Experimenting with infinite groups, I

A group is termed parafree if it is residually nilpotent and has the same nilpotent quotients as a given free group. Since free groups are residually nilpotent, they are parafree. Nonfree parafree groups abound and they all have many properties in common with free groups. Finitely presented parafree groups have solvable word problems, but little is known about the conjugacy and isomorphism problems. The conjugacy problem plays an important part in determining whether an automorphism is inner, which we term the inner automorphism problem. We will attack these and other problems about parafree groups experimentally, in a series of papers, of which this is the first and which is concerned with the isomorphism problem. The approach that we take here is to distinguish some parafree groups by computing the number of epimorphisms onto selected finite groups. It turns out, rather unexpectedly, that an understanding of the quotients of certain groups leads to some new results about equations in free and relatively free groups. We touch on this only lightly here but will discuss this in more depth in a future paper.

Central elements of the elliptic Zn monodromy matrix algebra at roots of unity

The central elements of the algebra of monodromy matrices associated with the Z(n) R-matrix are studied. When the crossing parameter w takes a special rational value w = n/N, where N and n are positive coprime integers, the center is substantially larger than that in the generic case for which the quantum determinant provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo. (c) 2004 Elsevier B.V. All rights reserved.

Better prediction of protein contact number using a support vector regression analysis of amino acid sequence

Background: Protein tertiary structure can be partly characterized via each amino acid's contact number measuring how residues are spatially arranged. The contact number of a residue in a folded protein is a measure of its exposure to the local environment, and is defined as the number of C-beta atoms in other residues within a sphere around the C-beta atom of the residue of interest. Contact number is partly conserved between protein folds and thus is useful for protein fold and structure prediction. In turn, each residue's contact number can be partially predicted from primary amino acid sequence, assisting tertiary fold analysis from sequence data. In this study, we provide a more accurate contact number prediction method from protein primary sequence. Results: We predict contact number from protein sequence using a novel support vector regression algorithm. Using protein local sequences with multiple sequence alignments (PSI-BLAST profiles), we demonstrate a correlation coefficient between predicted and observed contact numbers of 0.70, which outperforms previously achieved accuracies. Including additional information about sequence weight and amino acid composition further improves prediction accuracies significantly with the correlation coefficient reaching 0.73. If residues are classified as being either contacted or non-contacted, the prediction accuracies are all greater than 77%, regardless of the choice of classification thresholds. Conclusion: The successful application of support vector regression to the prediction of protein contact number reported here, together with previous applications of this approach to the prediction of protein accessible surface area and B-factor profile, suggests that a support vector regression approach may be very useful for determining the structure-function relation between primary sequence and higher order consecutive protein structural and functional properties.

SeqDoC: rapid SNP and mutation detection by direct comparison of DNA sequence chromatograms

Background: This paper describes SeqDoC, a simple, web-based tool to carry out direct comparison of ABI sequence chromatograms. This allows the rapid identification of single nucleotide polymorphisms (SNPs) and point mutations without the need to install or learn more complicated analysis software. Results: SeqDoC produces a subtracted trace showing differences between a reference and test chromatogram, and is optimised to emphasise those characteristic of single base changes. It automatically aligns sequences, and produces straightforward graphical output. The use of direct comparison of the sequence chromatograms means that artefacts introduced by automatic base-calling software are avoided. Homozygous and heterozygous substitutions and insertion/deletion events are all readily identified. SeqDoC successfully highlights nucleotide changes missed by the Staden package 'tracediff' program. Conclusion: SeqDoC is ideal for small-scale SNP identification, for identification of changes in random mutagenesis screens, and for verification of PCR amplification fidelity. Differences are highlighted, not interpreted, allowing the investigator to make the ultimate decision on the nature of the change.

