下载文档原格式
第30卷第6期2003年11月浙 江 大 学 学 报(理学版)Journa l of Zhej i ang Un iversity (Sc ience Ed ition )V o l .30N o .6N ov .2003氰酸酯与改性环氧树脂的共固化反应及固化物的性能研究纪 丽,阎红强,戚国荣(浙江大学高分子系,浙江杭州310027)收稿日期:2002212230.作者简介:纪丽(1978—),女,硕士,主要从事材料改性方面的研究.摘 要:用热机械曲线法(TM A )、傅立叶变换红外光谱(FT I R )研究了氰酸酯 低溴环氧树脂(1∶1)的共固化反应行为、历程,研究了氰酸酯改性不同环氧树脂体系层压板的耐热性能、介电性能和力学性能,同时用动态的T GA 研究了共固化体系的热稳定性.结果表明,当低溴环氧树脂 氰酸酯质量比为1 1时,固化反应首先是氰酸酯发生自聚形成三聚体(三嗪环),然后三嗪环很快与环氧基反应形成异氰脲酸酯,异氰尿酸酯再与环氧树基反应生成 唑烷酮.同时,氰酸酯单体直接与环氧基反应生成 唑啉进而转变成 唑烷酮.随着氰酸酯质量分数的增加,共固化物的玻璃化转变温度T g 和介电性能增加,抗弯强度减少,残碳量增加.关 键 词:氰酸酯;环氧树脂;层压板中图分类号:O 633.13 文献标识码:A 文章编号:1008-9497(2003)06-657-06J I 2L i ,YAN Hong 2qiang ,Q I Guo 2rong (D ep a rt m en t of P olym er S cience ,Z hej iang U n iversity ,H ang z hou 310027,Ch ina )Study on the properties and reaction of cured co m pound i n cyana te ester m od if ied epoxy co -cur i ng syste m .Jou rnal of Zhejiang U n iversity (Science Editi on ),2003,30(6):657-662Abstract :T he co 2cu ring behavi o r and reacti on m echan is m of low b rom inated epoxy (LBE ) cyanate (1 1)w ere studied by TM A and FT 2I R .D ielectric and m echan ical p roperties of lam inate m ade up of vari ou s cyanate 2modified epoxy resin w ere studied .In additi on ,thermo stab ility of co 2cu ring system w as also studied by TM A and dynam ic T GA .T he reacti on m echan is m (W low b rom inated epoxy W cyanate =1∶1)can be discribed as fo llow s :A t first it happen s cyclo tri m erizati on of cyanate .T hen ,the so fo rm ed tri m er react w ith epoxy group to give isocyanu rate ,and finally oxazo lidinone w as p roduced .A t the sam eti m e ,cyanate react w ith epoxy group directly to p roduce oxa 2zo line ,then it tran sfo rm s in to oxazo lidinone .Glass tran siti on temperatu re (T g )and char yield increase w ith in 2creasing con ten t of cyanate ,dielectric perfo rm ance is i m p roved .Key words :cyanate ester ;epoxy ;lam inate 环氧树脂是一种在复合材料中应用极广泛的热固性树脂,尤其是在电子行业中.如环氧基覆铜板具有优良的综合性能和适中的价格,目前已成为生产量大、用途广的一类基板材料.但近年来,随着航空航天、电子电气等事业的迅速发展,对所用热固性树脂基体提出了更高的要求.通用环氧树脂固化后含有部分羟基等极性基团,存在吸湿性大,尺寸稳定性和介电性能不足等缺点[1],从而使它在耐湿热性及介电性能,特别是高频介电性能方面存在不足,限制了它在高性能覆铜板领域的应用.氰酸酯(CE )是一类高性能的树脂,用其改性环氧树脂将大大地提高固化树脂的耐湿热性能和高频电性能,从而可制得适合于高频传输印制电路基板等高性能覆铜板[2].本文主要研究了氰酸酯固化低溴环氧树脂的机理和氰酸酯改性环氧树脂层压板性能的影响.1 实验部分1.1 原料低溴环氧树脂,环氧值0.22～0.24,工业级,昆山建滔积层板有限公司提供;基础环氧树脂,环氧值0.52～0.54,工业级,昆山建滔积层板有限公司提供;诺夫拉客环氧树脂,环氧值0.575,工业级,昆山建滔积层板有限公司提供;氰酸酯,自制;质量分数大于99%;双酚A,分析纯;三乙胺,分析纯;丙酮,分析纯;DM F,分析纯;溴,分析纯;KCN,分析纯. 1.2 试样的制备1.2.1 溴化氰的制备将装有搅拌器、温度计和滴液漏斗的三口烧瓶置于冰盐浴中,冷却使温度降至-10℃以下,加入一定量的液体溴,并在剧烈搅拌状态下缓慢滴加KCN水溶液,KCN过量,滴加速度以反应体系的温度不超过5℃为宜.反应过程中溶液颜色逐渐变浅,且有晶体析出,待溶液颜色转变为白色时停止滴加.这时将反应装置改成蒸馏装置,加热蒸馏得到白色晶体溴化氰,产率为86.7%.1.2.2 双酚A型氰酸酯单体的合成将装有搅拌器、温度计、滴液漏斗的四口烧瓶置于冰盐浴中,再加入过量B rCN的丙酮溶液.在剧烈搅拌下,分别缓慢滴加三乙胺和双酚A的丙酮溶液,三乙胺的滴加速度应慢于双酚A的滴加速度,反应温度在-5～-10℃.滴加完后,使体系温度维持在0～10℃之间继续搅拌2h,再使反应温度回升到室温,并在室温下搅拌30m in.在快速搅拌下将反应液倒入一定量的冰水中,使产物析出.过滤分离,初产物用蒸馏水洗涤至溶液呈中性.在50～60℃下真空干燥初产物,将初产物用环己烷重结晶,然后将产物在50～60℃下真空干燥,产率为79.8%,熔点为78～79℃.1.2.3 层压板的制备将环氧树脂与氰酸酯按一定比例(重量比)混合,加入一定量DM F和丙酮的混合溶液配制成胶液,再将7628型玻璃布浸润后制成的半固化片在一定条件下压制成层压板.实验中催化剂用量为环氧树脂的质量分数.1.3 仪器分析T g用TM A2940型进行测定;热失重采用Pyris1型热失重仪,在氮气氛中,升温速率为20℃ m in进行测定;FT2I R用V ECTO R22型傅立叶变换红外光谱进行测定,N aC l涂片或KB r压片制样;抗弯强度参照A STM D790标准在日本岛津A GS2H万能材料试验机上进行;电性能按GB4722方法用上海爱仪电子设备厂的QB G23B高频Q表进行测定;凝胶化时间按GB5259285用拔丝法进行测定;吸水率的测试,在25℃的水中浸泡24h后称质量的增加百分数.2 结果与讨论2.1 氰酸酯改性环氧树脂的固化机理实验中选择氰酸酯 低溴环氧树脂质量比为1 1无固化剂的体系为研究对象,在180℃固化温度及200℃处理温度下进行了一系列的红外光谱研究,跟踪固化反应,即每隔一定时间进行一次红外扫描.谱带的吸光度用峰高H表示,各基团的特征吸收频率如表1所示.以苯环830c m-1吸收峰作内标,计算H H830.H1756和H1693为与异氰脲酸酯和 唑烷酮中的羰基有关的吸收峰.定义环氧基的表观转化率X=1-X t X0[3],其中X0和X t分别是固化前和经t时间固化后的H H830,这样可分别计算绘制出环氧和氰酸酯基转化率与固化时间t的固化曲线,见图1,H1678 H830,H1756 H830和H1693 H830与固化时间t的固化曲线见图2.表1 低溴环氧树脂 氰酸酯(1 1)共聚反应官能团的特征吸收频率T ab le1 T he frequency of chem ical group abou t the copo lym erizati on of low b rom inated epoxy cyanatev c m-1227017561693167815641245915831 Chem ical group-OCN-C=O C=O>C=N-N-C=N芳醚环氧基苯环 注 低溴环氧树脂 氰酸酯为1 1856浙江大学学报(理学版)第30卷 图1 环氧基团和氰酸酯基团的转化率与时间的关系曲线 F ig .1 T he relati on betw een the conversi on ofepoxy group and cyanate group w ith ti me 图2 唑啉(1678c m -1)和 唑烷酮和异氰脲酸酯(1756c m -1,1693c m -1)的动力学曲线 F ig .2 K inetic cu rves of oxazo line (band at1678c m -1,oxazo lidinone and isocyanu rate (band at 1756c m -1,band at 1693c m -1) 氰酸酯改性环氧树脂的主要反应过程可以下式表示: 图3是低溴环氧树脂 氰酸酯体系在180℃固化温度下不同时间固化的红外光谱.由图3可知,在反应初期,氰酸酯基结构的特征峰2270c m -1和2235c m -1很快减弱,同时,环氧的特征峰915c m -1随着固化时间的增加也在不断减弱,并由图1可以看出环氧基的转化率小于氰酸酯基的转化率,说明反应初期氰酸酯基团的反应速率明显快于环氧基团.由图3可以看出,180℃固化5m in 时1678c m -1和1564c m -1的峰增强,这主要是因为反应初期环氧基团与氰酸酯基团反应生成 唑啉结构(Schem e 1)和氰酸酯的三聚反应.在180℃固化30m in 后,1678c m -1处的峰减弱,同时出现1756c m -1的吸收峰,此时 唑啉通过异构化反应生成 唑烷酮如Schem e 2,也可能同时存在Schem e 3和Schem e 4的反应.在180℃热处理75m in 时1678c m -1处的峰消失,说明 唑啉完全转变成 唑烷酮,同时在1693c m -1处出现吸收峰.继续在200℃下反应25m in 后1756c m -1和1693c m -1的吸收峰增强,而该两处吸收峰与 唑烷酮、异氰脲酸酯等结构相关,说明体系中发生了Schem e 3和Schem e 4的反应.在200℃处理95m in 后1756c m -1和1693c m -1等吸收峰强度基本不变,可以认为固化反应已经结束.可见固化体系中可由两种途径反应生成 唑烷酮:一是由环氧基与氰酸酯反应生成 唑啉并通过异构化956 第6期纪 丽,等:氰酸酯与改性环氧树脂的共固化反应及固化物的性能研究图3 氰酸酯 低溴环氧树脂(1 1)共固化的红外谱图 F ig.3 I R spectral changes in the cyanateepoxy copo lym erizati on1.180℃×0m in,2.180℃×5m in,3.180℃×10m in,4.180℃×15m in,5.180℃×25m in反应生成 唑烷酮,另一是通过一系列反应生成 唑烷酮(Schem e5).由红外谱图可知反应前期芳醚的特征峰1245c m-1增加,到中后期就几乎不变,说明生成芳醚的反应主要发生在前期.2.2 氰酸酯 环氧树脂共固化物的热失重由图4可知,在不同比例组成的低溴环氧树脂 氰酸酯体系中,样品的起始失重温度几乎没有差别均为350℃左右,但残碳量随着低溴环氧树脂含量的增加而降低.由图5可知,L21中含有氰酸酯均聚的吸收峰(三嗪环的吸收峰1564c m-1),而在L22和L23中几乎没有氰酸酯均聚的吸收峰,因为聚氰酸酯是一种芳香程度很高的交联网络结构,比较容易碳化,所以氰酸酯含量越多其残碳量越高.溴的引入虽能使环氧树脂有较好的阻燃性,但是降低了树脂体系的热分解温度[4],分解反应生成的HB r进一步促进了树脂的热裂解与氧化,所以随着低溴环氧树脂的增加热失重曲线越来越陡,在很窄的温度区间内很快失重.由图6可知,低溴环氧树脂 氰酸酯体系的初始失重温度和终了失重温度均低于其他两种树脂体系,且其在温度区间内失重很快.基础环氧树脂 氰酸酯固化物和诺夫拉客环氧树脂 氰酸酯固化物的初始失重温度和终止失重温度相近,但在失重前期,基础环氧树脂 氰酸酯固化物的失重温度高于诺夫拉客环氧树脂 氰酸酯固化物,失重后期基础环氧树脂 氰酸酯固化物的失重温度低于诺夫拉客环氧树脂 氰酸酯.诺夫拉客环氧树脂 氰酸酯固化物的残碳量最大,为25.90%.由于诺夫拉克树脂是多官能团,环氧交联密度高,所以其残碳量较高.图4 低溴环氧树脂 氰酸酯共固化物的热失重曲线 F ig.4 W eigh t residue cu res of cu redlow b rom inated epoxy cyanate b lendL1,L2,L3分别代表低溴环氧树脂与氰酸酯的质量比为1 1,2 1,3 1图5 低溴环氧树脂 氰酸酯共固化物的红外谱图 F ig.5 I R spectral changes of cu redlow b rom inated epoxy cyanate b lendL1,L2,L3同图4图6 不同环氧树脂 氰酸酯共固化物的热失重曲线 F ig.6 W eigh t residue cu res of cu reddifferen t Epoxy cyanate b lendN E CE—诺夫拉克环氧树脂 氰酸酯为1 1,BE CE—基础环氧树脂 氰酸酯为1 1,L E CE—低溴环氧树脂 氰酸酯为1 1 2.3 不同比例的氰酸酯 低溴环氧树脂层压板的性能表2是不同质量比的低溴环氧树脂 氰酸酯层压板的性能.由表2可以看出,随着CE质量分数的减少层压板的T g下降,电绝缘性能下降.由图5可知随着CE的减少最终固化物中三嗪环的特征吸收峰1556c m-1减弱直至消失.唑烷酮结构的特征峰1750c m-1和1698c m-1增强,芳醚的特征峰066浙江大学学报(理学版)第30卷 1245c m-1增强,说明随着CE减少,体系中低溴环氧树脂与氰酸酯倾向于共聚或低溴环氧树脂均聚.这都将使聚固化物结构中三嗪环结构的质量分数减少,而三嗪环是对称共振结构,在外电场作用下对极化松弛不敏感,表现出极低的介电常数和介电损耗值.另一方面由于三嗪环是具有三官能度的交联状结构,而 唑烷酮是脂肪族结构[2],体系中氰酸酯质量分数减少,从而较大幅度地降低了层压板的耐热性和电绝缘性能.胶化时间随着CE质量分数的增大而显著缩短,说明氰酸酯用量的增加能加快共混体系的固化反应,其原因也主要是由于氰酸酯用量多的体系中较易发生三聚反应生成三嗪环.结合反应机理可以看出三嗪环能促进共聚反应的进行,其量的多少对共聚反应有着显著的影响.氰酸酯用量减少使得固化体系的交联密度减少,因此层压板的脆性下降,抗弯强度增加.表2 低溴环氧树脂 氰酸酯层压板的性能T ab le2 T he p roperties of lam inates fo r low b rom inated epoxy cyanateEP CE胶化时间 s抗弯强度 Pa吸水率 %介电常数介电损耗T g ℃1∶12585.2160.082.730.009170 2∶13825.7160.093.220.016161 3∶14696.2830.083.790.029156 4∶17006.4030.094.210.0281462.4 氰酸酯改性不同环氧树脂层压板的性能表3是氰酸酯与不同种环氧树脂按质量比1∶1制成的层压板的性能.由表3可以看出,在氰酸酯与环氧树脂用量相同的条件下,氰酸酯与诺夫拉克环氧体系的胶化时间最短242s,玻璃化转变温度最高205℃,而氰酸酯与不同改性环氧树脂共混层压板的吸水率相差不大.介电性能是氰酸酯 低溴环氧树脂体系最好,氰酸酯 基础环氧树脂体系最差.这可能是由于实验中使用的3种环氧树脂的环氧值不同,低溴环氧树脂环氧值最小,诺夫拉克环氧树脂的环氧值最大,使用相同质量的环氧树脂但不同种环氧树脂的环氧基与氰酸酯基的摩尔比相差较大,低溴环氧体系中氰酸酯基的摩尔分数高,诺夫拉克环氧体系中氰酸酯基的摩尔分数最少,所以从基团的摩尔比来考虑介电性能应是低溴环氧树脂体系最好.诺夫拉克环氧是一种多官能度环氧树脂,胶化时打开的环氧基多、易于交联,所以胶化时间最短;且与其它固化后的氰酸酯 环氧树脂体系相比交联密度大,所以固化后T g高,吸水率最小,但性能较脆.表3 不同氰酸酯 环氧树脂层压板(1∶1)的性能T ab le3 T he p roperties of differen t lam inates compo sed of differen t k ind of epoxy cyanate 环氧树脂胶化时间 s T g ℃介电常数介电损耗吸水率 %低溴环氧树脂2581702.730.0090.08基础环氧树脂3911793.240.0230.09诺夫拉克环氧树脂2422053.100.0170.073 结 论采用FT2I R研究了低溴环氧树脂与氰酸酯质量比为1 1时固化机理.固化反应首先是氰酸酯发生自聚形成三聚体(三嗪环),然后三嗪环很快与环氧基反应形成异氰尿酸酯,同时也有氰酸酯直接与环氧基反应生成 唑啉进而转变成 唑烷酮,最后大量的环氧基与异氰尿酸酯反应生成 唑烷酮.氰酸酯改性低溴环氧树脂压制成层压板后,使板材的耐热性和介电性能有所提高,且随着氰酸酯质量分数的增加,T g和介电性能增加.氰酸酯与低溴环氧、基础环氧、诺夫拉克环氧共混体系的层压板的性能中,诺夫拉克环氧体系的T g最高达到205℃,胶化时间最短242s,吸水率最低0.07%;介电常数和介电损耗是低溴环氧体系最好,分别为2.73和0.009.参考文献:[1] 陈平,刘胜平.环氧树脂[M].北京:化学出版社,1999.13-17.CH EN P ing,L I U Sheng2p ing.Epoxy Resi n[M].166 第6期纪 丽,等:氰酸酯与改性环氧树脂的共固化反应及固化物的性能研究Beijing :P ress of Chem istry ,1999.13-17.[2] DON G S K .Effect of cyanate ester on the cu re be 2havi o r and therm al stab ility of epoxy resin [J ].Jour -na l of Applied Poly m er Sc ience ,1997,65(1):85-90.[3] 陈平,费敏明,唐传林.双氰胺固化环氧树脂的研究[J ].高分子学报,1990,(2):244-248.CH EN P ing ,FE I M in 2m ing ,TAN G Chuan 2lin .A study of epoxy resin s cu red w ith dicyandiam ide [J ].Acta Poly m er ica Si n ica ,1990,(2):244-248.[4] 肖卫东,何培新,黄年华,等.溴醚对环氧树脂固化物阻燃耐热性的影响[J ].热固性树脂,2002,17(3):4-7.X I AO W ei 2dong ,H E Pei 2x in ,HUAN G N ian 2hua ,et al.Influences of b romo 2ethers on flam e 2reterdancy and therm al stab ility of cu red epoxy resin [J ].Ther -m osetti ng Resi n ,2002,17(3):4-7.(责任编辑 涂 红)(上接第656页)除竞争冒险的目的.最后应当指出,本文对包含与输入跳变变量无关的乘积项C 的普遍分解形式的讨论完全能涵盖基于式(1)的传统分析.因为只要取C =0,竞争冒险产生的条件就由A B Cθ=1变为A B =1,而在增加冗余项(A B )后,相当于C =(A B ),于是有A B Cθ=A B (A B )=0,即已不可能产生竞争冒险.2 小 结本文的讨论表明了,以往对基于“与 或”二级门电路结构的竞争冒险分析是不充分的,因为没有考虑到在函数的SO P 形式中存在有与讨论变量无关的乘积项.完整的讨论应考虑该乘积项,而此时产生竞争冒险的重要条件,即输出门不被封锁,也就被发现.事实上,用增加冗余项消除竞争冒险的方法的本质就是破坏这一产生条件.最后指出,本文提出的对基于“与 或”二级门电路结构的竞争冒险分析可以推广到基于“或 与”二级门的电路结构,甚至可以推广到多值组合电路的竞争冒险分析[4]中去.参考文献:[1] HU FFM AN D .T he design and u se of hazard 2frees w itch ing netw o rk [J ].JAC M ,1957,(4):47-62.[2] E I CH ELBER GER EB .H azard detecti on in com b ina 2ti onal and sequen tial s w itch ing circu its [J ].IB M J ,1965,(9):90-99.[3] 罗朝杰.数字逻辑设计基础[M ].北京:人民邮电出版社,1982.LUO Zhao 2jie .Founda tion of D ig ita l L og ic D esign[M ].Beijing :Peop le’s Po st P ress ,1982.[4] 吴训威,沈继忠.三值组合电路的冒险分析[J ].计算机学报,1995,18(7):502-509.W U Xun 2w ei ,SH EN J i 2zhong .A nalysis of hazards fo r ternary com b inati onal circu its [J ].Ch i nese J Co m 2puter ,1995,18(7):502-509.(责任编辑 涂 红)266浙江大学学报(理学版)第30卷 。
