a r X i v :p h y s i c s /0407053v 1 [p h y s i c s .g e o -p h ] 12 J u l 2004
APS preprint
Multifractal Scaling of Thermally-Activated Rupture Processes
D.Sornette 1,2,3and G.Ouillon 1,3
1
Institute of Geophysics and Planetary Physics,University of California,Los Angeles,CA 900952
Department of Earth and Space Sciences,University of California,Los Angeles,CA 90095
3
Laboratoire de Physique de la Mati`e re Condens′e e,
CNRS UMR 6622and Universit′e de Nice-Sophia Antipolis,06108Nice Cedex 2,France ?
(Dated:February 2,2008)
We propose a “multifractal stress activation”model combining thermally activated rupture and long memory stress relaxation,which predicts that seismic decay rates after mainshocks follow the Omori law ～1/t p with exponents p linearly increasing with the magnitude M L of the mainshock and the inverse temperature.We carefully test this prediction on earthquake sequences in the Southern California Earthquake catalog:we ?nd power law relaxations of seismic sequences triggered by mainshocks with exponents p increasing with the mainshock magnitude by approximately 0.1?0.15for each magnitude unit increase,from p (M L =3)≈0.6to p (M L =7)≈1.1,in good agreement with the prediction of the multifractal model.
PACS numbers:91.30.Px ;89.75.Da;05.40.-a
Parisi and Frisch [1]and Halsey et al.[2]have intro-duced the extended concept of scale invariance,called multifractality,motivated by hydrodynamic turbulence and fractal growth aggregates https://www.doczj.com/doc/c010374907.html,e of the multifractal spectrum as a metric to characterize com-plex systems is now routinely used in many ?elds,in-cluding seismology to describe the hierarchical structure in space and time of earthquakes and faults (see for in-stance [3,4,5]).However,the origin of multifractal-ity is rarely identi?ed.This is certainly true for earth-quakes for which the possible existence of multifractal-ity is under scrutiny due to limited and corrupted data sets leading to biases [6]and its origin a matter of de-bate:fractal growth processes [7],self-organized critical-ity [4]or hierarchical cascades of stresses [8]are among the physical scenarios proposed to lead to multifractal-ity in fault and earthquake patterns.Here,we propose a physically-based “multifractal stress activation”model of earthquake interaction and triggering based on two sim-ple ingredients:(i)a seismic rupture results from ther-mally activated processes giving an exponential depen-dence on the local stress;(ii)the stress relaxation has a long memory.The interplay between these two physical processes are shown to lead to a multifractal organization of seismicity,which we observe quantitatively in real cat-alogs.
Thermal activation is relevant in all previously pro-posed physical processes underlying earthquakes:creep rupture,stress corrosion and state-and-velocity depen-dent friction.We model seismic activity λ( r ,t )at po-sition r and time t as the occurence of frictional slid-ing events and/or fault ruptures that are thermally ac-tivated processes facilitated by the applied stress ?eld:λ( r ,t )～exp [?βE ( r ,t )],where βis the inverse temper-ature and the energy barrier E ( r ,t )for rupture can be written as the sum of a contribution E 0( r )characterizing the material and of a term linearly decreasing with the
