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chunk_id string | paper_id int64 | section_title string | text string |
|---|---|---|---|
77ee0cf8303fc60b9816cb4254214c5f | 0 | ABSTRACT | additive models play an important role in semiparametric statistics .
this paper gives learning rates for regularized kernel based methods for additive models .
these learning rates compare favour additive models play an important role in semiparametric statistics .
this paper gives learning rates for regularized... |
600df1b642694a6597a8c352f0c6d182 | 0 | ARTICLE | additive models provide an important family of models for semiparametric regression or classification . some reasons for the success of additive models are their increased flexibility when compared to linear or generalized linear models and their increased interpretability when compared to fully nonparametric models . ... |
4b13e9d5155bbca8c6150bccbd75ffff | 0 | ARTICLE | many examples of such estimators belong to the large class of regularized kernel based methods over a reproducing kernel hilbert space [MATH] , see e.g. . in the last years
many interesting results on learning rates of regularized kernel based models for additive models have been published when the focus is on sparsi... |
cdbadd483b4491c0cb21b1c36222e833 | 0 | ARTICLE | this is in sharp contrast to kernel methods based on a lipschitz continuous loss function and on a bounded loss function , where results on upper bounds for the maxbias bias and on a bounded influence function are known , see e.g. for the general case and for additive models .
therefore , we will here consider the ca... |
ad2431fe54753537b8e14c94bf596514 | 0 | ARTICLE | such regularized kernel based methods are now often called support vector machines ( svms ) , although the notation was historically used for such methods based on the special hinge loss function and for special kernels only , we refer to . in this paper we address the open question , whether an svm with an additive ke... |
f4aadf3fa18dab867d0e3d96cd31191b | 0 | ARTICLE | we will not address the question how to check whether the assumption of an additive model is satisfied because this would be a topic of a paper of its own .
of course , a practical approach might be to fit both models and compare their risks evaluated for test data .
for the same reason we will also not cover spars... |
94fb60e31540aa4f4864c47aeaba214d | 0 | ARTICLE | a loss function [MATH] is used to measure the quality of a prediction function [MATH] by the local error [MATH] .
_ throughout the paper we assume that [MATH] is measurable , [MATH] , convex with respect to the third variable , and uniformly lipschitz continuous satisfying [MATH] with a finite constant [MATH] .
_ s... |
074dd2e6e30eb59f5a54ac2751eddaa4 | 0 | ARTICLE | the idea to shift a loss function has a long history , see e.g. in the context of m - estimators .
it was shown in that [MATH] is also a minimizer of the following optimization problem involving the original loss function [MATH] if a minimizer exists : [MATH] the additive model we consider consists of the _ input spa... |
330f49a660655f4bb5eb5e47ae8919c9 | 0 | ARTICLE | because these notations will only be used in different places and because we do not expect any misunderstandings , we think this notation is easier and more intuitive than specifying these quantities with different symbols .
the additive kernel [MATH] is defined in terms of mercer kernels [MATH] on [MATH] as [MATH] i... |
25b8af18029d6a23ec38c4f2b66ea166 | 0 | ARTICLE | the first example deals with gaussian rbf kernels .
all proofs will be given in section [ proofsection ] .
[ gaussadd ] let [MATH] , [MATH] $ ] and [MATH] ^ 2.$ ] let [MATH] and [MATH].\ ] ] the additive kernel [MATH] is given by [MATH] furthermore , the product kernel [MATH] is the standard gaussian kernel given b... |
7b7c1704fd897c5cdcf1deeaf87e8d5c | 0 | ARTICLE | it is an rkhs with a mercer kernel [MATH] defined on [MATH] ^ 2 $ ] .
if we take all the mercer kernels [MATH] to be [MATH] , then [MATH] $ ] for each [MATH] .
the additive kernel [MATH] is also a mercer kernel and defines an rkhs [MATH]\right\}.\ ] ] however , the multivariate sobolev space [MATH]^s)$ ] , consisti... |
b2ef71baa9969bea3c409609e506e5fe | 0 | ARTICLE | section [ ratessection ] contains our main results on learning rates for svms based on additive kernels . learning rates for quantile regression
are treated as important special cases .
section [ comparisonsection ] contains a comparison of our results with other learning rates published recently .
section [ proo... |
f59d9497c4183f1bea390014eaf4f011 | 0 | ARTICLE | the first condition is about the approximation ability of the hypothesis space [MATH] .
since the output function [MATH] is from the hypothesis space , the learning rates of the learning algorithm depend on the approximation ability of the hypothesis space [MATH] with respect to the optimal risk [MATH] measured by th... |
33c8783315ba09d85ab76e667c60592c | 0 | ARTICLE | then we can define the [MATH]-th power [MATH] of [MATH] by [MATH] this is a positive and bounded operator and its range is well - defined .
the assumption [MATH] means [MATH] lies in this range .
