.txt |@word limited:1 magnetic:1 four:18 entropy:4 tenuous:1 transversally:2 whose:1 replacements:1 under:4 worth:1 oganesyan:1 rise:1 figs:1 summarized:1 fazekas:2 admissible:1 ueda:1 plaquette:71 fradkin:3 elegant:1 likely:2 correlator:2 rigorous:1 estimated:2 even:4 established:2 above:6 new:6 increasing:1 ever:1 consisting:1 never:1 equals:2 here:7 nodeless:1 path:1 obtained:2 suitably:1 study:10 visualised:1 orthogonalization:1 suitable:1 projection:1 moessner:10 highly:1 turning:1 total:3 plot:6 would:7 negative:1 distributing:1 noting:2 call:4 therefore:4 midpoints:1 separated:1 composite:2 aware:1 berlin:1 correspondingly:1 origin:2 equilateral:1 join:1 mc:2 pursue:1 work:9 mi:2 theories:2 ere:1 example:3 wang:1 give:2 organized:1 degenerate:1 times:2 absolute:1 end:1 provide:1 feature:3 how:3 adjacent:1 preferable:1 orientational:5 description:1 replacing:1 thermodynamic:1 ladder:1 minimized:1 diagram:7 parallel:3 constants:1 effective:2 nussinov:2 correlation:22 order:19 operations:1 xj:1 interpretation:1 over:6 satisfies:1 lhuillier:1 xl:1 fix:1 exhibits:3 fig:30 eventually:1 them:5 combination:1 they:4 represents:1 alet:1 reasonable:1 each:11 bond:16 krauth:5 magnets:1 combining:1 laboratory:1 superposing:1 content:1 xu:1 rk:13 numerical:2 log2:5 linear:1 free:1 standard:6 estimate:4 corrections:1 generalizations:2 already:6 restrict:1 another:1 sutherland:1 similarly:3 needed:1 perturbations:1 antisymmetrized:1 ranging:1 mambrini:1 centered:3 distance:6 princeton:3 second:2 correlators:1 matter:2 classes:1 powers:1 fashion:1 chen:1 manner:1 seen:2 forced:2 strength:2 convenient:1 latter:1 completed:1 circles:1 shall:1 object:1 letter:1 phase:25 acknowledgements:1 partition:1 vertices:3 accounted:1 section:3 dou:1 pankov:2 microscopics:1 random:1 colors:4 gauge:3 tempted:1 d2:3 judges:1 proposed:2 topological:6 hamiltonians:3 do:8 establishes:2 klein:2 di:1 de:3 yielded:1 pocket:10 report:1 covering:7 interspersed:1 perron:1 imitate:1 generally:1 observed:1 decided:1 result:3 discussions:1 disturbing:1 best:1 said:2 away:2 yet:2 symmetric:1 unable:1 simplest:7 drawn:1 approach:1 yamashita:1 triplet:1 terms:4 extend:1 nature:2 weak:8 however:8 wu:2 suggested:2 essentially:1 cot:1 faces:1 contribution:2 com:1 2nl:2 concluding:1 2ns:2 basis:3 savit:1 three:6 been:9 pute:1 much:5 interest:1 fluctuation:1 ergodic:2 suppress:1 argument:1 coherent:1 2n0:1 spin:8 2n4:1 applied:1 rigorously:1 aim:1 multicritical:1 procedure:5 iv:1 ii:4 ij:2 cond:4 3ns:1 3np:1 ia:1 pathology:1 containing:3 complex:1 potentially:1 several:1 grows:1 independent:4 percolation:1 laboratoire:1 permutation:1 centred:4 centres:1 possesses:1 left:1 just:1 assigned:1 eigenstates:1 5x:3 candidate:2 belongs:1 easy:7 evidenced:1 occurring:1 breaks:1 possible:7 spanned:1 eorique:1 supercell:1 unique:2 apart:1 steps:1 valence:16 deconfined:2 cnrs:1 umr:1 ice:2 contributing:1 ob2:1 sαα:2 core:1 pose:1 properties:4 sepa:1 o:10 probabilities:1 ensure:1 de1:1 eight:2 automatically:1 paramekanti:1 presence:4 rotations:1 bound:9 multiply:1 initial:2 anderson:3 way:12 was:5 lowest:2 mostovoy:1 forming:2 differences:1 encodes:1 true:2 assaad:1 portions:1 la:1 attached:1 maximum:1 crystal:5 coverings:8 nnl:4 moore:1 computing:1 percolating:3 zeng:2 exist:2 simulations:3 check:6 triangles:2 physical:1 ni:4 nl:2 no:11 whereas:2 wavefunction:2 nd:17 ne:1 nx:2 ny:2 nz:2 interested:1 ns:19 picture:1 superposition:2 models:23 diep:1 shibata:1 kivelson:7 oscillates:1 faster:1 coulomb:1 assume:1 interval:2 together:1 time:16 n0:2 n1:4 n3:3 n4:3 azaria:1 chain:8 global:1 leads:1 grateful:1 mila:3 dimensionality:1 depend:1 graph:23 show:6 finally:2 analogous:1 advantage:1 orthogonal:6 springer:1 lro:1 geometrical:1 orientations:7 ma:1 visualized:1 turns:1 leave:1 quick:1 upper:2 mn:2 findings:2 sign:4 generalisations:1 adds:1 appear:3 celebrated:1 uniform:1 suspect:1 goes:1 shared:3 serban:1 supporting:1 den:1 prescriptions:1 understanding:2 magnetism:1 groups:1 along:1 appears:1 studied:3 simultaneous:1 domains:1 resonance:4 conveniently:1 plotted:3 useful:5 coinciding:1 translational:1 flavors:20 prove:1 sake:1 positive:4 going:2 encode:1 theoretical:2 sharing:1 appendix:9 everywhere:1 virtue:1 cases:1 fermionic:1 rotational:1 originally:1 values:2 jacobsen:2 following:6 making:2 nearest:7 percolates:1 arise:1 topic:1 dropped:1 allowed:3 divided:1 means:2 write:2 parameter:2 product:2 mat:3 may:3 max:1 snm:2 produce:3 mag:1 representations:1 revealed:1 natural:1 sectors:3 sw:2 su:41 so:12 sn:1 sm:7 representation:4 prefactor:1 exclusive:1 indeed:3 pointed:1 stability:1 course:4 statistical:1 cold:1 still:2 tendency:1 derive:1 thank:1 interesting:1 coordinates:3 main:1 hikihara:1 non:7 introduce:2 scaling:2 half:1 now:2 discuss:1 fla:1 term:11 equality:1 name:1 corners:2 drop:1 orthonormal:1 el:1 domain:3 square:6 ed:1 assumption:1 eq:5 shown:5 space:7 seriously:1 investigation:1 squares:1 shows:3 reformulation:1 theory:2 kondev:1 possibility:2 quite:1 complicated:1 besides:1 remainder:1 derivation:1 transition:23 turn:1 place:1 first:8 exotic:1 xk:1 xi:2 symmetry:8 xm:1 variables:2 xy:1 specifically:2 carry:2 open:2 size:6 given:12 checked:1 types:2 convention:1 white:1 accurately:1 transverse:2 x3:1 than:7 analyze:1 require:1 were:1 prospect:1 raman:1 generality:1 locations:3 generalization:1 say:3 occupied:2 any:8 computationally:1 form:9 note:6 potential:3 online:8 coincide:1 begin:1 multiple:1 decreasing:1 fcc:6 successive:2 pair:13 analytically:3 considered:3 average:2 typically:1 liquidity:1 quantity:3 precise:1 restriction:1 notations:1 decompositions:3 threshold:1 16x2:3 nll:3 ground:15 ensembles:1 written:2 only:18 explicitly:4 black:1 unimportant:1 cannot:2 invariant:5 regarding:1 yield:1 though:1 mapped:1 registry:1 reveals:1 connections:16 namely:1 inequivalent:2 uncorrelated:3 senthil:2 detect:1 ei2π:1 ways:5 sites:24 enough:1 plaquettes:58 between:9 notice:2 analyzed:1 nill:2 similar:3 according:3 flipped:1 dated:1 expression:1 comes:1 among:2 color:9 mirroring:1 sampling:1 translationally:1 ordered:7 actually:4 considering:1 tuning:2 combined:1 microscopic:2 direction:5 formed:4 observe:1 hardcore:1 spirit:2 those:3 case:24 disconnected:1 many:1 situation:2 planar:1 orientation:4 coupled:3 cluster:2 yj:1 zhang:2 different:12 same:18 arguments:1 constructed:3 investigated:1 singapore:1 octahedron:4 edges:1 changing:1 invariance:1 largely:1 without:4 solve:1 components:3 model:32 dimension:1 generalisation:1 being:3 captures:1 lowand:1 flavor:5 guides:1 leinaas:1 seems:1 lett:12 kingdom:1 eigenvalue:2 read:1 dark:1 using:5 mod:3 reduces:1 either:2 fully:2 reduced:1 twelve:1 nonzero:2 provided:2 dimensions:4 stops:1 mesons:1 critical:3 decomposition:4 provides:1 refer:1 measuring:1 scientific:1 ration:1 notably:1 broken:2 2m:2 vishwanath:1 aci:1 mixes:1 mutually:1 pockets:1 inclusion:1 numerically:2 accounts:1 operator:1 assumed:1 there:19 start:2 low:5 sachdev:2 longer:1 arranged:2 connect:2 strongly:9 rvb:4 certain:2 general:5 loops:16 formulation:1 controlled:1 moves:5 bishop:1 resonating:27 again:1 field:2 remarks:2 spatial:2 deviation:4 briefly:1 vertex:5 includes:4 a1:1 a3:1 a2:1 a4:1 included:2 subdivision:1 starting:1 original:6 represent:3 monte:2 consider:12 lack:1 nonlocal:6 tain:1 th:1 belonging:6 straightforward:2 very:6 difference:1 lecheminant:1 hamiltonian:14 joined:2 occurs:1 large:10 small:3 periodicity:1 zero:2 displays:1 further:4 what:1 sum:6 version:2 sup:1 erieure:1 method:1 contrast:2 condensed:1 full:2 ranged:1 component:2 orbitals:1 favourable:1 directions:1 strong:6 search:1 colored:6 inspired:1 allows:2 periodic:1 pick:1 uniquely:2 via:1 establish:5 readily:1 eye:2 takes:1 distinct:1 ψs:1 contains:3 nucl:2 taken:1 more:7 particular:2 known:2 pseudospin:2 none:2 science:1 caveat:1 share:2 states:23 sense:1 sharp:1 dress:1 axis:1 information:1 respective:1 minist:1 rather:3 breaking:2 ensemble:1 fu:1 choice:3 fl:1 short:1 onto:1 parameterized:1 sect:5 fundamental:2 tallahassee:1 help:1 ith:1 developed:2 paper:3 through:3 signs:4 existence:3 kinetic:3 its:4 roots:1 continued:1 fruitful:1 absence:4 penc:2 systems:5 might:2 yi:2 yk:1 good:1 yl:1 reflected:2 framework:1 walls:3 yz:1 oxford:4 2t:3 easily:1 2p:1 always:3 2x:1 2d:1 inequality:2 chandra:1 found:3 energetically:1 referred:2 energy:10 hard:3 idea:2 obtains:1 measurement:1 quantum:17 beyond:2 momoi:1 realising:2 since:1 research:1 acting:2 dominated:2 denoted:1 plotting:1 reason:1 members:1 definition:1 pairs:1 noted:1 undergo:1 hadrons:1 assign:2 reinforced:1 probability:4 number:16 done:1 construct:2 disordered:2 differ:1 introduction:3 moderately:1 least:3 twoform:1 relationship:1 part:12 spacings:1 center:1 albeit:1 kind:1 determines:2 determined:2 str:1 peierls:1 motivation:1 pasquier:2 qpm:17 creases:1 conjugate:1 orders:1 generalizes:1 costs:1 finding:3 honeycomb:1 singlet:19 most:9 nothing:1 measured:2 cover:1 hermele:1 exp:1 physics:7 joining:5 sector:1 phenomenon:1 relation:2 fine:2 find:7 parameters:1 ox1:1 generators:2 sd:2 closely:1 combinations:1 hij:7 arxiv:3 doubled:1 common:5 farnell:1 set:1 achieved:1 marston:1 see:7 individual:4 close:2 chayes:2 ergodicity:3 permuted:2 smallest:1 various:6 use:5 lowered:1 conditions:1 creating:1 eˆi:2 subdividing:1 both:2 recherche:1 cubes:7 last:1 henley:3 connection:7 finds:3 reside:1 point:18 simple:6 corresponds:3 dimensional:10 simply:2 adaptation:1 described:1 perspectives:1 due:2 strategy:2 pi:5 cantor:1 determination:1 assigning:2 equilibration:7 p0:4 p1:5 exponential:1 solid:4 while:10 replaced:1 compactness:1 error:2 richter:1 loop:13 fujimoto:1 encountered:1 itself:3 vor:1 grant:1 lengths:1 belong:5 products:1 higher:6 used:5 assignment:4 liquids:2 recent:1 normale:1 lower:4 task:1 analysis:4 obviously:1 solids:1 edge:5 entry:2 spend:2 comprise:1 distances:3 intervals:3 questions:1 world:1 location:1 remaining:1 spin3:1 evaluate:2 emanating:1 philos:1 emergence:1 imposed:1 follows:5 interestingly:1 manifest:1 separately:1 eel:1 yields:2 topologically:1 spins:6 some:9 b4:3 b5:1 b1:1 b2:1 b3:2 oscillations:2 balents:2 describing:1 measurements:6 per:2 connecting:3 8x:1 invade:1 minimal:1 run:1 dictates:1 perpendicular:3 step:3 dictated:1 hilbert:4 anything:1 constraint:8 simulation:3 range:8 extensions:1 into:7 retaining:1 appropriate:3 proportional:4 statistics:1 span:1 conceivably:1 fast:1 translate:1 properly:1 link:1 atom:1 considerable:1 persisting:1 intuitive:1 up:4 us:3 antiferromagnet:2 planes:1 fluctuations:1 frozen:1 called:2 eduardo:1 constant:3 defined:7 single:6 diverse:1 fixing:2 department:1 manhattan:4 elements:15 problems:1 replace:1 generated:2 fisher:1 correlated:1 implies:1 algorithm:6 neighbouring:2 far:1 requires:3 having:2 partial:1 results:5 illustrated:1 eds:1 gn:1 amplified:1 rokhsar:6 g2:15 g1:10 wave:8 matrices:1 trm:1 eigenvalues:1 trt:1 dimer:15 configurations:6 zl:1 smaller:2 zi:2 zj:1 zk:1 imply:1 zx:1 dynamics:6 carlo:2 index:1 experiment:1 3d:1 body:2 troyer:1 wavefunctions:2 led:1 lee:1 degree:2 leg:1 respectively:4 spacing:2 desired:3 packing:1 objects:5 separation:1 others:1 consideration:2 motrunich:1 remark:1 involved:1 larger:5 suggests:2 resulting:1 implement:1 involves:1 formulated:1 scales:1 decrease:1 confidence:1 feb:1 asymptotic:1 usa:2 commun:1 remains:2 next:4 few:1 depicted:2 doubling:1 ecole:1 becomes:2 factor:2 carrying:2 labelled:1 perronfrobenius:1 iii:3 frobenius:1 challenge:1 when:11 obvious:1 closing:1 process:2 high:2 native:1 ijkl:3 united:1 holds:2 instead:1 neighbor:4 efficiently:1 computations:1 light:1 separations:1 correspond:1 element:11 allow:2 bipartite:1 bins:1 six:2 insight:2 saturates:2 including:1 mentioned:1 thence:1 ln:3 li:3 degrees:8 choose:2 clusters:1 defining:1 violating:1 realize:2 february:1 university:4 misguich:3 identified:1 sufficiently:1 l2:1 l3:1 constraints:1 related:1 elementary:1 remove:1 measure:3 our:16 transitions:1 special:1 out:4 respects:1 matt:1 fundamentally:1 rev:28 maximized:1 ref:3 math:1 interactions:1 τeq:3 diagonal:8 analytical:1 approaches:1 interaction:6 geometry:1 could:1 florida:1 keep:1 length:11 ortiz:1 hence:1 rudolf:1 staggered:3 hypercubes:4 precisely:1 seidel:1 long:8 strict:1 ordering:14 system:7 their:9 final:1 explanation:1 exactly:2 liquid:6 limiting:1 amplitude:6 exhibit:4 symmetries:2 lines:1 curves:1 sondhi:8 need:4 constrained:1 clearly:2 min:3 studying:3 physique:1 heisenberg:2 centre:1 collaboration:1 who:1 connected:18 but:7 face:8 graphs:2 construction:2 snapshot:5 mechanical:1 typical:1 fact:5 text:1 supported:2 βhi:1 12x:1 trivial:2 coloring:2 based:1 knowledge:2 should:6 local:13 exchanged:1 cube:12 bonds:5 overall:1 words:1 exchanges:1 timing:1 processes:1 contain:2 shi:1 fixed:1 noncrossing:1 view:2 intervening:1 computed:3 national:1 correlations:4 p20:1 statistically:1 closer:1 phases:8 pattern:4 state:15 progress:2 boundary:1 frustrated:2 p2i:1 configuration:7 problem:11 restrictions:1 limits:1 taking:1 decay:2 equal:11 attributed:1 etc:1 jersey:1 comment:1 relevant:2 conclude:3 table:2 crystalline:3 singlets:2 columnar:5 define:5 arises:1 corresponding:5 route:1 sufficient:3 subspace:1 binning:3 neighbour:4 prescription:3 c1:2 present:5 unlike:2 appearance:1 value:7 choices:1 will:16 satisfying:1 almost:1 refs:1 thus:18 site:12 vs:3 partner:1 sits:1 orbital:2 unity:1 parts:3 largest:2 units:2 finite:3 unconventional:1 cubic:24 colouring:2 identity:1 off:5 reflection:1 colour:1 well:3 thought:1 undertaken:1 arising:1 realised:1 arbitrarily:1 less:1 rapid:1 wen:1 lattice:54 add:1 attractive:2 identical:1 dimers:11 increases:2 press:1 immediately:1 loss:1 sizes:1 alternatively:1 lose:1 become:1 parity:1 because:5 pauling:1 classical:9 sequence:2 phenomena:1 searching:1 growth:2 proper:1 huse:3 happens:2 lead:3 demonstrates:1 overlap:17 does:3 assuming:1 chains:4 demonstrated:1 obey:1 although:2 transformations:1 gained:2 about:4 carried:1 freedom:10 important:1 projectors:1 ising:1 equally:1 letters:1 en:1 utility:1 van:1 additional:2 transfer:4 flippable:1 frustration:1 function:20 basic:1 triangular:2 overlapping:4 hu:1 hi:1 gain:1 convergence:1 partially:1 made:1 compute:6 evident:1 whether:2 flip:2 bijectively:1 below:2 limit:5 distribution:1 mechanics:1 contribute:2 denote:3 ini:1 ing:1 functions:7 nonetheless:1 other:8 details:3 branch:1 conclusion:2 repeat:1 matrix:28 coupling:2 persistent:1 rule:1 understand:1 4d:1 expands:1
0705.0849.txt |@word consider:2 caused:1 bull:1 splitting:1 edm:3 leads:1 marion:1 microwave:2 consists:1 preferable:1 increase:1 calculate:1 aug:1 auckland:1 spin:2 gatchina:1 charge:1 petersburg:2 th:1 under:1 hints:1 γf:3 division:1 belonging:1 petitjean:2 advantage:1 very:10 frequencies:5 springer:1 choice:1 electron:9 2ry:1 varshalovich:1 difference:3 exact:1 school:1 europhys:1 vibrational:8 level:6 turns:2 list:1 applicable:1 large:4 shuryak:1 yale:3 small:2 setup:2 20th:1 degeneracy:1 upper:1 smaller:1 consistent:1 sign:3 approximation:3 second:2 enhancement:4 substituting:1 further:2 estimated:1 even:2 appear:1 sun:1 quadrupole:1 experiment:6 above:1 huber:1 new:4 d1:3 method:1 mp:9 satisfy:1 hollenstein:1 respectively:1 orbitals:1 atoms:1 strong:3 appears:1 change:1 obtained:1 search:3 institute:2 shift:6 study:3 larger:4 allows:2 maleki:1 suggests:1 usually:1 conveniently:2 narrow:3 studies:1 dysprosium:1 compare:2 private:1 austria:1 kozlov:2 select:1 quasi:1 would:1 eπ:1 eσ:2 comparing:1 nucl:1 therefore:5 relativistic:3 taken:1 scope:1 australian:1 godfrey:1 msc:1 theoretical:1 more:3 agafonova:1 binding:2 nguyen:2 known:2 cases:2 must:1 me:8 high:1 account:1 rotational:4 equation:1 work:2 oscillator:1 theories:1 reviews:1 values:5 publications:1 mr:6 following:2 making:1 example:1 ωel:6 control:1 ions:4 dedicated:1 odorico:1 chosen:1 calculation:3 expanding:1 states:6 numbers:1 council:1 absolute:1 needs:1 rather:1 get:2 range:2 write:4 located:2 varies:1 instead:2 parameter:4 ft:1 may:6 data:3 lamoreaux:3 constants:10 realized:1 natural:5 higgs:1 schneider:2 spectra:1 lines:1 correspond:1 element:4 shore:1 so:1 fundamental:11 order:7 complementary:1 hff:7 indeed:1 over:1 dy:2 paper:2 thesis:1 signs:1 mentioned:1 existence:1 linewidth:3 massey:1 rapidly:1 energies:1 interesting:1 temporal:3 decreases:2 better:1 wales:1 main:1 them:2 yb:2 bang:1 prestage:1 effects:4 dmitriev:2 now:2 chromodynamics:1 february:1 several:1 2q:1 always:1 university:3 dzuba:4 magnitude:4 trap:2 bonifacio:1 found:1 heavy:1 eh:4 energy:9 idea:1 related:1 nostrand:1 frequency:11 ubachs:1 expect:1 measure:2 quantum:4 our:2 transitions:8 eq:7 out:1 superscripts:1 matrix:4 space:1 since:1 rev:19 research:2 particles:1 si:1 rf:2 conclusions:1 rb:1 print:1 ref:4 unifying:1 uzan:1 foundation:1 arizona:1 interactions:2 possibility:1 standard:3 flambaum:13 proportionality:1 york:1 e4:1 estimate:8 jila:2 e2:2 torgerson:3 hc3:1 interaction:3 r0:5 widths:2 transition:11 times:1 oklo:1 levshakov:1 corrections:1 configurations:1 stimulate:1 south:1 first:6 fischer:1 number:5 demille:3 done:1 another:3 isaev:1 electronic:6 invariance:1 given:1 width:4 introduction:1 eqs:1 sep:1 approximately:1 needed:2 manifolds:2 2ωf:2 molecular:11 structures:1 frame:1 speaking:1 gives:2 exactly:1 took:1 electroweak:1 homonuclear:1 optical:2 favorable:1 july:1 than:4 coefficients:1 e3:1 distance:3 determines:3 d02:2 was:4 zero:2 final:1 determined:1 contrary:1 supposed:1 amplitude:1 russia:1 lowest:1 modern:1 few:1 st:1 any:1 strength:2 nucleosynthesis:1 gravity:1 predominantly:1 note:2 majority:1 potential:1 build:2 analogy:2 hyperfine:3 diatomic:4 molecule:6 most:1 petrov:2 zealand:1 considered:3 calculated:1 3c3:1 electrons:2 talk:2 cs2:4 typically:2 selection:2 particularly:1 reactor:1 molaro:1 violation:1 supported:1 mosyagin:1 earth:1 d5:1 fine:16 find:3 d0:3 ground:7 ratio:1 parameters:2 explain:1 hope:1 written:1 here:7 only:3 molecules:14 factor:5 local:1 γn:3 achieve:1 equilibrium:1 goes:1 means:1 expectation:1 international:1 report:1 becomes:1 qx:1 arxiv:14 bag:1 clocks:1 doublet:2 achieved:2 sensitivity:7 humans:1 relative:6 see:4 enhanced:3 close:5 best:2 hafnium:1 nuclear:4 currently:1 dipole:4 state:14 between:12 irc:2 comparable:2 nature:3 weak:3 however:5 jr:1 spectroscopic:1 ellipticity:1 group:2 amer:1 suppressed:1 lopez:1 isotopes:3 both:1 limits:2 many:1 invited:1 vibration:2 σg:1 according:2 fulfilled:1 sensitive:3 dated:1 ivanchik:2 expression:3 masses:2 experimental:2 cm:11 cl:8 appeared:1 corresponds:3 proton:2 cs:1 table:3 factors:1 conference:1 pp:1 marchenko:1 tuning:2 due:4 been:1 much:1 basic:1 expected:3 ph:5 meeting:1 life:1 corresponding:3 easy:2 qsd:1 coherence:1 precision:1 fund:1 6s:1 systematic:2 astron:1 c3:1 reinhold:1 irrelevant:1 present:3 case:1 laser:1 look:1 pacs:1 value:4 will:2 while:2 reliably:1 promising:2 35th:1 unpaired:1 λqcd:3 thus:3 non:1 unit:1 centuri:1 albany:1 different:10 fortier:1 grant:1 perform:1 suggest:1 make:1 same:4 orders:2 shifts:3 potentially:1 split:1 dimensionless:2 finite:1 grows:1 higher:4 independent:1 used:3 effect:2 hand:1 doublets:1 ion:10 moment:2 levels:12 hartree:1 recent:2 center:1 well:1 bohn:1 components:2 position:1 model:2 budker:2 r02:2 proposed:2 quasar:1 obtain:4 rest:1 intervals:4 atomic:9 summed:1 compared:1 cus:2 hint:1 cornell:2 absorption:1 conclude:1 internuclear:1 lett:11 sydney:1 5d:1 mod:1 excited:4 tests:1 australia:1 quasidegenerate:1 big:1 innsbruck:1 possible:4 harmonic:1 increases:1 mon:1 vacuum:1 using:6 accepted:1 advanced:1 apart:1 necessary:2 like:1 systematically:1 become:1 accuracy:4 reduced:3 webb:5 exceed:1 because:6 some:2 experiments:3 cancel:1 strongest:1 examples:1 moreover:1 proper:1 electric:1 happens:1 scale:5 bize:2 measurements:6 overlap:1 eliminate:1 assuming:2 demonstrated:1 scientific:1 reach:1 linewidths:5 tamm:3 stutz:1 br:1 meyer:1 comparison:1 about:4 valence:1 universe:2 discussed:2 dependence:4 mixes:1 cancelation:3 oz:1 reimers:1 titov:2 peik:4 introduced:1 soc:2 h2:1 into:2 lies:1 primarily:1 proportional:2 van:1 additional:2 area:1 assumed:1 there:3 long:1 strict:1 handbook:1 way:2 astrophysics:2 sections:1 hz:11 north:1 murphy:2 astro:3 properly:1 hn:1 atom:1 russian:1 hc:1 hg:1 gravitational:1 variations:1 flip:1 us:2 ωv:6 tucson:1 similar:6 ωf:10 strongly:2 interval:2 constant:5 defined:2 direction:1 chap:1 exist:1 laboratory:1 campus:1 beyond:1 no:2 field:1 other:3 spatial:2 proposal:1 herzberg:1 accidental:1 variation:22 important:4 astronomy:2 structure:12 karshenboim:4 physics:19 required:1 orbit:2 rule:1 mass:8 time:5 far:1 nuclei:1 2mω:1
0705.0850.txt |@word since:1 show:1 able:1 both:2 resolution:3 produced:1 statistical:3 edu:1 resol:2 parameters:2 scattering:2 its:1 previous:1 fits:1 fit:2 wspc:5 much:1 vs:1 should:1 values:1 charge:3 present:1 ordering:1 voloshin:1 pmts:1 divided:1 eventually:1 non:1 gev:7 di:3 v2obs:3 modifications:1 results:4 early:1 beam:2 every:1 subtraction:1 they:1 new:1 world:1 part:1 difference:4 moreover:1 rhic:4 represents:1 february:5 several:1 consist:1 particle:4 presented:1 university:1 arxiv:6 list:1 by3:1 yield:1 sin:1 whether:1 detected:1 fitted:2 each:2 references:1 dip:1 side:3 heavy:1 correct:1 bars:1 weighted:1 reference:1 hadronic:1 energy:2 revised:2 modified:1 observed:2 arise:1 second:1 used:2 ex:2 measure:3 bins:2 event:7 addition:1 will:2 shown:1 errors:1 dense:2 denote:1 opaque:1 gradient:1 nuclear:1 measurements:3 rev:1 wi:3 overlap:1 particles:2 collisions:6 future:1 jia:1 above:1 between:5 international:1 get:1 journal:1 counters:1 measuring:1 full:1 scientific:1 respectively:1 120th:1 error:1 however:2 expansion:2 traversing:1 labs:1 pressure:1 2σn:1 wt:2 included:1 york:1 represented:1 plots:1 yf:1 strong:1 hadron:13 peripheral:1 received:2 cos:5 central:1 pt:7 consistent:1 widths:2 study:4 studied:1 dependence:3 example:1 introduction:1 resulting:2 unknown:1 corrections:1 contribution:2 fourier:1 hadrons:10 south:1 biases:1 pmt:2 adjusted:1 acceptance:1 previously:1 into:1 fig:4 expect:1 2v2:1 done:1 determine:3 deflected:1 leads:1 respect:3 2φi:2 extracted:2 establish:1 estimate:1 better:1 200gev:1 acknowledgements:1 publishing:1 jet:8 indicate:1 phenix:7 assumed:1 adare:1 there:4 bbc:2 due:2 been:3 centrality:2 width:3 nucl:3 trigger:7 correlations:4 low:1 azimuthal:2 anisotropic:2 bbcs:2 type:4 final:1 therefore:1 function:7 hard:2 partons:1 triggered:4 reaction:12 zhang:1 company:1 serve:1 weight:1 volume:1 proportional:1 observe:1 determination:1 systematic:2 authors:1 given:1 true:1 than:1 those:3 states:1 made:1 applying:1 determining:2 flatten:1 collaborations:1 was:5 instruction:5 measured:2 see:1 comparing:1 employ:1 matter:2 near:3 determined:4 below:1 how:1 were:7 following:1 distribution:16 stages:1 could:1 result:2 method:2 compare:4 would:1 associated:7 figure:2 inclusive:7 correction:2 modern:1 ψrp:11 needs:1 high:5 flatness:1 medium:3 au:20 attain:1 file:5 simulations:6 comparative:3 corresponding:1 tan:1 simulation:1 distributions:1 eric:3 different:2 united:1 angle:5 form:2 no:5 dashed:1 discussion:1 yn:1 when:1 lett:1 same:2 data:1 ny:1 fitting:2 pair:1 anisotropy:1 changes:1 modification:4 most:2 finite:1 parameter:1 events:7 nevis:1 jets:1 columbia:2 may:1 corrected:1 collaboration:1 use:2 functions:4 multiplicity:2 mixed:1 ion:1 v2:23 plane:14 pythia:5 significant:3 preliminary:1 date:2 rp:1 colliding:1 comparison:1 extremely:2 quantify:1 baseline:1 compared:2 attempt:1 collision:1 using:4 snn:3 adler:1 typically:1 lines:1 analysis:3 st:1 appendix:1 sn:1 exp:2 correlation:4 north:1 weigh:1 nuclei:1 vazquez:3 physics:1 order:3 incomplete:1 once:2
