Maximum likelihood estimation of ordered multinomial parameters

The pool adjacent violator algorithm Ayer et al. (1955, The Annals of Mathematical Statistics, 26, 641-647) has long been known to give the maximum likelihood estimator of a series of ordered binomial parameters, based on an independent observation from each distribution (see Barlow et al., 1972, Statistical Inference under Order Restrictions, Wiley, New York). This result has immediate application to estimation of a survival distribution based on current survival status at a set of monitoring times. This paper considers an extended problem of maximum likelihood estimation of a series of 'ordered' multinomial parameters p(i)= (p(1i),p(2i),.,p(mi)) for 1 相似文献   

A stochastic-covariate failure model with an application to case-control analysis

A stochastic process X(t) is periodically stationary (and ergodic) if, for every k> or =1 and every (t(1),ellipsis,t(k)) in R(k), the sequence of random vectors (X(t(1)+n),ellipsis,X(t(k)+n))n=0,+1, ellipsis, is stationary (and ergodic). For such an ergodic process, let T be a positive random variable defined on the sample space of the process, representing a time of failure. The local failure-rate function is assumed to be of the form up(x),-infinity0 is a small number, tending to 0; and, for each u,T=T(u) is the corresponding failure-time. It is shown that X(T(u)) and uT(u) have, for u-->0, a limiting joint distribution and are, in fact, asymptotically independent. The marginal distributions are explicitly given. Let Y be a random variable whose distribution is the limit of that of X(T(u)). Under the hypothesis that p(x) is unknown or of known functional form but with unknown parameters, it is shown how p(x) can be estimated on the basis of independent copies of the random variable Y. The results are applied to the analysis of a case-control study featuring a 'marker' process X(t) and an 'event-time' T. The event in the study is considered to be particularly rare, and this is reflected in the assumption u-->0. The control-distribution is identified with the average marginal distribution of the (periodically stationary) marker process X(t), and the case-distribution is identified with that of Y. The particular application is a biomedical trial to determine the risk of stroke in terms of the level of an anticoagulant in the blood of the patient.     

Exact distribution for the local score of one i.i.d. random sequence.

Let X(1)...X(n) be a sequence of i.i.d. positive or negative integer-valued random variables and H(n) = max(0 < or = i < or = j < or = n)(X(i) +...+ X(j)) be the local score of the sequence. The exact distribution of H(n) is obtained using a simple Markov chain. This result is applied to the scoring of DNA and protein sequences in molecular biology.     

Speciation of phytate ion in aqueous solution. Sequestration of magnesium and calcium by phytate at different temperatures and ionic strengths, in NaCl(aq)

The formation and stability of Mg(2+) and Ca(2+)-phytate complexes was studied potentiometrically using an ISE-H(+) electrode. Measurements were performed at 10 degrees C and 25 degrees C in NaCl(aq) in the ionic strength range 0.1< or =I< or =0.75 mol L(-1). For both magnesium and calcium systems, the formation of ten M(i)PhyH(j)((12-2i-j)-) species was observed in the range 3< or =pH< or =7 with i=1, 2, 3 and j=3, 4, 5 (and i=3, j=2). These species are quite stable; here we report for example some quantitative data for the species Ca(i)PhyH(3)((9-2i)-), i=1, 2, 3 (equilibrium iCa(2+)+H(j)Phy((12-j)-)=Ca(i)PhyH(j)((12-j-2i)-): K(ij)) at I=0.25 mol L(-1) and t=25 degrees C: logK(13)=3.42, logK(23)=6.47 and logK(33)=9.41. The speciation of the Ca(2+)-phytate system was also checked by ISE-Ca(2+) measurements. Dependence on ionic strength was modeled using a simple Debye-Hückel type equation and formation constants were calculated at infinite dilution. The stability constants of complexes formed at pH>7 were estimated using an empirical predictive equation. The sequestering ability of phytate towards Mg(2+) and Ca(2+) was calculated in different experimental conditions and compared with those of other chelating agents.     