locally applied stress Σ( r ,t ):E ( r ,t )=E 0( r )?V Σ( r ,t ).V is a constant which has the dimension of a volume and Σ( r ,t )is the total stress at position r and time t .The decrease of the energy barrier E ( r ,t )as a function of the applied stress Σ( r ,t )embodies the various physical pro-cesses aiding rupture activation under stress.In addition,there are many evidences for a stress-controlled earth-quake activation process,suggesting that earthquakes trigger earthquakes directly and indirectly via dynami-cal and static stress transfers.Visco-elastic models of stress relaxation can account for the short-term relax-ation processes of the strain measured by geodetic meth-ods but,over long time scales,it is necessary to take into account the presence and geometry of lower crustal and mantle shear zones,which lead to slower decay-ing relaxation rates.We thus write the stress Σ( r ,t )at position r and time t as the sum of contributions from all past events at earlier times τ In this letter,we restrict our analysis to the time do-main.For this,we assume for simplicity that g ( r ,t )is separable as g ( r ,t )=f ( r )×h (t ).This obtains λ( r ,t )=λtec ( r ,t )exp β t ?∞ dτs ( r ,τ)h (t ?τ) ,(1) where s ( r ,τ)= d r ′?σ( r ′,τ)f ( r ? r ′)is the e?ective source at time τat point r resulting from all events occur-ring in the spatial domain at the same time τ.λtec ( r ,t )is the spontaneous seismicity rate in absence of stress 2 triggering by other earthquakes and accounts for the tec- tonic loading(far?eld stress),which may in general be non-homogeneous in space and perhaps depends on time. Since expression(1)is de?ned for any r,we drop the ref- erence to r without loss of generality. To go further,we specify the distribution P(s)of stress sources and the memory kernel h(t).On the ba- sis of theoretical calculations,simulations and measure- ments of rotations of earthquake focal mechanisms,Ka- gan[9]has suggested that P(s)should follow a symmetric Cauchy distribution.To capture in a phenomenological way the extended nature and complexity of earthquake ruptures,we use a more general power law distribution P(s)～C/|?s|1+μ,which generalizes the Cauchy case μ=1.To account for the slower-than-exponential stress relaxation processes discussed above,we postulate that h(t)=c1+θ λtec |ωM]=Pr[ω(t)>(1/β)ln λq 2 Var[ω(t)|ωM] , where E[ω(t)|ωM]=ωM Cov[ω(t),ωM] Var[ωM] .For power law stress sources,we use the insight that the natural gener- alization of the variance for power laws p(x)≈C/x1+μ with in?nite variance(i.e.,withμ<2)is the scale pa- rameter C(see Chap.4of[11]).In the power law case, due to the linear form ofωin(2),we can still write ω(t)=γ(t)ωM+?but withω(t),ωM and?being power law distributed random variables with the same expo- nentμand with scale factors equal respectively to Cω (forωandωM)and C?.The key idea is thatγcan be determined by forming the random variable de?ned as the productωωM=γω2M+?ωM.It is straightfor- ward to show that the distribution ofωωM consists of two main contributions,(i)a dominant power law with exponentμ/2and scale factor Cωω M =γμ/2Cω,and (ii)a sub-dominant power law with exponentμ(with a logarithmic correction)and scale factor CωC?.This has the following practical implication:if one measures or calculates the leading power law decay ofω×ωM, the measure of its scale factor gives access to the pa- rameterγthrough the expressionγ(t)=(Cωω M /Cω)2 2 2 ?t2/μ 1t?1c/t dy1y m 2 3 We thus obtain Pr[ω(t )>y |ωM ]=Pr[γωM +?> y |ωM ]=Pr[?>y ?γωM |ωM ]=ˉF (y ?γ(t )ωM ),where ˉF (?)is the complementary cumulative distribu- tion of ? .Putting these results in (2), this leads to Pr[λ(t )>λq |λM ]=ˉF (1/β)ln λq t p (M ) ,p (M )=aβM +bβ,(5) where a >0and M is the mainshock magnitude. Consider ?rst the case 2m =μ(1+θ)=1,such that the exponent m =(1+θ)μ/2de?ned in (3)equal to 1/2.Then, dγμ/2 t (T +c )1/2 (t +c )1/2 , showing that dγμ/2 (t +c )p , where B is a positive parameter introduced to account for the back-ground seismicity assumed to be superimposed over the genuine triggered sequences.The time shift c ensures the regularization of the seismic rate at t =0. The ?rst declustering method is essentially the same as de?ned in [10]:every event in the catalog is de?ned as a mainshock if it has not been preceded by an event with