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Showing papers by "National Tsing Hua University published in 2003"


Journal ArticleDOI
TL;DR: Six bacterial strains with the capability of degrading textile dyes were isolated from sludge samples and mud lakes and Aeromonas hydrophila was selected and identified because it exhibited the greatest color removal from various dyes.

726 citations


Journal ArticleDOI
TL;DR: In this paper, a different approach based on unequal probability sampling theory is proposed for the estimation of Shannon's index of diversity when the number of species and the species abundances are unknown.
Abstract: A biological community usually has a large number of species with relatively small abundances. When a random sample of individuals is selected and each individual is classified according to species identity, some rare species may not be discovered. This paper is concerned with the estimation of Shannon’s index of diversity when the number of species and the species abundances are unknown. The traditional estimator that ignores the missing species underestimates when there is a non-negligible number of unseen species. We provide a different approach based on unequal probability sampling theory because species have different probabilities of being discovered in the sample. No parametric forms are assumed for the species abundances. The proposed estimation procedure combines the Horvitz–Thompson (1952) adjustment for missing species and the concept of sample coverage, which is used to properly estimate the relative abundances of species discovered in the sample. Simulation results show that the proposed estimator works well under various abundance models even when a relatively large fraction of the species is missing. Three real data sets, two from biology and the other one from numismatics, are given for illustration.

697 citations


Journal ArticleDOI
TL;DR: A hand gesture recognition system to recognize continuous gesture before stationary background consisting of a real time hand tracking and extraction, feature extraction, hidden Markov model (HMM) training, and gesture recognition.

511 citations


Journal ArticleDOI
TL;DR: Convergent findings from the behavioral screen for memory mutants and DNA microarray analysis of transcriptional responses during memory formation in normal animals suggest the involvement of the pumilio/staufen pathway in memory.

486 citations


Journal ArticleDOI
TL;DR: Surprising cross-language correlations in naming latencies, frequency, and length challenge widely held assumptions about the lexical locus of length and frequency effects, suggesting instead that they may reflect familiarity and accessibility at a conceptual level that is shared over languages.
Abstract: Timed picture naming was compared in seven languages that vary along dimensions known to affect lexical access. Analyses over items focused on factors that determine cross-language universals and cross-language disparities. With regard to universals, number of alternative names had large effects on reaction time within and across languages after target-name agreement was controlled, suggesting inhibitory effects from lexical competitors. For all the languages, word frequency and goodness of depiction had large effects, but objective picture complexity did not. Effects of word structure variables (length, syllable structure, compounding, and initial frication) varied markedly over languages. Strong cross-language correlations were found in naming latencies, frequency, and length. Other-language frequency effects were observed (e.g., Chinese frequencies predicting Spanish reaction times) even after within-language effects were controlled (e.g., Spanish frequencies predicting Spanish reaction times). These surprising cross-language correlations challenge widely held assumptions about the lexical locus of length and frequency effects, suggesting instead that they may (at least in part) reflect familiarity and accessibility at a conceptual level that is shared over languages.

457 citations



Journal ArticleDOI
TL;DR: A new route for the design of electroluminescent polymers by grafting high-efficiency phosphorescent organometallic complexes as dopants and charge transport moieties onto alky side chains of fully conjugated polymers for polymer light-emitting diodes (PLED) with single layer/single polymers is reported.
Abstract: We report a new route for the design of electroluminescent polymers by grafting high-efficiency phosphorescent organometallic complexes as dopants and charge transport moieties onto alky side chains of fully conjugated polymers for polymer light-emitting diodes (PLED) with single layer/single polymers. The polymer system studied involves polyfluorene (PF) as the base conjugated polymer, carbazole (Cz) as the charge transport moiety and a source for green emission by forming an electroplex with the PF main chain, and cyclometalated iridium (Ir) complexes as the phosphorescent dopant. Energy transfer from the green Ir complex or an electroplex formed between the fluorene main chain and side-chain carbazole moieties, in addition to that from the PF main chain, to the red Ir complex can significantly enhance the device performance, and a red light-emitting device with the high efficiency 2.8 cd/A at 7 V and 65 cd/m2, comparable to that of the same Ir complex-based OLED, and a broad-band light-emitting device containing blue, green, and red peaks (2.16 cd/A at 9 V) are obtained.

