Efficient indexing of necklaces and irreducible polynomials over finite fields

We study the problem of indexing irreducible polynomials over finite fields, and give the first efficient algorithm for this problem. Specifically, we show the existence of poly(n, log q)-size circuits that compute a bijection between {1, ... , |S|} and the set S of all irreducible, monic, univariate polynomials of degree n over a finite field F_q. This has applications in pseudorandomness, and answers an open question of Alon, Goldreich, H{\aa}stad and Peralta[AGHP]. Our approach uses a connection between irreducible polynomials and necklaces ( equivalence classes of strings under cyclic rotation). Along the way, we give the first efficient algorithm for indexing necklaces of a given length over a given alphabet, which may be of independent interest

Integration of remote sensing and surface geophysics in the detection of faults

Remote sensing was included in a comprehensive investigation of the use of geophysical techniques to aid in underground mine placement. The primary objective was to detect faults and slumping, features which, due to structural weakness and excess water, cause construction difficulties and safety hazards in mine construction. Preliminary geologic reconnaissance was performed on a potential site for an underground oil shale mine in the Piceance Creek Basin of Colorado. LANDSAT data, black and white aerial photography and 3 cm radar imagery were obtained. LANDSAT data were primarily used in optical imagery and digital tape forms, both of which were analyzed and enhanced by computer techniques. The aerial photography and radar data offered supplemental information. Surface linears in the test area were located and mapped principally from LANDSAT data. A specific, relatively wide, linear pointed directly toward the test site, but did not extend into it. Density slicing, ratioing, and edge enhancement of the LANDSAT data all indicated the existence of this linear. Radar imagery marginally confirmed the linear, while aerial photography did not confirm it

Domino Tatami Covering is NP-complete

A covering with dominoes of a rectilinear region is called \emph{tatami} if no four dominoes meet at any point. We describe a reduction from planar 3SAT to Domino Tatami Covering. As a consequence it is NP-complete to decide whether there is a perfect matching of a graph that meets every 4-cycle, even if the graph is restricted to be an induced subgraph of the grid-graph. The gadgets used in the reduction were discovered with the help of a SAT-solver.Comment: 10 pages, accepted at The International Workshop on Combinatorial Algorithms (IWOCA) 201

Syntactic View of Sigma-Tau Generation of Permutations

We give a syntactic view of the Sawada-Williams $(\sigma,\tau)$-generation of permutations. The corresponding sequence of $\sigma-\tau$-operations, of length $n!-1$ is shown to be highly compressible: it has $O(n^2\log n)$ bit description. Using this compact description we design fast algorithms for ranking and unranking permutations.Comment: accepted on LATA201

Normal, Abby Normal, Prefix Normal

A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present results about the number $pnw(n)$ of prefix normal words of length $n$, showing that $pnw(n) =\Omega\left(2^{n - c\sqrt{n\ln n}}\right)$ for some $c$ and $pnw(n) = O \left(\frac{2^n (\ln n)^2}{n}\right)$. We introduce efficient algorithms for testing the prefix normal property and a "mechanical algorithm" for computing prefix normal forms. We also include games which can be played with prefix normal words. In these games Alice wishes to stay normal but Bob wants to drive her "abnormal" -- we discuss which parameter settings allow Alice to succeed.Comment: Accepted at FUN '1

Topological self-similarity on the random binary-tree model

Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary tree, and derive a recursive equation about branch orders. As an application of the analysis, topological self-similarity and its generalization is proved in an asymptotic sense. Also, some important examples are presented

Patterns within Patterns within the Smart Living Experience

Modern technology is increasingly being employed to create a “smart” living experience. These “smart” technology entities are producing copious of amounts data, which in turn rely on increased storage, distribution and computation capacity to manage the data. Depending on the scenario, the diversity of piecemeal solutions almost reflects the diversity of problems they address. But some solutions can be reapplied. In the field of computing, design patterns can provide a general, reusable solution to commonly recurring problems within a given context through software design. This work seeks to determine the core elements of a technology-independent design pattern format and an open software framework can be developed to capture, share and redeploy existing successful and reusable strategies for commonly encountered smart environment use cases. Applying in areas such as assistive technology, energy management and environmental monitoring. The underpinning notion of this paper is to introduce “how, where and why” a rule set based in “design pattern” format could contribute to describe a general “understanding” of given cases in the smart environment domain, as well as allow different processes to collaborate with each other

GBA variants in REM sleep behavior disorder: a multicenter study

To study the role of GBA variants in the risk for isolated rapid-eye-movement (REM)-sleep behavior disorder (iRBD) and conversion to overt neurodegeneration