On the Parity Problem in One-Dimensional Cellular Automata

We consider the parity problem in one-dimensional, binary, circular cellular automata: if the initial configuration contains an odd number of 1s, the lattice should converge to all 1s; otherwise, it should converge to all 0s. It is easy to see that the problem is ill-defined for even-sized lattices (which, by definition, would never be able to converge to 1). We then consider only odd lattices. We are interested in determining the minimal neighbourhood that allows the problem to be solvable for any initial configuration. On the one hand, we show that radius 2 is not sufficient, proving that there exists no radius 2 rule that can possibly solve the parity problem from arbitrary initial configurations. On the other hand, we design a radius 4 rule that converges correctly for any initial configuration and we formally prove its correctness. Whether or not there exists a radius 3 rule that solves the parity problem remains an open problem.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

Research in the Aloha system

The Aloha system was studied and developed and extended to advanced forms of computer communications networks. Theoretical and simulation studies of Aloha type radio channels for use in packet switched communications networks were performed. Improved versions of the Aloha communications techniques and their extensions were tested experimentally. A packet radio repeater suitable for use with the Aloha system operational network was developed. General studies of the organization of multiprocessor systems centered on the development of the BCC 500 computer were concluded

Work with an expert system

Includes bibliographical references.For my Capstone, I assisted Computer Science Instructor Kathi Davis with her implementation of an expert system to translate a conventional file system into a commercial database system. The main purpose of her expert system is to give users of conventional file systems a tool to use in the conversion to commercial database systems; an easy tool that will make the process less painful than it is today. The conventional file system is first translated into a conceptual Entity-Relationship model and this conceptual model is then translated into a commercial database system. The Entity-Relationship conceptual model assists the user in understanding what currently exists within his environment and helps in forming a new conceptual model of the desired database environment.B.S. (Bachelor of Science

Tensor network states and algorithms in the presence of a global SU(2) symmetry

The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to select a specific symmetry sector (e.g. with a given particle number or spin), to ensure the exact preservation of total charge, and to significantly reduce computational costs. Compared to the case of a generic tensor network, the practical implementation of symmetries in the MPS is simplified by the fact that tensors only have three indices (they are trivalent, just as the Clebsch-Gordan coefficients of the symmetry group) and are organized as a one-dimensional array of tensors, without closed loops. Instead, a more complex tensor network, one where tensors have a larger number of indices and/or a more elaborate network structure, requires a more general treatment. In two recent papers, namely (i) [Phys. Rev. A 82, 050301 (2010)] and (ii) [Phys. Rev. B 83, 115125 (2011)], we described how to incorporate a global internal symmetry into a generic tensor network algorithm based on decomposing and manipulating tensors that are invariant under the symmetry. In (i) we considered a generic symmetry group G that is compact, completely reducible and multiplicity free, acting as a global internal symmetry. Then in (ii) we described the practical implementation of Abelian group symmetries. In this paper we describe the implementation of non-Abelian group symmetries in great detail and for concreteness consider an SU(2) symmetry. Our formalism can be readily extended to more exotic symmetries associated with conservation of total fermionic or anyonic charge. As a practical demonstration, we describe the SU(2)-invariant version of the multi-scale entanglement renormalization ansatz and apply it to study the low energy spectrum of a quantum spin chain with a global SU(2) symmetry.Comment: 32 pages, 37 figure

Systematic Low-Energy Effective Field Theory for Electron-Doped Antiferromagnets

In contrast to hole-doped systems which have hole pockets centered at $(\pm \frac{\pi}{2a},\pm \frac{\pi}{2a})$, in lightly electron-doped antiferromagnets the charged quasiparticles reside in momentum space pockets centered at $(\frac{\pi}{a},0)$ or $(0,\frac{\pi}{a})$. This has important consequences for the corresponding low-energy effective field theory of magnons and electrons which is constructed in this paper. In particular, in contrast to the hole-doped case, the magnon-mediated forces between two electrons depend on the total momentum $\vec P$ of the pair. For $\vec P = 0$ the one-magnon exchange potential between two electrons at distance $r$ is proportional to $1/r^4$, while in the hole case it has a $1/r^2$ dependence. The effective theory predicts that spiral phases are absent in electron-doped antiferromagnets.Comment: 25 pages, 7 figure

Index to NASA Tech Briefs, 1974

The following information was given for 1974: (1) abstracts of reports dealing with new technology derived from the research and development activities of NASA or the U.S. Atomic Energy Commission, arranged by subjects: electronics/electrical, electronics/electrical systems, physical sciences, materials/chemistry, life sciences, mechanics, machines, equipment and tools, fabrication technology, and computer programs, (2) indexes for the above documents: subject, personal author, originating center

Energy: A continuing bibliography with indexes, supplement 2

This bibliography lists 405 reports, articles, and other documents introduced into the NASA Scientific and Technical Information System from April 1, 1974 through June 30, 1974

Management: A continuing literature survey with indexes, March 1975

A special bibliography listing 1,064 reports, articles, and other documents introduced into the NASA Scientific and Technical Information System in 1974 is presented