Families of Small Regular Graphs of Girth 5

In this paper we obtain $(q+3)$--regular graphs of girth 5 with fewer vertices than previously known ones for $q=13,17,19$ and for any prime $q \ge 23$ performing operations of reductions and amalgams on the Levi graph $B_q$ of an elliptic semiplane of type ${\cal C}$. We also obtain a 13-regular graph of girth 5 on 236 vertices from $B_{11}$ using the same technique

High-precision frequency measurements: indispensable tools at the core of the molecular-level analysis of complex systems

This perspective article provides an assessment of the state-of-the-art in the molecular-resolution analysis of complex organic materials. These materials can be divided into biomolecules in complex mixtures (which are amenable to successful separation into unambiguously defined molecular fractions) and complex nonrepetitive materials (which cannot be purified in the conventional sense because they are even more intricate). Molecular-level analyses of these complex systems critically depend on the integrated use of high-performance separation, high-resolution organic structural spectroscopy and mathematical data treatment. At present, only high-precision frequency-derived data exhibit sufficient resolution to overcome the otherwise common and detrimental effects of intrinsic averaging, which deteriorate spectral resolution to the degree of bulk-level rather than molecular-resolution analysis. High-precision frequency measurements are integral to the two most influential organic structural spectroscopic methods for the investigation of complex materials—NMR spectroscopy (which provides unsurpassed detail on close-range molecular order) and FTICR mass spectrometry (which provides unrivalled resolution)—and they can be translated into isotope-specific molecular-resolution data of unprecedented significance and richness. The quality of this standalone de novo molecular-level resolution data is of unparalleled mechanistic relevance and is sufficient to fundamentally advance our understanding of the structures and functions of complex biomolecular mixtures and nonrepetitive complex materials, such as natural organic matter (NOM), aerosols, and soil, plant and microbial extracts, all of which are currently poorly amenable to meaningful target analysis. The discrete analytical volumetric pixel space that is presently available to describe complex systems (defined by NMR, FT mass spectrometry and separation technologies) is in the range of 108–14 voxels, and is therefore capable of providing the necessary detail for a meaningful molecular-level analysis of very complex mixtures. Nonrepetitive complex materials exhibit mass spectral signatures in which the signal intensity often follows the number of chemically feasible isomers. This suggests that even the most strongly resolved FTICR mass spectra of complex materials represent simplified (e.g. isomer-filtered) projections of structural space

High girth column-weight-two LDPC codes based on distance graphs

Copyright © 2007 G. Malema and M. Liebelt. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.LDPC codes of column weight of two are constructed from minimal distance graphs or cages. Distance graphs are used to represent LDPC code matrices such that graph vertices that represent rows and edges are columns. The conversion of a distance graph into matrix form produces an adjacency matrix with column weight of two and girth double that of the graph. The number of 1's in each row (row weight) is equal to the degree of the corresponding vertex. By constructing graphs with different vertex degrees, we can vary the rate of corresponding LDPC code matrices. Cage graphs are used as examples of distance graphs to design codes with different girths and rates. Performance of obtained codes depends on girth and structure of the corresponding distance graphs.Gabofetswe Malema and Michael Liebel

Quasi-cyclic LDPC codes of column-weight two using a search algorithm

Copyright © 2007 G. Malema and M. Liebelt. This is an Open Access article distributed under the Creative Commons Attributions License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This article introduces a search algorithm for constructing quasi-cyclic LDPC codes of column-weight two. To obtain a submatrix structure, rows are divided into groups of equal sizes. Rows in a group are connected in their numerical order to obtain a cyclic structure. Two rows forming a column must be at a specified distance from each other to obtain a given girth. The search for rows satisfying the distance is done sequentially or randomly. Using the proposed algorithm regular and irregular column-weight-two codes are obtained over a wide range of girths, rates, and lengths. The algorithm, which has a complexity linear with respect to the number of rows, provides an easy and fast way to construct quasi-cyclic LDPC codes. Constructed codes show good bit-error rate performance with randomly shifted codes performing better than sequentially shifted ones.Gabofetswe Malema and Michael Liebel

Lexical selection in action: Evidence from spontaneous punning

Analysis of a corpus of spontaneously produced Japanese puns from a single speaker over a two-year period provides a view of how a punster selects a source word for a pun and transforms it into another word for humorous effect. The pun-making process is driven by a principle of similarity: the source word should as far as possible be preserved (in terms of segmental sequence) in the pun. This renders homophones (English example: band–banned) the pun type of choice, with part–whole relationships of embedding (cap–capture), and mutations of the source word (peas–bees) rather less favored. Similarity also governs mutations in that single-phoneme substitutions outnumber larger changes, and in phoneme substitutions, subphonemic features tend to be preserved. The process of spontaneous punning thus applies, on line, the same similarity criteria as govern explicit similarity judgments and offline decisions about pun success (e.g., for inclusion in published collections). Finally, the process of spoken-word recognition is word-play-friendly in that it involves multiple word-form activation and competition, which, coupled with known techniques in use in difficult listening conditions, enables listeners to generate most pun types as offshoots of normal listening procedures

Constrained generation of molecular graphs

The generation of molecular graphs by computer programs has undergone some changes. The development is reported with focus on various mathematical methods that are created and employed in this process. No attempt has been made to explicitely state and prove the theorems but this overview contains hints to the relevant literature. In particular, a new generator MOLGEN 4.0 is described that aims at highest flexibility in using constraints during the generation process and, thus, meeting the needs of practical applications