An Algebraic Framework for Discrete Tomography: Revealing the Structure of Dependencies

Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is typically a small discrete set. In this paper we present a framework for studying these problems from an algebraic perspective, based on Ring Theory and Commutative Algebra. A principal advantage of this abstract setting is that a vast body of existing theory becomes accessible for solving Discrete Tomography problems. We provide proofs of several new results on the structure of dependencies between projections, including a discrete analogon of the well-known Helgason-Ludwig consistency conditions from continuous tomography.Comment: 20 pages, 1 figure, updated to reflect reader inpu

Combinatorics and Geometry of Transportation Polytopes: An Update

A transportation polytope consists of all multidimensional arrays or tables of non-negative real numbers that satisfy certain sum conditions on subsets of the entries. They arise naturally in optimization and statistics, and also have interest for discrete mathematics because permutation matrices, latin squares, and magic squares appear naturally as lattice points of these polytopes. In this paper we survey advances on the understanding of the combinatorics and geometry of these polyhedra and include some recent unpublished results on the diameter of graphs of these polytopes. In particular, this is a thirty-year update on the status of a list of open questions last visited in the 1984 book by Yemelichev, Kovalev and Kravtsov and the 1986 survey paper of Vlach.Comment: 35 pages, 13 figure

Microstructural Quantification, Property Prediction, and Stochastic Reconstruction of Heterogeneous Materials Using Limited X-Ray Tomography Data

abstract: An accurate knowledge of the complex microstructure of a heterogeneous material is crucial for quantitative structure-property relations establishment and its performance prediction and optimization. X-ray tomography has provided a non-destructive means for microstructure characterization in both 3D and 4D (i.e., structural evolution over time). Traditional reconstruction algorithms like filtered-back-projection (FBP) method or algebraic reconstruction techniques (ART) require huge number of tomographic projections and segmentation process before conducting microstructural quantification. This can be quite time consuming and computationally intensive. In this thesis, a novel procedure is first presented that allows one to directly extract key structural information in forms of spatial correlation functions from limited x-ray tomography data. The key component of the procedure is the computation of a “probability map”, which provides the probability of an arbitrary point in the material system belonging to specific phase. The correlation functions of interest are then readily computed from the probability map. Using effective medium theory, accurate predictions of physical properties (e.g., elastic moduli) can be obtained. Secondly, a stochastic optimization procedure that enables one to accurately reconstruct material microstructure from a small number of x-ray tomographic projections (e.g., 20 - 40) is presented. Moreover, a stochastic procedure for multi-modal data fusion is proposed, where both X-ray projections and correlation functions computed from limited 2D optical images are fused to accurately reconstruct complex heterogeneous materials in 3D. This multi-modal reconstruction algorithm is proved to be able to integrate the complementary data to perform an excellent optimization procedure, which indicates its high efficiency in using limited structural information. Finally, the accuracy of the stochastic reconstruction procedure using limited X-ray projection data is ascertained by analyzing the microstructural degeneracy and the roughness of energy landscape associated with different number of projections. Ground-state degeneracy of a microstructure is found to decrease with increasing number of projections, which indicates a higher probability that the reconstructed configurations match the actual microstructure. The roughness of energy landscape can also provide information about the complexity and convergence behavior of the reconstruction for given microstructures and projection number.Dissertation/ThesisDoctoral Dissertation Mechanical Engineering 201

Materials sciences programs, Fiscal year 1997

The Division of Materials Sciences is responsible for basic research and research facilities in materials science topics important to the mission of the Department of Energy. The programmatic divisions under the Office of Basic Energy Sciences are Chemical Sciences, Engineering and Geosciences, and Energy Biosciences. Materials Science is an enabling technology. The performance parameters, economics, environmental acceptability and safety of all energy generation, conversion, transmission and conservation technologies are limited by the properties and behavior of materials. The Materials Sciences programs develop scientific understanding of the synergistic relationship among synthesis, processing, structure, properties, behavior, performance and other characteristics of materials. Emphasis is placed on the development of the capability to discover technologically, economically, and environmentally desirable new materials and processes, and the instruments and national user facilities necessary for achieving such progress. Materials Sciences subfields include: physical metallurgy, ceramics, polymers, solid state and condensed matter physics, materials chemistry, surface science and related disciplines where the emphasis is on the science of materials. This report includes program descriptions for 517 research programs including 255 at 14 DOE National Laboratories, 262 research grants (233 of which are at universities), and 29 Small Business Innovation Research Grants. Five cross-cutting indices located at the rear of this book identify all 517 programs according to principal investigator(s), materials, techniques, phenomena, and environment

Reports to the President

A compilation of annual reports for the 1989-1990 academic year, including a report from the President of the Massachusetts Institute of Technology, as well as reports from the academic and administrative units of the Institute. The reports outline the year's goals, accomplishments, honors and awards, and future plans

Microgravity Science and Applications: Program Tasks and Bibliography for Fiscal Year 1996

NASA's Microgravity Science and Applications Division (MSAD) sponsors a program that expands the use of space as a laboratory for the study of important physical, chemical, and biochemical processes. The primary objective of the program is to broaden the value and capabilities of human presence in space by exploiting the unique characteristics of the space environment for research. However, since flight opportunities are rare and flight research development is expensive, a vigorous ground-based research program, from which only the best experiments evolve, is critical to the continuing strength of the program. The microgravity environment affords unique characteristics that allow the investigation of phenomena and processes that are difficult or impossible to study an Earth. The ability to control gravitational effects such as buoyancy driven convection, sedimentation, and hydrostatic pressures make it possible to isolate phenomena and make measurements that have significantly greater accuracy than can be achieved in normal gravity. Space flight gives scientists the opportunity to study the fundamental states of physical matter-solids, liquids and gasses-and the forces that affect those states. Because the orbital environment allows the treatment of gravity as a variable, research in microgravity leads to a greater fundamental understanding of the influence of gravity on the world around us. With appropriate emphasis, the results of space experiments lead to both knowledge and technological advances that have direct applications on Earth. Microgravity research also provides the practical knowledge essential to the development of future space systems. The Office of Life and Microgravity Sciences and Applications (OLMSA) is responsible for planning and executing research stimulated by the Agency's broad scientific goals. OLMSA's Microgravity Science and Applications Division (MSAD) is responsible for guiding and focusing a comprehensive program, and currently manages its research and development tasks through five major scientific areas: biotechnology, combustion science, fluid physics, fundamental physics, and materials science. FY 1996 was an important year for MSAD. NASA continued to build a solid research community for the coming space station era. During FY 1996, the NASA Microgravity Research Program continued investigations selected from the 1994 combustion science, fluid physics, and materials science NRAS. MSAD also released a NASA Research Announcement in microgravity biotechnology, with more than 130 proposals received in response. Selection of research for funding is expected in early 1997. The principal investigators chosen from these NRAs will form the core of the MSAD research program at the beginning of the space station era. The third United States Microgravity Payload (USMP-3) and the Life and Microgravity Spacelab (LMS) missions yielded a wealth of microgravity data in FY 1996. The USMP-3 mission included a fluids facility and three solidification furnaces, each designed to examine a different type of crystal growth