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1.
Sensors (Basel) ; 24(4)2024 Feb 18.
Artículo en Inglés | MEDLINE | ID: mdl-38400471

RESUMEN

Addressing inherent limitations in distinguishing metrics relying solely on Euclidean distance, especially within the context of geo-indistinguishability (Geo-I) as a protection mechanism for location-based service (LBS) privacy, this paper introduces an innovative and comprehensive metric. Our proposed metric not only incorporates geographical information but also integrates semantic, temporal, and query data, serving as a powerful tool to foster semantic diversity, ensure high servifice similarity, and promote spatial dispersion. We extensively evaluate our technique by constructing a comprehensive metric for Dongcheng District, Beijing, using road network data obtained through the OSMNX package and semantic and temporal information acquired through Gaode Map. This holistic approach proves highly effective in mitigating adversarial attacks based on background knowledge. Compared with existing methods, our proposed protection mechanism showcases a minimum 50% reduction in service quality and an increase of at least 0.3 times in adversarial attack error using a real-world dataset from Geolife. The simulation results underscore the efficacy of our protection mechanism in significantly enhancing user privacy compared to existing methodologies in the LBS location privacy-protection framework. This adjustment more fully reflects the authors' preference while maintaining clarity about the role of Geo-I as a protection mechanism within the broader framework of LBS location privacy protection.

2.
Electrophoresis ; 44(15-16): 1210-1219, 2023 08.
Artículo en Inglés | MEDLINE | ID: mdl-37075199

RESUMEN

Wear debris analysis provides an early warning of mechanical transmission system aging and wear fault diagnosis, which has been widely used in machine health monitoring. The ability to detect and distinguish the ferromagnetic and nonmagnetic debris in oil is becoming an effective way to assess the health status of machinery. In this work, an Fe-poly(dimethylsiloxane) (PDMS)-based magnetophoretic method for the continuous separation of ferromagnetic iron particles by diameter and the isolation of ferromagnetic particles and nonmagnetic particles with similar diameter by type is developed. The particles experience magnetophoretic effects when passing through the vicinity of the Fe-PDMS where the strongest gradient of the magnetic fields exists. By choosing a relatively short distance between the magnet and the sidewall of the horizontal main channel and the length of Fe-PDMS with controlled particles flow rate, the diameter-dependent separation of ferromagnetic iron particles, that is, smaller than 7 µm, in the range of 8-12 µm, and larger than 14 µm, and the isolation of ferromagnetic iron particles and nonmagnetic aluminum particles based on opposite magnetophoretic behaviors by types are demonstrated, providing a potential method for the detection of wear debris particles with a high sensitivity and resolution and the diagnostic of mechanical system.


Asunto(s)
Imanes , Microfluídica , Hierro
3.
Entropy (Basel) ; 25(6)2023 Jun 08.
Artículo en Inglés | MEDLINE | ID: mdl-37372256

RESUMEN

We introduce a new family of quantum distances based on symmetric Csiszár divergences, a class of distinguishability measures that encompass the main dissimilarity measures between probability distributions. We prove that these quantum distances can be obtained by optimizing over a set of quantum measurements followed by a purification process. Specifically, we address in the first place the case of distinguishing pure quantum states, solving an optimization of the symmetric Csiszár divergences over von Neumann measurements. In the second place, by making use of the concept of purification of quantum states, we arrive at a new set of distinguishability measures, which we call extended quantum Csiszár distances. In addition, as it has been demonstrated that a purification process can be physically implemented, the proposed distinguishability measures for quantum states could be endowed with an operational interpretation. Finally, by taking advantage of a well-known result for classical Csiszár divergences, we show how to build quantum Csiszár true distances. Thus, our main contribution is the development and analysis of a method for obtaining quantum distances satisfying the triangle inequality in the space of quantum states for Hilbert spaces of arbitrary dimension.

4.
Entropy (Basel) ; 23(1)2021 Jan 18.
Artículo en Inglés | MEDLINE | ID: mdl-33477704

RESUMEN

According to the relevant theories on duality relation, the summation of the extractable information of a quanton's wave and particle properties, which are characterized by interference visibility V and path distinguishability D, respectively, is limited. However, this relation is violated upon quantum superposition between the wave-state and particle-state of the quanton, which is caused by the quantum beamsplitter (QBS). Along another line, recent studies have considered quantum coherence C in the l1-norm measure as a candidate for the wave property. In this study, we propose an interferometer with a quantum which-path detector (QWPD) and examine the generalized duality relation based on C. We find that this relationship still holds under such a circumstance, but the interference between these two properties causes the full-particle property to be observed when the QWPD system is partially present. Using a pair of polarization-entangled photons, we experimentally verify our analysis in the two-path case. This study extends the duality relation between coherence and path information to the quantum case and reveals the effect of quantum superposition on the duality relation.