0705.0851.txt |@word limited:2 concept:1 remarkable:1 caused:1 global:1 focus:4 existing:1 four:1 facilities:1 alt:1 asteroseismology:5 issues:1 whose:1 hunting:2 environment:1 messenger:1 nodes:3 include:3 worth:1 indicating:1 advantage:2 song:13 very:6 frequencies:2 readout:2 integration:1 vlt:1 minute:1 eds:1 radii:1 large:3 guiding:2 science:2 small:2 centauri:1 noted:1 measuring:1 oscillation:1 direct:1 past:1 across:1 zero:1 cost:2 design:9 spectrograph:13 further:2 implemented:1 targets:4 even:1 aim:2 what:1 errors:1 sun:1 availability:1 current:2 above:1 designing:1 new:1 increasing:1 acknowledgments:1 full:2 led:1 extrasolar:1 here:2 understanding:1 hours:3 reported:1 objects:1 groups:1 ratio:1 observing:8 change:1 great:2 study:3 allows:1 reason:1 vogt:2 resulting:1 narrow:1 changes:1 brightest:1 diameter:5 via:1 followed:1 addresses:1 campaign:1 tracking:1 apj:2 aimed:1 coatings:1 estimate:1 predicted:1 use:3 would:3 brighter:1 contains:1 few:4 noting:1 aperture:3 australian:1 type:2 more:2 echelle:2 comparison:1 successful:1 factor:1 normalized:1 airmass:1 excellent:1 known:3 mounted:1 autumn:2 granulation:1 gabriel:2 setup:1 work:1 measures:1 dramatically:1 values:1 example:1 4m:1 dedicated:5 iodine:4 odorico:1 figure:5 mirrors:1 thermally:3 purposes:1 high:11 slit:6 grec:1 numbers:1 council:1 axis:1 huge:1 provide:1 tilt:1 uves:6 arrangement:1 located:3 fourth:1 symposium:1 fr:2 information:1 may:3 after:1 diagram:1 hence:1 plane:1 snr:2 horizontal:1 data:4 realized:1 short:3 natural:1 outline:2 spectra:2 separations:2 interrupted:1 fraction:1 green:1 allow:4 decreasing:1 observability:1 order:7 kaufer:1 operations:1 help:2 frandsen:1 developed:1 over:1 mission:1 years:1 including:1 mayor:2 before:2 position:1 group:6 l75:1 detected:2 complex:1 fig:3 latitude:1 weeks:1 main:10 meridian:1 overcome:1 versus:1 geographical:1 evolution:1 number:2 effects:1 foot:2 rotation:1 now:1 easily:1 term:4 500nm:1 reflectivities:1 always:1 university:2 establishing:1 realistic:2 magnitude:1 transmitted:1 mode:4 reasonable:1 radial:4 found:1 side:1 2k:2 kann:1 week:2 financial:1 telescope:10 fossat:2 series:2 reduce:2 frequency:5 measure:1 our:3 operation:3 enclosure:1 out:4 ultimately:1 asteroseismic:2 network:19 space:1 since:1 research:1 specifications:1 dominated:1 hill:1 performs:1 internet:1 shows:2 foundation:2 christensen:2 housed:1 little:1 standard:2 campaigns:1 completely:1 imaging:2 org:1 detecting:1 telescopes:3 r4:1 could:1 carlsberg:1 keep:1 transfer:1 consequence:1 uses:1 support:1 feed:1 already:1 primary:2 adopted:1 reached:1 thick:1 quality:3 size:2 given:2 temperature:1 their:2 leading:1 least:1 remotely:1 needed:3 station:1 observations:7 iau:1 white:1 1m:1 smoothed:1 williams:1 danish:2 way:1 bouchy:2 continuous:1 accurately:1 employ:1 optical:4 than:4 modes:4 observed:4 observatory:2 rugged:1 target:1 aao:1 see:1 limiting:1 project:1 determined:2 risks:1 amplitude:2 were:2 pasp:1 motivation:2 correction:1 ages:2 spectrum:2 curves:1 kepler:1 need:2 allen:1 relatively:1 instrumentation:5 ohlich:2 efficient:1 able:1 isolated:2 anglo:1 contact:1 note:4 potential:1 performance:6 detector:4 aliasing:1 channel:1 accuracy:1 spectral:4 hires:2 investigations:1 object:2 arcsecond:5 most:2 optimized:2 eight:1 plan:1 significant:2 preliminary:2 phase:3 measured:2 class:1 bradford:1 equatorial:3 observation:3 dordrecht:1 clear:1 cover:1 drifts:1 points:1 soho:1 velocity:10 typically:1 golf:5 show:3 german:1 bright:2 600nm:1 networks:1 cell:3 slow:1 based:3 should:1 virgo:5 surroundings:1 only:2 going:1 black:1 equipped:1 darwin:1 dk:1 dekker:2 there:1 assumed:1 soon:1 beam:3 nearly:1 during:4 layout:1 runs:2 bar:1 denmark:1 arxiv:1 tenerife:1 teams:1 hemispheres:1 investigate:1 bison:1 processed:1 activity:1 through:1 fixed:2 bars:1 reference:1 achieved:2 frame:1 hα:1 aarhus:3 maximum:1 detection:2 intensity:5 result:1 close:1 best:3 phases:1 mechanically:1 vertical:1 harvey:6 currently:1 sites:5 its:1 ucles:2 conceptual:4 conditions:2 checks:1 discovery:1 available:1 infrastructure:1 terms:1 institution:1 nature:1 attention:1 dome:4 however:2 spectroscopic:1 efficiency:1 comm:1 fgk:1 configuration:2 distribution:1 improve:1 motivations:1 both:4 essentially:2 harps:2 many:2 region:2 corrector:1 planned:2 contribution:1 duty:4 chaplin:2 simple:1 initiative:1 table:3 thanked:1 due:2 been:4 quickly:1 reduction:1 spread:1 maintenance:2 basic:2 expected:2 ph:1 prototype:2 meeting:1 empty:1 adc:1 controlled:3 precision:6 observe:1 spie:2 case:1 atmospheric:1 mount:2 will:28 near:2 reliably:1 almost:2 thus:3 site:1 surface:1 bigelow:1 ambient:1 different:2 hubbard:1 baseline:2 pay:1 pepe:1 cross:2 same:4 parts:1 schematic:1 throughput:2 several:5 development:1 independent:1 satellite:1 used:3 http:2 camera:2 hand:1 running:1 moving:1 robotic:2 munkegade:1 focal:2 cycle:4 lower:1 task:1 reflection:1 makes:1 no:1 well:5 analysis:1 costs:2 components:4 howe:1 ccd:2 model:2 l105:1 being:1 tip:1 obtain:4 valuable:1 front:1 stored:1 coud:3 romero:1 generous:1 ny:1 sky:1 instrument:2 internal:1 slits:1 location:1 easy:1 grating:2 identical:2 around:2 demands:1 showing:1 results:1 possible:9 possibly:1 marcy:1 background:5 using:1 corot:1 projects:2 apart:1 necessary:1 like:6 success:1 signal:3 velocities:3 roth:1 mhz:2 either:2 stationary:1 reduced:1 node:1 www:1 methods:1 sequence:1 choosing:1 mirror:2 oscillations:15 imager:1 vol:1 scale:1 demonstrates:1 bedding:3 centre:1 extensively:1 per:1 does:1 eliminate:2 proc:3 demonstrated:1 limitations:1 noise:2 power:5 schedule:1 each:3 illustration:1 stellar:8 lamps:1 although:1 transported:1 properties:1 iris:1 pipeline:2 central:1 carried:4 months:1 discussed:1 shipping:2 carrier:1 ensure:2 queloz:1 seeing:2 equally:1 reidel:1 instruments:5 image:1 obtaining:1 beneficial:1 kjeldsen:2 references:1 determine:3 reducing:1 extremely:1 housing:1 initial:1 long:7 dispersion:1 width:3 collimated:1 window:1 low:5 stars:13 fnu:1 was:2 assumes:1 function:2 rasmussen:1 interest:1 extended:1 astro:2 butler:5 hemisphere:1 construction:2 solar:14 mnras:1 groundbased:1 line:2 utilizing:1 made:2 whether:1 assessment:1 access:2 variations:1 hosting:1 planet:2 record:1 un:1 limit:1 containers:1 spectroscopy:1 problem:1 similar:3 elsworth:1 detailed:3 gong:1 associated:1 dalsgaard:1 abstract:1 describe:3 single:1 au:1 periods:1 planets:1 simulations:3 az:1 diego:2 compared:2 calibration:1 dashed:1 drivers:1 when:1 envisaged:1 field:1 other:5 compares:1 department:1 poor:1 polar:1 briefly:1 star:2 problems:2 shown:4 variation:1 interferometric:1 peak:1 coverage:1 included:1 container:2 astronomy:1 exposure:1 building:4 implies:1 physics:2 required:1 diffraction:1 ensuring:1 status:1 pupil:1 time:5 walker:2 resolution:6 avoid:2
0705.0852.txt |@word represent:3 partial:1 consider:3 pointing:1 ali:1 rev:11 magnetic:53 fabricated:3 integration:1 leads:7 scalar:3 gb:37 go:1 gm:4 localized:1 layers:3 whose:2 inverse:1 const:1 calculate:1 bx1:1 concerned:5 bx2:1 expelling:3 tn:6 charge:23 according:1 squeezing:3 those:3 int:1 under:9 analogous:1 include:1 cm3:1 ingredient:1 eigenstate:3 g2:15 very:5 implicitly:1 rise:2 intriguing:1 results:3 prog:3 maskawa:1 putting:1 difficult:1 mixing:1 ninomiya:1 exact:1 condition:9 uehara:1 level:18 forth:2 solution:6 d2:6 girvan:1 large:3 discrete:1 vector:1 science:1 small:2 relation:3 refer:1 degeneracy:4 force:1 destroys:1 consistent:2 coefficient:1 direct:1 sign:1 approximation:2 zero:70 dynamics:1 odd:1 quite:1 even:9 what:1 plays:1 appear:3 dφd:1 giving:1 abi:4 section:8 xφ:1 realizing:2 melt:1 uniform:11 current:4 ρr:11 above:9 fractional:1 international:1 3g:5 exercise:2 satisfy:6 edited:1 condensed:6 exchange:1 respectively:2 loose:1 component:4 residual:2 here:6 condenses:1 address:2 directions:7 along:2 strong:5 equations:2 appears:1 change:1 obtained:3 rigorously:1 receive:1 involved:1 economics:1 suggests:2 amount:1 periodic:2 procedure:1 pick:1 decouple:1 makes:1 involves:1 york:1 composed:3 appropriately:1 yamada:1 spatially:8 gluons:84 semiconductors:5 explained:1 a22:1 rozowsky:1 d72:1 ask:1 electromagnetically:1 gluon:2 summation:1 ipx:2 shovkovy:2 imaginary:3 gaas:1 use:5 asymptotic:1 would:3 d75:1 positive:6 give:2 examined:1 negative:5 next:2 occupying:3 classically:1 nucl:5 compensate:1 examination:1 therefore:9 qcd:4 taken:2 yamawaki:2 more:7 th:2 ejected:1 abj:1 becomes:3 naive:2 stable:7 distribution:2 glass:6 ip0:9 normalized:1 bailin:1 known:1 cases:1 hold:1 iii:1 must:11 ρa:4 states:32 account:2 rotational:1 quartic:1 decouples:1 equation:8 work:1 regularity:1 ρn:5 nagoya:1 fock:3 values:1 temperatures:2 hashimoto:1 acj:1 following:6 ta:1 spontaneous:3 example:3 impose:1 abelian:1 predict:1 discussed:6 distributions:1 arise:8 neglected:4 near:1 nielsen:3 bgm:1 involve:1 effectively:7 minimum:4 degenerate:10 allowed:2 standard:1 gǫabc:1 mix:2 regularization:1 technology:1 discussion:3 holds:2 eigen:1 feature:3 chemical:1 far:4 nontrivial:1 answer:1 d69:1 verlag:1 φ2c:3 simplicity:1 may:14 after:1 derived:1 minimized:1 plane:1 coming:1 summarize:1 law:1 revealed:1 grow:3 gluonic:2 realized:1 miransky:1 natural:1 dynamical:5 effective:2 higgs:13 light:17 spectra:2 explicit:1 correspond:2 su:3 so:7 automatically:1 decreasing:2 chakrabarti:2 increase:1 order:8 typical:3 breaking:1 dx:17 pointed:2 move:3 vary:3 soon:1 years:1 produced:5 paper:6 including:1 looks:1 motions:2 argued:2 japan:1 kinetic:5 excitations:13 its:1 boosts:1 before:1 ld:4 longitudinal:28 how:1 energies:26 interesting:2 masses:1 solving:1 coordinates:1 actually:4 forms:1 absence:1 production:1 meissner:1 choose:1 prakash:1 h0:4 non:7 within:1 junction:1 eip0:1 introduce:1 landau:20 mention:1 repulsive:6 effects:4 they:9 iancu:2 rotation:1 now:5 discuss:2 possess:2 represents:8 term:18 several:1 dirac:1 university:1 hamiltonian:21 sufficiently:6 filling:2 2g:2 l2:2 mode:16 reasonable:1 each:9 2l:8 instability:4 2n:3 energetically:4 ap0:4 side:1 characterized:1 referred:1 lifted:1 transform:1 independent:2 generation:6 ed:1 energy:44 mclerran:1 constitute:1 inhomogeneous:1 owing:7 expect:2 quantum:49 our:8 operation:1 extract:2 out:3 prange:1 shown:14 space:4 furthermore:4 since:15 induces:3 denotes:3 particles:8 similarly:1 nakajima:1 denoted:4 induced:3 issue:1 shows:2 commutation:4 theory:5 interactions:5 favored:1 semipositivity:1 b156:1 free:1 quark:40 indices:2 completely:3 formation:4 ohtani:2 eigenvalues:4 put:3 pivovarov:1 pairs:5 interaction:12 βp:20 b152:1 created:1 transition:3 φc:39 diquark:5 thing:1 length:1 produce:1 δij:1 vac:4 hence:5 configurations:2 neglect:5 first:13 origin:2 xi:1 symmetry:2 variables:1 number:15 reaches:2 approximate:4 fija:1 least:3 directly:1 carry:1 compensated:1 πm:2 angular:3 wilczek:1 given:17 limited:1 rewritten:3 3p0:1 their:6 introduction:1 condensate:6 πn:1 system:2 approximately:5 parallel:7 indicate:2 assumption:1 fermions:1 realization:1 postulate:1 structures:1 relations:3 gives:1 relationship:1 baryon:5 transverse:14 rajagopal:1 favorable:2 x3:2 x0:2 x1:2 representing:4 than:6 center:1 eigenfunctions:1 ambjørn:1 third:4 roles:1 culture:1 approximations:1 aai:3 second:9 aaj:3 annihilation:4 matter:32 determined:5 contrary:1 speaking:1 were:1 perturbative:1 behaviors:1 function:2 chern:1 false:1 rewrite:2 fluctuation:1 occupies:1 argument:3 b160:1 already:1 need:2 apparently:3 any:6 ueda:1 strength:1 φap:7 aside:1 lp0:1 chiba:1 instance:2 high:1 potential:7 take:8 simplified:1 finding:1 new:1 channel:1 play:5 unless:1 electric:2 normal:2 denominator:1 wells:1 an4:2 most:2 tatsumi:1 involving:4 gauss:2 an3:2 phase:11 extremely:2 probable:1 4l2:1 average:1 possesses:1 astro:1 points:1 electrons:13 exp:9 charged:6 physics:1 width:4 fact:6 quantity:1 naively:1 show:11 nπ:1 please:1 supported:1 merit:1 notations:2 minimizing:7 gauge:24 expressed:2 trivial:4 find:13 ground:64 satisfies:2 transformation:1 explain:1 written:1 should:8 moments:1 only:17 explicitly:1 minimize:3 factor:2 over:3 ip:2 do:12 goes:3 notation:1 di:1 express:1 expectation:2 superconductor:2 ones:2 dz:4 words:4 invariant:1 penetrate:1 dt:1 densities:1 fields:21 gbl:1 arxiv:1 expansions:1 ministry:1 summary:1 common:1 through:1 occupy:1 2p0:4 set:1 reference:1 hadronic:1 j1:1 observed:3 unfavorable:2 namely:8 venugopalan:2 radius:1 result:4 existence:6 discussions:1 terms:17 αp0:5 particle:2 concern:1 αq:1 αp:11 phases:5 exploited:1 interacting:4 mentioned:4 nuclear:3 review:1 definite:6 yet:1 state:105 future:1 various:2 between:11 fermi:1 boundary:1 conditions:1 p20:1 never:2 recently:1 anti:5 screen:5 weak:2 however:1 huang:1 limitation:1 analyzed:1 eipx:2 configuration:4 remaining:2 last:4 many:17 taking:3 density:12 equal:1 against:2 quantization:6 assure:1 dated:1 contribution:1 ia2:2 comes:3 comment:5 strongly:2 jz:3 repulsively:1 cm:1 point:3 simple:5 others:1 2nd:1 dimensional:22 represented:2 grants:1 simply:4 decreases:1 cancel:1 ordered:1 rep:1 pq:1 described:1 bp0:3 addition:1 due:8 been:10 screened:1 defined:5 much:4 treat:1 fukushima:1 expected:2 ph:9 pl:7 treatment:5 direction:12 arises:8 corresponding:3 sufficient:1 formed:3 gas:3 6m:1 gap:7 coherent:5 external:2 general:1 spin:2 present:6 aid:1 case:10 p0:88 nishikawa:2 reliable:2 expanded:1 appearance:1 single:2 value:4 spontaneously:4 will:6 while:2 suppose:1 squeezed:1 situation:1 loop:3 grip:1 layer:6 larger:2 simons:1 λqcd:2 thus:16 them:2 surface:4 iv:1 ii:1 quantize:1 superconducting:9 ij:2 cone:17 wave:2 vanish:10 solutions:18 ig:6 around:5 φp:10 different:5 classified:1 suggest:1 make:4 harindranath:3 lett:6 same:3 complex:1 φd:1 diagonalize:4 φi:1 finite:8 φm:16 neutron:8 higher:2 gorbar:1 fairly:2 used:4 infinity:1 see:5 published:1 effect:2 hand:10 levels:2 maruyama:1 kim:1 supposing:1 savvidy:1 recent:2 lower:2 weakly:1 modes:66 analyzing:2 charges:3 well:27 analysis:1 obviously:4 2gb:4 without:2 solve:1 characterizing:2 components:8 consistency:1 coordinate:2 model:6 self:3 justify:1 uniquely:1 just:12 among:1 being:2 superconductors:5 obtain:2 vanishes:3 relevant:2 transforms:1 integer:5 love:1 momenta:5 rotates:1 scattering:1 eigenstates:4 alignment:1 previous:5 note:5 speculate:2 b582:1 candidate:1 infinitely:20 seems:3 except:1 hall:20 color:93 attractive:1 easy:6 diagonalization:1 excited:2 momentum:21 real:10 nakano:1 saturation:1 vii:1 eigenfunction:1 depends:1 easily:2 evaluate:2 couple:4 decomposed:1 possible:2 matters:7 increases:1 βp0:6 vacuum:10 confined:4 using:12 unique:1 mod:2 iida:1 rotate:1 necessary:1 like:8 semi:3 follows:1 b129:1 δp:4 10km:1 δn:1 remind:1 δm:3 unstable:13 morimatsu:3 arbitrary:1 decrease:1 nucleons:3 δb:4 reduced:1 spins:1 because:5 classical:24 vortices:1 plausible:2 creation:4 springer:1 japanese:1 calculated:1 specified:2 extended:1 δq:1 neglecting:6 diagonalizing:1 exists:1 happens:1 specific:1 scale:2 dense:15 lead:1 flux:1 gapped:4 quarks:11 extensively:1 overlap:1 lattimer:1 does:11 connecting:1 assuming:2 gapless:9 leonidov:1 2a:2 inserting:1 core:2 ij2:1 run:2 bc:1 bm:2 perpendicular:3 costs:1 bp:6 although:5 2m:2 similarity:1 analyses:4 exciting:1 proceed:2 about:2 ferromagnetic:17 constraint:1 freedom:1 anomalous:1 dependence:3 o:3 dett:2 nonvanishing:1 carries:3 a2:1 repulsion:2 done:1 consequently:1 gamma:1 vi:1 presence:8 maxwell:1 into:7 magnetars:4 domain:4 suppl:2 neutrality:1 appropriate:5 right:1 determine:2 operator:10 sports:1 iδij:1 hep:9 assumed:9 there:24 question:2 condense:5 start:3 quadratic:2 bosons:3 low:5 stars:8 analyze:2 was:2 naturally:1 lowest:17 form:20 hr:6 differences:1 but:24 volume:2 φn:2 hn:1 hm:3 clarify:1 true:2 partially:4 made:1 wish:4 generating:1 up:3 us:1 2πp:3 below:6 gaps:3 limit:6 sum:1 ix2:2 problem:2 similar:6 called:2 aa:2 ab:12 associated:1 ohi:1 ai:6 describe:1 am:8 determinant:1 denote:2 ap:13 examine:5 exist:6 formulation:7 politics:1 education:1 a1i:1 iwazaki:8 minimizes:1 ni:1 functions:1 nm:6 no:8 eq:21 when:6 detail:3 hn1:2 field:78 other:28 role:5 papers:1 department:1 you:1 screening:2 operators:12 generates:1 excitation:12 superconductivity:1 models:4 kashiwa:1 a1:1 a0:2 generated:5 important:8 bounded:1 n1:2 cooper:1 olesen:2 structure:3 ago:1 algaas:1 condensation:5 implies:7 coulomb:17 assume:5 thorn:2 factors:1 theor:3 having:1 mass:1 incomplete:1 time:4 n0:1 cores:1 n2:6 n3:3 n4:3 original:2
0705.0854.txt |@word limited:1 consider:1 remarkable:1 switched:1 caused:2 results:4 icf:5 four:9 avalanche:2 disc:2 whose:1 zone:3 technique:1 young:4 program:1 brown:3 photocount:2 zhang:2 far:4 wave:1 difficult:2 experimentally:1 dynasty:1 electronics:1 condition:1 rotating:1 modulator:2 presented:2 did:1 positions:1 convenience:1 coincidences:2 minimal:1 optics:1 setup:1 measuring:2 smaller:1 zh:1 pulse:4 fold:1 rate:5 chen:2 scientific:1 magill:1 speckle:1 diamanti:1 selected:1 near:1 experiment:5 above:1 crossed:1 d1:1 method:3 contrast:1 thin:2 pioneering:1 simultaneously:1 chose:1 respectively:5 here:1 directions:2 consideration:1 quite:1 obtained:5 shift:2 studied:1 reason:1 domains:1 birefringent:1 klyshko:4 plotted:1 formulated:1 followed:1 singlephoton:1 deadtime:1 counts:2 clockwise:1 establish:1 plot:1 fed:1 would:1 faint:1 next:1 camera:1 ursin:1 therefore:1 aperture:1 theoretical:4 separated:1 flat:1 penin:2 clearly:1 becomes:1 envelope:3 g123:2 visibility:30 glass:6 glan:2 normalized:10 varying:2 known:2 cases:1 account:1 mm:1 ferri:2 originally:1 averaged:7 zhao:1 bias:1 values:5 rectangle:3 drops:1 performed:1 figure:1 scan:2 calculation:1 high:9 slit:6 ivanova:1 numbers:1 counting:4 yang:1 varied:2 provide:4 s2:1 hanbury:3 very:1 rubin:1 criterion:3 fourth:7 instead:2 ordinary:3 inputs:2 product:1 description:1 may:1 after:2 horizontal:1 revealed:1 types:1 third:15 light:11 lines:3 correspond:1 rather:1 sh:3 so:4 correlation:5 acknowledges:1 counted:1 typical:1 pulsed:1 indeed:1 over:3 interpreted:1 thermal:11 experiments:7 including:1 filters:1 signs:1 still:2 fwhm:1 its:5 some:1 rapidly:1 fit:1 chosen:1 pulses:2 better:1 fig:18 image:2 arguments:1 maximal:5 non:2 diodes:1 reflected:1 scaling:1 effects:1 front:2 matched:1 several:1 always:1 university:1 2x:2 leninskie:1 sufficiently:1 magnitude:1 transmitted:1 mode:2 each:7 quarter:1 side:1 bache:3 mean:2 eh:1 bentley:1 used:7 lomonosov:1 prisms:2 interferometer:1 frequency:3 gating:1 measure:1 quantum:1 our:5 lithography:1 avoided:1 eq:5 really:1 shown:7 optic:1 since:3 interference:54 increase:1 modulation:2 formula:1 calcite:3 induced:1 ref:1 note:2 shows:4 foundation:1 lugiato:3 turning:1 standard:1 extraordinary:3 completely:1 dependencies:4 imaging:7 finite:1 r1:1 geometry:1 could:2 keep:1 turn:1 american:1 period:1 circuit:3 first:3 φaj:1 number:3 reaches:1 relations:2 another:1 thick:1 precisely:1 electronic:1 synchronously:1 passes:1 given:4 similarly:1 leading:1 eqs:1 achieved:6 system:1 approximately:2 glauber:4 rates:1 scheme:2 gives:1 relative:3 optical:1 somewhat:1 corresponded:1 photographic:1 than:8 distance:2 photograph:1 accordance:1 double:2 second:2 determined:1 intensities:3 amplitude:1 were:5 russia:1 gp2:1 hz:2 turned:1 bs1:1 curves:1 randomly:1 any:1 polarization:1 instance:2 φai:1 detector:8 moscow:2 circles:3 led:1 opposite:3 phase:12 measured:4 mach:1 zhai:1 observation:2 average:2 later:1 detectors:13 order:28 points:2 physics:4 icfs:7 fact:1 selection:1 show:9 supported:1 discovered:1 threshold:1 ground:1 o:1 ratio:1 depended:1 should:7 only:3 achieve:1 erasure:1 chekhova:2 notation:1 means:3 beams:2 tilting:1 beam:4 ones:4 nearly:1 3b:1 dv:1 arxiv:1 doubled:2 paper:1 processed:1 shots:1 through:1 fixed:1 view:1 scanning:1 attenuated:1 frame:6 correlations:3 observed:4 intensity:16 radius:2 result:1 close:1 arm:1 lee:1 phases:5 registering:1 placed:5 pattern:17 gage:1 state:1 brambilla:3 various:1 between:5 numerous:1 vertical:1 nature:3 importance:1 weak:1 however:2 wu:1 twophoton:2 configuration:1 pixels:3 both:8 cos:9 last:2 limits:1 many:1 according:1 gp1:1 sensitive:1 exceeds:1 passing:1 expression:1 experimental:4 otherwise:1 arbitrarily:1 among:1 adjusted:1 point:1 simple:1 ac:1 coincidence:8 grants:1 simply:1 respect:1 erased:2 described:1 addition:1 three:15 been:5 much:4 expected:1 yag:2 empty:3 sanders:1 direction:2 corresponding:1 observable:1 sufficient:1 formed:2 photon:38 zeilinger:1 coherent:13 bs2:1 repetition:2 case:13 multi:11 p1:1 laser:4 pacs:1 solid:3 value:4 rectangular:1 will:1 aspelmeyer:1 while:4 steinberg:1 φbj:1 φbi:1 photodiodes:1 mitchell:1 walther:1 pittman:1 almost:2 averaging:1 twiss:3 canon:1 equal:2 ij:11 triple:3 φij:1 rfbr:1 different:2 considerable:1 journal:1 suggest:1 radiation:10 same:4 orders:1 quant:1 split:1 incorrectly:1 units:1 plates:5 electro:2 grows:1 pan:2 higher:7 independent:1 attenuation:1 see:2 i1:2 zehnder:1 i3:2 i2:2 effect:1 counterparts:1 hand:3 mandel:4 moving:1 recent:1 interferometers:1 lower:2 accumulate:1 analysis:1 patterns:2 edge:1 coordinate:2 less:4 being:6 when:2 rotated:1 obtain:1 sources:22 voltage:2 yamamoto:1 speed:1 tcc:1 taken:1 oriented:1 density:1 photons:1 had:1 source:3 slits:2 lett:6 input:1 5a:2 remaining:1 5b:1 identical:1 fluctuating:1 digital:4 harmonic:1 dark:1 zukowski:1 entangled:2 using:1 part:1 disadvantage:1 necessary:1 sizes:1 schools:1 communications:1 either:1 exceed:2 because:3 classical:16 phenomena:1 uspekhi:2 duration:1 provided:3 dimensions:2 strekalov:2 recorded:2 exceeding:2 per:2 instantaneous:2 provides:1 visibilities:2 demonstrated:2 inserting:1 noise:1 obey:1 equivalent:1 processing:3 although:2 similarity:1 plots:2 noisy:1 gained:1 comparison:1 uniformity:1 based:1 dependence:2 recognized:1 range:1 ou:1 introduced:2 slightly:1 nsh:1 rev:15 beamsplitter:2 into:3 within:1 due:1 registration:1 frames:1 theoretically:1 statistics:2 area:2 support:2 spots:1 width:2 low:1 way:2 resulted:1 valencia:2 lundeen:1 was:28 function:3 considerably:3 boyd:1 sergienko:2 gory:1 registered:3 but:2 hk:1 neutral:1 nonclassicality:1 true:1 ph:2 made:2 applying:1 maximum:2 crystal:5 below:2 limit:3 gatti:3 distribution:9 similar:3 calculated:1 shih:4 khz:1 diffraction:3 measurement:2 influence:1 waks:1 images:1 single:5 scanned:3 periods:1 wavelength:1 work:1 distributions:1 again:1 functions:2 compared:1 nm:1 no:4 nd:2 field:5 other:5 spatial:6 department:1 ns:1 conclusion:1 coherence:2 nonclassical:3 variation:2 prepared:1 a1:2 a3:1 a2:2 suppression:1 structure:2 exposure:1 ghost:6 independently:1 practically:1 ghosh:1 apertures:2 pseudo:7 eom:5 time:4 resolution:1 having:1
0705.0855.txt |@word sci:1 consider:5 illustrates:1 particular:4 desirable:1 results:1 edu:2 localized:1 row:2 whose:1 dimensionality:5 aji:1 graph:4 send:2 finally:1 tk:28 γm:2 stable:15 nodes:21 di1:2 di2:2 random:1 very:1 seemingly:1 choice:1 lyapunov:3 every:1 entries:3 li:4 manageable:1 matrices:1 condition:2 dij:18 transmission:5 induction:1 solution:6 t0:3 large:1 discrete:10 convenience:1 vector:2 small:5 workloads:1 noted:2 proof:13 work:1 b22:2 b21:2 zero:4 directionality:1 chen:3 further:5 dynamics:3 linear:9 established:4 nonlinear:2 appear:1 section:5 near:1 above:8 new:8 increasing:2 except:1 degree:1 here:1 understanding:1 following:10 china:3 b2i:10 address:1 directions:1 obtained:2 remark:5 antisymmetric:1 noticeable:1 rigorously:2 receive:1 involved:1 study:2 studied:2 ignoring:1 amount:4 identity:1 subsequences:2 suitable:1 makes:1 named:1 addresses:1 extra:2 addressed:1 total:4 challenging:1 would:2 positive:12 permitted:1 therefore:5 criteria:2 taken:2 more:5 05e:1 company:1 under:2 varying:10 actual:1 cases:3 iii:1 evolves:3 science:1 overloaded:2 erd:1 values:1 concepts:3 growing:2 nlin:1 example:6 initial:13 sn0:3 process:2 expanding:5 share:2 topic:1 council:1 sense:5 robinson:1 absolute:2 requirements:1 varied:1 rather:2 s2:3 discussion:2 holds:1 renyi:1 allowable:2 parameter:2 simplicity:1 may:14 suppose:4 coined:1 after:1 hong:3 connectivity:3 inst:1 lay:1 end:1 law:1 data:16 constants:1 diagonal:1 attempt:1 dynamical:5 whenever:1 consequently:2 grant:3 sj:3 complexity:1 sh:1 so:4 fundamental:2 definitions:2 order:1 typical:1 evolutionary:1 indeed:1 vary:3 kong:3 stability:18 paper:2 including:1 satisfies:7 its:13 contaminated:2 difference:3 rapidly:1 directional:1 interesting:1 actually:2 systems:5 unbounded:6 main:1 s1:3 them:1 scaling:2 framework:1 transmissions:1 effects:1 they:1 yu:1 structural:1 2t:86 easily:3 several:3 explains:1 university:3 realistic:2 inequality:1 each:12 instability:4 characterized:1 referred:3 heavy:1 weighted:4 formulate:2 ee:1 owing:1 substantially:2 assumption:3 nonlinearities:1 special:4 out:1 shown:1 network:98 factors:1 restricted:2 since:7 chaos:3 research:3 si:18 internet:1 issue:2 math:1 foundation:1 theory:2 given:7 free:2 quite:2 ntk:4 complicated:1 asi:2 barab:2 definition:8 watts:2 r0:16 r2:1 computers:6 florida:1 moment:2 times:8 consequence:1 think:1 first:3 xj:17 major:1 already:1 features:1 omitted:1 symbolic:1 number:7 will:7 another:1 electronic:1 city:1 differ:1 become:2 introduction:1 system:29 least:3 their:3 station:1 listed:1 structures:1 gives:1 albert:2 immediate:1 x2:4 natural:1 x1:4 than:4 oscillate:1 require:1 imply:1 determined:1 behaviors:2 troublesome:2 βsi:6 generality:2 argument:2 say:1 need:1 sar:1 any:18 solitons:1 complete:1 αm0:2 min:5 latter:1 isolated:3 mechanism:1 note:1 causing:1 build:1 sufficiency:4 xi:15 province:1 play:1 added:4 2tk:5 most:1 virus:3 satisfying:3 rigor:1 letter:3 intrinsic:1 class:2 forever:1 cause:1 treats:1 considered:3 clear:4 scrambled:1 points:1 similarly:1 oscillates:1 typically:1 fact:2 quantity:15 particularly:1 phenomenon:1 show:2 supported:1 discovered:1 relation:2 keywords:1 fine:1 networks:20 based:2 should:1 only:10 local:1 dj:1 means:1 uncountable:1 simplest:1 next:1 cannot:1 aforementioned:1 becomes:1 runs:3 αm:1 arxiv:1 crc:1 common:1 shi:4 fixed:4 set:4 exists:13 j0:7 up:1 connections:4 namely:1 computer:21 result:2 enhanced:1 said:5 review:1 written:3 future:3 various:1 between:4 invariant:5 conditions:2 email:4 timevarying:1 hence:4 jx:1 nature:2 initially:1 however:2 modeling:3 both:5 many:8 conclusions:1 equal:4 connection:3 present:1 receives:1 contribution:1 whole:17 comes:1 otherwise:3 load:1 among:2 cn:1 point:10 simple:1 jinan:1 cd:1 dimensional:2 simply:1 sequences:5 moreover:5 endeavor:1 throughout:1 devil:17 described:7 second:4 addition:1 simplification:1 copies:1 pc:1 describes:1 interest:1 basic:2 choose:4 direction:1 corresponding:7 received:1 quantities:2 sufficient:2 external:1 rephrased:1 denote:1 spirit:1 those:4 case:16 engineering:1 value:4 aim:1 while:2 aii:1 aij:8 situation:3 revisited:1 property:17 inherits:1 larger:1 chaotic:4 thus:1 surprisingly:1 according:1 ii:4 triple:1 bij:1 c0:8 leaving:1 k0:3 different:3 verified:4 author:1 fractals:1 same:2 clearly:1 complex:5 xj0:4 finite:9 breakdown:2 used:2 infinity:1 i2:3 differing:1 publ:1 running:1 necessity:4 infinite:4 changing:1 infamous:1 recent:1 break:1 erdos:1 scenario:1 no:2 well:6 analysis:1 obviously:1 without:2 entry:1 model:24 nnsf:2 dimension:6 less:2 being:2 when:4 rest:1 stored:3 rn0:9 captured:1 infinitely:6 antisymmetrical:4 mathematically:4 other:4 theorem:14 input:3 divided:2 real:3 aspects:2 spectacular:1 represents:2 replaced:4 possible:1 increases:1 burden:2 press:1 world:4 rnt:2 loss:2 necessary:2 follows:12 server:17 specific:1 unstable:11 either:1 hung:1 output:5 works:1 essential:1 mathematical:4 exceed:1 acad:1 old:4 classical:5 sends:2 some:26 evaluated:1 b2:2 strogatz:2 xn0:2 scale:2 dimensions:6 sufficiently:1 affects:2 does:3 assuming:1 power:1 bi:1 restrictive:1 yorke:4 although:2 found:1 properties:2 integers:1 central:1 xnt:2 discussed:6 compatible:1 introduced:3 os:1 block:1 own:2 h2:1 h3:2 into:3 h1:1 down:1 references:1 conceptually:1 weight:1 deal:1 area:1 there:20 why:1 way:2 was:1 m0:31 sdu:1 elsewhere:1 form:2 forming:1 but:6 hk:1 line:1 removed:5 longer:1 directed:4 characteristic:1 maximum:23 w32:1 continuously:3 distribution:1 define:1 similar:8 called:7 b1:4 strongly:2 shandong:3 constant:18 defined:6 abstract:1 general:5 single:1 diverse:1 exist:4 inf:1 internal:1 variety:2 storage:9 book:1 b12:2 details:1 b11:2 department:2 mathematics:1 nt:50 conclusion:1 node:22 enyi:1 generates:1 completes:2 time:47 bounded:7 matrix:20 building:1 max:1 implies:1 coupling:2 assume:9 b1i:9 weights:4 memories:1 n0:33 starting:1