Seizure detection algorithm for neonates based on wave-sequence analysis

Objective: The description and evaluation of the performance of a new real-time seizure detection algorithm in the newborn infant. Methods: The algorithm includes parallel fragmentation of EEG signal into waves; wave-feature extraction and averaging; elementary, preliminary and final detection. The algorithm detects EEG waves with heightened regularity, using wave intervals, amplitudes and shapes. The performance of the algorithm was assessed with the use of event-based and liberal and conservative time-based approaches and compared with the performance of Gotman's and Liu's algorithms. Results: The algorithm was assessed on multi-channel EEG records of 55 neonates including 17 with seizures. The algorithm showed sensitivities ranging 83-95% with positive predictive values (PPV) 48-77%. There were 2.0 false positive detections per hour. In comparison, Gotman's algorithm (with 30 s gap-closing procedure) displayed sensitivities of 45-88% and PPV 29-56%; with 7.4 false positives per hour and Liu's algorithm displayed sensitivities of 96-99%, and PPV 10-25%; with 15.7 false positives per hour. Conclusions: The wave-sequence analysis based algorithm displayed higher sensitivity, higher PPV and a substantially lower level of false positives than two previously published algorithms. Significance: The proposed algorithm provides a basis for major improvements in neonatal seizure detection and monitoring. Published by Elsevier Ireland Ltd. on behalf of International Federation of Clinical Neurophysiology.

STAR: predicting recombination sites from amino acid sequence

Background: Designing novel proteins with site-directed recombination has enormous prospects. By locating effective recombination sites for swapping sequence parts, the probability that hybrid sequences have the desired properties is increased dramatically. The prohibitive requirements for applying current tools led us to investigate machine learning to assist in finding useful recombination sites from amino acid sequence alone. Results: We present STAR, Site Targeted Amino acid Recombination predictor, which produces a score indicating the structural disruption caused by recombination, for each position in an amino acid sequence. Example predictions contrasted with those of alternative tools, illustrate STAR'S utility to assist in determining useful recombination sites. Overall, the correlation coefficient between the output of the experimentally validated protein design algorithm SCHEMA and the prediction of STAR is very high (0.89). Conclusion: STAR allows the user to explore useful recombination sites in amino acid sequences with unknown structure and unknown evolutionary origin. The predictor service is available from http://pprowler.itee.uq.edu.au/star.

Thermal evolution of the ore-hosting Isa Superbasin: Central and Northern Lawn Hill Platform

Hydrocarbon migration pathways and organic mineral matter associations were used to identify brine pathways in Paleoproterozic to early Mesoproterozoic rocks from the Lawn Hill platform, Mount Isa. Several types of organic matter are identified, and their thermal imprints are used to reconstruct the thermal history of the northern to central parts of the Isa superbasin. Three major thermal hydrothermal episodes are recognized from the organic maturation studies. Isotherm plots on a 175-km-long structural-sedimentological north-south section of the Isa superbasin highlight specific fault systems that acted as hot fluid conduits during the geologic history of the basin. Some of these systems indicate continuing activity into the south Nicholson basin, supported by the presence of low reflectance (type B) bitumen. This bitumen has not been overprinted by later hydrothermal episodes and therefore represents the latest thermal event. Along the north-south profile a general southward increase in temperature is evident. The lowest temperatures are recorded in proximity to the basin margin on the southern flank of the Murphy inlier. Thermal processes and their sequence of events in the basin are recorded by organic maturation, subsequent hydrocarbon generation, its migration and destruction coincident with transport and precipitation of minerals. As some timing and trapping mechanisms for minerals may have analogues with hydrocarbon entrapment, relative timing of processes leading to organic maturation, hydrocarbon generation and migration are utilized in this study to enhance understanding of ore-grade mineralization. In the Proterozoic successions of the Mount Isa basin multiple hydrocarbon generation events are recognized. These events record the transient passage of potential metal-bearing fluids rather than background conductive heat flow from the basement. Such hydrothermal fluids are responsible for inverse maturation profiles in the vicinity of the Termite Range fault and extreme maturation (reflectance values) up to 6 percent Ro at the Grevillea prospect. At Century, intermediate Ro values of