5.
Entropy (Basel) ; 21(8)2019 Aug 07.
Artículo en Inglés | MEDLINE | ID: mdl-33267483

RESUMEN

A measure D [ t 1 , t 2 ] for the amount of dynamical evolution exhibited by a quantum system during a time interval [ t 1 , t 2 ] is defined in terms of how distinguishable from each other are, on average, the states of the system at different times. We investigate some properties of the measure D showing that, for increasing values of the interval's duration, the measure quickly reaches an asymptotic value given by the linear entropy of the energy distribution associated with the system's (pure) quantum state. This leads to the formulation of an entropic variational problem characterizing the quantum states that exhibit the largest amount of dynamical evolution under energy constraints given by the expectation value of the energy.

6.
Skin Res Technol ; 24(2): 196-202, 2018 May.
Artículo en Inglés | MEDLINE | ID: mdl-29057502

RESUMEN

BACKGROUND: Validated tools are essential to evaluate facial skin aging for both dermatological and cosmetic investigations. While many visual aging scales have been developed, few have been validated and none in terms of degree of distinguishability (DD). We developed and validated a series of visual scales using a novel digital interface for scoring facial skin aging in Caucasian women. MATERIALS AND METHODS: Three dermatologists independently established scales for 12 distinct aging signs from high-definition facial photographs of 400 adult women (Fitzpatrick phototypes I-IV) taken under standardized conditions. They then selected a consensus scale for each individual sign with a representative photo per grade. Scales were integrated into a digital interface allowing simultaneous viewing of all grades of each scale alongside the photograph of a test subject. Next, scales were validated by a different dermatologist, a general practitioner and a non-medical expert skin evaluator using photos of 350 women which had not been used for establishing the scales. RESULTS: Kappa estimates showed almost perfect agreement for wrinkle and skin aging scales (≥0.85) and moderate to substantial agreement for scales relating to color irregularities (telangiectasia, solar lentigines, freckles) for both inter- and intra-observer reproducibility. Intra-observer DD estimates were mostly high. Non-dermatologists performed well on reproducibility for both Kappa (from 0.6 to 0.9) and DD estimates. CONCLUSION: Our work demonstrates that the digital interface scales for 12 distinct aging features are highly suitable for use in clinical and epidemiological studies on skin aging by both dermatologists and non-dermatologists.


Asunto(s)
Envejecimiento de la Piel/patología , Población Blanca/etnología , Adulto , Anciano , Anciano de 80 o más Años , Cara , Femenino , Humanos , Persona de Mediana Edad , Variaciones Dependientes del Observador , Fotograbar , Valores de Referencia , Envejecimiento de la Piel/etnología , Pigmentación de la Piel/fisiología , Programas Informáticos , Encuestas y Cuestionarios/normas , Adulto Joven
7.
Entropy (Basel) ; 20(6)2018 Jun 15.
Artículo en Inglés | MEDLINE | ID: mdl-33265556

RESUMEN

A consensus seems to have developed that the Gibbs paradox in classical thermodynamics (the discontinuous drop in the entropy of mixing when the mixed gases become equal to each other) is unmysterious: in any actual situation, two gases can be separated or not, and the associated harmless discontinuity from "yes" to "no" is responsible for the discontinuity. By contrast, the Gibbs paradox in statistical physics continues to attract attention. Here, the problem is that standard calculations in statistical mechanics predict a non-vanishing value of the entropy of mixing even when two gases of the same kind are mixed, in conflict with thermodynamic predictions. This version of the Gibbs paradox is often seen as a sign that there is something fundamentally wrong with either the traditional expression S=klnW or with the way W is calculated. It is the aim of this article to review the situation from the orthodox (as opposed to information theoretic) standpoint. We demonstrate how the standard formalism is not only fully capable of dealing with the paradox, but also provides an intuitively clear picture of the relevant physical mechanisms. In particular, we pay attention to the explanatory relevance of the existence of particle trajectories in the classical context. We also discuss how the paradox survives the transition to quantum mechanics, in spite of the symmetrization postulates.

