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We propose tests for sphericity and identity of high-dimensional covariance matrices. The tests are nonparametric without assuming a specific parametric distribution for the data. They can accommodate situations where the data dimension is much larger than the sample size, namely the \"large p, small n\" situations. We demonstrate by both theoretical and empirical studies that the tests have good properties for a wide range of dimensions and sample sizes. We applied the proposed test on a microarray dataset on Yorkshire Gilts and tested for the covariance structure for the expression levels for sets of genes.

Hybrid zones occur in nature when populations with limited reproductive barriers overlap in space. Many hybrid zones persist over time, and different models have been proposed to explain how selection can maintain hybrid zone stability. More empirical studies are needed to elucidate the role of ecological adaptation in maintaining stable hybrid zones. Here, we investigated the role of exogenous factors in maintaining a hybrid zone between western gulls (Larus occidentalis) and glaucous‐winged gulls (L. glaucescens). We used ecological niche models (ENMs) and niche similarity tests to quantify and examine the ecological niches of western gulls, glaucous‐winged gulls, and their hybrids. We found evidence of niche divergence between all three groups. Our results support the bounded superiority model, providing further evidence that exogenous selection favoring hybrids may be an important factor in maintaining this stable hybrid zone. In this study, we investigated the role of exogenous factors in maintaining a hybrid zone between western gulls (Larus occidentalis) and glaucous‐winged gulls (L. glaucescens). We used ecological niche models (ENMs) and niche similarity tests and found evidence of niche divergence between all three groups. Our results best support the bounded superiority model, providing further evidence that exogenous selection favoring hybrids may be an important factor in maintaining this stable hybrid zone.

Scanner data can be obtained from a wide variety of retailers (supermarkets, home electronics, Internet shops, etc.) and provide information at the level of the barcode, i.e. the Global Trade Item Number or its European version: European Article Number. One of advantages of using scanner data in the Consumer Price Index measurement is the fact that they contain complete transaction information, i.e. prices and quantities for every sold item. One of new challenges connected with scanner data is the choice of the index formula which should be able to reduce the chain drift bias and the substitution bias. Multilateral index methods seem to be the best choice in the case of dynamic scanner data sets. These indices work on a whole time window and are transitive, which is a key property in eliminating the chain drift effect. Following the so-called identity test, however, one may expect that even when only prices return to their original values, the index becomes one. Unfortunately, the commonly used multilateral indices (GEKS, CCDI, GK, TPD, TDH) do not meet the identity test. The paper discusses the proposal of two multilateral indices, the idea of which resembles the GEKS index, but which meet the identity test and most of other tests. In an empirical study, these indices are compared, inter alia, with the SPQ index, which is relatively new and also meets the identity test. Analytical considerations as well as empirical study confirm the high usefulness of the proposed indices.

The mechanism underlying the uneven distribution of biodiversity has attracted considerable interest. In Eastern Asia (EAS) and Eastern North America (ENA), a more heterogeneous environment in the EAS is a key factor explaining the uneven distributed biodiversity. To test the hypothesis, shifts of potential distributions of Gleditsia (Fabaceae) from past to future were compared through ecological niche modeling (ENM). In the 58 environmental variables used for modeling, ENM, multivariate environmental similarity surfaces and most dissimilar variable analyses showed soil and temperature were the primary factors affecting the distributions. In the past, most species experienced contractions in the last glacial maximum (LGM) while expansions during the Middle Holecene. Distribution range sizes during the LGM in the EAS were much larger. In the future (2050 and 2070), northward movements and range expansions were shared between the EAS and ENA species. Projections of niche of the EAS species to the ENA region resulted in significantly smaller areas in the ENA, while similar areas were found for the vice versa projections. Principal component analysis indicated that ecological niches of the ENA species differed from those of EAS species. Niche identity and background tests showed that most species pairs (10/11) rejected (fully or partially) the null hypothesis of ecological niche equivalence. In conclusion, differences in environmental heterogeneity, historical environmental changes, and niches of Gleditsia species between the EAS and ENA contribute to different distribution shift patterns. This study provide additional insights into the biodiversity distribution bias observed in the Northern Hemisphere. To further understand the mechanism underlying the uneven distribution of biodiversity between Eastern Asia (EAS) and Eastern North America (ENA), we compared the shifts of potential distributions of Gleditsia from past to future. Distinct differences were observed in the past, whereas similar shifts were observed in the future. The combination of differences in environmental heterogeneity, historical environmental changes, and niche of Gleditsia species contributed to the different shift patterns of distributions in the EAS and ENA. Our findings improve the understanding of biodiversity distribution bias in the Northern Hemisphere.

