Optimization Techniques with FORTRAN

Magnetic resonance (MR) brain section images are segmented and then synthetically colored to give visual representations of the original data with three approaches: the literal and approximate fuzzy c-means unsupervised clustering algorithms, and a supervised computational neural network. Initial clinical results are presented on normal volunteers and selected patients with brain tumors surrounded by edema. Supervised and unsupervised segmentation techniques provide broadly similar results. Unsupervised fuzzy algorithms were visually observed to show better segmentation when compared with raw image data for volunteer studies. For a more complex segmentation problem with tumor/edema or cerebrospinal fluid boundary, where the tissues have similar MR relaxation behavior, inconsistency in rating among experts was observed, with fuzz-c-means approaches being slightly preferred over feedforward cascade correlation results. Various facets of both approaches, such as supervised versus unsupervised learning, time complexity, and utility for the diagnostic process, are compared. >

A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain

This paper examines some of the consequences of finite word lengths in digital control. It is shown that, in many cases of practical importance, the usual shift operator formulation is inferior to an alternative formulation which we designate the delta operator approach. This latter approach is shown to give better coefficient representation and less roundoff noise in many cases. We thus argue that the shift operator and its associated Z -transform can be replaced by delta operators and their associated transform which we designate a Δ-transform. An added advantage of this approach is that discrete designs and transforms converge to their continuous-time counterparts as the sampling rate is increased.

Improved finite word length characteristics in digital control using delta operators

The ancient study of the residue numbering system, or RNS, begins with a verse from a third-century book, Suan-ching, by Sun Tzu:* We have things of which we do not know the number, If we count them by threes, the remainder is 2, If we count them by fives, the remainder is 3, If we count them by sevens, the remainder is 2, How many things are there? The answer, 23. How to get the answer 23 is outlined in Sun Tzu's historic work. He presents a formula for manipulating remainders of an integer after division by 3, 5, and 7. We commemorate this contribution today by referring to one of the common rules of converting remainders, or residues, into integers as the Chinese Remainder Theorem, or CRT. This theorem, as well as the theory of residue numbers, was set forth in the 19th century by Carl Friedrich Gauss in his celebrated Disquisitiones Arithmetical.-t This 1700-year-old number system has been attracting a great deal of attention recently. Digital systems structured into residue arithmetic units may play an important role in ultra-speed, dedicated, real-time systems that support pure parallel processing of integer-valued data. It is a \"carry-free\" system that performs addition, subtraction, and multiplication as concurrent (parallel) operations, side-stepping one of the principal arithmetic delays managing carry information. The first attempt to use some of the unique RNS properties was made by D. H. Lenhmet who, in 1932, built a special-purpose machine he called the \"photo-electric sieve.\" This electro-mechanical device factored Mersenne *L. Dickson in the History of the Theorv of Numbers attributes the origin of the RNS to Sun Tsu (not Tzu) in the first centurv AD, but most scholars accept the Sun Tzu origin. numbers. Then in the mid-50's, the Czech researchers Svaboda and Valach conducted experiments on a hard-wired, small moduli RNS machine, which they used to study error codes. I The same idea apparently occurred to Aiken and Garner. 2 From the late 50's to mid-60's, the Department of Defense supported the RNS research by Szabo and Tanaka at Lockheed. They worked on a special-purpose digital correlator while a team from RCA looked into designing a general-purpose machine. Experimentally , these early efforts met with little success because winding the custom core memory required specialized residue mappings. The most tangible result of these early efforts was a comprehensive text written by Szabo and Tanaka, which survived only …

Residue Arithmetic A Tutorial with Examples

This paper presents a review of the ways in which optimal control theory interacts with cancer chemotherapy. There are three broad areas of investigation. One involves miscellaneous growth kinetic models, the second involves cell cycle models, and the third is a classification of "other models." Both normal and tumor cell populations are included in a number of the models. The concepts of deterministic optimal control theory are applied to each model in such a way as to present a cohesive picture. There are applications to both experimental and clinical tumors. Suggestions for designing better chemotherapy strategies are presented.

Role of optimal control theory in cancer chemotherapy.

Stochastic adaptive controllers have been developed for automatic control of blood pressure during infusions of cardiostimulatory or vasoactive drugs. An adaptive algorithm based upon a minimum variance control law is presented. A more advanced algorithm obtained by augmenting the performance measure to include the rate of charge of the control signal is also presented. An autoregressive-moving-average (ARMA) model, representing the dynamics of the system, and a recursive least-squares parameter estimation technique are used for both algorithms. A series of experiments was performed in dogs, utilizing an electronically activated drug infuser. Stable control was achieved, even when the circulatory state of the animal underwent major changes, using either algorithm. On the basis of theoretical considerations and experimental results, we expect that these adaptive controllers will significantly improve the performance of drug infusion systems in clinical applications.

Adaptive Control of Blood Pressure

A computational method is presented for finding the linear quadratic regulator such that the optimal closed-loop system has eigenvalues lying within a vertical strip in the complex plane. The proposed method is suitable for the two-stage optimal design of two-time scale systems.

Linear quadratic regulators with eigenvalue placement in a vertical strip

This paper presents a computer-based adaptive control system for left ventricular bypass assist devices consisting of air driven diaphragm pumps. The system provides for 1) synchronization of pumping with ECG signals and 2) control of atrial pressure at desired levels. The system design includes an adaptive control algorithm which is a self-tuning PID-controller based on pole placement. The performance of the system has been demonstrated by in vitro experiments_ on a mock circulatory system. When there is an increase in atrial pressure, the system responds with an increase in stroke volume. Following major changes in the circulatory system, the control algorithm retunes itself and restores the system to the desired state.

Adaptive control of left ventricular bypass assist devices

Technical communique: Adaptive control and identification of the dissolved oxygen process

This note presents recursive algorithms that are rapidly convergent and more stable for finding the principal square root of a complex matrix. Also, the developed algorithms are utilized to derive the fast and stable matrix sign algorithms which are useful in developing applications to control system problems.

B. McInnis

Papers

Adaptive Control of Blood Pressure

Linear quadratic regulators with eigenvalue placement in a vertical strip

Adaptive control of left ventricular bypass assist devices

Technical communique: Adaptive control and identification of the dissolved oxygen process

Fast and stable algorithms for computing the principal square root of a complex matrix