An MRI time course of 512 echo-planar images (EPI) in resting human brain obtained every 250 ms reveals fluctuations in signal intensity in each pixel that have a physiologic origin. Regions of the sensorimotor cortex that were activated secondary to hand movement were identified using functional MRI methodology (FMRI). Time courses of low frequency (< 0.1 Hz) fluctuations in resting brain were observed to have a high degree of temporal correlation (P < 10(-3)) within these regions and also with time courses in several other regions that can be associated with motor function. It is concluded that correlation of low frequency fluctuations, which may arise from fluctuations in blood oxygenation or flow, is a manifestation of functional connectivity of the brain.

Functional connectivity in the motor cortex of resting human brain using echo-planar MRI.

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

Mathematica--A System for Doing Mathematics by Computer.

Survey of Numerical Methods for Trajectory Optimization

This unique book provides an introduction to a subject whose use has steadily increased over the past 40 years. An update of Ramon Moore s previous books on the topic, it provides broad coverage of the subject as well as the historical perspective of one of the originators of modern interval analysis. The authors provide a hands-on introduction to INTLAB, a high-quality, comprehensive MATLAB toolbox for interval computations, making this the first interval analysis book that does with INTLAB what general numerical analysis texts do with MATLAB. Readers will find the following features of interest: elementary motivating examples and notes that help maximize the reader s chance of success in applying the techniques; exercises and hands-on MATLAB-based examples woven into the text; INTLAB-based examples and explanations integrated into the text, along with a comprehensive set of exercises and solutions, and an appendix with INTLAB commands; an extensive bibliography and appendices that will continue to be valuable resources once the reader is familiar with the subject; and a Web page with links to computational tools and other resources of interest. Audience: Introduction to Interval Analysis will be valuable to engineers and scientists interested in scientific computation, especially in reliability, effects of roundoff error, and automatic verification of results. The introductory material is particularly important for experts in global optimization and constraint solution algorithms. This book is suitable for introducing the subject to students in these areas. Contents: Preface; Chapter 1: Introduction; Chapter 2: The Interval Number System; Chapter 3: First Applications of Interval Arithmetic; Chapter 4: Further Properties of Interval Arithmetic; Chapter 5: Introduction to Interval Functions; Chapter 6: Interval Sequences; Chapter 7: Interval Matrices; Chapter 8: Interval Newton Methods; Chapter 9: Integration of Interval Functions; Chapter 10: Integral and Differential Equations; Chapter 11: Applications; Appendix A: Sets and Functions; Appendix B: Formulary; Appendix C: Hints for Selected Exercises; Appendix D: Internet Resources; Appendix E: INTLAB Commands and Functions; References; Index.

Introduction to Interval Analysis

The numerical methods employed in the solution of many scientific computing problems require the computation of derivatives of a function f: R{sup n} {yields} R{sup m}. Both the accuracy and the computational requirements of the derivative computation are usually of critical importance for the robustness and speed of the numerical method. ADIFOR (Automatic Differentiation In FORtran) is a source translation tool implemented using the data abstractions and program analysis capabilities of the ParaScope Parallel Programming Environment. ADIFOR accepts arbitrary Fortran-77 code defining the computation of a function and writes portable Fortran-77 code for the computation of its derivatives. In contrast to previous approaches, ADIFOR views automatic differentiation as a process of source translation that exploits computational context to reduce the cost of derivative computations. Experimental results show that ADIFOR can handle real-life codes, providing exact derivatives with a running time that is competitive with the standard divided-difference approximations of derivatives and which may perform orders of magnitude faster than divided-differences in cases. The computational scientist using ADIFOR is freed from worrying about the accurate and efficient computation of derivatives, even for complicated functions,'' and hence, is able to concentrate on the more important issues of algorithm design or system modeling.more » 35 refs.« less

ADIFOR: Fortran source translation for efficient derivatives

This is a bibliography of work related to interval arithmetic and validated computation. It represents the compilation of all works cited by the papers in this volume.

SCAN -98 Collected Bibliography

1 The reliability of the estimates for the location and the order of primary singularities is estimated by comparing two sets of estimates at the same stage instead of by comparing estimates from different stages 2 The system of nonlinear equations which must be solved for the location and order of the primary singularities at each stage is replaced by a linear system which is much easier to solve

On computing Darboux type series analyses

The COSY Infinity software package by Berz et al. is widely used in the beam physics community. We report execution-based testing of its interval and Taylor model arithmetics. The testing strategy is careful to avoid contamination by inevitable rounding errors. Tests were ported to Sun’s F95 and INTLAB. In each package, we uncovered violations of containment which have all been corrected by their authors. We encourage users of COSY and most other software packages to check author/vendor web sites regularly for possible updates and patches.

Interval Testing Strategies Applied to COSY's Interval and Taylor Model Arithmetic.

Forecasting Natural Gas Demand: The Role of Physical and Economic Factors

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