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

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Additive manufacturing of metallic components – Process, structure and properties

Lack-of-fusion porosity due to insufficient melting of the adjacent tracks and successive layers is a persistent problem in laser powder bed fusion (LPBF). A novel functional relation is proposed here following dimensional analysis for rapid estimation of the lack-of-fusion porosity fraction as a function of important process variables and alloy properties. The estimated values of the porosity fractions are found to be in fair agreement with the corresponding independent experimentally measured results for LPBF of five commonly used alloys for a wide range of process conditions. The proposed functional relation is used further to construct a set of process maps that can aid in the selection of important LPBF conditions to avoid lack-of-fusion porosity on the shop floor without doing any calculations.

Scaling analysis for rapid estimation of lack of fusion porosity in laser powder bed fusion

Tempering kinetics during multilayer laser additive manufacturing of a ferritic steel

Heat transfer and fluid flow during manual metal arc welding Of low alloy steels were investigated by solving the equations of conservation of mass, momentum and energy in three dimensions. Calculated cooling rates were coupled with an existing phase transformation model to predict the microstructure in low alloy steel welds. The computed results were found to be in good agreement with experimentally observed microstructures. The agreement indicates significant promise for predicting spatial distribution of weld metal microstructure from the fundamentals of transport phenomena.

/pdf/towards-predicting-weld-metal-microstructure-from-248s0a18o7.pdf

Tarasankar Debroy

Papers

Scaling analysis for rapid estimation of lack of fusion porosity in laser powder bed fusion

Tempering kinetics during multilayer laser additive manufacturing of a ferritic steel

Towards predicting weld metal microstructure from fundamentals of transport phenomena

Preface to the special issue ‘Additive Manufacturing’

Tailoring friction stir welds of aluminum alloys using a differential evolution and a transport phenomena based model