[ assumption1 ] we assume [MATH] and [MATH] where for some [MATH] and each [MATH] , [MATH] is a function of the form [MA... |
b7b951008272901dd57537c3b0d3f3a3 | 0 | ARTICLE | so it is natural for us to impose an additive expression [MATH] for the target function [MATH] with the component functions [MATH] satisfying the power condition [MATH] .
the above natural assumption leads to a technical difficulty in estimating the approximation error : the function [MATH] has no direct connection t... |
81fb9511721895697a9a87edac39f415 | 0 | ARTICLE | when we add up such functions [MATH] , we get a good approximation of the target function [MATH] , and thereby a good estimate of the approximation error .
this is the first novelty of the paper . |
4efdcb12efdf7f0419ba0c89229a0603 | 0 | ARTICLE | [ approxerrorthm ] under assumption [ assumption1 ] , we have [MATH] where [MATH] is the constant given by [MATH] the second condition for our learning rates is about the capacity of the hypothesis space measured by [MATH]-empirical covering numbers . let [MATH] be a set of functions on [MATH] and [MATH] for every [MAT... |
140e9a3e652fa2c6150e3bbba65d9708 | 0 | ARTICLE | [ capacitythm ] under assumption [ assumption2 ] , for any [MATH] and [MATH] , we have [MATH] the bound for the covering numbers stated in theorem [ capacitythm ] is special : the power [MATH] is independent of the number [MATH] of the components in the additive model .
it is well - known in the literature of functio... |
d05eadbc301fa319814522f65e39c890 | 0 | ARTICLE | the special bound in theorem [ capacitythm ] demonstrates an advantage of the additive model in terms of capacity of the additive hypothesis space .
the third condition for our learning rates is about the noise level in the measure [MATH] with respect to the hypothesis space . before stating the general condition
,... |
76960f9353c33030f7b123ff6dc38c18 | 0 | ARTICLE | , we consider a special case for quantile regression , to illustrate our general results .
let [MATH] be a quantile parameter .
the quantile regression function [MATH] is defined by its value [MATH] to be a [MATH]-quantile of [MATH] , i.e. , a value [MATH] satisfying [MATH] the regularization scheme for quantile re... |
085174a96ab8efa2fea6ed07608e8933 | 0 | ARTICLE | \tau \mbox{~~and~~ } q\bigl([t , \infty)\bigr ) \ge 1-\tau\bigr\}\,.\ ] ] it is well - known that [MATH] is a compact interval .
[ noisecond ] let [MATH] . 1 .
a probability measure [MATH] on [MATH] is said to have a * [MATH]-quantile of type [MATH] * , if there exist a [MATH]-quantile [MATH] and a constant [MATH] ... |
37f86d5e3e14533d0834607d34150410 | 0 | ARTICLE | one can show that a distribution [MATH] having a [MATH]-quantile of type [MATH] has a unique [MATH]-quantile [MATH] .
moreover , if [MATH] has a lebesgue density [MATH] then [MATH] has a [MATH]-quantile of type [MATH] if [MATH] is bounded away from zero on [MATH] $ ] since we can use [MATH]\}$ ] in ( [ tauquantileoft... |
665bb76153277cd196cfe86818341a57 | 0 | ARTICLE | if assumption [ assumption1 ] holds with [MATH] and [MATH] has a [MATH]-quantile of [MATH]-average type [MATH] for some [MATH] $ ] , then by taking [MATH] , for any [MATH] and [MATH] , with confidence at least [MATH] we have [MATH] where [MATH] is a constant independent of [MATH] and [MATH] and [MATH] please note that ... |
757a69b3c8a6750c6880a1ddaca24f97 | 0 | ARTICLE | , we need an assumption on a _ variance - expectation bound _ which is similar to definition [ noisecond ] in the special case of quantile regression .
