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951.
Daniel Lewandowski Dorota Kurowicka Harry Joe 《Journal of multivariate analysis》2009,100(9):1989-2001
We extend and improve two existing methods of generating random correlation matrices, the onion method of Ghosh and Henderson [S. Ghosh, S.G. Henderson, Behavior of the norta method for correlated random vector generation as the dimension increases, ACM Transactions on Modeling and Computer Simulation (TOMACS) 13 (3) (2003) 276–294] and the recently proposed method of Joe [H. Joe, Generating random correlation matrices based on partial correlations, Journal of Multivariate Analysis 97 (2006) 2177–2189] based on partial correlations. The latter is based on the so-called D-vine. We extend the methodology to any regular vine and study the relationship between the multiple correlation and partial correlations on a regular vine. We explain the onion method in terms of elliptical distributions and extend it to allow generating random correlation matrices from the same joint distribution as the vine method. The methods are compared in terms of time necessary to generate 5000 random correlation matrices of given dimensions. 相似文献
952.
Joachim Jelisiejew Grzegorz Kapustka Micha Kapustka 《Mathematische Nachrichten》2019,292(9):2018-2027
We study the degrees of generators of the ideal of a projected Veronese variety to depending on the center of projection. This is related to the geometry of zero dimensional schemes of length 8 in , Cremona transforms of , and the geometry of Tonoli Calabi‐Yau threefolds of degree 17 in . 相似文献
953.
Grzegorz Bobiński 《代数通讯》2013,41(6):2219-2234
Let 𝒜 = (A 1, A 12, A 2) be a locally D 8 amalgam with a finite completion G. Suppose that A 1 ∈ Syl 2(G) and N A 1 (A 12) is Abelian. We determine G/O(G). 相似文献
954.
On-line chain partition is a two-player game between Spoiler and Algorithm. Spoiler presents a partially ordered set, point by point. Algorithm assigns incoming points (immediately and irrevocably) to the chains which constitute a chain partition of the order. The value of the game for orders of width w is a minimum number val(w) such that Algorithm has a strategy using at most val(w) chains on orders of width at most w. We analyze the chain partition game for up-growing semi-orders. Surprisingly, the golden ratio comes into play and the value of the game is $\big\lfloor\frac{1+\sqrt{5}}{2}\; w \big\rfloor$ . 相似文献
955.
956.
Frances Y. Kuo Grzegorz W. Wasilkowski Henryk Woźniakowski 《BIT Numerical Mathematics》2009,49(3):543-564
We study approximation of multivariate functions from a general separable reproducing kernel Hilbert space in the randomized
setting with the error measured in the L
∞ norm. We consider algorithms that use standard information consisting of function values or general linear information consisting of arbitrary linear functionals. The power of standard or linear information is defined as, roughly speaking, the optimal rate of convergence of algorithms using n function values or linear functionals. We prove under certain assumptions that the power of standard information in the randomized
setting is at least equal to the power of linear information in the worst case setting, and that the powers of linear and
standard information in the randomized setting differ at most by 1/2. These assumptions are satisfied for spaces with weighted
Korobov and Wiener reproducing kernels. For the Wiener case, the parameters in these assumptions are prohibitively large,
and therefore we also present less restrictive assumptions and obtain other bounds on the power of standard information. Finally,
we study tractability, which means that we want to guarantee that the errors depend at most polynomially on the number of
variables and tend to zero polynomially in n
−1 when n function values are used. 相似文献
957.
Tero Harju Ion Petre Vladimir Rogojin Grzegorz Rozenberg 《Discrete Applied Mathematics》2008,156(14):2581-2597
The intramolecular model for gene assembly in ciliates considers three operations, , , and that can assemble any gene pattern through folding and recombination: the molecule is folded so that two occurrences of a pointer (short nucleotide sequence) get aligned and then the sequence is rearranged through recombination of pointers. In general, the sequence rearranged by one operation can be arbitrarily long and consist of many coding and noncoding blocks. We consider in this paper simple variants of the three operations, where only one coding block is rearranged at a time. We characterize in this paper the gene patterns that can be assembled through these variants. Our characterization is in terms of signed permutations and dependency graphs. Interestingly, we show that simple assemblies possess rather involved properties: a gene pattern may have both successful and unsuccessful assemblies and also more than one successful assembling strategy. 相似文献
958.
We investigate the following problem posed by Cabello Sanchéz, Castillo, Kalton, and Yost:Let K be a nonmetrizable compact space. Does there exist a nontrivial twisted sum of and , i.e., does there exist a Banach space X containing a non-complemented copy Y of such that the quotient space is isomorphic to ?Using additional set-theoretic assumptions we give the first examples of compact spaces K providing a negative answer to this question. We show that under Martin's axiom and the negation of the continuum hypothesis, if either K is the Cantor cube or K is a separable scattered compact space of height 3 and weight , then every twisted sum of and is trivial.We also construct nontrivial twisted sums of and for K belonging to several classes of compacta. Our main tool is an investigation of pairs of compact spaces which do not admit an extension operator . 相似文献
959.
The purpose of this note is to show a new series of examples of homogeneous ideals I in for which the containment fails. These ideals are supported on certain arrangements of lines in , which resemble Fermat configurations of points in , see [14]. All examples exhibiting the failure of the containment constructed so far have been supported on points or cones over configurations of points. Apart from providing new counterexamples, these ideals seem quite interesting on their own. 相似文献
960.
We show that several theorems about Polish spaces, which depend on the axiom of choice (\(\mathcal {AC}\)), have interesting corollaries that are theorems of the theory \(\mathcal {ZF} + \mathcal {DC}\), where \(\mathcal {DC}\) is the axiom of dependent choices. Surprisingly it is natural to use the full \(\mathcal {AC}\) to prove the existence of these proofs; in fact we do not even know the proofs in \(\mathcal {ZF} + \mathcal {DC}\). Let \(\mathcal {AD}\) denote the axiom of determinacy. We show also, in the theory \(\mathcal {ZF} + \mathcal {AD} + V = L(\mathbb {R})\), a theorem which strenghtens and generalizes the theorem of Drinfeld (Funct Anal Appl 18:245–246, 1985) and Margulis (Monatshefte Math 90:233–235, 1980) about the unicity of Lebesgue’s measure. This generalization is false in \(\mathcal {ZFC}\), but assuming the existence of large enough cardinals it is true in the model \(\langle L(\mathbb {R}),\in \rangle \). 相似文献