There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

(1991). Applied Linear Regression Models. Journal of Quality Technology: Vol. 23, No. 1, pp. 76-77.

Applied Linear Regression Models

IEEE transactions on computer-aided design of integrated circuits and systems : a publication of the IEEE Circuits and Systems Society

Micromachining and micro-electromechanical system (MEMS) technologies can be used to produce complex structures, devices and systems on the scale of micrometers. Initially micromachining techniques were borrowed directly from the integrated circuit (IC) industry, but now many unique MEMS-specific micromachining processes are being developed. In MEMS, a wide variety of transduction mechanisms can be used to convert real-world signals from one form of energy to another, thereby enabling many different microsensors, microactuators and microsystems. Despite only partial standardization and a maturing MEMS CAD technology foundation, complex and sophisticated MEMS are being produced. The integration of ICs with MEMS can improve performance, but at the price of higher development costs, greater complexity and a longer development time. A growing appreciation for the potential impact of MEMS has prompted many efforts to commercialize a wide variety of novel MEMS products. In addition, MEMS are well suited for the needs of space exploration and thus will play an increasingly large role in future missions to the space station, Mars and beyond. (Some figures in this article are in colour only in the electronic version)

https://iopscience.iop.org/article/10.1088/0964-1726/10/6/301/pdf

Microelectromechanical systems (MEMS):fabrication, design and applications

DIAGNOSIX is a comprehensive fault diagnosis methodology for characterizing failures in digital ICs. Using limited layout information, DIAGNOSIX automatically extracts a fault model for a failing IC by analyzing the behavior of the physical neighborhood surrounding suspect lines. Results from several simulated and over 800 failing ICs reveal a significant improvement in localization. More importantly, the output of DIAGNOSIX is an accurate model of the logic-level defect behavior that provides useful insight into the actual defect mechanism. Experiment results for the failing chips with successful physical failure analysis reveal that the extracted faults accurately describe the actual defects.

A Logic Diagnosis Methodology for Improved Localization and Extraction of Accurate Defect Behavior

Recent work in IC failure analysis strongly indicates the need for fault models that directly analyze the function of circuit primitives. The input pattern (IP) fault model is a functional fault model that allows for both complete and partial functional verification of every circuit module, independent of the design level. We describe the IP fault model and provide a method for analyzing IP faults using standard SSL-based fault simulators and test generation tools. The method is used to generate test sets that target the IP faults of the ISCAS85 benchmark circuits and a carry-lookahead adder. Improved IP fault coverage for the benchmarks and the adder is obtained by adding a small number of test patterns to tests that target only SSL faults. We also conducted fault simulation experiments that show IP test patterns are effective in detecting non-targeted faults such as bridging and transistor stuck-on faults. Finally, we discuss the notion of IP redundancy and show how large amounts of this redundancy exist in the benchmarks and in SSL-irredundant adder circuits.

Properties of the input pattern fault model

Microelectromechanical systems (MEMS) are miniature electromechanical sensor and actuator systems developed from the mature batch-fabricated processes of VLSI technologies. Projected growth in the MEMS market requires significant advances in CAD and manufacturing for MEMS. These advances must be accompanied with testing methodologies that ensure both high quality and reliability. We describe our approach for developing a comprehensive testing methodology for a class of MEMS known as surface micromachined sensors. Our first step involving manufacturing process and low-level mechanical simulations is illustrated by studying the effects of realistic contaminations on the folded-flexure comb-drive resonator. The simulation results obtained indicate that realistic contaminations can create a variety of defective structures that result in a wide spectrum of faulty behaviors.

Development of a MEMS testing methodology

In this paper, we propose a new technique, referred to as virtual probe (VP), to efficiently measure, characterize, and monitor spatially-correlated inter-die and/or intra-die variations in nanoscale manufacturing process. VP exploits recent breakthroughs in compressed sensing to accurately predict spatial variations from an exceptionally small set of measurement data, thereby reducing the cost of silicon characterization. By exploring the underlying sparse pattern in spatial frequency domain, VP achieves substantially lower sampling frequency than the well-known Nyquist rate. In addition, VP is formulated as a linear programming problem and, therefore, can be solved both robustly and efficiently. Our industrial measurement data demonstrate the superior accuracy of VP over several traditional methods, including 2-D interpolation, Kriging prediction, and k-LSE estimation.

/pdf/virtual-probe-a-statistical-framework-for-low-cost-silicon-4aexcdwbz0.pdf

Virtual Probe: A Statistical Framework for Low-Cost Silicon Characterization of Nanoscale Integrated Circuits

We introduce a new fault representation mechanism for digital circuits based on fault tuples. A fault tuple is a simple 3-element condition for a signal line, its value, and clock cycle constrain t. AND-OR expressions of fault tuples are used to represent arbitrary misbehaviors. A fault simulator based on fault tuples was used to conduct experiments on benc hmark circuits. Simulation results show that a 17% reduction of average CPU time is achiev ed when performing sim ulation on all fault types simultaneously, as opposed to individually. We expect further improvements in speedup when the shared characteristics of the various fault types are better exploited.

R.D. Blanton

Papers

A Logic Diagnosis Methodology for Improved Localization and Extraction of Accurate Defect Behavior

Properties of the input pattern fault model

Development of a MEMS testing methodology

Virtual Probe: A Statistical Framework for Low-Cost Silicon Characterization of Nanoscale Integrated Circuits

Universal fault simulation using fault tuples