Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes

Self-dual doubly even linear binary error-correcting codes, often referred to as Type II codes, are codes closely related to many combinatorial structures such as 5-designs. Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the automorphism group of a putative code C with the aforementioned properties has order 5 or dividing 24. In this work, we present a method and the results of an exhaustive search showing that such a code C cannot admit an automorphism group Z6. In addition, we present so far unpublished construction of the extended Golay code by P. Becker. We generalize the notion and provide example of another Type II code that can be obtained in this fashion. Consequently, we relate Becker's construction to the construction of binary Type II codes from codes over GF(2^r) via the Gray map.

The dual role of students with behavioural problems: an analysis of their experiences as bullies and victims /

The present study examined the bullying experiences of a group of students, age 10-14 years, identified as having behaviour problems. A total often students participated in a series of mixed methodology activities, including self-report questionnaires, story telling exercises, and interview style joumaling. The main research questions were related to the prevalence of bully/victims and the type of bullying experiences in this population. Questionnaires gathered information about their involvement in bullying, as well as about psychological risk factors including normative beliefs about antisocial acts, impulsivity, problem solving, and coping strategies. Journal questions expanded on these themes and allowed students to explain their personal experiences as bullies and victims as well as provide suggestions for intervention. The overall results indicated that all of the ten students in this sample have participated in bullying as both a bully and a victim. This high prevalence of bully/victim involvement in students from behavioural classrooms is in sharp contrast with the general population where the prevalence is about 33%. In addition, a common thread was found that indicated that these students who participated in this study demonstrate characteristics of emotionally dysregulated reactive bullies. Theoretical implication and educational practices are discussed.

New Building Blocks for Dual-Property Molecule-Based Magnets

Two classes of compounds have been prepared and characterized as building blocks for chiral magnets and ferromagnetic conductors. In the fIrst project, the organic framework of a pentadentate, (N302) macro cycle has been synthetically modifIed to introduce phenyl substituents into its organic framework and the synthesis of four new [Fe(In(N302)(CN)2] complexes (I) - (IV) is presented. [Molecular diagram availble in pdf] This work represents the fIrst structural and magnetic studies of a family of spin crossover macrocycles that comprise of both structural and stereo-isomers. Magnetic susceptibility and Mossbauer data for the R,R-complex (I) is consistent with both a thermal and a light induced spin crossover transition. The X-ray data supports a change in geometry accompanying the thermal spin transition, from a high spin (HS) 7 -coordinate complex at room temperature to a low spin (LS) 5-coordinate complex at 100 K. The crystal structure ofthe racemic complex (III) reveals a HS, 7-coordinate complex at 200 K that undergoes no signifIcant structural changes on cooling. In contrast, the magnetic - susceptibility and Mossbauer data collected on a powder sample of the racemic complex are consistent with a LS complex. Finally, the meso complex (IV) was prepared and its structure and magnetic properties are consistent with a 5-coordinate LS complex that remains low spin, but undergoes conformational changes on cooling in solution. The chiral [Fe(H)(N302)(CN)2] macro cycle (I), together with its Mn(H) and Fe(H) derivatives have also been exploited as building blocks for the self-assembly of chiral magnets. In the second project, a synthetic route for the preparation of tetrathiafulvalene (TTF) donors covalently attached to a diisopropyl verdazyl radical via a cross conjugated pyridyl linker IS presented. Following this strategy, four new TTF-py- (diisopropyl)verdazyl radicals have been prepared and characterized (V) - (VIII) . [Molecular diagram available in pdf] The first (2:1) charge transfer complex ofa TTF-py-(diisopropyl)verdazyl radical donor and a TCNQ acceptor has been prepared and structurally characterized. The crystal packing shows that the donor and acceptor molecules are organized in a mixed stacking arrangement consistent with its insulating behaviour. EPR and magnetic susceptibility data support intramolecular ferromagnetic interactions between the TTF and the verdazyl radicals and antiferromagnetic interactions between TTF donors within a stack. In an attempt to increase the intramolecular exchange interaction between the two radicals, a TTF-x-(diisopropyl)verdazyl radical (IX) was prepared, where the two radicals are connected ia a conjugated divinylene linker. The neutral radical donors stack in a more favourable head-to-head arrangement but the bulky isopropyl groups prevent the donor radicals from stacking close enough together to facilitate good orbital overlap. [Molecular diagram available in pdf].

Assessing the Reproducibility of Clustering of Molecular Dynamics Conformations on Self-Organizing Maps

The goal of most clustering algorithms is to find the optimal number of clusters (i.e. fewest number of clusters). However, analysis of molecular conformations of biological macromolecules obtained from computer simulations may benefit from a larger array of clusters. The Self-Organizing Map (SOM) clustering method has the advantage of generating large numbers of clusters, but often gives ambiguous results. In this work, SOMs have been shown to be reproducible when the same conformational dataset is independently clustered multiple times (~100), with the help of the Cramérs V-index (C_v). The ability of C_v to determine which SOMs are reproduced is generalizable across different SOM source codes. The conformational ensembles produced from MD (molecular dynamics) and REMD (replica exchange molecular dynamics) simulations of the penta peptide Met-enkephalin (MET) and the 34 amino acid protein human Parathyroid Hormone (hPTH) were used to evaluate SOM reproducibility. The training length for the SOM has a huge impact on the reproducibility. Analysis of MET conformational data definitively determined that toroidal SOMs cluster data better than bordered maps due to the fact that toroidal maps do not have an edge effect. For the source code from MATLAB, it was determined that the learning rate function should be LINEAR with an initial learning rate factor of 0.05 and the SOM should be trained by a sequential algorithm. The trained SOMs can be used as a supervised classification for another dataset. The toroidal 10×10 hexagonal SOMs produced from the MATLAB program for hPTH conformational data produced three sets of reproducible clusters (27%, 15%, and 13% of 100 independent runs) which find similar partitionings to those of smaller 6×6 SOMs. The χ^2 values produced as part of the C_v calculation were used to locate clusters with identical conformational memberships on independently trained SOMs, even those with different dimensions. The χ^2 values could relate the different SOM partitionings to each other.