Pseudo-diffusions and Quadratic term structure models
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细胞生物学专业词中英文对照第一章细胞学——Cytology细胞生物——Cell biology细胞学说——Cell theory原生质——protoplasm原生质体——protoplast有丝分裂——mitosis福尔根反应——Feulgen reaction哺乳动物雷帕霉素靶蛋白——mammalian target of rapamycin (mTOR)支原体——mycoplast真核细胞——rucaryotic cell真核生物——procaryote原核细胞——prokaryotic cell原核生物——prokaryote类群、域——domain古核细胞——archaea古核生物——archaeon古细菌——archaebacteria真细菌——eubacteria鞭毛——flagellum鞭毛蛋白——flagellin类核——nucleoid质粒——plasmid管蛋白——tubulin蓝细菌——cyanobacteria类囊体——thylakoid异形胞——heterocyst直系同源基因——orthologous gene 盐细菌——halobacteria热源体——thermoplasma硫氧化菌——sulfolobus核小体——nucleosome核纤层——nuclear lamina核纤层蛋白——lamin核基质——nuclear matrix纳米生物学——nanobiology自我装配——self-assembly协助装配——aided-assembly直接装配——direct-assembly次生代谢产物——secondary metabolite天然产物——natural product衣壳——capsid核壳体——nucleocapsid囊膜——envelope第二章光学显微镜——light microscope分辨率——resolution相差显微镜——phase-contrast microscope微分干涉显微镜——differential-interference microscope录像增差显微镜——video-enhance microscope荧光显微镜——fluorescence microscope绿色荧光蛋白——green fluorescent protein, GFP激光扫描共焦显微镜——laser scanning confocal microscope, LSCM全内反射荧光显微术——total internal reflection fluorescence microscopy 光激活定位显微术——photoactivated localization microscopy, PALM随机光学重构显微术——stochastic optical reconstruction microscopy受激发射损耗显微术——stimulated emission depletion microscopy结构照明显微术——structured-illumination microscopy, SIM电子显微镜——electron microscope, EM电荷耦合器件——charge-coupled device, CCD超薄切片——ultrathin section负染色技术——negative staining冷冻蚀刻技术——frezze etching快速冷冻深度蚀刻技术——quick freeze deep etching低温电镜技术——cryo-electron microscopy单颗粒分析技术——single particle analysis电子断层成像技术——electron tomography背散射电子成像——back scattered electron imaging扫描电镜——scanning electron microscope, SEM光-电关联技术——correlative light microscopy and electron microscopy 扫描隧道显微镜——Scanning tunnel microscope, STM原子力显微镜——atomic force microscope, AFM免疫印记——western blotting放射免疫沉淀——radioimmuno-precipitation原位杂交——in situ hybridization流式细胞术——flow cytometry原代细胞——primary culture cell传代细胞——subculture cell单层细胞——single layer cell细胞系——cell line有限细胞系——finite cell line永生细胞系——infinite cell line连续细胞系——continuous cell line细胞株——cell strain成纤维样细胞——fibroblast like cell上皮样细胞——epithelial like cell外殖体——explant愈伤组织——callus细胞融合——cell fusion电融合技术——electrofusion methodB淋巴细胞杂交瘤技术——B-lymphocyte hybridoma technique 单克隆抗体——monoclonal antibody胞质体——cytoplast核质体——karyoplast细胞松弛素B——cytochalasin B显微操作——micromanipulation微量注射——microinjection荧光漂白恢复技术——fluorescence photobleaching recovery, FPR 荧光恢复——fluorescence recovery酵母双杂交系统——yeast two-hybrid systemDNA结合域——DNA binding domain转录激活域——activation domain荧光共振能量转移——fluorescence resonance energy transfer, FRET 放射自显影技术——autoradiography第三章细胞质膜——plasma membrane细胞内膜系统——internal membrane生物膜——biomembrane单位膜模型——unit membrane model流动镶嵌模型——fluid mosaic model菌紫红质——bacteria rhodopsin脂筏模型——lipid raft model辛德毕斯病毒——sindbis virus, SbV甘油磷脂——glycerophosphatide鞘脂——sphingolipid固醇——sterol磷脂酰胆碱——phosphatidylcholine, PC(卵磷脂)磷脂酰乙醇胺——phosphatidylethanolamine, PE磷脂酰丝氨酸——phosphatidyserine, PS磷脂酰肌醇——phosphaditylinositol, PI心磷脂——cardiolipin鞘磷脂——sphingomyelin, SM磷脂——phospholipid豆固醇——stigmasterol麦角固醇——ergosterol翻转酶——flippase脂质体——liposome微团——micelle膜蛋白——membrane protein周边膜蛋白——peripheral membrane protein外在膜蛋白——extrinsic membrane protein整合膜蛋白——integral membrane protein内在膜蛋白——intrinsic membrane protein脂锚定膜蛋白——lipid-anchored membrane protein 磷脂酶——phospholipase蛋白聚糖——proteoglycan磷脂酰肌醇糖脂——glycosylphosphaditylinositol跨膜蛋白——transmembrane protein单次跨膜蛋白——single-pass transmembrane protein 多次跨膜蛋白——multipass transmembrane protein 孔蛋白——porin卷曲结构——coiled-coil水孔蛋白——aquaporin去垢剂——detergent微团临界浓度——critical micelle concentration,CMC相变温度——phase transition temperature扩散常数——diffusion constant细胞外表面——extrocytoplasmic surface, ES外小叶——outer leaflet原生质表面——protoplasmic surface, PS内小叶——inner leaflet细胞外小叶断裂面——extrocytoplasmic face,EF原生质小叶断裂面——protoplasmic face,PF脂肪细胞——adipocyte鞭毛——flagellum纤毛——cilium微绒毛——microvillus膜相关的细胞骨架——membrane associated cytoskeleton 肌动蛋白——actin基于肌动蛋白的膜骨架——actin-based membrane skeleton 细胞皮层——cortex血影——ghost血影蛋白(或红膜肽)——spectrin锚蛋白——ankyrin血型糖蛋白——glycoprotein内收蛋白——adducin阀蛋白——flotillin膜脂微区——membrane lipid microdomain 阿尔兹海默症——Alzheimer disease。
Biosensors and Bioelectronics 25 (2010) 1829–1833Contents lists available at ScienceDirectBiosensors andBioelectronicsj o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /b i osShort communicationMembraneless enzymatic biofuel cells based on graphene nanosheetsChang Liu a ,Subbiah Alwarappan a ,Zhongfang Chen b ,Xiangxing Kong a ,Chen-Zhong Li a ,∗a Nanobioengineering/Bioelectronics Laboratory,Department of Biomedical Engineering,Florida International University,10555W Flagler Street,Miami,FL 33174,United States bDepartment of Chemistry,Institute for Functional Nanomaterials,University of Puerto Rico,San Juan,PR 00931,United Statesa r t i c l e i n f o Article history:Received 3August 2009Received in revised form 29October 2009Accepted 11December 2009Available online 22 December 2009Keywords:Graphene nanosheets Biofuel cell Sol–gel Enzyme GlucoseMiniaturized power source Biomedical devicea b s t r a c tThe possibility of employing graphene sheets as a potential candidate for the construction of biofuel cells is reported in this paper.Initially,graphene sheets were chemically synthesized and characterized by surface characterization techniques.Following this,graphene was employed to fabricate the anode and cathode in the biofuel cell.The anode of the biofuel cell consists of a gold electrode on which we co-immobilized graphene –glucose oxidase using silica sol–gel matrix.Voltammetric measurements were conducted to quantitatively evaluate the suitability of employing graphene sheets as an electrode dopant and its performance was compared with single walled carbon nanotubes (SWCNTs).The cathode of the biofuel cell was constructed in a similar method except that graphene was co-immobilized with bilirubin oxidase.Finally,two membraneless enzymatic biofuel cells,one using graphene sheets and the other using SWCNTs,were constructed and their performances were compared.Upon comparison,graphene based biofuel cell exhibited a maximum power density of about 24.3±4W (N =3),which is nearly two times greater than that of the SWCNTs biofuel cell,and the performance of the graphene biofuel cell lasted for 7days.© 2009 Elsevier B.V. All rights reserved.1.IntroductionIn recent years,there has been considerable interest towards the development of enzymatic biofuel cells (EBFC)as they can be employed as an in vivo power source for implantable medical devices such as pacemakers,micro drug pumps,deep brain stim-ulators,etc.(Gao et al.,2007;Barton et al.,2004;Bullen et al.,2006;Kim et al.,2006;Ikeda and Kano,2003).The most attrac-tive feature of this EBFC is that they can utilize glucose or other carbohydrates abundantly present in the human body as a fuel.To date,there have been considerable efforts among many researchers to fabricate practical EBFC devices out of different theoretical con-cepts (Mano et al.,2002;Willner,2002;Service,2002;Katz et al.,2005;Katz and Willner,2003).Glucose,a major component of the human serum,is most widely used as the fuel for theses EBFCs.However,low power density and poor stability of the EBFC are the two major challenges to be rectified in the upcoming days.A non-compartmentalized glucose |O 2biofuel cell possessing a maximum power of 4W cm −2and a life time of 48h was reported (Katz et al.,1999),while an abiotically catalyzed glucose fuel cell exhibited a maximum power density of 3.3W cm −2with a life time of 224days (Kerzenmachera et al.,2008).In another study,a cell lifetime of up to 45days was reported with enzymes entrapped in a modi-∗Corresponding author.Tel.:+13053480120;fax:+13053486954.E-mail address:licz@fi (C.