orthogonal projections
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2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Sihang Liu ◽  
Benoit Tremblais ◽  
Phillippe Carre ◽  
Nanrun Zhou ◽  
Jianhua Wu

The representation of an image with several multiscale singular points has been the main concern in image processing. Based on the dual-tree complex wavelet transform (DT-CWT), a new image reconstruction (IR) algorithm from multiscale singular points is proposed. First, the image was transformed by DT-CWT, which provided multiresolution wavelet analysis. Then, accurate multiscale singular points for IR were detected in the DT-CWT domain due to the shift invariance and directional selectivity properties of DT-CWT. Finally, the images were reconstructed from the phases and magnitudes of the multiscale singular points by alternating orthogonal projections between the CT-DWT space and its affine space. Theoretical analysis and experimental results show that the proposed IR algorithm is feasible, efficient, and offers a certain degree of denoising. Furthermore, the proposed IR algorithm outperforms other classical IR algorithms in terms of performance metrics such as peak signal-to-noise ratio, mean squared error, and structural similarity.


2021 ◽  
Vol 40 ◽  
pp. 1-15
Author(s):  
Bilel Selmi

In this paper, we calculate the multifractal Hausdorff and packing dimensions of Borel probability measures and study their behaviors under orthogonal projections. In particular, we try through these results to improve the main result of M. Dai in \cite{D} about the multifractal analysis of a measure of multifractal exact dimension.


Molecules ◽  
2021 ◽  
Vol 26 (24) ◽  
pp. 7626
Author(s):  
Laela Hayu Nurani ◽  
Abdul Rohman ◽  
Anjar Windarsih ◽  
Any Guntarti ◽  
Florentinus Dika Octa Riswanto ◽  
...  

Curcuma longa, Curcuma xanthorrhiza, and Curcuma manga have been widely used for herbal or traditional medicine purposes. It was reported that turmeric plants provided several biological activities such as antioxidant, anti-inflammatory, hepatoprotector, cardioprotector, and anticancer activities. Authentication of the Curcuma species is important to ensure its authenticity and to avoid adulteration practices. Plants from different origins will have different metabolite compositions because metabolites are affected by soil nutrition, climate, temperature, and humidity. 1H-NMR spectroscopy, principal component analysis (PCA), and orthogonal projections to latent structures-discriminant analysis (OPLS-DA) were used for authentication of C. longa, C. xanthorrhiza, and C. manga from seven different origins in Indonesia. From the 1H-NMR analysis it was obtained that 14 metabolites were responsible for generating classification model such as curcumin, demethoxycurcumin, alanine, methionine, threonine, lysine, alpha-glucose, beta-glucose, sucrose, alpha-fructose, beta-fructose, fumaric acid, tyrosine, and formate. Both PCA and OPLS-DA model demonstrated goodness of fit (R2 value more than 0.8) and good predictivity (Q2 value more than 0.45). All OPLS-DA models were validated by assessing the permutation test results with high value of original R2 and Q2. It can be concluded that metabolite fingerprinting using 1H-NMR spectroscopy and chemometrics provide a powerful tool for authentication of herbal and medicinal plants.


2021 ◽  
Vol 12 (2) ◽  
pp. 164-172
Author(s):  
Gudrun Kalmbach H.E.

The Planck and other natural numbers are used for units of forces. They arise also as weights of Gleason operators, defined by 3-dimensional spin-like base triples GF and their weigths. The spin lengths are the spin GF weights for instance. The measuring GF operator triples arise by projective duality from 1-dimensional force vectors in projective to R5 extended Hilbert space H4. Color charges are set as a separate force, using a G-compass (figure 2). For the universes evolution after a big bang several maps are introduced, mostly belonging to the gravity field quantum rgb-graviton. It presents the neutral color charge of nucleons. Orthogonal projections of H4, also in spiralic and angular form, central or stereographic projective maps belong to them. They project also the S³ factor of the strong interation geometry S³xS5 down to the SU(2) geometry S³ of the Hopf map. Fiber bundle maps are added also to S5 with the same fiber S1 to the base space CP² for nucleons and atomic kernels. In octonian coordinates, listed by indices, 01234567, there are three projections from the energy space 123456 of SI to complex quaternionic 2x2-matrix presentations of spacetime 1234, of CP² as 3456 and of GR with mass and rgb-gravitons 1256. GR and CP² are projected into 1234 as the universes spacetime, observable as bubbles for atoms and matter 3456 and GR potentials and actions about and for mass carrying systems 1256.