414 citations


Journal ArticleDOI
TL;DR: In this paper, the X-ray diffraction (XRD) θ-scan curve shows a full width at half maximum (FWHM) value of 2°, indicating that the c-axes of the nanorods are along the normal direction of the substrate surface.
Abstract: Needle-like ZnO nanowires with high density are grown uniformly and vertically over an entire Ga-doped conductive ZnO film at 550 °C. The nanowires are grown preferentially in the c-axis direction. The X-ray diffraction (XRD) θ-scan curve shows a full width at half maximum (FWHM) value of 2°. This indicates that the c-axes of the nanorods are along the normal direction of the substrate surface. The investigation using high-resolution transmission electron microscopy (HRTEM) confirmed that each nanowire is a single crystal. A room-temperature photoluminescence (PL) spectrum of the wires consists of a strong and sharp UV emission band at 380 nm and a weak and broad green–yellow band. It reveals a low concentration of oxygen vacancies in the ZnO nanowires and their high optical quality. Field electron emission from the wires was also investigated. The turn-on field for the ZnO nanowires was found to be about 18 V μm–1 at a current density of 0.01 μA cm–2. The emission current density from the ZnO nanowires reached 0.1 mA cm–2 at a bias field of 24 V μm–1.

396 citations


Journal ArticleDOI
TL;DR: In this article, the critical thrust force at the onset of delamination is predicted and compared with the twist drill, and the effect of various drill geometries were discussed in analytical fashion.

360 citations


Journal ArticleDOI
TL;DR: In this paper, the existence of structural disorder at the particle surface that either does not form hydrogen bonding due to lack of adequate bonding parameters or forms a very weak dipolar bonding has been explained as a result of chemical interactions between the phosphate groups either with the surface adsorbed water or the hydroxyl groups at the surface of the nano-particles.

351 citations


Journal ArticleDOI
TL;DR: In this paper, the collapse of rotating magnetized molecular cloud cores is studied, focusing on rotation and magnetic braking during the main accretion phase of isolated star formation, where the collapse starts from the center and propagates outward in an inside-out fashion, satisfying exact selfsimilarity in space and time.
Abstract: We study numerically the collapse of rotating magnetized molecular cloud cores, focusing on rotation and magnetic braking during the main accretion phase of isolated star formation. Motivated by previous numerical work and analytic considerations, we idealize the precollapse core as a magnetized singular isothermal toroid, with a constant rotational speed everywhere. The collapse starts from the center and propagates outward in an inside-out fashion, satisfying exact self-similarity in space and time. For rotation rates and field strengths typical of dense low-mass cores, the main feature remains the flattening of the mass distribution along field lines—the formation of a pseudodisk, as in the nonrotating cases. The density distribution of the pseudodisk is little affected by rotation. On the other hand, the rotation rate is strongly modified by pseudodisk formation. Most of the centrally accreted material reaches the vicinity of the protostar through the pseudodisk. The specific angular momentum can be greatly reduced on the way, by an order of magnitude or more, even when the precollapse field strength is substantially below the critical value for dominant cloud support. The efficient magnetic braking is due to the pinched geometry of the magnetic field in the pseudodisk, which strengthens the magnetic field and lengthens the level arm for braking. Both effects enhance the magnetic transport of angular momentum from inside to outside. The excess angular momentum is carried away in a low-speed outflow that has, despite claims made by other workers, little in common with observed bipolar molecular outflows. We discuss the implications of our calculations for the formation of true disks that are supported against gravity by rotation.

Journal ArticleDOI
TL;DR: In this article, the mobilities of hole and electron in a series of compounds were studied computationally based on the Marcus electron transfer theory, using the DFT B3LYP/6-31G* method in the Gaussian 98 program suite.
Abstract: To enable the design of efficient organic electroluminescence (OLED) devices with desirable charge carrier transport properties, the mobilities of hole and electron in a series of compounds were studied computationally based on the Marcus electron transfer theory. MO calculations were performed, using the DFT B3LYP/6-31G* method in the Gaussian 98 program suite, on the following compounds: biphenyl (Bp), 4,4‘-biphenyldiamine (BA), triphenylamine (TPA), tri-p-tolylamine (TTA), 4-biphenylphenyl-m-tolylamine (BPTA), 4,4‘-bis(phenyl-m-tolylamino)biphenyl (TPD), naphthalene (Np), 1-naphthyldiphenylamine (NDPA), 1-biphenylnaphthylphenylamine (BNPA), and 4,4‘-bis(1-naphthylphenylamino)biphenyl (NPB). The geometries of these compounds in their neutral, cationic, and anionic states were optimized. The optimized geometries were then used to calculate the ionization potential, electron affinity, and reorganization energies. For compounds containing a biphenyl moiety (Bp, BA, BPTA, TPD, BNPA, and NPB), the inter-rin...

