Search

Two new compounds, schisandrulata A (1) and schisandrulata B (5), and nine known compounds, 6-O-benzoylgomisin O (2), kadsutherin (3), γ-schizandrin (4), pinotatol (6), schisphentetralone A (7), (–)-8′-epi-aristotetralone (8), (–)-8,8′-epi-aristotetralone (9), rel-(8R,8′R)-dimethyl-(7S,7′R)-bis(3,4-methylenedioxyphenyl)tetrahydrofuran (10) and (-)-machilusin (11) were isolated from the leaves of Schisandra perulata Gagnep. Their chemical structures were determined by means of HR-ESI-MS, NMR, and CD spectra. All the compounds were evaluated for their cytotoxic activity against the human oral cancer (CAL27) and human breast cancer (MDA-MB231) cell lines. Compounds 1, 4, 7, and 9 showed potent cytotoxic activity against CAL27 cell line with IC50 values of 1.8 ± 0.2, 1.2 ± 0.1, 1.2 ± 0.2, and 2.0 ± 0.1 μM, respectively, indicating that they have stronger cytotoxic activity than that of the positive control capecitabine (IC50 value of 8.20 ± 0.75 μM). Similarly, compounds 1, 4, 7, and 9 also exhibited potent activity against the MDA-MB231 cell line with IC50 values of 3.5 ± 0.1, 1.80 ± 0.2, 0.9 ± 0.2, and 3.4 ± 0.3 μM, respectively. These results indicated that compounds 1, 4, 7, and 9 could be potential anticancer reagents for further drug discovery research.

Ten triterpenoid glycosides including two undescribed compounds (1 and 2) were isolated from the methanol extract of Allium ascalonicum rhizomes. These compounds were structurally elucidated to be 3β-O-α-L-rhamnopyranosyl-(1→2)-α-L-arabinopyranosyl-19α-hydroxyolean-12-ene-28-oic acid 28-O-[α-L-rhamnopyranosyl-(1→2)-β-D-glucopyranosyl] ester (1), 3-O-β-D-glucopyranosyl-(1→3)-[α-L-rhamnopyranosyl-(1→2)]-α-L-arabinopyranosyl-3β,19α-dihydroxyoleanane-12-en-28-oic acid (2), lactifoloside C (3), lactifoloside H (4), randiasaponin IV (5), kudinoside G (6), ilexkudinoside W (7), lactifoloside G (8), kudinoside D (9), and ilexkudinoside T (10) by analyzing their HR-ESI-MS, NMR spectral data and by comparison with those reported in the literature. Compounds 1–10 were evaluated for anoctamin-1 (ANO1) inhibitory activity using yellow fluorescent protein reduction assays. At the concentration of 30 µM, compounds 2 and 9 displayed moderate ANO1 inhibitory percentages of 28.9 ± 0.85% and 26.2 ± 0.65%, respectively.