昆虫学百分率差异显著性统计分析的简易计算方法

昆虫学定量分析资料常有2类不同性质的百分率,即组成的百分率和独立的百分率。在进行差异显著性检验时,如果样本数n较大,则组成百分率可用标准正态变量μ检验。作者给出一个简便的计算公式:μ=n0.5|P1-P2|,其中ni,nj分别为第i,j组的频次数。如果只有2组,则μ=n0.5|P1-P2|,其中P1,P2分别为第1,2组的频次数。对独立的百分率进行F检验时,如果多数数据在30%～70%之外,则应通过反正弦变换使百分率变换为角度。这种变换的实际效果往往使差异显著性提高。     

中国产光萼苔科四种植物的核型研究

报道了中国产光萼苔科四种植物配子体有丝分裂中期的染色体数目和核型,四种植物的染色体数目均为n=8。核型为：细光萼苔陕西变种(P．gracillima vat．urogea)k(n)=8=8m或k(n)=8=4v 4(v);毛缘光萼苔(P．vernicosa)k(n)=8=5m 3sm或k(n)=8=6v 2J;密叶光萼苔(P．densifolia)k(n)=8=8m或k(n)=8=5v 3(v);多瓣苔(Macvicaria ulophylla)k(n)=8=6m 2sm或k(n)=8=6v 1(v) 1J．     

A Cytogeographical Study on Clintonia udensis (Liliaceae)

The genus Clintonia has four species in North America and one in eastern Asia (Fig．1)．In this paper,the karyotypes and the intraspecific morphological and cytogeographic differentiations of ten populations of C．udensis from China are analysed,and the probable origin area of the genus is also discussed．The conclusions are as follows： (1)Based On the chromosome numbers 2n=28 from the North American species,the Japanese and Himalayan groups,the earlier investigators established x=14 as the basic chromosome number of Clintonia,and they thought that there was polyploid in this genus except for aneuploid only in C．borealis (Utech,1975;Utech and Suda,1975),but a few authors(Sen,1975;Wang et al,1993)pointed out the x=7 basic number of this genus based on 2n=14 in C．udensis from Primorskiy Kray of Russia(Skolovskaya,1966)and Yunlong,Yunnan Province of China(Wang et al,1993)respectively．Our result along with there reports by previous authors(see table 1)shows that at least two ploid levels exist in C．udensis,i.e．2n＝14 and 2n＝28．The diploids are widely distributed from northwest Yunnan of China to Primorskiy Kray of Russia,while the tetraploids are located in northwest Yunnan,Himalayas,Japan,and a narrow area in Mt．Hualongshan of southern Shaanxi(07 population)(Fig．2)．Therefore,the basic chromosome number of Clintonia certainly is x=7 ratherthan x=14,while 2n=28 in North America,Japan and Himalayan area are tetraploid, not diploid, According to the previous data,so far no diploid taxa of Clintonia has been found in North America and Himalayas．So we consider that the primitive type of Clintonia is in eastern Asia,and the secondary diversity center and the present distribution center of this genus are in North America． (2)C．udensis is widely distributed in eastern Asia(Fig．2);it has two cytotypes．The karyotypes for all the diploid populations are remarkablely similar. Taken together, they can be roughly repersented by the formula:K(2n)=14=2V+6J+2v+4j(2NOR+2j). The chromosomes range in length 25.55～12.78 μm, with the ratio of the longest to the shortest 2.0. The karyotype belongs to Stebbins (1971)2A(→2B). For the tetraploid taxa, except for 07 population, karyotypes are also identical and may be roughly symbolized as: K (2n)=28=4V + 12J + 4v+8j ( 2NOR + 6j ). The length of chomosomes is from 27.87 to 13.93 μm, with the ratio of the longest to the shortest 2.0, and thus the karyotype belongs to 2A(→2B). The karyotype of 07 population is similar to those of above tetraploid taxa but also has some differences, especially in the position of satellites and the morphology of 10th and 14th pairs of chromosomes. Its formula is K(2n)=28=4V+12J(2NOR+10J)+4v+ 8j(2n=28=10m+16sm(2SAT)+2st). The ratio of the longest (23.72μm)to the shortest(12.97μm) chromosomes is 1.83. The Karyotype belongs to 2A. And the distribution range of this population is very narrow. We think that it is probably a recent evolutionary event in C. udensis. (3)Wether Clintonia in eastern Asia has 1 sp. or 2 spp. or 1 spp. and 1 var. has been debated for a long period. According to our observation, within C. udensis, only the size of seeds is related to its ploidy level, i.e. diploid individuals have smaller seeds and tetraploid ones have larger ones; the colour of seeds is related to its geographic distribution, i.e. the materials from the Himalayas through Yunnan, Sichuan to eastern Qinling Range have pale brown seeds, while those from Mt. Lüliang, Shanxi Province via Hebei, Liaoning, Jilin to Siberia and Japan have dark brown seeds. Some other morphological characters, such as the size of leaves and fruits, inflorescence type and flower numbers between individuals in one locality, even within one populaion have evident variation. Therefore, we consider that evidence(see Table 4 )for separating C. alpina or C. udensis var. alpina from C. udensis is notsufficient.     