Journal ArticleDOI
TL;DR: It was found that both genipin and carbodiimide are effective crosslinking agents for tissue fixation andGenipin crossl linking is comparatively slower than carbodiIMide crosslinks, and tissue fixation in genipIn and/or carbodiamide may produce distinctCrosslinking structures.
Abstract: The study was to investigate the crosslinking characteristics, mechanical properties, and resistance against enzymatic degradation of biological tissues after fixation with genipin (a naturally occurring crosslinking agent) and/or carbodiimide. Fresh tissue was used as a control. It was found that both genipin and carbodiimide are effective crosslinking agents for tissue fixation and genipin crosslinking is comparatively slower than carbodiimide crosslinking. Additionally, tissue fixation in genipin and/or carbodiimide may produce distinct crosslinking structures. Carbodiimide may form intrahelical and interhelical crosslinks within or between tropocollagen molecules, whereas genipin may further introduce intermicrofibrillar crosslinks between adjacent collagen microfibrils. The stability (denaturation temperature and resistance against enzymatic degradation) of the fixed tissue is mainly determined by its intrahelical and interhelical crosslinks. In contrast, intermicrofibrillar crosslinks significantly affect the mechanical properties (tissue shrinkage during fixation, tensile strength, strain at break, and ruptured pattern) of the fixed tissue. Moreover, the degree of enzymatic degradation of the fixed tissue may be influenced by three factors: the availability, to the enzyme, of recognizable cleavage sites, the degree of crosslinking, and the extent of helical integrity of tropocollagen molecules in tissue.

Journal ArticleDOI
TL;DR: Two neutral pyrazolato diimine rhenium(I) carbonyl complexes with formula [Re(CO)(3)(N-N)(btpz)], where N-N = 2,2'-bipyridine and 1,10-phenanathroline, and btpz = 3,5-bis(trifluoromethyl) pyrazolate, were synthesized and characterized by elemental analysis, routine spectroscopic methods,
Abstract: Two neutral pyrazolato diimine rhenium(I) carbonyl complexes with formula [Re(CO)3(N-N)(btpz)] where N-N = 2,2‘-bipyridine (1) and 1,10-phenanathroline (2), and btpz = 3,5-bis(trifluoromethyl) pyrazolate, were synthesized and characterized by elemental analysis, routine spectroscopic methods, and single-crystal X-ray diffraction study. Ground and excited state properties of these complexes were investigated by steady-state and time-resolved spectroscopies. Complexes 1 and 2 show photoluminescent emission in both solution and solid-state at room temperature, arising from metal to ligand charge-transfer (MLCT) transition with strong overlapping of intraligand π → π* transitions. The long-lived excited state lifetimes of complexes 1 and 2, which are on the order of microseconds, indicate the presence of phosphorescent emission. As these complexes hold the potential to serve as phosphors for organic light-emitting diodes (OLEDs), their electroluminescent performances were evaluated by employing them as dopant...

Journal ArticleDOI
01 Oct 2003-Polymer
TL;DR: In this paper, a chitosan gel bead was synthesized by a coupled ionic and chemical co-crosslinking mechanism, which was characterized by FTIR, UV and EDAX spectroscopy.

Journal ArticleDOI
TL;DR: It is established that the activity of immobilized lipase could be significantly increased when such alcohols were used for an immersion pretreatment of the enzyme.

Journal ArticleDOI
TL;DR: In this paper, the diameter of the nanoparticles is approximately 10nm with a specific surface area of 106.9mm 2 /g, and the particle size increases as the calcination temperature is increased.

Journal ArticleDOI
TL;DR: Examination of the mechanism of the decolorization process by cell beads indicated that it proceeded primarily by biologicalDecolorization associated with partial adsorption of the dye onto the entrapped cells and gel matrix.