-Z.Li).fied Nafion membrane (Moore et al.,2004).Furthermore,an EBFC employing glucose oxidase (GOx)and laccase as biocatalysts gen-erated a maximum power density of 5.49W cm −2using glucose as a fuel (Liu and Dong,2007).The low power density of the EBFC in comparison with conven-tional inorganic fuel cells is due to location of the active site of the enzyme buried deep under the protein shell hindering the electron transfer pathway between the enzyme’s active site and the elec-trode (Liu and Dong,2007).In order to overcome this issue,most researchers employ carbon nanotubes (CNTs)to decrease the elec-tron transfer resistance and increase the electrode surface area (Gao et al.,2007;Li et al.,2008;Lim et al.,2007;Liu and Dong,2007).The covalent binding of the enzyme with CNTs has resulted in a faster electron transfer rate.However,a complex chemical treat-ment process of CNTs has to be performed in order to create active binding sites on the edge of the CNTs.Such a process hinders the mass production of this electrode (Li et al.,2005;Imamura et al.,1995;Degani and Heller,1988).Furthermore,a number of redox mediators are widely used to boost the electron transfer rate.The redox potential of the mediator used should lie between the redox potential of the enzyme and that of the electrode.As a result,the electrons are gradually shuttled from the enzyme to the mediator and then to the electrode (Lim et al.,2007).Graphene,a two-dimensional (2D)nanostructure of carbon dis-covered in 2004,possesses a very large surface area of about 2630m 2g −1,which is about the size of a football stadium (Stoller et al.,2008).Further,the electrons on the graphene surface move0956-5663/$–see front matter © 2009 Elsevier B.V. All rights reserved.doi:10.1016/j.bios.2009.12.0121830 C.Liu et al./Biosensors and Bioelectronics25 (2010) 1829–1833ballistically over the sheet without any collisions with mobili-ties as high as10,000cm2V−1s−1at room temperature(Geim and MacDonald,2007;Novoselov et al.,2004).In addition,graphene was found to exhibit an excellent conductivity.In our previous work,a four-point probe method was used to measure the conduc-tance of graphene and it was calculated to be64mS cm−1,which is approximately60times more than that of SWCNTs(Alwarappan et al.,2009;Dai et al.,2007).It is also worth mentioning that graphene possesses a number of surface active functional moieties such as carboxylic,ketonic,quinonic and C C.Of these,the carboxylic and ketonic groups are reactive and can easily bind covalently with GOx.The presence of extended C C conjugation in graphene is also expected to shuttle electrons.Nonetheless,to the best of our knowl-edge,there are no reports available in literature which employs graphene as an electrode material for EBFC.The biocompatible sol–gel encapsulation method is widely pre-ferred to immobilize biomolecules such as proteins,nucleic acids and cells.The microstructured porous sol–gel matrix prevents the biomolecules from being denatured by pH or temperature and thus retains their long-term bioactivity(Kandimalla et al.,2006).On the other hand,the porous structure of the sol–gel matrix allows diffu-sion of the fuel towards the electrode surface for the redox reaction to occur.In the present work,we describe an EBFC system essen-tially based on silica sol–gel immobilized graphene sheets/enzyme composite electrodes.Further,we employ glucose oxidase(GOx) and bilirubin oxidase(BOD)as the anodic and cathodic enzyme, respectively(Komaba et al.,2008;Kuwahara et al.,2008,2009; Willner et al.,2009;).In addition,we employ ferrocenemethanol (FM)and2,2 -azinobis(3-ethylbenzothiazoline-6-sulfonic acid) diammonium salt(ABTS)(Lim et al.,2007)as anodic and cathodic mediators,respectively.Due to the specific catalytic activity of these enzymes,the proton exchange membrane is eliminated to facilitate the fabrication process.After the fabrication of graphene based membraneless EBFC,the maximum power density is found to be24.3±4W(N=3).After7days,the power output dropped to50%of its original power output.For comparison,a similar EBFC system was constructed using single walled carbon nan-otubes(SWCNTs)and the power output was measured by the same method.2.Experimental2.1.Chemicals and instrumentsGOx(E.C.1.1.3.4,from Aspergillus niger)and BOD(E.C.1.3.3.5, from Myrothecium verrucaria)were purchased from MP Biomedi-cals(Solon,OH).FM,ABTS and glucose were all obtained from VWR International Inc.(West Chester,PA).The stock glucose solution was left at room temperature for24h to mutarotate before use. Redox mediators FM and ABTS were dissolved in0.1M PBS(pH 7.4).SWCNTs were purchased from STREM Chemicals(Newbury-port,MA),Polyethylene Glycol(PEG)from Promega Co.(Madison, WI),Tetramethoxysilane(TMOS)from Alfa Aesar(Ward Hill,MA) and Hydrazine Hydrate from Aldrich(St.Louis,MO)were used as-received.Electrochemical measurements were performed using a CHI-630A electrochemical analyzer(CH Instruments Inc.).Cyclic voltammetric measurements were performed in a10mL cell with conventional three electrode set up consisting of a modified gold electrode as the working electrode,an Ag|AgCl reference electrode (3M KCl)and a platinum counter electrode.Raman spectroscopic measurements were conducted at room temperature using a Raman spectrometer in the back-scattering configuration.The514.5nm Ar+laser was operating at50mW.Fol-lowing this,afield emission scanning electron microscope(SEM) JEOL JSM6330F(model)was employed for observing the surface of graphene sheets and the porous structure of silica sol–gel matrices.2.2.Preparation of graphene based EBFC and SWCNT based EBFC 2.2.1.Synthesis of graphene sheetsInitially,graphene was synthesized as follows:Graphitic oxide (GO)was prepared from graphite powder as described by Hummers and Offeman(1958).GO thus obtained was then subjected to a seri-ous of chemical steps to yield graphene(Alwarappan et al.,2009).2.2.2.Preparation of anode and cathode and fabrication of EBFCThe TMOS sol–gel employed in this study is obtained by the hydrolysis followed by the condensation of TMOS(Lim et al.,2007). Briefly,we prepare TMOS sol as follows:7.5mL of TMOS was mixed with1.7mL of DI water and200L of0.04M HCl.In order to initi-ate hydrolysis,the mixture was sonicated in an ice bath for15min and stored at4◦C for24h.Following this,2mg of graphene was mixed with50L of PEG and sonicated for15min to yield uniform dispersion of graphene in PEG.The mechanism of the graphene based membraneless EBFC assembly employed in this work is shown in(Fig.1A).The anode and cathode of the graphene based EBFC was designed by mixing 100L of8mM FM PBS solution with2.5mg of GOx(for cathode GOx is replaced by BOD and FM by ABTS).The resulting mixture was then added to the foretold dispersion of graphene in PEG and thoroughly vortexed for a minute followed by the addition of50L of TMOS sol and vortexed for another40s.Soon after gelation,it was casted on a gold plate electrode(0.5cm×2.0cm)into a1mm thin layer.Both the anode and cathode were glued onto two self-designed Teflon holders which were then clamped together and separated using spacers in between them(Fig.1B).Prior to use,the biofuel cell assembly was stored in pH7.4PBS(0.1M)at4◦C for 24h for further gelation and mechanical stability of the sol–gel thin layer.Moreover,the SWCNT based EBFC was designed and tested using the same strategy.Finally,biofuel cell experiments were car-ried out in a25mL beaker containing100mM glucose PBS solution in which the previously assembled EBFC and Ag|AgCl reference electrode(not shown)were immersed(Fig.1C).After a stable open circuit voltage(V oc)was achieved,varying external loads(500 to 500k )were applied across the anode and cathode and the power outputs were obtained.3.Results and discussion3.1.Surface characterization of graphene sheets and silica sol–gel matricesThe stability of the enzymes and the diffusion of fuel towards the electrode surface were two crucial factors to achieve high power density and long-term activity of the EBFC.The microporous struc-ture of the sol–gel can act as cages to protect immobilized enzymes from being denatured and leaching out while also providing both glucose and oxygen sufficient access to the enzymes.In this case, the size of the sol–gel cages should be slightly larger than that of the graphene-enzyme complexes.To illustrate and compare the sizes of the sol–gel cages and graphene-enzyme complexes,SEM was used to observe the microstructure of the sol–gel matrices sur-faces(Fig.2A)and a single graphene sheet(Fig.2B).The length of a graphene sheet was found to be approximately5m,which is sim-ilar to the size of a sol–gel cage.Further,the SEM micrographs of a single graphene sheet looks like a“petal of aflower”and indicates that graphene possess an ordered and soft texture.Raman spectrum of graphene exhibited a D-band peak at 1363cm−1due to the breathing mode ofÄ-point phonons of A1gC.Liu et al./Biosensors and Bioelectronics25 (2010) 1829–18331831Fig.1.(A)Graphene based membraneless EBFC components;(B)EBFC test setup;(C)schematic configuration of the graphene based membraneless EBFC employing GOx|FM and BOD|ABTS functionalized electrodes as biocatalytic anode and cathode,respectively.Fig.2.