On singular values of large dimensional lag-τ sample auto-correlation matrices.

We study the limiting behavior of singular values of a lag-τ sample auto-correlation matrix Rτϵ of large dimensional vector white noise process, the error term ϵ in the high-dimensional factor model. We establish the limiting spectral distribution (LSD) that characterizes the global spectrum of Rτϵ, and derive the limit of its largest singular value. All the asymptotic results are derived under the high-dimensional asymptotic regime where the data dimension and sample size go to infinity proportionally. Under mild assumptions, we show that the LSD of Rτϵ is the same as that of the lag-τ sample auto-covariance matrix. Based on this asymptotic equivalence, we additionally show that the largest singular value of Rτϵ converges almost surely to the right end point of the support of its LSD. Based on these results, we further propose two estimators of total number of factors with lag-τ sample auto-correlation matrices in a factor model. Our theoretical results are fully supported by numerical experiments as well.

Incorporating the effect of the photon spectrum on biomass accumulation of lettuce using a dynamic growth model.

Cultivation studies in specialty crop optimization utilize models to estimate the fresh and dry mass yield. However, the spectral distribution and photon flux density (µmol m-2 s-1) affect plant photosynthetic rate and morphology, which is usually not incorporated in plant growth models. In this study, using data for indoor-grown lettuce (Lactuca sativa) cultivated under different light spectra, a mathematical model that incorporates these effects is presented. Different experimental cases are used to obtain a modified quantum use efficiency coefficient that varies with the spectral distribution. Several models for this coefficient are fitted using experimental data. Comparing the accuracy of these models, a simple first- or second-order linear model for light-use efficiency coefficient has about 6 to 8 percent uncertainty, while a fourth-order model has a 2 percent average error in prediction. In addition, normalizing overall spectral distribution leads to a more accurate prediction of the investigated parameter. A novel mathematical model based on normalized spectral irradiance integrated over wavelength for photosynthetically active radiation (PAR) wavebands and the far-red waveband is presented in this study. It accurately predicts lettuce dry mass grown indoors under different light spectra.

KCS-FCnet: Kernel Cross-Spectral Functional Connectivity Network for EEG-Based Motor Imagery Classification.

This paper uses EEG data to introduce an approach for classifying right and left-hand classes in Motor Imagery (MI) tasks. The Kernel Cross-Spectral Functional Connectivity Network (KCS-FCnet) method addresses these limitations by providing richer spatial-temporal-spectral feature maps, a simpler architecture, and a more interpretable approach for EEG-driven MI discrimination. In particular, KCS-FCnet uses a single 1D-convolutional-based neural network to extract temporal-frequency features from raw EEG data and a cross-spectral Gaussian kernel connectivity layer to model channel functional relationships. As a result, the functional connectivity feature map reduces the number of parameters, improving interpretability by extracting meaningful patterns related to MI tasks. These patterns can be adapted to the subject's unique characteristics. The validation results prove that introducing KCS-FCnet shallow architecture is a promising approach for EEG-based MI classification with the potential for real-world use in brain-computer interface systems.

Asymptotic behavior of an intrinsic rank-based estimator of the Pickands dependence function constructed from B-splines.

A bivariate extreme-value copula is characterized by its Pickands dependence function, i.e., a convex function defined on the unit interval satisfying boundary conditions. This paper investigates the large-sample behavior of a nonparametric estimator of this function due to Cormier et al. (Extremes 17:633-659, 2014). These authors showed how to construct this estimator through constrained quadratic median B-spline smoothing of pairs of pseudo-observations derived from a random sample. Their estimator is shown here to exist whatever the order m ≥ 3 of the B-spline basis, and its consistency is established under minimal conditions. The large-sample distribution of this estimator is also determined under the additional assumption that the underlying Pickands dependence function is a B-spline of given order with a known set of knots.

All-at-once multigrid approaches for one-dimensional space-fractional diffusion equations.

