Selected topics in the study of Cognitive Science.

Electrical oscillatory activity in the brain has been associated with memory, decision making, movement control and transfer of information between distant areas of the brain. This class has the same title as the famous book by Gyorgy Buzsaki, because this book represents a great of what we know today about electrical oscillations in the brain. How the oscillatory nature of the electrical activity of the brain leads to function, can be imagined in simple activities such as walking and breathing. Even though we will use Buzsaki’s book as an important landpost, the course will follow its own path. The course will be built upon three main ideas: Biophysical models of neuronal electrical communication, ideas from evolution and development and insights from Neurodegenerative diseases. We introduce the main techniques used in signal processing such as the Fast Fourier Transform (FFT), the Hilbert transform and how they are used to understand the Phase Amplitude Coupling (PAC) where the phase of low frequency oscillations controls the amplitude of the high frequency. Current theories of hippocampus function in memory suggest that the phase coupling maybe involved in the transfer of information to and from the hippocampus during the acquisition, consolidation and retrieval of memory. Numerical techniques to solve differential equations will be introduced and their accuracy and stability will be assessed using well known methods of approximation. A section will be dedicated to study finite elements method to solve differential equations. We will study several main areas of interest in neuroscience and cognition: memory and the underlying communication between hippocampus and cortical areas; movement control through the study of the cortico-basal-thalamic loops. Modulation of mesolimbic and nigrostriatal pathways by dopamine. Modulation of cortico-hippocampal circuits by acetylcholine and the participation of these circuits in the onset of Alzheimer disease. We will study the coherence of electrical oscillations in different parts of the brain and how that coherence can be disturbed in certain diseases such as schizophrenia. One of the objectives of this course is to provide advanced students in cognitive science, psychology, computer science and biology with the skills to develop numerical methods used in the study of neuroscience and cognition. The course is designed for advanced students in cognitive science, psychology, or computer science who are interested in developing computational models of cognition. Prerequisites are a basic familiarity with programming (as might be obtained from CS 61A or Eng 7), exposure to cognitive science (e.g., CogSci C1), comfort with basic calculus (e.g., Math 1A), and discrete math (e.g., Math 55 or CS 70). The main concepts from calculus and discrete math students will need to know to be successful in the class are: The fundamental theorem of calculus, numerical approximation of derivatives, Taylor expansion and basic concepts of linear algebra. These concepts will be reviewed in class.

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