larger magnitude within a ?xed space-time window T ×d ,with T =1year and d =50km.Looking for events trig-gered by this mainshock,we de?ne another space-time window following it.The time dimension of the window is also set to 1year,whereas the space dimension depends on the rupture length of the main event.This spatial win-dow is chosen as a circle of radius equal to the mainshock rupture length L =10?2.57+0.6M L ,which is the average relationship between L and magnitude M L for California [16].If any event falls within this space-time window,it is considered as triggered by the main event.We have also checked the stability of the results by considering a spatial neighborhood of radius 2L rather than L for the triggered events.The second declustering method is the same as the ?rst one,except for one element:the space window used for qualifying a mainshock is not ?xed to d =50km but is chosen to adapt to the size of the rupture lengths L (M i )given by L =10?2.57+0.6M L of all events of all possible magnitudes M L (i )preceding this potential mainshock. Figure 1shows sets of typical seismic decay rates of stacked sequences for several magnitude intervals of the mainshocks,for the period from 1932to 2003when using the ?rst declustering technique,with mainshock magni-tudes above M L =1.5.Very similar plots are obtained for di?erent time periods,with the second declustering method and by varying the size from L to 2L of the spa-tial domain over which the triggered sequences are se-lected [15].For large mainshock magnitudes,the roll-o? 4 FIG.1:Normalized seismic decay rates of stacked sequences for several magnitude intervals of the mainshocks,for the pe-riod from 1932to 2003when using the second declustering technique. at small times is due to the observational saturation and short-time lack of completeness of triggered sequences. FIG.2:p -values of the Omori law ～1/t p obtained by the procedure described in the text for mainshocks (de?ned using the second declustering algorithm)as a function of the main events’magnitude,for the di?erent sub-catalogs of lifespans given in the inset. Figure 2shows the ?tted p -values as a function of the magnitude of the mainshocks for each of the four sub-catalogs.We use a standard least-square ?t of the seismic rate as a function of time with a weight proportional to t for each bin to balance their relative importance.We also take into account the possible presence of a background term.We have also performed maximum likelihood esti-mations of the exponent p ,con?rming the results shown in Fig.2[15].To test the reliability and robustness of our results,we have simulated synthetic catalogs with the ETAS model with known statistical properties following exactly the same procedure as for the real catalogs.The model provides a particular strong null hypothesis rationalizes most of the phenomenological statisti-of earthquake catalogs [17].By construc-synthetic catalogs generated with the ETAS model exhibit Omori laws with magnitude-independent Applying our procedure to such synthetic allows us to investigate whether the magnitude-of the p -value reported above could result some bias introduced by our analysis rather than a genuine property of earthquake catalogs.We that p (M )obtained by our procedure is a con-independent of M equal to the input value used in of the synthetic catalog [15]. Let us conclude by o?ering an intuitive explanation of (5)using the properties of multifractal spectra.The temporal evolution of seismicity in a ?xed spatial domain de?nes a statistically stationary measure on the tempo-ral axis,the measure determining the rate of earthquakes at any possible instant.An Omori sequence with expo-nent p corresponds to a singularity (to the right)equal to 1?p (logarithmic for p =1).A large earthquake