Optical recording of various brain signals is becoming an indispensable technique for biological studies, accelerated by the development of new or improved biosensors and microscopy technology. A major challenge in leveraging the technique is to identify and quantify the rich patterns embedded in the data. However, existing methods often struggle, either due to their limited signal analysis capabilities or poor performance. Here we present Activity Quantification and Analysis (AQuA2), an innovative analysis platform built upon machine learning theory. AQuA2 features a novel event detection pipeline for precise quantification of intricate brain signals and incorporates a Consensus Functional Unit (CFU) module to explore interactions among potential functional units driving repetitive signals. To enhance efficiency, we developed BIdirectional pushing with Linear Component Operations (BILCO) algorithm to handle propagation analysis, a time-consuming step using traditional algorithms. Furthermore, considering user-friendliness, AQuA2 is implemented as both a MATLAB package and a Fiji plugin, complete with a graphical interface for enhanced usability. AQuA2's validation through both simulation and real-world applications demonstrates its superior performance compared to its peers. Applied across various sensors (Calcium, NE, and ATP), cell types (astrocytes, oligodendrocytes, and neurons), animal models (zebrafish and mouse), and imaging modalities (two-photon, light sheet, and confocal), AQuA2 consistently delivers promising results and novel insights, showcasing its versatility in fluorescent imaging data analysis. / Doctor of Philosophy / Understanding and effectively treating brain diseases requires a deep insight into how the brain operates. A crucial aspect of this exploration involves directly visualizing different signals within the brain, allowing researchers to delve into the functions of brain cells and their interactions. However, as data collection expands rapidly, analyzing this wealth of information presents a significant challenge. Existing methods often fall short due to their limited capacity to analyze signals or their subpar performance, failing to keep pace with current demands. In this work, we introduce Activity Quantification and Analysis (AQuA2), an innovative platform rooted in machine learning principles. AQuA2 features a novel event detection pipeline for accurately quantifying intricate brain signals. Additionally, it incorporates a Consensus Functional Unit (CFU) module, which facilitates the exploration of interactions among potential functional units associated with repetitive signals. To enhance efficiency and usability, we have developed acceleration algorithms and released AQuA2 in two versions: a MATLAB package and a Fiji plugin, each designed to address unique user requirements. AQuA2 has demonstrated its efficacy through real-world applications, effectively quantifying and analyzing signals across various platforms such as biosensors, cell types, animal models, and imaging modalities, with promising outcomes. Furthermore, the utilization of AQuA2 has facilitated the discovery of new insights, thereby augmenting its value. These findings emphasize its versatility as software for comprehensive analysis of diverse fluorescent imaging data, enabling a wide range of scientific inquiries.

Application domains such as Bio-informatics, DSP, Structural Biology, Fluid Dynamics, high resolution direction finding, state estimation, adaptive noise cancellation etc. demand high performance computing solutions for their simulation environments. The core computations of these applications are in Numerical Linear Algebra (NLA) kernels. Direct solvers are predominantly required in the domains like DSP, estimation algorithms like Kalman Filter etc, where the matrices on which operations need to be performed are either small or medium sized, but dense. Faddeev's Algorithm is often used for solving dense linear system of equations. Modified Faddeev's algorithm (MFA) is a general algorithm on which LU decomposition, QR factorization or SVD of matrices can be realized. MFA has the good property of realizing a host of matrix operations by computing the Schur complements on four blocked matrices, thereby reducing the overall computation requirements. We will use MFA as a representative Direct Solver in this work. We further discuss Given's rotation based QR algorithm for Decomposition of any matrix, often used to solve the linear least square problem. Systolic Array Architectures are widely accepted ASIC solutions for NLA algorithms. But the \can of worms" associated with this traditional solution spawns the need for alternative solutions. While popular custom hardware solution in form of systolic arrays can deliver high performance, but because of their rigid structure they are not scalable and reconfigurable, and hence not commercially viable. We show how a Reconfigurable computing platform can serve to contain the \can of worms". REDEFINE, a coarse grained runtime reconfigurable architecture has been used for systolic actualization of NLA kernels. We elaborate upon streaming NLA-specific enhancements to REDEFINE in order to meet expected performance goals. We explore the need for an algorithm aware custom compilation framework. We bring about a proposition to realize Faddeev's Algorithm on REDEFINE. We show that REDEFINE performs several times faster than traditional GPPs. Further we direct our interest to QR Decomposition to be the next NLA kernel as it ensures better stability than LU and other decompositions. We use QR Decomposition as a case study to explore the design space of the proposed solution on REDEFINE. We also investigate the architectural details of the Custom Functional Units (CFU) for these NLA kernels. We determine the right size of the sub-array in accordance with the optimal pipeline depth of the core execution units and the number of such units to be used per sub-array. The framework used to realize QR Decomposition can be generalized for the realization of other algorithms dealing with decompositions like LU, Faddeev's Algorithm, Gauss-Jordon etc with different CFU definitions .

Reversible circuits are similar to conventional logic circuits except that they are built from reversible gates. In reversible gates, there is a unique, one-to-one mapping between the inputs and outputs, not the case with conventional logic. Also, reversible gates require constant ancilla inputs for reconfiguration of gate functions and garbage outputs that help in keeping reversibility. Reversible circuits hold promise in futuristic computing technologies like quantum computing, quantum dot cellular automata, DNA computing, optical computing, etc. Thus, it is important to minimize parameters such as ancilla and garbage bits, quantum cost and delay in the design of reversible circuits. The first contribution of this dissertation is the design of a new reversible gate namely the TR gate (Thapliyal-Ranganathan) which has the unique structure that makes it ideal for the realization of arithmetic circuits such as adders, subtractors and comparators, efficient in terms of the parameters such as ancilla and garbage bits, quantum cost and delay. The second contribution is the development of design methodologies and a synthesis framework to synthesize reversible data path functional units, such as binary and BCD adders, subtractors, adder-subtractors and binary comparators. The objective behind the proposed design methodologies is to synthesize arithmetic and logic functional units optimizing key metrics such as ancilla inputs, garbage outputs, quantum cost and delay. A library of reversible gates such as the Fredkin gate, the Toffoli gate, the TR gate, etc. was developed by coding in Verilog for use during synthesis. The third contribution of this dissertation is the set of methodologies for the design of reversible sequential circuits such as reversible latches, flip-flops and shift registers. The reversible designs of asynchronous set/reset D latch and the D flip-flop are attempted for the first time. It is shown that the designs are optimal in terms of number of garbage outputs while exploring the best possible values for quantum cost and delay. The other important contributions of this dissertation are the applications of reversible logic as well as a special class of reversible logic called conservative reversible logic towards concurrent (online) and offline testing of single as well as multiple faults in traditional and reversible nanoscale VLSI circuits, based on emerging nanotechnologies such as QCA, quantum computing, etc. Nanoelectronic devices tend to have high permanent and transient faults and thus are susceptible to high error rates. Specific contributions include (i) concurrently testable sequential circuits for molecular QCA based on reversible logic, (ii) concurrently testable QCA-based FPGA, (iii) design of self checking conservative logic gates for QCA, (iv) concurrent multiple error detection in emerging nanotechnologies using reversible logic, (v) two-vectors, all 0s and all 1s, testable reversible sequential circuits.