(A)SEM picture of the porous structure of the silica sol–gelfilm;(B)SEM picture of a single graphene sheet;(C)Raman spectra of(a)graphene nanosheets and(b) SWCNTs[the inset is the RBM of SWCNTs];(D)cyclic voltammogram of(a)graphene based anode(b)SWCNT based anode in100mM glucose solution and(c)graphene based anode in PBS(PH7.4)without glucose(scan rate:500mV s−1).1832 C.Liu et al./Biosensors and Bioelectronics25 (2010) 1829–1833symmetry,a G-band peak at1596cm−1that corresponds to the first-order scattering of the E2g phonons(Choi et al.,2006)as shown in Fig.2C(a).The Raman features are consistent with a previous report(Choi et al.,2006),indicating that the resulting product at the end of our synthesis is graphene.On the other hand,the spec-trum of SWCNTs exhibited characteristic peaks centered at220, 1335,and1590cm−1due to the radial breathing mode,disordered D-band and tangential G-band respectively as shown in Fig.2C(b). Upon calculation,the intensity ratios I D/I G of graphene and SWCNTs were found to be0.55and0.35respectively indicating graphene’s greater sp2character.This enhanced sp2character of graphene is responsible for shuttling the electrons and assisting in the better performance of the EBFC.parison of electrochemical performances of graphene based anode and SWCNT based anodeTo demonstrate the suitability of graphene as an electrode mate-rial for the construction of EBFC,initially we performed a cyclic voltammetric experiment by employing a graphene based anode as the working electrode and is shown in Fig.2D(a).For compar-ison,a similar experiment was performed using a SWCNT based anode and the corresponding voltammogram is shown in Fig.2D(b). All these electrochemical measurements were performed using 100mM air saturated glucose solution in PBS(PH7.4)as an elec-trolyte at room temperature.Results indicated that the graphene based anode exhibited almost two times higher current than the SWCNT based anode.Further,another control experiment was also performed using a graphene based anode in PBS solution(PH7.4) in the absence of glucose and is shown in Fig.2D(c).Upon com-parison of Fig.2D(a)and(c),the catalyzed current generated from the glucose can be easily observed,which indicates that graphene has retained the bioactivity of the GOx.Moreover,a similar set of experiments were performed to evaluate the electrochemical per-formances of the graphene based cathode.The catalyzed current of the graphene based cathode was found to be approximately two times higher than that of the SWCNT cathode(Fig.S1a and b),and the bioactivity of the graphene-BOD complex was also evidenced by comparing the cyclic voltammograms with and without oxygen in the solution(Fig.S1a and c)(supplementary materials).From these results,it is evident that enzymatic electrodes based on graphene exhibited a larger current density than those based on SWCNTs. The observed performance of the graphene based electrode can be attributed to its larger surface area than its counterpart(SWC-NTs).Moreover,the larger number of dislocations and electroactive functional groups in graphene than in SWCNTs can covalently bind with more GOx or BOD,thereby catalysing the redox reactions more efficiently.In addition,the large amount of defects induced by reduction process of graphene oxide also provides ideal actives sites for further chemical modification.From the above compari-son,it is evident that graphene is an appropriate electrode material which can be employed to design the EBFC reported in this work.3.3.Evaluation of the performance of graphene based EBFCIn literature,there are numerous reports available that describe the development of EBFC by adding mediator together with the fuel (Lim et al.,2007;Liu and Dong,2007).However,such configura-tions are not feasible for future in vivo applications since human plasma does not contain any redox mediator.To overcome this difficulty,we designed a novel,robust and membraneless EBFC in which the redox mediators(FM and ABTS)are co-immobilized together with graphene and enzyme(GOx and BOD)onto the anode and the cathode,respectively.After assembling the graphene based membraneless EBFC(as described in the experimental section),the assembly was placed inside100mM air saturated glucose solution (fuel)taken in a25mL beaker.The V oc and the maximum current density of this graphene based EBFC were found to be0.58±0.05V (N=3)and156.6±25A cm−2(N=3),respectively.Similarly,the assembly of SWCNT based membraneless EBFC was tested under the same conditions,the V oc and maximum current density were found to be0.39±0.04V(N=3)and86.8±13A cm−2(N=3), respectively.The current–voltage behaviors at different external loads of the foretold two membraneless EBFC systems are shown in Fig.3A.Although the ideal cell voltage is determined by the dif-ference in the formal potentials of the fuel substrate and oxidizer, graphene based EBFC exhibited a0.19V higher V oc than its counter-part with the same fuel and oxidizer.The observed0.19V decrease in the V oc of the SWCNT based EBFC can be attributed to the leach-ing of the enzymes GOx and BOD out of the sol–gel.Such leaching is possibly due to the unfavorable interaction of3D SWCNTs with the enzymes as a result of the lack of active binding sites.In addition,the observed decrease in the V oc of the SWCNT based EBFC is also due to the kinetic limitation of electron transfer in the SWCNTs and higher ohmic resistance(Katz et al.,1999;Alwarappan et al.,2009).Simi-larly,the observed decrease in the maximum current density of the SWCNT based EBFC is caused by the diminished electron transfer rate of the SWCNTs.On the other hand,graphene possess a greater density of reactive functional groups such as–C O,O–C O,C C,–O–and results in the favorable interaction with the free terminals of GOx and BOD such as–NH2,giving rise to a strong covalent bond. As a result,the discrepancies of SWCNTs were not observed in2D graphene based EBFC which exhibits a higher V oc and maximum current density than its SWCNT counterpart.Further,the power densities of these two systems were calcu-lated and shown in Fig.3B.The maximum power density of the graphene based EBFC was found to be24.3±4W(N=3)at0.38V (load15k ),while the power density of the SWCNT based EBFC was found to be7.8±1.1W(N=3)at0.25V(load15k ).Inter-estingly,the V oc and the maximum current density of thegrapheneFig.3.(A)Current–voltage behaviors of( )graphene based EBFC and( )SWCNT based EBFC with different external loads in100mM glucose solution;(B)power densities at different cell voltage for( )graphene based EBFC and( )SWCNT based EBFC in100mM glucose solution;(C)stability of the assembled graphene based EBFC as a function of time.The external load in the test was15k .Other conditions are the same as those in(A)and(B).C.Liu et al./Biosensors and Bioelectronics25 (2010) 1829–18331833based EBFC are twice that of the SWCNT based EBFC.Moreover,the calculated maximum power density of the graphene based EBFC is found to be three times that of its counterpart.In order to evaluate the stability of the graphene based EBFC,the system was stored in PH7.4PBS solution at4◦C and tested every day with a15k exter-nal load.After thefirst24h,it had lost6.2%of its original power ter,the power output was found to decay slowly and becomes50%of its original power output after7days as shown in Fig.3C.In modern EBFC development,the biostability of the enzymes is the main factor to retain the long-term performance of the mem-braneless EBFC.However,no significant breakthrough has been achieved on the EBFC’s lifetime in our work.Thus,our future research focuses on the study of different enzyme immobilization methods to lengthen our EBFC’s lifetime(Habrioux et al.,2008).On the other hand,the improvement of power output can be achieved by optimizing the electrode geometry.Microporous gold or carbon based electrodes can be used as current collectors instead of the gold plate electrode used in this work(Imamura et al.,1995).4.ConclusionIn the present work,we successfully demonstrated the possibil-ity of employing graphene as a potential candidate for designing the anode and cathode of the membraneless EBFC.Further,our elec-trochemical results demonstrated that the catalytic efficiency of graphene based anodes is twice that of SWCNT based anodes.As a result,the graphene based EBFC yields a maximum power den-sity of24.3±4W cm−2(N=3)with a lifetime of7days,which is three times larger than the maximum power density generated by the SWCNT based EBFC.Another novelty of this design is that the mediators were entrapped within the sol–gel along with graphene-enzyme complexes,thereby offering a practical strategy for future in vivo study of the power generation device.AcknowledgementsWe would like to thank Dr.Srinivas Kulkarni and the Advanced Material Engineering Research Institute(AMERI)at FIU for helping us with the SEM.This current work is partially supported under grant FA9550-07-1-0344of the Department of Defense/Air Force Office of Scientific Research,NSF MRI0821582NSF Grant CHE-0716718,the Institute for Functional Nanomaterials(NSF Grant 0701525),and the US EPA Grant RD-83385601and the2008FIU Faculty Research Award to Dr.Chenzhong Li.Appendix A.Supplementary dataSupplementary data associated with this article can be found,in the online version,at doi:10.1016/j.bios.2009.12.012.ReferencesAlwarappan,S.,Erdem,A.,Liu,C.,Li,C.,2009.J.Phys.Chem.C113,8853–8857. 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分子生物学重要概念AAbundance (mRNA 丰度):指每个细胞中mRNA 分子的数目。
Abundant mRNA(高丰度mRNA):由少量不同种类mRNA组成,每一种在细胞中出现大量拷贝。
Acceptor splicing site (受体剪切位点):内含子右末端和相邻外显子左末端的边界。
Acentric fragment(无着丝粒片段):(由打断产生的)染色体无着丝粒片段缺少中心粒,从而在细胞分化中被丢失。
Active site(活性位点):蛋白质上一个底物结合的有限区域。
Allele(等位基因):在染色体上占据给定位点基因的不同形式。