We focus on a time-dependent one-dimensional space-fractional diffusion equation with constant diffusion coefficients. An all-at-once rephrasing of the discretized problem, obtained by considering the time as an additional dimension, yields a large block linear system and paves the way for parallelization. In particular, in case of uniform space-time meshes, the coefficient matrix shows a two-level Toeplitz structure, and such structure can be leveraged to build ad-hoc iterative solvers that aim at ensuring an overall computational cost independent of time. In this direction, we study the behavior of certain multigrid strategies with both semi- and full-coarsening that properly take into account the sources of anisotropy of the problem caused by the grid choice and the diffusion coefficients. The performances of the aforementioned multigrid methods reveal sensitive to the choice of the time discretization scheme. Many tests show that Crank-Nicolson prevents the multigrid to yield good convergence results, while second-order backward-difference scheme is shown to be unconditionally stable and that it allows good convergence under certain conditions on the grid and the diffusion coefficients. The effectiveness of our proposal is numerically confirmed in the case of variable coefficients too and a two-dimensional example is given.

Effects of the Serber first step in 3DHZETRN-v2.1.

3DHZETRN-v2 includes a detailed three dimensional (3D) treatment of neutron/light-ion transport based on a quasi-elastic/multiple production assumption allowing improved agreement of the neutron/light-ion fluence compared with results of three Monte Carlo (MC) codes in the sense that the variance with respect to the individual MC results is less than the variance among the MC code results. The current numerical methods are no longer the main limitation to HZETRN code development and further changes in the nuclear model are required. In a prior study, an improved quasi-elastic spectrum based on a solution of the transport approximation to nuclear media effects showed promise, but the remaining multiple-production spectrum was based on a database derived from the Ranft model that used Bertini multiplicities. In the present paper, we will implement a more complete Serber first step into the 3DHZETRN-v2 code, but we retain the Bertini-Ranft branching ratios and evaporation multiplicities. It is shown that the new Serber model in the 3HZETRN-v2 code reduces the variance with individual MC codes, which are largely due to nuclear cross section model differences. The code will be available through the software system, OLTARIS, for shield design and validation and provides a basis for personal computer software capable of space shield analysis and optimization.

Impact of location, type, and number of glycosidic substitutions on the color expression of o-dihydroxylated anthocyanidins.

Anthocyanins express many hues depending on environmental factors and structural aspects, of which aglycone structure and acylation have been considered most impactful. Effects of different glycosylations on anthocyanins' colors are less known. Twelve cyanidin and 3-deoxy-cyanidin (luteolinidin) derivatives were isolated from red cabbage and black carrot hydrolysates and from black sorghum, diluted in pH 1-9, and analyzed by spectrophotometry and colorimetry. Location, number, and structure of glycosylations affected λmax and spectral shape of o-dihydroxylated anthocyanins, playing important roles on color expression. Generally, glycosylation of cyanidin decreased its λmax (≤27 nm), greatest decreases by 3-monoglycosylation. All cyanidin-glycosides appeared red in pH 1-3 and paled in pH 4-6. However, cyanidin-3-glycosides did not decolor completely like 3,5-glycosides. In alkaline pH, glycosylation patterns affected color more greatly: Cy-3-glycosides expressed maroon-purple hues (300-20°), 5-glycosides were green (100-115°), and only 3,5-glycosides expressed blue (240-250°). Luteolinidin derivatives shifted from yellow to red-purple hues with increasing pH.

Signals of Systemic Immunity in Plants: Progress and Open Questions.

Systemic acquired resistance (SAR) is a defence mechanism that induces protection against a wide range of pathogens in distant, pathogen-free parts of plants after a primary inoculation. Multiple mobile compounds were identified as putative SAR signals or important factors for influencing movement of SAR signalling elements in Arabidopsis and tobacco. These include compounds with very different chemical structures like lipid transfer protein DIR1 (DEFECTIVE IN INDUCED RESISTANCE1), methyl salicylate (MeSA), dehydroabietinal (DA), azelaic acid (AzA), glycerol-3-phosphate dependent factor (G3P) and the lysine catabolite pipecolic acid (Pip). Genetic studies with different SAR-deficient mutants and silenced lines support the idea that some of these compounds (MeSA, DIR1 and G3P) are activated only when SAR is induced in darkness. In addition, although AzA doubled in phloem exudate of tobacco mosaic virus (TMV) infected tobacco leaves, external AzA treatment could not induce resistance neither to viral nor bacterial pathogens, independent of light conditions. Besides light intensity and timing of light exposition after primary inoculation, spectral distribution of light could also influence the SAR induction capacity. Recent data indicated that TMV and CMV (cucumber mosaic virus) infection in tobacco, like bacteria in Arabidopsis, caused massive accumulation of Pip. Treatment of tobacco leaves with Pip in the light, caused a drastic and significant local and systemic decrease in lesion size of TMV infection. Moreover, two very recent papers, added in proof, demonstrated the role of FMO1 (FLAVIN-DEPENDENT-MONOOXYGENASE1) in conversion of Pip to N-hydroxypipecolic acid (NHP). NHP systemically accumulates after microbial attack and acts as a potent inducer of plant immunity to bacterial and oomycete pathogens in Arabidopsis. These results argue for the pivotal role of Pip and NHP as an important signal compound of SAR response in different plants against different pathogens.

