Continuously controlledA-theory

To anycontrolled space over the metric spaceB we can associate itsboundedly controlled algebraic K-theory, a functor designed to give information about the space of stable bounded concordances of manifolds homotopy equivalent toX. Generalizing a construction of D. R. Anderson, F. X. Connolly, S. Ferry, and E. K. Pedersen, we define another functor, calledcontinuously controlled A-theory, which depends only on thetopology of the control space, not itsmetric properties. In the special case whereB=R ₊, this functor is (more or less by definition) the same asproper A-theory. We prove that under certain conditions on the controlled space the natural transformation from boundedly controlledA-theory to continuously controlledA-theory is a weak homotopy equivalence, and hence defines a generalized homology theory. Continuously controlledK-theory is used in the approaches of G. Carlsson, E. K. Pedersen, and S. Ferry, S. Weinbergervto theK-theory Novikov conjecture.     

Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. II

Ohne ZusammenfassungDies ist der zweite Teil einer aus technischen Gründen aufgeteilten Arbeit. Kenntnis des ersten Teils ([13]) ist notwendig für die Lektüre des zweiten Teils. Hinweise der Art (,), mit<=5, beziehen sich auf den ersten Teil.     

Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I

Ohne Zusammenfassung     

Topological Hochschild Homology

In the appendix to [20] Waldhausen discussed a trace map tr:K(R)HH(R),from the algebraic K-theory of a ring to its Hochschild homology,which can be used to obtain information about K(R) from HH(R).In [1] Bökstedt described a factorization of this tracemap. The intermediate functor THH(HR) is called the topologicalHochschild homology of the Eilenberg–MacLane spectrumHR associated with R, because it is constructed similarly toHochschild homology with the tensor product replaced by thesmash product of spectra.     

Identification of biomolecular conformations from incomplete torsion angle observations by hidden Markov models

We present a novel method for the identification of the most important conformations of a biomolecular system from molecular dynamics or Metropolis Monte Carlo time series by means of Hidden Markov Models (HMMs). We show that identification is possible based on the observation sequences of some essential torsion or backbone angles. In particular, the method still provides good results even if the conformations do have a strong overlap in these angles. To apply HMMs to angular data, we use von Mises output distributions. The performance of the resulting method is illustrated by numerical tests and by application to a hybrid Monte Carlo time series of trialanine and to MD simulation results of a DNA-oligomer.