A positivity result in the theory of Macdonald polynomials

We outline here a proof that a certain rational function Cn(q, t), which has come to be known as the “q, t-Catalan,” is in fact a polynomial with positive integer coefficients. This has been an open problem since 1994. Because Cn(q, t) evaluates to the Catalan number at t = q = 1, it has also been an open problem to find a pair of statistics a, b on the collection

Direct observation of iron-induced conformational changes of mitochondrial DNA by high-resolution field-emission in-lens scanning electron microscopy.

When respiring rat liver mitochondria are incubated in the presence of Fe(III) gluconate, their DNA (mtDNA) relaxes from the supercoiled to the open circular form dependent on the iron dose. Anaerobiosis or antioxidants fail to completely inhibit the unwinding. High-resolution field-emission in-lens scanning electron microscopy imaging, in concert with backscattered electron detection, pinpoints nanometer-range iron colloids bound to mtDNA isolated from iron-exposed mitochondria. High-resolution field-emission in-lens scanning electron microscopy with backscattered electron detection imaging permits simultaneous detailed visual analysis of DNA topology, iron dose-dependent mtDNA unwinding, and assessment of iron colloid formation on mtDNA strands.

Receptive field structure in the visual cortex: does selective stimulation induce plasticity?

Sensory areas of adult cerebral cortex can reorganize in response to long-term alterations in patterns of afferent signals. This long-term plasticity is thought to play a crucial role in recovery from injury and in some forms of learning. However, the degree to which sensory representations in primary cortical areas depend on short-term (i.e., minute to minute) stimulus variations remains unclear. A traditional view is that each neuron in the mature cortex has a fixed receptive field structure. An alternative view, with fundamentally different implications for understanding cortical function, is that each cell's receptive field is highly malleable, changing according to the recent history of the sensory environment. Consistent with the latter view, it has been reported that selective stimulation of regions surrounding the receptive field induces a dramatic short-term increase in receptive field size for neurons in the visual cortex [Pettet, M. W. & Gilbert, C. D. (1992) Proc. Natl. Acad. Sci. USA 89, 8366-8370]. In contrast, we report here that there is no change in either the size or the internal structure of the receptive field following several minutes of surround stimulation. However, for some cells, overall responsiveness increases. These results suggest that dynamic alterations of receptive field structure do not underlie short-term plasticity in the mature primary visual cortex. However, some degree of short-term adaptability could be mediated by changes in responsiveness.