Allelic exclusion(等位基因排斥):形容在特殊淋巴细胞中只有一个等位基因来表达编码的免疫球蛋白质。
Allosteric control(别构调控):指蛋白质一个位点上的反应能够影响另一个位点活性的能力。
Alu-equivalent family(Alu 相当序列基因):哺乳动物基因组上一组序列,它们与人类Alu家族相关。
Alu family (Alu家族):人类基因组中一系列分散的相关序列,每个约300bp长。
每个成员其两端有Alu 切割位点(名字的由来)。
α-Amanitin(鹅膏覃碱):是来自毒蘑菇Amanita phalloides 二环八肽,能抑制真核RNA聚合酶,特别是聚合酶II 转录。
Amber codon (琥珀密码子):核苷酸三联体UAG,引起蛋白质合成终止的三个密码子之一。
Amber mutation (琥珀突变):指代表蛋白质中氨基酸密码子占据的位点上突变成琥珀密码子的任何DNA 改变。
Amber suppressors (琥珀抑制子):编码tRNA的基因突变使其反密码子被改变,从而能识别UAG 密码子和之前的密码子。
Aminoacyl-tRNA (氨酰-tRNA):是携带氨基酸的转运RNA,共价连接位在氨基酸的NH2基团和tRNA 终止碱基的3¢或者2¢-OH 基团上。
ABC模型:即控制花形态发生的模型。
该模型把四轮花器官同时发生作为根本前提,强调花形态突变体产生不同花器官的生理位置变化。
该模型中正常花的四轮构造的形成是由三组基因A、B、C共同作用完成的,每一轮花器官特征的决定分别依赖于A、B、C三组基因中的一组或两组基因的正常表达oA组基因控制萼片、花瓣的发育,B组基因控制花瓣、雄蕊的发育,C组基因控制雄蕊、心皮的发育oA、C组基因互相拮抗,抑制对方在自身所控制的区域中表达,如其中任何一组或更多的基因发生突变而丧失功能,花的形态就出现异常。
AP位点(APsite):所有细胞中都带有不同类型、能识别受损核酸位点的糖苷水解酶,它能特异性切除受损核苷酸上的N-β糖苷键,在DNA链上形成去嘌呤或去嘧啶位点,统称为AP位点。
cDNA(plementaryDNA):在体外以mRNA为模板,利用反转录酶和DNA聚合酶合成的一段双链DNA。
C值(Cvalue):通常是指一种生物单倍体基因组DNA的总量,以每细胞内的皮克(pg)数表示。
C值反常现象〔Cvaluedox〕:也称C值谬误。
指C值往往与种系的进化复杂性不一致的现象,即基因组大小与遗传复杂性之间没有必然的联系,某些较低等的生物C值却很大,如一些两柄动物的C值甚至比哺乳动物还大。
Dane颗粒:HBV完整颗粒的直径为42nm,称为Dane颗粒,由外膜和核壳组成,有很强的感染性。
DNA〔deoxyribonucleicacid〕:脱氧核糖核酸,是世界上所有高等真核生物和绝大局部低等生物的遗传物质。
DNA的半保存复制〔semi-conservativereplication〕:DNA在复制过程中,每条链分别作为模板合成新链,产生互补的两条链。
这样新形成的两个DNA分子与原来DNA分子的碱基顺序完全一样。
因此,每个子代分子的一条链来自亲代DNA,另一条链那么是新合成的,这种复制方式被称为DNA的半保存复制。
DNA的半不连续复制〔serru-cliscontinuousreplication〕:DNA复制过程中前导链的复制是连续的,而另一条链,即后随链的复制是中断的、不连续的。
高三英语植物遗传修饰单选题50题1. The process of plant genetic modification often involves ____ genes from one organism to another.A. transferringB. transformingC. transmittingD. transplanting答案:A。
解析:本题考查与植物遗传修饰相关的动词辨析。
A选项transferring有转移、传递( 尤指将某物从一个地方、人或事物转移到另一个地方、人或事物)的意思,在植物遗传修饰中,经常涉及将基因从一个生物体转移到另一个生物体,符合概念。
B选项transforming主要表示改变、转变,强调的是形态、性质等方面的彻底改变,而不是基因的转移这个概念。
C选项transmitting侧重于传播、传送( 信号、信息等),不太适用于基因的操作。
D选项transplanting 主要指移植 器官、植物等),通常是比较宏观的物体,与基因的操作不符。
2. In plant genetic modification, a ____ is a small circular piece of DNA that can be used to carry new genes into a plant cell.A. plasmidB. plastidC. plasmodiumD. plasma答案:A。
解析:A选项plasmid(质粒)在植物遗传修饰中是一种小的环状DNA,可以用来携带新基因进入植物细胞,这是植物遗传修饰中重要的工具。
B选项plastid(质体)是植物细胞中的一种细胞器,与携带基因进入细胞的概念不同。
C选项plasmodium( 疟原虫)与植物遗传修饰毫无关系。
D选项plasma(血浆、等离子体)也与植物遗传修饰概念不相关。
3. Which of the following is a common method for plant genetic modification?A. Cross - breedingB. Mutation breedingC. Gene editingD. All of the above答案:D。
2001年研究生入学考试细胞生物学一、名词解释(2.5*10)1、apoptosis body2、receptor mediated endocytosis3、lamina4、nuclease hypersensitive site5、gap junction6、Hayflick limitation7、kinetochore8、molecular chaperones9、leader peptide10、dedifferentiation二、简答题5*81. 冰冻断裂术将溶酶体膜撕裂出PS,ES,PF,EF四个面,请绘一简图标明。
2. 医生对心脏已经停止跳动的病人采取电击抢救,请说明其心肌细胞是如何同步启搏的。
3. 为什么凋亡细胞的核DNA电泳图谱呈梯状分布带。
而病理坏死细胞却呈弥散状连续分布?4. 将某动物细胞的体细胞核移植到另一去核的体细胞之中,然后其余实验步骤完全按照动物克隆的方式,问能否培育出一头克隆动物来?为什么?5. 切取病毒感染马铃薯植株的顶芽进行组织培养,这是大量繁育无毒苗的成功技术。
试述其去除病毒的原因。
6. 有人认为既然已经有放大几十万倍的电镜,可以不用光镜了,请反驳这种观点的错误。
7. 出生6个月之内的婴儿可由母乳获得抗病的抗体,试述这些抗体是如何由母亲血液转到婴儿血液中的。
8. 1999年报道,我国科学家成功实现将离体的B型血液改造成O型,请解释其原理。
三、问答题(前两题10,最后一题15)1. 概述Cyclin与CDK在细胞周期调控的工作机制及其在各期引起的下游事件。
2. 试述在细胞质中合成的线粒体内膜蛋白及叶绿体类囊体膜蛋白是如何运送到位与装配的。
3. 综述细胞外被中糖蛋白在细胞内合成,组装和运输的全过程及其对于细胞的主要生理功能。
2002年细胞生物学一、名词解释2.5*101、nucleosome2、contact inhibition3、telomerase4、exocytosis5、Gap junction6、kinetochore7、heterochromatin8、channel protein9、dynein arm10、molecular switches二、简答题5*81. 分别以一句话简述1999年和2001年诺贝尔奖获奖项目中有关细胞生物学的内容。
第一章细胞遗传学基础细胞(cell)细胞膜(cell membrane)质膜(plasma membrane,plasmalemma)细胞质(cytoplasm)细胞器(organelle)基质(cytoplasmic matrix)线粒体(mitochondria)内质网(endoplasimic,ER)粗面内质网(rough reticulum,rER)滑面内质网(smooth endoplasmic reticulum,sER)高尔基体(Golgi body)中心体(centrosome)核糖体(ribosome)附着核糖体(attached ribosomes)游离核糖体(free ribosomes)核膜(nuclear membrane)核基质(nuclear matrix)核液(nuclear sap)核仁(nucleolus)染色质(chromatin)常染色质(euchromatin)异染色质(heterochromatin)结构异染色质(constitutive heterochromatin)兼性异染色质(facultative heterochromatin)染色体(chromosome)着丝粒(centromere)主缢痕(primary constriction)中着丝粒染色体(metacentric chromosome)近中着丝粒染色体(submetacentric 近端着丝粒染色体(subtelocentric 端着丝粒(te locentric chromosome)次缢痕(secondary constriction)随体(satellite)端粒(telomere)核小体(nucleosome)螺线体(solenoid)单倍体(haploidy)多倍体(polyploid)异源多倍体(allopolyploid)同源多倍体(autopolyploid)双精受精(disperm y)合子(zygote)组成型多倍体(constitutional polyploid)缺倍体(nulliploid)非整倍性(aneuploi dy)亚倍体(hypoploid)单体性(monosomy)缺对性(nullisomy)超二倍体(hyperploid)三体性(trisomy)双三体性(ditrisomy)四体性(tetrasomy),染色体不分离(nondisjunction)后期延迟(anaphase lag)后期延迟运动(delayed movement,lagging)混倍性(mixoploidy)镶嵌型(mosaicism)嵌合型(chimerism)细胞(cell)细胞膜(cell membrane)质膜(plasma membrane,plasmalemma)细胞质(cytoplasm)细胞器(organelle)基质(cytoplasmic matrix)线粒体(mitochondria)内质网(endoplasimic,ER)粗面内质网(rough reticulum,rER)滑面内质网(smooth endoplasmic reticulum,sER)高尔基体(Golgi body)中心体(centrosome)核糖体(ribosome)附着核糖体(attached ribosomes)游离核糖体(free ribosomes)核膜(nuclear membrane)核基质(nuclear matrix)核液(nuclear sap)核仁(nucleolus)染色质(chromatin)常染色质(euchromatin)异染色质(heterochromatin)结构异染色质(constitutive heterochromatin)兼性异染色质(facultative heterochromatin)染色体(chromosome)着丝粒(centromere)主缢痕(primary constriction)中着丝粒染色体(metacentric chromosome)近中着丝粒染色体(submetacentric 近端着丝粒染色体(subtelocentric 端着丝粒(te locentric chromosome)次缢痕(secondary constriction)随体(satellite)端粒(telomere)核小体(nucleosome)螺线体(solenoid)超螺线体(super solenoid)核型(karyotype)核型分析(karyotype analysis)核型模式图(idiogram)C分带(centromere banding)Q分带(quinacrine banding)G分带(Giemsa banding)R分带(reverse banding)N分带(N banding)高分辨显带(high-resolution banding)细胞周期(cell cycle)间期(interphase)有丝分裂(mitosis)减数分裂(meiosis)有丝分裂期(M phase)细线期(leptonema)凝线期(synizesis)偶线期(zygonema)联会(synapsis)联会复合体(synapt onemal complex,SC)粗线期(pachynema)双价体(bivalent)双线期(diplonema)交叉端化(terminalization of chiasmata)终变期(diakinesis)浓缩期(diakinesis)染色体重建(chromosome reconstruction)缺失(deletion)重复(duplication)倒位(inversion)易位(translocation)中间缺失(interstitial deletion)假显性现象(pseudo dominance)顺接重复(tandem duplication)反接重复(reverse duplication)不等交换(unequal crossing over)剂量效应(dosage effect)臂内倒位(paracentric inversion)臂间倒位(pericentric inversion)简单易位(simple translocation)相互易位(reciprocal transloca tion)移位易位(shift translocation)复合易位(complex translocation)等臂染色体(isochromosome)第二章分子遗传学基础基因gene 外显子exon内含子intron 基因组genome密码子codon 起始密码子initiator同义密码子synonym 多义密码子ambiguous codon核糖体ibosome 表观基因组学epigenomics启动子promoter 增强子enhancer沉默子silencer 化学修饰chemical modification基因突变gene mutation) 碱基base回复突变reversion) 暗修复dark repair)切除修复excision repair) 缺口修复gap repair错配修复mismatch repair 重组recombination同源重组homologous recombination 转座transposition限制性核酸内切酶restriction endonuclease 载体vector第三章免疫遗传学基础免疫力immunity 免疫防immunologic defence自我稳定homeostasis 自身免疫病autoimmune disease非特异性免疫non-special immunity 特异性免疫special immunity免疫应答immune response 细胞免疫应答cellular immune respons 免疫系统immune system 免疫球蛋白mmunoglobulin (Ig)抗体antibody (Ab) 结构域domain型群phenogroup 调理作用opsonization基因簇gene cluster 重组信号序列recombination signal sequence (RSS) 类别转换class switch 同种型转换isotype switch质量性状qualititative character 遗传descendiblity heredity inherit 染色体chromosome 性染色体sex chromosome常染色体euchromosome 伴性遗传sex-linked inheritance限性遗传sex—limited inheritance 从性遗传sex—influenced inheritance 血型blood group 显性上位作用dominant epistasis隐性上位作用recessive epistasis 重叠作用duplicate effect基因座位gene locus 等位基因allele复等位基因multiple alleles 上位基因epistatic gene性连锁基因sex-linked gene 显性性状dominant characters隐性性状recessive characters 育种breeding杂交育种cross breeding 伴性基因sex-linked genes隐性纯合子allozygote 杂合子heterozygote显性基因dominant gene 隐性基因recessive gene就巢性broodiness自别雌雄auto-sexing 骡鸭mule duck测交test cross 隐性致死recessive lethal半致死基因semi-lethal gene 标记基因marker gene父本male parent 母本female parent繁殖力fecundity 遗传效应genctic effect杂交优势heterotic vigor 经济性状practical characters碱基对base pair 遗传缺陷genetic defects下位基因hypostatic gene 基因文库gene library完全显性complete dominance 不完全显性incomplete dominance共显性codominance 连锁遗传linkage inheritance数量性状quantitative trait 表型值phenotypic value基因型值genotypic value 数量性状基因座quantitative trait locus主效基因major gene 上位效应epistatic effect系统环境效应systimatic evirenmental effect 随机环境效应randomatic envirenmental effect 加性效应additive effect 显性效应dominance effect育种值breeding value 重复力repeatability遗传力heritability 遗传相关g enetic correlation表型相关phenotypic correlation 环境相关environmental correlation广义遗传力heritability in the broad sense 狭义遗传力heritability in the narrow sense实现遗传力realized habitability最大可能生产力most Probable Producing Ability (MPPA)持久性环境效应permanent environment effect暂时性环境效应temporary environmental coefficient组内相关系数intra-class correlation coefficient最大似然法maximum Likelihood ( ML)约束最大似然法restricted Maximum likelihood (REML)最小范数二次无偏估计法minimum norm quadratic unbiased estimation (INQUE)最小方差二次无偏估计法minimum variance quadratic unbiased estimation, (MIVQUE)最佳线性无偏预测best Linear unbiased prediction (BLUP)最佳线性无偏估计best linear unbiased estimation (BLUP)混合模型方程mixed model equation (ME)方差分析analysis of variance (ANOV A) 类方差分析法ANOV A-like method第六章动物生长发育的规律生长growth 生长中心growth center 发育development胚胎期term of embryo 生后期term of birth after累积生长accumulation growth 相对生长relative growth绝对生长absolute growth 