0705.0856.txt |@word partial:5 consider:2 illustrates:5 global:1 results:4 four:1 parameterization:1 expressions:1 research:2 centers:2 calculate:1 concerned:1 young:1 finally:4 those:3 under:2 include:1 applied:1 sherbrooke:1 mpa:8 far:1 account:2 vegas:1 orientations:1 difference:2 illustrated:6 unlike:1 transmission:15 turns:4 list:1 mm:23 small:1 stiffer:1 rack:2 upper:1 2k6:1 smaller:8 force:6 10b:1 qinit:3 10a:2 direct:1 sign:1 translating:3 second:1 design:22 evaluated:1 dynamics:1 machines:1 theory:1 index:3 minimize:5 dept:1 section:2 axial:2 above:1 conduct:1 3c:2 3b:1 3a:1 journal:2 3d:1 simultaneously:1 lee:1 respectively:7 here:2 κc:5 reported:4 active:8 layout:1 along:5 κp:2 obtained:8 convert:1 golovin:1 parameters:8 broken:1 technical:2 study:1 compliance:1 allows:1 concurrently:1 amount:3 stiffness:1 usually:1 implement:1 suitable:3 makes:2 montreal:2 plotted:2 composed:3 diameter:2 named:2 formulated:1 regardless:1 secure:1 bounds:1 vii:1 cylinder:2 mecha:1 follower:13 h3a:1 motor:1 translational:3 apply:1 plot:1 use:2 john:1 pushes:1 usa:1 kinematics:3 distinct:1 positive:4 negative:3 france:2 m4:5 depicted:5 m1:3 therefore:6 m3:3 criteria:1 scope:3 more:7 sons:1 becomes:1 apparent:1 curvature:11 borisov:1 berlin:1 carrying:3 normalized:1 known:1 mounted:7 iii:8 must:1 ρc:14 balls:2 damien:2 work:2 rκ:1 caj:1 remain:1 values:5 thin:1 cam:100 strategies:1 root:1 example:1 control:1 figure:28 table:10 high:3 minimum:3 taking:1 want:2 allowed:1 tan:1 axis:5 counterpart:1 ones:1 end:3 eng:1 provide:1 machine:8 pure:4 frontiers:2 optimal:5 allowable:4 absolute:2 intelligent:1 sin:4 profile:17 fr:1 may:3 wiley:1 derived:1 applications:2 produce:1 fatigue:1 studies:1 shuman:1 parallel:2 las:1 realized:1 third:1 slightly:1 lines:2 maintain:1 used:3 sm:20 order:9 figs:4 operations:1 carra:1 produces:1 september:1 indeed:3 over:1 vary:1 nondimensional:1 produced:3 paper:7 thesis:1 pitch:12 ieee:1 its:3 outer:1 fit:1 la:1 interesting:2 coordinates:3 better:7 according:3 fig:17 derivative:4 main:2 easier:1 them:2 asme:12 thereby:2 noe:1 material:6 introduce:1 band:2 transmissions:2 effects:1 they:3 closer:1 rotation:4 now:1 equality:1 alez:2 parameter:2 university:3 alternately:1 slide:20 inequality:1 transmitted:10 2a:1 2b:2 each:3 contours:5 found:1 side:1 characterized:3 en:1 reduce:1 displacement:4 ec:1 extended:1 static:1 measure:1 approximated:1 pareto:14 eq:6 out:5 canada:1 shown:4 divide:1 frontier:13 quantify:1 furthermore:2 since:1 induces:1 denotes:2 increase:1 ψmin:2 nominal:1 ro:1 issue:2 occurs:1 shows:2 bouyer:2 after:1 linear:4 mechanisms:22 monotonic:1 reason:1 advantages:1 caro:3 besides:3 automation:1 e1:1 generate:1 e2:1 definition:1 pairs:1 geometry:1 feasible:4 motion:7 turn:1 machining:2 place:1 hence:1 moving:1 rudolf:1 first:2 origin:3 xl:3 opez:1 variables:7 number:16 long:2 pellegrini:1 comprises:1 thick:1 clarity:1 angular:1 size:10 given:5 cartesian:3 needed:2 introduction:1 compliant:1 relations:1 cosψ:1 their:7 too:1 nantes:3 sensitivity:10 pmax:26 gives:1 tool:1 continuous:1 slider:2 wenger:1 part:4 authors:1 translation:1 than:11 coefficients:2 whereby:1 steel:4 distance:3 cracks:1 determines:3 depends:3 limiting:1 matter:4 lmax:2 determined:2 supposed:1 iron:1 russia:1 projections:1 rad:1 torque:2 antagonistic:1 conjugate:27 screws:2 any:1 conversion:1 depict:2 angle:27 depending:1 prismatic:3 latter:2 able:1 mechanism:32 k2:3 k1:3 materials:3 take:3 objective:11 performance:6 moscow:2 accuracy:1 formulas:1 cnrs:1 multiple:2 mcgill:3 centre:1 denominator:1 jorge:1 most:1 significant:1 cams:33 popularity:1 dof:2 drive:4 proceedings:2 points:2 verlag:1 bodies:3 mechanical:4 velocity:3 fact:5 nψ:1 show:1 friction:3 radii:2 solutions:9 nevada:1 trivial:1 july:1 based:5 simulating:1 copyright:9 state:1 only:6 stephane:2 developed:1 local:2 notation:2 means:8 lobe:3 de:3 cannot:1 new:2 nm:1 aluminum:1 bearings:2 arxiv:1 qc:1 common:2 qi:4 fixed:1 view:1 bulky:2 rms:1 moduli:1 variations:7 frame:10 ends:3 grey:1 namely:3 computer:1 radius:10 cim:1 waldron:1 close:1 optimum:6 πe1:1 πe2:1 surfaces:1 evaluation:1 capacity:1 ways:1 pressures:3 written:1 closed:1 between:20 geometric:2 tolerance:1 email:2 knowing:1 publishers:2 notice:8 terms:2 nature:1 importance:3 however:4 york:2 wear:2 configuration:2 distribution:2 roller:26 both:3 cos:3 improved:2 influential:1 mono:1 pits:1 equal:3 iv:4 expression:1 otherwise:1 load:8 relevant:1 space:2 point:7 ca:1 robotics:1 motivation:1 dimensional:1 decreases:1 µmax:16 cs:1 respect:3 throughout:1 rpm:1 expensive:1 ct:1 pp:3 multiobjective:10 west:1 due:3 reduction:2 workshop:1 bauman:1 choose:1 stresses:6 life:1 controlled:1 xxx:1 recherche:1 determination:2 angles:1 denote:1 present:1 case:3 shaft:1 novel:4 reciprocal:1 engineering:3 value:8 heidelberg:1 will:3 cast:1 while:5 optimization:23 pressed:1 transactions:1 region:1 real:1 planar:1 vc:2 conferences:1 vol:3 vi:1 drawbacks:1 thus:1 non:1 surface:7 nomenclature:1 ii:8 characterize:1 vs:3 curved:1 claimed:1 vanish:1 different:5 same:3 clearly:1 parts:8 see:1 figures:2 several:1 higher:13 ball:2 http:1 poisson:1 closest:1 drives:2 counterparts:1 hand:5 driven:2 action:1 uses:1 robotic:1 infinite:1 robust:1 cycle:1 lower:17 center:4 nevertheless:3 com:1 min:1 well:1 analysis:5 obviously:1 academic:2 contact:27 involves:1 components:1 actuators:1 position:1 model:2 dimension:1 comprise:1 proposed:1 less:1 being:2 obtain:2 shape:1 speed:2 palacios:2 previous:1 kluwer:2 conclusions:1 had:1 recommended:2 location:4 theorem:1 input:4 16f:1 identical:1 smax:2 around:1 evaluate:4 punctual:1 kinzel:1 transmit:1 increases:1 pstat:3 descending:1 press:1 using:1 depicts:3 moreover:6 kennedy:1 detc:1 machinery:1 δr:1 δp:2 δq:3 communications:1 δl:1 either:1 fully:2 output:4 www:1 because:3 some:4 springer:1 b1:4 b2:5 b3:1 home:2 provided:1 umr:1 normal:1 recorded:3 per:2 prop:1 does:1 iso:2 provides:2 o2:4 o1:6 illustrate:2 power:2 derivatives:2 equivalent:1 rue:1 pressure:44 ratios:1 inherent:1 plots:1 dcs:14 takes:2 would:1 column:2 o:19 angeles:7 remains:2 range:1 ensure:1 trajectory:2 introduced:4 consequently:4 emilie:1 block:1 software:1 xu:3 computational:1 h2:1 into:6 within:5 three:23 variable:1 appropriate:1 references:1 determine:1 frames:1 reducing:2 rely:1 institut:1 stainless:1 transform:2 hertz:21 width:9 accordingly:1 low:4 actuator:1 analyze:1 was:3 synthesis:3 function:5 complete:2 form:3 m2:5 denoting:1 but:3 principles:1 volume:1 magnitude:1 related:1 line:4 highest:1 heinrich:1 made:1 cylinders:1 attached:1 maximum:13 devices:1 international:1 dordrecht:2 below:2 un:1 highlight:1 problem:11 piece:1 groove:2 called:2 uc:1 bearing:4 constant:3 pin:2 up:1 defined:6 likewise:1 abstract:1 convex:4 influence:3 general:1 globally:1 lobes:3 formulation:1 corresponding:9 gonz:2 inc:1 functions:10 compared:1 us:5 allow:1 when:11 arctan:1 other:4 profiles:1 department:1 gaining:1 elements:1 june:2 rolling:5 vein:3 architecture:1 longer:1 dψ:1 assume:2 rotational:3 curve:8 together:1 4f:1 failures:1 n2:3 4b:1 4a:1
0705.0857.txt |@word aided:2 limited:1 magnetic:1 comparatively:1 dynamic:4 entropy:2 parameterization:14 consists:3 localized:5 whose:3 voter:1 hermans:1 aug:1 unanswered:1 under:4 worth:1 alternating:1 rise:1 connects:1 every:1 summarized:1 experimentally:2 encounter:1 vibrational:1 solution:3 vector:1 shows:1 force:1 consistent:4 direct:1 approximation:3 surrounding:2 second:10 q1p:2 chen:2 berendsen:2 spect:1 implemented:1 even:5 established:1 interatomic:9 redistributed:1 specification:4 tully:3 en:2 above:6 new:18 net:4 consisting:1 coefficient:1 agreement:2 simultaneously:1 here:11 atoms:38 ionization:1 reported:2 represented:1 acceptor:7 obtained:12 derivable:1 tsai:2 leutwyler:1 study:5 saint:1 suitable:1 changes:1 modulates:1 9e:1 plenum:2 highly:1 stern:2 szabo:1 total:15 unit:2 would:3 keith:1 negative:1 noting:2 therefore:5 lennard:1 robertson:1 type:2 successful:3 kohn:2 award:1 tildesley:1 excellent:1 hold:1 must:4 tza:3 mm:1 work:17 mi:3 oxide:2 concepts:1 exceptions:1 example:3 jindal:1 impose:1 wang:2 preserving:1 table:33 involve:1 indicates:1 calvo:1 degenerate:2 dyke:2 provide:1 feature:2 hoh:12 how:1 methodology:2 symposium:1 description:3 replacing:1 thermodynamic:5 oscillators:1 earlier:1 minimized:1 dell:1 shukla:1 summarize:1 types:2 attempt:1 effective:11 enter:1 acknowledges:1 order:14 exotic:1 interpretation:1 eigen:1 over:3 vary:1 trickey:2 london:3 fit:7 del:1 nearest:3 distinguishing:1 fig:26 wales:4 schmidt:1 them:1 combination:2 repulsive:2 effects:15 they:9 elsner:1 catalysis:1 structural:8 represents:5 several:1 anion:1 oxygen:22 reasonably:3 classified:1 leading:1 mead:1 reasonable:3 each:18 sham:1 meam:6 bond:19 fairly:1 series:3 principles:1 literature:1 laboratory:2 thermo:1 burnham:2 madura:2 rp:12 network:1 rs:4 crucial:3 re:2 alloying:1 adapt:1 reader:1 xu:1 ri:19 rj:3 linear:4 associate:1 standard:1 formation:1 incorporates:3 enormous:1 r0:2 fleischer:1 iso:2 corrections:2 uses:2 onto:2 already:1 features:7 primary:2 wash:1 nonperturbative:1 another:3 semiempirical:3 dupuis:1 electronic:11 chargedensity:2 similarly:2 xii:4 eqs:9 approximately:1 needed:1 too:1 ranging:2 yip:1 centered:2 zeroth:3 elec:1 distance:14 roles:1 ac52:1 approximations:1 database:2 expt:5 project:3 tion:1 perturbative:2 kolchin:1 fashion:1 modern:1 mind:1 stillinger:1 manner:2 mishra:1 seen:3 relatively:5 strength:1 latter:2 isolated:12 relaxations:1 absorbed:2 nanoscale:1 forces:1 sakurai:1 swaminathan:1 shall:1 optimized:3 errors:1 phase:5 acknowledgements:1 singer:1 calculated:2 metal:1 yang:2 principle:3 upadhyay:1 sum:5 fitted:2 elliott:1 incorporate:2 attempts:2 solutions:1 subtle:1 d2:2 d1:2 quoted:1 implementation:5 topological:1 rick:1 hamiltonians:2 continuity:1 do:3 assignment:1 seifert:1 cheng:1 klein:2 coefficients:1 de:1 dc:1 da:1 despite:1 du:1 dr:8 dq:13 kollman:1 fields:1 pople:2 captures:1 reference:5 generally:2 roadmap:1 nun:1 depends:1 electrostatic:11 radius:2 result:1 patel:1 best:2 techniques:1 ghosez:1 yet:1 symmetric:9 unable:1 simplest:3 approach:7 terms:12 nature:7 oxidation:2 however:5 huang:1 modeling:6 suggested:1 essentially:1 refinement:1 cao:1 guyon:1 coe:1 coh:3 contribution:1 hwang:1 ease:1 con:1 basis:12 simplification:1 three:12 been:26 much:1 interest:1 basic:3 expected:4 flexible:1 ann:2 postma:1 θl:2 quantities:1 θe:4 jeon:1 curves:1 trimer:6 applied:1 tanh:2 aip:1 aim:21 near:1 viii:5 balance:1 elaborate:1 procedure:1 ix:3 concomitant:1 mexico:8 ir:1 tions:1 iv:6 ii:10 cond:2 conf:2 containing:2 perform:2 suggest:1 make:3 angew:1 complex:5 quant:1 dimensionless:1 electro:1 independent:2 numerical:1 hand:1 kim:4 potentials:35 hartree:2 shortly:1 lucas:1 materials:8 elstner:2 unified:1 proposed:4 photo:1 assigned:3 identify:1 unifies:1 campbell:2 modulate:1 previous:6 unique:1 regarded:2 wright:1 belongs:6 aral:1 cations:1 gave:1 rescaled:1 χ0i:2 possible:2 szalewicz:3 rahman:2 background:9 depicts:1 advanced:2 appearing:3 berne:2 specific:2 steps:1 b3lyp:1 arbitrary:2 valence:4 webb:1 www:1 acad:1 mishin:1 successfully:6 oh:22 born:2 debye:1 koster:1 contributing:1 schwarz:1 minimization:4 additively:1 conformation:2 popular:1 properties:24 tetramer:7 limitation:2 clough:1 anomalous:1 o:42 constituting:1 ensure:3 mahoney:1 slightly:1 book:4 automatically:1 considerations:1 soc:4 ahh:2 sol:1 lies:1 scherer:1 lieu:1 prefactors:1 methods:4 wan:1 rely:1 compression:1 support:2 initial:5 resulted:1 gin:1 was:14 lowest:1 multiscale:4 alloys:1 medium:2 form:18 differences:1 buckingham:1 true:2 portions:1 prevents:5 inside:1 equalization:2 bounds:1 truskett:1 dordrecht:1 sapphire:1 stages:1 examples:1 later:2 proved:1 computing:2 configurational:1 levitt:1 simulations:2 accounting:1 distributions:3 physical:5 nh:9 ni:2 no:8 when:4 doye:1 tin:1 role:4 papers:1 test:3 picture:4 initio:24 owdin:7 variable:1 transfers:1 qi2:1 jones:1 coulomb:2 assume:3 together:1 fact:2 nuclei:2 neighbors:1 roj:1 rok:1 chain:2 roo:13 varying:2 focus:4 roy:1 remarkably:1 viceversa:1 depend:1 technique:2 environment:12 charge:137 marks:1 anharmonic:1 division:1 broadly:1 zhang:1 emphasizes:1 choice:3 grigera:1 ro1:3 ro2:2 exact:3 dim:4 losada:1 greenlee:1 level:8 voronin:1 recall:1 der:4 prevent:1 illustrating:1 langmuir:1 heine:1 chair:3 schiffer:1 assistance:1 rationalized:1 uniform:1 current:3 shared:1 unrestricted:1 satisfy:1 pm3:1 multipole:1 westbrook:1 ρai:7 understanding:1 water:95 ostlund:1 address:3 along:7 buck:2 buch:1 52b:1 institute:1 vectors:1 boh:3 resonance:1 nected:1 studies:7 kcal:11 plotted:1 spatially:1 problematic:1 mehl:1 matsuoka:1 flexibility:2 relating:1 handled:1 hector:1 positive:1 predictions:1 gonze:1 scenarios:1 andy:1 films:1 theoretical:3 smeared:1 wavefunctions:1 nguyen:2 rigid:2 eθ:2 cases:2 insights:1 fly:1 parameterize:1 impey:1 originally:1 modified:3 reviews:1 labeled:1 fock:2 values:15 cam:1 following:7 heart:1 figure:1 predict:6 nemo:1 weighting:2 incremental:3 performed:3 unphysical:2 spc:2 hydrogen:45 occur:1 discussion:4 means:1 s4:2 chemical:14 pure:1 plus:2 parameter:1 map:1 mas:2 informa:1 mat:1 hydrogens:4 may:4 applications:3 birthday:1 designed:2 mag:3 data:7 dynamical:8 liquid:5 explicit:5 yielding:2 su:2 znl:1 elbert:1 switch:1 so:4 fortuitously:1 se:1 baskes:14 constituents:1 mainly:1 stability:5 course:1 experiments:2 ttm:1 argued:1 still:1 group:1 thank:2 chandrasekhar:2 interesting:1 vicinity:1 forms:7 constitutes:1 coordinated:1 non:9 noh:3 matches:1 scaling:1 tails:1 keefe:1 now:5 discuss:1 biomolecular:1 term:10 james:1 proteins:2 realistic:2 ji0:2 baldridge:1 weighted:1 ei:8 significantly:4 populated:1 ed:2 challenges:1 approximated:2 ev:8 eq:16 es:8 ultimately:3 impurity:1 factors:4 nominal:2 correct:8 chemically:1 reformulation:1 theory:17 variant:1 mechanisms:1 albuquerque:3 brooks:1 krishnan:1 aeh:5 e1:1 e0:3 rearrangements:1 qj:4 transition:2 turn:1 gordon:1 first:9 origin:1 xi:2 symmetry:3 omitted:1 variables:2 comprised:1 voth:5 ring:5 open:2 intermolecular:9 size:7 given:25 necessarily:1 crossings:1 indicate:2 chem:86 constants:3 structures:23 speaking:1 gives:3 asymmetric:2 accurately:6 representing:2 than:14 intrinsically:1 population:2 wide:2 accordance:1 require:2 pvtz:1 transferred:1 modelled:1 janssen:1 future:2 coulombic:7 were:8 addressing:1 sam:1 remained:1 correction:1 duin:2 argument:2 generalization:1 crossover:1 mater:2 stanley:1 allen:1 any:6 subsystems:5 gunsteren:1 efficient:1 pineda:1 note:10 emphasis:2 potential:50 take:1 online:1 performance:1 mayer:1 switching:5 begin:1 investigations:1 correlation:3 molecule:24 fcc:2 importantly:2 rationale:1 pair:15 proxies:1 precludes:1 imposition:1 sutton:2 failure:1 considered:1 average:1 adopt:3 highlight:1 ohta:1 pattern:1 typically:2 quantity:1 contemporary:1 corner:2 ground:3 specifically:1 ratio:1 written:1 analytic:1 only:4 alternation:1 correctly:1 kneller:1 rept:1 expectation:1 cannot:1 nearly:4 conjunction:3 justified:1 krishna:1 regarding:2 aluminum:1 assimilate:1 hinges:1 yield:2 summary:3 predicted:18 mtrl:1 06na25396:1 reveals:1 physically:2 relative:9 intramolecular:5 unaltered:1 concern:1 invoked:1 compounds:1 subsequent:1 review:3 sites:1 energetics:12 atomistic:3 outside:2 between:35 geometric:1 bromberg:1 useful:1 comp:5 jr:2 gratefully:1 pettifor:1 fluctuations:2 virial:1 concentrated:1 parentheses:3 many:12 jungnickel:1 contract:1 dated:1 embedding:30 manh:1 expression:5 comes:2 among:8 stretches:1 pol:2 bader:1 moreover:1 coker:1 unusual:1 aˇ:1 capable:8 stretch:3 abstract:1 direction:1 enable:2 saykally:10 formed:1 observe:2 extant:1 diffuse:1 those:3 case:4 scut:2 gamess:2 developing:5 irrespective:1 margin:1 planar:1 coupled:1 ellison:1 couples:1 cluster:55 pressing:1 diabatic:1 technology:1 binary:1 different:13 develop:3 pay:1 formulations:1 same:6 selfconsistent:1 html:1 arguments:1 runge:2 constructed:2 ludwig:1 jorgensen:3 dreizler:1 dasgupta:1 driven:1 costa:1 modes:1 largely:1 charges:36 frohlich:1 components:7 coordinate:1 ccd:1 model:44 charged:1 r02:1 minima:2 being:3 gainesville:1 guided:1 ch:2 aspect:2 captured:1 segal:1 mcdonald:1 parametrization:2 treatment:3 extensive:2 nakano:2 nielsen:1 marcus:1 sums:2 harmonic:1 early:2 mol:18 using:14 correcting:1 collective:2 serves:1 integrals:2 always:1 inter:6 stationary:1 twelve:1 isoenergetic:1 specified:3 matching:1 finnis:1 provided:1 dimensions:2 matsunaga:1 models:10 critical:1 decomposition:3 provides:3 o3:1 o2:3 o1:2 ωij:3 equivalent:2 radial:4 notable:1 refers:2 acc:2 comparison:6 stone:2 central:4 package:1 instantaneously:1 discussed:3 practical:3 neighbor:4 underway:1 mixed:1 gregory:1 nanoclusters:1 perturbed:1 cambridge:2 follows:3 accounts:1 jasper:2 determine:3 pullman:1 theoretically:1 ovchinnikov:1 refinements:1 there:9 los:3 assumes:1 complete:3 octamer:4 metastable:1 muromachi:1 sophisticated:1 embedded:13 ωi:3 agree:2 strongly:1 polymorphs:7 ac:1 taylor:2 hellman:1 ai:1 certain:1 ak:2 describe:5 am:3 ao:2 general:2 examine:1 formulation:7 corresponding:7 gradients:1 intra:6 film:1 again:4 assessing:1 hybrid:1 tight:2 prism:4 valid:1 spatial:1 d2d:2 seeger:1 deviation:2 polar:2 briefly:1 a1:2 a3:2 a2:2 nucleus:1 included:6 kieffer:1 building:1 partitioned:4 curve:2 nelson:1 remarkable:1 starting:5 original:7 represent:7 finney:1 sci:3 consider:4 pth:2 hartrees:2 lack:2 scc:2 generalize:1 expressions:1 atlanta:1 corrales:2 referring:1 nonlocal:2 spirit:1 alvarez:1 th:2 tb:3 global:3 jensen:1 very:6 hodges:3 oxides:1 interpreting:1 difference:6 al2:1 deformations:2 hamiltonian:1 evaluation:1 t2:4 t1:3 large:3 adjust:1 small:14 biological:2 kemper:1 mishima:1 ten:1 nocedal:1 zero:8 design:3 perspective:3 further:7 tronic:1 tip5p:7 section:9 frauenheim:2 version:1 fractional:1 method:7 contrast:3 edited:2 condensed:1 component:8 ansatz:1 strong:2 equations:4 amount:1 via:10 followed:1 vij:9 vii:2 aimed:2 select:8 readily:1 conventional:2 distinct:7 contains:3 finally:2 scient:1 taken:1 more:13 solvated:1 flat:1 particular:11 known:2 kulkarni:1 analogous:2 keeping:1 science:9 equation:1 nine:1 deg:1 ions:3 compare:2 challenging:1 brown:7 locating:1 states:15 minimum:8 arise:1 robinson:2 species:5 bonded:1 transduction:1 information:6 respective:4 rather:4 acts:2 utilize:4 maps:1 ensemble:4 simplicity:1 wiley:2 derived:4 plane:1 charmm:2 fi:9 fl:1 providˆencia:1 short:3 susan:1 enzymes:1 generalizations:1 departure:1 parameterized:9 fundamental:3 playing:1 ith:4 developed:3 paper:1 through:2 kinetic:1 excitations:1 its:16 izumi:1 energies:21 microscopic:1 systems:17 might:1 underestimate:1 uhf:12 good:2 motivated:1 number:12 framework:8 oxford:1 easily:1 polarizable:1 fully:1 presented:3 2d:1 experiencing:1 found:2 energetically:4 characterized:3 referred:1 reactions:2 weight:1 energy:70 expect:5 quantum:16 beyond:3 solvation:3 robert:1 since:6 research:1 denoted:1 induced:3 issue:3 asp:1 favored:2 onuchic:1 reason:1 bash:1 definition:3 pairs:1 rittner:1 benedict:1 american:1 twenty:1 consequence:3 zl:1 ability:5 reflected:1 utilized:2 done:2 takada:1 dunning:1 temperature:4 introduction:2 dft:3 assumption:1 calculations:22 molecular:17 listed:2 shifted:1 st2:1 roh:17 behind:1 immediate:2 homonuclear:1 alumina:1 part:3 jordan:4 parr:2 authors:2 spacings:1 ncc:1 tip4p:11 ogata:2 kind:1 polarized:2 cyclic:10 sth:1 grained:1 determined:4 str:1 dang:4 motivation:1 comput:3 defect:1 grest:1 conjugate:1 lie:2 generalizes:1 depending:6 self:6 melzer:1 liu:7 equaled:1 liq:2 donor:9 play:2 towards:1 serve:1 rhs:4 rhh:2 significant:4 rhb:7 extremely:1 henson:1 deviations:1 mobile:1 clear:2 clementi:3 traditional:2 h2o:2 exp:2 physics:6 thomas:2 particularly:1 binkley:1 relation:1 carefully:1 fine:1 believe:1 parameters:11 distributed:1 enzyme:1 factor:1 accurate:3 bfgs:2 notation:1 dependent:15 closely:2 combinations:1 during:1 md:1 arxiv:1 common:5 approaching:1 set:16 harrison:1 unpublished:1 collectively:1 see:6 individual:2 leslie:1 close:1 theoretic:1 lee:1 cutoffs:1 dipole:20 various:10 conditions:1 available:4 recently:6 missing:1 initially:2 sole:1 spectroscopic:2 ρaj:3 31g:7 both:14 connection:1 became:1 context:2 rodgers:1 experimental:12 point:9 simple:4 asymptotically:1 corresponds:7 proton:3 dimensional:1 simply:2 throughout:1 ps:1 described:7 pu:1 damp:1 due:2 screened:1 a210:1 ph:1 meeting:2 lett:17 gas:4 kuntz:2 hardness:1 exponential:1 solid:3 caged:1 empirical:10 evaluated:1 while:11 match:1 behavior:5 error:1 computed:13 vol:2 binding:8 itself:1 rij:4 grant:2 barnes:1 wherein:1 modification:1 products:1 higher:3 used:19 comprehensive:1 moment:21 moving:1 robust:2 implement:1 recent:2 lower:1 task:2 surrogate:1 analysis:2 phil:3 solids:1 consistency:5 chemistry:2 parametric:2 lin:1 distances:14 diagonalizations:1 cuboid:1 shape:4 atomic:40 questions:1 regardless:1 alternative:1 indexes:1 tables:2 dissociation:5 conclusions:1 internuclear:1 dixon:1 relevance:1 guarantees:1 remaining:3 cui:2 kaxiras:1 bim:3 march:2 integer:2 conformer:2 formal:3 imposed:2 semi:3 polymers:1 eeq:1 ees:3 separately:2 imposes:2 yields:2 translated:1 essential:4 often:1 some:5 understood:2 trends:1 added:1 b1:2 b2:2 b3:2 scale:1 describing:11 though:1 per:3 prog:1 prof:1 proc:4 use:10 step:3 rup:1 dictated:1 che:1 most:11 simulation:2 range:7 involving:2 extensions:2 stuart:1 consequently:4 truhlar:3 cutoff:5 computational:4 reidel:1 into:6 within:15 rothman:1 nsf:3 martinez:1 appropriate:5 middleton:1 steven:1 paradigmatic:1 sequence:1 signifies:1 hexamer:12 monomers:2 properly:1 atom:60 line:1 considerable:1 qeq:1 partitioning:2 zhu:4 intuitive:1 vacancies:1 up:1 ur:1 un:3 uk:1 4r0:1 similar:6 dill:1 associated:4 defined:10 metals:4 single:2 diverse:4 dftb:2 formalism:3 sasaki:1 fixing:2 cohesive:4 application:3 priori:1 department:4 elements:2 energetic:2 problems:1 bonding:7 structure:32 tailored:1 implies:1 required:1 equivalently:1 beers:1 dover:1 requires:1 extensibility:1 once:4 code:1 results:20 eds:2 ga:1 edu:1 contributions:6 issues:2 2r0:1 biol:1 monomer:21 alamos:3 byrd:1 stable:12 atlas:6 include:8 resources:1 logarithm:1 presently:1 implicitly:1 electron:28 2rp:3 positions:4 evb:3 fewer:1 assignments:1 refer:1 noted:5 dimer:19 configurations:2 concluded:1 smaller:1 carter:1 sin2:5 za:2 imply:1 concludes:1 notwithstanding:1 dynamics:6 odd:2 zr:1 auspices:1 index:2 expressed:6 experiment:7 sapt:2 b864:1 3d:2 body:10 justification:1 chose:1 respectively:3 papaconstantopoulos:1 believed:1 explore:1 focused:1 separation:1 others:3 slater:1 implicit:1 involved:3 larger:10 h2:13 suggests:3 resulting:3 chang:4 sulting:1 makes:1 honor:1 examining:1 formulated:1 stabilization:1 addresses:1 clark:1 scales:1 scaled:1 motor:1 apply:1 orderings:1 cloud:1 biophysical:2 asymptotic:1 usa:1 next:4 calculation:1 stage:1 reflects:1 formally:3 om:2 payne:1 normalized:1 iii:13 takayama:1 account:9 crosses:1 ρi:8 challenge:1 averaged:3 reproduce:4 obvious:1 thin:2 averages:1 perdew:2 kenny:1 biophys:2 process:1 rapp:2 purposes:1 high:3 effectively:3 bene:1 acs:1 varied:4 six:1 regions:1 varies:1 instead:3 puckered:1 blocks:1 collection:1 fits:3 martins:1 light:3 separations:1 correspond:1 element:1 dilatation:1 allow:1 insight:1 h9:1 including:4 alavi:2 write:1 blake:1 complicate:1 la:1 ln:6 inclusion:3 li:1 estimating:1 lu:1 degrees:9 choose:4 clusters:58 defining:2 mers:2 outlined:2 material:3 indexing:1 daw:5 h4:2 documented:1 h5:1 cage:4 day:1 biomol:1 february:1 profound:1 university:7 identified:4 sufficiently:2 mode:4 constraints:1 levy:2 related:3 rojas:2 society:1 static:2 interplay:1 measure:1 our:40 special:2 out:5 matt:1 matrix:2 loeser:1 rep:1 req:3 rev:32 aoo:3 mediated:1 ref:18 a1133:1 interactions:15 8g:1 approaches:8 york:6 interaction:13 organic:1 geometry:22 determining:1 could:1 florida:3 length:4 lundqvist:1 assumed:3 hence:1 footnotes:1 ionic:6 possessing:1 improvements:1 quality:2 seidel:1 sharon:1 long:6 ordering:2 revealed:1 system:17 their:11 siam:1 final:3 completed:1 constituent:4 ben:1 submitted:1 limiting:1 negatively:1 providing:2 abstracts:1 lines:1 rcut:8 constrained:2 clearly:2 viewed:1 mij:3 angle:9 able:3 si:2 mechanism:2 montgomery:1 polarization:10 decomposing:1 concerns:3 incorporating:1 singh:2 hydroxyl:1 guillot:3 intrinsic:3 itr:1 neighboring:8 oscillated:1 neutral:11 mechanical:6 χl:4 χi:1 12f:1 text:1 supported:1 purely:2 postdoctoral:1 hohenberg:1 subtracting:2 nominally:2 based:15 should:5 reactive:4 molecules:12 indeed:4 he:1 local:13 equilibrium:31 cube:2 handle:1 bonds:7 overall:4 bear:1 processes:4 densities:17 numerous:1 qa:2 qi:23 qh:19 fixed:6 qm:5 qo:3 qn:3 requirement:6 omission:1 constructing:1 acquired:1 national:3 correlations:2 computer:3 enhanced:1 tcut:3 goddard:6 phases:1 interacting:6 nuclear:1 dmr:2 state:10 identification:4 closed:1 routine:2 boundary:2 comparable:2 attention:2 reproduced:1 importance:2 implementing:1 reproduces:1 intermetallic:1 key:5 configuration:7 distribution:3 observable:1 taking:1 equal:3 attributed:1 chosen:5 estimation:3 otherwise:1 detailed:1 relevant:2 cc:2 cf:5 environments:3 millot:1 ab:24 respect:3 crystalline:1 ct:25 geometries:17 addition:3 immense:1 treat:1 ah:2 compensating:1 define:2 hernandez:1 field:1 diversity:1 cos:1 bulk:6 θeq:4 angles:11 derivative:1 c3:2 c2:2 c1:3 present:11 novel:1 unscaled:1 contexts:1 appearance:1 value:6 choices:1 will:6 halley:2 almost:3 vi:3 refs:8 thus:8 site:5 surface:6 examined:2 φij:11 orbital:1 capture:2 enumeration:1 units:1 finite:1 difficult:2 http:1 cubic:2 upon:1 effect:4 ion:13 compared:1 infinite:1 center:2 modeled:2 well:20 unm:2 baltimore:1 sets:2 position:3 arising:1 bending:1 less:3 moments:5 proximity:1 obtain:5 tip3p:1 underlying:3 predicts:2 paul:2 coordination:6 density:31 capabilities:1 thermodynamics:1 add:2 diffusivity:1 nato:1 natl:1 ado:3 dqi:9 adh:3 adi:1 identical:3 tests:1 fluctuating:1 dimers:1 devised:1 parameterizations:11 press:1 bukowski:4 necessary:3 like:3 success:4 schmitt:2 roth:1 martin:1 because:1 classical:8 smoothly:1 discontinuities:3 phenomena:3 muralidharan:4 growth:1 proper:4 transport:3 electronegativity:1 informationtheoretic:1 avoid:1 overlap:2 instantaneous:4 does:3 dipoles:1 dce:2 expansion:3 q2p:2 host:3 although:2 simpler:1 about:5 actual:3 carried:3 extension:2 dependence:7 important:12 reproducing:1 software:1 equally:2 hexamers:6 previously:2 h3:10 h1:3 functional:19 parameterizing:1 dataset:1 square:1 karplus:3 van:7 additional:2 elastic:1 transfer:56 quadratic:3 function:28 eam:54 but:3 hu:1 volume:3 hh:1 construction:2 oxygens:3 hf:5 auxiliary:1 compute:3 evident:1 whether:3 variations:1 placed:1 below:5 limit:1 problem:2 thirteen:1 mechanics:2 dagotto:1 int:3 universal:2 collier:1 effected:1 functions:14 chargetransfer:3 variety:1 detail:1 other:12 compares:1 details:3 theor:1 stat:1 zhou:3 expressible:1 shown:8 variation:6 additionally:2 stan:1 astronomy:3 coat:1 coupling:1 space:1 bcc:1 ortega:1 res:1 silica:4