triggers a strong burst of seismicity,giving rise to a strong singu-larity.For the relation α=1?p to be consistent with the multifractal description,a large earthquake must be associated with a strong singularity,a small α,hence a large p .Reciprocally,small moment orders q select weak seismic sequences,which are thus associated with small local mainshocks.Small q ’s are associated with large α’s,hence small p ’s.By a similar argument in the space do-main,the exponent of the spatial decay of the seismic rate induced by a mainshock of magnitude M L should increase with M L .Thus,in this view,the ETAS model is nothing but the mono-fractal approximation of a more general multifractal description of seismicity. This work was partially supported by NSF-EAR02-30429and by the Southern California Earthquake Center (SCEC). ? Electronic address:sornette@https://www.doczj.com/doc/c010374907.html, [1]Parisi,G.and Frisch,U.,in Proc.Int.School Enrico Fermi,eds.M.Ghil et al.(North Holland,Amsterdam,1985). [2]Halsey,T.C.et al.,Phys.Rev.A 33,1141(1986).[3]Godano C.et al.,Geophys.J.Int.136,99(1999).[4]Main,I.,Rev.Geophys.34,433(1996). [5]Ouillon G.et al.,J.Geophyss Res.101,5477(1996).[6]Ouillon,G.and Sornette D.,Geophys.Res.Lett.23,3409 (1996). [7]Sornette,A.et al.,J.Geophys.res.98,12111(1993).[8]Rodkin,M.V.,Izvestiya-Physics Sol.Earth.37,663 (2001). [9]Kagan,Y.Y.,Nonlinear Proc.Geophys.1,171(1994).[10]Helmstetter,A.,Phys.Rev.Lett.91,058501(2003).[11]Sornette,D.,Critical Phenomena in Natural Sciences, 2nd ed.(Springer,Heidelberg,2004). [12]Schmitt,F.and Marsan,D.,Eur.Phys.J.B 20,3(2001).[13]Muzy,J.-F.and E.Bacri,Phys.Rev.E 66,056121(2002).[14]Sornette,D.et al.,Risk 16,67(2003). 5 [15]Ouillon,G.and D.Sornette,cond-mat/0407208 [16]Wells, D.L.and Coppersmith,K.J.,Bull.Seism.Soc. Am.84,974(1994).[17]Helmstetter,A.and D.Sornette,J.Geophys.Res.108, 10.1029,2003. 如何写先进个人事迹 篇一：如何写先进事迹材料 如何写先进事迹材料 一般有两种情况：一是先进个人，如先进工作者、优秀党员、劳动模范等；一是先进集体或先进单位，如先进党支部、先进车间或科室，抗洪抢险先进集体等。无论是先进个人还是先进集体，他们的先进事迹，内容各不相同，因此要整理材料，不可能固定一个模式。一般来说，可大体从以下方面进行整理。 (1)要拟定恰当的标题。先进事迹材料的标题，有两部分内容必不可少，一是要写明先进个人姓名和先进集体的名称，使人一眼便看出是哪个人或哪个集体、哪个单位的先进事迹。二是要概括标明先进事迹的主要内容或材料的用途。例如《王鬃同志端正党风的先进事迹》、《关于评选张鬃同志为全国新长征突击手的材料》、《关于评选鬃处党支部为省直机关先进党支部的材料》等。 (2)正文。正文的开头，要写明先进个人的简要情况，包括：姓名、性别、年龄、工作单位、职务、是否党团员等。此外，还要写明有关单位准备授予他(她)什么荣誉称号，或给予哪种形式的奖励。对先进集体、先进单位，要根据其先进事迹的主要内容，寥寥数语即应写明，不须用更多的文字。 然后，要写先进人物或先进集体的主要事迹。这部分内容是全篇材料 的主体，要下功夫写好，关键是要写得既具体，又不繁琐；既概括，又不抽象；既生动形象，又很实在。总之，就是要写得很有说服力，让人一看便可得出够得上先进的结论。比如，写一位端正党风先进人物的事迹材料，就应当着重写这位同志在发扬党的优良传统和作风方面都有哪些突出的先进事迹，在同不正之风作斗争中有哪些突出的表现。又如，写一位搞改革的先进人物的事迹材料，就应当着力写这位同志是从哪些方面进行改革的，已经取得了哪些突出的成果，特别是改革前后的．经济效益或社会效益都有了哪些明显的变化。在写这些先进事迹时，无论是先进个人还是先进集体的，都应选取那些具有代表性的具体事实来说明。必要时还可运用一些数字，以增强先进事迹材料的说服力。 为了使先进事迹的内容眉目清晰、更加条理化，在文字表述上还可分成若干自然段来写，特别是对那些涉及较多方面的先进事迹材料，采取这种写法尤为必要。如果将各方面内容材料都混在一起，是不易写明的。在分段写时，最好在每段之前根据内容标出小标题，或以明确的观点加以概括，使标题或观点与内容浑然一体。 最后，是先进事迹材料的署名。一般说，整理先进个人和先进集体的材料，都是以本级组织或上级组织的名义；是代表组织意见的。因此，材料整理完后，应经有关领导同志审定，以相应一级组织正式署名上报。这类材料不宜以个人名义署名。 写作典型经验材料-般包括以下几部分： (1)标题。有多种写法，通常是把典型经验高度集中地概括出来，一 英语演讲稿：未来的工作 这篇《英语演讲稿范文：未来的工作》，是特地，希望对大家有所帮助！ 热门演讲推荐：竞聘演讲稿 | 国旗下演讲稿 | 英语演讲稿 | 师德师风演讲稿 | 年会主持词 | 领导致辞 everybody good afternoon:. first of all thank the teacher gave me a story in my own future ideal job. everyone has a dream job. my dream is to bee a boss, own a pany. in order to achieve my dreams, i need to find a good job, to accumulate some experience and wealth, it is the necessary things of course, in the school good achievement and rich knowledge is also very important. good achievement and rich experience can let me work to make the right choice, have more opportunities and achievements. at the same time, munication is very important, because it determines whether my pany has a good future development. so i need to exercise their municative ability. i need to use all of the free time to learn LS-DYNA FAQ 中英文版-Mass Scaling 质量缩放 质量缩放指的是通过增加非物理的质量到结构上从而获得大的显式时间步的技术。 