Instanton Floer homology and the Alexander polynomial

The instanton Floer homology of a knot in the three-sphere is a vector space with a canonical mod 2 grading. It carries a distinguished endomorphism of even degree,arising from the 2-dimensional homology class represented by a Seifert surface. The Floer homology decomposes as a direct sum of the generalized eigenspaces of this endomorphism. We show that the Euler characteristics of these generalized eigenspaces are the coefficients of the Alexander polynomial of the knot. Among other applications, we deduce that instanton homology detects fibered knots.Comment: 25 pages, 6 figures. Revised version, correcting errors concerning mod 2 gradings in the skein sequenc

Discontinuous conductance of bichromatically ac-gated quantum wires

We study the electron transport through a quantum wire under the influence of external time-dependent gate voltages. The wire is modelled by a tight-binding Hamiltonian for which we obtain the current from the corresponding transmission. The numerical evaluation of the dc current reveals that for bichromatic driving, the conductance depends sensitively on the commensurability of the driving frequencies. The current even possesses a discontinuous frequency dependence. Moreover, we find that the conductance as a function of the wire length oscillates with a period that depends on the ratio between the driving frequencies.Comment: 7 pages, 4 figure

Acoustic model adaptation for ortolan bunting (Emberiza hortulana L.) song-type classification

Automatic systems for vocalization classification often require fairly large amounts of data on which to train models. However, animal vocalization data collection and transcription is a difficult and time-consuming task, so that it is expensive to create large data sets. One natural solution to this problem is the use of acoustic adaptation methods. Such methods, common in human speech recognition systems, create initial models trained on speaker independent data, then use small amounts of adaptation data to build individual-specific models. Since, as in human speech, individual vocal variability is a significant source of variation in bioacoustic data, acoustic model adaptation is naturally suited to classification in this domain as well. To demonstrate and evaluate the effectiveness of this approach, this paper presents the application of maximum likelihood linear regression adaptation to ortolan bunting (Emberiza hortulana L.) song-type classification. Classification accuracies for the adapted system are computed as a function of the amount of adaptation data and compared to caller-independent and caller-dependent systems. The experimental results indicate that given the same amount of data, supervised adaptation significantly outperforms both caller-independent and caller-dependent systems

Galactic Models of Gamma-Ray Bursts

We describe observational evidence and theoretical calculations which support the high velocity neutron star model of gamma-ray bursts. We estimate the energetic requirements in this model, and discuss possible energy sources. we also consider radiative processes involved in the bursts.Comment: 16 pages Latex file in revtex format. Fourteen postscript figures come in a separate file. To appear in the Proceedings of the 1995 La Jolla Workshop "High Velocity Neutron Stars and Gamma-Ray Bursts", eds. R. Rorschild etal., AIP, New Yor

Non-commutative connections of the second kind

A connection-like objects, termed {\em hom-connections} are defined in the realm of non-commutative geometry. The definition is based on the use of homomorphisms rather than tensor products. It is shown that hom-connections arise naturally from (strong) connections in non-commutative principal bundles. The induction procedure of hom-connections via a map of differential graded algebras or a differentiable bimodule is described. The curvature for a hom-connection is defined, and it is shown that flat hom-connections give rise to a chain complex.Comment: 13 pages, LaTe