Background and Aim: Ultrasound is a non-invasive technique that enables animal evaluation and body condition classification of animals. Although it is not difficult to obtain an image, the analysis of this image can influence results quality. This study aimed to evaluate the repeatability and reproducibility of the technician trained in image interpretation obtained using different ultrasound frequencies. Materials and Methods: Ninety-six lambs were used, ranging in weight from 15 to 40 kg. The images were captured using a linear probe of 13 cm, with a 3.5 megahertz (MHz) frequency and an acoustic couplant aid \"standoff\" or using a multifrequency transducer (6 and 8 MHz), on B mode, with a linear probe and 8.0 MHz frequency. All measurements were performed by the same technician, on the left side, between the 12th and 13th rib. Five different evaluators, at two different times, with aid of Image J software measured the loin eye area (LEA; only for images obtained with 3.5 MHz), Longissimus thoracis et lumborum depth (DLM), subcutaneous fat thickness (SFT), subcutaneous fat thickness plus skin (SFST), and skin thickness (ST). Results: For LEA, DLM, SFT, SFST, and ST, variation was observed (p<0.01) between evaluators; however, there was no difference (p>0.05) between the 2 times of evaluation. Images measurements obtained with a frequency of 8.0 MHz had better repeatability indices and reproducibility indices. Accordingly, the identity test demonstrated that measurements performed on images obtained using 3.5 or 8.0 MHz were not equivalent. Conclusion: Ultrasound image measurements obtained using an 8.0 MHz frequency were more accurate and precise. It is important to use only one evaluator or providing the simultaneous training for all evaluators.

Measures of face-identification proficiency are essential to ensure accurate and consistent performance by professional forensic face examiners and others who perform face-identification tasks in applied scenarios. Current proficiency tests rely on static sets of stimulus items and so cannot be administered validly to the same individual multiple times. To create a proficiency test, a large number of items of “known” difficulty must be assembled. Multiple tests of equal difficulty can be constructed then using subsets of items. We introduce the Triad Identity Matching (TIM) test and evaluate it using item response theory (IRT). Participants view face-image “triads” ( N = 225) (two images of one identity, one image of a different identity) and select the different identity. In Experiment  3 , university students ( N = 197) showed wide-ranging accuracy on the TIM test, and IRT modeling demonstrated that the TIM items span various difficulty levels. In Experiment  3 , we used IRT-based item metrics to partition the test into subsets of specific difficulties. Simulations showed that subsets of the TIM items yielded reliable estimates of subject ability. In Experiments  3 a and b, we found that the student-derived IRT model reliably evaluated the ability of non-student participants and that ability generalized across different test sessions. In Experiment  3 c, we show that TIM test performance correlates with other common face-recognition tests. In summary, the TIM test provides a starting point for developing a framework that is flexible and calibrated to measure proficiency across various ability levels (e.g., professionals or populations with face-processing deficits).

Studies on applying of soil management practices in the management of paricá and the effects on growth and yield are essential to auxiliary its cultivation and would allow us to inform management and conservation decisions to reconciliate biodiversity, wellbeing, and sustainable production. This case study aimed to evaluate the growth and yield of paricá at different soil management practices, including consortium with an agricultural production, in the Brazilian Amazon. Paricá was implanted, consorted with soybean in the first year, and maize in the second, in a 5 × 2 m spacing. The treatments T1 = subsoiling, basal dressing, top-dressing, inoculation of microorganisms and consortium with soybean/maize were applied. In T2, T3, T4, and T5, we applied the same practices of T1, except subsoiling (T2), basal dressing (T3), top-dressing (T4) and inoculation of microorganisms (T5). T6 was the control, which used none of these practices, including the consortium with soybean/maize. The results indicate that the highest rate of plant survival occurred in T2, while T3 and T4 promoted greater intraspecific competition, compromising the growth in dbh and the yield (m3 ha−1) of plants in future ages. Growth in dbh and th and the yield of plants in the soybean/maize consortium period was higher in T2 and T6. In future ages, the dbh and yield of plants demonstrated higher growth trends in T6, T1, and T5. Agroforestry practices of soil management influence the growth and yield of paricá plants. However, there is a tendency for greater growth and yield for paricá plants cultivated in the absence of agroforestry practices for soil management proposed in this case study. When opting for AFS (paricá intercropped with soybean and maize), it is recommended for paricá a subsoiling, fertilization, and inoculation of microorganisms.