系统医学 2023 年 12 月第 8 卷第 24期分析三联、四联药物方案治疗胃溃疡的临床效果王昌盛1，陈兰2，廖小红21.广东药科大学附属第一医院药学部，广东广州510062；2.广东三九脑科医院药剂科，广东广州510510[摘要]目的探讨胃溃疡患者选择四联药物治疗后的临床效果。
方法选取2022年1月—2023年8月广东药科大学附属第一医院收治的76例胃溃疡患者为研究对象，依据投掷硬币法分组，参照组（38例）选择三联药物治疗，研究组（38例）选择四联药物治疗，比较两组治疗总有效率、胃灼痛评分、胃溃疡面积、上腹疼痛评分、临床症状改善时间。
结果研究组治疗总有效率为97.37%，明显高于参照组，差异有统计学意义（χ2= 6.176，P<0.05）。
治疗后，研究组胃灼痛评分、胃溃疡面积、上腹疼痛评分、临床症状改善时间均低于参照组，差异有统计学意义（P均<0.05）。
结论同三联药物比较，胃溃疡患者接受四联药物治疗，可显著提升临床效果，有效改善疾病症状，可促进胃溃疡患者的良好预后。
[关键词]胃溃疡；三联药物；四联药物；疗效[中图分类号]R573 [文献标识码]A [文章编号]2096-1782（2023）12(b)-0175-03 Clinical Effect of Triple and Quadruple Drug Regimens in the Treatment of Gastric UlcerWANG Changsheng1, CHEN Lan2, LIAO Xiaohong21.Department of Pharmacy, the First Affiliated Hospital of Guangdong Pharmaceutical University, Guangzhou, Guang⁃dong Province, 510062 China;2.Department of Pharmacy, Guangdong Sanjiu Brain Hospital, Guangzhou, Guangdong Province, 510510 China[Abstract] Objective To investigate the clinical effect of quadruple drug therapy in patients with gastric ulcer. Methods Seventy-six patients with gastric ulcer admitted to the First Affiliated Hospital of Guangdong Pharmaceuti⁃cal University from January 2022 to August 2023 were selected as the research object and divided into groups ac⁃cording to coin tossing method. The reference group (38 cases) received triple drug therapy, and the study group (38 cases) received quadruple drug therapy. The total effective rate, the score of heartburn pain, the area of gastric ulcer, the score of upper abdominal pain and the improvement time of clinical symptoms were compared between the two groups. Results The total effective rate of the study group was 97.37%, which was significantly higher than that of the reference group, and the difference was statistically significant (χ2=6.176, P<0.05). After treatment, the score of heartburn pain, the area of gastric ulcer, the score of upper abdominal pain and the improvement time of clinical symptoms in the study group were lower than those in the reference group, and the differences were statistically sig⁃nificant (all P<0.05). Conclusion Compared with triple drug, quadruple drug treatment for gastric ulcer patients can significantly improve the clinical effect, effectively improve the disease symptoms, and promote the good prognosis of patients with gastric ulcer.[Key words] Gastric ulcer; Triple drug; Quadruple drugs; Curative effect对于胃溃疡疾病而言，其属于一种胃肠道高发病[1-2]。
Cranial electrotherapy stimulation (CES) is a noninva-sive, prescriptive medical treatment approved by the Food and Drug Administration for anxiety, insom-nia, and depression. About the size of a smart phone, a CES device uses electrodes typically placed on both ear lobes to send a low level (less than 1 mA), pulsed electrical current transcranially through the brain.1 An EEG analysis of 30 subjects who received one 20 min-ute CES treatment showed significant increases in alpha activity (increased relaxation) and decreases in delta ac-tivity (increased alertness) and theta activity (increased ability to focus attention).2 These changes induce a calm, relaxed, yet alert state. A recent functional magnetic resonance imaging (fMRI) study provides irrefutable proof that CES causes cortical brain deactivation in the midline frontal and parietal regions of the brain after one 20 minute treatment.3 Many psychiatric and sleep problems are thought to be caused by cortical activation from anxiety or attention disorders.4,5 Thus, the fMRI study provides additional insight into the mechanism for the effectiveness of CES.Since the early 2000s, Department of Defense (DoD) and Department of Veterans Affairs (VA) practitioners have prescribed CES for the treatment of anxiety, Post-traumatic stress disorder (PTSD), insomnia, depression, pain, and headaches.6,7 CES is classed as a tier II modal-ity for pain by The Army Surgeon General’s Pain Man-agement Task Force.8 When CES is used primarily for centralized pain, it also can decrease anxiety, insomnia, and depression, common comorbidities of pain. Tan and colleagues9compared service members’ and veterans’ preferences for 5 different therapeutic modalities for de-creasing stress, anxiety, insomnia, and pain at a veterans’ outpatient pain management clinic. Participants could choose which device they wanted to use and could use a different device if they chose at future clinic visits. Cra-nial electrotherapy stimulation was selected 73% of the time (n=144), while the other 4 stress reducing modali-ties were selected from 4% to 11% of the time (n=53).The purpose of this nonprobability, purposive sampling survey was to examine service members’ and veterans’ perceptions of the effectiveness and safety of CES for the treatment of anxiety, PTSD, insomnia, and depres-sion. It was part of a postmarketing surveillance report for the Food and Drug Administration.S AFETYCranial electrotherapy stimulation has an excellent safe-ty profile. Electromedical Products International, Inc (EPI) (Mineral Wells, TX) reported, based on a surveyMilitary Service Member and Veteran SelfReports of Efficacy of Cranial Electrotherapy Stimulation for Anxiety, Posttraumatic Stress Disorder, Insomnia, and DepressionDaniel L. Kirsch, PhD Jeffrey A. Marksberry, MDLarry R. Price, PhD Katherine T. Platoni, PsyDFrancine Nichols, PhD, RNA BSTRACTCranial electrotherapy stimulation (CES) is being prescribed for service members and veterans for the treatment of anxi-ety, posttraumatic stress disorder (PTSD), insomnia and depression. The purpose of this study was to examine service members’ and veterans’ perceptions of the effectiveness and safety of CES treatment. Service members and veterans (N=1,514) who had obtained a CES device through the Department of Defense or Veterans Affairs Medical Center from 2006-2011 were invited to participate in the web based survey via email. One hundred fifty-two participants returned questionnaires. Data were analyzed using descriptive statistics. Participants reported clinical improvement of 25% or more from using CES for anxiety (66.7%), PTSD (62.5%), insomnia (65.3%) and depression (53.9%). The majority of these participants reported clinical improvement of 50% or more. Respondents also perceived CES to be safe (99.0%). Those individuals who were not taking any prescription medication rated CES more effective than the combined CES and prescription medication group. CES provides service members and veterans with a safe, noninvasive, nondrug, easy to use treatment for anxiety, PTSD, insomnia, and depression that can be used in the clinical setting or self-directed at home.Financial DisclosureDr Kirsch is a major shareholder and officer of Electromedical Products International, Inc.Dr Marksberry is an employee of Electromedical Products International, Inc.46 /amedd_journal.aspxof Alpha-Stim CES users, that during 2007-2011 there was a total of 8,248,920 Alpha-Stim CES treatments (1,982,520 individual users treatments plus 6,266,400 in-office treatments by practitioners).Any side effects that occurred were mild and self-limiting. Reported side effects from all sources (EPI survey and the scientific literature) are 1% or less. These include dizziness, skin irritation at electrode sites, and headaches. Headaches and dizziness are usually associated with a current set-ting too high for the individual. The symptoms normally resolve when the current is decreased. Irritation at the electrode site can be decreased by using alternate sites for placement of electrodes. There have been no seri-ous adverse effects reported from using CES during 31 years on the market in the United States.10E FFICACYThe first scientific investigations of the effect of CES were performed by Russian scientists in the 1950s and 1960s. These studies focused on the effect of CES on inducing sleep. After the 1966 International Symposia for Electro-therapeutic Sleep and Electroanesthesia in Graz, Austria, American scientists began investigating the effectiveness of CES for treating anxiety, insomnia, depression, and substance abuse. Numerous publications on these topics appeared during the 1970s. These early studies were typ-ically small