[ assumption3 ] we assume that there exist an exponent [MATH] $ ] and a positive constant [MATH] such that [MATH] assumption [ assumption3 ] always holds true for [MA... |
c899035034275d19193e2eb98e5ad9ed | 0 | ARTICLE | we now add some theoretical and numerical comparisons on the goodness of our learning rates with those from the literature . as already mentioned in the introduction
, some reasons for the popularity of additive models are flexibility , increased interpretability , and ( often ) a reduced proneness of the curse of hi... |
43a128140e62b2250e487fbca3bfbfea | 0 | ARTICLE | our learning rate in theorem [ quantilethm ] is new and optimal in the literature of svm for quantile regression .
most learning rates in the literature of svm for quantile regression are given for projected output functions [MATH] , while it is well known that projections improve learning rates . here the projection... |
a795467b3be1ffc435d7990b361909ad | 0 | ARTICLE | such results are given in .
for example , under the assumptions that [MATH] has a [MATH]-quantile of [MATH]-average type [MATH] , the approximation error condition ( [ approxerrorb ] ) is satisfied for some [MATH] , and that for some constants [MATH] , the sequence of eigenvalues [MATH] of the integral operator [MATH... |
e03be6f87785bc2e5dedb9cd61215de2 | 0 | ARTICLE | the learning rate in theorem [ quantilethm ] may be improved by relaxing assumption 1 to a sobolev smoothness condition for [MATH] and a regularity condition for the marginal distribution [MATH] .
for example , one may use a gaussian kernel [MATH] depending on the sample size [MATH] and achieve the approximation erro... |
f9e41470446714be3d75d1f70d69f524 | 0 | ARTICLE | this is done for quantile regression in .
since we are mainly interested in additive models , we shall not discuss such an extension .
[ gaussmore ] let [MATH] , [MATH] $ ] and [MATH] ^ 2.$ ] let [MATH] and the additive kernel [MATH] be given by ( [ gaussaddform ] ) with [MATH] in example [ gaussadd ] as [MATH].\ ]... |
3ac7f4269ef8b2e2a396c109fa0ce774 | 0 | ARTICLE | note that the kernel in the above example is independent of the sample size .
it would be interesting to see whether there exists some [MATH] such that the function [MATH] defined by ( [ gaussfcn ] ) lies in the range of the operator [MATH] .
the existence of such a positive index would lead to the approximation er... |
d35e6b85607918f368c2d6b3b3d0d2fd | 0 | ARTICLE | i.e. , we assume in particular that [MATH] is a probability measure on [MATH] $ ] and that the marginal distribution [MATH] has a lebesgue density [MATH] for some [MATH] . furthermore , suppose that the optimal decision function [MATH] has ( to make theorem [ mainratesthm ] applicable with [MATH] $ ] ) the additive str... |
1615f5fbc7510a5551614282f35d3514 | 0 | ARTICLE | it is well - known that the besov space [MATH] contains the sobolev space [MATH] for [MATH] , [MATH] , and [MATH] , and that [MATH] .
we mention that if all [MATH] are suitably chosen wendland kernels , their reproducing kernel hilbert spaces [MATH] are sobolev spaces , see ( * ? ? ?
* thm . 10.35 , p. 160 ) .
fu... |
488db76469cd47502719b8811146c834 | 0 | ARTICLE | 4.12 ) in this situation , if [MATH] provided the assumption of the additive model is valid .
table [ table1 ] lists the values of [MATH] from ( [ explicitratescz2 ] ) for some finite values of the dimension [MATH] , where [MATH] .
all of these values of [MATH] are positive with the exceptions if [MATH] or [MATH] .... |
caaf47828d2bc5f2521523d10d8f6ebc | 0 | ARTICLE | the figures seem to indicate that our learning rate from theorem [ mainratesthm ] is probably not optimal for small dimensions . however , the main focus of the present paper is on high dimensions .
.[table1 ] the table lists the limits of the exponents [MATH] from ( * ? ? ?
* cor . 4.12 ) and [MATH] from theorem [... |
d73721a05979b0dd54c3037a2f1627f8 | 1 | ABSTRACT | we have studied the leptonic decay [MATH] , via the decay channel [MATH] , using a sample of tagged [MATH] decays collected near the [MATH] peak production energy in [MATH] collisions with the cleo - we have studied the leptonic decay [MATH] , via the decay channel [MATH] , using a sample of tagged [MATH] decays colle... |
ea9cd26da4b00777a0a97625b557c1cc | 1 | ARTICLE | the leptonic decays of a charged pseudoscalar meson [MATH] are processes of the type [MATH] , where [MATH] , [MATH] , or [MATH] . because no strong interactions are present in the leptonic final state [MATH] , such decays provide a clean way to probe the complex , strong interactions that bind the quark and antiquark w... |
06d05f1d888a5a1fe846613b11a57802 | 1 | ARTICLE | the quantity [MATH] describes the amplitude for the [MATH] and [MATH]-quarks within the [MATH] to have zero separation , a condition necessary for them to annihilate into the virtual [MATH] boson that produces the [MATH] pair .
