Machine Learning-based Analysis of the Relationship Between the Human Gut Microbiome and Bone Health
on-square matrix. It has a wide range
of applications especially in Multiple Input-Multiple Output (MIMO) communication
systems. Unfortunately it has high computation complexity { for matrix size of nxn,
QRD has O(n3) complexity and back substitution, which is used to solve a system
of linear equations, has O(n2) complexity. Thus, as the matrix size increases, the
hardware resource requirement for QRD and back substitution increases signicantly.
This thesis presents the design and implementation of a
exible QRD and back substitution accelerator using a folded architecture. It can support matrix sizes of
4x4, 8x8, 12x12, 16x16, and 20x20 with low hardware resource requirement.
The proposed architecture is based on the systolic array implementation of the
Givens algorithm for QRD. It is built with three dierent types of computation blocks
which are connected in a 2-D array structure. These blocks are controlled by a
scheduler which facilitates reusability of the blocks to perform computation for any
input matrix size which is a multiple of 4. These blocks are designed using two
basic programming elements which support both the forward and backward paths to
compute matrix R in QRD and column-matrix X in back substitution computation.
The proposed architecture has been mapped to Xilinx Zynq Ultrascale+ FPGA
(Field Programmable Gate Array), ZCU102. All inputs are complex with precision
of 40 bits (38 fractional bits and 1 signed bit). The architecture can be clocked at
50 MHz. The synthesis results of the folded architecture for dierent matrix sizes
are presented. The results show that the folded architecture can support QRD and
back substitution for inputs of large sizes which otherwise cannot t on an FPGA
when implemented using a
at architecture. The memory sizes required for dierent
matrix sizes are also presented.
Results from this work aim to increase the accuracy and performance of the inverse solution process.
The inverse problem can be approached by constructing forward solutions where, for a know source, the scalp potentials are determined. This work demonstrates that the use of two variables, the dissipated power and the accumulated charge at interfaces, leads to a new solution method for the forward problem. The accumulated charge satisfies a boundary integral equation. Consideration of dissipated power determines bounds on the range of eigenvalues of the integral operators that appear in this formulation. The new method uses the eigenvalue structure to regularize singular integral operators thus allowing unambiguous solutions to the forward problem.
A major problem in the estimation of properties of neural sources is the presence of artifacts that corrupt EEG recordings. A method is proposed for the determination of inverse solutions that integrates sequential Bayesian estimation with probabilistic data association in order to suppress artifacts before estimating neural activity. This method improves the tracking of neural activity in a dynamic setting in the presence of artifacts.
Solution of the inverse problem requires the use of models of the human head. The electrical properties of biological tissues are best described by frequency dependent complex conductivities. Head models in EEG analysis, however, usually consider head regions as having only constant real conductivities. This work presents a model for tissues as composed of confined electrolytes that predicts complex conductivities for macroscopic measurements. These results indicate ways in which EEG models can be improved.
The computationally intensive parts of temporal mitigation are identified and hardware accelerated. The hardware implementation is based on sequential approach with optimizations applied on the individual components for better performance.
An extensive analysis using a range of fixed point data types is performed to find the optimal data type necessary.
Finally a hybrid combination of data types for different components of temporal mitigation is proposed based on results from the above analysis.
The constant information radar, or CIR, is a tracking radar that modulates target revisit time by maintaining a fixed mutual information measure. For highly dynamic targets that deviate significantly from the path predicted by the tracking motion model, the CIR adjusts by illuminating the target more frequently than it would for well-modeled targets. If SNR is low, the radar delays revisit to the target until the state entropy overcomes noise uncertainty. As a result, we show that the information measure is highly dependent on target entropy and target measurement covariance. A constant information measure maintains a fixed spectral efficiency to support the RF convergence of radar and communications. The result is a radar implementing a novel target scheduling algorithm based on information instead of heuristic or ad hoc methods. The CIR mathematically ensures that spectral use is justified.