Multidimensional Costas Arrays and Their Periodicity

A novel higher-dimensional definition for Costas arrays is introduced. This definition works for arbitrary dimensions and avoids some limitations of previous definitions. Some non-existence results are presented for multidimensional Costas arrays preserving the Costas condition when the array is extended periodically throughout the whole space. In particular, it is shown that three-dimensional arrays with this property must have the least possible order; extending an analogous two-dimensional result by H. Taylor. Said result is conjectured to extend for Costas arrays of arbitrary dimensions

Shift-Symmetric Configurations in Two-Dimensional Cellular Automata: Irreversibility, Insolvability, and Enumeration

The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have long been a central focus of complexity science and physics. To better grasp and understand symmetry of configurations in decentralized toroidal architectures, we employ group-theoretic methods, which allow us to identify and enumerate these inputs, and argue about irreversible system behaviors with undesired effects on many computational problems. The concept of so-called configuration shift-symmetry is applied to two-dimensional cellular automata as an ideal model of computation. Regardless of the transition function, the results show the universal insolvability of crucial distributed tasks, such as leader election, pattern recognition, hashing, and encryption. By using compact enumeration formulas and bounding the number of shift-symmetric configurations for a given lattice size, we efficiently calculate the probability of a configuration being shift-symmetric for a uniform or density-uniform distribution. Further, we devise an algorithm detecting the presence of shift-symmetry in a configuration. Given the resource constraints, the enumeration and probability formulas can directly help to lower the minimal expected error and provide recommendations for system's size and initialization. Besides cellular automata, the shift-symmetry analysis can be used to study the non-linear behavior in various synchronous rule-based systems that include inference engines, Boolean networks, neural networks, and systolic arrays.Comment: 22 pages, 9 figures, 2 appendice

Index to nasa tech briefs, issue number 2

Annotated bibliography on technological innovations in NASA space program

A Concept for an STJ-based Spectrograph

We describe a multi-order spectrograph concept suitable for 8m-class telescopes, using the intrinsic spectral resolution of Superconducting Tunneling Junction detectors to sort the spectral orders. The spectrograph works at low orders, 1-5 or 1-6, and provides spectral coverage with a resolving power of R~8000 from the atmospheric cutoff at 320 nm to the long wavelength end of the infrared H or K band at 1800 nm or 2400 nm. We calculate that the spectrograph would provide substantial throughput and wavelength coverage, together with high time resolution and sufficient dynamic range. The concept uses currently available technology, or technologies with short development horizons, restricting the spatial sampling to two linear arrays; however an upgrade path to provide more spatial sampling is identified. All of the other challenging aspects of the concept - the cryogenics, thermal baffling and magnetic field biasing - are identified as being feasible.Comment: Accepted in Monthly Notices of the Royal Astronomical Society, 12 pages with 10 figure

The combinatorics of binary arrays

This paper gives an account of the combinatorics of binary arrays, mainly concerning their randomness properties. In many cases the problem reduces to the investigation on difference sets.postprin