2021 ◽  
pp. 3-11
Author(s):  
N. Sal'kov

The translation "Descriptive geometry" is not entirely accurate. In fact, the phrase should be translated as "Narrative geometry". Based on this translation, it can be confidently stated that the science under consideration serves not only as a theoretical basis for orthogonal projections, a special case of which are ordinary drawings, but also for any images – in this the author of the article fully agrees with such authorities as N.A. Rynin, N.F. Chetverukhin, V.O. Gordon, S.A. Frolov, N.A. Sobolev and many others. The paper considers the origins of one of the directions of geometry – descriptive geometry. The hypothesis is put forward that in reality descriptive geometry, or rather, its elements, was originally involved in ancient times, during the primitive communal system when making drawings on the walls of caves and rocks. Orthogonal projections were used in the ancient world and in the Middle Ages, and Gaspard Monge at the end of the XVIII century systematized all the existing disconnected developments on descriptive geometry, adding his own research. Most likely, geometry in general was the very first science that originated when our ancestors who lived in caves faced the problem of increasing the living area due to population growth. And descriptive geometry began to develop from the moment when the first artist depicted scenes from life on the cave wall: hunting, fishing, tribal wars, events that shocked people, etc. Ancient artists existed on all continents of the globe, except perhaps Antarctica, since rock carvings were found on all other continents. And the earliest was performed somewhere 25-30 thousand years ago. Thus, the hypothesis that the elements of descriptive geometry originated in the primitive communal system can be considered proven.


Plants ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 2617
Author(s):  
Woo-Sung Park ◽  
Hye-Jin Kim ◽  
Atif Ali Khan Khalil ◽  
Dong-Min Kang ◽  
Kazi-Marjahan Akter ◽  
...  

Ulmus species (Ulmaceae) are large deciduous trees distributed throughout Korea. Although their root and stem bark have been used to treat gastrointestinal diseases and wounds in folk medicine, commercial products are consumed without any standardization. Therefore, we examined anatomical and chemical differences among five Ulmus species in South Korea. Transverse sections of leaf, stem, and root barks were examined under a microscope to elucidate anatomical differences. Stem and root bark exhibited characteristic medullary ray and secretary canal size. Leaf surface, petiole, and midrib exhibited characteristic inner morphologies including stomatal size, parenchyma, and epidermal cell diameter, as well as ratio of vascular bundle thickness to diameter among the samples. Orthogonal projections to latent structures discriminant analysis of anatomical data efficiently differentiated the five species. To evaluate chemical differences among the five species, we quantified (-)-catechin, (-)-catechin-7-O-β-D-apiofuranoside, (-)-catechin-7-O-α-L-rhamnopyranoside, (-)-catechin-7-O-β-D-xylopyranoside, (-)-catechin-7-O-β-D-glucopyranoside, and (-)-catechin-5-O-β-D-apiofuranoside using high-performance liquid chromatography with a diode-array detector. (-)-Catechin-7-O-β-D-apiofuranoside content was the highest among all compounds in all species, and (-)-catechin-7-O-α-L-rhamnopyranoside content was characteristically the highest in Ulmus parvifolia among the five species. Overall, the Ulmus species tested was able to be clearly distinguished on the basis of anatomy and chemical composition, which may be used as scientific criteria for appropriate identification and standard establishment for commercialization of these species