在一个动态分析中，任何时候增加非物理的质量来增大时间步将会影响计算结果（因为F=ma）。有时候这种影响不明显，在这种情况下增加非物理的质量是无可非议的。比如额外的质量只增加到不是关键区域的很少的小单元上或者准静态的分析（速度很小，动能相对峰值内能非常小）。总的来说，是由分析者来判断质量缩放的影响。你可能有必要做另一个减小或消除了质量缩放的分析来估计质量增加对结果的灵敏度。 你可以通过人工有选择的增加一个部件的材料密度来实现质量缩放。这种手动质量缩放的方法是独立于通过设置*Control_timestep卡DT2MS项来实现的自动质量缩放。 当DT2MS设置为一个负值时，质量只是增加到时间步小于TSSFAC*|DT2MS|的单元上。通过增加这些单元的质量，它们的时间达到TSSFAC*|DT2MS|。有无数种TSSFAC和DT2MS的组合可以得到同样的乘积，因而有相同的时间步，但是对于每一种组合增加的质量将是不一样的。一般的趋势是TSSFAC越小，增加的质量越多。作为回报，当TSSFAC减小时计算稳定性增加（就像在没有做质量缩放的求解中一样）。如果TSSFAC缺省的值0.9会导致稳定性问题，可以试试0.8或者0.7。如果你减小TSSFAC，你可以相应增加|DT2MS|，这样还是可以保证时间步乘积不变。 为了确定什么时候和位置质量自动增加了，可以输出GLSTAT和MATSUM文件。这些文件允许你绘出完整的模型或者单独部件所增加的质量对时间的曲线。为了得到由壳单元组成的部件增加的质量云图，将*database_extent_binary卡的STSSZ项设置为3。这样你可以用ls-prepost绘出每个单元的质量增加量的云图，具体方法是通过选择Fcomp>Misc>time step size。 在*control_timestep中设置DT2MS正值和负值的不同之处如下： 负值：初始时间步将不会小于TSSFAC*-DT2MS。质量只是增加到时间步小于TSSFAC*|DT2MS|的单元上。当质量缩放可接受时，推荐用这种方法。用这种方法时质量增量是有限的。过多的增加质量会导致计算任务终止。 正值：初始时间将不会小于DT2MS。单元质量会增加或者减小以保证每一个单元的时间步都一样。这种方法尽管不会因为过多增加质量而导致计算终止，但更难以作出合理的解释。 *control_timestep卡中的参数MS1ST控制是否只是在初始化时增加一次质量（MS1ST=1）还是任何需要维持由DT2MS所指定的时间步时都增加质量 （MS1ST=0)。 你可以通过在*control_termination卡片中设置参数ENDMAS来控制当质量增加到初始质量一定比率时终止计算（只对自动质量缩放有效） 小学生个人读书事迹简介怎么写800字 书,是人类进步的阶梯,苏联作家高尔基的一句话道出了书的重要。书可谓是众多名人的“宠儿”。历来,名人说出关于书的名言数不胜数。今天小编在这给大家整理了小学生个人读书事迹,接下来随着小编一起来看看吧! 小学生个人读书事迹1 “万般皆下品,惟有读书高”、“书中自有颜如玉,书中自有黄金屋”,古往今来,读书的好处为人们所重视,有人“学而优则仕”,有人“满腹经纶”走上“传道授业解惑也”的道路……但是,从长远的角度看,笔者认为读书的好处在于增加了我们做事的成功率,改善了生活的质量。 三国时期的大将吕蒙,行伍出身,不重视文化的学习,行文时,常常要他人捉刀。经过主君孙权的劝导,吕蒙懂得了读书的重要性,从此手不释卷,成为了一代儒将,连东吴的智囊鲁肃都对他“刮目相待”。后来的事实证明,荆州之战的胜利,擒获“武圣”关羽,离不开吕蒙的“运筹帷幄,决胜千里”,而他的韬略离不开平时的读书。由此可见,一个人行事的成功率高低,与他的对读书,对知识的重视程度是密切相关的。 的物理学家牛顿曾近说过,“如果我比别人看得更远,那是因为我站在巨人的肩上”,鲜花和掌声面前,一代伟人没有迷失方向,自始至终对读书保持着热枕。牛顿的话语告诉我们,渊博的知识能让我们站在更高、更理性的角度来看问题,从而少犯错误,少走弯路。 读书的好处是显而易见的,但是,在社会发展日新月异的今天,依然不乏对读书,对知识缺乏认知的人,《今日说法》中我们反复看到农民工没有和用人单位签订劳动合同,最终讨薪无果;屠户不知道往牛肉里掺“巴西疯牛肉”是犯法的;某父母坚持“棍棒底下出孝子”,结果伤害了孩子的身心,也将自己送进了班房……对书本,对知识的零解读让他们付出了惨痛的代价,当他们奔波在讨薪的路上,当他们面对高墙电网时,幸福,从何谈起?高质量的生活,从何谈起? 读书,让我们体会到“锄禾日当午,汗滴禾下土”的艰辛;读书,让我们感知到“四海无闲田,农夫犹饿死”的无奈;读书,让我们感悟到“为报倾城随太守,西北望射天狼”的豪情壮志。 读书的好处在于提高了生活的质量,它填补了我们人生中的空白,让我们不至于在大好的年华里无所事事,从书本中,我们学会提炼出有用的信息,汲取成长所需的营养。所以,我们要认真读书,充分认识到读书对改善生活的重要意义,只有这样,才是一种负责任的生活态度。 小学生个人读书事迹2 所谓读一本好书就是交一个良师益友,但我认为读一本好书就是一次大冒险,大探究。一次体会书的过程,真的很有意思,咯咯的笑声,总是从书香里散发;沉思的目光也总是从书本里透露。是书给了我启示,是书填补了我无聊的夜空,也是书带我遨游整个古今中外。所以人活着就不能没有书,只要爱书你就是一个爱生活的人,只要爱书你就是一个大写的人,只要爱书你就是一个懂得珍惜与否的人。可真所谓 硕037班 刘文3110038020 2011/4/20交互式多模型仿真与分析IMM算法与GBP算法的比较，算法实现和运动目标跟踪仿真，IMM算法的特性分析 多源信息融合实验报告 交互式多模型仿真与分析 一、 算法综述 由于混合系统的结构是未知的或者随机突变的，在估计系统状态参数的同时还需要对系统的运动模式进行辨识，所以不可能通过建立起一个固定的模型对系统状态进行效果较好的估计。针对这一问题，多模型的估计方法提出通过一个模型集{}(),1,2,,j M m j r == 中不同模型的切换来匹配不同目标的运动或者同一目标不同阶段的运动，达到运动模式的实时辨识的效果。 目前主要的多模型方法包括一阶广义贝叶斯方法（BGP1），二阶广义贝叶斯方法（GPB2）以及交互式多模型方法等（IMM ）。这些多模型方法的共同点是基于马尔科夫链对各自的模型集进行切换或者融合，他们的主要设计流程如下图： M={m1,m2,...mk} K 时刻输入 值的形式 图一 多模型设计方法 其中，滤波器的重初始化方式是区分不同多模型算法的主要标准。由于多模型方法都是基于一个马尔科夫链来切换与模型的，对于元素为r 的模型集{}(),1,2,,j M m j r == ，从0时刻到k 时刻，其可能的模型切换轨迹为 120,12{,,}k i i i k trace k M m m m = ，其中k i k m 表示K-1到K 时刻，模型切换到第k i 个， k i 可取1,2,,r ，即0,k trace M 总共有k r 种可能。再令1 2 1 ,,,,k k i i i i μ+ 为K+1时刻经由轨迹0,k trace M 输入到第1k i +个模型滤波器的加权系数，则输入可以表示为 0,11 2 1 12|,,,,|,,,???k k trace k k k i M k k i i i i k k i i i x x μ++=?∑ 可见轨迹0,k trace M 的复杂度直接影响到算法计算量和存储量。虽然全轨迹的 ?哈弗曼编码 A method for the construction of minimum-re-dundancy codes, 耿国华1数据结构1北京:高等教育出版社,2005:182—190 严蔚敏,吴伟民.数据结构(C语言版)[M].北京:清华大学出版社,1997. 冯桂,林其伟,陈东华.信息论与编码技术[M].北京:清华大学出版社,2007. 刘大有,唐海鹰,孙舒杨,等.数据结构[M].北京:高等教育出版社,2001 ?压缩实现 速度要求 为了让它(huffman.cpp)快速运行，同时不使用任何动态库，比如STL或者MFC。它压缩1M数据少于100ms（P3处理器，主频1G）。 压缩过程 压缩代码非常简单，首先用ASCII值初始化511个哈夫曼节点： CHuffmanNode nodes[511]; for(int nCount = 0; nCount < 256; nCount++) nodes[nCount].byAscii = nCount; 其次，计算在输入缓冲区数据中，每个ASCII码出现的频率： for(nCount = 0; nCount < nSrcLen; nCount++) nodes[pSrc[nCount]].nFrequency++; 然后，根据频率进行排序： qsort(nodes, 256, sizeof(CHuffmanNode), frequencyCompare); 哈夫曼树，获取每个ASCII码对应的位序列： int nNodeCount = GetHuffmanTree(nodes); 构造哈夫曼树 构造哈夫曼树非常简单，将所有的节点放到一个队列中，用一个节点替换两个频率最低的节点，新节点的频率就是这两个节点的频率之和。