Neural Modeling - Fall NEURAL TRANSFORMATION Strategy to discover the Brain Functionality Biomedical engineering Group School of Electrical Engineering Sharif University of Technology

Neural Modeling - Fall Transmission of Action Potential/ Dendrite potential: Corrected

Neural Modeling - Fall NEURAL TRANSFORMATION Neural representation paves the way for a useful understanding of neural transformation Can be characterized using linear decoding The representational decoder  A transformational decoder. Transformation on encoded information: To extract information other than what the population is taken to represent.

Neural Modeling - Fall Transformation vs Decode x Representation y Transformation Decode x F(x) What transformations a neural population can, in principle, support? How well a given neural population can support the transformations defined by a particular class of functions? observed in a neurobiological system. Neurons with certain response properties support particular transformations better than others we do not need to rely on training to have interesting, biologically plausible models.

Neural Modeling - Fall Static vs Dynamic Static computation of a function is not, alone, a good description of the kinds of transformations neurobiological systems typically exhibit. To characterize the dynamics of the transformations that neural populations support Engineering Tools: State Vectors Neural representations can play the role of “State Vectors” To address issues that have proven very difficult for other approaches

Neural Modeling - Fall About THREE PRINCIPLES OF NEURAL ENGINEERING Guiding assumptions of our approach. Numerous examples of detailed models of a wide variety of neurobiological systems To demonstrate how to use these principles A methodology for applying these principles.

Neural Modeling - Fall Principles P1: Neural representations are defined by the combination of nonlinear encoding (exemplified by neuron tuning curves) and weighted linear decoding P2: Transformations of neural representations are functions of variables that are represented by neural populations. Transformations are determined using an alternately weighted linear decoding (i.e., the transformational decoding as opposed to the representational decoding) P3: Neural dynamics are characterized by considering neural representations as control theoretic state variables. Thus, the dynamics of neurobiological systems can be analyzed using control theory Addendum : Neural systems are subject to significant amounts of noise. Therefore, any analysis of such systems must account for the effects of noise

Neural Modeling - Fall Methodology Central goal: To provide a general framework for constructing neurobiological simulations The guiding principles A methodology for applying those principles A software package in MatLab The models have been implemented with this package. Three stages: System description Design specification Implementation

Neural Modeling - Fall System description Identify the relevant neurobiological properties (e.g., tuning curves, connectivity, etc.). Specify the representations as variables (e.g., scalars, vectors, functions, etc.). Provide a functional description including specification of subsystems and overall system architecture. Provide a mathematical description of system function.

Neural Modeling - Fall Design specification Specify the range, precision, and signal-to-noise ratio for each variable. Specify the temporal and dynamic characteristics for each variable.

Neural Modeling - Fall Implementation Determine the decoding rules for implementing the specified transformations. Determine which parts of the model are to be simulated to which degrees of detail. Perform numerical experiments using resulting simulation.

Neural Modeling - Fall A POSSIBLE THEORY OF NEUROBIOLOGICAL SYSTEMS Presented: A ‘framework’ that consists of a set of three principles and a corresponding methodology. The possibility that the three principles can be properly called a theory of neurobiological systems. The practical utility of the framework itself is independent of whether this claim is found convincing

Neural Modeling - Fall The state of theories in neuroscience There aren’t any. There aren’t any good ones Churchland and Sejnowski 1992 Marder et al Stevens 1994 Crick and Koch 1998 Stevens 2000 Neuroscience is, in other words, “data rich, but theory poor” (Churchland and Sejnowski 1992, p. 16).