Multivariate polynomial systems arising in numerous applications have special structures. In particular, determinantal structures and invariant systems appear in a wide range of applications such as in polynomial optimization and related questions in real algebraic geometry. The goal of this thesis is to provide efficient algorithms to solve such structured systems. In order to solve the first kind of systems, we design efficient algorithms by using the symbolic homotopy continuation techniques. While the homotopy methods, in both numeric and symbolic, are well-understood and widely used in polynomial system solving for square systems, the use of these methods to solve over-detemined systems is not so clear. Meanwhile, determinantal systems are over-determined with more equations than unknowns. We provide probabilistic homotopy algorithms which take advantage of the determinantal structure to compute isolated points in the zero-sets of determinantal systems. The runtimes of our algorithms are polynomial in the sum of the multiplicities of isolated points and the degree of the homotopy curve. We also give the bounds on the number of isolated points that we have to compute in three contexts: all entries of the input are in classical polynomial rings, all these polynomials are sparse, and they are weighted polynomials. In the second half of the thesis, we deal with the problem of finding critical points of a symmetric polynomial map on an invariant algebraic set. We exploit the invariance properties of the input to split the solution space according to the orbits of the symmetric group. This allows us to design an algorithm which gives a triangular description of the solution space and which runs in time polynomial in the number of points that we have to compute. Our results are illustrated by applications in studying real algebraic sets defined by invariant polynomial systems by the means of the critical point method., Les systèmes polynomiaux multivariés apparaissant dans de nombreuses applications ont des structures spéciales et les systèmes invariants apparaissent dans un large éventail d'applications telles que dans l’optimisation polynomiale et des questions connexes en géométrie algébrique réelle. Le but de cette thèse est de fournir des algorithmes efficaces pour résoudre de tels systèmes structurés. Afin de résoudre le premier type de systèmes, nous concevons des algorithmes efficaces en utilisant les techniques d’homotopie symbolique. Alors que les méthodes d'homotopie, à la fois numériques et symboliques, sont bien comprises et largement utilisées dans la résolution de systèmes polynomiaux pour les systèmes carrés, l'utilisation de ces méthodes pour résoudre des systèmes surdéterminés n'est pas si claire. Hors, les systèmes déterminants sont surdéterminés avec plus d'équations que d'inconnues. Nous fournissons des algorithmes d'homotopie probabilistes qui tirent parti de la structure déterminantielle pour calculer des points isolés dans les ensembles des zéros de tels systèmes. Les temps d'exécution de nos algorithmes sont polynomiaux dans la somme des multiplicités des points isolés et du degré de la courbe d'homotopie. Nous donnons également des bornes sur le nombre de points isolés que nous devons calculer dans trois contextes: toutes les termes de l'entrée sont dans des anneaux polynomiaux classiques, tous ces polynômes sont creux, et ce sont des polynômes à degrés pondérés. Dans la seconde moitié de la thèse, nous abordons le problème de la recherche de points critiques d'une application polynomiale symétrique sur un ensemble algébrique invariant. Nous exploitons les propriétés d'invariance de l'entrée pour diviser l'espace de solution en fonction des orbites du groupe symétrique. Cela nous permet de concevoir un algorithme qui donne une description triangulaire de l'espace des solutions et qui s'exécute en temps polynomial dans le nombre de points que nous devons calculer. Nos résultats sont illustrés par des applications à l'étude d'ensembles algébriques réels définis par des systèmes polynomiaux invariants au moyen de la méthode des points critiques.

The aim of this study was to developed purple sweet corn inbred lines from a cross between purple waxy corn and white sweet corn in Vietnam. Twenty elite inbred lines were top crossed with two testers in Spring season 2020 to estimate the general combining ability. Nine lines with Brix > 16, thin pericarp 100mg/100g can be classified as super sweet purple sweet corn lines. Five lines had high GCA regarding marketable yield (UV10, UV24, UV40, UV46, UV71), two lines has high GCA on Brix (UV12, UV16), and five lines had high GCA on anthocyanin content (UV35, UV36, UV38, UV46, UV73). Taken together, UV10 and UV12 lines are super sweet purple sweet corn lines and have high GCA for marketable yield and quality, respectively. This is the first report on the development and selection of purple sweet corn inbred lines in Vietnam.