0705.0858.txt |@word consider:15 remarkable:4 lagrangian:16 global:9 results:5 invent:3 hurtubise:1 proposition:27 travaux:1 joachim:1 c2:3 consists:6 restrictions:1 compact:61 whose:17 inverse:1 referring:1 tx:79 re:1 paris:1 tt:1 tu:6 contained:3 γj:2 quasi:62 those:2 under:11 ebres:1 geom:3 analogous:1 include:1 presentation:2 spec:5 ingredient:1 applied:4 conjecture:3 lack:1 notations:1 orthogonal:2 very:4 falbel:2 pages:1 rise:10 compacts:2 choice:10 corollary:15 every:12 entries:1 lerman:3 matrices:13 convexity:107 dim:47 obvious:1 subsets:8 hamiltonian:105 did:1 induction:1 joined:3 t1:2 deals:1 involution:38 vector:14 guiding:1 recall:20 eigenvalues:3 shows:16 noted:1 zn:37 says:4 zi:4 dealing:1 consistent:1 japanese:1 horn:2 go:2 second:4 masson:1 concludes:2 incidentally:2 further:2 zp:3 victor:1 bilinear:1 established:1 what:1 sud:1 richard:1 dept:1 giving:4 diag:3 section:11 cell:7 version:6 above:14 mq:43 increasing:3 hilgert:6 contrast:1 compactness:1 satisfy:3 devoted:1 guillemin:12 nicolas:1 q0:24 continuing:1 even:3 component:17 here:7 understanding:1 tangent:3 groups:13 situation:1 alone:1 path:8 equations:1 appears:1 deduced:2 obtained:6 search:2 generalizing:1 rests:1 leaves:2 studied:3 homeomorphism:4 guide:1 p2:8 meinrenken:10 resulting:1 characterizing:1 adv:1 permutation:1 action:61 makes:1 quotient:3 uniquely:2 appropriately:2 schur:1 via:3 tightness:1 projection:5 classification:2 slices:5 explained:1 qzi:1 qzj:1 equivariant:6 carry:1 apply:10 circumvent:1 fr:1 use:8 takes:3 would:2 prove:18 remains:2 positive:5 continuous:4 contains:6 finally:3 guideline:1 distinct:1 comparing:1 call:2 therefore:40 associated:7 quotients:2 historically:1 decomposable:14 more:5 alg:1 kgs:5 alcove:26 becomes:1 stable:5 constructs:1 hermann:1 appendix:1 particular:36 known:5 projective:1 cases:1 iii:11 origin:1 yves:1 valued:6 join:1 characterize:1 science:1 work:5 london:1 pr:2 mu:1 examined:1 values:6 stabilizer:6 ms:168 following:30 field:3 trans:1 root:9 example:7 proof:61 hyperplane:1 do:4 wlt:3 cited:1 permutations:1 organized:1 sphere:1 contradicts:1 assumptions:5 cartan:9 degenerate:2 sense:9 verlinde:1 berenstein:1 conversely:3 generally:1 needs:1 end:5 w1t:1 turn:1 rather:1 s2:7 s1:9 acts:4 feature:1 centralizers:1 write:5 maps:15 criterion:1 actual:1 get:2 instead:4 hi:1 dedicata:1 polytopes:2 map:99 product:7 fs:4 description:5 algebra:9 may:12 max:8 earlier:1 orbits:5 collection:1 diagram:2 applications:6 duistermaat:14 representations:9 data:12 plank:6 arkady:1 ements:1 natural:2 varieties:1 lemmas:3 spectra:5 explicit:2 correspond:1 su:13 element:10 extremal:1 si:1 so:38 sn:2 fundamental:25 verify:2 representation:13 jacques:1 sg:1 order:3 xj:9 indeed:4 over:1 move:1 satisfied:1 paper:10 including:1 cuts:1 mentioned:1 existence:5 satisfies:4 still:2 its:12 roots:9 before:1 aj:6 orbifold:1 group:42 lc:2 karl:1 how:3 chosen:1 interesting:2 fix:1 affine:3 forms:1 tolman:1 θt:1 choose:3 lq:22 mail:1 main:5 into:3 overcome:1 eugene:2 maximal:35 non:26 motivated:2 combination:3 yn:8 propose:1 eckhard:2 introduce:2 number:1 differential:4 they:3 eµ:1 now:40 riemann:1 gets:1 equality:9 always:13 university:2 presented:1 appropriate:3 establishing:1 properness:1 2g:1 each:6 references:1 repeating:1 rk:3 referred:1 subset:42 el:1 domain:19 weyl:43 successively:1 another:1 commuting:1 reduce:1 idea:7 γl:1 society:1 used:1 our:11 mapping:4 thing:3 ep:1 special:5 out:2 ultimately:2 matrix:10 space:45 restricted:1 furthermore:2 since:65 crucial:4 rz:1 denotes:4 rd:2 studying:2 acting:3 at2:1 at3:2 convergent:1 at1:4 denoted:4 rn:4 suffices:1 math:18 she:1 benjamin:1 wentworth:2 maurer:3 linear:4 associate:1 hull:2 hyperplanes:2 diagonal:9 free:2 ascending:4 admits:2 difficulty:4 reason:3 lisa:1 org:2 subpolyhedron:2 definition:20 pairs:1 equivariantly:2 geometry:1 phrases:1 could:2 atj:4 v2:4 keep:1 ahler:2 βg:1 sjamaar:15 hence:24 promotion:1 onto:4 think:1 first:13 polyhedron:16 reversing:4 initial:1 xn:2 malkin:6 relate:1 conjugacy:22 geodesic:2 rank:15 system:6 restrict:1 clear:1 xx:4 directly:4 xr:2 stated:1 precisely:5 open:55 given:13 necessarily:6 πg:12 introduction:1 adjoint:7 restricts:1 construct:4 compatibility:4 electronic:1 their:2 assumption:9 too:1 statement:21 ordered:2 submersion:3 structures:1 final:2 gives:7 commutativity:1 sternberg:12 mostly:1 tuple:1 explanation:1 exactly:4 serve:1 immediate:3 transverse:1 x2:5 keio:1 translation:1 x1:10 than:1 target:1 showed:4 was:9 namely:2 rzi:2 matter:4 classes:7 pairwise:1 implication:1 punctured:1 shlomo:1 enables:4 minus:1 w2:5 pre:2 motivation:1 close:1 atl:15 ann:2 nonabelian:1 argument:2 generalization:2 direct:1 endomorphism:1 conjugate:2 need:2 take:11 any:31 neeb:6 lie:67 maxx:1 min:2 convenient:2 latter:2 able:3 ideas:3 converges:1 instance:11 concerns:1 generalized:2 objective:1 techniques:1 cl:30 polyhedral:9 play:1 induces:5 hiyoshi:1 shall:4 quote:3 sl:3 sequence:7 chart:1 most:1 said:4 connected:132 automorphism:8 pair:8 why:1 xµ:1 subspaces:1 give:14 especially:1 characterizes:1 kj:4 torus:26 later:4 cover:3 vertices:1 stating:4 points:17 principle:6 exp:198 anton:2 left:3 er:1 notion:9 fact:23 joining:3 precise:1 saying:1 show:14 supported:1 ending:1 discovered:1 purely:1 spaces:11 relation:1 cψ:5 tµ:19 centralizer:2 analogue:10 trivial:4 find:2 d0:2 fibre:4 aσ:3 bourbaki:1 based:6 knowledge:1 eigenspace:1 florent:16 assertion:1 topological:2 should:2 lemma:56 only:13 abs:2 subsection:23 qx:6 parabolic:1 constant:4 hamiltonians:1 local:29 interested:2 dn:7 abelian:10 handle:1 αg:1 notation:3 means:7 de:7 mreg:50 cannot:3 rest:2 words:1 new:1 uy:1 dt:1 du:4 ahlerian:1 closure:5 mumford:1 qy:1 approach:6 arxiv:3 fixes:1 factorization:1 consisting:2 qz:1 involutive:8 mapped:1 through:2 homeomorphic:9 fixed:24 valid:1 transversality:1 riemannian:1 strengthened:1 moduli:1 set:81 constructing:1 exists:21 smooth:3 hα:5 lyon:1 see:44 full:2 w3:1 result:24 w1:10 terms:2 dµ:7 best:1 subject:1 surfaces:1 hilbert:1 satisfying:18 bernard:1 review:1 nature:1 definite:1 justifies:1 symmetric:18 state:3 identification:2 closed:59 between:4 αi:1 invariant:4 enjoys:3 λl:1 conditions:2 stratified:2 homeomorphisms:1 wl:18 cλ1:2 cλ2:2 uuu:1 attention:1 focus:1 wj:1 killing:1 ws:75 key:2 amer:3 come:1 ker:12 topology:2 adapting:1 σj:7 essentially:1 polytope:14 kirwan:7 many:1 taking:1 σg:4 equal:11 vuv:1 present:1 symplectic:63 context:2 inspired:2 σq:15 genus:1 whole:2 comes:1 otherwise:1 strongly:1 βi:1 co:6 fields:1 point:22 simple:9 had:2 address:1 stiefel:1 eminaire:1 dimensional:6 written:2 anti:8 luis:1 fibres:12 considers:1 simpler:1 speak:1 considering:2 benoist:1 ensures:1 three:1 described:1 submanifold:22 basis:1 union:11 chapitre:1 locally:9 due:2 been:1 z1:5 implosion:1 defined:5 reduction:2 certain:6 algebras:1 universal:1 empty:14 systems:1 faced:1 describe:2 corresponding:3 θl:1 both:1 sufficient:2 subspace:8 remark:2 spectrum:3 moment:8 observe:20 univ:1 bull:1 θr:2 last:6 c1:26 general:14 manifolds:6 case:29 p1:9 exponential:10 discrete:1 will:45 equivariance:3 nβ:4 applies:3 indecomposable:1 property:2 study:4 loop:5 yokohama:1 ix:48 unitary:9 almost:1 endowed:8 metric:1 thus:3 them:1 surface:4 iv:7 ii:14 disjoint:4 itself:5 im:5 cone:4 dual:4 seen:3 vx:52 vy:1 vz:5 containing:9 nouvelle:1 inc:1 insofar:1 make:3 atiyah:6 cross:1 same:13 intersecting:5 equivalence:2 connectedness:1 products:2 finite:10 subalgebra:6 consequence:5 jeffrey:1 extended:2 http:2 eels:1 i0:4 effect:1 publ:1 usually:3 intersects:4 purpose:1 totally:4 cµ:13 subgroups:1 relies:3 shortly:1 groupes:3 no:3 well:2 morphisms:1 obviously:1 thought:2 without:1 kµ:1 components:1 sets:8 jussieu:1 dimension:11 usual:9 composed:1 manifold:18 βs:1 cj:8 being:6 woodward:5 obtain:12 actions:45 identify:3 immediately:2 facts:2 compositio:1 λn:1 previous:1 begin:3 unique:3 family:1 integer:1 density:2 similarities:1 conclude:2 guaranteed:1 setting:4 theorem:157 momentum:71 details:1 real:58 symplectiques:1 depends:3 involutions:2 showing:3 possible:12 careful:1 know:5 loos:1 press:1 using:7 intersection:10 complexification:1 domains:1 generated:1 necessary:1 like:2 semi:3 follows:13 diffeomorphic:1 chamber:16 ai:1 werner:1 either:1 arbitrary:9 simply:27 pointwise:6 terminology:2 because:5 often:2 classical:2 shea:9 some:12 back:3 understood:1 examples:5 choosing:2 convex:69 images:2 gave:1 molino:5 proofs:1 ourselves:1 homc:6 provided:1 vzi:4 slice:34 dense:28 iλj:3 sufficiently:1 stronger:1 establish:1 normal:3 extensively:1 comments:1 cv:3 does:2 exposition:1 compute:1 vzp:2 refer:9 antisymplectic:2 bg:3 sequently:1 equivalent:5 uj:9 bi:1 although:1 properties:12 proceed:3 chapter:1 integers:1 about:1 developped:2 idt:1 theorems:11 a3:4 o:18 compatible:6 addition:6 whence:1 regular:2 ov:3 vz1:6 introduced:2 consequently:11 automatically:2 functions:1 considerations:1 soc:3 cambridge:2 statements:2 inclusion:4 h2:5 image:19 h1:5 obtaining:1 claude:1 ut:3 lies:2 hermitian:6 right:1 accounts:1 factor:1 next:1 soon:1 cones:3 additional:1 canad:1 assumed:6 there:40 u1:16 class:8 start:1 jsps:1 way:4 sections:1 a2:14 function:2 form:28 enough:1 proving:1 converse:1 alekseev:6 but:24 volume:1 neutral:3 construction:16 ematique:1 trying:1 true:7 he:1 etrie:2 ωx:9 applying:1 ux:4 ιx:4 uu:9 wish:1 cells:4 uv:3 dazord:5 up:1 us:31 ul:10 v1:4 limit:2 submanifolds:4 sum:6 problem:2 define:2 similar:3 called:13 uc:4 b1:3 detailed:1 strata:2 proved:6 ad:14 ag:3 int:11 likewise:2 abstract:1 u2:9 condition:2 coadjoint:2 analoguous:1 denote:14 globally:2 proper:25 proves:6 exist:9 eom:2 face:1 openness:1 constructed:3 physics:1 lim:6 entirely:1 want:4 nonetheless:3 uµ:3 when:17 cˆ:7 application:12 other:3 role:1 neighbourhood:12 papers:1 mathematics:2 really:1 superfluous:1 nice:2 sue:1 briefly:1 elements:7 ku:1 vertex:3 shown:2 frances:1 a1:18 hausdorff:1 meaning:1 important:3 bounded:1 additionally:5 vectors:1 chris:1 describing:2 structure:5 freely:1 independently:1 implies:7 dω:2 assume:16 requires:1 dτ:4 stabilizes:1 orbit:8 together:1 having:1 equivalently:2 lying:1 already:1 moreover:7 ags:7 original:3
0705.0859.txt |@word limited:1 sci:1 consider:1 maximum:1 rev:4 magnetic:1 focus:2 leads:1 roy:1 cooperative:10 denotes:4 localized:2 devoted:1 dimensionality:1 referring:1 transferred:1 supported:1 program:1 tanaka:1 those:12 crest:1 resources:1 division:1 nσ:1 very:1 rise:1 induce:2 results:5 electron:3 mouri:1 every:1 figs:3 difference:1 matrices:1 vibrational:11 presented:1 turns:1 t2:2 solution:1 t1:1 large:1 solved:1 vector:1 small:1 chuang:1 precursor:1 smaller:1 computation:1 approximation:4 surrounding:1 rate:6 dynamics:24 estimated:1 10t:4 canonical:1 even:2 will:10 ˆr:1 plays:1 deeply:1 sum:3 tully:1 realizing:1 3t:1 current:2 above:2 new:3 method:5 filled:2 pioneering:1 edited:2 chose:1 respectively:1 component:2 here:1 atoms:1 focused:2 relaxation:1 equations:2 appears:1 change:3 differential:1 obtained:1 fsec:1 institute:1 study:10 studied:2 zener:2 published:1 domains:2 suitable:3 studies:4 composed:1 diameter:1 via:1 apply:1 glance:1 total:1 linearly:1 franck:2 conventional:2 reflected:1 takes:10 commun:1 jpn:1 cho:1 comparing:2 assistance:1 taken:9 scope:1 theoretical:3 reflects:1 more:4 zwick:1 becomes:3 operators:1 odinger:4 transient:1 controlling:1 labelled:1 particular:3 known:1 cases:4 states:24 account:8 rice:1 evolution:1 quantized:3 science:3 equation:6 work:1 modified:1 koda:1 remain:1 fock:2 crossed:1 tracing:1 following:2 making:1 example:2 control:6 nearest:7 references:2 computers:1 figure:11 give:2 calculation:6 cited:1 neglected:1 involve:1 indicates:1 information:2 winter:1 rather:1 conical:1 discussion:3 acts:1 feature:1 adjacent:4 opt:1 product:1 mat:1 cooperativity:2 may:1 advice:1 after:9 derived:1 applications:3 designed:2 cambridge:2 parallel:1 types:2 realized:2 natural:1 dynamical:2 computations:1 spectra:1 s2:1 representation:1 make:3 typical:4 reservoir:2 over:3 mainly:1 soc:2 distortion:12 paper:10 pulses:4 preliminary:1 mentioned:3 japan:3 suffer:1 before:3 sciences:1 outer:1 temporal:2 solving:1 coordinates:1 degrees:1 systems:8 overcome:1 them:1 within:1 return:1 pauli:1 propose:1 regarding:2 landau:2 mention:5 effects:1 they:2 thanks:1 multidimensional:1 discuss:3 teller:1 structural:2 2s:1 fully:2 university:2 hamiltonian:2 sufficiently:1 magnitude:1 mode:8 each:16 found:6 characterized:1 mean:2 reactions:1 domain:19 bifurcation:2 generation:1 density:1 energy:8 related:1 applicable:1 constitute:1 elementary:1 measure:1 quantum:8 our:1 transitions:5 eq:2 es:2 out:7 shown:8 a137:1 opened:1 space:2 since:8 induces:3 research:3 increase:2 dominated:1 denoted:3 rn:1 induced:2 ref:1 shows:6 benjamin:1 koshino:1 wiley:1 theory:2 barrier:1 interactions:6 given:1 york:1 estimate:1 beginning:1 generate:1 advance:1 pairs:1 interaction:12 organic:5 r1:1 r2:1 could:1 transition:6 keep:1 motion:4 place:9 transfer:5 hence:12 first:4 origin:1 features:1 variables:3 number:5 xr:2 electronic:20 intermolecular:10 size:1 properties:10 rewritten:1 utilization:1 introduction:1 top:1 behaves:1 system:9 vibrate:2 grow:2 their:4 calculations:6 molecular:15 unpublished:1 gives:1 interests:1 eyes:1 completed:1 continuous:1 stress:3 optical:4 authors:2 injected:2 translation:1 than:4 center:2 begins:2 distance:5 require:1 second:1 project:1 future:2 contrary:3 were:1 treated:1 raman:1 pointed:2 mino:1 ishida:5 modern:1 nakamura:1 seed:7 close:1 need:1 seem:1 misawa:2 glauber:1 complete:1 conversion:7 chem:3 pursued:1 mechanism:2 predominantly:1 note:1 decomposing:1 potential:3 take:3 ur2:2 schematically:1 switching:1 circles:3 play:2 multiple:2 though:1 molecule:25 jst:1 photoinduced:25 pr2:2 phase:2 analytically:1 photochemical:1 considered:2 calculated:3 later:1 order:4 phonons:4 electrons:7 ku:1 mechanical:5 ky:2 kx:2 section:3 fact:1 precise:1 drastically:1 particularly:2 show:4 arrayed:1 notations:1 relation:1 line:1 ground:5 reminiscent:1 slow:1 parameters:5 written:1 topological:1 should:7 only:8 condon:2 molecules:29 thompson:1 circle:2 population:11 interested:1 zts:1 diffusion:4 handle:1 means:4 dependent:2 simplest:2 nonequilibrium:2 words:1 propagated:1 during:2 takahashi:1 processes:25 fields:1 arxiv:1 yield:1 acknowledgments:1 experiments:1 common:1 kutta:1 through:2 discussing:1 valid:1 view:3 enhances:1 set:1 ser:2 exists:1 national:1 up:1 observed:2 intensity:1 individual:4 radius:2 result:3 existence:1 terms:1 institutes:1 quantizing:2 surfaces:2 annihilation:1 capacity:1 interacting:1 lots:1 review:2 takagi:1 sites:7 nucleation:25 case:1 state:27 converted:6 various:3 cooperation:1 between:9 consecutive:1 boundary:2 kek:1 extend:1 nature:1 initially:2 however:6 key:3 liq:1 understanding:1 reaction:1 cos:2 many:3 vibration:10 quantization:2 σz:1 hω:4 figures:1 receives:1 5t:4 contribution:1 whole:2 experimental:2 arbitrarily:1 detailed:1 ibaraki:1 relevant:6 nonadiabatic:9 point:3 others:2 period:1 dimensional:6 ab:1 sakai:1 respect:2 ogawa:2 runge:1 pr:2 described:5 basis:1 due:1 been:5 belongs:1 combined:1 basic:2 fig:6 contribute:1 both:2 sufficient:2 coherence:5 coherent:11 understand:6 coherently:3 c3:1 denote:2 spin:1 former:1 present:13 applied:1 laser:3 reciprocal:1 solid:1 value:4 employ:2 euclidean:1 while:1 salem:1 behavior:4 ntotal:4 property:1 guide:1 procedure:1 reflectance:1 psec:1 coupled:2 almost:2 thus:11 site:3 cluster:1 itself:1 cond:1 conf:2 diabatic:3 affected:1 technology:2 disappear:1 nielsen:1 different:1 vibronic:2 propagation:3 s2h:2 belong:1 cross:1 same:1 unity:1 schematic:2 physical:2 grows:2 higher:4 development:1 independent:1 moussa:1 embedding:1 see:2 singapore:2 luty:1 numerical:4 effect:2 hand:2 driven:4 average:4 moment:1 levels:1 takaoka:1 toshiba:1 recent:1 costa:1 shaded:1 schr:4 modes:2 scenario:1 materials:6 solve:1 tokura:2 coordinate:3 organization:1 model:17 chemistry:1 corporate:1 dimension:1 photoexcitation:2 proposed:1 less:1 obtain:2 rest:1 detail:1 atomic:3 aspect:1 momenta:1 scattering:1 coordination:1 previous:2 conclusions:2 absorption:1 conclude:1 except:1 lattice:8 internal:1 lett:1 easy:1 excited:19 momentum:1 jahn:1 resolved:1 b58:1 aspects:2 around:2 depends:1 decomposed:2 possible:3 corresponds:4 increases:6 mol:1 press:1 world:2 advanced:1 helpful:1 necessary:2 like:1 lost:1 follows:1 qualitative:1 adiabatic:3 nanoscience:1 specific:1 either:1 become:1 works:1 kawasaki:1 mext:1 therein:1 methods:5 classical:1 smoothly:1 creation:1 phenomena:12 zhao:1 understood:4 growth:11 ferroelectric:1 provided:1 scale:1 tsukuba:1 affects:1 per:1 pes:1 initio:1 does:3 prog:1 intersections:2 proc:1 minimal:2 refer:1 process:4 scientific:2 equivalent:1 wavefunctions:4 oscillating:1 cryst:2 σir:1 substituted:2 although:2 absorbance:1 drawn:1 super:1 hilbert:1 asai:1 stage:2 nonadiabaticity:2 central:1 carried:1 freedom:1 discussed:2 dependence:1 o:1 simulation:1 range:1 obeys:1 neighbor:7 act:1 introduced:1 takeda:1 computational:4 real:1 into:10 successive:2 numerically:1 sol:1 three:1 down:1 device:3 appropriate:1 square:2 rising:1 determine:1 sov:1 operator:2 proportional:1 next:2 few:1 assumed:1 initial:9 dispersion:1 start:1 series:1 was:4 function:2 survives:1 elsewhere:1 triggered:1 but:1 larger:1 subsidiary:1 injection:3 longer:2 made:2 zhu:1 mtrl:1 flip:1 ur:13 pess:7 spectroscopy:1 cahill:1 similar:2 clear:1 strongly:1 oho:1 constant:2 horikoshi:1 computing:2 defined:2 abstract:1 describe:4 general:3 single:7 ar:10 moln:1 crystals:1 moves:1 proceeds:2 regime:2 functions:2 thermodynamical:1 dotted:1 corporation:1 wavefunction:10 when:7 inset:1 graduate:1 field:3 photoexcited:3 other:11 role:3 details:2 papers:2 nr:12 theor:1 manhattan:1 picture:1 stat:1 excitation:2 separate:1 models:1 sqr:1 important:9 ising:1 structure:5 lang:1 coupling:6 coulomb:6 nasu:4 assume:1 values:8 4t:1 required:4 phonon:3 appendix:1 time:17 ultrafast:1 decoherence:6 requires:1 once:2
0705.0860.txt |@word limited:1 lagrangian:4 four:13 localized:4 whose:1 violate:1 segments:1 picariello:1 under:18 rise:1 connects:1 affect:1 solution:2 correct:2 jhep:6 direct:2 approximation:6 elegant:1 second:3 chen:1 implemented:2 even:5 established:1 above:1 new:3 mee:4 uncompactified:1 lavoura:5 here:9 asymmetry:2 pati:1 quark:22 ωa3:2 ωa2:3 obtained:10 suitably:1 study:1 adopting:1 suitable:4 classification:8 remnant:1 moral:1 neutrino:37 total:1 unit:4 quasi:1 would:11 motivate:1 negative:2 m1:19 therefore:3 m3:18 m2:18 type:2 merlo:1 aligned:1 must:2 me:3 md:2 ma:15 ml:2 setup:1 work:1 mi:1 mp:1 ms:1 root:1 example:14 renormalization:1 indicated:1 give:1 table:7 generically:2 involve:1 indicates:2 want:1 times:1 guarantee:1 provide:3 verify:1 feature:1 mµ:3 how:4 ordinary:2 classify:1 lam:1 description:3 transforming:2 after:3 law:1 attempt:1 effective:2 keeps:1 operate:1 order:24 feedback:1 zee:2 diagonalizes:1 over:3 satisfied:1 satisfies:1 before:1 fit:3 petcov:2 better:1 fig:3 renormalizable:2 schmidt:1 versus:1 eventually:1 them:4 affected:1 combination:2 break:1 effects:3 they:5 eigenvalue:3 classified:2 reasonable:2 each:11 side:1 mean:1 m2atm:17 schemes:1 t2:2 attenuation:1 driving:4 rs:1 crucial:2 particles:2 mν:13 rh:3 mτ:3 linear:3 free:1 standard:1 assures:1 corrections:11 already:3 features:1 perkins:2 restrict:1 relations:7 another:1 similarly:2 top:2 approximately:2 needed:3 too:9 burgess:1 murayama:1 unbroken:1 convention:1 lower:1 barbieri:3 likely:1 matter:3 classes:2 powers:5 spectrum:10 seen:4 unaffected:1 relatively:1 latter:1 baldo:1 acquire:2 shall:2 volkas:1 extending:1 regular:2 phase:4 nussinov:1 observation:1 vertices:6 points:8 principle:1 section:5 random:2 implying:1 attempts:1 gauge:4 solutions:1 d4:1 spite:1 explain:1 constant:1 do:5 di:2 ix6:1 de:4 dc:1 preferred:1 report:1 covering:1 fields:22 nδ:1 torrente:1 observed:3 radius:1 symmetric:2 future:1 simplest:2 approach:3 µc:10 wd:6 terms:14 extend:1 nature:1 modify:3 wl:9 weak:1 however:4 essentially:1 distinction:2 2nd:2 represented:2 basis:10 radiative:1 three:9 been:12 much:6 basic:1 expected:1 dynamically:1 dots:4 supersymmetric:2 quantities:2 grimus:5 remaining:1 near:4 characterizing:1 redefinitions:1 played:1 ii:1 interacts:1 make:1 complex:6 potentially:1 hierarchies:2 independent:2 hand:1 characters:7 potentials:1 rome:1 roma:1 left:8 unified:3 proposed:1 transforms:4 yet:2 previous:3 enters:1 mix:1 character:2 easy:2 yukawa:2 koide:1 breaks:1 possible:4 possibly:1 unification:1 unique:1 apart:1 appearing:1 specific:1 n1:2 right:7 understand:2 successfully:1 proceeding:1 bottom:1 normal:15 kobayashi:2 minimization:1 leptons:19 properties:2 mohapatra:7 o:7 d69:2 yasue:2 d67:1 raised:1 presence:2 rotations:1 bound:4 down:2 tetrahedral:1 transform:6 way:7 triplets:4 call:1 was:7 lowest:2 form:3 offer:1 denoting:1 solar:2 true:1 vevs:8 flavour:10 versions:1 compactification:5 maximum:1 examples:2 later:2 abstract:2 commuting:1 triangles:1 physical:1 no:9 whereas:2 generally:1 vanishes:1 handed:9 reality:1 role:3 picture:4 models:31 convincing:1 minakata:1 tribimaximal:3 assume:6 interval:3 together:1 time:11 serious:1 n2:2 n3:2 n4:2 quarks:14 remarkable:2 alternatives:1 leads:4 vev:7 certainly:1 inverse:5 finally:5 division:1 string:1 advantage:3 zhang:2 frequencies:1 entries:4 exact:1 dim:1 impressive:1 presented:3 turns:1 accidentally:2 discrete:6 gut:3 upper:4 dealing:1 prediction:1 stands:2 b687:1 goes:1 boost:1 satisfy:5 understanding:2 cos2:1 groups:2 along:2 appears:4 change:2 knowledge:1 shift:2 hospitality:1 extra:7 f2:1 1st:2 illumination:1 d70:2 axionic:1 predictions:1 introducing:1 duality:1 rigid:1 virtue:1 valle:2 values:5 following:5 making:1 degenerate:7 figure:3 permutations:5 smirnov:3 vckm:5 unveiled:1 allowed:2 conversely:1 occur:1 kyu:1 s2:1 discussion:1 exceptional:5 absolute:2 parameter:5 dominance:1 product:7 may:2 sno:1 produce:3 improving:1 representations:14 data:4 natural:7 dynamical:5 sectors:5 higgs:4 sv:1 su:11 st:9 ghg:1 so:18 sm:1 sc:1 representation:7 typical:8 indeed:8 years:1 stability:1 experiments:2 statistical:1 still:3 group:26 thank:1 interesting:11 τc:2 coordinates:1 forms:2 mail:1 main:1 non:6 altarelli:9 fukuyama:1 ahn:1 introduce:4 now:3 discuss:5 developments:1 term:6 realistic:2 flavons:2 rajasekaran:1 square:1 kang:2 eg:1 ec:12 proportional:2 ev:4 eq:19 matias:1 shown:6 watanabe:2 3rd:2 space:12 squared:2 suggesting:1 formula:2 viable:2 shows:1 theory:7 carr:1 fisica:1 possibility:3 quite:1 unwanted:1 besides:2 forbids:1 turn:1 invitation:1 first:8 origin:2 simplifies:1 vacua:1 symmetry:40 xb:2 xa:6 xd:2 approximate:2 open:1 size:1 interchange:1 given:17 checked:1 realization:4 structures:1 gives:1 cope:1 continuous:4 electroweak:3 eliminated:1 than:6 x5:1 unfortunately:1 m2sol:4 require:1 yoshioka:1 hagedorn:2 protected:1 were:1 correction:1 hierachy:1 saw:11 any:3 ideas:2 note:4 potential:4 take:3 trace:1 opposite:2 track:1 neutrinos:12 beta:1 rationale:1 surprising:1 considered:3 average:1 adopt:2 mrr:3 gouvea:1 typically:3 quantity:2 precise:1 show:1 imagined:1 fifth:1 ratio:1 texture:1 only:6 going:1 gev:1 get:2 cannot:4 nearly:2 progress:1 gen:1 frampton:2 ut:1 through:3 comparable:1 relative:3 inequivalent:5 ei2π:1 ways:1 review:3 boundaries:1 enough:1 vu2:8 between:14 diagonalized:2 checks:1 notice:3 medeiros:3 concentrate:1 fluctuations:1 suppressed:4 many:5 region:2 according:3 called:4 embedding:1 expression:1 duty:1 among:2 key:1 characterization:1 satisfaction:1 cancel:1 moreover:1 branes:5 tuning:3 come:1 absence:6 differently:1 direction:1 6d:5 offered:1 those:4 case:10 trick:1 maximal:14 orientation:1 couples:2 susy:8 different:11 develop:2 same:17 bimaximal:4 kovtun:1 extended:1 assigns:1 raidal:2 doublets:7 kubo:1 running:1 edges:2 invariance:1 minimize:1 without:2 solve:1 components:4 coordinate:1 model:25 dimension:7 charged:26 wolfenstein:1 flavon:5 minima:2 being:5 when:6 relevant:3 harrison:7 semiquantitative:1 leptogenesis:1 except:1 improvement:1 lett:26 versa:1 ross:3 real:5 jake:1 represents:1 read:1 dark:1 vacuum:5 mod:2 identifying:1 discarded:1 kitabayashi:2 either:3 fully:1 satisfactory:1 masina:2 xing:4 dimensions:6 2xa:1 2xb:1 extensively:1 decomposition:1 provides:2 moderate:1 refer:1 power:1 equivalent:1 notably:1 broken:4 ratios:1 haba:2 discussed:9 greatly:1 variable:2 caravaglios:1 references:2 determine:1 operator:1 lavignac:1 conceptually:1 hep:83 her:1 assumed:3 there:17 start:1 lot:1 decisive:1 complete:1 ωz:1 arranged:1 minkowski:1 obtains:3 strongly:1 ad:1 deep:1 general:7 formulation:2 yanagida:1 az:1 again:1 field:8 spatial:1 massless:1 unobservable:1 deviation:1 separate:2 vertex:1 includes:2 a1:14 a3:11 a2:11 bounded:1 a4:62 suited:1 realised:1 building:1 mass:33 starting:2 represent:1 sci:1 consider:2 splitting:1 scalar:6 commute:1 follow:3 tv:1 equivalence:3 presentation:1 tc:1 straightforward:1 very:13 translations:2 induce:1 difference:1 varzielas:3 list:3 large:16 small:25 fogli:2 wmap:1 bilinear:1 villanova:1 sub:1 diag:2 sum:2 version:3 fractional:1 acknowledgments:1 full:1 component:3 venice:1 modular:5 directions:4 strong:1 equations:1 allows:2 amount:2 superpotential:8 permutation:1 via:1 family:1 requiring:1 contains:2 charge:2 nucl:7 hirsch:1 more:8 ramond:2 thus:8 operators:7 particular:7 keeping:2 recall:1 del:1 f1:1 compare:1 f3:1 νr:1 ann:1 minimum:3 numbers:2 νc:1 sense:1 needs:2 breaking:11 maps:1 explains:1 derived:2 plane:1 coming:1 horizontal:1 derives:1 adhikary:1 transposed:1 negligibly:2 prefers:1 yτ:7 assign:1 lhu:2 negligible:1 fundamental:4 baryogenesis:1 help:1 hierarchy:16 soon:1 scott:7 signs:1 y2:1 its:7 actually:3 detected:1 tentatively:1 good:6 motivated:1 ye:10 obeyed:1 uhp:3 yu:5 bigger:1 easily:3 2r:6 2s:1 always:1 level:3 2d:3 2a:1 irreducible:4 found:2 2a3:1 heavy:1 generation:2 energy:2 idea:1 used:1 expect:5 quantum:1 yµ:7 anarchy:7 since:4 research:1 acting:3 induced:3 localization:1 sparked:1 pleasant:1 reason:2 constraining:1 eqs:3 number:6 least:1 introduction:1 leading:11 construct:2 scheme:3 exponents:2 observations:2 warmly:1 baryon:1 sizably:1 immediate:1 part:4 king:5 kind:1 double:2 charges:3 contrary:1 conjugate:1 built:1 depending:2 lin:2 empirically:1 build:1 antiquarks:2 towards:1 singlet:9 most:4 significant:1 measured:2 appear:1 deviations:2 clear:3 coincides:1 unreasonable:1 subgroup:4 physics:2 sector:23 particularly:4 3x3:3 relation:6 fine:2 find:3 parameters:4 generators:1 dominant:1 notation:3 dependent:1 express:1 accomodated:1 ϕl:11 closely:1 combinations:1 disregarding:2 remove:1 switzerland:1 doublet:4 nasri:5 set:5 achieved:1 collectively:1 see:26 close:7 learnt:2 rodejohann:2 smallest:1 probably:2 hold:1 recently:2 missing:2 vanishing:1 m23:2 both:5 last:1 kamland:1 romao:1 context:5 whole:2 experimental:2 point:3 simple:2 corresponds:1 dimensional:8 simply:2 described:3 transformations:9 due:5 reduction:1 ph:80 generating:1 renormalisable:1 look:1 solid:2 tetrahedron:2 empirical:1 while:14 guido:2 couplings:1 ceolin:1 unitary:8 encountered:1 reads:2 itself:1 vanish:3 fermion:7 italy:1 baseline:1 neutrinoless:1 belong:3 rules:2 carone:1 grand:2 higher:6 literature:1 comprehensive:1 moving:1 purpose:1 recent:3 eigenvectors:1 subleading:2 analysis:2 edge:1 self:1 reviewed:1 λc:1 alternative:1 alignment:14 cut:2 unspecified:1 conclusions:1 guaranteed:1 input:1 transformation:12 irges:1 couple:1 displace:1 smallness:1 quest:1 modifications:1 follows:3 separately:1 weiner:1 essential:1 malinsky:2 some:11 understood:1 strongest:1 added:2 b1:9 b2:9 b3:9 oscillations:1 scale:5 describing:1 prop:1 cabibbo:3 minimal:1 bc:2 s13:1 s12:2 agreement:2 integers:1 constraint:1 range:2 involving:2 frigerio:1 cutoff:1 into:3 within:2 eisele:1 long:2 sections:2 arise:1 forbidding:1 uu:2 characteristic:1 up:8 us:3 2πr:1 ud:2 similar:1 torus:1 uc:1 associated:1 defined:4 inferred:1 single:1 department:1 franceschini:1 elements:5 generates:1 accidental:1 problems:3 generated:5 allowing:1 suppression:1 structure:7 ago:1 independently:1 implies:1 vice:1 required:1 far:3 romanino:3 results:4 go:1 contributions:3 compact:1 concerned:1 include:2 lindner:1 g5:1 g4:1 g3:1 g2:1 g1:1 mixing:28 matrices:10 categories:1 arrange:1 tri:4 tre:1 eve:1 assignments:2 eigenvalues:6 majorana:8 smaller:2 compensated:1 sin2:1 peccei:1 dynamics:1 odd:1 index:1 plays:2 giving:1 experiment:3 3b:1 3a:1 lee:1 exchange:5 respectively:6 desired:4 explore:1 objects:1 separation:4 z4:7 consideration:1 z1:6 z2:11 z3:14 great:3 cern:2 involved:1 larger:3 contradiction:1 leaving:1 suggests:3 products:1 lujan:1 implement:1 makes:1 formulated:1 scales:2 apply:1 use:2 next:2 simpler:1 kim:1 becomes:2 carrying:1 babu:2 labelled:3 arranging:1 account:1 challenge:1 insists:1 salam:1 reproduce:2 splittings:1 control:1 lτ:2 lorentz:1 triangle:1 tan:1 six:1 lepton:27 instead:2 mysteries:1 sin:2 stand:3 collection:1 multiplication:1 realized:5 λ2c:1 lines:1 correspond:3 element:5 allow:2 subsequently:1 interpreted:1 produced:1 feruglio:7 including:1 2st:1 regions:2 le:3 lc:1 la:1 raby:2 masses:29 lh:1 inspecting:1 defining:1 ly:3 dirac:3 identified:3 sufficiently:2 universita:1 l2:3 l3:3 l1:3 arxiv:42 related:3 inverted:4 seesaw:1 decays:1 our:8 erties:1 luhn:1 special:7 out:3 matrix:38 rev:21 reformulate:1 m2i:2 matm:2 ref:9 tanimoto:1 achievements:1 interactions:2 diagonal:13 completely:2 8y:2 usual:1 interaction:1 geometry:1 could:6 m22:1 keep:1 length:1 lµ:2 hence:1 reached:1 precisely:4 ordering:1 unknown:1 adopted:2 b622:1 their:6 fermions:2 adopts:1 exactly:5 inversely:1 appealing:2 light:1 providing:2 symmetries:3 unchanged:1 need:4 clearly:2 angle:4 able:1 mechanism:5 instance:5 nishiura:1 ghosal:1 accuracy:1 definitions:1 class:6 χr:3 ckm:1 χg:1 proceedings:1 hierarchical:4 normally:2 fact:7 χh:1 violation:4 bring:1 trivial:1 decade:1 based:3 criterium:1 should:7 local:4 achieve:1 equilibrium:1 means:1 lebed:1 mgu:3 applying:2 transposition:1 fixed:11 generations:3 predictive:1 triplet:7 geometrically:1 acquires:1 phases:3 pattern:4 invariant:7 luo:1 ends:2 reproduced:2 orbifold:11 spoil:1 configuration:1 distribution:1 undetermined:1 observable:1 taking:1 decay:1 equal:5 mixings:17 etc:1 ll:11 otherwise:1 detailed:4 ch:2 conclude:1 cc:1 dipartimento:1 cz:1 respect:2 cp:2 singlets:6 addition:2 define:1 determinant:5 corresponding:2 cos:12 bulk:3 angles:6 c3:2 c2:2 c1:2 dvali:1 present:8 c4:3 atmospheric:1 g6:1 contexts:1 value:17 will:7 frustrating:1 layer:1 vd:4 almost:1 refs:3 vl:3 instantons:1 vs:2 vt:1 compactified:1 generic:1 largest:1 units:2 φi:3 finite:4 difficult:1 cubic:1 effect:3 v0:3 v2:1 infinite:1 lopsided:1 identity:3 off:3 well:3 s23:1 sets:3 latest:1 buchmuller:1 obtain:9 sources:1 underlying:1 guts:2 hall:4 add:1 attractive:1 diagonalization:3 identical:1 five:1 know:1 immediately:4 necessary:1 like:6 xsu:2 qualitative:1 become:1 works:1 soft:4 parity:3 exceed:1 because:5 righthanded:2 proper:1 diagonalizing:1 keum:1 lead:1 broad:1 morisi:2 does:9 economical:2 assuming:2 expansion:3 stage:1 about:3 column:1 universe:1 introduces:1 compatible:6 important:4 introduced:1 letters:1 previously:1 sl2:1 aranda:1 additional:9 restricts:1 naturally:1 brane:2 but:17 hu:6 construction:2 hd:2 he:2 made:4 tan2:5 below:1 converted:1 limit:4 problem:7 contribute:2 denote:3 families:1 proceeds:1 compared:1 orbifolding:5 hps:13 detail:2 other:11 θc:4 conclusion:3 zhou:2 lanck:1 chance:1 coupling:2 uncoupled:1 4r:1 determination:2 4d:3
