The Magnus embedding of a free metabelian group induces the embedding of partially commutative metabelian group SΓ in a group of matrices MΓ. Properties and the universal theory of the group MΓ are studied.

The combined horseradish peroxidase retrograde transport-peroxidase-antiperoxidase immunohistochemical procedure was utilized in the present study to ascertain the sites of origin of serotonin and neurotensin projections to the rodent nucleus raphe magnus. The major serotonin inputs to the raphe magnus arise from the B-8 and B-9 groups of Dahlstrom and Fuxe (Dahlstrom, A., and K. Fuxe (1964) Ac...

Input "Retina" The term "intentionality" arises in connection with natural language understanding in a computer. The problem is not one of speech recognition. It remains a problem even if the words of the language were perfectly encoded by a speech recognizer, or even typed on a keyboard. It is believed that the ability to visualize events when hearing sentences that describe them is a clue to ...

Sensitivity analysis stands in contrast to diagnostic testing in that sensitivity analysis aims to answer the question of whether it matters that a nuisance parameter is non-zero, whereas a diagnostic test ascertains explicitly if the nuisance parameter is different from zero. In this paper, we introduce and derive the finite sample properties of a sensitivity statistic measuring the sensitivit...

In the evolution of eukaryotic genes, introns are believed to have played a major role in increasing the probability of favorable duplication events, chance recombinations, and exon shuffling resulting in functional hybrid proteins. As a rule, prokaryotic genes lack introns, and the examples of prokaryotic introns described do not seem to have contributed to gene evolution by exon shuffling. St...

Abstract The signature of a path can be described as its full non-commutative exponential. Following T. Lyons, we regard expectation, the expected , space analogue classical moment generating function. logarithm thereof, taken in tensor algebra, defines cumulant . We establish universal functional relation general semimartingale context. Our work exhibits importance Magnus expansions algorithmi...

One con repair’. *Autho Stem Cell Section, Laboratory of Neurosciences, National Institute on Aging, NIH, 333 Cassell Drive, Room 406A, Baltimore, MD 21224, USA Children’s Research Center of Michigan, The Carman and Ann Adams Department of Pediatrics, Wayne State University School of Medicine, Children’s Hospital of Michigan, Detroit, MI 48201, USA Corporate Research Laboratories, Invitrogen Co...

In the present paper we consider numerical methods to solve the Schr\"odinger equation with a time dependent Hamiltonian. We will consider both short-range interactions, which lead to evolution equations involving sparse matrices, and long-range interactions, which lead to dense matrices. Both of these settings show very different computational characteristics. We use Magnus integrators for tim...