In this work we study two, seemingly unrelated, notions. Locally decodable codes (LDCs) are codes that allow the recovery of each message bit from a constant number of entries of the codeword. Polynomial identity testing (PIT) is one of the fundamental problems of algebraic complexity: we are given a circuit computing a multivariate polynomial and we have to determine whether the polynomial is identically zero. We improve known results on LDCs and on polynomial identity testing and show a relation between the two notions. In particular we obtain the following results: (1) We show that if $E: \\mathbb{F}^n \\mapsto \\mathbb{F}^m$ is a linear LDC with two queries, then $m = \\exp(\\Omega(n))$. Previously this was known only for fields of size $\\ll 2^n$ [O. Goldreich et al, Comput. Complexity, 15 (2006), pp. 263-296]. (2) We show that from every depth 3 arithmetic circuit ($\\Sigma\\Pi\\Sigma$ circuit), ${\\cal C}$, with a bounded (constant) top fan-in that computes the zero polynomial, one can construct an LDC. More formally, assume that ${\\cal C}$ is minimal (no subset of the multiplication gates sums to zero) and simple (no linear function appears in all the multiplication gates). Denote by $d$ the degree of the polynomial computed by ${\\cal C}$ and by $r$ the rank of the linear functions appearing in ${\\cal C}$. Then we can construct a linear LDC with two queries that encodes messages of length $r/{\\operatorname{polylog}(d)}$ by codewords of length $O(d)$. (3) We prove a structural theorem for $\\Sigma\\Pi\\Sigma$ circuits, with a bounded top fan-in, that compute the zero polynomial. In particular we show that if such a circuit is simple, minimal, and of polynomial size, then its rank, $r$, is only polylogarithmic in the number of variables (a priori it could have been linear). (4) We give new PIT algorithms for $\\Sigma\\Pi\\Sigma$ circuits with a bounded top fan-in: (a) a deterministic algorithm that runs in quasipolynomial time, and (b) a randomized algorithm that runs in polynomial time and uses only a polylogarithmic number of random bits. Moreover, when the circuit is multilinear, our deterministic algorithm runs in polynomial time. Previously deterministic subexponential time algorithms for PIT in bounded depth circuits were known only for depth 2 circuits (in the black box model) [D. Grigoriev, M. Karpinski, and M. F. Singer, SIAM J. Comput., 19 (1990), pp. 1059-1063; M. Ben-Or and P. Tiwari, Proceedings of the 20th Annual ACM Symposium on Theory of Computing, ACM Press, New York, 1988, pp. 301-309; A. R. Klivans and D. Spielman, Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, ACM Press, New York, 2001, pp. 216-223]. In particular, for the special case of depth 3 circuits with three multiplication gates our result resolves an open question asked by Klivans and Spielman.

Current methods for the identification of BCG vaccine in quality control settings involve acid-fast staining with microscopic examination. However, this method is unable to distinguish the many different sub-strains of BCG, or to differentiate BCG strains from virulent members of the Mycobacterium tuberculosis complex. A multiplex PCR (mPCR) which uses six target regions in mycobacteria has been developed to identify specific sub-strains of BCG. This study reports the findings from an international collaborative study to assess the accuracy, robustness and reproducibility of this mPCR method to differentiate BCG sub-strains. The method was found to fulfil these criteria successfully and was able to distinguish BCG sub-strains in vaccine preparations. The majority of the participants in the study generated the expected PCR product profiles indicating the method is also robust.

The objective of this study was to identify a nonlinear regression model that better describes the milk production and the percentages of fat and protein curves, and to identify the season and age of calving that result in higher productions. For the analysis, 8,047 records of milk production and percentages of fat and protein obtained from 1,330 Holstein breed cows raised in Rio Grande do Sul, born from 1989 to 2011, were used. After determining the most appropriate nonlinear regression model, the identity of models and the equality of parameter tests for the different classes of season and age of calving were performed. Residual mean square, mean absolute deviation, mean squared prediction error and percentage of estimated curves per animal, indicated the Linear Hyperbolic Function (LHF) as the most appropriate to describe the milk production and the levels of fat and protein curves. Cows calving in the autumn and winter seasons yield higher quantities of milk and lower fat and protein content than those calved in the spring and summer seasons. Cows aged between 46 and 93 months at calving yield higher milk quantities, and those with calving age between 94 and 118 months produced more fat. RESUMO: Objetivou-se identificar o modelo de regressão não linear que melhor descreve as curvas de produção de leite e de porcentagens de gordura e proteína; a estação e idade ao parto que resultam em maiores produções. Nas análises, foram utilizados 8047 registros de produção de leite e porcentagens de gordura e proteína provenientes de 1330 vacas da raça Holandesa, criadas no Rio Grande do Sul, nascidas de 1989 a 2011. Após a definição do modelo de regressão não linear mais adequado, procedeu-se à realização do teste de identidade de modelos e de igualdade de parâmetros para as diferentes classes de estação e idade da vaca ao parto. O quadrado médio do resíduo, desvio médio absoluto, erro quadrático médio de predição e a porcentagem de curvas estimadas por animal apontaram a Função Linear Hiperbólica (FLH) como a mais adequada para descrever as curvas de produção de leite e teores de gordura e proteína. Vacas com ocorrência de partos nas estações de outono e inverno produzem maior quantidade de leite e menor teor de gordura e proteína do leite do que aquelas que parem nas estações de primavera e verão. Vacas com idades ao parto entre 46 e 93 meses produzem maior quantidade de leite e as com 94 a 118 meses, maior teor de gordura do leite.