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1.
We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming. 相似文献
2.
We construct the complex simple Lie algebras using elementary algebraic geometry. We use our construction to obtain a new
proof of the classification of complex simple Lie algebras that does not appeal to the classification of root systems. 相似文献
3.
4.
Using a combinatorial approach that avoids geometry, this paper studies the structure of KT(G/B), the T-equivariant K-theory of the generalized flag variety G/B. This ring has a natural basis
(the double Grothendieck polynomials), where
is the structure sheaf of the Schubert variety Xw. For rank two cases we compute the corresponding structure constants of the ring KT(G/B) and, based on this data, make a positivity conjecture for general G which generalizes the theorems of M. Brion (for K(G/B)) and W. Graham (for HT*(G/B)). Let [Xλ]KT(G/B) be the class of the homogeneous line bundle on G/B corresponding to the character of T indexed by λ. For general G we prove “Pieri–Chevalley formulas” for the products
,
,
, and
, where λ is dominant. By using the Chern character and comparing lowest degree terms the products which are computed in this paper also give results for the Grothendieck polynomials, double Schubert polynomials, and ordinary Schubert polynomials in, respectively K(G/B), HT*(G/B) and H*(G/B). 相似文献
5.
Gabriela Jeronimo Teresa Krick Juan Sabia Martín Sombra 《Foundations of Computational Mathematics》2004,4(1):41-117
We present a bounded probability algorithm for the computation of the
Chowforms of the equidimensional components of an algebraic variety. In particular,
this gives an alternative procedure for the effective equidimensional decomposition
of the variety, since each equidimensional component is characterized by its Chow
form.
The expected complexity of the algorithm is polynomial in the size and the geometric
degree of the input equation system defining the variety. Hence it improves (or
meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects,
which constitutes a further contribution of the paper.
The algorithm is based on elimination theory techniques, in line with the geometric
resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators.
In fact, ours can be considered as an extension of their algorithm for zero-dimensional
systems to the case of positive-dimensional varieties. The key element for dealing
with positive-dimensional varieties is a new Poisson-type product formula. This
formula allows us to compute the Chow form of an equidimensional variety from a
suitable zero-dimensional fiber.
As an application, we obtain an algorithm to compute a subclass of sparse resultants,
whose complexity is polynomial in the dimension and the volume of the input
set of exponents. As another application, we derive an algorithm for the computation
of the (unique) solution of a generic overdetermined polynomial equation system. 相似文献
6.
C. A. Beattie M. B. Boisen Jr. L. W. Johnson 《Journal of Optimization Theory and Applications》1991,68(1):203-203
Corrections to the last two equations of Ref. 1 are given. 相似文献
7.
Shaul K. Bar-Lev Daoud Bshouty Peter Enis Gérard Letac I-Li Lu Donald Richards 《Journal of Theoretical Probability》1994,7(4):883-929
A natural exponential family (NEF)F in ? n ,n>1, is said to be diagonal if there existn functions,a 1,...,a n , on some intervals of ?, such that the covariance matrixV F (m) ofF has diagonal (a 1(m 1),...,a n (m n )), for allm=(m 1,...,m n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? k and ? n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? n , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? n , under what conditions is its projectionp(F) in ? k , underp(x 1,...,x n )∶=(x 1,...,x k ),k=1,...,n?1, still an NEF in ? k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV F (m 1,...,m n ) does not depend on (m k+1,...,m n ). 相似文献
8.
