Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank

This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive cone and the associated natural metric. The resulting Riemannian space has strong geometrical properties: it is geodesically complete, and the metric is invariant with respect to all transformations that preserve angles (orthogonal transformations, scalings, and pseudoinversion). A meaningful approximation of the associated Riemannian distance is proposed, that can be efficiently numerically computed via a simple algorithm based on SVD. The induced mean preserves the rank, possesses the most desirable characteristics of a geometric mean, and is easy to compute. © 2009 Society for Industrial and Applied Mathematics.

Statistics anxiety, state anxiety during an examination, and academic achievement.

BACKGROUND: A large proportion of students identify statistics courses as the most anxiety-inducing courses in their curriculum. Many students feel impaired by feelings of state anxiety in the examination and therefore probably show lower achievements. AIMS: The study investigates how statistics anxiety, attitudes (e.g., interest, mathematical self-concept) and trait anxiety, as a general disposition to anxiety, influence experiences of anxiety as well as achievement in an examination. SAMPLE: Participants were 284 undergraduate psychology students, 225 females and 59 males. METHODS: Two weeks prior to the examination, participants completed a demographic questionnaire and measures of the STARS, the STAI, self-concept in mathematics, and interest in statistics. At the beginning of the statistics examination, students assessed their present state anxiety by the KUSTA scale. After 25 min, all examination participants gave another assessment of their anxiety at that moment. Students' examination scores were recorded. Structural equation modelling techniques were used to test relationships between the variables in a multivariate context. RESULTS: Statistics anxiety was the only variable related to state anxiety in the examination. Via state anxiety experienced before and during the examination, statistics anxiety had a negative influence on achievement. However, statistics anxiety also had a direct positive influence on achievement. This result may be explained by students' motivational goals in the specific educational setting. CONCLUSIONS: The results provide insight into the relationship between students' attitudes, dispositions, experiences of anxiety in the examination, and academic achievement, and give recommendations to instructors on how to support students prior to and in the examination.

Response Specificity to Advertisement Vocalization in the Chinese Alligator (Alligator sinensis)

Stringency in the identification of conspecific call properties is essential among sympatric species to ensure conspecific mating, as the risk of improper recognition and heterospecific mating is high. In this study we investigated the basic signal structure required for intraspecies communication in the Chinese alligator (Alligator sinensis), a species that has no relatives living in sympatry, by playback of signals modified in the temporal (truncating original bellows with first 1/4, 1/2, 3/4 or last 1/4, 1/2, 3/4 portion) or frequency domain (with low- or high-pass filters at frequencies 100, 250, 500 and 1000 Hz), or by reversal of natural bellows. The playback experiments revealed that relatively large modifications in bellow temporal or frequency structure failed to impair Chinese alligators' bellowing behavior; even reversed bellows effectively evoked a positive response. In general, the first half of the bellow in temporal domain and frequencies below 500 Hz were critical for behavioral induction, while the last half of the bellow in temporal domain and frequencies above 500 Hz failed to produce a single positive response, implying a potential functional signal redundancy. The observed high tolerance to bellow variations in Chinese alligators may be an evolutionary adaptation to (1) the acoustic constraints of propagation imposed by dense vegetative habitats; or (2) a lack of selection pressure due to the low risk of incorrect conspecific recognition and heterospecific mating.

Positive effects of continuous low nitrate levels on growth and photosynthesis of Alexandrium tamarense (Gonyaulacales, Dinophyceae)

The growth and photosynthesis of Alexandrium tamarense (Lebour) Balech in different nutrient conditions were investigated. Low nitrate level (0.0882 mmol/L) resulted in the highest average growth rate from day 0 to day 10 (4.58 x 10(2) cells mL(-1) d(-1)), but the lowest cell yield (5420 cells mL(-1)) in three nitrate level cultures. High nitrate-grown cells showed lower levels of chlorophyll a-specific and cell-specific light-saturated photosynthetic rate (P-m(chl a) and P-m(cell)), dark respiration rate (R-d(chl a) and R-d(cell)) and chlorophyll a-specific apparent photosynthetic efficiency (alpha(chl a)) than was seen for low nitrate-grown cells; whereas the cells became light saturated at higher irradiance at low nitrate condition. When cultures at low nitrate were supplemented with nitrate at 0.7938 mmol/L in late exponential growth phase, or with nitrate at 0.7938 mmol/L and phosphate at 0.072 mmol/L in stationary growth phase, the cell yield was drastically enhanced, a 7-9 times increase compared with non-supplemented control culture, achieving 43 540 cells mL(-1) and 52 300 cells mL(-1), respectively; however, supplementation with nitrate in the stationary growth phase or with nitrate and phosphate in the late exponential growth phase increased the cell yield by no more than 2 times. The results suggested that continuous low level of nitrate with sufficient supply of phosphate may facilitate the growth of A. tamarense.