the experimental determination of decay constants is one of the most important tests of ca... |
e0d1eb6b93529d7f74ebf7856c2112d2 | 1 | ARTICLE | the charm mesons , [MATH] and [MATH] , are better instruments to study the leptonic decays of heavy mesons since these decays are either less ckm suppressed or favored , _
i.e. _ , [MATH] and [MATH] are much larger than [MATH] .
thus , the decay constants [MATH] and [MATH] determined from charm meson decays can be ... |
53b0b8e508417d73463da06a6d172039 | 1 | ARTICLE | depending on the non - sm features , the ratio of [MATH] could be affected , as could the ratio [MATH] .
any of the individual widths might be increased or decreased .
there is an indication of a discrepancy between the experimental determinations of [MATH] and the most recent precision lqcd calculation .
this di... |
277d5b9c77711a271070b73ab57de815 | 1 | ARTICLE | the data sample consists of an integrated luminosity of [MATH] [MATH] containing [MATH] [MATH] pairs .
we have previously reported measurements of [MATH] and [MATH] with a subsample of these data . a companion article reports measurements of [MATH] from [MATH] and [MATH] , with [MATH] , using essentially the same dat... |
18dab724f017b2366482e50e732a2021 | 1 | ARTICLE | the chambers achieve a momentum resolution of [MATH]% at [MATH] gev/[MATH] .
the main drift chamber also provides specific - ionization ( [MATH] ) measurements that discriminate between charged pions and kaons .
the rich detector covers approximately [MATH]% of [MATH] and provides additional separation of pions and... |
1dbf0bbac2a7e119a38856fe11bf6eb4 | 1 | ARTICLE | physics events are generated by evtgen , tuned with much improved knowledge of charm decays , and final - state radiation ( fsr ) is modeled by the photos program .
the modeling of initial - state radiation ( isr ) is based on cross sections for [MATH] production at lower energies obtained from the cleo - c energy sc... |
ce6901f7938048610af23d083eedf4f9 | 1 | ARTICLE | the [MATH] reconstructed in the st sample can be either primary or secondary from [MATH] ( or [MATH] ) .
the st yield can be expressed as [MATH] where [MATH] is the produced number of [MATH] pairs , [MATH] is the branching fraction of hadronic modes used in the st sample , and [MATH] is the st efficiency .
the [MAT... |
150ccacf6ef1f7ff2b4cec8d95fce21d | 1 | ARTICLE | our double - tag ( dt ) sample is formed from events with only a single charged track , identified as an [MATH] , in addition to a st .
the yield can be expressed as [MATH] where [MATH] is the leptonic decay branching fraction , including the subbranching fraction of [MATH] decay , [MATH] is the efficiency of finding... |
42e359ff146b440f7cb5fe2aa56f8fc8 | 1 | ARTICLE | hence , the ratio [MATH] is insensitive to most systematic effects associated with the st , and the signal branching fraction [MATH] obtained using this procedure is nearly independent of the efficiency of the tagging mode . to minimize systematic uncertainties , we tag using three two - body hadronic decay modes with ... |
eda692fb4f0d36600e4e1a451c83a183 | 1 | ARTICLE | the effect of the tag bias [MATH] can be expressed in terms of the signal efficiency [MATH] defined by [MATH] where [MATH] is the st efficiency when the recoiling system is the signal leptonic decay with single [MATH] in the other side of the tag .
as the general st efficiency [MATH] , when the recoiling system is an... |
85ef2809d25fdfaae8d54dd303f6d1a5 | 1 | ARTICLE | we require the resonance decay to satisfy the following mass windows around the nominal masses : [MATH] ( [MATH] mev ) and [MATH] ( [MATH] mev ) .
we require the momenta of charged particles to be [MATH] mev or greater to suppress the slow pion background from [MATH] decays ( through [MATH] ) .
we identify a st by ... |
80b01af4124bbee18ce26f97f63547ab | 1 | ARTICLE | we require the recoil mass to be within [MATH] mev of the [MATH] mass .
this loose window allows both primary and secondary [MATH] tags to be selected . to estimate the backgrounds in our st and dt yields from the wrong tag combinations ( incorrect combinations that , by chance , lie within the [MATH] signal region )... |
9024fc935bbc06bfd050921b432c6abb | 1 | ARTICLE | [ fig : dm ] and the st yield and [MATH] sideband scaling factor are summarized in table [ table : data - single ] .
we find [MATH] summed over the three tag modes .