辽宁地区产6种乌头(Aconitum)的细胞分类学研究

对我国辽宁地区毛莨科(Ranunculaceae)乌头属(Aconitum) 6个种的染色体的数目和形态进行了研究,并进行了核型分析。其染色体基数为X=8,核型公式为:两色乌头:2n=2x=2m+10sm+4st;蛇岛乌头为:2n=4x=10m+20sm(SAT)+2st+2B;黄花乌头为:2n=4x=4m+12sm(SAT)+8st+1B;北乌头三倍体为:2n=3x=2M+4m+18sm;北乌头4倍体为2n=4x=4m+28sm。同时,对乌头属下某些种的分类学问题进行了探讨。     

山东10种植物的核型分析

对山东１０ 种植物进行了核型分析。茴茴蒜（ Ｒａｎｕｎｃｕｌｕｓｃｈｉｎｅｎｓｉｓ Ｂｇｅ－） 染色体数目２ｎ ＝１６ , 核型公式Ｋ（２ｎ） ＝ ２ｘ ＝ １６ ＝ ２ Ｍ ＋ ２ｍ ＋ ２ｓｍ ＋ １０ｓｔ, “３Ａ”类型; 五脉地椒（ Ｔｈｙｍｕｓｑｕｉｎｑｕｅｃｏｓｔａｔｕｓ Ｃｅｌａｋ－） 染色体数目２ｎ＝ ２６ , 核型公式Ｋ （２ｎ） ＝ ２ｘ＝ ２６ ＝ ８ Ｍ ＋ １８ｍ , “１Ａ”类型; 蛇床（ Ｃｎｉｄｉｕｍ ｍｏｎｎｉｅｒｉ（Ｌ－） Ｃｕｓｓ－） 染色体数目２ｎ＝ ２０ , 核型公式Ｋ （２ｎ） ＝ ２ｘ＝ ２０ ＝ ２Ｍ＋ １６ｍ ＋ ２ｓｍ , “２Ｂ”类型; 波斯菊（ Ｃｏｓｍｏｓ ｂｉｐｉｎｎａｔｕｓ Ｃａｖ－） 染色体数目２ｎ ＝ ２４ , 核型公式Ｋ（２ｎ） ＝ ２ｘ ＝ ２４ ＝ １６ｍ ＋ ２ｍ （ｓａｔ） ＋ ６ｓｍ , “２Ａ”类型; 白车轴草（ Ｔｒｉｆｏｌｉｕｍ ｒｅｐｅｎｓ Ｌ－） 染色体数目２ｎ＝ ３２ , 核型公式Ｋ （２ｎ） ＝ ４ｘ ＝ ３２ ＝ ３２ｍ , “１Ａ”类型; 铁苋菜（ Ａｃａｌｙｐｈａ ａｕｓｔｒａｌｉｓ Ｌ－）染色体数目２ｎ ＝ ３２ , 核型公式Ｋ （２ｎ） ＝ ２ｘ＝ ３２ ＝ ３２ｍ , “１Ｂ”类型; 地构叶（ Ｓｐｅｒａｎｓｋｉａ ｔ?     

