Microstructural enrichment functions based on stochastic Wang tilings

This paper presents an approach to constructing microstructural enrichment functions to local fields in non-periodic heterogeneous materials with applications in Partition of Unity and Hybrid Finite Element schemes. It is based on a concept of aperiodic tilings by the Wang tiles, designed to produce microstructures morphologically similar to original media and enrichment functions that satisfy the underlying governing equations. An appealing feature of this approach is that the enrichment functions are defined only on a small set of square tiles and extended to larger domains by an inexpensive stochastic tiling algorithm in a non-periodic manner. Feasibility of the proposed methodology is demonstrated on constructions of stress enrichment functions for two-dimensional mono-disperse particulate media.Comment: 27 pages, 12 figures; v2: completely re-written after the first revie

Applied Mathematics at the U.S. Department of Energy: Past, Present and a View to the Future

Over the past half-century, the Applied Mathematics program in the U.S. Department of Energy's Office of Advanced Scientific Computing Research has made significant, enduring advances in applied mathematics that have been essential enablers of modern computational science. Motivated by the scientific needs of the Department of Energy and its predecessors, advances have been made in mathematical modeling, numerical analysis of differential equations, optimization theory, mesh generation for complex geometries, adaptive algorithms and other important mathematical areas. High-performance mathematical software libraries developed through this program have contributed as much or more to the performance of modern scientific computer codes as the high-performance computers on which these codes run. The combination of these mathematical advances and the resulting software has enabled high-performance computers to be used for scientific discovery in ways that could only be imagined at the program's inception. Our nation, and indeed our world, face great challenges that must be addressed in coming years, and many of these will be addressed through the development of scientific understanding and engineering advances yet to be discovered. The U.S. Department of Energy (DOE) will play an essential role in providing science-based solutions to many of these problems, particularly those that involve the energy, environmental and national security needs of the country. As the capability of high-performance computers continues to increase, the types of questions that can be answered by applying this huge computational power become more varied and more complex. It will be essential that we find new ways to develop and apply the mathematics necessary to enable the new scientific and engineering discoveries that are needed. In August 2007, a panel of experts in applied, computational and statistical mathematics met for a day and a half in Berkeley, California to understand the mathematical developments required to meet the future science and engineering needs of the DOE. It is important to emphasize that the panelists were not asked to speculate only on advances that might be made in their own research specialties. Instead, the guidance this panel was given was to consider the broad science and engineering challenges that the DOE faces and identify the corresponding advances that must occur across the field of mathematics for these challenges to be successfully addressed. As preparation for the meeting, each panelist was asked to review strategic planning and other informational documents available for one or more of the DOE Program Offices, including the Offices of Science, Nuclear Energy, Fossil Energy, Environmental Management, Legacy Management, Energy Efficiency & Renewable Energy, Electricity Delivery & Energy Reliability and Civilian Radioactive Waste Management as well as the National Nuclear Security Administration. The panelists reported on science and engineering needs for each of these offices, and then discussed and identified mathematical advances that will be required if these challenges are to be met. A review of DOE challenges in energy, the environment and national security brings to light a broad and varied array of questions that the DOE must answer in the coming years. A representative subset of such questions includes: (1) Can we predict the operating characteristics of a clean coal power plant? (2) How stable is the plasma containment in a tokamak? (3) How quickly is climate change occurring and what are the uncertainties in the predicted time scales? (4) How quickly can an introduced bio-weapon contaminate the agricultural environment in the US? (5) How do we modify models of the atmosphere and clouds to incorporate newly collected data of possibly of new types? (6) How quickly can the United States recover if part of the power grid became inoperable? (7) What are optimal locations and communication protocols for sensing devices in a remote-sensing network? (8) How can new materials be designed with a specified desirable set of properties? In comparing and contrasting these and other questions of importance to DOE, the panel found that while the scientific breadth of the requirements is enormous, a central theme emerges: Scientists are being asked to identify or provide technology, or to give expert analysis to inform policy-makers that requires the scientific understanding of increasingly complex physical and engineered systems. In addition, as the complexity of the systems of interest increases, neither experimental observation nor mathematical and computational modeling alone can access all components of the system over the entire range of scales or conditions needed to provide the required scientific understanding

Extended amygdala-parabrachial circuits alter threat assessment and regulate feeding

An animal\u27s evolutionary success depends on the ability to seek and consume foods while avoiding environmental threats. However, how evolutionarily conserved threat detection circuits modulate feeding is unknown. In mammals, feeding and threat assessment are strongly influenced by the parabrachial nucleus (PBN), a structure that responds to threats and inhibits feeding. Here, we report that the PBN receives dense inputs from two discrete neuronal populations in the bed nucleus of the stria terminalis (BNST), an extended amygdala structure that encodes affective information. Using a series of complementary approaches, we identify opposing BNST-PBN circuits that modulate neuropeptide-expressing PBN neurons to control feeding and affective states. These previously unrecognized neural circuits thus serve as potential nodes of neural circuitry critical for the integration of threat information with the intrinsic drive to feed

