The Mathematical Sciences in 2025 (2013) / Chapter Skim
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Appendix D: Examples of the Mathematical Sciences Support of Science and Engineering
Appendix D: Examples of the Mathematical Sciences Support of Science and Engineering
Pages 175-189
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From page 175... ...
This report poses several major challenges for that field that in turn pose associated challenges for the mathematical sciences. For example, Challenge 1: Understanding the structure and dynamics of the Sun's inte rior, the generation of solar magnetic fields, the origin of the solar cycle, the causes of solar activity, and the structure and dynamics of the corona.1 This challenge will require advances in multiscale methods and complex simulations involving turbulence.
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From page 176... ...
The program advocates both the development of coupled global models and the synergistic investigation of well-chosen, distinct theoretical problems. For major advances to be made in understanding coupling complexity in space physics, sophisticated computational tools, fundamental theoretical analysis, and state-of-the-art data analysis must all be integrated under a single umbrella program.2 The coming decade will see the availability of large space physics databases that will have to be integrated into physics-based numerical models.
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From page 177... ...
The mathematical model consists of the relativistic equations of motion for particles, plus Maxwell's equations for the electric and magnetic fields they induce (a set of coupled first-order PDEs)
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From page 178... ...
Following is a list of 11 of those challenges that depend on corresponding advances in the mathematical sciences, along with thoughts about the particular mathematical science research that will be needed. • Make solar energy economical.
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From page 179... ...
Life-cycle analysis.7 It is striking that six of the seven items are inextricably linked with the mathematical sciences. While it is obvious that Item 3 depends on mathematical advances and Item 4 relies on statistical concepts and analyses, Items 1, 2, 5, and 7 are all dependent on advances in simulation capabilities that have enabled them to represent processes of ever-increasing complexity and fidelity.
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From page 180... ...
. Current research in the computer simulation of physical systems should be expanded to include the simulation and modeling of proposed energy-saving technologies, as well as advances in the basic techniques of simulation and modeling.9 Second, the mathematical sciences underpin cryptography and provide tools for systems analyses: The federal government should invest in a national, long-term, multi agency research initiative on NIT that assures both the security and the robustness of cyber-infrastructure -- o discover more effective ways to build trustworthy computing and t communications systems, -- o continue to develop new NIT defense mechanisms for today's infra t structure, and most importantly, -- o develop fundamentally new approaches for the design of the underly t ing architecture of our cyber-infrastructure so that it can be made truly resilient to cyber-attack, natural disaster, and inadvertent failure.10 Third, the mathematical sciences are strongly entwined with R&D for privacy protection, large-scale data analysis, high-performance computing, and algorithms: The federal government must increase investment in those fundamental NIT research frontiers that will accelerate progress across a broad range of priorities .
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From page 181... ...
The world is completely different today: It is full of diverse and overlapping networks, including the Internet, the World Wide Web, wireless networks operated by multiple service providers, and social networks, as well as networks arising in scientific and engineering applications, such as networks that describe intra- and intercellular processes in biology. Modern technologies built around the Internet are consumers of mathematics: for example, many innovations at Google, such as search, learning, and trend discovery, are based on the mathematical sciences.
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From page 182... ...
ILLUSTRATIVE DEMANDS FROM BIOLOGY The 2009 NRC report A New Biology for the 21st Century13 had a great deal to say about emerging opportunities that will rely on advances in the mathematical sciences. Following are selected quotations: • undamental understanding will require .
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From page 183... ...
This integration has the potential to generate breakthroughs in our ability to monitor ecosystem function, identify ecosystems at risk, and develop effective interventions to protect and restore ecosystem function.15 • ecent advances are enabling biomedical researchers to begin to study R humans more comprehensively, as individuals whose health is deter mined by the interactions between these complex structural and meta bolic networks. On the path from genotype to phenotype, each network is interlocked with many others through intricate interfaces, such as feedback loops.
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From page 184... ...
Algorithms from statistics and machine learning are applied to genome-wide association studies and to prob lems of classification, clustering and feature selection arising in the analysis of large-scale gene expression data.19 As another illustration, the 2008 NRC report The Potential Impact of High-End Capability Computing on Four Illustrative Fields of Science and Engineering20 identified essential challenges for evolutionary biology, a number of which are strongly mathematical. Following are selected quotations: • tandard phylogenetic analysis comparing the possible evolutionary S relationships between two species can be done using the method of maximum parsimony, which assumes that the simplest answer is the best one, or using a model-based approach.
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From page 185... ...
In model-based ap proaches, in particular, such procedures are computationally intensive, and the model structure scales significantly with the size of the number of taxa and the heterogeneity of the data. In addition, more attention is being paid to statistical models of molecular evolution.22 • serious major computational challenge is to generate qualitative and A quantitative models of development as a necessary prelude to applying sophisticated evolutionary models to understand how developmental processes evolve.
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From page 186... ...
To compare dozens of related sequences, phylogenetic methods must be integrated with signal detection.26 ILLUSTRATIVE DEMANDS FROM MEDICINE There is increasing awareness in medicine of the benefits from collaboration with mathematical scientists, including in areas where past focus has 24 Ibid., pp.
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From page 187... ...
The role of the mathematical sciences in medicine has become so important that one can provide only a few examples. One example is a program of the Office of Physcal Sciences Oncology,27 funded by the National Cancer Institute, to support innovative approaches to understanding and controlling cancer, which is explicitly seeking teams that may include mathematical scientists.
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From page 188... ...
As an example of the latter, Nieuwenhuis et al.30 reviewed 513 behavioral, systems, and cognitive neuroscience articles in five top-ranking journals, looking for articles that specifically compared two experimental effects to see if they differed significantly. Out of the 157 articles that focused on such a comparison, they found that 78 used the correct statistical procedure of testing whether the difference of the two effects is significantly different from 0; 79 used a blatantly incorrect procedure.
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From page 189... ...
This problem, often called the "multiplicity" or "multiple testing" problem, is of central importance not only in drug development, but also in microarray and other bioinformatic analyses, syndromic surveillance, highenergy physics, high-throughput screening, subgroup analysis, and indeed any area of science facing an inundation of data (which most of them are)
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