Positive selection on multiple antique allelic lineages of transferrin in the polyploid Carassius auratus

Transferrin polymorphism has been studied in the polyploid Carassius auratus by cloning and sequence analysis of cDNAs from its three subspecies C. auratus gibelio, C. auratus auratus, and C. auratus cuvieri. DNA polymorphism of extremely high extent was shown for the transferrin gene by the 248 segregation sites among coding region sequences of its alleles. The deduced amino acid sequences of the transferrin alleles showed variable theoretical physicochemical parameters, which might constitute molecular basis for their electrophoretic heterogeneity. Positive selection was inferred by the replacement/synonymous ratios larger than 1 in partial allelic lineages which was subsequently confirmed by likelihood simulation under neutral or selection models. Furthermore, the correspondent sites to these selected codons were collectively located at two planes in the crystallographic structure of rabbit transferrin, which suggested that the rapid evolution of C. auratus transferrin might correlate to its adaptation to variable environmental elements such as oxygen pressure. The minimal 26 recombination events were detected among coding sequences of C. auratus transferrin, with partial mosaic sequences and breakpoints identified by identity scanning and information site analyses. Phylogenetic analyses revealed multiple antique allelic lineages of transferrin, which was estimated to diverge fifteen to twenty MYA. All these features strongly suggested the role of balancing selection in long persistence of high transferrin polymorphism in C. auratus. Furthermore, owing to its particular evolutionary backgrounds, the silver crucian carp might possess a distinctive balancing selection mechanism.

Development of a positive-negative selection procedure for gene targeting in fish cells

The gene targeting technique is a powerful tool for analyzing functions of cloned genes and for generating transgenic animals with site-directed integration of foreign genes. In order to develop this technique in fish, positive-negative selection (PNS) and homologous recombination vectors were constructed, and their expression was examined in fish cells. A vector (pNK) for PNS consists of the neomycin resistance gene (neo) as a positive selectable marker gene and the herpes simplex virus (HSV) thymidine kinase (tk) gene as a negative selectable marker gene. Positive selection with geneticin (G418) of epithelioma papulosum of carp (EPC) cells transfected with linearized pNK vector yielded 350 colonies, while double selection of transfected EPC cells with G418 and gancyclovir (Gc) resulted in nearly complete cell death, demonstrating that the PNS procedure is effective in fish cells. Homologous recombination vectors consist of the Xiphophorus melanoma receptor kinase (X mrk(Y)) gene as homologous sequence in addition to the neo and tk genes. Conditions for homologous recombination vector transfection and drug selection were established. After verification of the feasibility of expression of homologous recombination vectors in EPC cells, the first gene targeting experiments were attempted in the Xiphophorus melanoma cell line, PSM. Positive-negative selection of the targeting vector-transfectants led to a low enrichment in this particular cell line. The reasons for the low enrichment in PSM cells were discussed. (C) 2002 Elsevier Science B.V. All rights reserved.

Positive magnetoresistance in In0.53Ga0.47As/In0.52Al0.48As quantum well

Magnetotransport measurements have been carried out on In0.53Ga0.17As/In0.52Al0.48 As quantum wells in a temperature range between 1.5 and 77 K. We have observed a large positive magnetoresistance in the low magnetic field range, but saturating in high magnetic fields. The magnetoresistance results from two occupied subbands in the two-dimensional electron gas. With the intersubband scattering considered, we obtained the subband mobility by analyzing the positive magnetoresistance. It is found that the second subband mobility is larger than that of the first due to the existence of the intersubband scattering.

Effect of implantation of nitrogen into SIMOX buried oxide on its fixed positive charge density

In order to obtain greater radiation hardness for SIMOX (separation by implanted oxygen) materials, nitrogen was implanted into SIMOX BOX (buried oxide). However, it has been found by the C-V technique employed in this work that there is an obvious increase of the fixed positive charge density in the nitrogen-implanted BOX with a 150 out thickness and 4 x 10(15) cm(-2) nitrogen implantation dose, compared with that unimplanted with nitrogen. On the other hand, for the BOX layers with a 375 nm thickness and implanted with 2 x 10(15) and 3 x 10(15) cm(-2) nitrogen doses respectively, the increase of the fixed positive charge density induced by implanted nitrogen has not been observed. The post-implantation annealing conditions are identical for all the nitrogen-implanted samples. The increase in fixed positive charge density in the nitrogen-implanted 150 nm BOX is ascribed to the accumulation of implanted nitrogen near the BOX/Si interface due to the post-implantation annealing process according to SIMS results. In addition, it has also been found that the fixed positive charge density in initial BOX is very small. This means SIMOX BOX has a much lower oxide charge density than thermal SiO2 which contains a lot of oxide charges in most cases.

Large positive and negative lateral displacements from total internal reflection configuration with a weakly absorbing dielectric film

It is theoretically shown that the simultaneously large positive and negative lateral displacements will appear when the resonant condition is satisfied for a TE-polarized light beam reflected from the total internal reflection configuration with a weakly absorbing dielectric film. Appearance of the enhanced negative lateral displacement is relative to the incidence angle, absorption of the thin Elm and its thickness. If we select an appropriate weakly absorbing dielectric film and its thickness, the simultaneously enhanced positive and negative lateral displacements will appear at different resonant angles. These phenomena may lead to convenient measurements and interesting applications in optical devices.

Controllable negative and positive group delay in transmission through a single quantum well at finite magnetic fields

We investigate the controllable negative and positive group delay in transmission through a single quantum well at the finite longitudinal magnetic fields. It is shown that the magneto-coupling effect between the longitudinal motion component and the transverse Landau orbits plays an important role in the group delay. The group delay depends not only on the width of potential well and the incident energy, but also on the magnetic-field strengthen and the Landau quantum number. The results show that the group delay can be changed from positive to negative by the modulation of the magnetic field. These interesting phenomena may lead to the tunable quantum mechanical delay line. (c) 2007 Elsevier B.V. All rights reserved.