Multivariate polynomial systems arising in numerous applications have special structures. In particular, determinantal structures and invariant systems appear in a wide range of applications such as in polynomial optimization and related questions in real algebraic geometry. The goal of this thesis is to provide efficient algorithms to solve such structured systems. In order to solve the first kind of systems, we design efficient algorithms by using the symbolic homotopy continuation techniques. While the homotopy methods, in both numeric and symbolic, are well-understood and widely used in polynomial system solving for square systems, the use of these methods to solve over-detemined systems is not so clear. Meanwhile, determinantal systems are over-determined with more equations than unknowns. We provide probabilistic homotopy algorithms which take advantage of the determinantal structure to compute isolated points in the zero-sets of determinantal systems. The runtimes of our algorithms are polynomial in the sum of the multiplicities of isolated points and the degree of the homotopy curve. We also give the bounds on the number of isolated points that we have to compute in three contexts: all entries of the input are in classical polynomial rings, all these polynomials are sparse, and they are weighted polynomials. In the second half of the thesis, we deal with the problem of finding critical points of a symmetric polynomial map on an invariant algebraic set. We exploit the invariance properties of the input to split the solution space according to the orbits of the symmetric group. This allows us to design an algorithm which gives a triangular description of the solution space and which runs in time polynomial in the number of points that we have to compute. Our results are illustrated by applications in studying real algebraic sets defined by invariant polynomial systems by the means of the critical point method.; Les systèmes polynomiaux multivariés apparaissant dans de nombreuses applications ont des structures spéciales et les systèmes invariants apparaissent dans un large éventail d'applications telles que dans l’optimisation polynomiale et des questions connexes en géométrie algébrique réelle. Le but de cette thèse est de fournir des algorithmes efficaces pour résoudre de tels systèmes structurés. Afin de résoudre le premier type de systèmes, nous concevons des algorithmes efficaces en utilisant les techniques d’homotopie symbolique. Alors que les méthodes d'homotopie, à la fois numériques et symboliques, sont bien comprises et largement utilisées dans la résolution de systèmes polynomiaux pour les systèmes carrés, l'utilisation de ces méthodes pour résoudre des systèmes surdéterminés n'est pas si claire. Hors, les systèmes déterminants sont surdéterminés avec plus d'équations que d'inconnues. Nous fournissons des algorithmes d'homotopie probabilistes qui tirent parti de la structure déterminantielle pour calculer des points isolés dans les ensembles des zéros de tels systèmes. Les temps d'exécution de nos algorithmes sont polynomiaux dans la somme des multiplicités des points isolés et du degré de la courbe d'homotopie. Nous donnons également des bornes sur le nombre de points isolés que nous devons calculer dans trois contextes: toutes les termes de l'entrée sont dans des anneaux polynomiaux classiques, tous ces polynômes sont creux, et ce sont des polynômes à degrés pondérés. Dans la seconde moitié de la thèse, nous abordons le problème de la recherche de points critiques d'une application polynomiale symétrique sur un ensemble algébrique invariant. Nous exploitons les propriétés d'invariance de l'entrée pour diviser l'espace de solution en fonction des orbites du groupe symétrique. Cela nous permet de concevoir un algorithme qui donne une description triangulaire de l'espace des solutions et qui s'exécute en temps polynomial dans le nombre de points que nous devons calculer. Nos résultats sont illustrés par des applications à l'étude d'ensembles algébriques réels définis par des systèmes polynomiaux invariants au moyen de la méthode des points critiques.

Ten triterpenoid glycosides including two undescribed compounds (

We study the computation of canonical bases of sets of univariate relations $(p_1,\ldots,p_m) \in \mathbb{K}[x]^{m}$ such that $p_1 f_1 + \cdots + p_m f_m = 0$; here, the input elements $f_1,\ldots,f_m$ are from a quotient $\mathbb{K}[x]^n/\mathcal{M}$, where $\mathcal{M}$ is a $\mathbb{K}[x]$-module of rank $n$ given by a basis $\mathbf{M}\in\mathbb{K}[x]^{n\times n}$ in Hermite form. We exploit the triangular shape of $\mathbf{M}$ to generalize a divide-and-conquer approach which originates from fast minimal approximant basis algorithms. Besides recent techniques for this approach, we rely on high-order lifting to perform fast modular products of polynomial matrices of the form $\mathbf{P}\mathbf{F} \bmod \mathbf{M}$. Our algorithm uses $O\tilde{~}(m^{\omega-1}D + n^{\omega} D/m)$ operations in $\mathbb{K}$, where $D = \mathrm{deg}(\det(\mathbf{M}))$ is the $\mathbb{K}$-vector space dimension of $\mathbb{K}[x]^n/\mathcal{M}$, $O\tilde{~}(\cdot)$ indicates that logarithmic factors are omitted, and $\omega$ is the exponent of matrix multiplication. This had previously only been achieved for a diagonal matrix $\mathbf{M}$. Furthermore, our algorithm can be used to compute the shifted Popov form of a nonsingular matrix within the same cost bound, up to logarithmic factors, as the previously fastest known algorithm, which is randomized., Comment: 8 pages, uses acmart sigconf