For any research field to have a lasting impact, there must be a firm theoretical foundation. Neural networks research is no exception. Some of the founda­ tional concepts, established several decades ago, led to the early promise of developing machines exhibiting intelligence. The motivation for studying such machines comes from the fact that the brain is far more efficient in visual processing and speech recognition than existing computers. Undoubtedly, neu­ robiological systems employ very different computational principles. The study of artificial neural networks aims at understanding these computational prin­ ciples and applying them in the solutions of engineering problems. Due to the recent advances in both device technology and computational science, we are currently witnessing an explosive growth in the studies of neural networks and their applications. It may take many years before we have a complete understanding about the mechanisms of neural systems. Before this ultimate goal can be achieved, an­ swers are needed to important fundamental questions such as (a) what can neu­ ral networks do that traditional computing techniques cannot, (b) how does the complexity of the network for an application relate to the complexity of that problem, and (c) how much training data are required for the resulting network to learn properly? Everyone working in the field has attempted to answer these questions, but general solutions remain elusive. However, encouraging progress in studying specific neural models has been made by researchers from various disciplines.

The traditional systems disciplines of communications, computation, control and signal processing are becoming increasingly important in addressing major technological challenges of the coming century, in fields such as materials processing, manufacturing automation, speech recognition and ubiquitous personal communications, among many others. Moreover the boundaries between these separate disciplines are being rapidly blurred by the many demands of these applications. This Tribute, dedicated to Thomas Kailath for his many seminal contributions to these areas, highlights several recent trends and results, described by leading scientists and engineers from around the world.The 36 papers in this volume present important results on, among others, interference cancellation in multipath channels, decision feedback equalization for packet transmission, blind equalization and smart antennas for mobile communications, displacement structure, fast and stable algorithms in numerical linear algebra, nonconvex optimization problems, issues in nanoelectronic computation, fundamental limits of control system performance, LQG control with communication constraints, nonlinear control, adaptive nonlinear control, model identification, tomographic deconvolution, and higher-order statistics. The applications discussed herein include packet radio, robotics, very flexible mechanical systems, power systems and power electronics, moving object detection, complexity management and several others. The volume starts out with a survey by Professor Kailath entitled `Norbert Wiener and the Development of Mathematical Engineering', a term suggested by Wiener that can serve as a compact description of the variety of fields described herein.

For any research field to have a lasting impact, there must be a firm theoretical foundation. Neural networks research is no exception. Some of the founda­ tional concepts, established several decades ago, led to the early promise of developing machines exhibiting intelligence. The motivation for studying such machines comes from the fact that the brain is far more efficient in visual processing and speech recognition than existing computers. Undoubtedly, neu­ robiological systems employ very different computational principles. The study of artificial neural networks aims at understanding these computational prin­ ciples and applying them in the solutions of engineering problems. Due to the recent advances in both device technology and computational science, we are currently witnessing an explosive growth in the studies of neural networks and their applications. It may take many years before we have a complete understanding about the mechanisms of neural systems. Before this ultimate goal can be achieved, an­ swers are needed to important fundamental questions such as (a) what can neu­ ral networks do that traditional computing techniques cannot, (b) how does the complexity of the network for an application relate to the complexity of that problem, and (c) how much training data are required for the resulting network to learn properly? Everyone working in the field has attempted to answer these questions, but general solutions remain elusive. However, encouraging progress in studying specific neural models has been made by researchers from various disciplines.

A. Paulraj*, V. Roychowdhury**, and C. Schaper* * Dept. of Electrical Engineering, Stanford University ** Dept. of Electrical Engineering, UCLA Innumerable conferences are held around the world on the subjects of commu­ nications, computation, control and signal processing, and on their numerous subdisciplines. Therefore one might not envision a coherent conference encom­ passing all these areas. However, such an event did take place June 22-26, 1995, at an international symposium held at Stanford University to celebrate Professor Thomas Kailath's sixtieth birthday and to honor the notable con­ tributions made by him and his students and associates. The depth of these contributions was evident from the participation of so many leading figures in each of these fields. Over the five days of the meeting, there were about 200 at­ tendees, from eighteen countries, more than twenty government and industrial organizations, and various engineering, mathematics and statistics faculties at nearly 50 different academic institutions. They came not only to celebrate but also to learn and to ponder the threads and the connections that Professor Kailath has discovered and woven among so many apparently disparate areas. The organizers received many comments about the richness of the occasion. A distinguished academic wrote of the conference being "the single most rewarding professional event of my life. " The program is summarized in Table 1. 1; a letter of reflections by Dr. C. Rohrs appears a little later.

For any research field to have a lasting impact, there must be a firm theoretical foundation. Neural networks research is no exception. Some of the founda­ tional concepts, established several decades ago, led to the early promise of developing machines exhibiting intelligence. The motivation for studying such machines comes from the fact that the brain is far more efficient in visual processing and speech recognition than existing computers. Undoubtedly, neu­ robiological systems employ very different computational principles. The study of artificial neural networks aims at understanding these computational prin­ ciples and applying them in the solutions of engineering problems. Due to the recent advances in both device technology and computational science, we are currently witnessing an explosive growth in the studies of neural networks and their applications. It may take many years before we have a complete understanding about the mechanisms of neural systems. Before this ultimate goal can be achieved, an­ swers are needed to important fundamental questions such as (a) what can neu­ ral networks do that traditional computing techniques cannot, (b) how does the complexity of the network for an application relate to the complexity of that problem, and (c) how much training data are required for the resulting network to learn properly? Everyone working in the field has attempted to answer these questions, but general solutions remain elusive. However, encouraging progress in studying specific neural models has been made by researchers from various disciplines.

