A generalization of the Moore-Penrose inverse related to matrix subspaces of C(nxm)

[EN]A natural generalization of the classical Moore-Penrose inverse is presented. The so-called S-Moore-Penrose inverse of a m x n complex matrix A, denoted by As, is defined for any linear subspace S of the matrix vector space Cnxm. The S-Moore-Penrose inverse As is characterized using either the singular value decomposition or (for the nonsingular square case) the orthogonal complements with respect to the Frobenius inner product. These results are applied to the preconditioning of linear systems based on Frobenius norm minimization and to the linearly constrained linear least squares problem.

A generalization of the optimal diagonal approximate inverse preconditioner

[EN ]The classical optimal (in the Frobenius sense) diagonal preconditioner for large sparse linear systems Ax = b is generalized and improved. The new proposed approximate inverse preconditioner N is based on the minimization of the Frobenius norm of the residual matrix AM − I, where M runs over a certain linear subspace of n × n real matrices, defined by a prescribed sparsity pattern. The number of nonzero entries of the n×n preconditioning matrix N is less than or equal to 2n, and n of them are selected as the optimal positions in each of the n columns of matrix N. All theoretical results are justified in detail…

Generalization of amygdala LTP and conditioned fear in the absence of presynaptic inhibition

Pavlovian fear conditioning, a simple form of associative learning, is thought to involve the induction of associative, NMDA receptor-dependent long-term potentiation (LTP) in the lateral amygdala. Using a combined genetic and electrophysiological approach, we show here that lack of a specific GABA(B) receptor subtype, GABA(B(1a,2)), unmasks a nonassociative, NMDA receptor-independent form of presynaptic LTP at cortico-amygdala afferents. Moreover, the level of presynaptic GABA(B(1a,2)) receptor activation, and hence the balance between associative and nonassociative forms of LTP, can be dynamically modulated by local inhibitory activity. At the behavioral level, genetic loss of GABA(B(1a)) results in a generalization of conditioned fear to nonconditioned stimuli. Our findings indicate that presynaptic inhibition through GABA(B(1a,2)) receptors serves as an activity-dependent constraint on the induction of homosynaptic plasticity, which may be important to prevent the generalization of conditioned fear.

Direct and indirect associations between plant species richness and productivity in grasslands: regional differences preclude simple generalization of productivity-biodiversity relationships

Plant species richness of permanent grasslands has often been found to be significantly associated with productivity. Concentrations of nutrients in biomass can give further insight into these productivity- plant species richness relationships, e.g. by reflecting land use or soil characteristics. However, the consistency of such relationships across different regions has rarely been taken into account, which might significantly compromise our potential for generalization. We recorded plant species richness and measured above-ground biomass and concentrations of nutrients in biomass in 295 grasslands in three regions in Germany that differ in soil and climatic conditions. Structural equation modelling revealed that nutrient concentrations were mostly indirectly associated with plant species richness via biomass production. However, negative associations between the concentrations of different nutrients and biomass and plant species richness differed considerably among regions. While in two regions, more than 40% of the variation in plant species richness could be attributed to variation in biomass, K, P, and to some degree also N concentrations, in the third region only 15% of the variation could be explained in this way. Generally, highest plant species richness was recorded in grasslands where N and P were co-limiting plant growth, in contrast to N or K (co-) limitation. But again, this pattern was not recorded in the third region. While for two regions land-use intensity and especially the application of fertilizers are suggested to be the main drivers causing the observed negative associations with productivity, in the third region the little variance accounted for, low species richness and weak relationships implied that former intensive grassland management, ongoing mineralization of peat and fluctuating water levels in fen grasslands have overruled effects of current land-use intensity and productivity. Finally, we conclude that regional replication is of major importance for studies seeking general insights into productivity-diversity relationships.

A generalization of Ramsey theory for graphs, with stars and complete graphs as forbidden subgraphs /

Includes bibliographical references.

A generalization of Ramsey theory for graphs /

Bibliography: p. 16.

Learning and generalization of structural descriptions : evaluation criteria and comparative review of selected methods /

"February 1980."

Interval generalization of switching theory,

Includes bibliographical references.

A generalization of Ramsey theory for graphs /

Includes bibliographical references.

Situational specificity and validity generalization results for apprentice occupations /

Bibliography: p. 25.

On a generalization of the Oberwolfach problem

Let e(1),e(2),... e(n) be a sequence of nonnegative integers Such that the first non-zero term is not one. Let Sigma(i=1)(n) e(i) = (q - 1)/2, where q = p(n) and p is an odd prime. We prove that the complete graph on q vertices can be decomposed into e(1) C-pn-factors, e(2) C-pn (1)-factors,..., and e(n) C-p-factors. (C) 2004 Elsevier Inc. All rights reserved.

Generalization by symbolic abstraction in cascaded recurrent networks

Generalization performance in recurrent neural networks is enhanced by cascading several networks. By discretizing abstractions induced in one network, other networks can operate on a coarse symbolic level with increased performance on sparse and structural prediction tasks. The level of systematicity exhibited by the cascade of recurrent networks is assessed on the basis of three language domains. (C) 2004 Elsevier B.V. All rights reserved.