and had methodological limitations reflect-ing the research designs used in the time period during which they were conducted. However, the findings from the studies were consistently positive, showing CES de-creased anxiety, insomnia, and depression.1October – December 2014 47Over the past 15 years or so, the sophistication of the research designs and the quality of CES research im-proved substantially. Four randomized clinical trials (RCTs) investigated the efficacy of CES in treating state anxiety (Table 1).Three of the RCTs, used a double-blind sham controlled design, while one RCT used an investigator-blind de-sign. In these RCTs, the active CES group had signifi-cantly lower scores on state anxiety outcome measures than the sham or control group. Three RCTS on anxi-ety included Cohen’s d effect sizes that ranged from d=-0.60 (moderate) to d=-0.88 (high). Two open clini-cal studies found a significant difference from base-line to the endpoint of the study, with subjects having lower state anxiety scores at the endpoint of the study. Bystritsky and colleagues reported Cohen’s d effects sizes for 2 anxiety outcome measures: d=-1.53 on the Hamilton Anxiety Rating Scale (very high) and d=-0.75 (moderate) on the Four-Dimensional Anxiety and De-pression Rating Scale. Cranial electrotherapy stimula-tion was also shown to significantly decrease insomnia and depression (Table 2). All studies that investigated the effect of CES used reliable and valid scales for the measurement of outcomes.M ETHODSThe CES DeviceThe Alpha-Stim CES device with ear clips electrodes (0.5 Hz, 100–600 μA, 50% duty cycle, biphasic asym-metrical rectangular waves) was used in this study. Two electrodes that clip onto the ear lobes are used to send a mild electrical current through the brain. Treatment duration is a minimum of 20 minutes, but may be an hour at least one time daily. PTSD patients sometimes do a one hour CES treatment several times a day. Dur-ing acute PTSD episodes, patients may use CES for ex-tended periods of time (several hours) until symptoms decrease. While CES treatments should last a minimum of 20 minutes to achieve the desired effect, extended use of CES has no adverse side effects and is well tolerated. The QuestionnaireOne thousand five hundred fourteen (N=1,514) active duty service members and veterans who obtained an Alpha-Stim CES device through the DoD or VA medical centers from 2006 to 2011 were invited to participate in the web-based survey via email. Email addresses were obtained from prescription information for CES devices that was on file at EPI, the manufacturer of the device. All of the potential participants had been taught, using a standardized DoD or VA CES protocol, how to use self-directed CES at home. Participants either voluntarily chose to respond or not to respond to the questionnaire. Survey Monkey is the professional website (http://www. ) for survey research that was used for this study. Respondents completed the questionnaireon-line from September 1, 2011, to October 1, 2011. Of the 1,514 persons who were invited to participate in the survey, 152 (N) responses to the questionnaire were re-ceived, yielding a response rate of 10%. Although re-sponse rates vary by the population sampled, a response rate somewhere between 15% and 40% is common for web-based surveys.19,20The questionnaire contained 27 questions that covered demographic information, prescription medication use, and current exercise activity, as well as questions asking respondents to rate the effectiveness of CES technology for treating anxiety, PTSD, insomnia, and depression. A single item, 7-point Likert scale, which has established validity in the literature,21 was used to measure respon-dents’ perceived effectiveness of CES for anxiety, PTSD, insomnia, and depression. A sample question follows:If you are using CES for your PTSD, since starting CES, rate your improvement as:a. Worse (negative change)b. No change (0%)c. Slight improvement (1% to 24%)d. Fair improvement (25% to 49%)e. Moderate improvement (50% to 74%)f. Marked improvement (75% to 99%)g. Complete recovery (100%)R ESULTSData were analyzed using descriptive statistics. The characteristics of respondents, their use of CES technol-ogy, conditions for which they used CES, how often they used CES, and the length of time they had used CES are shown in Table 3. In addition to analysis of improve-ment-related questions on anxiety, PTSD, insomnia, and depression, questions were also interpreted in consid-eration of respondents’ use of prescription medication while using CES. There were 152 responses to the ques-tionnaire. Seven questionnaires did not include any ef-fectiveness and safety data. Thus, the valid sample size was N=145 for the analysis of these questions.Safety and Overall Perceived EfficacyOf the 145 persons responding to “Do you consider CES safe and effective?”, 99% reported that they view CES as safe and effective. Of the 1% of respondents (n=2) report-ing CES as unsafe or ineffective, the reasons given were (1) that they were never shown how to use CES properly, and (2) CES was ineffective for their medical condition.MILITARY SERVICE MEMBER AND VETERAN SELF REPORTS OF EFFICACY OF CRANIAL ELECTROTHERAPY STIMULATION FOR ANXIETY, POSTTRAUMATIC STRESS DISORDER, INSOMNIA, AND DEPRESSION48 /amedd_journal.aspxTHE ARMY MEDICAL DEPARTMENT JOURNALAnxietyThirty-one subjects (21.3%) reportedthat they were not currently usingCES for anxiety. One hundred four-teen subjects (combined sample tak-ing and not taking prescription medi-cations regularly) using CES for anx-iety responded to, “If you are usingCES for anxiety, since starting CES,rate your improvement as ….” Figure1 shows the results for the total group(N=114), the CES only no medica-tion group (n=26), and the CES andmedication group (n=88).Posttraumatic Stress DisorderFifty-six of the subjects (38.6%)reported not using CES for PTSD.Although PTSD is an anxiety dis-order, it was included as a separatevariable because of its importancein the treatment of service membersand veterans.22 Eighty-eight subjects(combined sample taking and nottaking prescription medication regu-larly) using CES for PTSD respondedto “If you are using CES for PTSD, since starting CES, rate your improvement as....” The findings of the total group (N=88), CES only no medication group (n=18), and CES and medication group (n=70) are shown in Fig-ure 2.InsomniaForty-six subjects (31.7%) reported that they did not use CES for insomnia. Ninety-eight subjects (combined sample taking and not taking prescription medication regularly) who used CES for insomnia responded to , “If you are using CES for insomnia, since starting CES, rate your improvement as….”The findings of the total group (N=98), CES only no medication group (n=21), and CES medication group (n=77) are shown in Figure 3. DepressionFifty-six subjects (38.6%)reported that they were not using CES for depression. Eighty-nine subjects (sub-jects combined sample taking and not taking prescrip-tion medication regularly) using CES for depression re-sponded to “If you are using CES for depression, since starting CES, rate your improvement as….” The find-ings of the total group (N=89), CES only no medication group (n=13), and CES medication group (n=76) are shown in Figure 4.Determining Important Clinical ImprovementDworkin and colleagues23 defined the criteria for impor-tant clinical improvement as follows:Improvement of moderate clinical importance is 30% to 49%, and improvement of substantial clinical impor-tance, the highest category, is 50% or more.While the criteria were developed to evaluate clini-cal trial outcomes on chronic pain, it provides a useful framework for the assessment of clinical improvement in anxiety, PTSD, insomnia, and depression as well. For this study, improvement of moderate clinical impor-tance was defined as 25% to 49% because the Likert scale which has been validated for use in measuring CES outcomes used 25% increments for categories. Using a conservative approach, the “Slight Improvement” (1% to 24%) category on the 2011 Alpha-Stim CES service members and Veterans survey was excluded, leaving the top 4 categories of “Fair Improvement” (25% to 49%), “Moderate Improvement” (50% to 74%), “Marked Im-provement” (75% to 99%) and “Complete Improvement” (100%). Participants reported clinical improvement of 25% or more from using CES for anxiety (66.7%), PTSD (62.5%), insomnia (65.3%), and depression (53.9%). The majority of service members and veterans who report-ed improvement of 25% or more had improvement inOctober – December 20144950/amedd_journal.aspxthe highest category, “substantial clinical importance,” (50% or more) on all variables: anxiety, PTSD, insomnia, and depression, as shown in Figure 5.Prescription Medication Use Of the 112 respondents who reported they took at least one