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Fix two lattice paths P and Q from ð0; 0Þ to ðm; rÞ that use East and North steps with P never going above Q: We show that the lattice paths that go from ð0; 0Þ to ðm; rÞ and that remain in the region bounded by P and Q can be identified with the bases of a particular type of transversal matroid, which we call a lattice path matroid. We consider a variety(More)
We prove that if a graph H has the same Tutte polynomial as the line graph of a d-regular, d-edge-connected graph, then H is the line graph of a d-regular graph. Using this result we prove that the line graph of a regular complete t-partite graph is uniquely determined by its Tutte polynomial. We prove the same result for the line graph of any complete(More)
1. Transcranial magnetic stimulation was performed using a figure-of-eight-shaped coil over the right motor cortex with the aim of identifying those areas involved with activation of the diaphragm. 2. The response of the right and left hemi-diaphragms was recorded using surface electrodes in either the 7th or 8th intercostal spaces 3 cm lateral to the(More)
1. The response of the diaphragm to both transcranial magnetic stimulation and electrical phrenic nerve stimulation was studied in thirteen normal subjects under conditions of either a 'reflex' drive to ventilation with inhaled CO2 or during volitional ventilation of similar magnitude. 2. The induced compound action potential in the diaphragm was recorded(More)
BACKGROUND It is known that automatic breathing is controlled by centres in the lower brain stem, whereas volitional breathing is controlled by the cerebral cortical centres. In hemiplegia, lesions above the brain stem result in paralysis of limb muscles. This study was performed to determine whether the diaphragm might also be affected in patients with(More)
We present a complete solution to the so-called tennis ball problem, which is equivalent to counting lattice paths in the plane that use North and East steps and lie between certain boundaries. The solution takes the form of explicit expressions for the corresponding generating functions. Our method is based on the properties of Tutte polynomials of(More)