Hyperbolic knots with three toroidal Dehn surgeries

It is conjectured that a hyperbolic knot admits at most three Dehn surgeries which yield closed three manifolds containing incompressible tori. We show that there exist infinitely many hyperbolic knots which attain the conjectural maximum number. Interestingly, those surgeries correspond to consecutive integers.Comment: 10 pages, 10 figure

Coding of auditory space

Behavioral, anatomical, and physiological approaches can be integrated in the study of sound localization in barn owls. Space representation in owls provides a useful example for discussion of place and ensemble coding. Selectivity for space is broad and ambiguous in low-order neurons. Parallel pathways for binaural cues and for different frequency bands converge on high-order space-specific neurons, which encode space more precisely. An ensemble of broadly tuned place-coding neurons may converge on a single high-order neuron to create an improved labeled line. Thus, the two coding schemes are not alternate methods. Owls can localize sounds by using either the isomorphic map of auditory space in the midbrain or forebrain neural networks in which space is not mapped

Deciphering the brain's codes

The two sensory systems discussed use similar algorithms for the synthesis of the neuronal selectivity for the stimulus that releases a particular behavior, although the neural circuits, the brain sites involved, and even the species are different. This stimulus selectivity emerges gradually in a neural network organized according to parallel and hierarchical design principles. The parallel channels contain lower order stations with special circuits for the creation of neuronal selectivities for different features of the stimulus. Convergence of the parallel pathways brings these selectivities together at a higher order station for the eventual synthesis of the selectivity for the whole stimulus pattern. The neurons that are selective for the stimulus are at the top of the hierarchy, and they form the interface between the sensory and motor systems or between sensory systems of different modalities. The similarities of these two systems at the level of algorithms suggest the existence of rules of signal processing that transcend different sensory systems and species of animals