Journal ArticleDOI
TL;DR: In this paper, the role of the copper species in the CO oxidation reaction was investigated in terms of species transformation and change in the number of surface lattice oxygen ions, and the light-off behaviors were observed over both Cu and Cu2O powders.
Abstract: Carbon monoxide oxidation activities over Cu, Cu2O, and CuO were studied to seek insight into the role of the copper species in the oxidation reaction. The activity of copper oxide species can be elucidated in terms of species transformation and change in the number of surface lattice oxygen ions. The propensity of Cu2O toward valence variations and thus its ability to seize or release surface lattice oxygen more readily enables Cu2O to exhibit higher activities than the other two copper species. The non-stoichiometric metastable copper oxide species formed during reduction are very active in the course of CO oxidation because of its excellent ability to transport surface lattice oxygen. Consequently, the metastable cluster of CuO is more active than CuO, and the activity will be significantly enhanced when non-stoichiometric copper oxides are formed. In addition, the light-off behaviors were observed over both Cu and Cu2O powders. CO oxidation over metallic Cu powders was lighted-off because of a synergistic effect of temperature rises due to heat generation from Cu oxidation as well as CO oxidation over the partially oxidized copper species.

Journal ArticleDOI
TL;DR: A naturally occurring crosslinking agent (genipin) was used to crosslink gelatin microspheres as a biodegradable drug-delivery system for intramuscular administration and indicated that the genipin-crosslinked gelatinmicrospheres may be used as a long-acting drug carrier for intramscular administration.
Abstract: Gelatin microspheres have been widely evaluated as a drug carrier. Nevertheless, gelatin dissolves rather rapidly in aqueous environments, making the use of the polymer difficult for the production of long-term delivery systems. This adverse aspect requires the use of a crosslinking agent in forming nonsoluble networks in microspheres. However, the use of crosslinking agents such as formaldehyde and glutaraldehyde can lead to toxic side effects owing to residual crosslinkers. In an attempt to overcome this problem, a naturally occurring crosslinking agent (genipin) was used to crosslink gelatin microspheres as a biodegradable drug-delivery system for intramuscular administration. Glutaraldehyde was used as a control. In the in vitro study, the morphology, dynamic swelling, and antienzymatic degradation of test microspheres were evaluated. In the in vivo study, the biocompatibility and degradability of test microspheres were implanted in the skeletal muscle of a rat model via intramuscular injection. The results obtained in the study suggested that crosslinking of gelatin microspheres with glutaraldehyde or genipin may produce distinct crosslinking structures. The water transport mechanism in both the glutaraldehyde- and genipin-crosslinked gelatin microspheres exhibit anomalous behavior ranging from Fickian to Case-II extremes. The increase of the swelling diameter for the genipin-crosslinked microspheres was significantly less than that observed for the glutaraldehyde-crosslinked microspheres. In the animal study, it was found that the degree in inflammatory reaction for tissues implanted with the genipin-crosslinked microspheres was significantly less than that implanted with the glutaraldehyde-crosslinked microspheres. Additionally, the degradation rate of the genipin-crosslinked microspheres was significantly slower than their glutaraldehyde-crosslinked counterparts. These results indicated that the genipin-crosslinked gelatin microspheres may be used as a long-acting drug carrier for intramuscular administration.

Patent
06 Jun 2003
TL;DR: In this paper, a non-volatile memory cell is constructed from a chalcogenide alloy structure and an associated electrode side wall, where the memory cells are accessed through address lines and address circuitry created during the formation of memory cells.
Abstract: A non-volatile memory cell is constructed from a chalcogenide alloy structure and an associated electrode side wall The electrode is manufactured with a predetermined thickness and juxtaposed against a side wall of the chalcogenide alloy structure, wherein at least one of the side walls is substantially perpendicular to a planar surface of the substrate The thickness of the electrode is used to control the size of the active region created within the chalcogenide alloy structure Additional memory cells can be created along rows and columns to form a memory matrix The individual memory cells are accessed through address lines and address circuitry created during the formation of the memory cells A computer can thus read and write data to particular non-volatile memory cells within the memory matrix