Stimulant Reduction Intervention using Dosed Exercise (STRIDE) - CTN 0037: Study protocol for a randomized controlled trial

Background: There is a need for novel approaches to the treatment of stimulant abuse and dependence. Clinical data examining the use of exercise as a treatment for the abuse of nicotine, alcohol, and other substances suggest that exercise may be a beneficial treatment for stimulant abuse, with direct effects on decreased use and craving. In addition, exercise has the potential to improve other health domains that may be adversely affected by stimulant use or its treatment, such as sleep disturbance, cognitive function, mood, weight gain, quality of life, and anhedonia, since it has been shown to improve many of these domains in a number of other clinical disorders. Furthermore, neurobiological evidence provides plausible mechanisms by which exercise could positively affect treatment outcomes. The current manuscript presents the rationale, design considerations, and study design of the National Institute on Drug Abuse (NIDA) Clinical Trials Network (CTN) CTN-0037 Stimulant Reduction Intervention using Dosed Exercise (STRIDE) study. Methods/Design: STRIDE is a multisite randomized clinical trial that compares exercise to health education as potential treatments for stimulant abuse or dependence. This study will evaluate individuals diagnosed with stimulant abuse or dependence who are receiving treatment in a residential setting. Three hundred and thirty eligible and interested participants who provide informed consent will be randomized to one of two treatment arms: Vigorous Intensity High Dose Exercise Augmentation (DEI) or Health Education Intervention Augmentation (HEI). Both groups will receive TAU (i.e., usual care). The treatment arms are structured such that the quantity of visits is similar to allow for equivalent contact between groups. In both arms, participants will begin with supervised sessions 3 times per week during the 12-week acute phase of the study. Supervised sessions will be conducted as one-on-one (i.e., individual) sessions, although other participants may be exercising at the same time. Following the 12-week acute phase, participants will begin a 6-month continuation phase during which time they will attend one weekly supervised DEI or HEI session

Development and application of a Japanese model of the WHO fracture risk assessment tool (FRAX™)

SUMMARY: The present study estimated the 10-year probability using the Japanese version of WHO fracture risk assessment tool (FRAX) in order to determine fracture probabilities that correspond to intervention thresholds currently used in Japan and to resolve some issues for its use in Japan. INTRODUCTION: The objective of the present study was to evaluate a Japanese version of the WHO fracture risk assessment (FRAX) tool to compute 10-year probabilities of osteoporotic fracture in Japanese men and women. Since lumbar spine bone mineral density (BMD) is used preferentially as a site for assessment, and densitometers use Japanese reference data, a second aim was to investigate the suitability and impact of this practice in Japan. METHODS: Fracture probabilities were computed from published data on the fracture and death hazards in Japan. Probabilities took account of age, sex, the presence of clinical risk factors and femoral neck BMD. Fracture probabilities were determined that were equivalent to intervention thresholds currently used in Japan. The difference between T-scores derived from international reference data and that using Japanese-specific normal ranges was estimated from published sources. The gradient of risk of BMD for fracture in Japan was compared to that for BMD at the lumbar spine in the Hiroshima cohort. RESULTS: The 10-year probabilities of a major osteoporosis-related fracture that corresponded to current intervention thresholds ranged from approximately 5% at the age of 50 years to more than 20% at the age of 80 years. The use of femoral neck BMD predicts fracture as well as or better than BMD tests at the lumbar spine. There were small differences in T-scores between those used for the model and those derived from a Japanese reference population. CONCLUSIONS: The FRAX mark tool has been used to determine possible thresholds for therapeutic intervention, based on equivalence of risk with current guidelines. The approach will need to be supported by appropriate health economic analyses. Femoral neck BMD is suitable for the prediction of fracture risk among Japanese. However, when applying the FRAX model to Japan, T-scores and Z-scores should be converted to those derived from the international reference

An Updated Algorithm for the Generation of Neutral Landscapes by Spectral Synthesis

Background: Patterns that arise from an ecological process can be driven as much from the landscape over which the process is run as it is by some intrinsic properties of the process itself. The disentanglement of these effects is aided if it possible to run models of the process over artificial landscapes with controllable spatial properties. A number of different methods for the generation of so-called ‘neutral landscapes’ have been developed to provide just such a tool. Of these methods, a particular class that simulate fractional Brownian motion have shown particular promise. The existing methods of simulating fractional Brownian motion suffer from a number of problems however: they are often not easily generalisable to an arbitrary number of dimensions and produce outputs that can exhibit some undesirable artefacts. Methodology: We describe here an updated algorithm for the generation of neutral landscapes by fractional Brownian motion that do not display such undesirable properties. Using Monte Carlo simulation we assess the anisotropic properties of landscapes generated using the new algorithm described in this paper and compare it against a popular benchmark algorithm. Conclusion/Significance: The results show that the existing algorithm creates landscapes with values strongly correlated in the diagonal direction and that the new algorithm presented here corrects this artefact. A number of extensions of the algorithm described here are also highlighted: we describe how the algorithm can be employed to generate landscapes that display different properties in different dimensions and how they can be combined with an environmental gradient to produce landscapes that combine environmental variation at the local and macro scales