8.
Theor Popul Biol ; 105: 53-63, 2015 Nov.
Artículo en Inglés | MEDLINE | ID: mdl-26226230

RESUMEN

Model predictions for species competition outcomes highly depend on the assumed form of the population growth function. In this paper we apply an alternative inferential method based on statistical mechanics, maximizing Boltzmann entropy, to predict resource-constrained population dynamics and coexistence. Within this framework, population dynamics and competition outcome can be determined without assuming any particular form of the population growth function. The dynamics of each species is determined by two parameters: the mean resource requirement θ (related to the mean metabolic rate) and individual distinguishability Dr (related to intra- compared to interspecific functional variation). Our theory clarifies the condition for the energetic equivalence rule (EER) to hold, and provide a statistical explanation for the importance of species functional variation in determining population dynamics and coexistence patterns.


Asunto(s)
Conducta Competitiva , Dinámica Poblacional , Humanos , Modelos Biológicos , Asignación de Recursos , Especificidad de la Especie
9.
Stat Med ; 33(1): 117-28, 2014 Jan 15.
Artículo en Inglés | MEDLINE | ID: mdl-23825013

RESUMEN

The analysis of concordance among repeated measures has received a huge amount of attention in the statistical literature leading to a range of different approaches. However, because all the approaches are able to assess the closeness among the readings taken on the same subject, the conclusions about the degree of concordance should be similar regardless the approach applied. Here, two indices to assess the concordance among continuous repeated measures, the intraclass correlation coefficient and the total deviation index, are applied and compared in two case examples. The first example concerns the repeatability of individual nutrient allocation strategy assessed by stable isotope analysis. The second example dealt with the assessment of the concordance of functional magnetic resonance imaging data that shows spatial correlation. The results differ depending upon the approach applied leading to contradictory conclusions about the degree of concordance. The reason behind these results is discussed reaching the conclusion that the total deviation index is just assessing agreement among repeated measurements, whereas the intraclass correlation coefficient assesses the concept of distinguishability among subjects that involves agreement among repeated measurements and spread of subjects at once. Therefore, the best way to select the right approach is to understand the right question behind the research hypothesis.


Asunto(s)
Biometría/métodos , Reproducibilidad de los Resultados , Albúminas/análisis , Animales , Charadriiformes/metabolismo , Huevos/análisis , Femenino , Humanos , Imagen por Resonancia Magnética/métodos , Isótopos de Nitrógeno/análisis , Umbral Sensorial/fisiología
10.
Physiol Meas ; 45(4)2024 Apr 16.
Artículo en Inglés | MEDLINE | ID: mdl-38624240

RESUMEN

Objective.Electrical impedance tomography (EIT) is a noninvasive imaging method whereby electrical measurements on the periphery of a heterogeneous conductor are inverted to map its internal conductivity. The EIT method proposed here aims to improve computational speed and noise tolerance by introducing sensitivity volume as a figure-of-merit for comparing EIT measurement protocols.Approach.Each measurement is shown to correspond to a sensitivity vector in model space, such that the set of measurements, in turn, corresponds to a set of vectors that subtend a sensitivity volume in model space. A maximal sensitivity volume identifies the measurement protocol with the greatest sensitivity and greatest mutual orthogonality. A distinguishability criterion is generalized to quantify the increased noise tolerance of high sensitivity measurements.Main result.The sensitivity volume method allows the model space dimension to be minimized to match that of the data space, and the data importance to be increased within an expanded space of measurements defined by an increased number of contacts.Significance.The reduction in model space dimension is shown to increasecomputational efficiency, accelerating tomographic inversion by several orders of magnitude, while the enhanced sensitivitytolerates higher noiselevels up to several orders of magnitude larger than standard methods.


