Plenary Lecture
Mathematical Models in Neuroscience
Professor Alina Gavrilut
Al. I. Cuza University Iaşi
Romania
E-mail: gavrilut@uaic.ro
Abstract: I. A theoretical exercise in neuroscience: The semantic system of the brain and the semantic logic ñ the logic that is specific to the human brain. The meanings of words and language are represented in a semantic system distributed across much of the cerebral cortex. Each semantic concept is represented in multiple semantic areas and each semantic area represents multiple semantic concepts. The semantic system of the brain shows that words are grouped by meaning, thus revealing how complicated and widespread the word maps in our heads are. The semantic logic and the semantic system of the brain could generate new strategies in the cognitive-behavioral approach by using and reevaluating the therapeutic stories, metaphors, symbols and rituals in a creative way. II. A mathematical-physical model in neuroscience: The mirror neurons paradigm. Considering that any biological structure can be assimilated to a fractal (both structurally and functionally), a athematical-physical model is proposed in order to explain the mirror neurons paradigm. Extending de Broglieís idea concerning the wave-corpuscle duality by means of the information (in its implicit and explicit) form, we are lead to assume the existence of a fractal medium, which can store and transmit information in the form of a natural field (that will be called ëía fractal fieldíí). In such conjecture, Cooper type pairs structures can be generated by means of the spontaneous symmetry breaking of such field. In consequence, the mirror neurons transmitting mechanism can be explained by this spontaneous symmetry breaking, in which the specific neuronal network and specific logic appear.
Brief Biography of the Speaker: Alina Cristiana Gavriluţ, Lecturer within Mathematics Department at Al.I. Cuza University from Iaşi, Romania, graduate BA in Mathematics at the Faculty of Mathematics, Al.I. Cuza University from Iaşi, Romania, specialization Mathematics (1993-1997), PhD in Mathematics (2000-2006). She is Editor and member of Editorial Board in several international mathematical journals. Her interests are in theoretical and applied Mathematical Analysis, focused on classical and non-additive (set-valued) measure theory, general topology and hypertopology, fractals. She published over 40 articles in ISI journals, 15 ISI proceedings, 40 BDI papers, 7 books, 7 book chapters and gave many communications at national and international scientific manifestations.