生长波growth wave第七章性别决定与性别控制雄异配型male heterogamety 雌异配型female heterogamety异配性别heterogametic sex 同配性别homogametic sex性反转sex-reversal 半合基因hemizygous gene从性遗传sex-conditioned inheritance 限性遗传sex-limited inheritanc伴性遗传或性连锁遗传sex-linked inheritance睾丸决定因子(TDF) testis determining factor拟(伪)常染色体区域( PAR) pseudoautosomal-regionY染色体性别决定区sex-determiningregion of Y chromosome第二性征(副性征)secondary sexual character第八章遗传病与遗传病控制染色体病chromosomal disease 线粒体遗传病mitochondrial disease单基因遗传病monogenetic disease 多基因遗传病polygenetic or multigene disorder 失显non penetrance 不完全外显incomplete dominance不规则外显irreqular dominance并蹄syndactylism 多趾polydactylism性连锁遗传病sex-linked disorder 抗病育种breeding for disease resistance性转变sex reversal 诱变剂mutagen断裂剂clastogen 致畸剂teratogen猪的应激综合征porcine stress syndrome (PSS)恶性高热综合症milignant hyperthermia syndrome (MHS)常染色体显性遗传autosomal dominant disorder常染色体隐性遗传病autosomal recessive disorder第九章畜禽品种物种species 品种breed 品系strain, line专用品种special-purpose breed 兼用品种dual-purpose breed海福特牛Hereford 夏洛莱牛charolais利木赞牛limousine 安格斯牛angus阿伯丁-安格斯牛aberdeen-angus 契安尼娜牛chianina荷斯坦牛Holstein 中国荷斯坦牛china holstein西门塔尔牛Simmental 尼里-拉维水牛nili-ravi世界西门塔尔牛联合会WSF 澳洲美利奴羊australian merino丹麦红牛danish red 摩拉水牛murrah婆罗门牛Brahman 圣格鲁迪牛santa gertrudis肉牛王beefmaster 婆朗格斯牛brangus婆罗福特牛braford 西门婆罗牛simbrah夏白雷ch arbray辛地红牛red sindhi纯血马thoroughbred 阿尔登马ardennes超细毛型super fine merino 细毛型fine merino中毛型medium wool merino 强毛型strong wool merino罗姆尼羊romney marsh 无角陶赛特羊poll dorset萨福克羊Suffolk 诺福克羊norfolk考力代羊corriedale 夏洛莱羊charollais萨能山羊sannen安哥拉山羊angora goat努比亚山羊Nubian 波尔山羊boer goat大白猪large white 长白猪landrace杜洛克猪duroc 汉普夏猪hampshire皮特兰猪pietrain隐性白羽鸡recessive white来航鸡leghorn 罗斯褐蛋鸡ross brown layer海波罗肉鸡hybro broilers 咔叽·康贝尔鸭khaki campbell ducks 枫叶鸭maple ducks 樱桃谷肉鸭cherry valley meat ducks 莱茵鹅rhine geese 郎德鹅landoise geese王鸽king pigeons 非洲鸵鸟african ostriches美国七彩雉鸡american seven-colour common pheasants第十章动物生产性能测定生产性能测定performance testing猪应激综合征porcine stress syndrome (PSS)测定站测定station test 场内测定on-farm test肉用家畜butcher’s beast肉嫩度meat tenderness体尺测量body measurement 线性外貌评定linear classification system 产奶量milk yield 排乳速度milking rate产蛋性能egg laying performance 蛋品质egg quality羊毛品质wool quality 繁殖性能breeding performance第十一章质量性状选择原理与方法质量性状qualitative trait 选择selection显性基因dominant gene 隐性基因recessive gene伴性遗传sex-linked inheritance 测交test cross随机交配群体mendelian population or randomized mating population检验概率probability of detection第十二章数量性状的选择原理与方法多性状的选择multiple-trait selection 单性状的选择single trait selection间接选择indirect selection 直接选择direct selection表型值phenotypic value 选择差selection differential选择反应selection response 选择强度selection intensity选择指数selection index 顺序选择tandem selection独立淘汰independent Culling (level)家系family家系内选择intra-family selection 家系选择family selection遗传进展genetic gain 数量遗传学quantitative genetics阈模型threshold model 阈性状threshold trait阈值threshold value 遗传同化genetic assimilation第十三章个体遗传评定分子血缘相关阵numerator relationship matrix估计育种值estimated breeding value (EBV)估计传递力estimated transmitting ability (ETA)相对育种值relative breeding value (RBV)最佳线性无偏预测best linear unbiased prediction (BLUP)混合模型方程组法mixed model equations (MME)综合育种值total breeding value 经济加权值economic weight系谱测定pedigree testing 同胞测定sib testing后裔测定progeny testing 顺序选择法tandem selection独立淘汰法independent culling 综合选择指数selection index动物模型animal model 公畜模型sire model公畜-母畜模型sire-dam model 外祖父模型maternal grandsire model 孟德尔抽样Mendelian sampling 对数据迭代iteration on data生产质量quality of production第十四章交配系统交配体制mating system 交配系统mating system选型交配ssortative mating 同型交配positive assorrtative mating异型交配negative assortative mating 近交衰退inbreeding depression近交inbreeding 远交outbreeding生长growth 繁殖reproduce适应性adaptability 活力vigor敏感susceptible 遗传致死因子hereditary lethals近交系数inbreeding coefficient 亲缘系数coefficient of relationship畸形abnormalities 环境条件critical environmental conditions第十五章杂交体系与杂种优势的利用级进杂交grading crossing 导入杂交Introduction crossing育成杂交rearing crossing 简单经济杂交simple corssing三元杂交three—way crossing 轮回杂交rotational crossing顶交top crossing 生产性双杂交double cross近交系inbred line 专门化品系specialized strain合成系synthetic strain 杂种优势heterosis一般配合力general combining ability 特殊配合力specific combining ability 双列杂交(diallel crossing)合成群体synthetic population相互轮回选择reciprocal recurrent selection第十六章品种与品系培育艾维因avian 单系monooringinator line迪卡delcalb 地方品系local line,local strain地方品种local breed 父系sire line近交系inbred line 母系dam line品系strain,line 品系繁育1ine breeding品种breed 群系polygenesic line通用品系general purpose line 物种species育成杂交crossbreeding for formation a new breed正反交反复选择法reciprocal Recurrent Selection中国荷斯坦牛chinese Holstein 专门化品系specialized line群体遗传学population genetics 基因频率gene frequency基因库gene pool 随机交配random mating遗传漂变genetic drift 群体有效含量population effective size 保种breeds conservation 平均数mean质量性状qualitative character 数量性状quantitative character数量遗传学quantitative genetics 标准差standard deviation加性效应additive effect 显性效应dominant effect变异系数coefficient of variation 相关系数correlation coefficient纯合子homozygote 杂合子heterozygote表型值phenotype value 育种值breeding value遗传力heritability 遗传相关genetic correlation育种breeding 繁育体系breeding & multiplication system纯种purebred 品种退化degeneration品群variety population 群体继代选育法systematic breeding家系family 纯种繁育pure breeding杂交繁育cross breeding 系谱pedigree后裔测验progeny test 种畜breeding stock选种selection 世代间隔generation interval遗传进展genetic progress, genetic advance 个体选择individual selection家系选择family selection 综合指数选择法comprehensive index method 选配mating system 近交inbreeding同质选配mating like to like 异质选配mating unlike to unlike近交系数inbreeding coefficient 杂交crossing杂种crossbred, hybrid 杂种优势heterosis, hybrid vigor配合力combining ability第十七章动物遗传资源保护与利用遗传资源genetic resources 生物多样性genetic diversity物种入侵species invade 形态学morphological平均数mean 变异系数variation coefficient基因频率gene frequency 基因型频率genotype frequency参数parameter 平均杂合度average heterozygosity核苷酸多态性nucleotide polymorphism 系统发育phylogeny数据库database 生态系统ecosystem生物群落biopopulation 基因组genome数据库管理系统database management system 地理信息系geography information system 图象分析系统imaging analysis system 远程登陆Telnet internet家畜livestock 迁徙migration细胞库cell bank 细胞系cell line扩增片段长度多态性amplified fragment length polymorphism (AFLP)随机扩增多态DNA random amplified polymorphic DNA(RAPD)单位点微卫星多态性single locus microsatellite polymorphism序列标记微卫星sequence marker polymorphic遗传多样性保护genetic diversity conservationDNA单链构象多态性DNA single strand conformational polymorphism核苷酸替代平均数目nucleotide substitution average number第十八章现代生物技术与动物育种生物技术biotechnology 基因工程gene engineering蛋白质工程protein engineering 细胞工程cell engineering发酵工程fermentation engineering 人工授精artificial insemination (AI)胚胎移植embryo transfer ( ET) 核移植nuclear transplantation遗传标记genetic marker 免疫遗传标记immunogenetical marker型群phenogroup生化遗传标记biochemical genetic marker基因组genomics 基因芯片gene chip动物转基因技术transgenic technology or transgenesis第十九章动物育种规划与繁育体系育种规划breeding scheme 育种目标性状breeding goal traits育种目标breeding goal 经济加权系数economic weighting coefficients 遗传差距genetic lag 综合育种值total breeding value时间差距time lag 主动育种群active breeding herd贴现discount 基因流动法gene flow method边际效益marginal profit 传递矩阵transmission matrix育种效益breeding returns 育种投入量breeding costs选择周期cycle of selection 选择通径paths of selection第二十章动物育种数据管理与软件应用育种数据Breeding data 育种记录Breeding records校正因子Adjustment factors 加性校正因子Additive adjustment factors 乘性校正因子Multiplicative adjustment factors 遗传组模型Genetic group model Bartlett’s检验Bartlett’s test Levene's 检验Levene's test计量数据Quantitative data 计数数据Count data无序分类数据Unordered Categorical Data 有序分类数据Ordered Categorical Data方差组分V ariance components 非求导算法Derivative-free algorithmR法Method R 公畜模型Sire model协方差函数Covariance functions 随机回归模型Random regression model动物模型Animal model 重复力模型Repeatability model传递力Transmitting ability 遗传趋势Genetic trend母体效应模型Maternal effect model 母体遗传效应Maternal genetic effect母体永久环境效应Maternal permanent environmental effect最佳线性无偏估计Best linear unbiased estimation (BLUE)最佳线性无偏预测Best linear unbiased prediction (BLUP)约束最大似然法Restricted maximum likelihood期望最大化算法Expectation maximum algorithm平均信息算法A verage information algorithm马尔克夫链蒙特卡洛Markov chain Monte Carlo (MCMC)Newton-Raphson(NR)算法Newton-Raphson(NR)algorithmFisher判分法(MSC)Method of scoring (MSC)Choleskey分解Choleskey decomposition数据库管理系统Database management system系统环境因素Systematic environmental factors。