Efficiency of light utilization of Chlamydomonas reinhardtii under medium-duration light/dark cycles

The light regime inside a photobioreactor is characterized by a light gradient with full (sun)light at the light-exposed surface and darkness in the interior of the bioreactor. Consequently, depending on the mixing characteristics, algae will be exposed to certain light/dark cycles. In this study the green alga Chlamydomonas reinhardtii was cultivated under five different light regimes: (1) continuous illumination; (2) a square-wave light/dark cycle with a light fraction (epsilon) of 0.5 and a duration (t(c)) of 6.1 s; (3) epsilon=0.5, t(c)=14.5 s; (4) epsilon=0.5, t(c)=24.3 s and (5) epsilon=0.8, t(c)=15.2 s. The biomass yield on light energy, protein per photons, decreased under light/dark cycles (epsilon=0. 5) in comparison to continuous light (CL), from 0.207 (CL) to 0.117-0.153 g mol(-1) (epsilon=0.5). Concomitantly, the maximal specific photosynthetic activity, oxygen production per protein, decreased from 0.94 (CL) to 0.64-0.66 g g(-1) h(-1) (epsilon=0.5). Also the quantum yield of photochemistry, yield of the conversion of light energy into chemical energy, decreased from 0.47 (CL) to 0. 23 (epsilon=0.5, t(c)=24.3 s). Apparently, C. reinhardtii is not able to maintain a high photosynthetic capacity under medium-duration light/dark cycles and since specific light absorption did not change, light utilization efficiency decreased in comparison to continuous illumination.     

Quantitative structure toxicity relationships for phenols in isolated rat hepatocytes

Quantitative structure toxicity relationship (QSTR) equations were obtained to predict and describe the cytotoxicity of 31 phenols using logLD(50) as a concentration to induce 50% cytotoxicity of isolated rat hepatocytes in 2 h and logP as octanol/water partitioning: logLD(50) (microM)=-0.588(+/-0.059)logP+4.652(+/-0.153) (n=27, r(2)=0.801, s=0.261, P<1 x 10(-9)). Hydroquinone, catechol, 4-nitrophenol, and 2,4-dinitrophenol were outliers for this equation. When the ionization constant pK(a) was considered as a contributing factor a two-parameter QSTR equation was derived: logLD(50) (microM)=-0.595(+/-0.051)logP+0.197(+/-0.029)pK(a)+2.665(+/-0.281) (n=28, r(2)=0.859, s=0.218, P<1 x 10(-6)). Using sigma+, the Brown variation of the Hammet electronic constant, as a contributing parameter, the cytotoxicity of phenols towards hepatocytes were defined by logLD(50) (microM)=-0.594(+/-0.052)logP-0.552(+/-0.085)sigma+ +4.540(+/-0.132) (n=28, r(2)=0.853, s=0.223, P<1 x 10(-6)). Replacing sigma+ with the homolytic bond dissociation energy (BDE) for (X-PhOH+PhO.-->X-PhO.+PhOH) led to logLD(50) (microM)=-0.601(+/-0.066)logP-0.040(+/-0.018)BDE+4.611(+/-0.166) (n=23, r(2)=0.827, s=0.223, P<0.05). Hydroquinone, catechol and 2-nitrophenol were outliers for the above equations. Using redox potential and logP led to a new correlation: logLD(50) (microM)=-0.529(+/-0.135)logP+2.077(+/-0.892)E(p/2)+2.806(+/-0.592) (n=15, r(2)=0.561, s=0.383, P<0.05) with 4-nitrophenol as an outlier. Our findings indicate that phenols with higher lipophilicity, BDE, or sigma+ values or with lower pK(a) and redox potential were more toxic towards hepatocytes. We also showed that a collapse of hepatocyte mitochondrial membrane potential preceded the cytotoxicity of most phenols. Our study indicates that one or a combination of mechanisms; i.e. mitochondrial uncoupling, phenoxy radicals, or phenol metabolism to quinone methides and quinones, contribute to phenol cytotoxicity towards hepatocytes depending on the phenol chemical structure.     