这样，新节点就是两个被替换节点的父 关于坚持的英语演讲稿 Results are not important, but they can persist for many years as a commemoration of. Many years ago, as a result of habits and overeating formed one of obesity, as well as indicators of overall physical disorders, so that affects my work and life. In friends to encourage and supervise, the participated in the team Now considered to have been more than three years, neither the fine rain, regardless of winter heat, a day out with 5:00 time. The beginning, have been discouraged, suffering, and disappointment, but in the end of the urging of friends, to re-get up, stand on the playground. 成绩并不重要，但可以作为坚持多年晨跑的一个纪念。多年前，由于庸懒习惯和暴饮暴食，形成了一身的肥胖，以及体检指标的全盘失常，以致于影响到了我的工作和生活。在好友的鼓励和督促下，参加了晨跑队伍。现在算来，已经三年多了，无论天晴下雨，不管寒冬酷暑，每天五点准时起来出门晨跑。开始时，也曾气馁过、痛苦过、失望过，但最后都在好友们的催促下，重新爬起来，站到了操场上。 In fact, I did not build big, nor strong muscles, not a sport-born people. Over the past few years to adhere to it, because I have a team behind, the strength of a strongteam here, very grateful to our team, for a long time, we encourage each other, and with sweat, enjoying common health happy. For example, Friends of the several run in order to maintain order and unable to attend the 10，000 meters race, and they are always concerned about the brothers and promptly inform the place and time, gives us confidence and courage. At the same time, also came on their own inner desire and pursuit for a good health, who wrote many of their own log in order to refuel for their own, and inspiring. 其实我没有高大身材，也没健壮肌肉，天生不属于运动型的人。几年来能够坚持下来，因为我的背后有一个团队，有着强大团队的力量，在这里，非常感谢我们的晨跑队，长期以来，我们相互鼓励着，一起流汗，共同享受着健康带来的快 LZ77压缩算法实验报告 一、实验内容 使用C++编程实现LZ77压缩算法的实现。 二、实验目的 用LZ77实现文件的压缩。 三、实验环境 1、软件环境：Visual C++ 6.0 2、编程语言：C++ 四、实验原理 LZ77 算法在某种意义上又可以称为“滑动窗口压缩”，这是由于该算法将一个虚拟的，可以跟随压缩进程滑动的窗口作为术语字典，要压缩的字符串如果在该窗口中出现，则输出其出现位置和长度。使用固定大小窗口进行术语匹配，而不是在所有已经编码的信息中匹配，是因为匹配算法的时间消耗往往很多，必须限制字典的大小才能保证算法的效率；随着压缩的进程滑动字典窗口，使其中总包含最近编码过的信息，是因为对大多数信息而言，要编码的字符串往往在最近的上下文中更容易找到匹配串。 五、LZ77算法的基本流程 1、从当前压缩位置开始，考察未编码的数据，并试图在滑动窗口中找出最长的匹 配字符串，如果找到，则进行步骤2，否则进行步骤3。 2、输出三元符号组( off, len, c )。其中off 为窗口中匹 配字符串相对窗口边 界的偏移，len 为可匹配的长度，c 为下一个字符。然后将窗口向后滑动len + 1 个字符，继续步骤1。 3、输出三元符号组( 0, 0, c )。其中c 为下一个字符。然后将窗口向后滑动 len + 1 个字符，继续步骤1。 六、源程序 /********************************************************************* * * Project description: * Lz77 compression/decompression algorithm. * *********************************************************************/ #include 关于工作的优秀英语演讲稿 Different people have various ambitions. Some want to be engineers or doctors in the future. Some want to be scientists or businessmen. Still some wish to be teachers or lawers when they grow up in the days to come. Unlike other people, I prefer to be a farmer. However, it is not easy to be a farmer for Iwill be looked upon by others. Anyway,what I am trying to do is to make great contributions to agriculture. It is well known that farming is the basic of the country. Above all, farming is not only a challenge but also a good opportunity for the young. We can also make a big profit by growing vegetables and food in a scientific way. Besides we can apply what we have learned in school to farming. Thus our countryside will become more and more properous. I believe that any man with knowledge can do whatever they can so long as this job can meet his or her interest. All the working position can provide him with a good chance to become a talent. 1 ————来源网络整理，仅供供参考 个人先进事迹简介 01 在思想政治方面,xxxx同学积极向上,热爱祖国、热爱中国共产党,拥护中国共产党的领导.利用课余时间和党课机会认真学习政治理论,积极向党组织靠拢. 在学习上,xxxx同学认为只有把学习成绩确实提高才能为将来的实践打下扎实的基础,成为社会有用人才.学习努力、成绩优良. 在生活中,善于与人沟通,乐观向上,乐于助人.有健全的人格意识和良好的心理素质和从容、坦诚、乐观、快乐的生活态度,乐于帮助身边的同学,受到师生的好评. 02 xxx同学认真学习政治理论,积极上进,在校期间获得原院级三好生,和校级三好生,优秀团员称号,并获得三等奖学金. 