a r X i v :c o n d -m a t /0212249v 2 [c o n d -m a t .s t a t -m e c h ] 5 A p r 2004PSEUDO-DIFFUSIONS AND QUADRATIC TERM STRUCTURE MODELS SERGEI LEVENDORSKI ˇI Department of Economics,The University of Texas at Austin Abstract.The non-gaussianity of processes observed in financial markets and rela-tively good performance of gaussian models can be reconciled by replacing the Brownian motion with L´e vy processes whose L´e vy densities decay as exp(−λ|x |)or faster,where λ>0is large.This leads to asymptotic pricing models.The leading term,P 0,is the price in the Gaussian model with the same instantaneous drift and variance.The first correction term depends on the instantaneous moments of order up to three,that is,the skewness is taken into account,the next term depends on moments of order four (kurtosis)as well,etc.In empirical studies,the asymptotic formula can be applied without explicit specification of the underlying process:it suffices to assume that the instantaneous moments of order greater than two are small w.r.t.moments of order one and two,and use empirical data on moments of order up to three or four.As an application,the bond pricing problem in the non-Gaussian quadratic term structure model is solved.For pricing of options near expiry,a different set of asymptotic formulas is developed;they require more detailed specification of the process,especially of its jump part.The leading terms of these formulas depends on the jump part of the process only,so that they can be used in empirical studies to identify the jump characteristics of the process.Key words:Quadratic term structure models,L´e vy processes,asymptotic solutions2S.LEVENDORSKIˇI1.IntroductionTo account for fat tails,skewness and excessive kurtosis of empirical probability dis-tributions of returns in real Financial Markets,it has become increasingly popular to model the dynamics of market factors as a L´e vy process.L´e vy models are more realistic than Gaussian ones but the latter are much more tractable.Indeed,in the Gaussian framework,explicit pricing formulas are known for a wide range of options and other contingent claims both without and with early exercise features,whereas in the L´e vy models,most of the pricing formulas have been obtained for contingent claims of the European type,with the deterministic life-span.There are some explicit analytic re-sults for options with early exercise features:see Boyarchenko and Levendorskiˇi(2000, 2001,2002a,b),Mordecki(2002)and the bibliography therein for pricing of perpetual American options,and Boyarchenko and Levendorskiˇi(2002b,c)for pricing of barrier options andfirst touch digitals.However,the pricing formulas are complicated and diffi-cult for numerical implementation except for a rather special case of pricing of perpetual American options under exponential jump-diffusions or spectrally one-sided processes. Another obstacle for non-Gaussian modelling arises when one considers more general Markov processes.The explicit pricing formulas in affine term structure models and certain L´e vy-driven Ornstein-Uhlenbeck models are known in the case of contingent claims with the deterministic life span only–see Duffie et al.(2000,2002),Chacko and Das(2002),and Barndorff-Nielsen and Shephard(2001b),Barndorff-Nielsen et al (2002),respectively;for non-Gaussian variants of the HJM-model,see Eberlein and Raible(1999).In the general case,the dependance on the state variable does not allow one to obtain explicit analytical answers.The following observation helps to obtain efficient approximate solutions.As Barndorff-Nielsen and Levendorskiˇi(2001)notice,typically,a goodfit to the data can be achieved with L´e vy processes whose L´e vy densities decay as exp(−λ|x|)or faster,whereλ>0(the steepness parameter of the exponential L´e vy process)is large.They used this property to derive an asymptotic pricing formula for European options under certain class of Feller processes.The same observation was used in Boyarchenko and Levendorskiˇi(2002a,b,d) and Kudryavzev and Levendorskiˇi(2002)to derive efficient approximate formulas for perpetual American and Bermudan options,andfirst-touch-digitals,respectively.It was shown in Boyarchenko and Levendorskiˇi(2002a,b)that the simple approximate formula is of the same form as the corresponding formula in a Gaussian model even when the underlying L´e vy process has no Gaussian component.It can be shown that the leading term of the approximate pricing formula in Barndorff-Nielsen and Levendorskiˇi (2001)can also be written as the pricing formula in a Gaussian model.These observations can serve as an analytical explanation of relatively good performance of Gaussian models in apparently non-Gaussian situations.Thus,as far as pricing formulas are concerned, L´e vy processes with large steepness parameters behave almost as the Brownian motion, and Feller processes with large steepness parameters considered in Barndorff-Nielsen and Levendorskiˇi(2001)behave almost as Gaussian diffusions.It seems reasonable to use thePSEUDO-DIFFUSIONS AND QTSMS3 nomer pseudo-diffusions for L´e vy processes and more general L´e vy-like Feller processes with large steepness parameters.The modelling with pseudo-diffusions allows one to obtain an efficient approximation to the price;in some situations,the asymptotic expansion of the price can be obtained, of the form(1.1)P(x,t)∼P0(x,t)(1+λ−1P1(x,t)+λ−2P2(x,t)+···),where the leading term,P0,is the price in the Gaussian model with the same instan-taneous drift and variance.Thefirst correction term takes into account the moments of order three as well(skewness),the second correction term accounts for moments of order four,etc.Notice that though the leading term looks as the pricing formula in the Gaussian model,the“drift”and“variance-covariance matrix”used in the formula for the leading term are not the same as the ones of the Gaussian component of the process unless it is purely Gaussian.Indeed,a L´e vy process may have no diffusion component at all.The aim of the paper is to apply the approximate pricing approach to quadratic term structure models(QTSM)when the stochastic factor follows a mean-reverting pseudo-diffusion process of the simplest form(it is unlikely that in the QTSM model,an explicit pricing formula can be obtained unless the process process is Gaussian),and derive a pricing formula of the form(1.1).For the discussion about advantages of the Gaussian QTSM model,see Ahn et al(2002,2003)and Chen and Poor(2002).Cheng and Scaillet (2002)consider an affine-quadratic model,and allow for jumps but only in the dynamics of affine variables of the model.Notice that the use of jumps in QTSM models adds additionalflexibility in joint modelling under the historic and a risk-neutral measures, and one may hope that the performance of QTSM models can be improved by introducing jumps.1Another improvement(and quite sizable one)is expected in pricing of out-of-the-money options near expiry,where the main contribution to the price comes from the jump part of the process.Near expiry,however,a different approximate formulas are needed,which use more detailed information about the jump part of the processes than the skewness and kurtosis.These formulas are similar to approximate formulas for out-of-the-money options on stocks developed in Levendorskiˇi(2003),and can be derived by the same reasoning.1.1.Plan of the paper.In Section2,we list families of exponential L´e vy processes used in empirical and theoretical studies offinancial markets.In Section3,we formulate the pricing problem for an interest rate derivative of the European type,and by using the Feynman-Kac theorem,reduce the pricing problem to the boundary problem for an integro-differential equation.We also explain the scheme of the asymptotic pricing.In Section4,we recall the solution of the bond pricing problem in the one-factor Gaussian case,and indicate the properties of the solution which are crucial for our asymptotic4S.LEVENDORSKIˇImethod.In Section5,we demonstrate our method in the simplest case of the one-factor L´e vy model for the bond price,and present numerical examples.In Section6, we consider possible specifications of the market price of risk,the generalization for the multi-factor case,derive approximate formulas for interest rate derivatives near expiry, and suggest a procedure of parameterfitting based on the asymptotic expansions.In Section7,we summarize our results,and compare the L´e vy QTSM with multi-factor Gaussian QTSM.In the appendix,technical results are proven.2.L´e vy processes in financial modellingAs early as in1963,Mandelbrot suggested to use stable L´e vy processes.The modelling with stable L´e vy processes is not quite realistic since the tails of L´e vy stable distributions are too fat(polynomially decaying),whereas the tails of distributions of returns observed in realfinancial markets exhibit exponential decay.Moreover,the second moment of a L´e vy stable distribution is infinite(unless it is a Gaussian one).This contradicts the observed convergence to the Gaussian distribution over a longer time scale,and even worse,the underlying stock itself should have the infinite price under the stable L´e vy process,which makes the model inconsistent for pricing purposes.Starting with the beginning of the90th,several families of L´e vy processes with probability distributions having exponentially decaying tails have been used to describe the behavior of stock prices in realfinancial markets:•Variance Gamma Processes(VGP)constructed and used by Madan and co-authors in a series of papers during90th(see Madan et al.(1998)and the bibliography therein);•Hyperbolic Processes(HP)were constructed and used by Eberlein and co-authors (see Eberlein et al.