山东米口袋属植物的核型分析

对山东米口袋属 ( Gueldenstaedtia Fisch.)植物进行了核型分析。米口袋 ( G.multiflora Bge.)核型公式 K( 2 n) =2 x=14 =14 m ,相对长度组成 2 n=14 =6 M2 +8M1,“1A”类型 ;狭叶米口袋 ( G.stenophylla Bge.)核型公式 K( 2 n) =2 x=14 =14 m,相对长度组成 2 n=14 =8M2 +6 M1,“1A”类型 ;光滑米口袋 ( G.maritimaMaxim.)核型公式 K( 2 n) =2 x=14 =12 m+2 sm,相对长度组成 2 n=14 =4 M2 +10 M1,“1A”类型。     

A higher-order generalized singular value decomposition for comparison of global mRNA expression from multiple organisms

The number of high-dimensional datasets recording multiple aspects of a single phenomenon is increasing in many areas of science, accompanied by a need for mathematical frameworks that can compare multiple large-scale matrices with different row dimensions. The only such framework to date, the generalized singular value decomposition (GSVD), is limited to two matrices. We mathematically define a higher-order GSVD (HO GSVD) for N≥2 matrices D(i)∈R(m(i) × n), each with full column rank. Each matrix is exactly factored as D(i)=U(i)Σ(i)V(T), where V, identical in all factorizations, is obtained from the eigensystem SV=VΛ of the arithmetic mean S of all pairwise quotients A(i)A(j)(-1) of the matrices A(i)=D(i)(T)D(i), i≠j. We prove that this decomposition extends to higher orders almost all of the mathematical properties of the GSVD. The matrix S is nondefective with V and Λ real. Its eigenvalues satisfy λ(k)≥1. Equality holds if and only if the corresponding eigenvector v(k) is a right basis vector of equal significance in all matrices D(i) and D(j), that is σ(i,k)/σ(j,k)=1 for all i and j, and the corresponding left basis vector u(i,k) is orthogonal to all other vectors in U(i) for all i. The eigenvalues λ(k)=1, therefore, define the "common HO GSVD subspace." We illustrate the HO GSVD with a comparison of genome-scale cell-cycle mRNA expression from S. pombe, S. cerevisiae and human. Unlike existing algorithms, a mapping among the genes of these disparate organisms is not required. We find that the approximately common HO GSVD subspace represents the cell-cycle mRNA expression oscillations, which are similar among the datasets. Simultaneous reconstruction in the common subspace, therefore, removes the experimental artifacts, which are dissimilar, from the datasets. In the simultaneous sequence-independent classification of the genes of the three organisms in this common subspace, genes of highly conserved sequences but significantly different cell-cycle peak times are correctly classified.     

葱属植物物种生物学研究 Ⅰ.葱属6种材料的核型研究

分析了葱属(Allium L.)5个种6个居群的细胞学特征。这些种是太白韭(A.prattii C.H.Wright apud Forb.et Hemsl.),该种包括两个居群(Ⅰ、Ⅱ)。居群Ⅰ:K(2n)=2x=16=9m+1m(SAT)+4sm+2st,居群Ⅱ:K(2n)=2x=16=10m+5sm+1sm(SAT);天蒜(A.paepalanthoides Airy-Shaw):K(2n)=2x=16=14m+2sm+3B;多叶韭(A.Plurifoliatum Rendle):K(2n)=2x=16=14m+2sm+1B;合被韭(A.tubiflorum Rendle):K(2n)=2x=16=12m+2m(SAT)+2sm;峨眉韭(A.omeiense Z.Y.Zhu):K(2n)=2x=22=2m+18sm+2T(SAT)。所研究的6批材料均为二倍体,除合被韭的核型为“1A”型,蛾眉韭的核型为“3A”型外,其余4批材料的核型均为“2A”型。其中峨眉韭和多叶韭的染色体数目为首次报道,天蒜和多叶韭的细胞中首次发现B染色体,并对其相互关系进行了探讨。     

甘肃萱草属植物的核型研究

本文研究了甘肃萱草属6种、1变种的染色体核型;黄花菜K(2n)=22=12m+10sm(2SAT);小黄花菜K(2n)=22=10m+12sm;北萱草K(2n)=22=8m+14sm;北黄花菜K(2n)=22=14m+6sm+2st;萱草K(2n)=22=12m+8sm+2st;重瓣萱草K(2n)=33=18m+12sm+3st:折叶萱草K(2n)=22=10m+10sm+2st。以上核型可自然地分成两大类群,第一类群包括小黄花菜、北萱草、黄花菜;第二类群包括折叶萱草、萱草、重瓣萱草、北黄花菜。     

