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131.
A QSAR model for predicting the blood brain barrier permeability (BBBP) in a large and heterogeneous variety of compounds (136 compounds) has been developed using approximate similarity (AS) matrices as predictors and PLS as multivariate regression technique. AS values fuse information of both the isomorphic similarity and nonisomorphic dissimilarity with the purpose of achieving an accurate predictive space. In addition to the fact of applying AS values to heterogeneous data sets, a new concept on graph isomorphism based on the extended maximum common subgraph (EMCS) is defined for the building of AS spaces considering the atoms and bonds, which are bridges between the isomorphic and nonisomorphic substructures. This new isomorphism detection has as objective to take into account the position and nature of the nucleus substituents, thus allowing the development of accurate models for large and diverse sets of compounds. After an outliers study, the training and test stages were made and the results obtained using several AS approaches were compared. Several validation processes were carried out by means of employing several test sets, and high predictive ability was obtained for all the cases (Q(2) = 0.81 and standard error in prediction, SEP = 0.29). 相似文献
132.
Simple examples are given of proper algebraic actions of the additive group of complex numbers on ?5 whose geometric quotients are, respectively, a?ne, strictly quasia?ne, and algebraic spaces which are not schemes. Moreover, a Zariski locally trivial action is given whose ring of invariant regular functions defines a singular factorial a?ne fourfold embedded in ?12. The geometric quotient for the action embeds as a strictly quasia?ne variety in the smooth locus of the algebraic quotient with complement isomorphic to the normal a?ne surface with the A2?singularity at the origin. 相似文献
133.
Philipp Walk Peter Jung Götz E. Pfander 《Applied and Computational Harmonic Analysis》2017,42(1):117-134
We give a stability result for sparse convolutions on for torsion-free discrete Abelian groups G such as . It turns out, that the torsion-free property prevents full cancellation in the convolution of sparse sequences and hence allows to establish stability, that is, injectivity with an universal lower norm bound, which only depends on the support cardinalities of the sequences. This can be seen as a reverse statement of the Young inequality for sparse convolutions. Our result hinges on a compression argument in additive set theory. 相似文献
134.
As shown in [1], for each compact Hausdorff space K without isolated points, there exists a compact Hausdorff P′-space X but not an F-space such that C(K) is isometrically Riesz isomorphic to a Riesz subspace of C(X). The proof is technical and depends heavily on some representation theorems. In this paper we give a simple and direct proof without any assumptions on isolated points. Some generalizations of these results are mentioned. 相似文献
135.
Edith Hemaspaandra Lane A. Hemaspaandra Stanis?aw P. Radziszowski 《Discrete Applied Mathematics》2007,155(2):103-118
We investigate the relative complexity of the graph isomorphism problem (GI) and problems related to the reconstruction of a graph from its vertex-deleted or edge-deleted subgraphs (in particular, deck checking (DC) and legitimate deck (LD) problems). We show that these problems are closely related for all amounts c?1 of deletion:
- (1)
- , , , and .
- (2)
- For all k?2, and .
- (3)
- For all k?2, .
- (4)
- .
- (5)
- For all k?2, .
136.
Choonkil Park 《Journal of Mathematical Analysis and Applications》2007,327(1):101-115
In this paper, we prove the Hyers-Ulam-Rassias stability of homomorphisms in C∗-ternary algebras and of derivations on C∗-ternary algebras for the following Cauchy-Jensen additive mappings:
(0.1) 相似文献
137.
In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality:‖f (x) + f (y) + 2f (z) + 2f (w)‖≤‖ 2f x + y2 + z + w ‖(0.1)This is applied to investigate isomorphisms between C*-algebras, Lie C*-algebras and JC*-algebras, and derivations on C*-algebras, Lie C*-algebras and JC*-algebras, associated with the Cauchy-Jensen functional equation 2f (x + y/2 + z + w) = f(x) + f(y) + 2f(z) + 2f(w). 相似文献
138.
139.
Let ? be a prime ring with 1 containing a nontrivial idempotent E, and let ?′ be another prime ring. If Φ:? → ?′ is a multiplicative Lie isomorphism, then Φ(T + S) = Φ(T) + Φ(S) + Z′ T,S for all T, S ∈ ?, where Z′ T,S is an element in the center 𝒵′ of ?′ depending on T and S. 相似文献
140.
In this article, we investigate limitations of importing methods based on algorithmic information theory from monoplex networks into multidimensional networks (such as multilayer networks) that have a large number of extra dimensions (i.e., aspects). In the worst-case scenario, it has been previously shown that node-aligned multidimensional networks with non-uniform multidimensional spaces can display exponentially larger algorithmic information (or lossless compressibility) distortions with respect to their isomorphic monoplex networks, so that these distortions grow at least linearly with the number of extra dimensions. In the present article, we demonstrate that node-unaligned multidimensional networks, either with uniform or non-uniform multidimensional spaces, can also display exponentially larger algorithmic information distortions with respect to their isomorphic monoplex networks. However, unlike the node-aligned non-uniform case studied in previous work, these distortions in the node-unaligned case grow at least exponentially with the number of extra dimensions. On the other hand, for node-aligned multidimensional networks with uniform multidimensional spaces, we demonstrate that any distortion can only grow up to a logarithmic order of the number of extra dimensions. Thus, these results establish that isomorphisms between finite multidimensional networks and finite monoplex networks do not preserve algorithmic information in general and highlight that the algorithmic information of the multidimensional space itself needs to be taken into account in multidimensional network complexity analysis. 相似文献