0705.0861.txt |@word consider:3 excellent:3 results:13 existing:3 four:3 gc:1 per:1 llc:1 expressions:1 contributions:5 careful:1 technique:1 λn1:3 γk:2 γj:1 summarised:1 program:1 present:7 determinations:1 under:2 include:2 ingredient:1 overlaps:1 case:2 breathing:1 advantage:1 orthogonal:1 mn1:15 supercomputer:1 conditions:1 focus:1 puzzles:1 pn:1 interpolator:28 eq:6 li:2 difference:3 matrices:5 condition:1 identity:3 illustrated:1 school:1 level:6 proc:2 nucl:3 occurs:1 leave:1 discrete:1 interpolating:13 science:1 small:7 enhance:1 configurations:3 smaller:5 findings:3 consistent:5 plaquette:1 sign:2 threshold:2 likely:4 further:3 implemented:1 odd:11 analogue:3 approached:1 spectral:2 established:1 abc:3 appear:2 blum:1 section:1 burch:16 near:2 expressed:1 agrees:1 access:1 3i:1 above:1 new:3 increasing:1 method:2 filled:1 coefficient:1 quenched:8 agreement:2 lee:1 prescriptions:2 respectively:4 compilation:2 component:3 here:1 understanding:1 reported:2 mev:6 smearing:8 ansatz:1 others:1 directions:2 along:3 strong:2 observing:1 appears:2 obtained:7 heplat:2 shift:1 study:17 larger:8 allows:1 guide:1 suggests:1 periodic:1 total:1 action:6 resonance:15 narrow:2 studies:5 annihilates:1 bare:1 via:1 followed:1 projection:8 ix:1 ground:11 pp:1 apply:2 meson:1 m2π:2 propagators:1 standing:1 use:8 d71:1 proceed:3 usa:1 commun:1 distinct:1 positive:7 pluses:1 negative:1 next:2 linear:3 examination:1 therefore:8 qcd:12 taken:2 australian:3 eral:1 reflects:1 more:3 smeared:2 th:1 successful:1 initial:1 operators:5 stable:1 constructs:1 employed:1 known:1 iii:2 must:1 high:2 crosses:1 mb:3 recall:1 work:6 oscillator:1 sweeps:4 reproduce:1 slices:1 labeled:3 growing:1 making:1 example:1 history:1 council:1 figure:1 calculation:3 expanding:1 suggestions:1 uat:2 states:30 lorentz:1 performed:4 degenerate:3 mn:5 simple:1 information:3 respective:2 sit:1 verify:1 discussion:2 six:2 enlarge:1 write:3 how:3 guichon:1 significance:1 d69:1 those:2 eight:1 ensemble:1 edinburgh:3 product:1 d74:1 may:2 db:2 earlier:5 elusive:1 lab:2 br:9 d65:2 explored:1 lat:12 wave:11 data:9 fm:21 diagonal:2 short:1 physical:7 dynamical:1 third:2 light:1 spectra:1 lines:2 correspond:1 hanhart:1 element:1 en1:8 allow:1 correlation:53 representation:3 sa:1 superscript:2 interpretation:1 nucleon:27 numbers:3 indeed:1 over:4 years:1 including:4 statistical:1 suffer:1 excitations:4 its:1 horizontally:2 b164:1 thank:1 fit:7 energies:3 masses:39 actually:1 absence:1 fig:12 relate:1 jacobi:1 ours:1 krewald:1 emphasize:1 non:4 good:1 motivated:1 greater:1 evaluate:3 outlined:1 nation:1 scaling:1 effects:4 they:3 now:2 inversion:1 gev2:2 pµn:10 university:2 presented:2 identified:6 labeling:1 sufficiently:1 newport:1 reasonable:1 radial:1 2eb:2 found:9 difficult:1 side:1 mean:1 individually:5 spinor:5 hadronic:1 energy:12 gaussian:2 eb:12 expect:3 combining:2 quantum:3 our:24 extract:4 06or23177:1 special:1 after:3 large:6 kamleh:1 matrix:39 space:1 restricted:1 furthermore:2 since:3 rev:15 projected:10 research:2 acting:1 squares:1 ref:15 correct:1 math:1 shows:2 creating:1 temporal:1 mπ:2 given:4 quark:23 indices:1 earliest:1 r0:1 chiral:2 created:1 bern:2 creates:1 ordering:5 massive:1 βb:1 eqs:4 south:1 first:4 already:1 pn1:16 jackknife:1 number:2 fits:1 determination:1 clarity:2 open:1 size:6 little:1 rightmost:1 similarly:2 introduction:1 adjoint:2 system:1 conclusion:1 their:4 mukhopadhyay:1 intermediate:1 fermions:1 calculations:6 variational:1 ranging:1 williams:2 too:3 shell:1 nuclth:1 m0:1 enhancing:1 baryon:6 reversed:3 part:4 somewhat:1 basak:16 focusing:1 constituent:1 zanotti:5 than:3 coefficients:1 wide:2 hepph:1 hopping:1 showed:2 largely:1 enabled:1 second:3 correlators:2 project:2 matter:1 future:1 were:3 accessed:1 tion:1 providing:2 minus:2 extracting:2 function:15 symmetries:1 remained:1 c62:1 partnership:2 mind:1 spectrum:13 need:3 seen:2 seem:1 any:3 relatively:3 lie:1 wilson:1 strength:1 zero:4 general:1 latter:1 isolate:1 note:7 extracted:32 jefferson:4 take:1 strengths:1 channel:2 hyperfine:1 circles:2 even:26 begin:2 multiple:1 trace:1 centre:1 collaboration:8 most:1 propagate:5 but:1 significant:4 baryons:5 acknowledgements:1 why:1 interacting:2 considered:4 average:2 stronger:1 doe:1 points:4 ohta:1 exp:4 typically:1 sum:1 lying:5 3p:2 2pµ:1 cdb:1 show:4 supported:3 bring:1 attempts:1 gauge:5 keywords:1 substituting:2 melnitchouk:3 label:3 fine:1 find:4 principal:1 current:1 highest:2 based:3 parameters:3 explain:1 written:4 should:2 only:6 regensburg:2 ambiguity:1 factor:1 various:1 burkert:1 ieb:2 local:4 rectangle:1 carlson:1 do:3 gev:2 sufficent:1 dependent:1 diamonds:2 overall:1 dc:4 d51:1 report:4 lattices:1 interpreted:1 becomes:1 unfortunately:1 following:2 graz:2 continuum:1 λb:3 fields:9 arxiv:1 summary:1 source:6 fixed:2 fierz:3 approaching:2 sev:1 requirement:1 set:5 exists:1 subatomic:1 relative:2 namely:1 individual:1 sec:4 result:1 terms:6 observed:1 best:5 techniques:9 closer:1 fails:1 degree:1 luscher:2 avenue:1 review:4 missing:1 definite:1 tend:1 state:68 αb:1 identification:1 closed:1 between:4 invariant:2 boundary:3 approach:4 αn:1 available:1 accord:1 recently:2 spectroscopy:1 extend:3 nature:2 spacing:2 weak:1 however:6 key:1 contamination:1 probing:1 news:1 improve:1 suggested:1 both:6 hypercubic:1 improved:2 candidate:1 weisz:2 equal:1 contract:1 uc:3 context:1 contribution:2 argue:1 finds:1 experimental:2 sink:2 strongly:1 leinweber:5 relevant:1 point:3 βn1:8 effective:3 harmonic:1 grants:1 projector:2 adding:1 table:2 throughout:1 considers:1 considering:1 ǫabc:5 finally:1 mathur:5 basis:13 addition:3 invert:2 roper:21 three:8 been:7 pb:2 interest:1 expected:1 ph:1 anomaly:1 choose:1 field:7 direction:1 partly:1 scalars:1 sufficient:1 subscripts:1 covariance:1 6p:1 understand:2 bayesian:5 last:1 evidence:6 spin:37 standard:1 p2:2 eip:2 multi:2 pacs:1 solid:2 expanded:2 empirical:2 value:1 transformation:1 will:3 euclidean:1 while:2 spin3:2 evaluating:2 error:1 aid:1 couplings:3 va:1 vectors:1 almost:1 ip:7 refs:5 thus:1 herein:1 discrepancy:1 iv:2 ii:2 αn1:13 fermion:10 different:7 combination:4 grant:1 suggest:1 make:1 3jz:1 cross:1 same:1 d70:1 triangles:2 largest:4 resulting:1 finite:4 higher:2 independent:1 used:12 i3:1 disagree:1 hand:1 scale:1 potentials:1 expand:1 recent:1 eigenvectors:3 lower:3 modes:1 thy:1 pµ:2 amπ:2 ıvely:1 well:2 remain:1 analysis:30 without:1 components:3 dashed:1 firstly:1 left:1 3p2:1 obtain:3 actions:1 sources:5 identify:8 world:1 glue:1 scattering:3 λn:1 cssm:8 previous:5 onset:3 generous:1 adp:1 conclusions:1 conclude:2 had:1 attractive:1 lattice:43 setting:1 plateau:4 δpp:1 excited:39 momentum:8 pparc:1 real:3 makes:1 australia:1 ample:1 secondorder:1 phenomenology:1 possible:2 corresponds:2 know:1 vacuum:1 using:18 speth:1 advanced:3 displaced:3 imposed:1 like:2 particle:1 identifying:1 serves:1 steps:1 lowlying:1 tower:1 valence:2 summarise:1 replacement:1 parity:41 because:4 d46:1 imaginary:1 some:1 back:2 slice:6 sommer:1 p0:1 interpolators:18 proceeding:1 dimensions:1 cσ:2 resonances:1 octet:1 overlap:9 b605:1 does:2 leftmost:1 adjoints:1 demonstrated:1 either:4 inserting:2 d72:3 particular:1 equivalent:1 each:9 analysed:1 expansion:1 step:1 although:2 2m:1 cγ:3 analyses:8 properties:1 hadron:4 tuning:1 comparison:4 central:1 would:4 extending:1 freedom:1 discussed:4 factors:1 o:3 simulation:2 remains:1 important:1 plus:1 d68:1 mixed:1 importantly:1 d67:1 consequently:1 heavy:1 final:1 previously:1 within:1 splitting:1 due:1 appropriate:4 right:1 raises:1 determine:4 operator:7 proportional:1 reducing:1 statistics:5 hep:13 additional:1 artifacts:1 there:5 question:2 transform:1 long:1 restricts:1 low:4 fraction:3 cγ5:2 was:8 naturally:1 lowest:4 complete:3 attempted:1 jul:1 volume:5 pµν:3 elimination:1 line:7 ha:1 true:1 mb2:1 made:1 gi3:3 whether:2 ut:4 up:1 us:1 eh9:1 below:3 limit:3 uk:1 similar:6 calculated:4 flic:2 ub:4 detailed:1 computing:2 recognize:1 contribute:1 hatsuda:1 singly:1 denote:2 dirac:3 single:1 associates:1 exist:1 aw:1 simulations:1 corresponding:2 check:1 sasaki:6 adelaide:2 functions:7 compared:3 discriminate:1 no:6 na:1 whereas:1 hybrid:1 detail:1 application:1 other:4 details:1 spatial:5 department:1 nt:1 pν:4 poor:1 elements:10 suppl:2 excitation:5 models:2 shown:8 includes:1 a2:1 included:1 structure:1 jlab:1 regime:1 coupling:3 algorithm:1 physics:3 required:1 speculations:1 equivalently:1 portion:1 mass:40 χi:2 volumes:2 time:14 n1:17 correla:1 lett:4 restored:1
0705.0862.txt |@word consider:1 gp:4 results:10 leads:1 roy:5 ge:1 computation:1 consists:1 gn:8 expressions:1 research:2 whose:4 inverse:1 depend:1 ulis:1 finally:6 tanaka:1 those:3 th:1 analogous:1 worth:1 case:10 belonging:2 g2:2 straightforward:3 orthogonal:1 very:2 rise:3 choice:5 l127:1 casas:2 nieto:1 exact:2 condition:5 annihilated:2 hamiltonian:8 bn:4 irreducible:6 t2:2 solution:2 discrete:5 differential:2 annihilates:1 eigenvalues:4 alternatively:2 employing:1 2k0:3 occurrence:1 dutra:2 consistent:1 direct:2 approximation:1 go:3 second:3 chen:2 further:1 odd:2 canonical:2 even:2 will:1 tkachuk:2 nonlinear:2 developed:1 brackets:1 giving:1 sun:1 section:12 expressed:2 d3:1 zhedanov:2 goes:2 new:4 d1:1 method:1 coefficient:2 full:2 hern:1 degree:1 respectively:4 nena:1 here:5 understanding:1 following:1 les:1 ansatz:1 groups:1 along:1 equations:11 change:1 deduced:1 obtained:8 generalizing:1 difficulty:1 jia:1 inspired:1 studied:2 allows:2 cari:1 resulting:2 characterizing:1 action:4 changes:2 via:1 useful:2 4a2:1 hermite:1 semiconductors:1 apply:1 establish:1 use:1 eψ:1 would:2 prove:2 distinct:2 positive:9 ψp:10 contains:1 quasi:2 intense:1 comparing:1 nucl:1 ψn:45 m0:1 bender:2 taken:1 type:4 minor:2 more:4 lowering:3 multiplying:1 clearly:1 becomes:1 operators:13 factor:4 odinger:16 curvature:1 clue:1 eν:2 appendix:3 observations:1 particular:1 known:5 cases:1 iii:2 must:1 topic:1 springer:1 deformed:13 equation:30 work:2 oscillator:16 cak:2 values:2 mr:1 growing:1 making:1 arrive:2 root:1 example:1 ducible:1 allowed:1 2rm:1 states:3 chin:1 arise:1 nth:1 positiondependent:1 counterpart:3 end:1 g1:3 provide:1 means:1 daskaloyannis:4 how:5 instead:1 parameter:3 classifying:1 algebra:34 may:6 oscillators:2 after:3 derived:1 different:3 reflect:1 applications:1 spectum:1 fd:1 kokkotas:1 representations:4 wave:1 excited:1 constants:1 short:1 physical:2 dynamical:1 effective:3 whenever:1 linear:3 lines:1 su:22 rather:1 cannot:1 so:3 representation:6 order:4 commutator:3 reuter:1 help:1 indeed:4 over:4 satisfied:1 years:1 course:1 termed:1 paper:2 ity:1 cassou:1 existence:2 satisfies:1 wherein:2 its:4 before:1 τn:3 derive:3 rapidly:1 curly:1 la:1 interesting:2 ll:2 solving:2 coordinates:1 writing:1 systems:6 ozer:2 jacobi:4 clusters:2 arias:1 defining:2 deformation:1 correspondence:1 boettcher:1 them:5 serra:2 ya:2 nada:1 puente:1 mention:1 effects:1 they:4 souza:2 now:7 yu:3 nos:1 easily:2 term:1 2p:12 2r:2 fully:1 4n2:1 appropriate:2 2d:2 filling:1 orc:1 radial:13 2l:5 universit:1 side:2 characterized:3 referred:1 hermiticity:1 schemes:1 retrieve:1 dong:3 generation:1 series:5 energy:10 related:1 extended:1 sketched:1 quantum:12 our:3 navarro:1 shown:4 matrix:2 space:1 open:1 furthermore:3 since:5 rev:7 denotes:1 looking:1 attracted:1 contained:1 ra:1 hott:1 ladder:4 math:25 8k:1 wiley:1 theory:2 associate:1 retrieved:1 abramowitz:1 limα:1 diagonal:1 standard:8 admits:1 1f:1 boulevard:1 included:2 york:3 smirnov:1 generate:2 additional:1 definition:3 pairs:1 derivation:1 r2:4 recast:1 transition:1 nonnegative:1 motion:2 turn:1 santander:1 consequence:1 first:5 separable:1 uler:1 ganguly:1 laguerre:2 variables:1 powerful:1 number:3 ddimensional:2 construct:3 another:2 bonatsos:1 mustafa:2 ring:1 electronic:1 angular:2 illustrate:1 given:10 perturbation:1 checked:1 rigo:1 plaine:1 introduction:1 leading:4 amsterdam:1 system:1 relations:12 πr:4 their:3 superintegrable:2 calculations:3 realization:1 veff:4 gives:3 way:3 tool:1 exactly:5 editions:1 x2:2 jiang:1 than:3 coefficients:1 kind:1 determines:1 third:3 namely:3 nations:1 determined:4 roychoudhury:4 providing:1 gp0:1 lowest:4 resentation:1 eliminating:1 stegun:1 explicit:3 ann:5 modern:1 wybourne:1 spectrum:21 close:1 intertwining:1 seen:1 lozada:1 demonstration:1 any:2 lie:5 wilson:1 built:2 depending:4 check:1 convenient:1 latter:6 physique:3 note:1 potential:7 build:2 coincide:1 completed:1 eff:4 andez:1 shall:3 gatica:1 eaire:1 satisfying:1 eight:1 plan:1 termination:1 phase:4 class:5 eigenfunctions:1 considered:4 clear:2 metal:1 scholtz:1 hahne:1 boronat:1 mechanical:4 sigma:1 fact:1 quantity:1 2m0:1 show:4 bagchi:6 relation:7 solutions:4 keywords:1 find:1 ground:1 parameters:3 title:1 written:3 should:3 identifies:1 only:5 going:1 generators:16 subsection:1 libre:1 hamiltonians:1 oct:1 do:1 dk:2 get:4 dependent:5 de:6 barranco:1 ones:3 dx:3 during:1 dt:2 du:1 dr:4 gen:14 dp:2 prime:1 evolution:1 conditions:3 bastard:1 arxiv:1 yield:2 λp0:4 europhys:4 physicists:1 qj:2 valid:1 satisfy:3 set:3 above:3 constructing:6 exists:1 achieved:2 unpublished:1 testing:1 relative:1 see:5 result:3 corre:1 recently:2 mazharimousavi:2 techniques:1 αr:4 commutation:6 nondegenerate:1 nuclear:1 review:1 schuck:1 symmetric:1 hammann:2 state:9 future:1 between:7 conceptual:1 simplifying:1 αk:10 semiconductor:1 approach:5 hence:1 multiplied:1 terms:6 right:1 nature:1 plastino:2 attention:1 transpose:1 jr:2 kress:2 key:1 distinguish:1 2αl:1 optional:1 ja:1 suggested:1 both:4 contrasted:1 2n:22 many:2 πr2:1 according:2 etc:1 pdm:20 unc:1 context:1 casimir:6 whole:1 16l:1 point:1 leipzig:1 harmonic:12 dimensional:20 anti:1 polynomial:4 proved:2 pr:2 transformations:1 pt:1 basis:9 16p2:2 three:7 been:8 much:1 combined:3 interest:2 basic:1 harwood:1 ph:2 algebras:13 pn:12 choose:1 dots:1 askey:1 generating:16 enable:1 supersymmetric:2 commutes:1 ψp0:1 body:1 else:1 observe:4 understand:1 kalnins:2 systematic:1 derivative:1 c2:2 c1:2 former:1 present:5 applied:2 p0:8 pacs:1 polls:1 value:1 transformation:2 aim:1 while:4 abrupt:1 miller:2 study:2 procedure:1 alhaidari:1 unitary:7 quesne:12 determination:1 tions:2 ii:3 need:1 reads:5 brod:1 rid:1 id:1 fabrocini:1 lengthy:2 righthand:1 generic:1 recursion:3 make:1 belong:1 lett:18 same:8 campus:1 highlighted:2 quant:1 units:1 dimensionless:1 gets:2 yi:1 a2p:5 used:3 unconventional:1 effect:2 hand:1 liquids:1 purpose:3 infinite:2 changing:1 invariance:1 brussels:1 normalization:4 recent:1 schr:16 e2ν:4 expression:1 no:1 well:6 mod:4 sets:2 coordinate:1 position:4 signalled:2 dimension:3 spherical:1 λp:3 just:1 resp:7 obtain:4 detail:1 shape:1 underlying:1 transforms:1 aspect:1 followed:1 momenta:1 heterostructures:1 k3:1 like:1 preprint:1 generator:3 ny:4 conclude:2 except:1 bp0:1 k0:27 treatment:1 easy:1 apart:1 solvable:5 remaining:2 momentum:3 real:2 eigenvalue:1 read:2 showing:1 possible:1 spanned:1 corresponds:1 eorique:1 know:1 belgium:1 using:4 moshinsky:1 occurring:1 theor:1 necessary:1 replacing:3 obvious:1 performing:1 exploiting:1 specific:3 yields:2 either:3 integrals:2 follows:1 multiplicative:1 become:2 reduced:2 fulfil:1 parity:4 because:3 methods:4 classical:2 czech:1 some:24 back:1 n2:2 shortcoming:1 choosing:1 respect:1 ourselves:1 δn:2 proceeding:1 dimensions:1 channel:1 circumvent:1 conditionally:1 eliminate:1 provides:1 assuming:1 koca:2 inserting:2 considering:1 equivalent:3 wavefunctions:10 bp:3 although:3 substitution:3 properties:4 simpler:1 recur:1 extending:1 dependence:1 o:5 αx2:4 important:1 extensions:1 lipparini:1 introduced:2 consequently:1 mathematical:1 almeida:2 presence:2 into:2 bound:8 due:1 bruxelles:1 hermitian:5 en:9 references:1 inverting:1 determine:2 operator:10 proportional:2 substitutions:1 mere:1 deal:1 few:1 there:4 specifically:1 start:4 quadratic:25 handbook:1 saavedra:1 lot:1 cartesian:1 therefore:2 function:4 banerjee:1 form:5 phenomena:1 differences:1 but:1 repeated:1 construction:1 ioffe:1 line:4 raising:3 he:1 reset:1 made:2 applying:1 ut:1 up:4 us:12 ul:6 below:1 un:1 limit:13 uk:1 problem:4 define:1 similar:5 agree:1 mechanics:3 required:1 constant:20 defined:3 ko:5 abstract:1 combining:1 geyer:1 general:5 ap:5 single:6 exist:1 together:1 corresponding:8 simplest:2 sasaki:1 constructed:2 again:1 functions:4 ematique:1 nn:6 2dr:1 mostafazadeh:2 whereas:1 wavefunction:2 when:1 vanishes:1 field:1 other:2 sponding:1 pi:1 ap0:1 conclusion:2 triomphe:1 elements:2 completes:1 provided:2 models:1 setting:1 problems:2 polynomials:5 odake:1 a1:2 n0:11 generated:2 a2:2 allowing:2 variable:6 gap:1 sides:1 jones:1 algebraic:2 implies:1 physics:1 factors:2 pseudo:1 4p:2 having:1 4n:2 equivalently:1 mass:27 parafermionic:1 time:2 far:1 n1:4 nuclei:1 dover:1 rep:1
0705.0863.txt |@word limited:1 consider:4 pointing:1 desirable:1 results:1 four:1 roy:1 spiridonov:1 constants:1 lebedev:1 research:1 paris:1 concerned:2 bx2:1 contained:1 quasi:16 those:5 th:2 under:2 differing:1 presentation:1 applied:1 zhang:2 very:1 p0:4 wave:11 redefinition:1 exact:22 annihilated:1 basics:1 presented:2 turns:2 nucl:1 list:3 solution:5 large:2 solved:4 science:2 eigenvalues:5 anal:1 noted:1 a126:1 zl:2 zn:2 force:1 ten:2 zk:53 sukhatme:1 sin2:6 ornstein:1 cosh:3 fold:1 zero:5 masson:1 concludes:1 fonction:1 even:1 what:2 nonlinear:1 plays:1 appear:1 section:6 expressed:2 poles:4 above:1 new:4 staff:1 method:7 coefficient:5 degree:1 respectively:2 component:1 here:7 china:2 ansatz:20 aid:1 consideration:2 equations:50 appears:1 z2:3 obtained:2 institute:2 larger:1 periodic:1 resulting:1 usually:1 hospitality:1 taipei:1 useful:5 classification:4 vii:3 2wn:4 tools:1 planck:7 derivatives:1 use:1 additive:1 proceed:1 would:3 positive:2 eφ:1 negative:3 sports:1 depicted:1 doubt:1 call:1 therefore:2 associated:5 type:13 bethe:21 more:3 becomes:1 operators:1 factor:2 odinger:23 2w0:1 berlin:2 normalized:1 known:3 cases:4 iii:3 nodes:2 must:2 springer:2 defines:2 recall:1 equation:42 work:1 oscillator:3 reads:1 kamran:2 values:4 concepts:1 following:2 cab:2 arrive:1 example:4 give:5 process:2 relativistic:1 respective:1 states:7 junker:1 numbers:1 council:1 sense:2 verlag:2 normalize:1 information:2 needs:3 rather:1 discussion:1 far:1 instead:2 ryu:1 sin:4 classify:2 sato:2 fp:52 simplicity:1 de:1 mat:1 algebra:8 dx2:3 residues:1 applications:1 inst:1 choice:2 types:3 dw0:2 so:11 fundamental:1 ho1:1 words:1 closely:1 developed:1 choose:4 paper:3 through:1 statistical:1 mentioned:2 japan:3 facilitates:1 still:2 its:3 roots:8 before:2 clh:2 render:1 termed:1 ln:10 solving:2 2zk:1 systems:22 lp:1 derivative:2 andrianov:1 main:1 defining:2 h0:6 supersymmetry:2 normalizable:3 non:4 good:2 finance:1 combination:1 hφ0:1 often:1 mention:1 they:3 half:1 now:9 discuss:2 possess:1 represents:1 term:2 2w:2 dirac:1 alez:1 university:4 hamiltonian:8 2x:4 factorizable:2 mode:2 2b:3 each:3 found:4 2n:1 square:2 financial:1 ed:1 energy:1 related:8 owing:1 combining:1 quantum:9 our:2 eq:1 out:3 shown:1 space:2 restricted:1 furthermore:1 since:4 denotes:1 acting:1 rational:1 denoted:1 math:9 theory:2 8a:1 quite:1 completely:1 base:1 khare:1 members:1 finite:1 definition:1 ministry:1 takasaki:1 hence:5 first:8 origin:2 there:3 probability:2 opez:1 number:7 approximate:4 clear:1 directly:1 4bn:1 illustrate:2 given:4 rewritten:1 similarly:1 introduction:1 system:8 construct:3 their:3 intermediate:1 zeros:1 listed:13 calculations:4 bagrov:1 scheme:2 gives:3 shifted:2 2ac:1 a34:1 aoyama:2 exactly:16 part:4 x2:8 than:1 coefficients:2 diffusion:2 wide:1 kind:2 unfortunately:1 namely:1 determined:2 were:2 treated:2 lowest:3 generality:1 rewrite:1 fluctuation:1 ann:2 spectrum:2 say:1 manner:1 seen:2 any:3 indeed:1 lie:7 zlk:1 depending:1 lin:1 lp0:1 note:2 sciences:1 potential:17 take:1 finding:1 shall:9 collaboration:1 sl:19 plugging:1 riccati:3 most:2 said:2 tanaka:1 future:1 class:7 considered:2 chosen:2 later:1 exp:9 link:1 physics:5 fact:3 sector:2 particularly:1 rayleigh:1 supported:1 recipe:1 merit:1 relation:1 solutions:6 substituting:1 d2:6 find:2 ground:10 based:17 knowledge:1 parameters:6 inozemtsev:4 less:1 αc:1 should:2 only:15 generators:3 ambiguity:1 essence:2 integrable:1 hamiltonians:1 oct:2 hope:1 viewpoint:4 dependent:1 between:2 obtain:4 ones:2 dz:5 dx:11 during:1 areas:1 prime:1 ushveridze:3 arxiv:1 summary:2 view:2 satisfy:2 set:5 constructing:1 exists:1 national:3 j0:1 lett:4 culture:1 see:5 result:2 w0:19 discussions:3 recently:1 satisfies:3 concern:1 satisfying:1 eigenfunctions:7 αx:5 review:2 definite:1 eigenstates:2 state:12 classes:5 various:2 simplest:1 invariant:1 approach:5 meromorphic:1 terms:5 olver:2 extend:1 wn:17 however:1 2αx:1 comm:3 2αc:1 russ:1 problem:2 thank:3 both:2 cos:2 cot:3 la:1 according:6 etc:2 connection:2 dated:1 bristol:1 whole:1 comes:1 among:1 adjusted:1 cn:8 point:4 simple:4 ca:2 harmonic:1 2nd:1 dimensional:4 simply:2 applicability:2 kzk:1 polynomial:2 respect:1 rep:2 considering:1 second:5 basis:2 three:4 been:4 z1:2 int:1 yao:2 interest:1 basic:1 pn:4 define:5 corresponding:17 sufficient:1 argument:1 external:1 demand:1 fokker:7 present:3 case:8 multi:1 pacs:1 expanded:1 value:5 will:2 contemp:3 while:2 proves:1 suppose:3 viii:1 situation:1 procedure:2 ix:1 vi:2 thus:3 them:1 vn:19 iv:4 ii:3 ik:1 cond:1 kikuchi:1 vanish:1 technology:1 different:2 grant:3 belong:1 problems:1 admit:2 same:6 sasaki:1 pauli:1 several:1 φn:29 higher:2 independent:6 used:1 effect:1 iop:1 v0:2 b553:1 purpose:1 potentials:6 infinite:1 normalization:2 mech:1 schr:23 center:1 programs:1 nevertheless:2 hφ:1 choon:1 well:3 obviously:1 without:2 solve:1 zk2:1 sets:4 model:4 chemistry:1 dimension:1 left:1 unified:3 just:2 λt:1 being:1 generally:2 trigonometric:3 solvability:16 reviewed:1 shape:1 identify:2 using:3 taiwan:3 λn:28 previous:1 letting:1 density:3 guaranteed:1 interested:2 transformed:1 treatment:1 easy:1 theorem:1 republic:2 extensive:1 solvable:21 eigenstate:3 real:6 yukawa:2 eigenfunction:7 depends:1 eigenvalue:11 read:1 possible:4 admitting:1 corresponds:5 know:1 samsonov:1 integer:1 mod:2 loss:1 necessary:2 like:4 particle:2 follows:4 serves:1 private:1 arbitrary:2 stationary:5 gauge:1 classified:2 methods:3 deal:2 some:6 stat:1 algebraically:2 understood:2 qes:53 gaudin:1 examples:4 table:5 extended:1 scale:2 cooper:1 onde:1 footing:1 2a:3 biology:1 scientific:1 bc:4 kyoto:3 equivalent:1 2c:3 expansion:7 visits:1 post:1 bx:1 hilbert:2 about:1 extension:1 algebraic:4 freedom:1 discussed:6 dependence:1 o:1 practical:1 range:1 uhlenbeck:1 consequently:1 book:1 previously:2 communication:1 into:4 nsc:2 integral:2 latter:1 accounts:1 determine:1 sov:1 operator:2 wada:1 prepotentials:1 schrodinger:1 log:1 removing:1 support:2 initial:1 b503:1 transform:1 plyushchay:1 accordingly:1 quadratic:1 way:3 astrophysics:1 function:16 transformable:1 form:4 but:9 properly:2 hn:30 ho:2 ioffe:1 4z:1 line:1 a36:1 evident:1 up:1 us:5 theoretical:3 below:2 shifman:3 fluctuations:1 distribution:4 similar:1 called:8 mechanics:6 required:1 constant:11 prepotential:16 defined:4 certain:1 general:1 single:3 diverse:1 supersymmetric:4 education:1 check:1 gonz:1 constructed:2 again:2 functions:4 no:7 zhong:2 when:4 rs:2 plugged:1 acknowledgments:1 nz:1 other:5 role:1 department:1 theor:1 node:4 a14:1 briefly:1 kinds:2 expressible:1 models:1 preceding:1 drift:12 polynomials:1 a2:1 a4:1 variable:1 risken:1 implies:3 assume:1 bzk:1 factors:1 turbiner:9 together:4 4n:1 equivalently:2 4j:2 time:3 appl:1 having:3 4a:1
