Title: Sparse algorithms for decoding and identification of neural circuits
Description: The brain, as an information processing machine, surpasses any man-made computational device, both in terms of its capabilities and its efficiency. Neuroscience research has made great strides since the foundational works of Cajal and Golgi. However, we still have very little understanding about the algorithmic underpinnings of the brain as an information processor. Identifying mechanistic models of the functional building blocks of the brain will have significant impact not just on neuroscience, but also on artificial computational systems. This provides the main motivation for the work presented in this thesis, summarily i) biologically-inspired algorithms that can be efficiently implemented in silico, ii) functional identification of the processing in certain types of neural circuits, and iii) a collaborative ecosystem for brain research in a model organism, towards the synergistic goal of understanding functional mechanisms employed by the brain. First, this thesis provides a highly parallelizable, biologically-inspired, motion detection algorithm that is based upon the temporal processing of the local (spatial) phase of a visual stimulus.

The relation of the phase based motion detector to the widely studied Reichardt detector model, is discussed. Examples are provided comparing the performance of the proposed algorithm with the Reichardt detector as well as the optic flow algorithm, which is the workhorse for motion detection in computer vision. Further, it is shown through examples that the phase based motion detection model provides intuitive explanations for reverse-phi based illusory motion percepts. Then, tractable algorithms are presented for decoding with and identification of neural circuits, comprised of processing that can be described by a second-order Volterra kernel (quadratic filter). It is shown that the Reichardt detector, as well as models of cortical complex cells, can be described by this structure. Examples are provided for decoding of visual stimuli encoded by a population of Reichardt detector cells and complex cells, as well as their identification from observed spike times. Further, the phase based motion detection model is shown to be equivalent to a second-order Volterra kernel acting on two normalized inputs.

Subsequently, a general model that computes the ratio of two non-linear functionals, each comprising linear (first order Volterra kernel) and quadratic (second-order Volterra kernel) filters, is proposed. It is shown that, even under these highly non-linear operations, a population of cells can encode stimuli faithfully using a number of measurements that are proportional to the bandwidth of the input stimulus. Tractable algorithms are devised to identify the divisive normalization model and examples of identification are provided for both simulated and biological data. Additionally, an extended framework, comprising parallel channels of divisively normalized cells each subjected to further divisive normalization from lateral feedback connections, is proposed. An algorithm is formulated for identifying all the components in this extended framework from controlled stimulus presentation and observed outputs samples. Finally, the thesis puts forward the Fruit Fly Brain Observatory (FFBO), an initiative to enable a collaborative ecosystem for fruit fly brain research.

Key applications in FFBO, and the software and computational infrastructure enabling them, are described along with case studies.