在学习上遇到不理解的地方也常常向老师请教,还勇于向老师提出质疑.在完成自己学业的同时,能主动帮助其他同学解决学习上的难题,和其他同学共同探讨,共同进步. 在社会实践方面,xxxx同学参与了中国儿童文学精品“悦”读书系,插画绘制工作,xxxx同学在班中担任宣传委员,工作积极主动,认真负责,有较强的组织能力.能够在老师、班主任的指导下独立完成学院、班级布置的各项工作. 03 xxx同学在政治思想方面积极进取,严格要求自己.在学习方面刻苦努力,不断钻研,学习成绩优异,连续两年荣获国家励志奖学金；作 为一名学生干部,她总是充满激情的迎接并完成各项工作,荣获优秀团干部称号.在社会实践和志愿者活动中起到模范带头作用. 04 xxxx同学在思想方面,积极要求进步,为人诚实,尊敬师长.严格 要求自己.在大一期间就积极参加了党课初、高级班的学习,拥护中国共产党的领导,并积极向党组织靠拢. 在工作上,作为班中的学习委员,对待工作兢兢业业、尽职尽责 的完成班集体的各项工作任务.并在班级和系里能够起骨干带头作用.热心为同学服务,工作责任心强. 在学习上,学习目的明确、态度端正、刻苦努力,连续两学年在 班级的综合测评排名中获得第1.并荣获院级二等奖学金、三好生、优秀班干部、优秀团员等奖项. 在社会实践方面,积极参加学校和班级组织的各项政治活动,并 在志愿者活动中起到模范带头作用.积极锻炼身体.能够处理好学习与工作的关系,乐于助人,团结班中每一位同学,谦虚好学,受到师生的好评. 05 在思想方面,xxxx同学积极向上,热爱祖国、热爱中国共产党,拥护中国共产党的领导.作为一名共产党员时刻起到积极的带头作用,利用课余时间和党课机会认真学习政治理论. 在工作上,作为班中的团支部书记,xxxx同学积极策划组织各类 团活动,具有良好的组织能力. 在学习上,xxxx同学学习努力、成绩优良、并热心帮助在学习上有困难的同学,连续两年获得二等奖学金. 在生活中,善于与人沟通,乐观向上,乐于助人.有健全的人格意 识和良好的心理素质. 实验名称：LZSS压缩算法实验报告 一、实验内容 使用Visual 6..0 C++编程实现LZ77压缩算法。 二、实验目的 用LZSS实现文件的压缩。 三、实验原理 LZSS压缩算法是词典编码无损压缩技术的一种。LZSS压缩算法的字典模型使用了自适应的方式，也就是说，将已经编码过的信息作为字典， 四、实验环境 1、软件环境：Visual C++ 6.0 2、编程语言：C++ 五、实验代码 #include -- need byte-swap function for big endian CPU */ #define READ_LE32(X) *(uint32_t *)(X) #define WRITE_LE32(X,Y) *(uint32_t *)(X) = (Y) /* this assumes sizeof(long)==4 */ typedef unsigned long uint32_t; /* text (input) size counter, code (output) size counter, and counter for reporting progress every 1K bytes */ static unsigned long g_text_size, g_code_size, g_print_count; /* ring buffer of size N, with extra F-1 bytes to facilitate string comparison */ static unsigned char g_ring_buffer[N + F - 1]; /* position and length of longest match; set by insert_node() */ static unsigned g_match_pos, g_match_len; /* left & right children & parent -- these constitute binary search tree */ static unsigned g_left_child[N + 1], g_right_child[N + 257], g_parent[N + 1]; /* input & output files */ static FILE *g_infile, *g_outfile; /***************************************************************************** initialize trees *****************************************************************************/ static void init_tree(void) { unsigned i; /* For i = 0 to N - 1, g_right_child[i] and g_left_child[i] will be the right and left children of node i. These nodes need not be initialized. Also, g_parent[i] is the parent of node i. These are initialized to NIL (= N), which stands for 'not used.' For i = 0 to 255, g_right_child[N + i + 1] is the root of the tree for strings that begin with character i. These are initialized to NIL. Note there are 256 trees. */ for(i = N + 1; i <= N + 256; i++) g_right_child[i] = NIL; for(i = 0; i < N; i++) g_parent[i] = NIL; } /***************************************************************************** Inserts string of length F, g_ring_buffer[r..r+F-1], into one of the trees (g_ring_buffer[r]'th tree) and returns the longest-match position and length via the global variables g_match_pos and g_match_len. If g_match_len = F, then removes the old node in favor of the new one, because the old one will be deleted sooner. 关于工作的英语演讲稿 【篇一：关于工作的英语演讲稿】 关于工作的英语演讲稿 different people have various ambitions. some want to be engineers or doctors in the future. some want to be scientists or businessmen. still some wish to be teachers or lawers when they grow up in the days to come. unlike other people, i prefer to be a farmer. however, it is not easy to be a farmer for iwill be looked upon by others. anyway,what i am trying to do is to make great contributions to agriculture. it is well known that farming is the basic of the country. above all, farming is not only a challenge but also a good opportunity for the young. we can also make a big profit by growing vegetables and food in a scientific way. besides we can apply what we have learned in school to farming. thus our countryside will become more and more properous. i believe that any man with knowledge can do whatever they can so long as this job can meet his or her interest. all the working position can provide him with a good chance to become a talent. 