Root discrimination of closely related crop and weed species using FT MIR-ATR spectroscopy.

Root discrimination of species is a pre-condition for studying belowground competition processes between crop and weed species. In this experiment, we tested Fourier transform mid-infrared (FT MIR)-attenuated total reflection (ATR) spectroscopy to discriminate roots of closely related crop and weed species grown in the greenhouse: maize/barnyard grass, barley/wild oat, wheat/blackgrass (Poaceae), and sugar beet/common lambsquarters (Chenopodiaceae). Fresh (moist) and dried root segments as well as ground roots were analyzed by FT MIR-ATR spectroscopy. Root absorption spectra showed species specific peak distribution and peak height. A clear separation according to species was not possible with fresh root segments. Dried root segments (including root basis, middle section, and root tip) of maize/barnyard grass and sugar beet/common lambsquarters formed completely separated species clusters. Wheat and blackgrass separated in species specific clusters when root tips were removed from cluster analysis. A clear separation of dried root segments according to species was not possible in the case of barley and wild oat. Cluster analyses of ground roots revealed a 100% separation of all tested crop and weed species combinations. Spectra grouped in Poaceae and Chenopodiaceae clusters. Within the Poaceae cluster, C3 and C4 species differed significantly in heterogeneity. Thus, root spectra reflected the degree of kinship. To quantify species proportion in root mixtures, a two- and a three-species model for species quantification in root mixtures of maize, barnyard grass, and wild oat was calculated. The models showed low standard errors of prediction (RMSEP) and high residual predictive deviation values in an external test set validation. Hence, FT MIR-ATR spectroscopy seems to be a promising tool for root research even between closely related plant species.

Inflammatory Acne in the Asian Skin Type III Treated with a Square Pulse, Time Resolved Spectral Distribution IPL System: A Preliminary Study.

BACKGROUND AND AIMS: Acne remains a severe problem for both patients and clinicians. Various approaches using photosurgery and phototherapy have been reported with varying degrees of success and robustness of results. An improved intense pulsed light (IPL) system has become available with interesting beam characteristic which might improve IPL treatment of inflammatory acne in the Asian skin, Fitzpatrick type III/IV. SUBJECTS AND METHODS: The 18 study subjects comprised 15 females and 3 males with active mild to moderately severe inflammatory acne (mean age 25.3 ± 7.70 yr, range 17-47 yr, Burton scale 1-4, all Fitzpatrick type III Asian skin). They were treated once (8 subjects) or twice (10 subjects) with an IPL system offering both square pulse and time resolved spectral distribution technologies (420 nm cut-off filter, 30 ms pulse, 8 - 12 J/cm(2), 2-3 passes). Clinical photography was taken at baseline and at 4 weeks after the final treatment. Percentage of acne clearance was assessed by an independent dermatological panel and graded from zero to 5, 5 being total clearance. RESULTS: All subjects completed the study. Post-treatment side effects were mild and transient, with virtually no downtime or postinflammatory hyperpigmentation (PIH) experienced by any subject. All subjects had some improvement and no exacerbation was seen in any subject. Clearance was evaluated by the panel as grade 4 in 5 subjects, grade 3 in 8, grade 2 in 4 and grade 1 in 1, so that 14 of 18 subjects (78%) had clearance of at least 60%. Patient evaluation was in general slightly better than that of the panel. CONCLUSIONS: The special beam characteristics of the IPL system used in the present preliminary study achieved good to very good results in the treatment of acne in the Fitzpatrick type III Asian skin without PIH induction. The results suggested that acne treatment in the Asian skin using this system is both safe and effective, and merits larger population studies to further optimize parameters and standardize top-up treatments.