0705.0864.txt |@word limited:1 partial:1 consider:1 represent:2 caused:1 separates:1 fabricated:4 cao1:1 york:1 consists:4 gaithersburg:1 amplified:1 disk:3 layers:1 increase:3 heller:1 etching:1 segments:2 illustrates:2 charge:1 monotonically:1 solomon:2 under:4 te:2 dramatically:1 sent:1 division:1 lack:2 advantage:3 outside:3 far:2 springer:1 wave:2 electron:1 crosses:1 figs:1 refractive:4 resonant:1 experimentally:4 difference:3 exact:1 deformations:3 northwestern:1 facilitate:1 presented:3 positions:4 12µm:2 ikeda:2 large:4 solved:1 small:2 shows:8 optics:1 10k:1 strongly:1 smaller:1 coordinate:2 insignificant:1 past:1 located:1 zero:1 value:1 pass:1 dynamics:1 carlo:1 leakage:2 spectral:1 index:4 nonlinear:1 rate:5 nef:2 section:3 brief:1 uniform:5 experiment:3 above:6 increasing:2 waveguide:1 consisting:3 outgoing:1 full:1 simultaneously:1 lee:1 whose:1 focused:1 address:1 along:12 quite:1 equations:2 change:1 obtained:7 almost:4 ref:1 mations:1 study:2 studied:1 reason:1 exiting:1 suggests:1 periodic:3 lightwave:1 microcavities:2 usually:4 formation:1 chang:1 narrow:4 changes:1 plotted:2 via:1 spatially:2 investigate:1 extra:1 namely:1 while:2 highly:1 total:1 select:1 gaas:21 use:1 remains:1 lasing:84 contains:1 rightmost:1 optimize:1 few:2 camera:1 until:2 taken:1 themselves:1 selects:2 theoretical:2 minor:6 more:2 door:1 populations:2 started:1 neglected:1 stable:1 emission:11 berlin:1 controlling:3 normalized:1 particular:2 antennas:1 actual:2 iii:1 must:1 md:1 account:1 recombination:6 locked:1 indicates:2 deformed:2 gabriel:1 facilitating:1 cao:3 narimanov:2 trans:1 spontaneous:2 example:2 stimulating:1 control:2 figure:8 attribute:1 organized:1 sample:1 pushed:1 minimum:1 cryostat:1 point:1 scar:10 occur:1 axis:7 rays:3 varied:2 carriers:4 discussion:2 six:3 chemical:1 how:1 varies:2 elliptical:2 opt:1 instead:1 circular:3 profile:4 may:5 minimized:2 uniaxial:1 epitaxy:1 cylinder:2 waves:4 spectrometer:1 horizontal:2 revealed:1 parallel:1 types:5 realized:2 short:1 liquid:1 light:9 spectra:2 correspond:1 nonradiative:1 so:4 wavelengths:1 electromagnetic:1 over:2 mainly:3 years:1 paper:2 through:2 looks:1 lasers:5 husimi:3 cold:1 ieee:2 its:11 hackenbroich:1 delay:1 directional:2 inas:4 exhibits:3 fig:23 deformation:16 non:2 propose:1 band:1 fang1:1 billiard:2 they:3 half:4 miyasaka:1 escaping:1 realize:1 dielectric:3 matched:1 represents:2 500nm:1 indeed:1 braun:1 fully:3 university:2 level:1 2d:1 into:1 stopped:1 mode:54 each:4 found:2 side:1 em:2 domain:1 quadrupole:1 aida:1 reduce:1 frequency:5 measurement:3 quantum:5 laboratory:1 approximated:1 summary:1 extract:1 special:1 out:1 shown:7 factors:2 quality:15 furthermore:1 since:2 interference:6 chaos:3 semiconductor:6 method:4 suggesting:1 formula:1 squares:2 forth:1 predicted:1 trajectories:1 perfectly:1 pumping:7 possibility:1 orbits:8 completely:2 jacquod:1 advantages:1 imaging:1 ase:13 rises:1 finite:2 determining:1 could:2 scars:1 filter:7 length:3 produce:1 wiersig:1 davis:2 stone:3 onto:1 first:24 major:6 initial:1 probability:1 reveals:1 reflected:1 reaches:1 7nm:1 utilized:1 unexpected:1 spots:6 another:3 array:1 electronic:3 angular:1 size:2 given:1 temperature:1 quadrupolar:2 introduction:1 leading:2 top:5 system:4 their:6 appl:2 too:1 monotonously:1 realization:1 dwell:1 molecular:1 ranging:1 calculations:1 pump:1 wavelength:4 relative:1 continuous:1 took:1 transverse:1 optical:9 injected:2 constituent:3 believe:1 than:3 modes:36 wide:1 1nm:2 polarized:1 ben:1 effective:2 surrounding:1 to2:1 sections:1 measured:1 depends:2 final:1 nevertheless:1 states:1 contrary:2 amplitude:4 were:3 toward:1 traveling:1 exhibit:1 lowest:1 photolithography:1 spectrum:19 curves:4 curved:3 confirms:1 slab:1 any:1 ray:8 angle:1 100nm:1 able:2 polarization:1 extracted:5 high:16 internal:1 absorbed:1 interior:3 detector:1 fukushima:4 circles:4 experienced:1 relatively:3 electric:3 sunada:1 systems:1 falls:1 insets:2 most:2 optimized:1 experiences:1 significant:1 position:1 device:1 extremely:1 gallery:1 yamilov:1 especially:2 surprising:1 clear:1 cover:1 part:2 typically:2 lying:1 phenomenon:1 intensity:15 mrsec:1 supported:2 halting:1 bright:5 threshold:22 data:1 agrees:2 ratio:7 state:1 incident:1 only:2 convoluted:1 factor:8 circle:1 partially:1 local:1 thresholds:2 achieve:1 do:2 get:1 beams:1 expectation:2 beam:2 bandwidth:2 nearly:7 despite:3 dr:1 substrate:2 qw:4 fields:1 arxiv:1 gutzwiller:1 tuned:3 microscope:1 common:2 contain:1 fixed:2 nist:2 view:2 scanning:1 set:1 nitrogen:1 observed:4 see:1 individual:1 radius:2 result:10 sea:1 discussions:1 close:2 sem:4 optimum:4 guided:1 fang:3 scattering:2 away:6 segment:1 dmr:1 boundaries:1 microdisk:5 various:4 between:3 boundary:22 across:2 wg:3 reflection:2 vertical:1 nature:1 initially:1 weak:1 however:4 efficiency:2 reproduces:2 harayama:4 phasespace:1 both:4 nishimura:1 region:1 acknowledge:1 according:1 attributed:1 lase:1 refraction:1 microcavity:13 experimental:7 detailed:2 characterization:2 wall:1 ca:1 corresponds:3 dimensional:1 decreases:2 maximize:1 whispering:1 moreover:1 tuning:5 leads:3 aligning:1 due:1 been:1 mark:2 reduction:2 describes:1 detrimental:1 stadium:61 expected:2 monotonic:1 spoiling:3 dots:1 direction:1 corresponding:7 coherence:1 photon:1 podolskiy:1 confinement:2 understand:1 external:1 former:1 those:1 case:1 multi:1 traced:1 laser:16 unlike:1 solid:9 straight:3 profiles:1 air:1 near:16 behavior:1 error:1 situation:1 leaves:1 polymer:1 layer:6 find:1 coupled:1 chaotic:14 thus:7 surface:8 iv:1 ii:1 middle:1 rim:1 il:1 seen:1 around:1 grown:1 confirmed:2 open:2 grant:2 lett:6 same:8 poincar:1 simultaneous:1 virtually:1 several:4 higher:2 perimeter:1 used:1 peaks:1 numerical:3 effect:5 effectively:1 upos:11 kim:1 fabrication:2 propagat:1 lower:2 fourier:1 center:2 minimize:4 well:2 analysis:2 without:3 simulated:3 very:1 ccd:2 left:2 lauret:1 schwefel:1 just:1 less:1 proximity:1 shape:10 atomic:1 followed:1 speed:1 eigenstates:1 projection:3 note:1 rapid:1 density:1 conclude:1 evanston:1 passive:6 developments:1 wet:1 eigenstate:1 gave:1 identical:4 increased:2 results:9 comparing:1 objective:1 increases:4 using:1 loss:2 shaped:3 follows:1 serves:1 manifest:1 shapes:2 unstable:2 always:3 output:7 reduced:2 cooled:2 twelve:2 because:4 classical:5 resonances:3 fresnel:1 some:4 back:1 global:1 calculated:11 escape:4 images:4 peter:1 gradually:1 dense:1 cavity:18 demonstrates:1 recorded:1 extensively:1 overlap:1 does:2 connecting:1 prof:1 propagating:3 demonstrated:1 2a:2 digitized:1 slight:1 jumps:1 wavefunctions:1 constructive:1 although:2 properties:1 comparison:1 about:1 central:1 cavities:2 tracing:4 200nm:1 o:1 simulation:4 distinct:1 range:2 carrier:1 concentrations:1 ti:1 slightly:2 soc:1 rev:8 real:4 maxwell:1 image:14 within:4 integral:1 nsf:1 three:2 phase:5 right:2 determine:1 ellipse:1 area:8 assumed:1 there:3 question:1 transform:1 long:3 occupy:2 much:1 low:7 was:10 opens:1 therefore:1 function:3 medium:1 enough:2 but:2 volume:2 collected:1 gain:25 line:2 highest:1 observation:1 pull:1 cylinders:1 embedded:1 stanford:2 whether:1 inside:3 maximum:8 different:9 below:1 critical:1 sapphire:1 pumped:1 continuously:1 demonstrate:1 distribution:9 similar:2 called:1 bandpass:6 distance:1 mechanics:3 fdtd:3 constant:2 defined:1 certain:2 abstract:1 contribute:1 am:1 single:1 exist:3 our:6 lifetime:3 work:3 distributions:1 four:3 dotted:2 no:4 dashed:7 tailoring:1 when:9 field:16 other:1 electrical:1 details:1 spatial:6 department:1 conclusion:2 optically:1 repeat:1 time:2 rex:1 variation:1 lens:2 technol:1 peak:4 vaccaro:1 astronomy:1 structure:1 algaas:3 implies:1 longer:1 photonics:1 physics:3 space:7 curve:11 orbit:3 together:1 inset:9 broad:3 resolution:2
0705.0865.txt |@word consider:2 crucial:1 iib:3 focus:1 four:8 scalar:12 squarks:12 computation:3 consists:2 gn:1 contributions:4 issues:1 compact:1 whose:4 certainly:1 terms:4 calculate:1 aug:1 attracted:1 tr:9 finally:1 mediated:5 fayet:10 th:9 under:3 ingredient:1 witten:1 g4:3 amplitudes:1 string:14 g1:1 very:3 induce:2 results:1 wtree:1 mf:10 summarized:1 mixing:1 difference:1 condition:1 common:1 leads:1 trn:1 turns:2 tokyo:4 t3:3 fewer:1 large:5 vector:5 gut:9 small:1 reliable:3 degeneracy:1 prevent:1 smaller:2 orientifold:1 renormalized:1 consistent:2 lightest:1 prediction:1 sign:2 fold:3 imply:1 perspective:1 follow:1 further:1 dynamics:1 tev:5 even:5 what:2 stands:1 section:13 near:1 d3:19 reheating:1 above:4 fractional:8 suppose:1 contrast:1 coefficient:1 full:1 ibid:1 respectively:2 trivedi:1 here:5 ranges:1 following:1 2m:6 cos2:1 groups:4 directions:1 depend:1 along:5 strong:6 table:3 z2:1 obtained:1 morrison:1 sectors:1 institute:1 involved:1 study:2 larger:1 approaches:2 superpotential:3 resulting:1 antoniadis:1 makes:1 9m:1 leptons:1 extra:2 vb:1 messengers:6 visible:6 addressed:1 gluon:1 apply:1 meson:3 use:3 charge:1 cosmological:2 would:6 positive:2 negative:13 almost:1 mediate:1 m6:1 m1:8 therefore:3 m3:7 m2:14 ψa:1 type:4 theoretical:1 diagrams:5 more:8 introducing:1 becomes:4 operators:1 stable:1 due:1 stabilization:1 warp:1 appendix:10 normalized:1 particular:2 high:2 mg:1 tachyonic:8 integrating:1 deformed:7 science:1 equation:2 mi:1 modified:1 theories:1 remain:2 mq:1 mp:2 carefully:1 those:9 ggut:2 example:2 figure:7 calculation:2 anomalous:1 arise:2 organized:1 purposes:1 involve:2 14d:1 minimum:6 something:1 want:2 allowed:1 verlinde:1 tions:1 g2:2 erratum:1 straightforward:1 hinders:1 caption:1 rather:2 discussion:1 breaking:46 gcm:3 located:2 hot:1 pure:1 ordinary:2 parameter:14 sin:2 tension:1 product:2 rept:1 description:3 algebra:1 replacing:1 after:4 produce:1 fi:3 summarize:1 constants:1 aα:4 realized:2 malyshev:1 natural:1 dynamical:7 effective:6 higgs:1 light:3 klebanov:3 lines:3 su:40 bunkyo:1 dilaton:3 cannot:3 negligible:2 fundamental:1 representation:1 order:24 typical:1 representa:1 over:1 dine:1 mαα:2 gauged:1 thermal:1 paper:2 through:2 izawa:1 japan:3 kinetic:1 still:1 its:5 group:13 how:3 chosen:4 interesting:2 masses:27 nontrivial:1 conjugation:1 li:1 window:2 parts:1 choose:1 nakayama:2 hidden:26 main:1 defining:1 deformation:1 supersymmetry:2 split:2 non:11 gaugino:23 integral:1 introduce:1 number:1 break:4 effects:1 they:3 singularity:11 discuss:1 possess:1 term:40 hereafter:1 ouyang:1 university:2 presented:2 identified:4 senger:1 2d:1 realistic:2 good:1 2g:1 radial:2 found:3 referred:1 financial:1 directly:1 ek:1 instability:1 energy:10 idea:1 related:1 constitute:1 society:1 martin:2 extended:1 quantum:1 our:7 happen:1 ev:5 eq:1 special:2 out:4 shown:1 matrix:2 factors:2 furthermore:2 since:6 squared:22 vcm:1 denotes:2 particles:5 may:9 contained:2 sfermions:3 messenger:32 denoted:1 rattazzi:1 m2f:3 issue:1 shows:3 theory:32 barrier:1 interactions:4 mechanisms:2 mψ:1 free:4 standard:13 reason:1 complicated:2 hohenegger:1 estimate:2 shortest:1 pairs:1 interaction:1 hamed:2 chiral:8 language:1 geometry:4 could:1 m21:2 m22:3 m23:2 ahler:6 massive:1 hence:3 promotion:1 generalizations:1 first:3 origin:1 major:1 there:7 vacua:1 symmetry:29 blown:2 requirement:1 rank:1 approximate:1 warped:3 nonperturbative:1 another:1 representations:3 carry:1 impossible:1 thick:1 fluxes:1 open:3 size:1 given:5 perturbation:1 temperature:1 their:1 introduction:2 leading:8 eqs:1 system:2 construct:2 needed:1 assumption:2 seiberg:3 too:1 calculations:1 convention:1 wrapped:3 recent:1 gives:1 holomorphic:1 m0:2 phenomenology:2 ratio:1 explanation:1 exactly:3 electroweak:1 part:4 than:8 coefficients:1 iliopoulos:10 expanding:1 wide:1 unfortunately:1 giudice:2 tree:1 zero:2 probe:4 matter:8 supposed:1 toward:1 steep:1 perturbative:7 symmetries:5 explicit:1 cohen:1 argument:2 generalization:1 direct:1 already:1 need:1 seen:3 confirms:1 any:4 contents:2 relatively:1 strength:2 angle:1 depending:1 ation:1 responsible:2 mills:3 gravity:4 note:4 potential:15 absorbed:1 generalized:3 kaplan:1 so:7 brane:8 unless:1 trace:1 most:1 regular:1 propagate:2 pair:1 acknowledgements:1 class:1 magnitude:1 takes:1 clear:1 mediation:23 coincides:1 yang:3 principle:1 ku:2 zaffaroni:1 physics:3 review:1 fact:1 sector:36 text:1 sfermion:3 taki:1 gauge:61 calculable:2 ibe:1 threshold:7 d7:9 d4:6 d5:1 d2:2 find:4 based:1 proposed:1 parameters:7 baryonic:1 should:4 freedoms:1 only:5 gb2:4 factor:3 local:6 thresholds:1 axion:2 do:2 dominant:1 gev:4 viewpoint:1 distance:1 familiar:1 simplest:2 expectation:7 ssm:5 ones:2 lighter:1 invariant:1 report:1 meguro:1 represented:1 2li2:1 fields:18 arxiv:21 fixes:1 yield:1 predicted:1 ut:2 fixed:5 minasian:1 valid:1 generations:1 view:1 satisfy:1 moduli:11 notice:2 grana:1 calabi:4 namely:1 discussions:2 close:1 ways:1 positivity:1 supergravity:3 enough:1 various:1 between:1 probably:1 sorts:1 keff:2 αn:1 preserve:1 comparable:1 embeddings:3 nature:1 however:4 vanishing:9 butti:1 article:2 suppressed:1 motivations:1 both:4 cos:3 freely:2 density:1 assure:1 embedding:1 contribution:4 expression:1 comes:1 otherwise:2 arbitrarily:1 aa:3 mes:1 cm:4 point:2 color:1 superfield:2 dimensional:1 superstring:1 m12:2 bα:4 cancel:1 associated:1 branes:18 ensures:1 described:2 second:1 yau:4 come:1 locally:1 induces:1 three:6 been:1 quickly:1 much:4 interest:1 ph:12 anomaly:1 komaba:2 lett:3 generating:1 controlled:1 relaxing:1 scalars:1 suppress:1 formed:1 photon:2 essentially:1 new:2 spectrum:2 2g12:1 former:1 present:2 case:5 solid:1 straight:1 originate:1 value:12 will:1 while:4 replaced:1 evaluating:1 situation:1 conformal:4 couplings:2 loop:10 resolved:6 notation:1 coupled:11 phenomenological:4 decoupling:1 thus:6 poppitz:1 itself:1 dual:2 susy:56 vanish:1 fermion:1 containing:1 constrained:1 develop:1 generic:1 make:1 dimopoulos:1 same:4 unity:3 complex:1 virtually:2 4g12:1 largest:2 ξb2:2 finite:2 couple:1 higher:2 independent:1 used:1 see:9 luty:1 hand:3 parametrized:1 running:1 invariance:1 stack:1 cycle:10 wijnholt:1 scenario:13 charges:1 well:2 roughly:1 analysis:4 concrete:1 without:2 hgm:1 unification:3 model:34 charged:1 manifold:2 just:7 less:2 αgut:6 obtain:5 thanks:1 sufficiently:2 hongo:1 multiplet:4 flavor:3 λn:1 leptogenesis:1 blow:1 4m2:2 conclusions:1 scales:1 seems:1 except:1 exclusively:1 realize:2 simple:1 add:1 internal:2 attractive:1 heavier:2 remaining:1 nucl:5 take:2 real:2 around:5 depends:2 multiplets:12 breaks:6 possible:5 corresponds:4 dark:2 possibly:1 five:3 know:2 vacuum:9 immediately:1 emergence:1 intersection:1 m11:3 theor:1 necessary:3 like:6 particle:3 follows:1 reduces:1 yields:1 either:2 arbitrary:1 completely:1 become:5 weiner:1 soft:12 essential:1 therein:1 parity:2 because:13 often:1 successfully:1 some:5 petrini:1 examples:1 choosing:1 respect:1 multiple:1 scale:28 lead:1 bottom:1 electromagnetic:1 avoid:3 quarks:1 fox:1 superfields:2 contributing:2 does:6 connecting:1 assuming:2 prog:1 masato:1 majorana:1 blowing:1 ba:3 power:1 equivalent:1 lose:1 expansion:1 broken:6 although:1 rsymmetry:1 super:4 asymptotic:3 about:2 gravitino:10 world:1 constraint:3 discussed:6 meaning:1 o:5 reduced:1 compatible:1 dilogarithm:1 range:1 a2:2 introduced:2 rev:2 slepton:1 inclusion:3 into:1 numerically:2 copies:1 down:4 references:2 wα:8 operator:4 proportional:1 75m:1 technically:1 hep:21 log:8 m4:1 jhep:6 assumed:3 support:1 λ3n:4 m7:1 long:2 u2:1 strassler:1 supergraphs:2 low:4 way:2 sleptons:12 dymarsky:1 opposed:1 function:1 relic:1 form:4 qcd:1 but:8 volume:2 neutral:1 construction:1 line:1 level:1 longer:1 made:1 embedded:1 whether:3 compactification:7 up:4 us:3 placed:1 below:5 limit:2 problem:4 similar:2 called:1 b1:3 strongly:10 later:1 constant:3 b2:2 flat:5 defined:3 abstract:1 contribute:1 direction:6 covers:1 evidence:1 single:1 yanagida:2 supersymmetric:1 regime:2 chance:1 again:1 conifold:19 no:5 dressed:1 when:6 vanishes:2 field:8 other:9 details:3 gauginos:3 department:1 massless:3 naive:2 conclusion:1 li2:2 models:11 problems:1 a1:3 generated:2 important:4 ξb:5 arkani:2 condensation:10 coupling:9 practically:1 assume:5 typically:1 space:2 pseudo:1 together:1 original:1 4m:1 mass:42 nelson:3 far:2 romanino:1 resolution:2 strings:3 restored:2 once:2
0705.0866.txt |@word homomorphism:2 consider:4 pointing:1 magnetic:1 global:1 results:6 gy:3 four:1 scalar:6 commute:12 grateful:1 gn:3 expressions:1 gk:2 gj:3 gi:6 devoted:1 whose:5 inverse:1 remarkable:1 assigning:1 reversely:1 containing:1 presents:1 finally:3 according:2 manifolds:1 th:2 under:6 include:2 sorkin:3 case:8 g2:1 orthogonal:3 very:2 rise:3 translations:2 nipne:1 electron:2 difference:2 matrices:3 bρ:3 leads:1 specify:2 e44:1 hamiltonian:5 irreducible:1 nucl:2 large:1 discrete:3 vector:11 progress:1 science:1 manifestly:1 eigenvalues:2 superalgebras:5 strongly:1 mn:4 carter:2 b137:1 second:1 involution:1 horv:1 dyon:1 odd:2 gm:3 theory:22 even:6 gibbons:4 appear:2 giving:4 diag:2 section:5 expressed:1 current:1 version:1 subspaces:1 selecting:1 kleinert:1 new:8 ground:1 bn:2 exercise:1 satisfy:6 relationships:1 ibid:1 d1:3 respectively:1 here:9 understanding:1 reported:1 b2m:6 represented:1 ak2:3 xα:1 equations:1 spec1:1 box:1 antisymmetric:1 horvathy:3 remarks:1 institute:1 involved:4 study:1 vectors:4 allows:1 step:3 yˆ:8 products:1 akn:2 action:1 hoker:1 suitable:2 anticommutators:1 relation:1 jˆi:2 useful:2 projection:5 extra:2 compare:1 replace:1 brought:1 ask:1 b342:1 b226:1 b274:1 total:3 p42:3 select:1 use:2 projector:1 would:1 commun:1 covariant:2 positive:2 contains:1 next:2 anticommutation:3 linear:3 explicitly:1 therefore:3 associated:4 type:14 theoretical:1 ψd:2 more:4 flat:1 becomes:2 operators:90 hereby:1 odinger:2 berlin:1 carrying:1 observing:1 particular:1 known:2 ασi:1 producing:1 g2n:5 fermionic:7 taub:12 obeying:2 springer:1 valued:1 mm:1 local:1 equation:4 fµν:3 theories:1 remain:1 values:3 three:6 following:6 example:4 ceex:1 b183:1 f2:1 indicated:1 relativistic:5 ak:2 arise:1 organized:1 sense:5 rescaling:1 occur:1 visinescu:10 verlag:1 end:1 notation:1 fortunately:1 verify:1 s0:6 off:2 write:3 dependent:1 fourth:2 εijk:3 those:2 parameter:1 fourdimensional:1 b188:2 b502:1 algebra:33 may:5 dx4:1 mapping:1 collection:1 embed:1 produce:2 multiplication:1 representations:4 types:1 realized:2 natural:1 dynamical:10 sectors:2 prefers:1 spectra:1 explicit:1 correspond:1 su:5 element:1 ψe:1 si:2 kacmoody:1 so:12 fundamental:1 representation:13 a2ρ:1 playing:1 typical:2 forced:2 help:3 produces:1 indeed:1 pointed:2 dy:4 uvt:1 interpreted:1 produced:1 mentioned:3 existence:1 satisfies:2 its:3 qkn:3 constituted:1 group:3 how:1 interesting:7 relativity:1 lj:1 encapsulated:2 coordinates:2 writing:2 forms:3 offers:2 slodowy:2 differently:1 mail:2 hidden:6 main:3 defining:1 supersymmetry:2 non:11 runge:7 obtaining:1 introduce:2 mention:1 they:6 instead:1 rotation:1 now:5 e2n:3 association:1 above:2 represents:2 term:3 finite:5 dirac:41 spacetimes:1 explains:1 university:1 presented:1 backgrounds:1 appropriate:1 possibilities:1 l2:1 2b:1 each:3 2l:1 2m:1 limit:2 2i:1 2j:1 em:1 spinor:5 domain:2 en:3 ei:1 directly:2 ej:1 energy:6 between:4 related:9 constitute:1 frames:1 2hk:2 static:4 obtains:3 proportional:1 quantum:13 our:14 avoided:1 eq:4 special:4 out:3 respects:2 shown:1 perry:3 space:28 furthermore:1 since:12 rev:8 research:1 content:2 replacing:2 acting:1 ajm:1 reader:1 denoted:3 fronsdal:1 ro:3 ref:4 math:7 commutation:8 mρ:3 ackel:1 diagonal:6 governing:1 standard:5 reason:2 bρ2:1 put:2 van:2 generate:1 e2:1 partner:1 chiral:1 fµ1:2 geometry:6 qm:1 could:3 1v:1 ds2:1 times:1 ahler:2 int:2 gordon:6 δij:3 hence:1 first:4 xk:1 romania:2 xi:3 features:1 symmetry:6 possessing:2 number:2 system:2 clear:1 spinning:1 2δij:4 relations:12 another:2 peters:1 open:9 angular:5 herdeiro:1 given:9 cartesian:5 their:3 introduction:1 opportunity:1 eqs:11 behaves:1 twisted:13 construct:3 holten:2 indicate:1 fermions:1 calculations:1 superscript:1 dt2:1 structures:2 national:1 gps:5 johnson:3 completed:1 continuous:2 part:10 x2:2 x3:3 x0:1 x1:2 than:1 x4:2 covariantly:3 last:4 showed:1 was:3 see:1 jonge:1 determined:1 were:1 gives:3 magurele:1 symmetries:6 rewrite:1 ann:1 spectrum:5 generalization:1 say:3 kepler:11 manner:4 curved:2 subjects:1 st:1 any:13 elsewhere:1 symmetrized:1 lie:4 genuine:1 mappings:1 zero:1 depending:1 self:1 note:5 ideal:1 potential:1 take:2 gkn:2 objective:1 coincide:1 raifeartaigh:1 kac:2 play:2 added:1 chart:1 anticommute:1 algebraic:8 involving:1 work:1 automorphism:1 reducible:3 why:1 xµ:1 kk:2 kj:4 ki:15 gk2:1 kn:2 km:5 countable:2 mechanical:1 yano:3 physics:5 eigenspinors:1 fact:1 sector:5 hyper:2 particularly:1 phenomenon:1 show:6 supported:1 notations:2 bring:1 spaces:1 gauge:9 subtle:1 superalgebra:44 trivial:4 find:3 d0:13 principal:1 aρ:3 q2:3 based:1 commutators:1 should:2 only:6 anticommutes:2 generators:10 geodesics:1 rich:2 factor:2 kaluza:1 over:1 achieve:1 do:2 closed:1 klein:7 get:1 df:1 express:1 ones:4 words:1 cota:1 gen:1 covering:1 qy:2 fields:4 arxiv:1 grav:3 acknowledgments:1 qb:2 qi:12 qk:3 qj:3 aem:8 qn:7 ignored:1 set:4 exists:3 nut:12 eˆ4:1 nambu:1 b201:1 namely:3 projections:1 w0:6 discussions:1 close:2 jni:6 tensor:8 nuclear:1 review:1 µv:1 µr:4 symmetric:1 written:2 correctly:1 simplest:1 mihai:1 approach:2 notice:2 triplet:2 terms:3 iεijk:37 attention:1 focus:1 however:5 killing:5 jm:3 vanishing:1 eˆk:2 ji:13 key:1 jk:3 separately:1 qim:1 tensors:8 σk:4 both:2 σi:19 piece:1 improved:1 cot:9 σl:7 many:3 taking:2 eˆj:2 dl2:2 σy:1 context:1 casimir:17 σr:3 σp:3 whole:1 ck:1 among:3 jj:1 point:1 simple:4 b2n:8 corresponds:1 lk:2 dimensional:20 concluding:1 exploit:1 anti:1 conjugation:1 moreover:7 li:8 bρi:3 transformations:3 basis:3 addition:6 west:1 charts:2 ai:9 interest:1 pj:2 pk:1 ph:1 pi:3 abstract:1 define:9 obtained:2 generating:2 rather:1 corresponding:7 commutes:2 formed:1 subspace:1 fortschr:1 coherent:1 observe:4 external:2 cosmology:1 c2:5 c1:5 denote:1 spin:7 present:2 eαˆ:1 paying:1 macfarlane:1 splits:1 p4:24 pacs:1 circumstances:2 engineering:1 hdy:2 will:2 euclidean:13 while:5 ain:6 freely:1 property:2 loop:15 program:1 iq:1 metric:2 thus:10 systems:1 iv:2 vp:1 ih:1 reads:3 itself:1 dual:1 seen:4 fn:3 ave:1 mod:5 ib:2 id:1 orbital:2 different:5 recover:1 d11:1 grant:1 eigenvalue:1 connection:1 same:6 b317:1 parts:1 quant:1 arguments:1 pauli:15 units:1 resulting:2 constructed:7 subalgebra:4 iγ:3 isometries:4 independent:2 supercharge:1 used:1 ruback:2 qjm:1 trivially:1 hand:1 ion:1 purpose:1 supposing:1 infinite:15 totally:1 identity:5 g2m:3 schr:2 modes:2 kni:6 nevertheless:1 barut:2 de:1 without:1 commutations:2 components:7 sets:1 coordinate:3 model:1 arising:1 possesses:1 usual:7 isometry:2 manifold:4 graded:1 just:5 being:1 half:1 obtain:4 vanishes:1 feher:4 grades:2 transforms:1 previous:1 vπ:1 adding:1 generator:3 αx:2 regarded:1 seems:1 iψ:1 bni:4 interested:1 combine:1 lett:12 cex:1 interprets:1 heidelberg:1 momentum:6 generalized:1 real:3 rescaled:1 manton:1 depends:1 rµ:3 showing:2 background:1 using:2 chakrabarti:1 moody:2 like:3 obvious:1 reduces:1 e00:1 manifest:1 specific:3 remind:1 gjm:4 either:3 follows:1 completely:1 become:1 athy:1 valence:4 terminology:1 bucharest:1 because:3 classical:1 some:3 deduce:1 choosing:1 respect:1 eˆij:1 mclenaghan:2 2xi:1 gross:3 lippmann:3 affects:1 cρ:5 kµ1:1 does:5 particles:1 closely:1 leader:1 demonstrated:1 b359:1 obey:2 rescale:1 bm:2 equivalent:1 arbitrary:1 quaternion:1 fµ:1 qˆ:1 properties:5 simpler:1 hypercomplex:2 cncsis:1 central:2 carried:2 o:10 aˆi:1 carrier:2 consequently:2 subset:1 presence:1 jn:4 eˆα:1 rotations:5 due:1 down:1 pair:1 hermitian:1 references:1 artifice:1 operator:57 algebras:9 bosonic:7 mere:1 spinors:3 ixi:1 hep:2 governed:1 taubnut:2 there:9 transform:1 nova:1 class:3 start:4 way:6 infinitedimensional:1 gin:2 dx:4 naturally:1 complete:1 form:12 but:3 transformed:1 hk:2 construction:2 trum:1 line:1 themselves:1 e4i:1 evident:1 versions:1 us:5 nonconserved:1 considered:2 f2n:3 complications:1 sum:2 demonstrate:2 problem:11 monopole:4 similar:5 called:4 mechanics:1 qin:7 constant:3 b2:3 qˆ2:2 defined:9 universal:1 aj:1 direction:1 general:3 supersymmetries:2 conserved:25 arises:1 pˆ:1 soara:2 laszlo:1 commuting:4 physical:8 functions:1 compared:1 vaman:2 ingredients:1 fixing:1 when:2 supercharges:4 intend:1 field:5 other:8 role:3 department:1 weights:2 enlarged:1 massless:1 conclusion:1 briefly:1 thaller:1 star:1 generates:2 models:1 problems:3 generated:8 a2:1 allowing:1 lenz:7 structure:4 building:1 coulomb:1 assume:1 vinet:1 factors:1 pseudo:1 rule:1 appendix:3 mass:1 presenting:2 time:9 observables:1 timi:2 starting:1 having:2