prescription medication, 98 provided the name of the drug or condition for which it was taken. The number of prescription medications taken ranged from one to 11, with a mean of 2.6 and a median of 2.0. The typesof medications taken are shown in Table 4. Medica-tions that are used clinically for anxiety and depression were placed in the anxiety category.24 Medications used primarily for depression were placed in the depressionNo Change (0%)Slight (1%-24%)Fair (25%-49%)Moderate (50%-74%)Marked (75%-99%)9.7%7.7%32.5%14.0%15.4%19.2%26.9%21.6%10.2%20.2%25.0%23.7%30.8%34.1%9.1%Total GroupCES OnlyCES with Medications353025201510504017.1%16.7%14.8%22.7%22.9%22.2%22.2%24.3%23.9%31.8%31.4%33.3%5.6%6.8%4.3%Total GroupCES OnlyCES with MedicationsNo Change Slight Fair Moderate Marked 35302520151050MILITARY SERVICE MEMBER AND VETERAN SELF REPORTS OF EFFICACY OF CRANIAL ELECTROTHERAPYSTIMULATION FOR ANXIETY, POSTTRAUMATIC STRESS DISORDER, INSOMNIA, AND DEPRESSIONOctober – December 201451THE ARMY MEDICAL DEPARTMENT JOURNALcategory. Only those medications catego-rized as sedative hypnotics were placed in the insomnia category. Only those drugs speci fically approved for migraine head-aches were included in the migraine head-ache category, while all narcotic and other pain medications were included in the pain category, the subject of a separate paper.Comparison of CES with Drug Therapy Several of the most common drugs used to treat anxiety, PTSD, insomnia, depression, pain and headaches were compared to the findings of the Alpha-Stim service member and civilian surveys as shown in Figure 6. CES data from October 2011 Military Service Member and Veterans study (N=152) and the CES Ci-vilian User Survey (N=1,745) August 2011 were used. Pharmaceutical Survey Data were obtained from on-line WebMD user surveys (/drugs).The Alpha-Stim CES civilian survey was conducted in August 2011 from data collected between July 2006 and July 2011 (). The final sam-ple size from the civilian survey was 1,745 responders from a mail survey of 4,590 (38% useable responses). The WebMD drug survey asked civilians the question:“This medication has worked for me?” Respondents could choose to answer in one of 5 categories, with “1” being the lowest to “5” being the most effective. The sample size for the drugs selected ranged from N=62 to N=2,238. The CES survey questionnaire asked respondents to rate their improve-ment for a speci fic condition based on us-ing CES. Subjects could choose one of 7 categories: worse (negative change), no improvement (0%), slight improvement (1% to 24%), fair improvement (25% to 49%), moderate improvement (50% to74%), marked improvement (75% to 99%),and complete recovery (100%). While the questions in the WebMD and CES sur-veys were slightly different, all surveys asked questions about effectiveness. The WebMD data were changed to percentages and ranged from 1% to 100%. Two catego-ries were excluded from the CES survey as they were not included in the WebMD survey: worse (negative change) and no change (0%). The categories of “worse (negative change)” or “no change” re flected less than 1% of the responses in all instances (ie, on all questions).The upper 5 categories which ranged from 1% to 100%were used for comparison. The scale was the same, 1% to 100% for the data from all surveys. The comparison of the data from the 2 surveys is both appropriate and justi fiable based on the item content (ie, content/con-struct validity) and the format of item response.19C OMMENTIt is not surprising that the response rate to the survey was not higher. The majority of persons asked to par-ticipate in the survey were active duty service members.Table 4. Prescription Medi-cations Use by Condition.Anxiety 45.9%Depression 44.8%Pain 38.7%Insomnia 27.5%Hypertension 16.3%Seizure Control 11.2%Migraine Headache 9.0%Schizophrenia/Bipolar 9.0%19.5%15.6%14.3%21.4%18.1%16.3%18.4%20.4%22.0%23.8%23.4%21.4%42.9%Total GroupCES OnlyCES with Medications3530252040455052/amedd_journal.aspxMany email addresses may not have been valid because the survey covered a 6-year period and some may have moved, were discharged, or may have elected not to re-spond to the email if they were no longerusing CES. This study supports the ef-ficacy and safety of CES technology for the treatment of anxiety, PTSD, insomnia,and depression in service members andveterans. The findings are consistent with findings of previous research studies on CES. The effectiveness of CES in a mili-tary population was comparable to theeffectiveness of drugs commonly used in the treatment of the same conditions in the civilian population.Ninety-nine percent of subjects in this survey considered CES technology to be safe. An important safety bene fit of CES is that it leaves the user alert and relaxed after treatment, in contrast to drugs that can have adverse side effects and affect service members’ ability to function on missions that require intense focus and attention.25 This is particularly true in the combat theater of operations.The information on prescription medica-tion use provides a general view of drugsused by respondents for their speci fic condition(s). The findings that a high percentage of respondents took pre-scription medications for anxiety (45.9%), depression 13.5%10.5%30.1%25.0%22.5%23.0%17.1%18.0%15.4%26.3%24.7%21.0%21.4%23.1%3530252015Total GroupCES OnlyCES with Medications20.2%46.5%21.6%43.2%15.4%57.7%66.7%, N=7664.8%, n=5773.1%, n=1960.0%, n=4272.2%, n=1362.5%, N=5559.8%, n=4665.2%, N=6423.9%38.6%24.3%35.7%22.2%50.0%20.4%44.8%19.5%40.3%Total Group CES CES & Med Total Group CES & MedCES CES & Med Total Group Improved 25% to 49%Improved 50% or more MILITARY SERVICE MEMBER AND VETERAN SELF REPORTS OF EFFICACY OF CRANIAL ELECTROTHERAPYSTIMULATION FOR ANXIETY, POSTTRAUMATIC STRESS DISORDER, INSOMNIA, AND DEPRESSIONOctober – December 2014 53THE ARMY MEDICAL DEPARTMENT JOURNAL(44.8%), pain (38.7%), and insomnia (27.5%) is consistent with the literature.6,7The importance of controlling for medi-cation type and dosage in future CES studies is a valuable outcome of this sur-vey. It would also be helpful to classify the severity of illness of the subjects in future studies. While it appears that med-ication may in fluence the effectiveness of CES technology, it is possible that respon-dents taking prescription medication had far more serious symptoms and medical and psychological conditions than the no medication group. The group sizes were group was considerably smaller, ranging from 13 to 26 subjects, in comparison to the CES medication groups that ranged from 53 to 88 subjects. This may account for the differences in scores between the groups. However, the effect of medication appears to be an important confounding variable when investigating the ef ficacy of CES.C ONCLUSIONSThe results of this survey are compelling and provide the foundation for a rigorous placebo controlled RCT that investigates the effectiveness of CES for treating anx-iety, PTSD, insomnia, and depression in service mem-bers and veterans. In addition, this study also examines the in fluence of medication on CES ef ficacy outcomes. This study provides evidence that service members and veterans perceived CES as an effective treatment for anxiety, PTSD, insomnia, and depression. CES can be used either as an adjunct to pharmaceutical therapy or as a standalone therapy, providing service members and veterans with a safe, noninvasive, nonpharmacologic treatment for anxiety, PTSD, insomnia, and depression that can be used in the clinic setting, including the war-time theater clinics, or self-directed at home.R EFERENCES1.Kirsch D. The Science Behind Cranial Electro-therapy Stimulation . Edmonton, Alberta, Canada: Medical Scope Publishing; 2002.2.Kennerly R. QEEG analysis of cranial electro-therapy: a pilot study [abstract]. J Neurother . 2004;8(2):112-113. Available at: /wp-content/uploads/CES_Research/kennerly-qeeg.pdf. Accessed July 11, 2014.3.Feusner JD, Madsen S, Moody TD, Bohon C, Hem-bacher E, Bookheimer SY, Bystritsky A. Effects of cranial electrotherapy stimulation on resting state brain activity. Brain Behav . 2012;2(3):211-220.4.Y assa MA, Hazlett RL, Stark CE, Hoehn-Saric R. Functional MRI of the amygdala and bed nucleus of the stria terminalis during conditions of uncer-tainty in generalized anxiety disorder. J Psychiatr Res, 2012;46(8):1045-1052.5.Bonnet MH, Arand DL. Hyperarousal and in-somnia: state of the science. Sleep Med Rev. 2010;14(1):9-15.6.Bracciano AG, Chang WP , Kokesh S, Martinez A, Moore K. Cranial electrotherapy stimulation in the treatment of posttraumatic stress disorder. a pilot study of two military veterans. J Neurother . 2012;16(1):60-69.7.Tan G, Rintala D, Jensen MP, et al. Ef ficacy of cranial electrotherapy stimulation for neuro-pathic pain following spinal cord injury. a multi-site randomized controlled trial with a secondary 6-month open-label phase. J Spinal Cord Med . 