Journal ArticleDOI
TL;DR: The results indicate that the structure and properties of the second shell are dictated by those of the first layer, and the outer shell is apparently designed to stabilize/protect the inner-shell and complement/enhance its properties.
Abstract: The role of the second shell in the process of metal binding and selectivity in metalloproteins has been elucidated by combining Protein Data Bank (PDB) surveys of Mg, Mn, Ca, and Zn binding sites with density functional theory/continuum dielectric methods (DFT/CDM). Peptide backbone groups were found to be the most common second-shell ligand in Mg, Mn, Ca, and Zn binding sites, followed (in decreasing order) by Asp/Glu, Lys/Arg, Asn/Gln, and Ser/Thr side chains. Aromatic oxygen- or nitrogen-containing side chains (Tyr, His, and Trp) and sulfur-containing side chains (Cys and Met) are seldom found in the second coordination layer. The backbone and Asn/Gln side chain are ubiquitous in the metal second coordination layer as their carbonyl oxygen and amide hydrogen can act as a hydrogen-bond acceptor and donor, respectively, and can therefore partner practically every first-shell ligand. The second most common outer-shell ligand, Asp/Glu, predominantly hydrogen bonds to a metal-bound water or Zn-bound histidine and polarizes the H-O or H-N bond. In certain cases, a second-shell Asp/Glu could affect the protonation state of the metal ligand. It could also energetically stabilize a positively charged metal complex more than a neutral ligand such as the backbone and Asn/Gln side chain. As for the first shell, the second shell is predicted to contribute to the metal selectivity of the binding site by discriminating between metal cations of different ionic radii and coordination geometries. The first-shell-second-shell interaction energies decay rapidly with increasing solvent exposure of the metal binding site. They are less favorable but are of the same order of magnitude as compared to the respective metal-first-shell interaction energies. Altogether, the results indicate that the structure and properties of the second shell are dictated by those of the first layer. The outer shell is apparently designed to stabilize/protect the inner-shell and complement/enhance its properties.

Journal ArticleDOI
TL;DR: Three redundancy analysis algorithms which can be implemented on-chip based on the local-bitmap idea are presented: the local repair-most approach is efficient for a general spare architecture, and the local optimization approach has the best repair rate.
Abstract: With the advance of VLSI technology, the capacity and density of memories is rapidly growing. The yield improvement and testing issues have become the most critical challenges for memory manufacturing. Conventionally, redundancies are applied so that the faulty cells can be repairable. Redundancy analysis using external memory testers is becoming inefficient as the chip density continues to grow, especially for the system chip with large embedded memories. This paper presents three redundancy analysis algorithms which can be implemented on-chip. Among them, two are based on the local-bitmap idea: the local repair-most approach is efficient for a general spare architecture, and the local optimization approach has the best repair rate. The essential spare pivoting technique is proposed to reduce the control complexity. Furthermore, a simulator has been developed for evaluating the repair efficiency of different algorithms. It is also used for determining certain important parameters in redundancy design. The redundancy analysis circuit can easily be integrated with the built-in self-test circuit.

Journal ArticleDOI
TL;DR: In this article, the optimal range of chisel edge length with respect to drill diameter is derived for a pre-drilled pilot hole, which can reduce the delamination rate significantly.
Abstract: Drilling-induced delamination often occurs both at the entrance and the exit of the workpiece during drilling of composite material. Investigators have studied analytically and experimentally that delamination in drilling can be correlated to the thrust force of the drill. With a pre-drilled pilot hole, the delamination can be reduced significantly. Early reference reported models of drilling-induced delamination, however, the effect of chisel edge length and pilot hole diameter on delamination is rarely discussed. The optimal range of chisel edge length with respect to drill diameter is derived in this paper.

Journal ArticleDOI
TL;DR: Under optimum conditions, the binary method of immobilization yielded a higher protein loading and an activity of 13.8 U/g-chitosan as compared to the immobilized lipase prepared by activation and by cross-linking.
Abstract: Industrial application of lipase requires efficient methods to immobilize the enzyme, yielding a biocatalyst with high activity and stability compared to free lipase. In the present study, lipase was immobilized to chitosan beads utilizing its amino and the hydroxyl groups, which is called “binary immobilization”. Lipase was first immobilized to chitosan beads by activating its hydroxyl groups with carbodiimide followed by cross-linking more lipase to the amino groups with glutaraldehyde. Under optimum conditions, the binary method of immobilization yielded a higher protein loading of 287.2 μg/g-chitosan and an activity of 13.8 U/g-chitosan as compared to the immobilized lipase prepared by activation and by cross-linking. Broader pH tolerance and higher heat stability could be achieved by this method. Immobilized lipase retained 74% residual activity after ten hydrolysis cycles and 67% after 7 days of storage. Kinetic parameters V max and K m and the energy of activation ( E a ) were determined for the immobilized lipase.