For any research field to have a lasting impact, there must be a firm theoretical foundation. Neural networks research is no exception. Some of the founda­ tional concepts, established several decades ago, led to the early promise of developing machines exhibiting intelligence. The motivation for studying such machines comes from the fact that the brain is far more efficient in visual processing and speech recognition than existing computers. Undoubtedly, neu­ robiological systems employ very different computational principles. The study of artificial neural networks aims at understanding these computational prin­ ciples and applying them in the solutions of engineering problems. Due to the recent advances in both device technology and computational science, we are currently witnessing an explosive growth in the studies of neural networks and their applications. It may take many years before we have a complete understanding about the mechanisms of neural systems. Before this ultimate goal can be achieved, an­ swers are needed to important fundamental questions such as (a) what can neu­ ral networks do that traditional computing techniques cannot, (b) how does the complexity of the network for an application relate to the complexity of that problem, and (c) how much training data are required for the resulting network to learn properly? Everyone working in the field has attempted to answer these questions, but general solutions remain elusive. However, encouraging progress in studying specific neural models has been made by researchers from various disciplines.

The traditional systems disciplines of communications, computation, control and signal processing are becoming increasingly important in addressing major technological challenges of the coming century, in fields such as materials processing, manufacturing automation, speech recognition and ubiquitous personal communications, among many others. Moreover the boundaries between these separate disciplines are being rapidly blurred by the many demands of these applications. This Tribute, dedicated to Thomas Kailath for his many seminal contributions to these areas, highlights several recent trends and results, described by leading scientists and engineers from around the world.The 36 papers in this volume present important results on, among others, interference cancellation in multipath channels, decision feedback equalization for packet transmission, blind equalization and smart antennas for mobile communications, displacement structure, fast and stable algorithms in numerical linear algebra, nonconvex optimization problems, issues in nanoelectronic computation, fundamental limits of control system performance, LQG control with communication constraints, nonlinear control, adaptive nonlinear control, model identification, tomographic deconvolution, and higher-order statistics. The applications discussed herein include packet radio, robotics, very flexible mechanical systems, power systems and power electronics, moving object detection, complexity management and several others. The volume starts out with a survey by Professor Kailath entitled `Norbert Wiener and the Development of Mathematical Engineering', a term suggested by Wiener that can serve as a compact description of the variety of fields described herein.

For any research field to have a lasting impact, there must be a firm theoretical foundation. Neural networks research is no exception. Some of the founda­ tional concepts, established several decades ago, led to the early promise of developing machines exhibiting intelligence. The motivation for studying such machines comes from the fact that the brain is far more efficient in visual processing and speech recognition than existing computers. Undoubtedly, neu­ robiological systems employ very different computational principles. The study of artificial neural networks aims at understanding these computational prin­ ciples and applying them in the solutions of engineering problems. Due to the recent advances in both device technology and computational science, we are currently witnessing an explosive growth in the studies of neural networks and their applications. It may take many years before we have a complete understanding about the mechanisms of neural systems. Before this ultimate goal can be achieved, an­ swers are needed to important fundamental questions such as (a) what can neu­ ral networks do that traditional computing techniques cannot, (b) how does the complexity of the network for an application relate to the complexity of that problem, and (c) how much training data are required for the resulting network to learn properly? Everyone working in the field has attempted to answer these questions, but general solutions remain elusive. However, encouraging progress in studying specific neural models has been made by researchers from various disciplines.

A. Paulraj*, V. Roychowdhury**, and C. Schaper* * Dept. of Electrical Engineering, Stanford University ** Dept. of Electrical Engineering, UCLA Innumerable conferences are held around the world on the subjects of commu­ nications, computation, control and signal processing, and on their numerous subdisciplines. Therefore one might not envision a coherent conference encom­ passing all these areas. However, such an event did take place June 22-26, 1995, at an international symposium held at Stanford University to celebrate Professor Thomas Kailath's sixtieth birthday and to honor the notable con­ tributions made by him and his students and associates. The depth of these contributions was evident from the participation of so many leading figures in each of these fields. Over the five days of the meeting, there were about 200 at­ tendees, from eighteen countries, more than twenty government and industrial organizations, and various engineering, mathematics and statistics faculties at nearly 50 different academic institutions. They came not only to celebrate but also to learn and to ponder the threads and the connections that Professor Kailath has discovered and woven among so many apparently disparate areas. The organizers received many comments about the richness of the occasion. A distinguished academic wrote of the conference being "the single most rewarding professional event of my life. " The program is summarized in Table 1. 1; a letter of reflections by Dr. C. Rohrs appears a little later.

For any research field to have a lasting impact, there must be a firm theoretical foundation. Neural networks research is no exception. Some of the founda­ tional concepts, established several decades ago, led to the early promise of developing machines exhibiting intelligence. The motivation for studying such machines comes from the fact that the brain is far more efficient in visual processing and speech recognition than existing computers. Undoubtedly, neu­ robiological systems employ very different computational principles. The study of artificial neural networks aims at understanding these computational prin­ ciples and applying them in the solutions of engineering problems. Due to the recent advances in both device technology and computational science, we are currently witnessing an explosive growth in the studies of neural networks and their applications. It may take many years before we have a complete understanding about the mechanisms of neural systems. Before this ultimate goal can be achieved, an­ swers are needed to important fundamental questions such as (a) what can neu­ ral networks do that traditional computing techniques cannot, (b) how does the complexity of the network for an application relate to the complexity of that problem, and (c) how much training data are required for the resulting network to learn properly? Everyone working in the field has attempted to answer these questions, but general solutions remain elusive. However, encouraging progress in studying specific neural models has been made by researchers from various disciplines.