Rice blast is a serious threat to rice yield. Breeding disease-resistant varieties is one of the most economical and effective ways to prevent damage from rice blast. The traditional identification of resistant rice seeds has some shortcoming, such as long possession time, high cost and complex operation. The purpose of this study was to develop an optimal prediction model for determining resistant rice seeds using Ranman spectroscopy. First, the support vector machine (SVM), BP neural network (BP) and probabilistic neural network (PNN) models were initially established on the original spectral data. Second, due to the recognition accuracy of the Raw-SVM model, the running time was fast. The support vector machine model was selected for optimization, and four improved support vector machine models (ABC-SVM (artificial bee colony algorithm, ABC), IABC-SVM (improving the artificial bee colony algorithm, IABC), GSA-SVM (gravity search algorithm, GSA) and GWO-SVM (gray wolf algorithm, GWO)) were used to identify resistant rice seeds. The difference in modeling accuracy and running time between the improved support vector machine model established in feature wavelengths and full wavelengths (200–3202 cm−1) was compared. Finally, five spectral preproccessing algorithms, Savitzky–Golay 1-Der (SGD), Savitzky–Golay Smoothing (SGS), baseline (Base), multivariate scatter correction (MSC) and standard normal variable (SNV), were used to preprocess the original spectra. The random forest algorithm (RF) was used to extract the characteristic wavelengths. After different spectral preproccessing algorithms and the RF feature extraction, the improved support vector machine models were established. The results show that the recognition accuracy of the optimal IABC-SVM model based on the original data was 71%. Among the five spectral preproccessing algorithms, the SNV algorithm’s accuracy was the best. The accuracy of the test set in the IABC-SVM model was 100%, and the running time was 13 s. After SNV algorithms and the RF feature extraction, the classification accuracy of the IABC-SVM model did not decrease, and the running time was shortened to 9 s. This demonstrates the feasibility and effectiveness of IABC in SVM parameter optimization, with higher prediction accuracy and better stability. Therefore, the improved support vector machine model based on Ranman spectroscopy can be applied to the fast and non-destructive identification of resistant rice seeds. 相似文献
9.
《Arabian Journal of Chemistry》2021,14(11):103412
Grape plant (Vitis vinifera L.) is a species of the family Vitaceae. It is an economically important fruit plant abundantly grown all over the world. Vitaceae comprised of 900 species distributed across tropical, sub-tropical and partially temperate sorts of climatic zones. In the current study we aimed to evaluate the antioxidant activities of grape leaves extract from different Pakistani varieties.We have analyzed the crude methanolic extract from the leaves of Pakistani grape varieties (i.e. NARC Black, Sundar Khani, Shogran-1, Shogran-2, Haita, Sheghali, Perlette, and Sultania-C) cultivated in various soil compositions. Total phenolic contents (TPC) of the extract were determind by using Folin-ciocalteu reagent method. Total flavonoid contents (TFC) were determind by the Aluminum Chloride Calorimetric method. Antioxidant activities of the extracts of different concentration were evaluated using Phosphomolybdenum method, Reducing power and DPPH (2, 2-disphenyl-1-picryl-hydrazyl) assays. Assays performed for grape varieties showed great antioxidant potential. All varieties significantly depicted with variation in polyphenolic contents and antioxidant potential with changes in the soil conditions. The highest TPC and TFC were quantified in Shogran-1 97.58 ± 0.09 (GAE, g−1) and Sultania-C 97.47 ± 0.12 (µg QE/g DE) varieties respectively which were grown in (T6) and (T5), while lower were recorded in Sundar khani 5.16 ± 0.23 in (T6). Likewise, Shogran-1 128.26 ± 0.23 (µg AAE/g extract) variety grown in (T6) depicted highest total antioxidant capacity, NARC black 182.06 ± 0.24 (µg AAE/g extract) variety grown in (T6) resulted in maximum reducing power while DPPH free radical scavenging potential were determinded in Sultania-C 80.91 ± 0.10 (T4) equivalent µg/g. In the terms of bioassays, the promising results were showed by compost + sand + clay (T4), compost + clay + dung (T5) and sand + clay + dung (T6). Therefore, we conclude that variation in soil composition has a significant contribution in the quantity of phytochemicals and antioxidants expression. Our study further suggest that use of organic fertilizer (Compost) and loamy sort of soil enhance functioning of most of the varieties in terms of important phytochemicals. 相似文献
10.
Evangelia Gazaki 《Mathematische Nachrichten》2019,292(8):1716-1726
In this short note we extend some results obtained in [7]. First, we prove that for an abelian variety A with good ordinary reduction over a finite extension of with p an odd prime, the Albanese kernel of A is the direct sum of its maximal divisible subgroup and a torsion group. Second, for a semi‐abelian variety G over a perfect field k, we construct a decreasing integral filtration of Suslin's singular homology group, , such that the successive quotients are isomorphic to a certain Somekawa K‐group. 相似文献