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This will allow Dr Reynolds to pursue research aimed at improving brain function after strokes, while Dr Bradley will pursue the study of super-fluids.
The research fellowships each provide up to $200,000 a year over five years, including a contribution towards salaries and research costs.
The two Otago University researchers are among a record eight Dunedin scientists to gain national science honours in a recent annual awards ceremony, hosted by the Royal Society of New Zealand, in Christchurch.
Dr Reynolds, a senior lecturer in anatomy and structural biology, plans to focus his research on a "balancing act" aimed at improving brain function after disorders such as stroke and epilepsy.
He aims to use experimental approaches to alter the normal balance between excitation and inhibition in the brain, to try to improve function in these brain disorders.
Dr Bradley, a physicist, says his "pretty exciting" fellowship will provide "a real shot in the arm" for his research on turbulence in super-fluids, which has implications for aerospace, shipping and energy management.
Prof Frank Griffin, the Otago University head of microbiology and immunology, received the Royal Society's Pickering Medal for "excellence and innovation" in technology.
The award also reflected his contribution to work in developing diagnostics tests for detecting two major bacterial diseases in deer and a vaccine for the prevention of the bacterial disease yersiniosis in deer, award officials said.
Gaining this "very special" medal reflected a great deal of collaborative effort, including by New Zealand's highly innovative deer industry and scientific colleagues at AgResearch, Prof Griffin said.
The Dame Joan Metge Medal for social sciences was awarded to Otago University Prof Richie Poulton and Prof Richard Bedford, of AUT.
Prof Poulton, who is director of the internationally recognised Otago Longitudinal Study of human health and development, was honoured for his "influential and far-reaching achievements".
The study follows the health and development of more than 1000 babies born in Dunedin (1972-73).
Prof Poulton was "greatly honoured" by the award, which was a "fitting acknowledgment of the long-term commitment from everyone involved over so many years".
The Hutton Medal for "excellence in plant sciences" was awarded to Dr David Galloway, a research associate at Landcare Research, Dunedin, and reflected his "great advances in knowledge" of New Zealand lichens.
Otago University Prof Stephen Robertson was awarded the Liley Medal by the Health Research Council for an "outstanding contribution" to health and medical sciences.
His research showed "the critical nature of developmental timing of key genetic events" and would "encourage new ways of thinking about cancer", officials said.
Prof Keith Gordon, of the Otago chemistry department and the MacDiarmid Institute for Advanced Materials and Nanotechnology, received the New Zealand Institute of Chemistry Maurice Wilkins Centre Prize for Chemical Science.
His work involves molecular electronic materials, including understanding their electronic properties.
The eighth recipient was Otago University molecular biologist Prof Warren Tate, who was awarded New Zealand's top science and technology medal, the Rutherford medal, for his work on how proteins are built in living cells.