.[table : data - single ] summary of single - tag ( st ) yields , where [MATH] is the yield in the st mass signal region , [MATH] is the yield in the ... |
4bbce1ceda71314f98664679bf7c5e23 | 1 | ARTICLE | uncertainty in the signal yield due to nonpeaking background ( [MATH] ) is assessed by varying the semileptonic decay branching fractions by the precision with which they are known .
imperfect knowledge of [MATH] gives rise to a systematic uncertainty in our estimate of the amount of peaking background in the signal ... |
3d9c2d79e7aeb1dd926e4ed206fba25d | 1 | ARTICLE | we obtain a correction of [MATH] for the extra energy requirement and systematic uncertainties on each of the three requirements of [MATH] ( all equal , by chance ) .
the non-[MATH] background in the signal [MATH] candidate sample is negligible ( [MATH] ) due to the low probability ( [MATH] per track ) that hadrons (... |
535f07f69292bf662fa57605119028db | 1 | ARTICLE | is estimated to be [MATH] .
other possible sources of systematic uncertainty include [MATH] ( [MATH] ) , tag bias ( [MATH] ) , tracking efficiency ( [MATH] ) , [MATH] identification efficiency ( [MATH] ) , and fsr ( [MATH] ) . combining all contributions in quadrature ,
the total systematic uncertainty in the branc... |
7bee8e791006faa1ba528d608ed66ff6 | 1 | ARTICLE | ( [ eq : f ] ) with known values [MATH] gev[MATH] , [MATH] mev , [MATH] mev , and [MATH] s. we assume [MATH] and use the value [MATH] given in ref .
we obtain [MATH] combining with our other determination of [MATH] mev with [MATH] and [MATH] ( [MATH] ) decays , we obtain [MATH] this result is derived from absolute br... |
cf46659b10fee3f20b14584556e5d92e | 1 | ARTICLE | , we obtain [MATH] using this with our measurement of [MATH] , we obtain the branching fraction ratio [MATH] this is consistent with [MATH] , the value predicted by the sm with lepton universality , as given in eq .
( [ eq : f ] ) with known masses .
we gratefully acknowledge the effort of the cesr staff in providi... |
2ee7c5b2434c0dc333e20009c13cbb51 | 1 | ARTICLE | lett . * 97 * , 251802 ( 2006 ) .
b. aubert _ et al .
_ ( babar collaboration ) , phys . rev .
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phys . * 111 * , 295 ( 2004 ) .
j. l. hewett , arxiv : hep - ph/9505246 .
w. s. hou , phys... |
91ffeae9488144fa3250b12a27d2546f | 1 | ARTICLE | lett . * 99 * , 071802 ( 2007 ) .
k. m. ecklund _ et al . _
( cleo collaboration ) , phys . rev .
lett . * 100 * , 161801 ( 2008 ) .
j. p. alexander _ et al .
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instrum .
a * 320 ... |
adc22dbc91fea539174b335328e45cf8 | 2 | ABSTRACT | in 84 , 258 ( 2000 ) , mateos conjectured that current reversal in a classical deterministic ratchet is associated with bifurcations from chaotic to periodic regimes .
this is based on the compariso in 84 , 258 ( 2000 ) , mateos conjectured that current reversal in a classical deterministic ratchet is associated with... |
d79aa2d4b942bbe19d2d5e1ddddfea88 | 2 | ABSTRACT | in 84 , 258 ( 2000 ) , mateos conjectured that current reversal in a classical deterministic ratchet is associated with bifurcations from chaotic to periodic regimes .
this is based on the compariso used to generate it , as well as conditions for convergent behavior ( that is , independent of the details of the ensem... |
dc0c128dbf6ab9913b109cc8982de562 | 2 | ARTICLE | the transport properties of nonlinear non - equilibrium dynamical systems are far from well - understood .
consider in particular so - called ratchet systems which are asymmetric periodic potentials where an ensemble of particles experience directed transport .
the origins of the interest in this lie in considerati... |
f048fcd0cc123903acdb3ed20c25dfcc | 2 | ARTICLE | that is , the phase - space structure is usually relatively complicated , consisting of stability islands embedded in chaotic seas , for examples , or of simultaneously co - existing attractors .
this can change significantly as parameters change .
for example , stability islands can merge into each other , or brea... |
1acc2d0c0bab41366f1c4e4719297128 | 2 | ARTICLE | he looked at an ensemble of particles , specifically the velocity for the particles , averaged over time and the entire ensemble .