0705.0867.txt |@word neighbors:1 chebyshev:3 logarithms:1 consider:5 chain:1 results:9 proposition:32 µ2s:1 follow:1 expressions:1 denotes:1 devoted:1 whose:16 depend:1 wish:3 graph:28 deterministic:1 tr:19 charles:1 focs:1 ruci:1 tj:8 th:1 under:2 hermann:1 stochastic:1 analogous:4 undirected:3 applied:2 supported:2 choice:3 corollary:4 wishes:1 every:9 additional:2 summarized:1 mixing:10 exact:2 condition:2 statistica:1 school:1 induced:1 ρg:2 immediately:2 irreducible:1 specifies:1 vertex:25 fewer:1 t1:11 large:7 convenience:1 disc:1 avoiding:1 small:1 eigenvalues:4 markov:2 specified:2 noted:1 20th:1 upper:1 smaller:4 tel:5 zi:7 miller:1 estimates:4 nski:1 approximation:3 rate:19 cost:1 royle:1 further:5 estimated:1 zr:3 theory:2 spectral:3 index:1 what:1 appear:2 giving:3 3r:1 section:9 µlt:1 uniform:3 experiment:3 above:21 sup:1 replaced:3 increasing:1 method:2 contrast:1 satisfy:2 multivariate:10 sharper:1 probabilit:1 degree:5 aij:2 component:1 here:1 ranges:1 concluding:2 path:5 along:4 sieve:16 appears:3 remark:5 study:2 studied:2 allows:1 contradiction:1 expander:15 survey:2 poisson:17 makes:10 examining:1 eµt:1 via:1 useful:2 stray:1 claim:6 amplified:1 first:2 limn:2 apply:1 counts:1 establish:2 estimate:7 use:3 additive:1 takes:1 would:5 prove:10 sake:2 e1:5 visit:1 negative:1 definition:6 next:3 few:1 call:1 therefore:12 25th:1 theoretical:1 more:5 israel:3 ir:32 said:1 started:1 becomes:1 naive:2 adjacency:1 particular:5 known:8 maze:1 cases:2 hold:1 must:2 reingold:1 states:2 springer:2 balls:9 room:1 frobenius:1 ed:2 science:3 equation:1 work:2 mi:11 mj:26 erd:1 mt:7 values:5 ms:2 mr:6 following:22 sets:1 root:1 example:3 proof:31 define:3 tau:2 del:1 weaker:1 stated:3 process:1 organized:1 high:14 assumptions:1 numbers:1 want:1 sense:1 counting:3 occur:3 absolute:3 lamb:1 information:2 ti:33 requirements:3 goal:2 provide:3 verify:1 holds:14 nontrivial:2 ent:12 answer:3 instead:2 parameter:1 undesirable:1 simplicity:2 efficient:3 description:1 may:12 max:4 after:5 eighty:1 collection:5 applications:4 produce:1 distances:7 faculty:2 end:2 fixed:22 sz:1 short:2 natural:3 imply:3 eµj:2 whenever:1 os:3 correspond:1 element:2 sk:1 complexity:1 sons:1 algorithms:3 allow:1 definitions:1 subsequently:1 bipartite:3 bins:8 typical:7 words:1 essence:2 amplifying:1 conserving:1 multicommodity:1 paper:4 london:1 mentioned:4 its:8 before:1 traverse:1 tending:2 exclusion:1 chosen:2 2rs:6 fix:1 inclusion:1 exhibits:1 aviv:5 estimating:1 window:3 version:10 benjamini:2 expanders:5 τt:1 main:1 maximal:12 eyal:1 non:41 motivated:1 budapest:1 isomorphic:1 mention:2 they:4 optimal:1 schools:1 now:2 wiley:3 possess:1 eigenvalue:3 term:12 equality:1 2s:11 always:2 university:4 annals:1 events:6 inequality:4 l2:2 each:2 found:1 2h:1 side:3 referred:1 directly:1 formulate:1 t2:2 logloglogn:11 society:3 logd:6 extended:2 ex:2 combining:6 our:1 event:3 out:1 shown:3 matrix:2 space:3 open:2 furthermore:5 since:6 crucial:1 research:2 looking:3 fellowship:1 contained:3 ajk:1 imperative:1 istituto:1 lecture:1 get:5 xu:25 induction:3 ri:6 math:2 shows:2 foundation:2 earlier:1 linear:1 asz:2 argument:4 surveys:1 like:1 indices:4 base:2 surely:5 york:2 superiore:1 puv:11 inductive:1 e3:7 e2:5 thrown:1 cycles:2 derivation:1 connectivity:2 geometry:1 starts:1 could:1 transition:2 times:16 length:27 exponentially:1 hence:3 discussions:1 exhibited:1 xj:1 major:1 xi:45 sinclair:1 probability:26 feige:1 variables:14 number:40 reaches:1 randomized:2 long:3 another:1 xr:7 precisely:8 miss:1 xt:4 size:1 1p:3 given:6 necessarily:2 exists:1 similarly:1 introduction:2 xij:18 sackler:2 least:13 their:3 assumption:8 rates:2 statement:1 siam:1 cycle:2 bits:11 gives:5 completed:1 proving:3 part:1 simulate:2 authors:4 x2:5 x0:2 x1:9 than:14 specify:1 distance:15 kind:1 john:1 bonferroni:5 showed:2 require:4 classi:1 tree:2 second:6 limiting:4 bolyai:2 classes:2 pairwise:7 doubly:1 were:1 visited:8 tion:1 enables:1 solely:1 exhibit:2 mini:1 motivation:1 rewrite:1 xji:2 spectrum:1 generalization:1 summing:1 meyer:1 pvi:9 manner:1 need:8 final:2 st:1 any:9 paths:1 janson:1 subgraph:1 depending:1 thoroughly:1 ideas:4 converges:2 note:2 sciences:2 z1:3 maxi:4 generalized:2 so:2 lipton:1 tool:1 even:3 play:1 definitions:1 transitive:1 et0:2 krivelevich:1 most:6 regular:16 connected:4 position:2 remarks:2 sufficient:3 probabilistic:1 inequalities:5 characterizes:1 clear:1 later:3 stronger:2 vertices:43 order:2 ks:2 graphs:22 principle:1 exp:11 typically:6 notion:3 fact:13 quantity:3 precise:3 nω:1 paul:1 selection:1 wormald:1 show:8 text:1 random:79 converge:3 notations:1 forbidding:1 xl:1 relation:1 preece:1 suffices:3 threshold:3 substituting:1 analogue:1 longer:2 trivial:2 backtracking:31 µm:1 indicator:4 ratio:2 parameters:1 series:1 negligible:2 universal:3 should:1 tuples:4 only:1 aperiodic:1 indeed:6 lubetzky:3 over:7 probabilities:1 do:1 notation:3 means:1 µj:11 overall:1 firenze:1 cannot:1 closely:1 altogether:2 determines:2 stoc:2 ramanujan:1 regarding:1 approach:3 arxiv:1 yield:1 noga:1 twice:3 investigate:1 multiplicity:1 perron:1 fixed:11 remains:3 requirement:5 set:19 computed:1 fascinating:1 backtrack:2 throwing:3 testing:1 ends:1 up:7 plausible:1 edition:1 see:7 computer:2 result:13 w1:3 w0:14 primality:1 alternative:2 closer:2 instance:2 israeli:1 exploited:2 exponent:1 µt:10 µs:3 µr:3 symmetric:1 state:1 µn:2 µi:10 closed:2 between:6 consecutive:3 conditions:2 email:2 αn:1 godsil:1 effect:3 notice:2 terms:3 extend:1 wn:1 wm:2 wk:2 however:2 wi:6 wj:2 spare:1 analyzed:1 infinity:2 both:3 essentially:1 improved:5 many:3 alon:4 equal:2 anos:1 calcolo:1 sudakov:1 embedding:1 interesting:1 mean:1 expression:1 asked:2 otherwise:1 load:3 point:2 simple:12 had:1 asymptotically:6 cf:1 walk:54 sequences:1 εeµ:2 proved:4 throughout:1 pr:41 better:4 pp:8 pv:5 basis:1 addition:2 lt:1 quickly:2 ai:4 much:1 slowly:2 treat:1 interest:1 expected:1 utilizing:1 improve:1 sufficiently:6 define:3 direction:2 enable:1 general:3 concerning:1 mikl:1 scienze:1 new:2 gap:3 last:3 careful:1 onyi:1 those:1 case:15 chains:1 subsets:4 examine:2 value:6 will:7 while:1 suppose:3 bounds:2 behavior:2 error:5 di:2 delle:2 elaborate:1 girth:35 bin:1 larger:4 satisfying:5 played:1 almost:5 vi:9 vj:18 walks:19 thus:2 according:3 ii:9 disjoint:6 vr:7 ij:54 il:2 turns:1 concentration:1 containing:1 nnt:1 grant:1 barnes:1 problems:3 same:3 clearly:2 member:1 largest:1 avoids:1 resulting:1 several:1 grows:1 smallest:1 independent:6 calculation:1 used:2 raymond:2 i1:34 upon:1 hand:5 v1:12 moment:3 recall:3 sodin:1 rabin:1 lower:2 center:1 acknowledgement:1 studies:1 min:1 well:13 roughly:1 without:1 components:1 lim:3 organization:1 model:1 spencer:1 arbitrarily:2 less:5 being:2 adjustments:1 2c:2 obtain:7 rest:1 distant:2 λd:4 facts:2 regardless:1 λi:1 briefly:1 univariate:1 λn:2 letting:5 integer:2 mix:2 characterization:1 seems:3 k1:2 other:7 easy:1 theorem:36 take:1 real:1 minerva:1 depends:1 showing:2 sums:1 possible:3 possibly:1 background:1 press:1 using:10 bit:1 unique:2 apart:1 necessary:3 replacing:3 excluding:1 alternatively:1 tend:1 ignore:2 continue:1 steps:5 sparse:1 follows:10 beverly:2 feller:1 stationary:3 mathematical:4 luczak:1 exceed:2 right:3 often:1 classical:2 sequence:1 some:31 deduce:5 moreover:1 teoria:1 provided:1 vol:4 leaf:1 xv:6 µti:2 thank:1 models:1 t0:9 provides:1 tends:8 proc:2 minimal:1 selecting:1 dictates:1 expansion:2 step:2 polynomials:1 positions:2 properties:5 karp:1 simpler:1 integers:2 usa:1 extension:1 algebraic:1 completing:3 dependence:1 o:113 distinct:2 range:1 seeds:1 extensions:2 neighbor:1 iff:2 2k:2 slightly:1 raised:1 cambridge:2 presence:1 h2:1 bound:5 three:1 lies:2 references:1 determine:2 factor:1 bsf:1 statistics:1 log:122 combinatorics:3 there:4 question:3 approximate:2 fast:2 sampling:2 brun:16 conservation:2 lov:2 fraction:1 crucially:1 var:3 m1:6 was:6 ρk:2 opposed:1 function:2 complete:2 form:6 governs:1 denoting:2 but:2 volume:1 construction:1 related:5 amplification:1 convergence:11 true:1 partially:1 made:5 applying:1 versions:1 whether:2 minkowski:1 uv:1 maximum:5 po:5 below:2 supk:1 sum:2 distribution:27 defining:1 similar:1 recalling:4 strongly:1 nnn:1 ac:2 constant:2 computing:1 defined:1 flow:1 abstract:1 describe:1 denote:32 single:5 formulation:1 families:2 kl:1 distributions:1 compared:2 no:6 when:6 defined:4 graduate:1 application:3 setting:4 role:2 itai:1 mathematics:3 nt:38 elements:3 completes:1 extra:1 time:1 uniformly:11 visits:39 includes:2 replace:1 important:1 bounded:2 variable:1 traversal:1 nn1:1 nn0:1 independently:3 implies:8 faster:2 algorithm:2 assume:1 requires:1 required:4 pseudo:2 satisfies:3 resembles:1 n1:1 n2:4 starting:8 assump:1 once:2
0705.0868.txt |@word breadth:8 monte:2 allowed:1 consider:4 pointing:1 represent:1 series:2 lack:2 rod:7 results:10 menon:1 fluids:8 unmixed:1 disc:1 entropy:8 ramaswamy:1 parameterization:1 consists:2 follow:2 expressions:2 denotes:2 rectangles:34 inhomogenous:1 demixed:3 certainly:2 dimensionality:2 depend:3 remarkable:1 comunidad:1 graph:1 concerned:2 disorder:4 should:3 interactions:3 granular:1 quasi:2 does:3 aut:3 excluded:8 stable:9 segregates:1 te:2 presentation:1 applied:1 amplitudes:3 straightforward:1 orthogonal:2 very:9 desirable:1 reader:2 keeping:2 induce:1 geometrical:4 stat:1 crosses:2 orientations:1 stays:1 mixing:6 experimentally:1 variance:1 exact:4 states:2 inset:3 induced:1 exponential:1 level:1 ref:10 tokyo:1 proposals:1 solution:5 correct:2 large:7 frozen:2 settle:1 small:6 provided:1 c02:1 shows:2 der:3 configurations:1 possibility:1 upper:10 approximately:4 force:1 disordered:1 trend:1 consistent:1 disclination:1 direct:4 ph:1 filled:7 approximation:12 located:4 second:19 fractionation:5 evaluated:3 segregate:1 scarce:1 rigorous:1 qualitatively:1 dynamics:1 implemented:1 carlo:2 remarkably:1 even:4 aim:2 what:2 plays:1 appear:3 giving:1 contributions:2 sum:1 selected:1 remain:1 xτ:2 uniform:3 current:1 aperiodic:1 above:5 new:4 construction:2 increasing:2 method:1 contrast:3 thin:1 body:1 carnahan:1 lee:1 ibid:1 mechanisms:1 gathered:1 never:3 component:24 here:11 behaviour:12 reported:2 packing:9 focused:1 governing:1 address:5 directions:1 ratio:29 along:2 standard:3 observing:1 appears:5 change:1 calculate:1 obtained:6 instituto:1 balance:2 numerator:1 rigorously:1 involved:1 study:4 studied:2 allows:1 approaches:2 leaving:1 spheres:1 amount:1 resulting:3 torquato:1 published:1 conveniently:1 fourier:4 studies:4 involves:4 emerge:1 via:5 spatially:4 although:1 discontinuous:1 inducing:1 sistemas:1 treatment:1 raphson:1 scaled:11 monolayers:4 translational:1 total:2 unit:3 predicted:2 presents:1 use:3 additive:3 figure:1 would:7 sake:1 term:2 finally:7 next:1 error:1 calculation:3 depicted:1 therefore:5 save:1 taken:3 survive:2 themselves:2 care:1 type:7 ciencia:2 diagrams:7 more:10 fractions:5 xν:3 jpn:2 rich:1 schematic:1 h1:8 becomes:7 ti:2 mismatch:2 about:2 spinodal:13 appendix:7 labelled:4 orientationally:2 known:2 cases:9 iv:1 iii:4 tnt:1 account:2 include:2 onsager:5 a11:1 indicates:7 recall:1 equation:4 work:10 theories:2 debated:1 values:12 minimisation:3 island:6 following:5 making:1 arrive:1 example:2 beautiful:1 persists:1 φid:2 indicated:8 predict:2 expanding:1 rotational:1 sense:1 spt:13 near:1 high:7 sphere:2 way:1 uam:2 performed:2 arise:1 sharp:1 rods:8 heras:2 enrique:2 calculated:7 absolute:1 preempted:1 end:10 s3:2 biaxial:1 discussion:1 breaking:2 feature:1 occur:5 regions:6 far:2 varies:1 pure:4 instead:1 hi:2 axis:4 parameter:1 sin:1 polit:1 nematic:40 rise:1 blocks:1 mat:1 entropically:2 thermodynamic:3 after:3 derived:1 containing:3 polydisperse:1 diagram:22 applications:1 independent:1 plane:11 tackle:1 horizontal:1 cuesta:5 parallel:8 lifting:1 las:2 changes:2 short:1 attempt:1 liquid:1 resemble:1 computations:1 lines:7 correspond:1 parameterized:1 scenarios:1 complexity:1 ϕn:1 so:4 expression:3 fundamental:1 correlation:1 species:14 ingredients:1 lν:1 order:56 figs:2 reproduced:1 saturated:1 closely:1 minimising:1 indeed:1 over:3 kimura:1 mainly:1 soc:1 stability:6 cotter:2 thermal:1 experiments:3 including:2 looks:1 mentioned:2 existence:1 arrangement:1 its:3 tendency:1 before:1 perfect:3 superior:1 difference:4 group:1 evans:1 la:3 chosen:5 interesting:5 solving:2 reentrant:2 exhibits:4 actually:1 destroyed:1 absence:1 degrees:4 systems:7 entropies:2 decreased:1 freely:5 might:4 dubois:1 s1:1 eventually:1 non:8 good:1 motivated:1 fourth:2 practice:1 fig:24 introduce:1 number:2 framework:1 course:1 effects:6 they:2 stabilise:2 now:5 kumar:1 considerably:2 escuela:1 easily:2 february:1 several:1 always:3 presented:6 2x:1 requires:1 sufficiently:6 ussr:1 l2:5 2b:1 l1:7 found:10 talbot:1 circular:1 side:2 carlos:1 mean:4 orientational:23 bifurcation:11 vanishingly:1 challenged:1 scheme:1 energy:8 hard:84 inhomogeneous:2 investigated:1 interplay:1 changed:1 loops:1 our:11 approximated:1 transitions:11 orient:1 special:3 out:5 shown:11 jackson:3 schiller:1 driving:1 restricted:1 rep:1 since:17 induces:2 unknown:1 explicitely:1 research:3 particles:33 may:17 daniel:1 baus:1 8x:1 demixing:57 squares:28 issue:3 occurs:10 math:1 common:2 baron:1 exactly:2 straley:1 theory:14 associate:1 perfectly:1 positional:1 ısica:2 departamento:3 quite:1 completely:4 yuri:2 8r:2 onoma:3 beginning:1 generate:1 log:3 resumed:1 director:1 competes:1 interaction:2 bates:1 geometry:8 could:2 transition:24 diminished:1 consequences:1 metastable:1 ordering:3 length:6 produce:1 place:1 isotropic:23 incorporated:1 universidad:4 forms:1 crystallisation:1 diminishes:1 facilitate:1 exhibited:1 first:21 origin:3 initial:2 features:3 symmetry:10 conform:1 possessing:3 reflected:1 explored:1 tricritical:26 will:8 done:1 defects:1 thick:1 avenida:1 electronic:3 angular:1 occurrence:1 given:4 necessarily:1 tangent:1 exists:1 table:2 indicate:3 introduction:2 leading:2 fmt:3 diameter:2 system:2 least:4 compatibility:1 their:12 intermediate:1 chem:20 types:4 calculations:8 eqn:4 ordered:5 molecular:1 final:1 gives:4 free:7 fraction:7 mostly:1 introducing:1 continuous:3 required:2 part:1 too:1 parameterisation:5 probably:2 x1:6 than:4 coefficients:5 begins:1 observed:1 variational:2 esp:1 counteract:1 double:1 approximations:1 summary:3 richer:1 packed:2 strategies:1 2kφ:2 future:2 contrary:1 were:7 garland:1 toward:2 treated:1 exhibit:7 function:5 parameterised:2 symmetries:2 survives:2 ram:1 coulon:1 unbinding:1 curves:1 already:2 rat:9 adding:1 variable:2 recovers:1 further:5 close:3 seen:4 concentration:2 element:1 occupied:1 any:2 viewed:1 relatively:3 affairs:1 strength:1 angle:2 depending:1 efficient:1 essentially:1 latter:5 aside:1 mechanism:4 defines:3 oriented:4 mix:1 ideal:2 s21:1 take:3 hs:2 forming:1 performance:1 coincide:1 subject:1 circles:4 play:1 experienced:1 polym:2 though:2 wojciechowski:1 5z:1 needle:1 disallowing:1 most:3 involving:4 connected:1 preliminary:1 phase:120 grossly:1 analytically:1 es:4 abe:1 observation:1 surprising:1 hk:3 considered:6 σi:1 average:1 sometimes:2 stronger:3 complejos:1 physica:1 mech:1 wacker:2 uni:1 points:22 rev:24 principle:1 kt:34 effect:4 left:2 section:1 fact:8 quantity:1 incorporate:1 particularly:2 show:4 v12:1 supported:3 binodal:3 brief:2 rotating:5 x2:8 minimizing:1 propagates:1 subtle:1 thickness:1 trivial:1 find:5 substituting:1 impact:1 henceforth:1 believe:1 based:7 parameters:9 chester:1 implementation:2 much:5 explain:1 written:2 topological:1 thermodynamically:1 increasingly:1 only:11 version:1 candidates:2 lebowitz:1 molecules:2 circle:9 ministerio:1 local:1 rectangle:6 equilibrium:3 do:7 mixture:45 closed:2 means:5 dependent:2 de:16 overall:1 fluid:25 inclusion:1 cannot:2 ϕi:7 negative:1 lighter:1 despite:1 locations:1 respectively:5 procedures:1 routine:1 secondary:1 gray:8 exhibiting:1 consisting:1 introduced:2 seemed:1 approach:6 areas:7 arxiv:1 dijkstra:4 disco:2 rotationally:1 investigate:2 discs:8 cf:1 ecnica:1 analytical:1 scott:1 fixed:2 dissimilar:2 coefficient:2 set:2 questions:1 reference:1 hν:8 generally:3 unpublished:1 correlations:3 a9:1 lett:8 maximum:2 relative:1 depends:3 computer:6 result:6 enhanced:1 terms:11 meet:1 analog:1 ability:2 phases:40 still:2 ways:1 mol:3 educaci:1 incorporating:1 label:1 symmetric:1 pressures:5 state:3 un:1 various:3 roots:5 correctly:2 between:26 si:1 limit:6 previous:4 conditions:1 materiales:1 rowlinson:1 pv1:14 pv2:4 recently:4 cabrera:1 extend:1 nature:5 importance:3 comp:1 focus:1 however:9 jr:1 efficiency:1 extent:1 immiscibility:2 virial:5 configuration:1 distribution:4 assess:1 originates:1 concentrated:1 both:13 cos:13 cubes:3 last:1 contemplate:1 roij:3 many:1 region:21 uncertainty:1 according:1 against:1 sensitive:1 layered:1 present:8 dated:1 context:2 rigby:1 operating:1 contribution:2 whole:2 hτ:1 otherwise:1 arbitrarily:2 detailed:3 point:36 aticas:1 excess:1 coexistence:4 parametrization:1 dimensional:29 concluding:1 taylor:1 simply:2 decreases:1 xi:1 lagrange:1 wider:1 respect:12 crystalline:4 16r:2 considering:1 destabilised:2 strong:3 described:2 geometries:2 addition:2 equations:1 interdisciplinar:1 due:6 been:24 shortening:2 mart:9 cosine:2 combined:1 interest:4 galindo:3 anisotropic:2 nicol:1 topology:1 hardly:1 partial:1 choose:1 direction:3 arises:1 corresponding:8 derivatives:1 restrictions:1 ınez:9 concerning:1 gas:1 search:1 fis2005:1 matem:1 25z:1 a8:2 gisc:1 understand:2 dimensionalities:1 demand:1 suspected:1 evidence:7 former:3 spain:5 case:15 main:2 hdr:14 unlike:5 stillinger:1 solid:1 crossed:3 efficiently:1 definition:1 counterbalances:2 value:15 rectangular:3 intimately:1 sci:2 while:13 none:1 promising:1 orica:2 properly:2 property:1 hampering:1 loop:1 pack:1 shortened:1 thouless:2 larger:5 played:4 almost:1 refs:1 formulation:1 thus:1 them:1 surface:1 equal:10 ii:3 continues:1 vs:8 cond:1 contract:1 triple:2 affected:1 mod:1 seem:2 binary:2 different:22 open:4 prior:1 lengths:1 acknowledgments:1 cross:1 same:18 clearly:1 shorter:1 unity:1 parts:1 potentially:1 arguments:1 gibbs:1 mixtures:64 units:1 plates:1 finite:1 composition:21 higher:7 fairly:1 compositions:1 used:5 velasco:9 imply:1 see:13 numerical:1 unimodal:1 hand:1 driven:5 v1:8 v2:7 smectic:1 sooner:1 vibrated:2 caps:1 recent:5 lower:12 shaded:2 off:3 scenario:1 immaterial:1 disappears:3 no:11 well:2 reduced:2 analysis:13 obviously:3 s22:1 without:2 components:14 quantitative:1 model:4 possesses:2 bodies:4 usual:5 s2:1 teramoto:1 proposed:1 less:1 being:7 qν:3 lengthy:1 newton:1 obtain:3 assigned:1 shape:2 underlying:1 aspect:25 followed:1 alternative:1 frenkel:6 yet:2 alignment:1 divide:1 note:4 vτ:1 candidate:1 density:15 similarities:1 regarded:1 conclude:3 seems:1 except:3 uniaxial:21 lattice:6 priori:1 location:5 easy:1 continuation:1 constant:1 possess:2 euler:1 details:5 explained:1 increased:2 ample:1 situation:3 big:1 showing:2 possible:6 corresponds:2 possibly:1 increases:3 know:1 acronyms:1 destroy:1 confined:1 using:10 lekkerkerker:7 vν:3 projects:1 ruled:1 necessary:1 like:3 particle:39 sizes:1 alternatively:1 collective:2 shapes:1 either:7 corners:1 starling:1 odijk:1 hansen:2 soft:1 reduces:1 indications:2 representation:1 mulder:2 classical:1 a14:1 madrid:7 macromolecules:2 phenomena:5 somehow:1 competition:1 self:1 understood:1 trends:1 added:2 choosing:1 convex:4 proper:2 intend:1 treatments:1 sufficient:1 stabilised:2 consensus:1 entropic:2 scale:1 colloidal:1 dimensions:8 merge:1 checked:2 liq:1 size:9 legan:1 extensively:1 per:2 critical:29 tends:1 prog:1 narayan:1 leland:1 demonstrated:1 refer:2 inserting:1 core:3 particular:8 assembly:1 minimization:1 slight:3 elucidate:1 equivalent:4 landau:1 analysed:5 expansion:3 itou:1 paper:1 pressure:28 meets:1 ratios:6 instability:2 pv:1 article:1 analysing:1 adds:1 carried:3 extension:1 rederived:1 freedom:4 introduces:1 o:1 simulation:4 mutually:1 range:14 a2:1 spinodals:1 mixed:7 a5:1 cajal:1 referred:1 denote:1 considerations:1 equally:1 contains:1 tn:7 unfavourable:2 presence:1 h2:8 into:10 within:6 numerically:2 functional:13 three:15 down:1 remarks:2 square:5 assessed:1 burton:1 proportional:1 reducing:1 depicting:1 theoretically:1 constraint:1 terminated:1 perera:2 van:6 additional:4 featureless:1 area:20 koda:1 support:4 there:12 question:2 approximate:1 long:6 krauth:1 growing:1 quadratic:2 low:7 frustration:1 stabilises:2 was:7 lowest:1 semicircle:1 complete:3 form:3 hr:24 some:19 collapsed:1 differences:4 analyse:3 but:14 sophisticated:3 volume:13 expected:1 needles:1 segregation:13 line:6 promote:2 true:4 considerable:1 hd:2 topologically:1 absent:1 made:2 qualitative:1 whether:1 variations:2 up:5 us:4 theoretical:5 below:3 c03:1 those:3 minor:1 how:1 fluctuations:3 problem:3 similar:3 called:3 condensada:2 expect:1 strongly:2 separated:1 settled:1 later:3 associated:10 computing:1 defined:8 4r:1 abstract:1 measure:1 influence:1 expands:1 b73:1 general:4 single:2 donev:1 exist:1 together:1 a12:1 simulations:9 follows:2 proceeds:1 constructed:1 flory:1 again:1 functions:9 beyond:2 completeness:1 purdy:3 varga:3 variety:2 when:16 vanishes:2 field:4 other:10 role:7 ellipses:1 spatial:4 tech:1 nt:37 nu:31 materia:2 a15:1 explaining:1 briefly:1 met:2 kinds:1 a10:1 a13:1 separate:1 aggregates:1 asterisk:1 ultimately:1 a1:1 a3:1 important:3 bounded:3 a4:1 a7:3 a6:1 included:1 columnar:1 grupo:1 2i:1 structure:1 conclusive:1 building:1 implies:1 longer:3 dφ:3 uc3m:1 adsorbed:1 interval:1 curve:2 parsons:1 governed:1 equivalently:2 directors:3 kayser:1 compete:2 presenting:1 back:1 time:1 kosterlitz:2 starting:1 having:2
0705.0869.txt |@word katz:1 partial:4 rev:5 results:10 four:4 consists:2 disk:1 whose:2 calculate:1 rightmost:1 under:4 indicating:1 supported:1 amplitudes:4 frequencies:8 fabricated:2 refractive:3 resonant:1 experimentally:2 difference:1 deformations:2 northwestern:1 squares:1 polson:1 positions:1 ikeda:1 microlaser:2 optics:1 ten:2 direct:2 pulse:3 past:1 zero:1 cost:1 value:2 dynamics:1 leakage:1 spectral:1 index:3 what:1 rate:1 slight:1 near:2 thickness:1 rhodamine:2 experiment:2 cao:3 method:2 lee:1 spacing:8 focused:1 groups:13 along:6 chinn:1 change:2 great:1 study:1 larger:2 yoshino:1 periodic:2 lightwave:1 microcavities:4 usually:1 resonance:1 chang:1 changes:1 plotted:2 diameter:1 projection:2 maximizing:1 marked:2 highly:1 inorganic:1 schilling:1 select:1 gaas:3 plot:1 would:1 distinct:1 lasing:37 contains:1 therefore:1 themselves:1 type:3 reflects:1 stable:1 emission:2 normalized:1 given:3 iii:6 must:1 crosses:1 work:1 values:4 following:1 stimulating:1 weaker:1 figure:5 high:9 sense:1 scar:8 axis:1 provide:1 varies:2 adjacent:2 opt:2 instead:1 circular:1 may:3 spot:1 orbits:6 waves:6 spectrometer:1 horizontal:1 wave:4 compatibility:1 types:1 realized:1 light:2 spectra:3 correspond:3 order:1 over:1 fall:1 mainly:1 soc:1 lasers:1 husimi:2 its:1 group:15 directional:1 harmonics:1 decades:1 deformation:4 versus:2 them:1 good:1 fourth:1 they:3 half:2 miyasaka:1 developments:1 represents:1 500nm:1 fully:3 university:1 2d:2 mode:16 each:5 found:1 side:1 domain:1 significantly:1 energy:2 aida:1 frequency:22 measure:1 our:6 summary:1 ring:1 out:3 shown:2 factors:3 quality:14 since:2 interference:10 semiconductor:1 modulation:5 induced:1 ref:1 shows:5 numerical:5 pumping:4 advantages:1 finite:1 organic:1 determining:1 could:1 silicon:1 length:2 wiersig:1 davis:2 onto:1 there:2 gonokami:1 quadrupole:1 thick:1 open:1 size:1 differ:1 oscillation:1 their:7 top:1 approximately:2 indicate:1 ranging:1 mostly:1 optical:4 jordan:1 constituent:5 spacings:1 believe:1 than:3 oscillate:3 relative:1 ben:2 second:1 solomon:1 determined:1 intensities:1 amplitude:6 were:2 nishimura:1 traveling:1 exhibit:1 photolithography:1 spectrum:6 ray:2 angle:1 objective:1 10hz:1 circles:2 multiple:4 electric:1 normal:1 incidence:1 falls:1 letter:1 phase:3 kuwata:1 measured:2 patterned:1 deviations:1 surprising:1 calculated:4 dissolved:1 physics:2 fact:1 spaced:4 doped:1 frolov:1 threshold:1 uniform:1 find:2 ratio:1 parameters:1 outside:1 molecules:1 factor:8 circle:1 local:3 regularly:3 beam:1 ones:1 dye:2 reveal:4 substrate:2 arxiv:1 consisting:2 investigate:2 fixed:1 nist:1 reveals:1 set:2 exists:1 observed:6 intensity:2 sea:1 discussions:1 close:2 vardeny:2 fang:3 pump:5 various:3 between:2 boundary:3 across:1 terms:1 vertical:1 however:2 efficiency:1 incident:3 analyzed:1 harayama:3 both:2 many:1 acknowledge:1 attributed:2 sensitive:1 lase:1 microcavity:1 experimental:4 among:1 point:1 corresponds:1 height:1 maximize:1 fukushima:3 leads:1 three:3 been:3 mark:1 stadium:23 expected:1 yag:1 fig:14 observe:1 understand:2 repetition:1 spin:1 those:1 multi:3 laser:4 solid:1 straight:1 profiles:3 while:1 behavior:1 error:1 polymer:10 layer:1 studied:1 chaotic:8 simulations:4 thus:1 iv:5 ii:7 rim:1 il:1 different:5 grant:2 belong:2 same:6 another:2 several:1 higher:2 perimeter:1 peaks:3 trajectories:1 effect:4 upos:8 kim:1 fabrication:1 recent:1 lower:2 kept:1 modes:49 minimize:1 well:2 materials:1 coordinate:1 maxima:3 lauret:1 schwefel:1 hexadecapole:1 when:1 thz:2 identify:1 ozawa:1 had:1 except:1 evanston:1 lett:7 excited:1 identical:4 mrsec:1 depends:1 know:1 using:1 shaped:3 polymers:1 resin:1 manifest:1 shapes:2 unstable:1 output:1 because:1 classical:2 some:2 dense:1 cavity:3 connecting:1 unit:2 provides:1 prof:1 propagating:4 coated:1 2µm:1 constructive:1 although:2 served:1 plots:1 intense:1 stone:1 carried:1 o:1 simulation:1 range:1 ensure:1 gregory:1 equally:1 into:1 within:3 nsf:1 due:1 ellipse:1 theoretically:1 area:4 segment:1 twodimensional:1 spiral:1 long:1 appl:5 low:1 was:7 yamilov:1 medium:1 but:2 collected:1 gain:7 made:1 embedded:1 inside:1 maximum:1 dmr:1 pumped:1 distribution:3 similar:1 mechanics:1 fdtd:1 constant:4 defined:2 certain:4 abstract:1 am:1 evidence:2 fujii:1 single:1 1nm:1 film:1 compared:1 no:4 nd:1 slusher:1 field:1 other:1 details:1 spatial:5 department:1 photoresist:3 optically:1 uniformly:1 rex:1 variation:7 spectrally:1 lens:2 technol:1 peak:2 vaccaro:1 astronomy:1 typically:1 space:2 orbit:3 inset:2 confinement:2 time:1 silica:1 resolution:1