2011;34(3):285-296.8.Pain Management Task Force: Final Report . Wash-ington, DC: US Dept of the Army, Of fice of the Surgeon General; May 2010.70%67%83%56%78%84%68%81%Sonata (n=62) 462) 163)98)1198)2028) 311)89)Service MembersCiviliansWebMD Survey9. Tan G, Dao TK, Smith DL, Robinson A, JensenMP. Incorporating complementary and alterna-tive medicine (CAM) therapies to expand psycho-logical services to veterans suffering from chronicpain. Psychol Serv. 2010;7(3):148-16110. Petitioner Presentation to Neurological DevicesPanel for Reclassification of Alpha-Stim CES De-vices From Class III to Class II. Mineral Wells, TX:Electromedical Products International, Inc; Febru-ary 10, 2012. Available at: http://www.alpha-stim.com/wp-content/uploads/EPIs-fda-presentation.pdf. Accessed July 11, 2014.11. Kim HJ, Kim WY, Lee YS, Chang M, Kim JH, ParkYC. The effect of cranial electrotherapy stimula-tion on preoperative anxiety and hemodynamic re-sponses. Korean J Anesthesiol. 2008;55(6):657-661.12. Cork RC, Wood PM, Norbert C, Shepherd JE, PriceL. The effect of cranial electrotherapy stimulation(CES) on pain associated with fibromyalgia. Inter-net J Anesthesiol[serial online]. 2004;8(2). Avail-able at: /IJA/8/2/12659. AccessedJuly 11, 2014.13.Lichtbroun AS, Raicer MC, Smith RB. The treat-ment of fibromyalgia with cranial electrotherapystimulation. J Clin Rheumatol. 2001;7(2):72-78. 14. Winick RL. Cranial electrotherapy stimulation(CES): a safe and effective low cost means ofanxiety control in a dental practice. Gen Dent.1999;47(1):50-55.15. Bystritsky A, Kerwin L, Feusner J. A pilot studyof cranial electrotherapy stimulation for gen-eralized anxiety disorder. J Clin Psychiatry.2008;69:412-417.16. Overcash SJ. Cranial electrotherapy stimulationin patients suffering from acute anxiety disorders.Am J Electromedicine. 1999;16(1):49-51.17. Taylor AG, Anderson JG, Riedel SR, Lewis JE,Kinser PA, Bourguignon C. Cranial electrical stim-ulation improves symptoms and functional statusin individuals with fibromyalgia. Pain Manag Nurs.2013;14(4):327-335.18. Mellon RR, Mackey W: Reducing sheriff’s officers’symptoms of depression using cranial electrothera-py stimulation (CES): a control experimental study.Correct Psychologist. 2009;41(1):9-15.19. Dillman D. Mail and Internet Surveys. 2nd ed.Hoboken, NJ: John Wiley & Sons; 2007.20. Czaja R, Blair J. Designing Surveys: A Guide toDecisions and Procedures. 2nd ed. Thousand Oaks,CA: Pine Forge Press; 2005.21. Davey HM, Barratt AL, Butow PN, Deeks JJ. Aone-item question with a Likert or visual analogscale adequately measured current anxiety. J ClinEpidemiol. 2007;60(4):356-360.22. US Department of Veterans Affairs, National Cen-ter for PTSD. Available at: /.Accessed May 10, 2012.23.Dworkin RH, Turk DC, Wyrwich KW, et al. Inter-preting the clinical importance of treatment out-comes in chronic pain clinical trials: IMMPACTrecommendations. J Pain. 2008;9(2):105-121.24. Mental Health Indications: What medications areused to treat anxiety disorders?. National Insti-tute of Mental Health Website; 2008. Availableat: /health/publications/mental-health-medications/index.shtml. AccessedJuly 11, 2014.25. Tilghman A, McGarry B. Medicating the military:use of psychiatric drugs has spiked; concerns surfaceabout suicide, other dangers. Army Times. March 17,2010. Available at: /art i c l e/20100317/N E W S/3170315/M e d icating-military. Accessed July 11, 2014.A UTHORSDr Kirsch is President, American Institute of Stress, Fort Worth, Texas.Dr Price is Director of Faculty Research and Professor of Psychometrics and Statistics, College of Education and Department of Mathematics, Texas State University, San Marcos, Texas.Dr Nichols is a research consultant and retired Professor, Georgetown University, Washington, DC.Dr Marksberry is Director, Science and Education, Elec-tromedical Products International, Inc, Minerals Wells, Texas.When this article was written, COL Platoni was Army Reserve Psychology Consultant to the Chief, US Army Medical Services Corp. Now retired from the Army Reserve, Dr Platoni is in private practice in Centerville, Ohio.MILITARY SERVICE MEMBER AND VETERAN SELF REPORTS OF EFFICACY OF CRANIAL ELECTROTHERAPY STIMULATION FOR ANXIETY, POSTTRAUMATIC STRESS DISORDER, INSOMNIA, AND DEPRESSION54 /amedd_journal.aspx。
基于单向拉伸的glare板力学性能测试郎利辉;张闫飞;关世伟【摘要】目的研究使用新方法制造小型大曲率glare板零件的可能性.方法通过使用传统的模具来充液成形/普通拉深成形含有半固化玻璃纤维预浸料的glare板,成形后再进行固化.在室温下,使用单向拉伸方法分别对金属、含半固化玻璃纤维预浸料的glare板和固化之后的glare板进行力学性能测试.结果含半固化玻璃纤维预浸料的glare板主要失效形式为金属板断裂,固化之后的glare板的主要失效形式为玻璃纤维断裂;含半固化玻璃纤维预浸料的glare板有着和金属相近的断后伸长率,具有较好的塑性,固化之后的glare板的断后伸长率远小于金属的断后伸长率,塑性极差.结论通过使用传统的模具来充液成形/普通拉深成形含有半固化玻璃纤维预浸料的glare板,成形后再固化的方法来制造小型大曲率glare板零件是有可能的.【期刊名称】《精密成形工程》【年(卷),期】2018(010)006【总页数】4页(P30-33)【关键词】glare板;单向拉伸;成形性能;失效形式;断后伸长率【作者】郎利辉;张闫飞;关世伟【作者单位】北京航空航天大学机械工程及自动化学院,北京100089;北京航空航天大学机械工程及自动化学院,北京100089;北京航空航天大学机械工程及自动化学院,北京100089【正文语种】中文【中图分类】TG306纤维金属层板(Fibres Metal Laminates,FMLs)是一种新型复合材料[1]，是由较薄的轻合金金属片和纤维相互铺层后在一定的压力和温度下固化而成的。
普通轻合金疲劳性能差、强度低，纤维材料刚度低、拉深成形性能差，因此两者都不能满足实际需求。
而纤维金属层板不仅避免了二者的缺点，同时还融合了纤维和轻合金共同的优点，具有良好的损伤容限性能、高比强度、高比模量、耐高温、抗疲劳、抗磨、减振、高导电(热)、尺寸稳定、不吸潮等诸多优良性能，且有些性能比基体金属材料高几倍，甚至几十倍[2]。
词语辨析（3）1、deceit/ deceptiondeceit 指“通过隐瞒或歪曲实情去蒙骗”, 一般指某个人的品质,习惯,行为等,有很强的贬义色彩He was trustful and without deceit.deception指“任何形式的欺骗”,也指“一种行动, 它给人一错误的观念, 但并不一定有欺诈的目的”. (一般不指某个人的品质,习惯,而只指其行为).●practise deception on sb. 欺骗某人。
2、dependable / dependent / dependantdependable adj.(有被动含义)可信赖的；可靠的= reliabledependent adj.(有主动含义) 依靠的, 依赖的, 从属的, 隶属的, 受控制的, = reliant●be dependent on 依靠随...而定; 依...而转移dependant n. (=dependent (A))”靠别人养活的人”3、distinct / distinctive /instinctivedistinct清晰的; 明显的; 确定无疑的● a man of very distinct character一个个性很强的人●distinct statement确切的声明●(as) distinct from 与...不同(的)●be distinct in...from... 在某方面与...不同distinctive adj.特殊的；独特的；不一般的Beer has a very distinctive smell.啤酒有一种特殊的味道。
instinctive adj.本能的●an instinctive fear of snakes;对蛇本能的恐惧；●instinctual behavior. 本能的行为4、economic /economicaleconomic adj.经济(上)的, 经济学的, 实用的, 经济的; 节省的(=economical)●economic bankruptcy经济破产She let her house at an economic rent. 她以合算的方式把房子租出去。
科技英语翻译重点句子总结1、P23 【例1】时态翻译The waster radiation is revolutionizing X-ray science, enabling researchers to see things on an atomic level with eyes that are a million times more powerful than ever before.这种歧视为废物的辐射使X射线科学发生了一场革命：它使科研工作者能用眼睛看到原子级的东西，这一放大率比以往提高了100万倍。
2、P24 【例3】虚拟语气If the reaction took hours, and not seconds, the fuel costs would be prohibitive.如果这一反应要花费数小时，而不是几秒钟，燃料费就太高了。
3、P24 【例6】虚拟语气Moving parts of a machine would wear much more rapidly without being oiled.机器的运动部件如果不加油就会磨损的非常快。
4、P24 【例7】祈使句Keep the batteries in dry places, and electricity may not be made to leak away.（如果）把蓄电池放在干燥的地方，就不会漏电。
5、P25 【例12】被动语态In other words mineral substances which are found on earth must be extracted by digging, boring holes, artificial explosions, or similar operations which make them available to us.换言之，矿物就是存在于地球上，但须经过挖掘、钻孔、人工爆破或类似作业才能获得的物质。
Abstract:The karst mud limestone of Triassic Badong formation (T2 b) is the serious engineering geological problem newly discovered in the population resettlement project in the Three Gorges Reservoir region. There are very complex structures in mud limestone, involving old structures, new structures and surface deformation structures, which coordinately control the karstification. In the old structures, the local structures such as folds and fault zones control the important segments and layers of karstification; and the mini structures such as joint and layer face popularize the karstification. The surface uplift and river cutting in new tectonic period put forward the unload and loose of rock mass, widening of karstification paths. The surface deformation structures densify the karstification paths and intensify the karstification. The mechanism of karst hazards yields to the regulation of structure controlling over karstification in mud limestone terrain, Three Gorges Reservoir region , which brings about hazards with features of broad range , huge scale and complex structure. The types of karst hazards involve uneven subsidence, fissure, landslide, collapse,mudflow and cave in.三峡库区三叠系巴东组(T2b)泥灰质岩石岩溶是移民迁建中发现的重大工程地质问题。