he showed that this quantity , which is an intuitively reasonable definition of ` the current ' , could be either positive or negative depending on the amplitude [MATH] of the periodic fo... |
25d1ada1a5ff4fa3c63ab16f5852cfaa | 2 | ARTICLE | these organizing principles would allow some handle on characterizing the many different kinds of behavior that are possible in such systems .
a later investigation of the mateos conjecture by barbi and salerno , however , argued that it was not a valid rule even in the specific system considered by mateos .
they p... |
8db50de422d9f6711b52c711f9e18411 | 2 | ARTICLE | this implicitly assumes that the dynamics of the system are ergodic .
this is not true in general for chaotic systems of the type being considered . in particular , there can be extreme dependence of the result on the statistics of the ensemble being considered .
this has been pointed out in earlier studies which l... |
cd7ab0fc5b56549e2bb26d9024a96e5d | 2 | ARTICLE | it is therefore interesting to probe the results of barbi and salerno with regard to the details of the ensemble used , and more formally , to see how ergodicity alters our considerations about the current , as we do in this paper .
we report here on studies on the properties of the current in a chaotic deterministic... |
d55658834ae9170c989f05b71fe5251f | 2 | ARTICLE | having established this , we then proceed to discuss the connection between the bifurcation diagram for individual particles and the behavior of the current .
we find that while we disagree with many of the details of barbi and salerno s results , the broader conclusion still holds .
that is , it is indeed possible... |
7ff9e48f99b5de4168b09a437da8c630 | 2 | ARTICLE | that is , in general , bifurcations for trajectory dynamics as a function of system parameter seem to be associated with abrupt changes in the current .
depending on the specific value of the current , these abrupt changes may lead the net current to reverse direction , but not necessarily so .
we start below with ... |
cc8fc53c58189de54dd49a2e36677804 | 2 | ARTICLE | after this , we are able to compare details of specific trajectory bifurcation curves with current curves , and thus justify our broader statements above , after which we conclude .
the goal of these studies is to understand the behavior of general chaotic ratchets .
the approach taken here is that to discover heur... |
4ebac2e1590b7558ef18756f304799f8 | 2 | ARTICLE | there is no noise in the system , so it is completely deterministic , although there is damping .
the equations of motion for an individual trajectory for such a system are given in dimensionless variables by [MATH] where the periodic asymmetric potential can be written in the form [MATH] + \frac{1}{4 } \sin [ 4\pi (... |
dfff8f914fc1efc66928ecb9a5788e42 | 2 | ARTICLE | that is , individual trajectories have one of following possible time - asymptotic behaviors : ( i ) inside the potential wells , trajectories and all their properties oscillate , leading to zero net transport . outside the wells , the trajectories either ( ii ) librate to the right or ( iii ) to the left , with corres... |
0d39b252c11b78f040e33964e8474104 | 2 | ARTICLE | when the driving is turned on , the phase - space becomes chaotic with the usual phenomena of intertwining separatrices and resulting homoclinic tangles .
the dynamics of individual trajectories in such a system are now very complicated in general and depend sensitively on the choice of parameters and initial conditi... |
60e1ec9e8bf4acaac3f7aa72ca8546aa | 2 | ARTICLE | now iterate an initial condition , recording the value of the particle s position [MATH] at times [MATH] from its integrated trajectory ( sometimes we record [MATH] .
this is done stroboscopically at discrete times [MATH] where [MATH] and [MATH] is an integer [MATH] with [MATH] the maximum number of observations made... |
58a38fc231cfd958b8e2cc4b48f91b19 | 2 | ARTICLE | all other orbits , including periodic orbits of incommensurate period result in a simply - connected or multiply - connected dense set of points . for the next value [MATH] , the last computed value of [MATH] at [MATH] are used as initial conditions , and previously , results are stored after cutoff and so on until [MA... |
f9a05ed18ef157a9d40bccfb724e5b0d | 2 | ARTICLE | we have made several plots , as a test , with different initial conditions and the diagrams obtained are identical .
we show several examples of this kind of bifurcation diagram below , where they are being compared with the corresponding behavior of the current .
having broadly understood the wide range of behavio... |
d9c1fe280ad69ac459d4ae681bff8af2 | 2 | ARTICLE | the current [MATH] for an ensemble in the system is defined in an intuitive manner by mateos as the time - average of the average velocity over an ensemble of initial conditions .
that is , an average over several initial conditions is performed at a given observation time [MATH] to yield the average velocity over th... |
db9bf3616b7131d7d92f45acf2512f51 | 2 | ARTICLE | that is , the transport properties of an ensemble in a chaotic system depend in general on the part of the phase - space being sampled .
it is therefore important to consider many different initial conditions to generate a current . the first straightforward result we show in fig .