0705.0870.txt |@word measurements:2 sci:2 consider:2 illustrates:2 rev:15 magnetic:16 varying:1 focus:2 existing:1 ge:6 generalize:1 higher:1 research:1 increase:1 depend:2 calculate:1 producing:1 technique:1 waveplate:2 charge:2 those:1 th:3 under:2 hermann:1 analogous:1 include:1 cm2:1 fishman:1 supported:1 premium:1 advantage:1 very:1 conditions:1 results:3 electron:17 experimentally:3 difference:2 unlike:1 modulator:2 accompanying:2 transmission:3 applicable:1 large:3 solid:1 vector:1 small:5 enhance:1 darpa:1 configurations:3 possibility:1 oscillator:1 sin2:1 direct:2 pulse:6 rate:6 street:1 profiles:1 dynamics:4 chem:1 driel:1 even:2 ǫs:1 diam:1 adds:1 sub:1 richard:1 sum:1 near:2 shares:1 uniform:1 current:24 beard:1 above:3 spintronics:1 net:2 contributes:1 contrast:1 thin:1 coefficient:1 edited:1 degree:3 awschalom:1 respectively:1 component:2 here:3 agreement:1 reported:1 mev:3 focused:1 governing:1 relaxation:1 alone:2 based:1 along:3 observing:1 appears:2 gfactor:1 ot:1 institute:2 shift:24 study:6 larger:5 allows:1 through:2 suggests:1 within:1 fourier:2 makes:1 lowers:1 golden:1 via:2 spatially:1 modulates:1 clark:1 semiconductors:6 decrease:2 should:1 sge:1 linearly:2 wang:1 gaas:14 derivatives:1 use:4 exciting:1 takes:1 would:3 whittaker:1 finally:1 comparing:1 bender:1 attribute:1 survive:1 themselves:1 type:2 theoretical:2 today:1 more:5 separated:1 populations:1 ti:1 emission:5 transient:1 particular:1 known:2 hole:23 aligned:1 iii:1 must:1 me:2 states:4 mm:1 setup:2 work:5 mi:1 mh:1 mw:1 vs:1 values:1 temperatures:1 following:2 example:2 jagadish:1 sinusoidal:1 compare:2 challenging:1 semicond:1 give:3 process:1 lock:1 neglected:3 dependence:3 sample:8 indicates:2 minimum:1 hilton:2 arise:1 absolute:1 pinj:1 bigot:1 monitoring:1 goal:1 carriers:8 rather:2 describes:1 discussion:1 six:1 regions:1 far:3 varies:2 axis:3 sin:4 circular:3 profile:2 fs:4 klar:1 mat:1 information:1 may:2 after:1 spot:2 minimized:2 produce:1 lax:1 mag:1 verified:1 minimizes:1 wave:3 data:3 parallel:3 types:1 hannover:3 effective:4 kikkawa:1 light:8 photodiode:1 acknowledged:1 ubner:2 provide:2 so:9 fundamental:1 definitions:1 order:6 zuti:1 least:1 enhances:1 over:2 fraser:1 vary:1 choose:2 characteristic:1 experiments:2 including:1 kinetic:1 still:1 its:2 gµb:2 1a7:1 rapidly:3 symmetry:3 τh:3 decay:11 energies:1 temporal:2 appl:2 inas:1 detected:1 microscopic:1 systems:1 total:3 defining:2 split:2 ced:1 motivated:1 camus:1 polarizations:1 impossible:2 investigated:1 newman:1 band:16 effects:1 they:3 half:3 complement:1 rotation:1 yu:1 easily:1 term:2 several:1 university:2 accompanies:1 good:1 magnitude:1 wurtzite:1 mode:1 2b:3 each:2 found:3 soc:1 quarter:3 side:1 bond:1 heavy:2 oestreich:1 generation:2 ed:1 energy:2 idea:1 related:1 frequency:2 see:1 expect:1 measure:3 our:3 beyond:1 eq:3 out:1 canada:1 shown:2 dominates:2 literature:1 matrix:2 solved:1 since:6 washed:1 george:1 semiconductor:3 dominated:1 maximized:2 formula:1 induced:2 znte:2 red:1 shows:1 linear:3 state:3 little:1 free:2 difficulty:1 proportionality:1 element:1 estimate:3 rises:1 created:1 geometry:1 widths:1 could:2 times:4 turn:1 length:1 plane:1 onto:2 crossings:1 first:3 major:1 already:2 manuscript:1 magneton:1 number:1 bhat:1 long:1 directly:4 radiate:5 thick:4 angular:1 size:1 pryor:2 given:4 needed:2 top:1 amsterdam:1 approximately:1 their:5 1b:1 constants:1 calculations:2 gives:2 pump:5 contribute:2 sin3:2 flatte:1 optical:20 injected:21 off:2 than:9 coefficients:2 population:2 toronto:2 distance:1 nanostructures:1 polarized:12 showed:1 chadi:1 measured:3 second:1 determined:1 amplitude:1 were:3 uhle:1 providing:1 modulating:1 elsevier:1 turner:1 st:1 any:1 relatively:3 strength:6 angle:7 zero:1 eter:1 davies:1 polarization:20 sciences:1 high:1 materials:6 combining:1 online:2 transmit:1 green:1 strengths:3 blue:1 electric:4 populate:1 investigations:2 quote:1 incidence:3 most:1 germany:1 preliminary:1 device:1 intrinsic:1 picoseconds:1 calculated:1 stronger:1 points:1 electrons:9 left:1 typically:2 dragged:1 lying:1 selection:1 show:3 detection:1 probe:4 lda:1 focusing:1 lloyd:1 zakharchenya:1 fine:1 find:3 slow:1 ratio:6 just:1 conduction:3 written:1 short:2 only:1 black:1 factor:12 parabolic:1 employed:1 µeff:1 plate:1 wide:2 dependent:1 mainly:3 overall:2 expectation:1 beam:6 nearly:1 closely:1 despite:1 processes:1 increasing:1 m5s:1 fields:2 arxiv:1 common:1 though:1 prevents:1 pulses:2 view:1 sipe:4 requirement:1 achieved:2 lifetimes:3 sensitivity:1 tilde:1 operates:1 relative:4 nserc:1 intensity:5 radius:1 result:1 discussions:1 close:3 techniques:5 radiates:2 exploited:1 ways:1 pattern:2 µv:2 dipole:3 propagates:1 µm:5 enough:5 various:1 radiated:2 between:7 boundary:1 approach:2 across:1 µb:5 available:1 comparable:1 attention:1 recently:1 reflection:1 vertical:2 weak:1 interfaces:1 emitted:7 subject:1 however:8 incident:2 distinguish:2 come:1 laman:1 thank:1 both:8 cos:3 fit:2 many:4 taking:1 bristow:1 attributed:1 enabling:1 propagation:1 refraction:1 contribution:1 expression:2 experimental:8 timescale:2 point:1 simple:1 rad:1 sampling:2 ii:1 simply:1 faraday:1 pp:1 addition:1 curve:1 been:7 defined:1 much:5 interest:1 expected:6 pn:1 sarma:1 fig:9 direction:5 arises:1 controlled:1 excite:1 gap:3 bulk:6 systematic:1 θr:3 perel:1 spin:26 present:1 associated:1 hughes:1 laser:4 exponential:1 tang:2 appearance:1 ǫn:2 value:4 will:7 while:1 behavior:2 error:1 promoted:1 ultra:1 planar:1 orientation:17 almost:1 characteristics:2 von:1 thus:3 surface:7 subpicosecond:1 bias:1 cond:1 against:1 photoelastic:1 different:2 formalism:1 irradiate:1 pseudopotential:1 circularly:2 radiation:26 same:3 clearly:1 shorter:2 emphasize:1 pauli:1 evaluate:1 units:1 plates:1 electro:2 difficult:1 calculation:1 used:4 optic:2 schilfgaarde:1 effect:10 hand:2 average:3 moment:8 recent:2 relies:1 luminescence:1 delivers:1 center:1 largely:1 studies:1 roughly:2 analysis:2 bohr:2 patterns:1 edge:3 allow:1 coordinate:1 usual:2 spurred:1 magnetization:33 proposed:1 less:1 moments:3 photo:1 observed:1 thz:46 σnz:3 sources:15 underlying:1 voltage:1 spinorbit:1 useful:1 yet:1 note:1 overlapped:1 cm:1 density:10 absorption:3 photons:1 had:1 signals:1 source:13 interested:1 lett:5 easy:1 mod:1 plasma:1 excited:2 momentum:2 opt:1 depends:1 rules:1 bands:3 disagreement:1 possible:2 picosecond:2 using:5 unique:1 color:2 qwp:4 necessary:1 like:2 follows:3 signal:16 extremely:1 temporally:1 roth:4 mhz:1 epoxy:2 valence:1 spins:8 deviation:2 because:5 methods:1 oriented:1 fresnel:2 some:2 back:1 hartmann:1 mirror:1 photogalvanic:2 scale:1 trace:2 confirm:1 normal:3 recorded:1 injects:1 per:1 meier:1 pem:3 fabian:1 dipoles:2 provides:1 betz:1 volz:1 2a:2 measuring:2 linfield:1 2µn:1 processing:1 strained:1 perpendicular:1 terahertz:1 host:2 although:3 offset:1 refers:1 comparison:1 about:5 central:1 agele:1 origins:1 freedom:1 factors:4 simulation:1 range:2 carrier:5 weisbuch:1 johnston:2 mean:2 bloch:1 vi:1 photovoltaic:1 presence:1 maxwell:1 into:5 rectification:3 splitting:1 due:3 down:1 right:1 accounts:1 castro:1 determine:1 proportional:1 theoretically:1 baltz:1 ontario:2 van:3 additional:1 elastic:1 few:1 assumed:2 there:5 fast:3 hed:1 detectable:1 low:1 way:1 series:2 resulted:1 was:2 function:3 survives:1 pd:1 differences:1 but:4 displacement:1 collected:1 hemisphere:2 ethz:2 injection:12 made:1 evident:1 mtrl:1 inside:2 maximum:1 crystal:4 fermi:1 sapphire:1 define:2 similar:2 called:2 detailed:2 khz:1 ab:3 constant:2 hwp:2 certain:1 universal:1 measurement:3 am:1 general:1 chap:1 scanned:1 together:1 inj:8 wavelength:1 lifetime:2 moves:1 internal:1 regime:6 effected:1 nj:1 avoided:1 nm:2 no:2 dashed:1 when:4 cˆ:1 field:15 other:5 details:1 spatial:2 department:1 conclusion:1 optically:3 burnham:1 excitation:10 variation:4 includes:1 technol:1 peak:5 variable:1 structure:5 tailored:1 implies:1 longer:1 photonics:1 physics:2 required:2 holes:14 orbit:1 rule:1 depth:1 krishnamurthy:1 time:3 ultrafast:8 indirectly:1
0705.0871.txt |@word magnetic:3 fortiori:2 consists:1 localized:2 relationships:1 calculate:1 whatsoever:1 under:3 worth:1 rise:5 every:1 summarized:1 postpone:1 encounter:1 identity:2 solution:9 convenience:2 vector:3 gracey:11 indices:2 bornyakov:1 jhep:5 consistent:7 estimates:1 direct:1 elegant:1 second:3 qualitatively:1 implemented:1 even:3 established:3 δaaµ:1 above:1 new:5 here:9 q12:3 path:6 quark:3 contraction:1 obtained:1 suitably:1 study:6 changed:1 approaches:2 complicated:2 suitable:3 changes:1 orthonormality:1 gluons:7 explained:1 plenum:1 highly:1 visible:2 counts:2 total:1 propagators:5 derivatives:4 would:19 cohomological:3 negative:14 phenomenological:1 call:2 therefore:6 m2:98 survive:2 type:2 composite:4 naive:1 aware:1 ward:1 must:10 quartic:2 henri:1 work:9 mi:12 theories:26 ms:3 rij:1 example:5 renormalization:7 indicated:1 give:7 organized:1 want:3 david:1 guarantee:1 end:4 turn:3 provide:3 gbµν:2 hom:1 how:10 nontrivial:4 significance:1 answer:2 ordinary:5 massive:18 lai:2 transforming:1 after:7 confirmed:2 demanding:1 dµab:3 meaningful:1 constants:1 effective:11 summing:1 parisi:1 green:1 enter:1 order:27 restriction:1 interpretation:3 over:1 expects:1 derivates:1 before:4 pomeron:1 fix:2 renormalizable:10 hidden:1 maximal:3 eventually:2 them:2 affected:1 combination:2 effects:3 they:4 represents:2 by11:1 reasonable:1 each:2 mean:1 mdn:1 series:2 used:7 ghosts:4 goi:1 particles:10 adapt:1 reader:1 aja:4 independence:2 turning:2 linear:11 assured:1 given:16 free:30 standard:2 created:1 δil:2 πj:1 δij:3 δik:2 corrections:4 adjoint:1 already:19 restrict:1 clear:6 ℓi:3 nonperturbative:5 2a0:2 toy:2 top:3 a0:39 confirming:1 dwell:1 ranging:1 rouet:1 serve:1 morozov:1 somewhat:1 distance:2 iωq:1 showed:1 princeton:1 correlators:1 matter:2 minus:1 perturbative:9 seminal:1 fashion:3 entail:1 rewrite:4 spectrum:2 knecht:1 seen:3 seem:1 forced:3 convenient:2 amemiya:1 exactly:1 x0i:2 shall:27 simplify:2 nonlinear:3 calculated:1 inferred:1 yang:25 principle:2 sum:1 fitted:1 infrared:2 implying:1 gauge:85 solutions:4 d4:25 d2:4 d3:32 finally:1 proposed:1 explain:3 πsk:1 bρσ:2 constant:4 do:11 assignment:1 klein:1 dd:1 preferred:1 dx:4 despite:1 sarandy:5 dt:1 bar:2 fields:44 acknowledgments:1 mathematically:1 phenomenologically:3 δjk:2 testing:1 δjl:2 observed:1 result:3 discussions:1 dµ:1 alternative:3 best:1 techniques:1 said:4 tensor:1 supergravity:3 yet:1 unable:1 approach:8 terms:22 confusion:1 however:15 essentially:1 zakharov:3 0i:9 adapted:2 a2µ:15 appeared:1 applicability:1 polynomial:1 micheli:1 decoupling:1 cohom:2 radiative:1 been:8 quickly:1 much:1 expected:1 mcn:1 quantities:4 concerning:1 comprehensible:1 confinement:5 maximally:2 applied:2 originate:1 air:1 employ:1 euclidean:2 applies:2 property:2 aia:4 procedure:4 opt:1 iq:1 yangmills:1 ij:4 im:23 j0µ:2 id:1 containing:5 xfµν:6 perform:1 things:1 make:4 complex:2 phenomenology:1 several:3 hermiticity:1 independent:11 nia:2 counterparts:1 hand:2 fourier:17 whereby:1 ope:7 xjk:1 left:3 just:2 mills:25 assigned:1 identify:2 depart:1 eigenstates:1 previous:5 εm:2 candidate:1 nilpotent:17 character:1 easy:2 mcmullan:1 noether:2 iδ:3 possibly:1 lco:2 disadvantage:1 appearing:3 remind:1 steps:1 arbitrary:2 papavassiliou:1 beneficial:1 eiqx:10 kugo:1 bottom:3 dropping:1 quarks:2 gubarev:3 minimization:1 dropped:1 illustration:1 constructive:1 substitution:1 properties:1 plug:1 aguilar:2 anomalous:3 o:4 nonvanishing:1 ensure:1 efforts:1 mbn:1 presence:4 dyson:1 down:1 δui:3 hermitian:3 prefactors:1 iδij:5 iq0:3 influencing:1 way:9 threshhold:1 was:18 gij:1 lowest:2 underestimated:1 form:14 verschelde:13 encoded:1 prevents:1 maximum:1 inclusive:1 abstract:1 sq0:1 proven:5 evidence:1 conserved:1 proves:1 exist:6 simulations:2 commuting:2 check:2 constructed:2 ni:5 nm:1 no:5 whereas:1 when:20 vanishes:1 schwinger:1 schroeder:1 setting:2 role:3 papers:1 company:1 picture:2 describe:2 regime:2 longer:1 assume:4 together:2 time:11 n1:15 n2:14 n3:22 others:4 precise:3 concept:1 switched:1 skip:1 global:3 leads:7 devoted:1 certainly:1 inverse:1 depend:1 eigenbasis:1 technique:1 answered:1 charge:29 εijk:6 semenov:1 analogous:2 orthogonal:1 exact:7 annihilated:6 presented:2 did:3 leave:1 solved:1 shanskii:1 unaware:1 application:2 fµν:12 sign:6 wherefore:1 cost:1 dσab:6 stands:1 foregoing:1 current:2 annals:2 multipole:3 tachyons:1 along:2 appears:1 change:3 institute:1 vectors:1 decouple:2 studies:1 useful:2 extra:9 merely:1 prefer:1 modifying:1 ipq:1 gluon:24 schaden:1 working:2 prove:2 covariant:11 positive:9 suppl:1 symbolizes:1 wondering:1 ib0:1 diagrams:1 introducing:4 vandersickel:2 validity:1 appendix:2 virtue:1 misconception:1 fermionic:1 valued:2 originally:2 yjk:1 oscillator:2 modified:2 fock:1 gνβ:2 following:14 making:4 arrive:1 ma3:2 topic:1 performed:1 allowed:1 unphysical:3 counting:2 occur:4 s9:1 s2:6 s1:14 s0:47 amputated:1 plus:1 parameter:7 pathway:1 product:4 may:6 4th:1 δvi:6 mai:4 revealed:1 man:1 yaouanc:1 sy:2 natural:1 outline:1 6th:1 explicit:4 yielding:2 su:3 so:13 sn:3 verify:1 representation:1 typical:1 indeed:3 pointed:1 mainly:1 course:4 motions:3 still:9 lsz:1 derive:6 group:4 thank:1 interesting:2 hot:2 forms:1 window:1 εji:1 decades:1 non:11 thereby:1 processes:1 introduce:6 identically:1 vermaseren:1 now:12 killed:1 nor:1 possess:1 term:3 equality:2 polikarpov:1 drop:1 orthonormal:1 quintero:1 conventions:1 entering:1 ev:2 eq:1 shown:5 3rd:1 space:16 furthermore:2 squared:1 looking:1 investigation:1 correct:3 theory:29 derived:1 gribov:2 rely:2 possibility:1 quite:8 unwanted:1 nonunitarity:1 care:1 language:5 impose:4 iterative:1 motion:17 thing:1 gordon:1 neglect:1 first:10 origin:2 symmetry:17 variables:2 natale:2 specifically:1 directly:1 impossible:1 open:1 grosso:1 little:2 necessarily:5 checked:1 unitarity:18 2ωq:7 2ωk:5 structures:2 speaking:2 gives:3 proving:1 cornwall:1 transverse:1 seminarov:1 x2:1 x0:2 than:5 coefficients:8 unfortunately:2 accordance:1 require:4 altaba:1 were:3 decompose:3 generality:1 dynamically:4 turned:1 argument:1 say:1 any:1 martinelli:1 potential:5 curci:2 petronzio:1 multiple:1 trace:1 normal:3 correlation:1 paid:1 falls:1 algebraic:3 beta:1 formulae:1 remarks:2 gρσ:2 ritbergen:1 considered:4 later:5 feynman:2 ferrari:2 ferrara:1 2m2:8 lebedev:1 show:3 frolov:1 inconsistent:1 decompositions:1 aχ:1 written:2 analytic:1 only:17 explicitly:2 aµν:3 gev:1 viewpoint:1 get:2 rept:1 satisfied:2 nilpotency:4 cannot:6 prime:1 namely:1 cim:1 nonlocality:1 wonder:2 fails:1 invoked:2 commutation:13 review:4 functionals:1 αc:2 rephrase:1 between:15 αi:25 enjoys:7 diagonalized:3 checks:1 notice:7 concentrate:1 multiplier:1 come:7 concentrated:1 region:4 ballpark:1 according:1 multipoles:1 expression:4 zapiski:1 afterwards:1 color:2 overview:1 jk:1 mℓ2:2 mℓ1:2 maintained:2 anti:4 cancel:1 ordered:2 considering:3 sensible:4 slavnov:2 zimmermann:1 suppressed:1 acν:1 relations:19 obscuring:1 those:1 case:22 eis:6 trick:1 invoking:1 situation:1 narison:1 conformal:1 coupled:4 endowed:2 teitelboim:1 different:4 develop:4 d12:1 assure:1 pay:1 same:13 selfconsistent:1 antisymmetry:1 coworkers:1 physical:42 extended:1 trivially:3 doublets:1 lavelle:2 πia:3 invariance:4 modes:19 sssr:1 roughly:1 without:10 solve:6 components:2 very:3 model:43 dimension:13 hphys:10 actions:1 unclear:1 lemes:9 generator:4 hint:1 seems:1 interested:1 lett:14 π0j:1 momentum:2 real:2 chromodynamics:1 psi:1 read:3 decomposed:2 preference:1 vacuum:5 confined:3 using:12 mod:2 particle:4 reduces:3 pole:2 gjk:1 output:1 reduced:3 deduce:2 moreover:4 dimensions:1 decomposition:4 content:2 refer:1 faddeev:3 power:3 equivalent:4 broken:2 2m:2 comparison:2 oi:3 discussed:2 generated:11 practical:1 act:3 bjk:1 references:1 determine:5 elementary:1 hep:1 there:9 start:5 low:3 complete:6 bµν:20 aµ:17 applying:2 ωq:6 minkowski:2 ωk:4 ωa:1 ωc:1 define:8 aa:1 ab:3 cbe:1 ai:14 certain:6 aj:2 am:5 general:2 aq:2 ap:2 πjn:1 ensuing:1 formulation:1 lifetime:1 tedious:1 grassmann:1 completeness:1 field:11 valid:3 massless:12 a1:18 commutator:3 a3:18 a2:19 observables:2 included:1 aµa:7 condensation:3 perturbatively:3 investigated:2 mass:57 asymtotic:1 starting:4 original:10 scl:5 consider:8 induces:1 lack:1 sca:2 scalar:1 λabcd:9 mε:4 equivalence:4 nonlocal:10 th:1 te:1 tyutin:1 norm:18 belonging:3 straightforward:2 far:3 mn1:2 mn2:2 mn3:2 corollary:1 surprise:1 condition:4 hamiltonian:19 picariello:2 applicable:1 large:1 kondo:1 2k0:1 renormalized:2 zero:9 perspective:1 further:5 canonical:3 casu:3 what:1 abc:11 abd:1 brackets:3 section:16 version:4 aaν:7 method:1 condensed:1 full:1 loose:1 behaviour:2 investigating:1 strong:1 equations:30 transformation:7 search:1 antisymmetric:1 identifiable:1 allows:1 stella:1 base:1 action:62 jackiw:1 via:3 followed:2 requiring:1 ask:1 analyzing:2 viz:1 establish:1 readily:1 conventional:2 proceed:1 distinct:1 ψp:22 contains:3 quasi:2 nucl:6 qcd:11 taken:1 possible:4 more:20 operators:17 corrected:1 particular:5 known:10 upsilon:1 tachyonic:2 quantized:2 suganuma:1 recall:1 equation:10 evolved:1 learn:1 canonically:1 singularities:1 rodriguez:1 ojima:1 states:22 minimum:1 arise:3 mn:7 axis:1 recapitulating:1 needs:1 rather:4 browne:3 influences:1 simplicity:1 algebra:2 variant:1 short:3 leroy:1 perhaps:3 help:1 gauges:13 soon:1 paper:7 through:2 signs:2 existence:1 excitations:5 its:7 energies:7 solving:1 πkl:2 actually:2 pene:1 systems:1 jacobi:1 might:11 supersymmetry:4 peskin:1 propose:4 noticing:1 framework:1 2t:4 easily:2 2v:1 finite:3 always:3 level:4 φm:6 found:9 2i:4 generation:10 energy:11 reduce:3 idea:1 finish:1 expect:5 measurement:1 quantum:6 operation:2 beyond:1 stodolsky:1 nuovo:1 since:31 parametrizing:1 research:3 acting:3 induced:2 issue:2 µνa:1 localization:2 reason:1 sba:1 put:1 generate:2 definition:1 consequence:2 hadrons:2 xij:2 number:3 done:2 construct:4 calculational:1 perturbation:6 introduction:3 leading:2 interact:1 least:4 aa0:1 statement:1 stora:1 hundred:2 shifted:1 behind:1 part:14 authors:1 norms:2 translation:1 kind:1 scheme:2 aai:1 becchi:1 annihilation:7 determined:1 supposed:2 y0i:1 treated:3 motivation:1 sb:1 nonabelian:1 conjugate:11 cumbersome:1 orders:6 depending:2 ruegg:1 aaµ:15 k1:10 internal:1 generalized:3 jacobian:1 play:1 electric:2 reckon:1 most:4 plan:2 nothing:3 probabilistic:1 appear:6 ki:1 kn:6 km:4 kr:1 physics:1 naively:2 sector:5 krijgslaan:1 relation:1 find:12 parameters:2 heavily:1 bfm:1 halzen:1 generators:1 ruiz:1 abelian:19 notation:5 dependent:1 lehmann:1 express:3 closely:1 combinations:1 continuum:1 arxiv:1 remove:5 common:1 doublet:4 set:11 unpublished:1 see:13 analog:1 learns:1 learnt:1 positivity:1 dipole:1 various:3 available:1 recently:3 initially:1 complement:1 ikx:6 vanishing:1 conjugates:1 δab:2 both:4 collaborators:2 last:3 quantization:16 connection:1 context:2 finds:1 point:4 simple:1 asymptotically:4 dimensional:1 addisonwesley:1 throughout:1 complication:1 pq:1 described:1 transformations:3 pt:1 due:11 laplacian:1 reduction:2 describes:1 pi:1 generating:1 covariance:2 gap:3 fund:1 determination:2 demand:1 look:9 while:4 b02:1 langfeld:1 couplings:2 loop:4 stueckelberg:5 unitary:12 vol:1 confining:1 ready:1 belong:3 rules:3 conflict:1 higher:7 literature:1 bonus:1 nontrivially:1 moment:2 sorella:12 lower:4 task:2 analysis:11 obviously:3 machinery:1 consistency:6 spend:1 press:2 questions:2 λi:1 conclusions:1 theorem:5 relevance:1 input:1 remaining:1 useless:1 demands:1 nonphysical:4 couple:1 quest:1 bit:4 formal:2 follows:3 continue:3 yields:3 translated:1 essential:1 terminology:1 mathematical:1 popov:3 creation:8 some:9 understood:1 b0:20 b2:5 ijk:6 ourselves:3 scale:4 describing:1 affects:1 behave:1 eliminate:1 prog:1 run:1 ba:38 kleingordon:1 bn:1 step:5 relating:1 obscured:1 dictated:1 hilbert:1 soft:1 gνα:2 consequently:7 into:9 within:1 integral:6 appropriate:2 δbµν:1 lesson:1 classically:1 question:6 long:1 bosons:1 analyze:3 sections:2 propagator:4 gaµν:5 xµν:2 up:6 us:21 ui:6 similar:3 called:1 associated:2 defined:12 piguet:1 formalism:3 amounts:1 fixing:3 anticommuting:1 department:1 nice:1 elements:1 meaning:6 restrained:1 structure:1 ago:1 required:1 implied:1 schellekens:1 requires:2 having:3 once:5 ambiguities:1 results:7 existing:1 gf:11 ga:1 contributions:2 cases:1 disposal:3 concerned:3 groundstate:1 stable:1 g2:3 putting:1 mixing:1 continued:2 notes:1 try:3 interpolating:2 noted:1 configurations:1 chernodub:1 index:1 giving:1 analogously:1 expressed:4 expresses:1 exercise:3 exchange:1 desired:2 explore:1 eikx:4 ghent:2 hkg:4 yµν:2 involved:1 gent:1 resulting:1 aνa:1 iδab:4 scales:2 anomalies:1 condensates:4 apply:2 sgf:4 use:15 asymptotic:3 remains:4 next:7 few:4 capri:2 δgµν:1 summarizing:2 started:1 becomes:6 acoleyen:1 px0:1 account:2 ρi:16 f0i:3 infinitesimal:2 obvious:1 thin:1 decoupled:2 proof:2 calculation:1 dudal:14 high:5 lorentz:1 something:1 rescaling:1 holds:4 evidently:2 located:1 reducible:1 ta0:1 ta3:1 renormalizability:13 introduced:4 advocated:1 correspond:2 redundant:2 gµβ:2 gµα:2 allow:3 discussion:3 δmn:2 move:1 including:1 mentioned:2 write:5 le:1 longitudinal:1 ln:1 masses:2 lm:2 lk:6 li:68 lect:1 degrees:10 spoiling:3 derivative:2 eur:1 polarizations:4 landau:7 mention:6 university:3 dominance:2 l2:5 l3:4 l1:6 disregard:1 modo:1 subset:1 related:3 constitute:1 operator:39 decays:1 our:26 special:1 out:12 matrix:5 symanzik:1 rev:9 wick:1 integrated:2 interactions:1 diagonal:4 completely:5 york:1 anyhow:1 interaction:3 m28:1 determining:1 could:11 times:1 counterpart:1 hence:6 quadratically:2 franke:1 powerful:1 precisely:5 πc:2 ordering:3 condensate:6 πi:1 πn:3 system:1 πl:3 their:16 perfectly:1 final:3 shell:10 acquire:1 manipulation:2 constituent:1 dynamical:13 appealing:2 symmetries:5 unchanged:2 need:8 chetyrkin:1 constrained:1 apparently:3 clearly:6 min:2 studying:1 able:5 mechanism:2 brst:38 polarization:1 concerns:1 εi:4 subject:1 heisenberg:3 sobreiro:8 unless:1 deploy:1 plugging:2 connected:2 preliminary:1 class:7 linearized:1 gµν:22 fact:9 emerging:1 bring:2 postdoctoral:1 rough:1 trivial:8 q1:3 q0:37 q2:5 based:5 knowledge:2 commutators:4 should:15 local:11 means:6 ones:1 words:1 evolution:4 differential:5 contain:2 krein:1 view:1 requirement:4 multiplying:1 constructing:1 quantizing:1 closer:1 steklov:1 interacting:2 clearing:1 state:11 closed:3 invariant:19 neither:1 reinhardt:1 ends:1 attention:2 implementing:2 job:3 key:1 configuration:1 observable:4 taking:4 equal:3 fulfilled:2 chosen:2 expand:1 passing:2 otherwise:3 detailed:1 relevant:2 conclude:6 cb:8 ca:39 cohomology:5 table:2 addition:1 treat:2 choose:1 multiplicatively:1 corresponding:17 commutes:1 sufficient:1 subspace:24 fellow:1 present:3 novel:1 πjl:1 appearance:2 value:1 will:23 reliability:1 au:1 advisable:1 almost:1 vi:12 thus:11 quantize:7 vt:1 generic:1 cross:2 unity:1 parts:1 diagonalize:1 gets:1 infer:2 φn:9 difficult:1 reexpress:1 zumino:1 again:5 upon:1 functions:6 ion:1 infinite:1 warming:1 off:9 nevertheless:1 well:14 s20:2 english:1 firstly:1 arising:1 usual:2 less:1 obtain:2 localize:1 momenta:11 a0a:4 preprint:1 discuss:4 lattice:5 add:3 skl:1 identical:1 tests:1 henneaux:1 know:3 belgium:1 immediately:7 intersection:1 loss:1 necessary:2 like:10 δx:1 δy:1 δu:1 δs:5 δl:6 become:4 δb:1 accessible:1 because:2 classical:13 phenomena:1 q20:1 proofs:1 happens:1 avoid:6 manipulations:1 does:7 dipoles:1 assuming:1 expansion:2 although:3 imaginary:2 publishing:1 about:3 adµ:2 actual:1 getting:1 freedom:10 dependence:1 compatible:2 important:3 constraints:1 equally:1 h0:23 functional:4 bosonic:3 skg:1 van:2 additional:2 ugent:3 condense:1 noticed:1 quadratic:4 notices:1 function:1 but:12 volume:1 boucaud:1 construction:4 coupling:5 made:1 compute:1 whether:4 below:1 limit:1 problem:9 rq0:1 int:2 inadequate:1 contribute:1 identities:1 mutual:1 compared:2 oab:5 detail:1 other:10 details:1 theor:1 conclusion:4 repeat:3 astronomy:1 ghost:10 auxiliary:2 factors:2 4q:1
0705.0874.txt |@word gt:1 partial:1 consider:3 gq:2 splitting:1 invent:1 four:1 proposition:10 edu:2 consists:1 12s:4 whose:1 chain:1 equivalence:1 recurrence:1 finally:2 tj:5 γl:2 ta:2 adviser:1 2rc:2 results:1 corollary:1 witten:12 coprime:1 entries:1 difference:1 continued:13 2rp:1 induction:4 assignments:3 vector:4 indices:1 lecture:1 dimensional:1 sign:8 approximation:1 second:1 melvin:2 substitute:1 theory:1 even:2 index:1 sj2:1 sum:6 expressed:1 version:2 above:6 new:1 satisfy:2 mr:4 lem:3 stmt:2 modular:1 identifications:1 objects:3 address:1 along:2 appears:1 morphisms:1 obtained:7 remark:1 study:1 studied:1 allows:1 sjt:3 sjl:3 permutation:1 kauffman:1 studies:1 composed:1 divide:1 cobordism:2 replace:2 decrease:1 apply:1 use:8 lens:14 would:5 prove:4 give:4 bundles:1 uniqueness:1 next:2 m1:15 therefore:5 reciprocity:3 m2:4 means:1 more:1 tm1:2 factor:3 particular:1 known:1 projective:1 iii:3 me:1 erp:3 rβ:6 contradicts:1 equation:4 work:5 mi:13 vr:5 theories:1 mt:21 mv:2 erc:6 following:6 my:1 def:3 proof:9 links:3 stated:1 process:3 preserving:2 turaev:11 want:1 e2r:10 holds:3 s4:1 write:1 fourth:1 e2m:1 e2n:1 sin:1 map:1 product:1 may:2 derived:2 mapping:3 corrections:1 date:1 gluing:4 third:1 chern:1 explicit:2 su:1 element:2 sj:4 so:14 sl:9 representation:15 sa:3 prefactor:1 over:3 lsu:2 braids:1 its:3 before:1 derive:1 group:7 thank:1 acknowledge:1 matrices:4 solving:1 tori:1 wrt:2 parts:1 imt:12 mail:1 main:2 inductively:1 tjm:5 tjl:1 introduce:1 number:2 tjt:1 maslov:1 st:1 front:1 now:11 represents:2 equality:3 2q:1 2r:4 invariants:13 university:1 im1:2 each:1 found:1 2n:5 2i:3 weighted:2 weight:4 doing:1 series:1 idea:2 functor:1 quantum:2 our:1 ep:8 er:13 category:5 shown:2 rp:5 matrix:5 space:8 since:2 lagrangian:1 publish:1 denotes:2 replacing:1 rational:4 formula:11 evaluation:1 math:10 linear:1 homeomorphism:2 axioms:1 definition:1 pairs:1 phrases:1 signature:1 hence:7 first:5 knots:3 encouraging:1 linking:1 another:1 2a1:1 ring:2 given:10 dedekind:2 introduction:2 relations:3 convention:1 recovered:1 denominators:1 way:1 tuple:1 gilmer:3 j1:10 2at:4 tqft:11 jordan:1 coefficients:6 γj0:12 zero:1 gives:1 symmetries:3 ann:1 need:2 confirms:1 any:5 k1:1 generalized:1 unknot:2 opposite:1 quote:2 involving:1 gauss:1 successive:1 pair:1 class:4 considered:1 clear:1 adopt:1 bracket:1 exp:3 kt:2 skein:1 notion:1 nψ:1 2m1:3 terminate:2 spaces:10 substituting:1 d0:1 based:2 ier:3 enough:1 topological:1 should:1 lemma:12 explicitly:1 generators:3 equipped:1 identification:1 do:2 notation:1 get:3 de:1 overall:1 aγ:3 words:1 dt:2 rademacher:1 dq:1 qq:1 arxiv:1 blanchet:1 coefficient:1 set:3 computed:1 exists:1 j0:31 δjl:1 j2:9 see:1 result:6 surgery:3 surfaces:1 satisfying:1 behind:1 2πiα:1 closed:1 between:3 invariant:6 boundary:4 multiplied:1 notice:1 never:1 terms:9 ikt:7 jt:39 wl:3 however:1 jl:3 hypothesis:1 here:4 key:1 amer:1 topology:2 last:2 according:1 jt2:1 dl2:1 expression:1 ci:4 conclude:2 simple:1 framings:1 2nd:1 semiclassical:1 moreover:1 j02:16 ct:49 e4r:1 ps:2 described:1 commutative:1 khaled:6 due:1 been:2 defined:1 ph:1 define:2 corresponding:2 commutes:1 2ir:1 fund:1 observe:1 monogr:1 c0:1 manifolds:4 case:5 p1:1 solid:2 value:1 will:3 suppose:1 di:2 inspired:1 orientation:3 vogel:1 simons:1 thus:1 surface:3 iv:1 ii:2 erat:8 cocycle:1 ia:2 same:1 complex:1 composition:2 independent:1 phi:1 used:1 expand:1 roughly:1 thm:1 dimension:1 manifold:4 obtain:6 torus:5 underlying:1 integer:6 previous:2 conjugates:1 preprint:1 combine:2 theorem:2 iπ:1 motivating:1 around:1 kirby:2 sums:1 iζ:1 department:1 know:2 using:6 unique:2 mod:38 reshetikhin:10 like:4 follows:3 diffeomorphic:1 continue:1 yields:1 heegaard:1 rolfsen:1 page:2 parity:1 www:1 because:1 some:1 back:1 b0:1 specified:3 jeffery:2 tmt:1 prop:1 tmi:1 ict:1 bc:1 equivalent:1 bi:2 expansion:12 bt:2 step:1 bp:2 substitution:3 integers:4 about:1 actual:2 commun:2 factors:2 km2:2 km1:2 ti:1 introduced:1 morphism:2 soc:1 mλ2:1 h1:1 three:1 en:1 references:1 her:2 rct:2 removing:1 there:4 condense:1 long:1 jeffrey:1 low:1 fraction:14 was:10 function:2 elsewhere:2 but:1 construction:2 link:2 removed:1 j12:1 applying:1 2πi:2 wish:1 us:1 url:1 masbaum:1 similar:1 called:2 a1t:1 associated:2 ad:1 ai:2 abstract:1 denote:3 transl:1 associates:1 inc:1 nj:1 nm:1 no:2 field:1 details:1 np:1 mathematics:3 repeat:2 subspace:1 printing:1 variation:2 a1:6 a0:3 a2:1 structure:1 implies:1 assume:4 required:2 together:1 equivalently:1 perish:1 weights:1 walker:1 cobordisms:2