(1998),Eberlein and Prause(1999));hyperbolic distributions were constructed by Barndorff-Nielsen(1977));•Normal Inverse Gaussian Processes(NIG)were introduced by Barndorff-Nielsen (1998)and used to model German stocks by Barndorff-Nielsen and Jiang(1998);•Truncated L´e vy Processes(TLP)constructed by Koponen(1995)were used for modeling in realfinancial markets by Bouchaud and Potters(1997),Cont et al(1997)and Matacz(2001);the extended Koponen family was constructed in Boyarchenko and Levendorskiˇi(2000)(the generalization was needed since prob-ability distribution of Koponen’s family have tails of the same rate of exponential decay whereas in realfinancial markets,the left tail is usually much fatter;in Carr et al(2002)and Boyarchenko and Levendorskiˇi(2002a,b),the extended Koponen family is called CGMY-model and KoBoL family,respectively).•Normal Tempered Stable L´e vy processes were constructed in Barndorff-Nielsen and Levendorskiˇi(2001)and Barndorff-Nielsen and Shephard(2001a);they con-tain NIG as a subclass.In Boyarchenko and Levendorskiˇi(2000),a general class of L´e vy processes,which con-tained all the classes listed above modulo certain reservation about VGP was introduced,PSEUDO-DIFFUSIONS AND QTSMS5 under the name Generalized Truncated L´e vy ter,in Barndorff-Nielsen and Levendorskiˇi(2001),the name:“Regular L´e vy processes of exponential type”(RLPE) was suggested.For a more detailed exposition,see Boyarchenko and Levendorskiˇi(2002a, 2002b).In order to present examples,recall that a L´e vy process can be completely spec-ified by its characteristic exponent,ψ,definable from the equality E[e i ξ,X(t) ]=e−tψ(ξ). The characteristic exponent is given by the L´e vy-Khintchine formula(2.1)ψ(ξ)=−i b,ξ +12ξ2−ibξ+ic+ξλ−+iξ,whereσ2≥0and b∈R are the variance and drift of the Gaussian component.The ψ(ξ)is analytic in the stripℑξ∈(λ−,λ+).Example2.2.The characteristic exponent of a process of KoBoL family in1D is of the form(2.2)ψ(ξ)=−iµξ+cΓ(−ν)[λν+−(λ++iξ)ν+(−λ−)ν−(−λ−−iξ)ν],whereν∈(0,2),ν=1,c>0,λ−<0<λ+,andµ∈R;it is analytic in a strip ℑξ∈(λ−,λ+),and(3.8)-(3.9)are satisfied in this strip.Example2.3.The characteristic exponent of a Normal Inverse Gaussian process in1D is of the form(2.3)ψ(ξ)=−iµξ+δ[(α2−(β+iξ)2)1/2−(α2−β2)1/2],whereν∈(0,2),δ>0,andα>|β|;it is analytic in the stripℑξ∈(−α+β,α+β),and (3.8)-(3.9)are satisfied in this strip,withν=1.Since the sum of the characteristic exponents of two RLPE’s is the characteristic exponent of an RLPE,the list of model examples can easily be expanded.For multi-dimensional examples,see Boyarchenko and Levendorskiˇi(2002b).6S.LEVENDORSKIˇIExamples2.1–2.3are examples of pseudo-diffusions ifλ+,|λ−|,andα±βare large. Typically,processes observed in empirical studies offinancial markets(hyperbolic pro-cesses and variance gamma processes including)enjoy this property.The majority of papers on L´e vy models deal with asset pricing.Eberlein and Raible (1999)consider the HJM-model driven by a L´e vy process(see also Eberlein and¨Ozkan (2001)).For the usage of jump-diffusion processes and more general L´e vy processes in affine term structure models of interest rates,see Duffie et al.(2000,2002),Chacko and Das(2002)and the bibliography therein.Barndorff-Nielsen and Shephard(2001b) suggested to use L´e vy-driven Ornstein-Uhlenbeck processes for interest rate modelling purposes.For the subsequent developments,see Barndorff-Nielsen et al(2002).3.The model3.1.L´e vy-driven QTSM.In the Gaussian QTSM,the instantaneous interest rate is represented as a quadratic function of the state variables,and the latter are specified as diffusions.We assume that under an EMM chosen by the market,the SDE of the state variables can be written as(3.1)dX(t)=(˜θ(t)−κX(t))dt+dZ(t),where{Z(t)}is an n-dimensional L´e vy process,˜θ:R n→R is a continuous vector-function,andκis a constant n×n matrix,whose eigenvaluesλj satisfy the condition (3.2)ℜλj>0.The interest rate is modelled as(3.3)r(X(t))=R0+2 R1,X(t) + ΓX(t),X(t) ,where R0∈R,R1∈R n are constant scalar and vector, ·,· is the standard inner product in R n,andΓis a positively definite symmetric matrix.The last condition ensures thatr(X(t))= Γ(X(t)+Γ−1R1),X(t)+Γ−1R1 +R0−||Γ−1R1||2is semi-bounded from below.By choosing R0,R1andΓappropriately,one can ensure any lower bound on r(X(t)).Notice that if one wishes to price a derivative of a stock whose dynamics is characterized by X,then one may allow r to depend only on some of the factors X j(t),say,r=r(X1(t),...,X m(t)),where m<n;in this case,in(3.3), R1∈R m,andΓis an m×m matrix.If Z has no jump component then the bond pricing problem reduces to a system of ODE(Riccati equations),which can easily be solved numerically,and in the one-factor case,even analytically.(In the multi-factor case,a system of Riccati equations can be reduced to a linear system;for the explicit realization in the framework of the Gaussian QTSM,see Kim(2003)).It seems unlikely that a reasonably simple exact solution exists for a general L´e vy process but we manage to obtain an asymptotic solution if X is aPSEUDO-DIFFUSIONS AND QTSMS7 pseudo-diffusion,that is,the L´e vy density of Z decays exponentially,and the rate of decay is large.The leading term of the asymptotics is the price in the Gaussian model with the same instantaneous moments of order one and two,and the correction terms are polynomials in the factors with coefficients depending on the time to expiry.After the leading term is found,they can be calculated recursively,by using only integration procedures in1D.Thus,the suggested method is relatively simple(though in multi-factor models,the number of additional integration procedures may be rather large;it is important that all the integrations remain one-dimensional,even in a multi-factor model).In the one-factor case,thefirst correction term is proportional to skewness, and the second one depends on the skewness and kurtosis;to be more precise,thefirst correction is proportional to skewness,and the second one is the sum of two terms,one of which is proportional to the square of the skewness,and the other to the kurtosis.In many cases,the contribution of the kurtosis is small relative to the other terms;if we omit the last term,then the pricing formula becomes a sum of the leading term which looks as the price in the Gaussian model,and the correction term,which is a quadratic polynomial w.r.t.to skewness.Similar formula for the forward rate and numerical examples show that thefirst cor-rection term has a pronounced upward hump,if the skewness is negative;in the result, the corrected forward rate curve can be hump shaped even when the Gaussian forward rate curve is not,and all parameters of the model are time-independent.By changing the parameters,various shapes of the forward rate curve can be obtained.Empirical studies show that both skewness and kurtosis can be fairly large,and hence, the corrections to the Gaussian price quite sizable.Consider,for instance,the statistics for the daily change interest rates(dr)from Table1in Das(2002).(The table presents descriptive statistics for the Fed Funds rate over the period January1988to December 1997,and the unit is1percent).Mean:m=−0.0005;standard deviation:σ=0.2899; skewness:λ3=0.3950;excess kurtosis:k4=19.8667.Recall that for probability distribution P(dx),m:= x := +∞−∞xP(dx),σ2:= (x−m)2 ,λ:= (x−m)3 /σ3,k4:= (x−m)4 /σ4−3,and that if P(dx)=P∆t(dx)is the probability distribution of a L´e vy process with the characteristic exponentψ,thenm(∆t)/∆t=iψ′(0);σ2(∆t)/∆t=ψ′′(0);(x−m)3 (∆t)/∆t=−iψ(3)(0);[ (x−m)4 (∆t)−3σ4(∆t)]/∆t=−ψ(4)(0). We see that the coefficients in the third and fourth terms in the Taylor series forψaround zero are smaller than the second one but non-negligible whereas in the Gaussian case all coefficients starting from the third one are zero.8S.LEVENDORSKIˇIThe skewness and kurtosis of the process under an EMM can assume essentially ar-bitrary values provided they are small w.r.t.variance;in particular,one should expect that the skewness of the process under EMM is negative even when the one under his-toric measure is positive as in the empirical example above.This means that even the one-factor approximate non-Gaussian model has two free additional parameters(albeit small)which can be used to get a betterfit to the data than in the Gaussian model.In multi-factor models,the number of additional free parameters is larger still.3.2.Reduction of a pricing problem to a boundary problem.Consider a con-tingent claim with the maturity date T and payoffg(X(T)).Its price at time t<T is given by(3.4)f(X(t),t)=E t exp − T t r(X(s))ds g(X(T)) .