Optimization of solvation models for predicting the structure of surface loops in proteins

A novel procedure for optimizing the atomic solvation parameters (ASPs) sigma(i) developed recently for cyclic peptides is extended to surface loops in proteins. The loop is free to move, whereas the protein template is held fixed in its X-ray structure. The energy is E(tot) = E(FF)(epsilon = nr) + summation operator sigma(i)A(i), where E(FF)(epsilon = nr) is the force-field energy of the loop-loop and loop-template interactions, epsilon = nr is a distance-dependent dielectric constant, and n is an additional parameter to be optimized. A(i) is the solvent-accessible surface area of atom i. The optimal sigma(i) and n are those for which the loop structure with the global minimum of E(tot)(n, sigma(i)) becomes the experimental X-ray structure. Thus, the ASPs depend on the force field and are optimized in the protein environment, unlike commonly used ASPs such as those of Wesson and Eisenberg (Protein Sci 1992;1:227-235). The latter are based on the free energy of transfer of small molecules from the gas phase to water and have been traditionally combined with various force fields without further calibration. We found that for loops the all-atom AMBER force field performed better than OPLS and CHARMM22. Two sets of ASPs [based on AMBER (n = 2)], optimized independently for loops 64-71 and 89-97 of ribonuclease A, were similar and thus enabled the definition of a best-fit set. All these ASPs were negative (hydrophilic), including those for carbon. Very good (i.e., small) root-mean-square-deviation values from the X-ray loop structure were obtained with the three sets of ASPs, suggesting that the best-fit set would be transferable to loops in other proteins as well. The structure of loop 13-24 is relatively stretched and was insensitive to the effect of the ASPs.     

Studies on the Karyotype of 5 Samples of Allium Sect. Bromatorrhiza Ekberg

The karyotypes of 5 samples in Allium Sect. Bromatorrhiza Ekberg were analysed in this paper. In Allium wallichii Kunth, the first sample is a diploid, with genome formula is AA and karyotype formula is K(2n)=2x=14=2m(SAT)+2m+10sm. The second is an autotetraploid, with genome formula AAAA, karyotype formul K(2n)=4x=28=2m(SAT)+6m+20sm. These two karyotypes belong to “3A”. The two karyotypes of A. wallichii Kunth are similar in morphology, though different in ploidy. In Allium hookeri Thwaites, the first sample is a dibasic autoallotriploid. Its genome formula is AAB₁; the basic number of the genome A is 7 and that of the genome B₁ is 8. The karyotype formula is K(2n)=2x+x'=22=(12sm+2t)+(1m+4sm+1st+2t). The second is also an autoallotriploid. The genomes in pairs are similar to those in the first sample in size and morphology of chromosomes. However, the unpaired genome differs from the first one apparently. Therefore, its genome formula is AAB₂, and karyotype formula is K(2n)=2x+ x'=22=(12sm+2t)+(3m+1sm+2st+2t). The third is doubling of the first karyotype. It is an autoallohexaploid, with genome formula AAAAB₁ B₁ and karyotype formula K(2n)=4x+2x'= 44= (24sm+4t) + (2m+8sm+2st+4t). These three karyotypes belong to “3A”.     