Asunto(s)
Algoritmos , Tomografía Computarizada por Rayos X , Impedancia Eléctrica , Tomografía/métodos , Conductividad Eléctrica
11.
MethodsX ; 10: 101981, 2023.
Artículo en Inglés | MEDLINE | ID: mdl-36619369

RESUMEN

The falsification problems associated with golden coins, banknotes, and legal documents could be solved through "antipode elements," microfiber materials selected to have the exact opposite (antipode) properties when incorporated into gold, paper, or any other tangible manufactured object. Any discrepancies in gold or banknotes could be found using various non-destructive testing machinery. This research focus was given to help a student or junior lab technician replicate all steps and conclude that a fully functional product is ready for the alpha test. It requires minimal interdisciplinary knowledge in statistics, programming, and metrology, along with chemical, material, and digital electronics engineering. The research methodology can be categorized into four tracks: material selection and method validation. The two validation steps were kept short and low level, that is, minimal and only to guide reproducibility, due to limitations in presentation, procedural specification, pricing, consumable options, and software modules. A last-minute development occurred by describing the procedures in the current submission, not initially granted in the invention patents. This technique is an innovative design to capture raw sensor data straight from the photodiode pad. These Big-Data are manipulated using the presented and future data analytics methodologies.

12.
Adv Sci (Weinh) ; 9(23): e2202326, 2022 08.
Artículo en Inglés | MEDLINE | ID: mdl-35676221

RESUMEN

Early detection and diagnosis are vitally important in reducing the mortality rate of fatal diseases but require highly sensitive detection of biomarkers. Presently, detection methods with the highest sensitivity require in vitro processing, while in vivo compatible fluorescence detections require a much higher concentration of biomarkers or limit of detection (LOD). In this paper, a fundamentally new strategy for ultrasensitive detection based on color-switchable lasing with a cavity-enhanced reduction of LOD is demonstrated, down to 1.4 × 10-16  mg ml-1 for a quantitative detection, lower than both the fluorescence method and plasmonic enhanced method. For a qualitative or a yes/no type of detection, the LOD is as low as 10-17  mg ml-1 . The approach in this work is based on a dye-embedded, in vivo compatible, polystyrene-sphere cavity, penetrable by biomarkers. A polystyrene sphere serves the dual roles of a laser cavity and an in vivo bio-reactor, in which dye molecules react with a biomarker, reporting biomarker information through lasing signals. The cavity-enhanced emission and lasing with only a single biomarker molecule per cavity allow improved visual distinguishability via color changes. Furthermore, when combined with a narrow-band filter, the color-switchable lasers act as an "on-off" logic signal and can be integrated into multiplexing detection assay biochips.


Asunto(s)
Rayos Láser , Poliestirenos , Biomarcadores , Luz , Límite de Detección
13.
Comput Biol Med ; 141: 105118, 2022 02.
Artículo en Inglés | MEDLINE | ID: mdl-34971979

RESUMEN

There are many difficulties in extracting and using knowledge for medical analytic and predictive purposes from Real-World Data, even when the data is already well structured in the manner of a large spreadsheet. Preparative curation and standardization or "normalization" of such data involves a variety of chores but underlying them is an interrelated set of fundamental problems that can in part be dealt with automatically during the datamining and inference processes. These fundamental problems are reviewed here and illustrated and investigated with examples. They concern the treatment of unknowns, the need to avoid independency assumptions, and the appearance of entries that may not be fully distinguished from each other. Unknowns include errors detected as implausible (e.g., out of range) values that are subsequently converted to unknowns. These problems are further impacted by high dimensionality and problems of sparse data that inevitably arise from high-dimensional datamining even if the data is extensive. All these considerations are different aspects of incomplete information, though they also relate to problems that arise if care is not taken to avoid or ameliorate consequences of including the same information twice or more, or if misleading or inconsistent information is combined. This paper addresses these aspects from a slightly different perspective using the Q-UEL language and inference methods based on it by borrowing some ideas from the mathematics of quantum mechanics and information theory. It takes the view that detection and correction of probabilistic elements of knowledge subsequently used in inference need only involve testing and correction so that they satisfy certain extended notions of coherence between probabilities. This is by no means the only possible view, and it is explored here and later compared with a related notion of consistency.


