Martin G. Gulbrandsen

Early recognition of regional cardiac ischemia using a 3-axis accelerometer sensor.

Perioperative mortality in coronary artery bypass grafting is usually caused by reduced left ventricular function due to regional myocardial ischemia or infarction. Post-operative graft occlusion is a well-known problem in coronary surgery. A sensitive tool to detect graft occlusion and monitor myocardial function may give the opportunity to revise malfunctioning grafts before departure from the hospital. This paper describes how a new method can detect cardiac ischemia using a 3-axis piezoelectric accelerometer. In three anesthetized pigs, a 3-axis piezoelectric accelerometer was sutured on the lateral free wall of the left ventricle. The left anterior descending (LAD) was occluded for different time periods and the accelerometer data were sampled with a PC. Short-time Fourier transform was calculated based on the accelerometer time series. The results were visualized using a 2D color-coded time-frequency plot. In the area of occlusion, a change to stronger power of higher harmonics was observed. Consequently, a difference value between the instant frequency pattern and a reference frequency pattern showed a rise in absolute value during the occlusion period. The preliminary results indicate that early recognition of regional cardiac ischemia is possible by analyzing accelerometer data acquired from the three animal trials using the prototype 3-axis accelerometer sensor.

Donaldson-Thomas invariants for complexes on abelian threefolds

Donaldson–Thomas invariants for moduli spaces M of perfect complexes on an abelian threefold X are usually zero. A better object is the quotient

Vector Bundles and Monads On Abelian Threefolds

{K=[M/X\times\widehat{X}]}

Schottky via the punctual Hilbert scheme

of complexes modulo twist and translation. Roughly speaking, this amounts to fixing not only the determinant of the complexes in M, but also that of their Fourier–Mukai transform. We modify the standard perfect symmetric obstruction theory for perfect complexes to obtain a virtual fundamental class, giving rise to a DT-type invariant of the quotient K. It is insensitive to deformations of X, and respects derived equivalence. As illustrations we examine the case of Picard bundles and of Hilbert schemes of points.

Counting Sheaves on Calabi–Yau and Abelian Threefolds

We generalize the classical Hilbert–Mumford criteria for GIT (semi-)stability in terms of one parameter subgroups of a linearly reductive group G over a field k, to the relative situation of an equivariant, projective morphism

Lagrangian fibrations on generalized Kummer varieties

{X \rightarrow \,{\rm Spec}\,\, A}