( [ figure2 ] ) is that in the ca... |
1700e28247ca21180cc99b7a2627b97e | 2 | ARTICLE | ( [ figure3 ] ) where we superimpose the different curves resulting from varying the number of points in the initial ensemble .
first , the curve is significantly smoother as a function of [MATH] for larger [MATH] . even more relevant is the fact that the single trajectory data ( [MATH] ) may show current reversals t... |
41304d17ca79635f658de514e3bd84dc | 2 | ARTICLE | current [MATH] versus the number of trajectories [MATH] for [MATH] ; dashed lines correspond to a regular motion with [MATH] while solid lines correspond to a chaotic motion with [MATH] .
note that a single trajectory is sufficient for a regular motion while the convergence in the chaotic case is only obtained if the... |
b09a1c35a2060074916902cb92e10821 | 2 | ARTICLE | this arises from the fact that an arbitrarily chosen ensemble has particles with idiosyncratic behaviors which often average out . as our result , with these ensembles we see typical [MATH] for example , while barbi and salerno report currents about [MATH] times greater .
however , it is not true that only a few traj... |
78ea94fe5d333dc903cf7ab01d1bf69f | 2 | ARTICLE | . it should also be clear that there is a dependence of the current on the location of the initial ensemble , this being particularly true for small [MATH] , of course .
the location is defined by its centroid [MATH] . for [MATH] , it is trivially true that the initial location matters to the asymptotic value of the ... |
23091d0bdc0e425a02c82392899216d9 | 2 | ARTICLE | notice also that in fig .
( [ current - bifur1 ] ) , at [MATH] and [MATH] , the deviations between the different ensembles is particularly pronounced .
these points are close to bifurcation points where some sort of symmetry breaking is clearly occuring , which underlines our emphasis on the relevance of specifying... |
fe256c0004325f82dff72cd03f2538d1 | 2 | ARTICLE | however , we are not in the hamiltonian situation when the damping is turned on in this case , the phase - space consists in general of attractors .
that is , if transient behavior is discarded , the current is less likely to depend significantly on the location of the initial conditions or on the spread of the initi... |
46006a9a051d7f8524cd5dff2f80b011 | 2 | ARTICLE | however , in the regular regime , it is not important to take a large ensemble and a single trajectory can suffice , as long as we take care to discard the transients .
that is to say , in the computation of currents , the definition of the current needs to be modified to : [MATH] where [MATH] is some empirically obt... |
7243da91640ca5f46317b2477acd0bcb | 2 | ARTICLE | ( [ figure5 ] ) fig .
( [ rev - nobifur ] ) , in each of which we plot both the ensemble current and the bifurcation diagram as a function of the parameter [MATH] .
the main point of these numerical results can be distilled into a series of heuristic statements which we state below ; these are labelled with roman n... |
cf196a2574ffefc8f2d615cdd8d2f8f5 | 2 | ARTICLE | note , however , that the current is not without structure it changes fairly dramatically as a function of parameter .
this point is made even more clearly in fig .
( [ figure6 ] ) where the current remains consistently below [MATH] , and hence there are in fact , no current reversals at all .
note again , howeve... |
7d20d7371cf2f143d72e601c6a676c88 | 2 | ARTICLE | notice the current stays consistently below [MATH].,title="fig:",width=302 ] current and bifurcations versus [MATH] . in ( a ) and ( b )
we show ensemble dependence , specifically in ( a ) the black curve is for an ensemble of trajectories starting centered at the stable fixed point [MATH] with a root - mean - square... |
3bc991e6cfbf23c834cbb7b1c3fec89c | 2 | ARTICLE | the initial conditions for the ensembles are centered at [MATH] with a mean root square gaussian of width [MATH] .
( d ) is the corresponding bifurcation diagram.,title="fig:",width=302 ] it is possible to find several examples of this at different parameters , leading to the negative conclusion , therefore , that * ... |
d1ff4024cc0700f8c007cb969dd640d5 | 2 | ARTICLE | ( 2,3a,3b ) , where they scan the parameter region [MATH] .
the distinction between their results and ours is that we are using _
ensembles _ of particles , and are investigating the convergence of these results as a function of number of particles [MATH] , the width of the ensemble in phase - space , as well as tr... |
7e2f844d23268609b85e948a60701375 | 2 | ARTICLE | ( b ) the ensemble results are consistent with barbi and salerno in general , although disagreeing in several details .