Rank-Based Similarity Search:Reducing the Dimensional DependenceMichael E.Houle and Michael NettAbstract—This paper introduces a data structure for k-NN search,the Rank Cover Tree(RCT),whose pruning tests rely solely on the comparison of similarity values;other properties of the underlying space,such as the triangle inequality,are not employed.Objects are selected according to their ranks with respect to the query object,allowing much tighter control on the overall execution costs.A formal theoretical analysis shows that with very high probability,the RCT returns a correct query result in time that depends very competitively on a measure of the intrinsic dimensionality of the data set.The experimental results for the RCT show that non-metric pruningstrategies for similarity search can be practical even when the representational dimension of the data is extremely high.They also show that the RCT is capable of meeting or exceeding the level of performance of state-of-the-art methods that make use of metric pruning or other selection tests involving numerical constraints on distance values.Index Terms—Nearest neighbor search,intrinsic dimensionality,rank-based searchÇ1I NTRODUCTIONO F the fundamental operations employed in data mining tasks such as classification,cluster analysis,and anom-aly detection,perhaps the most widely-encountered is that of similarity search.Similarity search is the foundation of k-nearest-neighbor(k-NN)classification,which often pro-duces competitively-low error rates in practice,particularly when the number of classes is large[26].The error rate of nearest-neighbor classification has been shown to be ‘asymptotically optimal’as the training set size increases [14],[47].For clustering,many of the most effective and popular strategies require the determination of neighbor sets based at a substantial proportion of the data set objects [26]:examples include hierarchical(agglomerative)meth-ods such as ROCK[22]and CURE[23];density-based meth-ods such as DBSCAN[17],OPTICS[3],and SNN[16];and non-agglomerative shared-neighbor clustering[27].Con-tent-basedfiltering methods for recommender systems[45] and anomaly detection methods[11]commonly make use of k-NN techniques,either through the direct use of k-NN search,or by means of k-NN cluster analysis.A very popu-lar density-based measure,the Local Outlier Factor(LOF), relies heavily on k-NN set computation to determine the rel-ative density of the data in the vicinity of the test point[8].For data mining applications based on similarity search, data objects are typically modeled as feature vectors of attributes for which some measure of similarity is defined. Often,the data can be modeled as a subset S&U belonging to a metric space M¼ðU;dÞover some domain U,with distance measure d:UÂU!Rþsatisfying the metric pos-tulates.Given a query point q2U,similarity queries over S are of two general types:k-nearest neighbor queries report a set U S of size k elements satisfying dðq;uÞdðq;vÞfor all u2U andv2S n U.Given a real value r!0,range queries report the set v2S j dðq;vÞrf g.While a k-NN query result is not necessarily unique,the range query result clearly is.Motivated at least in part by the impact of similarity search on problems in data mining,machine learning,pat-tern recognition,and statistics,the design and analysis of scalable and effective similarity search structures has been the subject of intensive research for many decades.Until rel-atively recently,most data structures for similarity search targeted low-dimensional real vector space representations and the euclidean or other L p distance metrics[44].How-ever,many public and commercial data sets available today are more naturally represented as vectors spanning many hundreds or thousands of feature attributes,that can be real or integer-valued,ordinal or categorical,or even a mixture of these types.This has spurred the development of search structures for more general metric spaces,such as the Multi-Vantage-Point Tree[7],the Geometric Near-neighbor Access Tree(GNAT)[9],Spatial Approximation Tree(SAT)[40],the M-tree[13],and(more recently)the Cover Tree(CT)[6].Despite their various advantages,spatial and metric search structures are both limited by an effect often referred to as the curse of dimensionality.One way in which the curse may manifest itself is in a tendency of distances to concen-trate strongly around their mean values as the dimension increases.Consequently,most pairwise distances become difficult to distinguish,and the triangle inequality can no longer be effectively used to eliminate candidates from con-sideration along search paths.Evidence suggests that when the representational dimension of feature vectors is highM.E.Houle is with the National Institute of Informatics,2-1-2Hitotsuba-shi,Chiyoda-ku,Tokyo101-8430,Japan.E-mail:meh@nii.ac.jp.t is with Google Japan,6-10-1Roppongi,Minato-ku,Tokyo106-6126,Japan.E-mail:mnett@.Manuscript received13Sept.2012;revised14Apr.2014;accepted27May2014.Date of publication25July2014;date of current version5Dec.2014.Recommended for acceptance by nckriet.For information on obtaining reprints of this article,please send e-mail to:reprints@,and reference the Digital Object Identifier below.Digital Object Identifier no.10.1109/TPAMI.2014.23432230162-8828ß2014IEEE.Personal use is permitted,but republication/redistribution requires IEEE permission.See /publications_standards/publications/rights/index.html for more information.(roughly20or more[5],[49]),traditional similarity search accesses an unacceptably-high proportion of the data ele-ments,unless the underlying data distribution has special properties[6],[12],[41].Even though the local neighbor-hood information employed by data mining applications is both useful and meaningful,high data dimensionality tends to make this local information very expensive to obtain.The performance of similarity search indices depends crucially on the way in which they use similarity informa-tion for the identification and selection of objects relevant to the query.Virtually all existing indices make use of numeri-cal constraints for pruning and selection.Such constraints include the triangle inequality(a linear constraint on three distance values),other bounding surfaces defined in terms of distance(such as hypercubes or hyperspheres)[25],[32], range queries involving approximation factors as in Local-ity-Sensitive Hashing(LSH)[19],[30],or absolute quantities as additive distance terms[6].One serious drawback of such operations based on numerical constraints such as the triangle inequality or distance ranges is that the number of objects actually examined can be highly variable,so much so that the overall execution time cannot be easily predicted.In an attempt to improve the scalability of applications that depend upon similarity search,researchers and practi-tioners have investigated practical methods for speeding up the computation of neighborhood information at the expense of accuracy.For data mining applications,the approaches considered have included feature sampling for local outlier detection[15],data sampling for clustering [50],and approximate similarity search for k-NN classifica-tion(as well as in its own right).Examples of fast approxi-mate similarity search indices include the BD-Tree,a widely-recognized benchmark for approximate k-NN search;it makes use of splitting rules and early termination to improve upon the performance of the basic KD-Tree.One of the most popular methods for indexing,Locality-Sensi-tive Hashing[19],[30],can also achieve good practical search performance for range queries by managing parame-ters that influence a tradeoff between accuracy and time. The spatial approximation sample hierarchy(SASH)simi-larity search index[29]has had practical success in acceler-ating the performance of a shared-neighbor clustering algorithm[27],for a variety of data types.In this paper,we propose a new similarity search struc-ture,the Rank Cover Tree(RCT),whose internal operations completely avoid the use of numerical constraints involving similarity values,such as distance bounds and the triangle inequality.Instead,all internal selection operations of the RCT can be regarded as ordinal or rank-based,in that objects are selected or pruned solely according to their rank with respect to the sorted order of distance to the query object. Rank thresholds precisely determine the number of objects to be selected,thereby avoiding a major source of variation in the overall query execution time.This precision makes ordinal pruning particularly well-suited to those data min-ing applications,such as k-NN classification and LOF out-lier detection,in which the desired size of the neighborhood sets is limited.As ordinal pruning involves only direct pair-wise comparisons between similarity values,the RCT is also an example of a combinatorial similarity search algo-rithm[21].The main contributions of this paper are as follows:A similarity search index in which only ordinalpruning is used for node selection—no use is madeof metric pruning or of other constraints involvingdistance values.Experimental evidence indicating that for practical k-NN search applications,our rank-based method isvery competitive with approaches that make explicituse of similarity constraints.In particular,it compre-hensively outperforms state-of-the-art implementa-tions of both LSH and the BD-Tree,and is capable ofachieving practical speedups even for data sets ofextremely high representational dimensionality.A formal