Dynamic stability of passive dynamic walking on an irregular surface

Falls that occur during walking are a significant health problem. One of the greatest impediments to solve this problem is that there is no single obviously "correct" way to quantify walking stability. While many people use variability as a proxy for stability, measures of variability do not quantify how the locomotor system responds to perturbations. The purpose of this study was to determine how changes in walking surface variability affect changes in both locomotor variability and stability. We modified an irreducibly simple model of walking to apply random perturbations that simulated walking over an irregular surface. Because the model's global basin of attraction remained fixed, increasing the amplitude of the applied perturbations directly increased the risk of falling in the model. We generated ten simulations of 300 consecutive strides of walking at each of six perturbation amplitudes ranging from zero (i.e., a smooth continuous surface) up to the maximum level the model could tolerate without falling over. Orbital stability defines how a system responds to small (i.e., "local") perturbations from one cycle to the next and was quantified by calculating the maximum Floquet multipliers for the model. Local stability defines how a system responds to similar perturbations in real time and was quantified by calculating short-term and long-term local exponential rates of divergence for the model. As perturbation amplitudes increased, no changes were seen in orbital stability (r(2)=2.43%; p=0.280) or long-term local instability (r(2)=1.0%; p=0.441). These measures essentially reflected the fact that the model never actually "fell" during any of our simulations. Conversely, the variability of the walker's kinematics increased exponentially (r(2)>or=99.6%; p<0.001) and short-term local instability increased linearly (r(2)=88.1%; p<0.001). These measures thus predicted the increased risk of falling exhibited by the model. For all simulated conditions, the walker remained orbitally stable, while exhibiting substantial local instability. This was because very small initial perturbations diverged away from the limit cycle, while larger initial perturbations converged toward the limit cycle. These results provide insight into how these different proposed measures of walking stability are related to each other and to risk of falling.     

七种药用植物的染色体研究

对山东７种药用植物的染色体进行了研究。结果表明：田旋花（ＣｏｎｖｏｌｖｕｌｕｓａｒｖｅｎｓｉｓＬ）的染色体数目为２ｎ＝７８;蜜柑草（ＰｈｙｌａｎｔｈｕｓｍａｔｓｕｍｕｒａｅＨａｖａｔａ）的染色体数目为ｎ＝８８;挂红灯（ＰｈｙｓａｌｉｓａｌｋｅｋｅｎｇｉＬｖａｒｆｒａｎｃｈｅｔｉ（Ｍａｓｔ）Ｍａｋｉｎｏ）的染色体数目为２ｎ＝２４,核型公式为Ｋ（２ｎ）＝２４＝２ｍ＋１８ｓｍ＋２ｓｔ＋２ｓｔ（ｓａｔ）,核型“２Ａ”型;无剌曼陀罗（ＤａｔｕｒａｓｔｒａｍｏｎｉｕｍＬｖａｒｉｎｅｒｍｉｓ（Ｊａｃｑ）ＳｃｈｉｎｚｅｔＴｈｅｌ）的染色体数目为２ｎ＝２４,核型公式为Ｋ（２ｎ）＝２４＝２０ｍ＋４ｓｍ,核型“１Ｂ”型;决明（ＣａｓｉａｔｏｒａＬ）的染色体数目为２ｎ＝２６,核型公式为Ｋ（２ｎ）＝２６＝２４ｍ＋２ｓｍ,核型“１Ａ”型;荔枝草（ＳａｌｖｉａｐｌｅｂｅｉａＲＢｒ）的染色体数目为２ｎ＝１６,核型公式为Ｋ（２ｎ）＝１６＝６ｍ＋１０ｓｍ,核型“２Ａ”型;车前（ＰｌａｎｔａｇｏａｓｉａｔｉｃａＬ）的染色体数目为２ｎ＝３６,核型公式为Ｋ（２ｎ）＝３６＝３２ｍ＋４ｓｍ,核型“１Ａ”型。     

五种苏铁属植物的核形态

报道了苏铁属（Cycas L.)5种植物的染色体数目和核型,除多歧苏铁外,其他种均为首次报道。5个种的体细胞中期染色体核型公式分别为：滇南苏铁C.diannanensis K(2n)=2x=22=2m 4sm 4st 12T;潭清苏铁C.tanqingii K(2n)=2x=22=2m 8sm 2st 10T;多歧苏的Cmultipinnata K(2n)=2x=22=4m 8st 2st 8T;巴兰萨苏铁C.balansae K(2n)=2x=xx=2m 4sm 6st 10T。石山苏铁C.miquelii K(2n)=22=2m 6sm(1SAT) 4st 10T;核型均属于3B型。本研究结果支持苏铁属植物的核型从不对称进化的观点;同时,支持将巴兰萨苏铁和石山苏铁归入攀枝花苏铁组的台湾苏铁亚组的观点。