Diffusion Phenomena by R. GhezReview by: J. David LoganSIAM Review, Vol. 44, No. 3 (Sep., 2002), pp. 500-501Published by: Society for Industrial and Applied MathematicsStable URL: http://www.jstor.org/stable/4148399 .

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500 BOOK REVIEWS

concrete examples are given on how to ap- ply this theory to specific queuing networks with multiple classes. Some models (e.g., ones with feedback) do not easily fall into this theory, so the authors introduce the concepts of "generalized conservation laws" and "extended polymatroids." In Chapter 12 a deterministic multiclass fluid network is considered; here one seeks to minimize a weighted sum of fluid levels at the nodes for all times t. The optimization is with respect to the processing time allotted to each sta- tion and depends on the initial fluid levels, as well as the input and output rates. A "myopic" procedure is discussed for piecing together optimal solutions over successive time intervals. The optimization problem is converted to a linear programming one. Its solution is outlined in general and pre- sented in full detail for the single node case. The last two chapters would have benefitted from a brief introduction to matroids and linear programming. For example, includ- ing a brief section on these at the beginning of chapter 11 would give the reader some ba- sic background in much the same way that chapter 1 gives the background on queuing.

To summarize, this text gives a well- organized and clearly written introduction to stochastic networks, as well as a complete description of some aspects of current work on these problems. It will probably appeal more to mathematicians than to engineers, especially ones interested in the theoreti- cal aspects of diffusion and fluid approxi- mations to complicated queuing networks. Where possible, the authors illustrate the basic concepts on a simpler form of the model, and the exercises are well chosen. The text is quite free of errors.

REFERENCES

[1] G. F. NEWELL, Approximate Behavior of Tandem Queues, Springer-Verlag, New York, 1979.

[2] G. J. FOSCHINI, Equilibria for diffusion models for pairs of communicat- ing computers--symmetric case, IEEE Trans. Inform. Theory, 28 (1982), pp. 273-284.

[3] J.A. MORRISON, Diffusion approximation for head-of-the-line processor sharing

for two parallel queues, SIAM J. Appl. Math., 53 (1993), pp. 471-490.

CHARLES KNESSL

University of Illinois at Chicago

Diffusion Phenomena. By R. Ghez. Kluwer Academic, Dordrecht, The Netherlands, 2001. $65.00. xv+315 pp., hardcover. ISBN 0-306- 46526-4.

Many may be familiar with R. Ghez's little book, A Primer of Diffusion Problems [1], which appeared in 1988. This new edition, which carries a different title, seeks to de- fine diffusion in a broader context and not merely give an introductory set of problems relating to diffusion.

The new edition has been revised ex- tensively; it contains new exercises, three new appendices, and a new chapter enti- tled "Surface Rate Limitations and Segre- gation." Like the first edition, the coverage is not encyclopedic; the emphasis is on mod- eling and methodology, and the goal is to teach basic ideas of diffusion phenomena through well-chosen physical examples.

Typically, the examples in the book come from heat conduction and are based on in- dustrial applications coming out of the au- thor's years of experience at IBM. In this sense the book is a bit narrow. However, the examples are interesting and elemen-

tary, and any beginner reading this book would get a firm grounding in the basic ideas surrounding the diffusion equation and its solutions. Differential equations and some simple notions of thermodynamics are the only prerequisites. Among the problems discussed are the thermal oxidation of sili- con, crystal growth, precipitation, laser pro- cessing, and several Stefan problems. There is an introductory chapter on Laplace trans- forms, and all the basic techniques are pre- sented, including Green's functions, simi- larity methods, and finite differences; the discussion of separation of variables and diffusion on bounded domains is brief and is contained in an appendix. The entire

subject of diffusion is introduced in an eas-

ily understood manner via one-dimensional random walks.

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BOOK REVIEWS 501

The new chapter on surface conditions will be of interest to both novices and vet- erans. The issue is to clarify the notion of local equilibrium at a phase boundary, i.e., When can one assert that the concentration at a phase boundary is pinned to its equilib- rium value, even as an adjacent bulk phase undergoes nonequilibrium processes? Such questions arise, for example, in the cat- alytic properties of metal surfaces and in the change in doping character of semicon- ductors during annealing. Ghez discusses how Gibbs's theory of equilibrium can be extended to diffusion processes, which are nonequilibrium. The analysis leads to a gen- eralization of the Stefan condition. There is also a section on diffusion in a grain bound- ary that separates two different bulk phases.

In summary, this is a highly readable, excellent introduction to diffusion processes and the diffusion equation. It would be use- ful as a text for an upper division undergrad- uate course or graduate course in modeling, or in a special topics course on diffusion itself. Several challenging exercises comple- ment the exposition, and notes at the end of the chapters steer the reader to further explorations. Even veteran practitioners of diffusion can get a different perspective.

REFERENCE

[1] R. GHEZ, A Primer of Diffusion Problems, Wiley, New York, 1988.

J. DAVID LOGAN

University of Nebraska at Lincoln

Principles of Data Mining. By David Hand, Heikki Mannila, and Padhraic Smyth. MIT Press, Cambridge, MA, 2001. $50.00. xxxii+546 pp., hardcover. ISBN 0-262-08290-X.

Is data mining the same as statistics? The distinguished authors of Principles of Data Mining struggle to make a distinction be- tween the two subjects. In the end, what they have written is a fine applied statistics text. They state, "the most fundamental difference between classical statistical ap- plications and data mining is the size of the data set." Perhaps not surprisingly then,

their "principles of data mining" turn out to be much the same as the "principles of applied statistics." The sad fact is that statistics education, both graduate and un- dergraduate, has largely failed to respond to the challenges and opportunities presented by larger scale data sets. Breiman lamented the longstanding divorce of statistics from data (see Olshen [1]), and it is certainly true that statistics researchers continue to be more enamored of mathematics than of computing. This text redresses the balance somewhat.

Principles of Data Mining revolves around the notion of a "data mining algo- rithm." The authors decompose standard

statistical/data mining activities in terms of the five basic components of a data mining algorithm:

1. the task the algorithm is used to address (e.g., classification, visualization, etc.);

2. the structure of the model or pattern being fitted to the data (e.g., linear regres- sion, Gaussian mixture, etc.);

3. the score function used to assess the quality of the fit to the observed data (e.g., AIC, squared error, etc.);

4. the search or optimization method used to search over parameters and struc- ture (e.g., gradient descent);

5. the data management technique used for storing, indexing, and retrieving of data.

This systematic view of data mining works well in my graduate-level data mining class and is a valuable contribution. Chap- ters 5-8 deal with these components in a fairly abstract way. Chapters 9-11 then deal more conventionally with descriptive and predictive models and cover a large range of topics, albeit in a superficial manner. Chap- ters 12-14 are somewhat detached from the rest of the text and deal with elemen- tary database concepts, rule mining, and retrieval by content.

The extensive scope of the text re-

quires that most topics receive curt treat- ment. For example, the 30-page chapter "Predictive Modeling for Regression" in- cludes linear models (least squares, maxi- mum likelihood, transformations, variable selection), generalized linear models, arti- ficial neural networks, generalized additive

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