(We consider the pricing under a risk-neutral measure chosen by the market).In appli-cations,the payoffg is measurable(usually,continuous),and it may grow at infinity.In the latter case,additional conditions on Z may be needed.For instance,if g grows not faster than an exponential:(3.5)|g(x)|≤Ceω|x|,where C andω>0are independent of x,then it suffices to assume that there exists λ>ωsuch that for allµin the ball|µ|<λ,and some t>0,(3.6)E[e µ,Z(t) ]<∞,which implies that the tails of probability densities of the process Z decay exponentially: faster than exp(−ρ|x|),for anyρ<λ.It follows from(3.6),that for anyξ=η+iτ∈C n from the tube domain R n+iUλ:= {ξ||ℑξ|=|τ|<λ}(in the one-factor case,a tube domain is a strip),and any t>0, (3.7)E[e i ξ,Z(t) ]<∞.(Instead of balls Uλ,one can use more general open sets containing the origin.)It is immediate from(3.7),thatψ(ξ)and its derivatives w.r.t.the complex argumentξare well-defined in the same tube domain R n+iUλ(one says thatψ(ξ)is analytic in R n+iUλ),and we may use the latter condition onψinstead of the former condition (3.7).To justify the use of the Feynman-Kac formula,we assume that Z is a regular L´e vy process of exponential type(RLPE).This means thatψadmits a representation (3.8)ψ(ξ)=−i µ,ξ +φ(ξ),whereµ∈R n,andφsatisfies the following condition:there exist c>0,ν∈(0,2]and ν1<νsuch that asξ→∞in the tube domain R n+iUλ,(3.9)φ(ξ)=c|ξ|ν+O(|ξ|ν1)(see Boyarchenko and Levendorskiˇi(2002b)).Theνand Uλare called the order and type of the process.PSEUDO-DIFFUSIONS AND QTSMS9 To simplify the justification of the use of the Feynman-Kac formula,we add unnec-essary condition:for any multi-indexα=(α1,...,αn),there exists a constant Cαsuch that for allξin the tube domain R n+iUλ,(3.10)|∂αφ(ξ)|≤Cα(1+|ξ|)ν−|α|,where|α|=α1+···+αn.Notice that this condition holds for all model classes of RPPE’s.In the appendix,by making use of the Feynman-Kac formula,we will prove the fol-lowing theorem.Theorem3.1.Let the stochastic factor satisfy(3.1),(3.2),(3.3),(3.6),(3.8),(3.9), and(3.10),let r be given by(3.3),and let g be a continuous function,which admits a bound(3.5).Then a)the stochastic expression(3.4)defines a continuous function f,which admits an estimate(3.11)|f(x,t)|≤C1eω|x|,where C1is independent of x and t≤T;b)f is a unique solution to the following problem:(3.12)(∂t+ ˜θ(t)−κx,∂x +L−r(x))f(x,t)=0,t<T,(3.13)f(x,T)=g(x),where L is the infinitesimal generator of Z.Recall that the infinitesimal generator of the L´e vy process Z,L,can be represented in the form of a pseudo-differential operator(PDO)with the symbol−ψ:L=−ψ(D x).A PDO A=a(D)with the symbol a acts on sufficiently regular functions as follows:(Au)(x)=(2π)−n R n e i x,ξ a(ξ)ˆu(ξ)dξ,whereˆu is the Fourier transform of u:ˆu(ξ)= R n e−i x,ξ u(x)dx.In particular,the partial derivative∂x is the PDO with the symbol iξ.3.3.Asymptotic pricing.The asymptotic pricing formulas will be derived under the following conditions.Assume that the characteristic exponent of the driving L´e vy process depends on a small parameterǫ>0:ψ(ξ)=ψ(ǫ,ξ)and satisfies the following three conditions.First,we require that theλin the definition of the tube domain R n+iUλsatisfiesλ>>ǫ−1/2.The next two conditions are formulated forξin the tube domain R n+iUλ:1)in the region|ξ|>ǫ−1/2,ψ(ǫ,ξ)admits an estimate(3.14)ℜψ(ǫ,ξ)≥c|ξ|ν,10S.LEVENDORSKIˇIwhereν∈(0,2]and c>0are independent of(ǫ,ξ)in the region;2)in the region|ξ|≤ǫ−1/2,ψ(ǫ,ξ)admits an asymptotic expansion:in the one-factor case,(3.15)ψ(ǫ,ξ)=−iµξ+σ22||ΣTξ||2−∞j=3ǫj−2k j(iξ),where k j(ξ)is a homogeneous polynomial of order j,which admits a bound(3.18)|k j((ΣT)−1iξ)|≤C|ξ|j,where C is independent of j.The asymptotic solution will be found in the following sections.Here we explain the main idea in the one-factor case.We look for the solution in the form(3.19)f=f0+ǫf1+ǫ2f2+···.From(3.15),we can formally write(3.20)L=µ∂x+σ22∂2x−r(x)is of the same form as the operator in the Gaussian model,andL l=k l+2∂l+2x,l=1,2,....By multiplying out in(3.21)and gathering terms of the same order inǫ,we obtain the following series of problems.The leading term of the asymptotics is found fromL0f0(x,t)=0,t<T;f0(x,T)=g(x),PSEUDO-DIFFUSIONS AND QTSMS11 which is the pricing problem in the Gaussian model;and the following terms are found step by step,by solving problemsL0f l(x,t)=−lj=1k j+2∂j+2x f l−j(x,t),t<T,f l(x,T)=0,for l=1,2,....We believe that for practical purposes,it suffices to use an approximate formula(3.19)with terms up to order2;this allows one to take into account the skewness and kurtosis.This approximate solution can be written as(3.22)f≈f0+ǫk3f1+(ǫk3)2f21+ǫ2k4f22,where f1,f21and f22solve equationsL0f1(x,t)=−∂3x f0(x,t),L0f21(x,t)=−∂3x f1(x,t),L0f22(x,t)=−∂4x f0(x,t)in the half-space t<T,subject to zero boundary condition.The explicit formulas for the bond price can be found in Section4and Section5.Formula(3.22)may seem somewhat inconvenient for practical applications since it depends on the small parameterǫ,which is not explicitly specified.Notice,however,thatǫk3=−iψ(3)(0)/3!,ǫ2k4=−ψ(4)(0)/4!,and the derivatives of the characteristic exponent at0can be inferred from empirical data-see Introduction.Thus,we may write(3.22)withoutǫ:(3.23)f≈f0−i ψ(3)(0)3! 2f21−ψ(4)(0)12S.LEVENDORSKIˇI4.Bond pricing:Gaussian model,one-factor caseIn this section,we recall the solution of problem(3.12)-(3.13)in the one-factor Gauss-ian case,whenψ(ξ)=−iµξ+σ2ξ2/2,and L=µ∂x+σ22∂2x−r(x))f(x,τ)=0,τ>0,(4.2)f(x,0)=g(x) (4.3)in the form(4.4)f(x,τ)=expΦ0(x,τ),where(4.5)Φ0(x,τ)=A(τ)x2+B(τ)x+C(τ).By substituting(4.4)into(4.2),we obtain(4.6)(exp(−Φ0)L expΦ0)(x,τ)−r(x)=0, where(4.7)L=−∂τ+(θ(τ)−κ)∂x+σ22B(τ)2+θ(τ)B(τ)−R0=0.(4.10)Equation(4.8)is solved by separation of variables: (4.11)A(τ)=A1A21−eωτPSEUDO-DIFFUSIONS AND QTSMS 13where A 1<0<A 2are roots of the quadratic equation 2σ2A 2−2κA −1=0,and ω=2σ2(A1−A 2)<0.A (τ)having being found,we can calculate B (τ)from the linear equation (4.9):(4.12)B (τ)=2e ω1τ(A 2I 1(τ)−A 1I 2(τ))ω1(1−e −ω1τ),I 2(τ)=A 2θ−R 1(A 2−A 1)(A 2−A 1e ωτ)(4.13)× A 2(A 1θ−R 1)ω1−ω(e ω1τ−e ωτ).Finally,we find C (τ)from (4.10)by integration:(4.14)C (τ)= τ0σ2A (s )+σ2A 2−A 1τ=A 1A 22σ2τ=−τ.Hence,for any τ∈(0,T ],f (x,τ)decays as exp(−τx 2),as x →±∞,and ˆf(ξ,τ),the Fourier transform of f (x,τ)w.r.t.the first argument,decays as τ−1/2exp(−ξ2/(4τ)),as14S.LEVENDORSKI ˇIξ→±∞.To be more specific,ˆf (ξ,τ)= +∞−∞e −ixξ+A (τ)x 2+B (τ)x +C (τ)dx(4.17)=12ξ2−iµξ=∞ j =3ǫj −2k j (iξ)j =ǫ∞ j =3ǫj −3k j (iξ)j .We also have the initial condition(5.2)f 1(x,0)=0.From (3.16)and (4.18),the following estimate for the RHS in (5.1)follows:(5.3)|D 1(ǫ,ξ)ˆf 0(ξ,τ)|≤C 0ǫτ−1/2exp(−ξ2/(8τ)),where C 0is independent of ǫ∈(0,1)and τ∈(0,T ].By making the inverse Fourier transform,we obtain(5.4)||D 1(ǫ,D x )f 0(x,τ)||C (R ×[0,T ])≤Cǫ,PSEUDO-DIFFUSIONS AND QTSMS15 where C is independent ofǫ∈(0,1).By applying the Feynman-Kac theorem to(5.1)-(5.2),the representation of f1in the form of the stochastic integral results:f1(x,τ)=E−τ 0−τexp − s−τr(X(s′))ds′ D(ǫ,D x)f0(x,s)ds ,and from(5.4),we derive an estimate(5.5)|f1(x,τ)|≤Cǫ,where C is independent ofǫ∈(0,1),x∈R andτ∈(0,T].5.2.First correction term.Estimate(5.5)shows that f0is indeed the leading term of the asymptotics of f asǫ→0,and in view of(3.15),it is natural to look for thefirst correction term in the formǫf1,where f1is the solution to the following problem:σ2(5.6)(−∂τ+(θ(τ)−κx)∂x+16S.LEVENDORSKIˇIwhere˜g0(x,τ):=8A3x3+12A2Bx2+(12A2+6AB2)x+6AB+B3,σ2L1:=∂τ+(−θ1(τ)+κ1(τ)x)∂x−PSEUDO-DIFFUSIONS AND QTSMS17 Unlike(5.5),we have a polynomially growing factor(1+|x|2)3/2in the RHS of(5.23). Notice,however,that for practical purposes,one needs to know the bond price for small values of r(X(t)),hence for small values of X(t),and therefore the polynomially growing factor(1+|x|2)3/2does not matter much.5.3.First correction term II:the derivation based on the change of variables. To simplify the calculation of the next terms of the asymptotics,it is advantageous to change the variables in equations similar to(5.11):(5.24)x=−θ2(τ)+eκ2(τ)y,whereκ2is given by(5.17),andθ2is the solution to the Cauchy problemθ′2(τ)−κ2(τ)θ2(τ)=θ1(τ),θ2(0)=0,that is,θ2(τ)=eκ2(τ) τ0e−κ2(s)θ1(s)ds.The same change of the variables simplifies the calculation of˜f1.Introduce an operator S by S(f)(y,τ)=f(x(y),τ).Under the change of variables(5.24),−∂τ+(θ1(τ)−κ1(τ))∂x→−∂τand∂x→e−κ2(τ)∂y,thereforeσ2L2:=S−1L1S=∂τ−18S.LEVENDORSKIˇIwhose coefficients can easily be found by integration:F1,3(τ)= τ0G0,3(s)ds,(5.27)F1,2(τ)= τ0G0,2(s)ds,(5.28)F1,1(τ)= τ0(G0,1(s)+3σ2e2κ2(τ)G0,3(s))ds,(5.29)F1,0(τ)= τ0(G0,0(s)+σ2e2κ2(τ)G0,2(s))ds.(5.30)After that we make the inverse change of variables y=e−κ2(τ)(x+θ2(τ)),and calculate ˜f1=S−1F1.5.4.Next terms of the asymptotics.Suppose that the approximation of order j≥1 has been found:f=f0· 1+j l=1ǫl k l+2˜f l =f0j l=0ǫl k l+2˜f l,where k2=1,f0=eΦ0,˜f0≡1,and˜f l,1≤l≤j,are polynomials in x with coefficients depending on onτ:(5.31)˜f l(x,τ)=m l s=0a ls(τ)x s.We look for the next term of the asymptotics in the formǫj+1k j+3f0˜f j+1,where f j+1:= f0˜f j+1is the solution to the problem(L−r(x))f j+1(x,τ)=−g j(x,τ),τ>0,(5.32)f j+1(x,0)=0,(5.33)whereǫj+1g j is the collection of terms of orderǫj+1in the expression∞p=3ǫp−2k p∂p x j l=0ǫl k l+2f0˜f l ,that is,g j=j+3p=3k p k j+5−p∂p x(f0˜f j+3−p).。