Asunto(s)
Medicina , Lenguaje , Probabilidad
14.
Neural Netw ; 122: 364-373, 2020 Feb.
Artículo en Inglés | MEDLINE | ID: mdl-31760371

RESUMEN

With the growing demand for an intelligent system to prevent abnormal events, many methods have been proposed to detect and locate anomalous behaviors in surveillance videos. However, most of these methods contain two shortcomings mainly: distraction of the network and insufficient discriminating ability. In this paper, we propose a local distinguishability aggrandizing network (LDA-Net) in a supervised manner, consisting of a human detection module and an anomaly detection module. In the human detection module, we obtain segmented patches of specific human subjects and take them as the input of the latter module to focus the network on learning motion characteristics of each person. In addition, considering that the auxiliary information, such as the specific type of an action, can aggrandize the whole network to extract distinguishable detail features of normal and abnormal behaviors, the proposed anomaly detection module comprises a primary binary classification sub-branch and an auxiliary distinguishability aggrandizing sub-branch, through which we can jointly detect anomalies and recognize actions. To further reduce the misclassification of the extremely imbalanced datasets, we design a novel inhibition loss function and embed it into the auxiliary sub-branch of the anomaly detection module. Experiments on several public benchmark datasets for frame-level and pixel-level anomaly detection show that the proposed supervised LDA-Net achieves state-of-the-art results on UCSD Ped2 and Subway Exit datasets.


Asunto(s)
Redes Neurales de la Computación , Algoritmos , Humanos
15.
Body Image ; 34: 155-166, 2020 Sep.
Artículo en Inglés | MEDLINE | ID: mdl-32593946

RESUMEN

Issues of construct commonality and distinguishability in body image research are typically addressed using structural equal models, but such methods can sometimes present problems of interpretation when data patterns are complex. One recent-developed tool that could help in summarising complex data patterns is Item Pool Visualisation (IPV), an illustrative method that locates item pools from within the same dataset and illustrates these in the form of single or nested radar charts. Here, we demonstrate the utility of IPV in visualising data patterns vis-à-vis positive body image. Five-hundred-and-one adults from the United Kingdom completed seven widely-used measures of positive body image and data were subjected IPV. Results demonstrated that, of the included measures, the Body Appreciation Scale-2 provided the closest and most precise measurement of a core positive body image construct. The Functionality Appreciation Scale and the Authentic Pride subscale of the Body and Appearance Self-Conscious Emotions Scale tapped more distal aspects. Our results also highlight possible limitations with the use of several other instruments as measures of positive body image. We discuss implications for research aimed at better understanding the nature of positive body image and interpreting complex data patterns in body image research more generally.


Asunto(s)
Imagen Corporal/psicología , Visualización de Datos , Psicometría/métodos , Adulto , Conjuntos de Datos como Asunto , Femenino , Humanos , Análisis de Clases Latentes , Masculino , Persona de Mediana Edad , Reino Unido
16.
Genetics ; 209(4): 1235-1278, 2018 08.
Artículo en Inglés | MEDLINE | ID: mdl-29844134

RESUMEN

Purifying selection reduces genetic diversity, both at sites under direct selection and at linked neutral sites. This process, known as background selection, is thought to play an important role in shaping genomic diversity in natural populations. Yet despite its importance, the effects of background selection are not fully understood. Previous theoretical analyses of this process have taken a backward-time approach based on the structured coalescent. While they provide some insight, these methods are either limited to very small samples or are computationally prohibitive. Here, we present a new forward-time analysis of the trajectories of both neutral and deleterious mutations at a nonrecombining locus. We find that strong purifying selection leads to remarkably rich dynamics: neutral mutations can exhibit sweep-like behavior, and deleterious mutations can reach substantial frequencies even when they are guaranteed to eventually go extinct. Our analysis of these dynamics allows us to calculate analytical expressions for the full site frequency spectrum. We find that whenever background selection is strong enough to lead to a reduction in genetic diversity, it also results in substantial distortions to the site frequency spectrum, which can mimic the effects of population expansions or positive selection. Because these distortions are most pronounced in the low and high frequency ends of the spectrum, they become particularly important in larger samples, but may have small effects in smaller samples. We also apply our forward-time framework to calculate other quantities, such as the ultimate fates of polymorphisms or the fitnesses of their ancestral backgrounds.