Journal ArticleDOI
TL;DR: In this article, the grey relational analysis is applied for optimizing the electropolishing of 316L stainless steel with multiple performance characteristics, including surface roughness and passivation strength.

Journal ArticleDOI
TL;DR: Classifications for the three sets of ultrasonic liver images reveal that the fractal feature vector based on M-band wavelet transform is trustworthy and the criterion for feature selection is specified and employed for performance comparisons herein.
Abstract: Describes the feasibility of selecting a fractal feature vector based on M-band wavelet transform to classify ultrasonic liver images - normal liver, cirrhosis, and hepatoma The proposed feature extraction algorithm is based on the spatial-frequency decomposition and fractal geometry Various classification algorithms based on respective texture measurements and filter banks are presented and tested Classifications for the three sets of ultrasonic liver images reveal that the fractal feature vector based on M-band wavelet transform is trustworthy A hierarchical classifier, which is based on the proposed feature extraction algorithm is at least 967% accurate in the distinction between normal and abnormal liver images and is at least 936% accurate in the distinction between cirrhosis and hepatoma liver images Additionally, the criterion for feature selection is specified and employed for performance comparisons herein

Journal ArticleDOI
TL;DR: It is shown that this three trophic level food chain model with ratio-dependent Michaelis-Menten type functional responses is rich in boundary dynamics and is capable of generating extinction dynamics.
Abstract: While biological controls have been successfully and frequently implemented by nature and human, plausible mathematical models are yet to be found to explain the often observed deterministic extinctions of both pest and control agent in such processes. In this paper we study a three trophic level food chain model with ratio-dependent Michaelis-Menten type functional responses. We shall show that this model is rich in boundary dynamics and is capable of generating such extinction dynamics. Two trophic level Michaelis-Menten type ratio-dependent predator-prey system was globally and systematically analyzed in details recently. A distinct and realistic feature of ratio-dependence is its capability of producing the extinction of prey species, and hence the collapse of the system. Another distinctive feature of this model is that its dynamical outcomes may depend on initial populations levels. Theses features, if preserved in a three trophic food chain model, make it appealing for modelling certain biological control processes (where prey is a plant species, middle predator as a pest, and top predator as a biological control agent) where the simultaneous extinctions of pest and control agent is the hallmark of their successes and are usually dependent on the amount of control agent. Our results indicate that this extinction dynamics and sensitivity to initial population levels are not only preserved, but also enriched in the three trophic level food chain model. Specifically, we provide partial answers to questions such as: under what scenarios a potential biological control may be successful, and when it may fail. We also study the questions such as what conditions ensure the coexistence of all the three species in the forms of a stable steady state and limit cycle, respectively. A multiple attractor scenario is found.

Journal ArticleDOI
01 Mar 2003-Ecology
TL;DR: Solow and Polasky as mentioned in this paper proposed a modified estimator that incorporates a measure of heterogeneity among species abundances, which is statistically justified from a Bayesian approach, although the estimator exhibits moderate negative bias for predicting larger samples in highly heterogeneous communities.
Abstract: In evaluating the effectiveness of further sampling in species taxonomic surveys, a practical and important problem is predicting the number of new species that would be observed in a second survey, based on data from an initial survey. This problem can also be approached by estimating the corresponding expected number of new species. A. R. Solow and S. Polasky recently proposed a predictor (or estimator), with the form of a sum of many terms, that was derived under the assumption that all unobserved species in the initial sample have equal relative abundances. We show in this paper that the summation can be expressed as only one term. We provide a direct justification for the simplified estimator and connect it to an extrapolation formula based on a special type of species accumulation curve. Using the proposed justification, we show that, for large sample sizes, the estimator is also valid under an alternative condition, i.e., species that are represented the same number of times in the initial sample have equal relative abundances in the community. This condition is statistically justified from a Bayesian approach, although the estimator exhibits moderate negative bias for predicting larger samples in highly heterogeneous communities. In such situations, we recommend the use of a modified estimator that incorporates a measure of heterogeneity among species abundances. An example using field data from the extant rare vascular plant species patterns in the southern Appalachians is presented to compare the various methods. Corresponding Editor: A. R. Solow