2021 ◽  
Author(s):  
James W. Webber ◽  
Kevin M. Elias

Background: High dimensionality, i.e. p>n, is an inherent feature of machine learning. Fitting a classification model directly to p-dimensional data risks overfitting and a reduction in accuracy. Thus, dimensionality reduction is necessary to address overfitting and high dimensionality. Results: We present a novel dimensionality reduction method which uses sparse, orthogonal projections to discover linear separations in reduced dimension space. The technique is applied to miRNA expression analysis and cancer prediction. We use least squares fitting and orthogonality constraints to find a set of orthogonal directions which are highly correlated to the class labels. We also enforce L^1 norm sparsity penalties, to prevent overfitting and remove the uninformative features from the model. Our method is shown to offer a highly competitive classification performance on synthetic examples and real miRNA expression data when compared to similar methods from the literature which use sparsity ideas and orthogonal projections. %Specifically, our method offers a more consistent performance in terms of sensitivity and AUC, particularly in the case $p>n$, and when the training samples are weighted towards one class. Discussion: A novel technique is introduced here, which uses sparse, orthogonal projections for dimensionality reduction. The approach is shown to be highly effective in reducing the dimension of miRNA expression data. The application of focus in this article is miRNA expression analysis and cancer prediction. The technique may be generalizable, however, to other high dimensionality datasets.


Endocrinology ◽  
2021 ◽  
Author(s):  
Nadia Saadat ◽  
Muraly Puttabyatappa ◽  
Venkateswaran R Elangovan ◽  
John Dou ◽  
Joseph N Ciarelli ◽  
...  

Abstract Prenatal testosterone (T)-treated female sheep manifest peripheral insulin resistance, ectopic lipid accumulation and insulin signaling disruption in liver and muscle. This study investigated transcriptional changes and transcriptome signature of prenatal T excess-induced hepatic and muscle-specific metabolic disruptions. Genome-wide coding and non-coding (nc) RNA expression in liver and muscle from 21-month-old prenatal T-treated (T propionate 100mg intramuscular twice weekly from days 30 to 90 of gestation; Term: 147 days) and control females were compared. Prenatal T (1) induced differential expression of mRNAs in liver (15 down, 17 up) and muscle (66 down, 176 up) (FDR<0.05, absolute log2 fold change>0.5); (2) downregulated mitochondrial pathway genes in liver and muscle; (3) downregulated hepatic lipid catabolism and PPAR signaling gene pathways; (4) modulated ncRNA metabolic processes gene pathway in muscle and (5) downregulated 5 uncharacterized long ncRNA (lncRNA) in the muscle but no ncRNA changes in the liver. Correlation analysis showed downregulation of lncRNAs LOC114112974 and LOC105607806 was associated with decreased TPK1, and LOC114113790 with increased ZNF470 expression. Orthogonal Projections to Latent Structures Discriminant Analysis identified mRNAs HADHA and SLC25A45, and miRNAs MIR154A, MIR25 and MIR487B in liver and ARIH1 and ITCH and miRNAs MIR369, MIR10A and MIR10B in muscle as potential biomarkers of prenatal T-excess. These findings suggest downregulation of mitochondria, lipid catabolism, and PPAR signaling genes in liver and dysregulation of mitochondrial and ncRNA gene pathways in muscle are contributors of lipotoxic and insulin resistant hepatic and muscle phenotype. Gestational T excess programming of metabolic dysfunctions involve tissue-specific ncRNA modulated transcriptional changes.


Author(s):  
Lorenzo Botti ◽  
Daniele A. Di Pietro

AbstractWe propose a p-multilevel preconditioner for hybrid high-order (HHO) discretizations of the Stokes equation, numerically assess its performance on two variants of the method, and compare with a classical discontinuous Galerkin scheme. An efficient implementation is proposed where coarse level operators are inherited using $$L^2$$ L 2 -orthogonal projections defined over mesh faces and the restriction of the fine grid operators is performed recursively and matrix-free. Both h- and k-dependency are investigated tackling two- and three-dimensional problems on standard meshes and graded meshes. For the two HHO formulations, featuring discontinuous or hybrid pressure, we study how the combination of p-coarsening and static condensation influences the V-cycle iteration. In particular, two different static condensation procedures are considered for the discontinuous pressure HHO variant, resulting in global linear systems with a different number of unknowns and matrix non-zero entries. Interestingly, we show that the efficiency of the solution strategy might be impacted by static condensation options in the case of graded meshes.


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