for instance , ( c ) the bifurcation at [MATH] has a much gentler impact on the ensemble current , which has been growing for a while , while the single - trajectory result changes abruptly . note ,... |
4026689ea46c35b6a9c6b5209b1f01a4 | 2 | ARTICLE | ( [ current - bifur2 ] ) , at [MATH] of current reversal that does not seem to be associated with bifurcations .
in this spike , the current abruptly drops below [MATH] and then rises above it again .
the single trajectory current completely ignores this particular effect , as can be seen .
the bifurcation diagra... |
3a03a5a22e688d28028ea2e181a5329f | 2 | ARTICLE | * where does this leave us in the search for ` positive ' results , that is , useful heuristics ?
one possible way of retaining the mateos conjecture is to weaken it , i.e. make it into the statement that * ( iii ) _ most _ current reversals are associated with bifurcations . * same as fig .
( [ current - bifur1 ] ... |
bf9cb57ac6b4142469b31f07e78fa421 | 2 | ARTICLE | we see reversals without bifurcations in ( a ) whereas the zoomed version ( c ) shows that there are windows of periodic and chaotic regimes .
this is further evidence that jumps in the current correspond in general to bifurcation.,title="fig:",width=302 ] for [MATH] and [MATH] , current ( upper ) and bifurcation dia... |
9f4c0962aef8367feb5916adf2ea6d01 | 2 | ARTICLE | if this current jump or spike goes through zero , this coincides with a current reversal , making the mateos conjecture a special case .
the physical basis of this argument is the fact that ensembles of particles in chaotic systems _ can _ have net directed transport but the details of this behavior depends relativel... |
bd0107f105c3815274cfe9c8bf812bb0 | 2 | ARTICLE | , it completely captures the behaviour of fig .
( [ figure6 ] ) which can not be understood as either an example of the mateos conjecture , or even a failure thereof . as such
, this rule significantly enhances our ability to characterize changes in the behavior of the current as a function of parameter .
a furth... |
c7e67258c684ee2e3f1717d3840caf68 | 2 | ARTICLE | this is therefore consistent with our statement that sudden current changes are associated with bifurcations .
each of the transitions from periodic behavior to chaos and back provides opportunities for the current to spike .
however , in not all such cases can these hidden bifurcations be found .
we can see an e... |
7363f0d2557275423b388b754a849cd7 | 2 | ARTICLE | we note , however , that we have seen that these broad arguments hold when we vary other parameters as well ( figures not shown here ) . in conclusion ,
in this paper we have taken the approach that it is useful to find general rules of thumb ( even if not universally valid ) to understand the complicated behavior of... |
ddf932fb18fa394bf8b2d5d533496c32 | 2 | ARTICLE | current reversals are a special case of this
. however , not all spikes or jumps correspond to a bifurcation , nor vice versa .
the open question is clearly to figure out if the reason for when these rules are violated or are valid can be made more concrete .
a.k . gratefully acknowledges t. barsch and kamal p. s... |
ef8414ad68928307adb6cb37a1a613fc | 2 | ARTICLE | 476 , edited by j. parisi , s.c .
mueller , and w. zimmermann ( springer verlag , berlin , 1996 ) , pp.294 - 308 ; r.d .
asturmian , science * 276 * , 917 ( 1997 ) ; f. jlicher , a. ajdari , and j. prost , rev . mod .
phys . * 69 * , 1269 ( 1997 ) ; c. dring , nuovo cimento d*17 * , 685 ( 1995 ) s. flach , o. yev... |
e5c736471e15796aa1f2d420868d5d26 | 3 | ABSTRACT | the effect of a random phase diffuser on fluctuations of laser light ( scintillations ) is studied .
not only spatial but also temporal phase variations introduced by the phase diffuser are analyzed the effect of a random phase diffuser on fluctuations of laser light ( scintillations ) is studied .
not only spatial... |
762d2cc83b9d7cddde2d2dba2192123d | 3 | ARTICLE | studies of laser beams propagating through turbulent atmospheres are important for many applications such as remote sensing , tracking , and long - distance optical communications .
howerver , fully coherent laser beams are very sensitive to fluctuations of the atmospheric refractive index .
the initially coherent ... |
807f2bfeb25c47d3dd728ab6012c9d12 | 3 | ARTICLE | the coherent laser beam can be transformed into a partially coherent beam by means of a phase diffuser placed near the exit aperture .
this diffuser introduces an additional phase ( randomly varying in space and time ) to the wave front of the outgoing radiation .
statistical characteristics of the random phase det... |
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