【篇二：关于责任感的英语演讲稿】 im grateful that ive been given this opportunity to stand here as a spokesman. facing all of you on the stage, i have the exciting feeling of participating in this speech competition. the topic today is what we cannot afford to lose. if you ask me this question, i must tell you that i think the answer is a word---- responsibility. in my elementary years, there was a little girl in the class who worked very hard, however she could never do satisfactorily in her lessons. the teacher asked me to help her, and it was obvious that she expected a lot from me. but as a young boy, i was so restless and thoughtless, i always tried to get more time to play and enjoy myself. so she was always slighted over by me. one day before the final exam, she came up to me and said, could you please explain this to me? i can not understand it. i 多媒体数据压缩实验报告 篇一：多媒体实验报告_文件压缩 课程设计报告 实验题目：文件压缩程序 姓名：指导教师：学院：计算机学院专业：计算机科学与技术学号： 提交报告时间：20年月日 四川大学 一，需求分析： 有两种形式的重复存在于计算机数据中，文件压缩程序就是对这两种重复进行了压 缩。 一种是短语形式的重复，即三个字节以上的重复，对于这种重复，压缩程序用两个数字：1.重复位置距当前压缩位置的距离；2.重复的长度，来表示这个重复，假设这两个数字各占一个字节，于是数据便得到了压缩。 第二种重复为单字节的重复，一个字节只有256种可能的取值，所以这种重复是必然的。给 256 种字节取值重新编码，使出现较多的字节使用较短的编码，出现较少的字节使用较长的编码，这样一来，变短的字节相对于变长的字节更多，文件的总长度就会减少，并且，字节使用比例越不均 匀，压缩比例就越大。 编码式压缩必须在短语式压缩之后进行，因为编码式压缩后，原先八位二进制值的字节就被破坏了，这样文件中短语式重复的倾向也会被破坏（除非先进行解码）。另外，短语式压缩后的结果：那些剩下的未被匹配的单、双字节和得到匹配的距离、长度值仍然具有取值分布不均匀性，因此，两种压缩方式的顺序不能变。 本程序设计只做了编码式压缩，采用Huffman编码进行压缩和解压缩。Huffman编码是一种可变长编码方式，是二叉树的一种特殊转化形式。编码的原理是：将使用次数多的代码转换成长度较短的代码，而使用次数少的可以使用较长的编码，并且保持编码的唯一可解性。根据 ascii 码文件中各 ascii 字符出现的频率情况创建 Huffman 树，再将各字符对应的哈夫曼编码写入文件中。同时，亦可根据对应的哈夫曼树，将哈夫曼编码文件解压成字符文件. 一、概要设计： 压缩过程的实现: 压缩过程的流程是清晰而简单的: 1. 创建 Huffman 树 2. 打开需压缩文件 3. 将需压缩文件中的每个 ascii 码对应的 huffman 编码按 bit 单位输出生成压缩文件压缩结束。 关于人英语演讲稿(精选多篇) 关于人的优美句子 1、“黑皮小子”是我对在公交车上偶遇两次的一个男孩的称呼代号。一听这个外号，你也定会知道他极黑了。他的脸总是黑黑的；裸露在短袖外的胳膊也是黑黑的；就连两只有厚厚耳垂的耳朵也那么黑黑的，时不时像黑色的猎犬竖起来倾听着什么；黑黑的扁鼻子时不时地深呼吸着，像是在警觉地嗅着什么异样的味道。 2、我不知道，如何诠释我的母亲，因为母亲淡淡的生活中却常常跳动着不一样的间最无私、最伟大、最崇高的爱，莫过于母爱。无私，因为她的爱只有付出，无需回报；伟大，因为她的爱寓于 普通、平凡和简单之中；崇高，是因为她的爱是用生命化作乳汁，哺育着我，使我的生命得以延续，得以蓬勃，得以灿烂。 3、我的左撇子伙伴是用左手写字的，就像我们的右手一样挥洒自如。在日常生活中，曾见过用左手拿筷子的，也有像超级林丹用左手打羽毛球的，但很少碰见用左手写字的。中国汉字笔画笔顺是左起右收，适合用右手写字。但我的左撇子伙伴写字是右起左收的，像鸡爪一样迈出田字格，左看右看，上看下看，每一个字都很难看。平时考试时间终了，他总是做不完试卷。于是老师就跟家长商量，决定让他左改右写。经过老师引导，家长配合，他自己刻苦练字，考试能够提前完成了。现在他的字像他本人一样阳光、帅气。 4、老师，他们是辛勤的园丁，帮助着那些幼苗茁壮成长。他们不怕辛苦地给我们改厚厚一叠的作业，给我们上课。一步一步一点一点地给我们知识。虽然 他们有时也会批评一些人，但是他们的批评是对我们有帮助的，我们也要理解他们。那些学习差的同学，老师会逐一地耐心教导，使他们的学习突飞猛进。使他们的耐心教导培养出了一批批优秀的人才。他们不怕辛苦、不怕劳累地教育着我们这些幼苗，难道不是美吗？ 5、我有一个表妹，还不到十岁，她那圆圆的小脸蛋儿，粉白中透着粉红，她的头发很浓密，而且好像马鬓毛一样的粗硬，但还是保留着孩子一样的蓬乱的美，卷曲的环绕着她那小小的耳朵。说起她，她可是一个古灵精怪的小女孩。 6、黑皮小子是一个善良的人，他要跟所有见过的人成为最好的朋友！这样人人都是他的好朋友，那么人人都是好友一样坦诚、关爱相交，这样人与人自然会和谐起来，少了许多争执了。 7、有人说，老师是土壤，把知识化作养分，传授给祖国的花朵，让他们茁壮成长。亦有人说，老师是一座知识的桥梁，把我们带进奇妙的科学世界，让 Capacity Scaling Algorithm Jan.10, 2012 ① Set b b =:' and ()0:=e f for all ()G E e ∈. Set ??m ax logb 2=γ , where ()(){}G V v v b b ∈=:max max . ② If 0'=b then stop , Else choose a vertex s with ()γ≥s b ' . Choose a vertex t with ()γ-≤t b ' such that t is reachable from s in f G . If there is no such s or t then go to ⑤ ③ Find an s-t-Path P in f G of minimum weight. ④ Set ()()γ-=s b s b '': and ()()γ+=t b t b '':. Augment f along P by γ. Go to ②. ⑤ If 1=γ then stop .(There exists no flow b -.) Else set 2 :γ γ= and go to ②. Description: Capacity Scaling Algorithm is used to solve M INIMUM C OST F LOW Capacity Scaling Algorithm I nput: A digraph G with infinite capacities u (e )=∞ (E(G) e ∈), numbers b : V (G ) → Z with ()() 0=∑ ∈G V v v b , and conservative weights c : E (G ) → R. Output: A minimum cost b -flow f .如何写先进个人事迹
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