theoretical analysis of performance show-ing that RCT k-NN queries efficiently produce cor-rect results with very high probability.Theperformance bounds are expressed in terms of ameasure of intrinsic dimensionality(the expansionrate[31]),independently of the full representationaldimension of the data set.The analysis shows thatby accepting polynomial sublinear dependence ofquery cost in terms of the number of data objects n,the dependence on the intrinsic dimensionality islower than any other known search index achievingsublinear performance in n,while still achievingvery high accuracy.To the best of our knowledge,the RCT is thefirst practical similarity search index that both depends solely on ordinal pruning,and admits a formal theoretical analysis of correct-ness and performance.A preliminary version of this work has appeared in[28].The remainder of this paper is organized as follows. Section2briefly introduces two search structures whose designs are most-closely related to that of the RCT:the rank-based SASH approximate similarity search structure [29],and the distance-based Cover Tree for exact similarity search[6].Section3introduces basic concepts and tools needed to describe the RCT.Section4presents the algorith-mic details of the RCT index.In Section5we provide a for-mal theoretical analysis of the theoretical performance guarantees of the RCT.Section6compares the practical performance of the RCT index with that of other popular methods for similarity search.Concluding remarks are made in Section7.2R ELATED W ORKThis paper will be concerned with two recently-proposed approaches that on the surface seem quite dissimilar:the SASH heuristic for approximate similarity search[29],and the Cover Tree for exact similarity search[6].Of the two, the SASH can be regarded as combinatorial,whereas the Cover Tree makes use of numerical constraints.Before for-mally stating the new results,wefirst provide an overview of both the SASH and the Cover Tree.2.1SASHA(SASH)is a multi-level structure recursively constructed by building a SASH on a half-sized random sample S0&S of the object set S,and then connecting each object remainingoutside S0to several of its approximate nearest neighbors from within S0.Queries are processed byfirst locating approximate neighbors within sample S0,and then using the pre-established connections to discover neighbors within the remainder of the data set.The SASH index relies on a pair-wise distance measure,but otherwise makes no assumptions regarding the representation of the data,and does not use the triangle inequality for pruning of search paths.SASH construction is in batch fashion,with points inserted in level order.Each node v appears at only one level of the structure:if the leaf level is level1,the probabil-ity of v being assigned to level j is1j.Each node v is attached to at most p parent nodes,for some constant p!1,chosen as approximate nearest neighbors from among the nodes at one level higher than v.The SASH guarantees a constant degree for each node by ensuring that each can serve as the parent of at most c¼4p children;any attempt to attach more than c children to an individual parent w is resolved by accepting only the c closest children to w,and reassign-ing rejected children to nearby surrogate parents whenever necessary.Similarity queries are performed by establishing an upper limit k j on the number of neighbor candidates to be retained from level j of the SASH,dependent on both j and the number of desired neighbors k(see Fig.1).The search starts from the root and progresses by successively visiting all children of the retained set for the current level,and then reducing the set of children to meet the quota for the new level,by selecting the k j elements clos-est to the query point.In the case of k-NN search,when the quota values are chosen ask j¼max k1Àj log2n;12 pc&';the total number of nodes visited is bounded byk1þ1log2n k1log2nÀ1þpc22log2n¼~Oðkþlog nÞ:SASH construction can be performed in O pcn log nðÞtimeand requires O cnðÞspace.The SASH was proposed as aheuristic structure with no formal analysis of query accu-racy;however,its lack of dependence on the representa-tional dimension of the data,together with tight control onthe execution time,allow it to achieve very substantialspeed-ups(typically1-3orders of magnitude)for real datasets of sizes and representational dimensions extending intothe millions,while still consistently achieving high accuracyrates[27],[29].Very few other efficient similarity search methods areknown to use rank information as the sole basis for accessor pruning.The recent algorithm of[48]proposes a rank-based hashing scheme,in which similarity computationrelies on rank averaging and other arithmetic operations.No experimental results for this method have appeared inthe research literature as yet.Another algorithm we consid-ered,the combinatorial random connection graph searchmethod RanWalk[21],is mainly of theoretical interest,sincethe preprocessing time and space required is quadratic inthe data set size.Due to these impracticalities,both meth-ods are excluded from the experimentation presented inSection6.2.2Cover Trees and the Expansion RateIn[31],Karger and Ruhl introduced a measure of intrinsicdimensionality as a means of analyzing the performance ofa local search strategy for handling nearest neighborqueries.In their method,a randomized structure resem-bling a skip list[42]is used to retrieve pre-computed sam-ples of elements in the vicinity of points of interest.Eventual navigation to the query is then possible by repeat-edly shifting the focus to those sample elements closest tothe query,and retrieving new samples in the vicinity of thenew points of interest.The complexity of their methoddepends heavily on the rate at which the number of visitedelements grows as the search expands.Accordingly,theylimited their attention to sets which satisfied the followingsmooth-growth property.LetB Sðv;rÞ¼f w2S j dðv;wÞr gbe the set of elements of S contained in the closed ball ofradius r centered at v2S.Given a query set U,S is said tohaveðb;dÞ-expansion if for all q2U and r>0,j B Sðq;rÞj!b¼)j B Sðq;2rÞj dÁj B Sðq;rÞj:The expansion rate of S is the minimum value of d such thatthe above condition holds,subject to the choice of minimumball set size b(in their analysis,Karger and Ruhl choseb¼O log j S jðÞ).Karger and Ruhl’s expansion rates havesince been applied to the design and analysis of routingalgorithms and distance labeling schemes[1],[10],[46].One can consider the value log2d to be a measure of theintrinsic dimension,by observing that for the euclidean dis-tance metric in R m,doubling the radius of a sphereincreases its volume by a factor of2m.When sampling R mby a uniformly distributed point set,the expanded spherewould contain proportionally as many points.However,as pointed out by the authors themselves,low-dimensional subsets in very high-dimensional spacescan Fig.1.SASH routine forfinding approximate k-nearest neighbors.have very low expansion rates,whereas even for one-dimensional data the expansion rate can be linear in the size of S .The expansion dimension log 2d is also not a robust mea-sure of intrinsic dimensionality,in that the insertion or dele-tion of even a single point can cause an arbitrarily-large increase or decrease.Subsequently,Krauthgamer and Lee [34]proposed a structure called a Navigating Net ,consisting of a hierarchy of progressively finer "-nets of S ,with pointers that allow navigation from one level of the hierarchy to the next.Their analysis of the structure involved a closely-related alterna-tive to the expansion dimension that does not depend on the distribution of S .The doubling constant is defined as the minimum value d Ãsuch that every ball B S ðq;2r Þcan be entirely covered by d Ãballs of radius r .Analogously,the doubling dimension is then defined as log 2d Ã.Although Gupta et al.[24]have shown that the doubling dimension is more general than the expansion dimension,the latter is more sensitive to the actual distribution of the point set S .In [33],Krauthgamer and Lee furthermore showed that without additional assumptions,nearest neighbor queries cannot be approximated within a factor of less than 7,unless log d Ã2O log log n ðÞ.For real-world data sets,the values of the expansion rate can be very large,typically greatly in excess of log 2n [6].In terms of d ,the execution costs associated with Navigating Nets are prohibitively high.Beygelzimer et al.