Asunto(s)
Biología Computacional/métodos , Mutación , Selección Genética , Simulación por Computador , Evolución Molecular , Frecuencia de los Genes , Aptitud Genética , Variación Genética , Modelos Genéticos
17.
Artículo en Inglés | MEDLINE | ID: mdl-26106322

RESUMEN

Modeling the Hemodynamic Response Function (HRF) is a critical step in fMRI studies of brain activity, and it is often desirable to estimate HRF parameters with physiological interpretability. A biophysically informed model of the HRF can be described by a non-linear time-invariant dynamic system. However, the identification of this dynamic system may leave much uncertainty on the exact values of the parameters. Moreover, the high noise levels in the data may hinder the model estimation task. In this context, the estimation of the HRF may be seen as a problem of model falsification or invalidation, where we are interested in distinguishing among a set of eligible models of dynamic systems. Here, we propose a systematic tool to determine the distinguishability among a set of physiologically plausible HRF models. The concept of absolutely input-distinguishable systems is introduced and applied to a biophysically informed HRF model, by exploiting the structure of the underlying non-linear dynamic system. A strategy to model uncertainty in the input time-delay and magnitude is developed and its impact on the distinguishability of two physiologically plausible HRF models is assessed, in terms of the maximum noise amplitude above which it is not possible to guarantee the falsification of one model in relation to another. Finally, a methodology is proposed for the choice of the input sequence, or experimental paradigm, that maximizes the distinguishability of the HRF models under investigation. The proposed approach may be used to evaluate the performance of HRF model estimation techniques from fMRI data.

18.
Ciênc. rural ; Ciênc. rural (Online);42(2): 189-196, fev. 2012. tab
Artículo en Portugués | LILACS | ID: lil-618097

RESUMEN

Estudos envolvendo descritores adicionais têm sido de importância para o melhoramento genético de soja. Por isso, neste trabalho, objetivou-se estimar o coeficiente de repetibilidade do comprimento do hipocótilo, do epicótilo, do internódio entre o nó das folhas unifolioladas e da primeira folha trifoliolada, do pecíolo e da raque da primeira folha trifoliolada e determinar o número mínimo de avaliações necessário para predizer o valor real dos genótipos. O trabalho foi desenvolvido na Universidade Federal de Viçosa, analisando-se 85 genótipos de soja em quatro experimentos, no delineamento inteiramente casualizado. A partir das estimativas dos coeficientes de repetibilidade e de determinação obtidos pelos métodos - da análise de variância, dos componentes principais e da análise estrutural -, foram calculados os números de avaliações necessárias. Concluiu-se que os comprimentos do hipocótilo, do epicótilo e do internódio requereram menor quantidade de medição em comparação com os comprimentos do pecíolo e da raque, para o mesmo nível de confiabilidade; e com 15 medições obteve-se 85 por cento de confiabilidade para comprimento do hipocótilo pelos métodos ANOVA e AE(correl) e 90 por cento para CP(correl) e CP(cov); 90 por cento de confiabilidade para comprimento do epicótilo e do internódio pelos métodos ANOVA, CP(correl), CP(cov) e AE(correl); 80 por cento de confiabilidade para comprimento da raque da primeira folha trifoliolada pelos métodos ANOVA, CP(correl), CP(cov) e AE(correl); e, para o comprimento do pecíolo da primeira folha trifoliolada, seriam necessárias 21 medições para confiabilidade de 80 por cento pelos métodos ANOVA e AE(correl) e de 85 por cento pelos CP(correl) e CP(cov).


Studies involving additional descriptors has been important for soybean genetic improvement, so this study aimed to estimate the repeatability the length coefficient of hypocotyl, epicotyl, the internode between the unifoliated leaf nodes and the first trifoliate leaf, from the petiole and from the rachis of the first trifoliate leaf stage and determine the minimum number of evaluations needed to predict the real value of the genotypes. The study was conducted at the Universidade Federal de Viçosa, analyzing 85 soybean genotypes in four experiments in a completely randomized design. The numbers of necessary evaluations were calculated from the estimates of repeatability and coefficient of determination obtained by the methods of analysis of variance of the principal component and by the structural analysis. It was concluded that the lengths of the hypocotyl, epicotyl and the internode required fewer measurements compared with the length of the petiole and rachis to the same level of reliability, and with 15 measurements 85 percent of reliability was obtained for hypocotyl length by ANOVA and AE(correl) methods and 90 percent by CP(correl) and CP(cov) methods; 90 percent reliability was obtained for epicotyl and internode length by ANOVA, CP(correl), CP(cov) and AE(correl) method; 80 percent reliability was obtained for rachis length by ANOVA, CP(correl), CP(cov) and AE(correl) methods; and for petiole length, 21 measurements were needed for reliability by ANOVA and AE(correl) methods and 85 percent for CP(correl) and CP(cov) methods.

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