Model-based molecular phylogenetics plays an important role in comparisons of genomic data, and model selection is a key step in all such analyses. We present ModelFinder, a fast model-selection method that greatly improves the accuracy of phylogenetic estimates by incorporating a model of rate heterogeneity across sites not previously considered in this context and by allowing concurrent searches of model space and tree space.

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ModelFinder: fast model selection for accurate phylogenetic estimates

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

[1] Atmospheric gravity waves have been a subject of intense research activity in recent years because of their myriad effects and their major contributions to atmospheric circulation, structure, and variability. Apart from occasionally strong lower-atmospheric effects, the major wave influences occur in the middle atmosphere, between ∼ 10 and 110 km altitudes because of decreasing density and increasing wave amplitudes with altitude. Theoretical, numerical, and observational studies have advanced our understanding of gravity waves on many fronts since the review by Fritts [1984a]; the present review will focus on these more recent contributions. Progress includes a better appreciation of gravity wave sources and characteristics, the evolution of the gravity wave spectrum with altitude and with variations of wind and stability, the character and implications of observed climatologies, and the wave interaction and instability processes that constrain wave amplitudes and spectral shape. Recent studies have also expanded dramatically our understanding of gravity wave influences on the large-scale circulation and the thermal and constituent structures of the middle atmosphere. These advances have led to a number of parameterizations of gravity wave effects which are enabling ever more realistic descriptions of gravity wave forcing in large-scale models. There remain, nevertheless, a number of areas in which further progress is needed in refining our understanding of and our ability to describe and predict gravity wave influences in the middle atmosphere. Our view of these unknowns and needs is also offered.

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Gravity wave dynamics and effects in the middle atmosphere

We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically meaningful interpretations of the underlying dynamic processes.

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A new view of nonlinear water waves: the Hilbert spectrum

Summary. The 
$L^2$
 Monge-Kantorovich mass transfer problem [31] is reset in a fluid mechanics framework and numerically solved by an augmented Lagrangian method.

A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Advanced mathematical methods for scientists and engineers, by Carl M. Bender and Steven A. Orszag. Pp xiv, 593. 1978. SBN 0 07 004452 X (McGraw-Hill)

Fundamentals of cryptology: a professional reference and interative tutorial, by Henk C. A. van Tilborg. Pp. 505 with a CD-ROM. £110.50. 1999. ISBN 0 7923 8675 2 (Kluwer Academic Publishers). In a fast-changing field like cryptology, a textbook needs regular updating. In revising his 1988 book An introduction to cryptology, Henk van Tilborg has added new chapters on elliptic curve methods and on authentication codes. He has also updated and extended other sections. However, the most significant addition is probably the CD-ROM, which contains an interactive Mathematica based tutorial. The book starts gently with classical cryptosystems (such as the Caesar and Playfair ciphers), shift-register sequences and block ciphers. There is then a short chapter on Shannon theory, including the concepts of entropy and redundancy, followed by a discussion of data-compression techniques and Huffman codes. Attention then shifts to public-key cryptography based on discrete logarithms and RSA systems. Next come chapters on coding systems based on elliptic curves, coding theory, and the knapsack method. The new chapter on authentication is followed by a short discussion of zero-knowledge protocols and longer consideration of secret sharing systems. Distinctive feature of this book include the many references to the interactive CD-ROM and the attention paid to methods of breaking the codes, which in turn motivates the discussion of refinements and alternative methods. There are appendices on number theory, finite fields and relevant famous mathematicians. This book would suit someone who wanted an in-depth and practical understanding of cryptology.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/CC73A70879F382D217D9CEF3D1292F99/S0025557200169517a.pdf/div-class-title-span-class-italic-practical-methods-of-optimization-2nd-edn-span-by-r-fletcher-pp-436-34-95-2000-isbn-0-471-49463-1-wiley-div.pdf

Practical methods of optimization (2nd edn) , by R. Fletcher. Pp. 436. £34.95. 2000. ISBN 0 471 49463 1 (Wiley).

A variational principle for the conduction of heat

/pdf/73-52-spearman-s-rank-correlation-coefficient-1vokc5qyaq.pdf

Ll. G. Chambers

Papers

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Advanced mathematical methods for scientists and engineers, by Carl M. Bender and Steven A. Orszag. Pp xiv, 593. 1978. SBN 0 07 004452 X (McGraw-Hill)

Practical methods of optimization (2nd edn) , by R. Fletcher. Pp. 436. £34.95. 2000. ISBN 0 471 49463 1 (Wiley).

A variational principle for the conduction of heat

73.52 Spearman’s rank correlation coefficient