[6]haveproposed an improvement upon the Navigating Net with execution costs depending only on a constant number of factors of d .They showed that the densely-interconnected graph structure of a Navigating Net could be thinned into a tree satisfying the following invariant covering tree condi-tion:for every node u at level l À1of the structure,its par-ent v at level l is such that d ðu;v Þ<2l .Nearest-neighbor search in the resulting structure,called a Cover Tree ,pro-gresses by identifying a cover set of nodes C l at every tree level l whose descendants are guaranteed to include all nearest neighbors.Fig.2shows the method by which the cover sets are generated,adapted from the original descrip-tion in [6].It assumes that the closest pair of points of S have unit distance.The asymptotic complexities of Cover Trees and Navi-gating Nets are summarized in Fig.3.Both methods have complexities that are optimal in terms of n ¼j S j ;however,in the case of Navigating Nets,the large (polynomial)dependence on d is impractically high.Experimental results for the Cover Tree show good practical performance for many real data sets [6],but the formal analysis still depends very heavily on d .The Cover Tree can also be used to answer approximate similarity queries using an early termination strategy.How-ever,the approximation guarantees only that the resulting neighbors are within a factor of 1þ"of the optimal distan-ces,for some error value ">0.The dependence on distance values does not scale well to higher dimensional settings,as small variations in the value of "may lead to great varia-tions in the number of neighbors having distances within the range.3P RELIMINARIESIn this section,we introduce some of the basic concepts needed for the description of the RCT structure,and prove a technical lemma needed for the analysis.3.1Level SetsThe organization of nodes in a Rank Cover Tree for S is sim-ilar to that of the skip list data structure [37],[42].EachnodeFig.2.Cover tree routine for finding the nearest neighbor ofqFig.3.Asymptotic complexities of Rank Cover Tree,Cover Tree,Navigating Nets (NavNet),RanWalk,and LSH,stated in terms of n ¼j S j ,neighborset size k ,and 2-expansion rate d .The complexity of NavNet is reported in terms of the doubling constant d Ã.For the RCT,we show the k -NN com-plexity bounds derived in Section 5for several sample rates,both constant and sublinear.f is the golden ratio ð1þffiffiffi5p Þ=2.For the stated bounds,the RCT results are correct with probability at least 1À1n c .The query complexities stated for the CT and NavNet algorithms are for single nearest-neighbor (1-NN )search,in accordance with the published descriptions and analyses for these methods [6],[34].Although a scheme exists for apply-ing LSH to handle k -NN queries (see Section 6),LSH in fact performs ð1þ"Þ-approximate range search.Accordingly,the complexities stated for LSH are for range search;only the approximate dependence on n is shown,in terms of r ,a positive-valued parameter that depends on the sensitivity of the family of hash functions employed.The dimensional dependence is hidden in the cost of evaluating distances and hash functions (not shown),as well as the value of r .The query bound for RanWalk is the expected time required to return the exact 1-NN .of the bottom level of the RCT(L0)is associated with a unique element of S.Definition1.A random leveling of a set S is a sequence L¼L0;L1;...ðÞof subsets of S,where for any integer j!0 the membership of L jþ1is determined by independently select-ing each node v2L j for inclusion with probability1D,for some real-valued constant D>1.The level ðvÞof an element v2S is defined as the maxi-mum index j such that v2L j;a copy of v appears at every level in the range L0;...;L j.The smallest index h such that L h¼;is the height of the random leveling.Other properties that will prove useful in analyzing the performance of Rank Cover Trees include:ðvÞis a geometrically-distributed random variable with expected value E ðvÞ½ ¼D DÀ1.The probability that v2S belongs to the non-empty level set L j is Pr ðvÞ!j½ ¼1j.The size of a random leveling,that is the sum of the cardinalities of its level sets,has expected valueEXv2S ðvÞ"#¼j S jD DÀ1:The expected height of a random leveling is logarith-mic in j S j;moreover,the probability of h greatlyexceeding its expected value is vanishingly small(see[37]):Pr½h>ðcþ1ÞE½h 1=j S j c:3.2Rank FunctionTree-based strategies for proximity search typically use a distance metric in two different ways:as a numerical(lin-ear)constraint on the distances among three data objects(or the query object and two data objects),as exemplified by the triangle inequality,or as an numerical(absolute)constraint on the distance of candidates from a reference point.The proposed Rank Cover Tree differs from most other search structures in that it makes use of the distance metric solely for ordinal pruning,thereby avoiding many of the difficul-ties associated with traditional approaches in high-dimen-sional settings,such as the loss of effectiveness of the triangle inequality for pruning search paths[12].Let U be some domain containing the point set S and the set of all possible queries.We assume the existence of an oracle which,given a query point and two objects in S, determines the object most similar to the query.Note that this ordering is assumed to be consistent with some under-lying total order of the data objects with respect to the query.Based on such an oracle we provide an abstract for-mulation of ranks.Definition 2.Let q2U be a query.The rank function r S:UÂS!N yields r Sðq;vÞ¼i if and only if v1;...;v nðÞis the ordering provided by the oracle for q and v¼v i.The k-nearest neighbor(k-NN)set of q is defined as NNðq;kÞ¼f v2S j r Sðq;vÞk g.To facilitate the analysis of the RCT,we assume that the oracle rankings are induced by a distance metric on the items of S relative to any given query point q2U.In this paper,for the sake of simplicity,we will assume that no pair of items of S have identical distances to any point in U.When desired, the uniqueness of distance values can be achieved by means of a tie-breaking perturbation scheme[20].Furthermore,the total ranking of S can also serve to rank any subset of S.For each level set L j2L,we define the rank function r Lj:UÂL j!N as r Ljðq;vÞ¼jf u2L j j rðq;uÞrðq;vÞgj,and hence-forth we take r j and r to refer to r Ljand r S,respectively.3.3Expansion RateAs with the Cover Tree,the RCT is analyzed in terms of Karger and Ruhl’s expansion rate.With respect to a query set U,a random leveling L that,for all q2U and L j2L,sat-isfies j B Ljðq;irÞj d iÁj B Ljðq;rÞj for some real value d i>0 and some integer i>1,is said to have an i-expansion of d i. We consider random levelings with2-and3-expansion rates d2and d3,respectively.For simplicity,in this version of the paper we will place no constraints on the minimum ball size,although such constraints can easily be accommodated in the analysis if desired.Henceforth,we shall take B jðq;rÞto refer to B Ljðq;rÞ.Note also that the expansion rates of random levelings may be higher than those based only on the data set itself(level0).One of the difficulties in attempting to analyze similarity search performance in terms of ranks is the fact that rank information,unlike distance,does not satisfy the triangle inequality in general.To this end,Goyal et al.[21]intro-duced the disorder inequality,which can be seen as a relaxed, combinatorial generalization of the triangle inequality.A point set S has real-valued disorder constant D if all triples of points x;y;z2S satisfyrðx;yÞDÁrðz;xÞþrðz;yÞðÞ;and D is minimal with this property.We can derive a simi-lar relationship in terms of expansion rates of a set S. Lemma1(Rank Triangle Inequality).Let d2and d3be the2-and3-expansion rates for U and the random leveling L of S.Then for any level set L l2L,and any query object q2U andelements u;v2S,r lðq;vÞmaxÈd2Ár lðq;uÞ;minÈd22;d3ÉÁr lðu;vÞÉ: Proof.From the triangle inequality,we know thatdðq;vÞdðq;uÞþdðu;vÞ:There are two cases to consider,depending on therelationship between dðq;uÞand dðq;vÞ.First,let us suppose that dðq;uÞ!dðu;vÞ.In this case,dðq;vÞ2dðq;uÞ.Since B lðq;dðq;vÞÞ B lðq;2dðq;uÞÞ,and since r lðq;vÞ¼j B lðq;dðq;vÞÞj;we haver lðq;vÞj B lðq;2dðq;uÞÞjd2j B lðq;dðq;uÞÞj d2r lðq;uÞ:。
Errors in Scientific English Writing1.汉句：这种方法具有效率高、容易调整的特点。
错句：This kind of new method have the advantage of high efficiency, easy adjustment.♦This new method has the advantages of high efficiency and easy adjustment.2.汉句：本文首先讨论了这种信号的特点，然后讨论了它的产生。
错句：This paper first discusses the features of this signal, and then its generation is described.♦This paper first discusses the features of this signal, and then describes its generation.Or:♦This paper begins with discussion on…, followed by the description of its generation.3.汉句：这台设备的特点是操作简便、价格低廉。
错句：The features of this device are easy in operation and low in price.The features of this device are easy operation and low price.4.汉句：我们的方法与以前讨论同一问题的文章中所述的不同。
错句：Our method is different from previous articles discussed the same question.Our method is different from those presented(or:described) in the papers available(or: published before) discussing5.汉句：只有通过对该系统性能的研究，我们才能了解它的优点。