Sombreamento de plantas de Catharanthus roseus (L. ) G. Don 'Pacifica White' por malhas coloridas: desenvolvimento vegetativo / Shading of 'Pacifica White' Catharanthus roseus (L. ) G. Don plants with colored nets: vegetative development

As malhas coloridas têm sido utilizadas para manipular o desenvolvimento vegetativo, melhorando a utilização da radiação solar por plantas ornamentais. Objetivou-se, neste trabalho estudar o efeito da redução de 50% da radiação fotossinteticamente ativa sobre o crescimento vegetativo de plantas de Catharanthus roseus (L.) G. Don, por meio de malhas azul e vermelha e malha preta, em comparação com plantas crescidas na ausência de sombreamento (pleno sol). As plantas foram obtidas a partir de sementes e tratadas por 180 dias. Foram avaliados o ganho de biomassa e a distribuição de matéria seca nas plantas, o conteúdo de pigmentos foliares (clorofilas e carotenóides) e de nitrogênio foliar. A malha vermelha provocou um aumento de matéria seca total e de área foliar das plantas em comparação com as malhas azul, preta e ao tratamento a pleno sol, porém, exceto em relação a esse tratamento, a malha vermelha causou menor conteúdo de nitrogênio e pigmentos foliares. A maior relação raiz/parte aérea e relação clorofila a/b, menores razões de área foliar e de massa foliar das plantas crescidas a pleno sol em relação às plantas sombreadas indicam um efeito mais proeminente da irradiância mais alta do que da alteração do espectro de luz. O sombreamento altera significativamente a distribuição de matéria seca e o uso de malhas de diferentes cores modifica o conteúdo de pigmentos fotossintéticos dessa espécie.

Colored shade nets have been used to manipulate the vegetative development, improving the utilization of solar radiation by ornamental plants. This work aimed to study the effect of 50 % reduction of PAR on vegetative growth of plants of Catharanthus roseus (L.) G. Don, using blue and red nets, and black net, in comparison to plants growing under full sunlight (lack of shading). The plants were obtained from seeds and treated for 180 days. Biomass increment and distribution, pigment content (chlorophylls and carotenoids) and foliar nitrogen were evaluated. The red net caused an increase of total dry mass and total leaf area of plants when compared to the blue net, black net and the full sunlight treatment, however, except in relation to the last treatment, the red net caused lower contents of foliar nitrogen and pigments. The higher root/stem and chlorophyll a/b ratios and the lower leaf area and leaf dry mass of plants growing under full sunlight in relation to shaded plants indicate a more prominent effect of the higher irradiance than the spectral alteration. Shading alters significantly the dry matter distribution and the use of shade nets of different colors affects the content of photosynthetic pigments of this species.

Density Fluctuations in Fluids Having an Internal Degree of Freedom.

The frequency spectrum of density fluctuations is calculated for a fluid whose molecules possess an internal degree of freedom which is weakly coupled to the translational degree of freedom of the fluid. Irreversible thermodynamics is used to obtain an equation of motion for the internal degree of freedom. This equation plus the linearized hydrodynamic equations are solved for the frequency spectrum of density fluctuations. The results are compared with a similar calculation involving a frequency dependent volume viscosity. The results are identical for structural relaxation but there is a difference for thermal relaxation. The origin of the difference is discussed and the magnitude of the difference is examined for CC14, and for CS2.

Thermal Relaxation and Brillouin Scattering in Liquids.

Weak coupling of internal degrees of freedom of molecules to the translational degrees of freedom of a fluid results in additional modes of motion for density fluctuations. These new modes affect the spectral distribution of light scattered by density fluctuations so that the Landau-Placzek ratio is not satisfied. The case of thermal relaxation with a single relaxation time is worked out in detail. Formulas for the spectral distribution of the scattered light, for the ratio of the intensities of the central (Rayleigh) to the Brillouin components and for the phonon velocity are derived and applied to carbon disulfide and carbon tetrachloride. The data for carbon tetrachloride are shown to be inconsistent with the single relaxation time model for thermal relaxation.