On the permutation behaviour of Dickson polynomials of the second kind

The known permutation behaviour of the Dickson polynomials of the second kind in characteristic 3 is expanded and simplified. (C) 2002 Elsevier Science (USA).

The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

Response to Orr and Siegler - collective intentionality and procreative desires: the permissible view on consent to posthumous conception

Orr and Siegler have recently defended a restrictive view concerning posthumous sperm retrieval and conception, which would limit insemination to those cases where the deceased man has provided explicit consent for such a procedure. The restrictive view dominates current law and practice. A permissible view, in contrast, would allow insemination and conception in all but those cases where the posthumous procedure has been explicitly refused, or where there is no reasonable evidence that the deceased person desired children. I describe a phenomenology of procreative desires which supports the permissible view, and which is compatible with requirements concerning the interests of the decedent, concepts of medical infertility, and the welfare of the future child. The account illustrates how our current obsession with individual rights and autonomy can be self-defeating and repressive.

Structure and folding of potato type II proteinase inhibitors: Circular permutation and intramolecular domain swapping

Potato type II serine proteinase inhibitors are proteins that consist of multiple sequence repeats, and exhibit a multidomain structure. The structural domains are circular permutations of the repeat sequence.. as a result or intramolecular domain swapping. Structural studies give indications for the origins of this folding behaviour, and the evolution of the inhibitor family.

Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

Acyclic permutants of naturally occurring cyclic proteins - Characterization of cystine knot and beta-sheet formation in the macrocyclic polypeptide kalata B1

Kalata B1 is a prototypic member of the unique cyclotide family of macrocyclic polypeptides in which the major structural features are a circular peptide backbone, a triple stranded beta-sheet, and a cystine knot arrangement of three disulfide bonds. The cyclotides are the only naturally occurring family of circular proteins and have prompted us to explore the concept of acyclic permutation, i.e. opening the backbone of a cross-linked circular protein in topologically permuted ways. We have synthesized the complete suite of acyclic permutants of kalata B1 and examined the effect of acyclic permutation on structure and activity. Only two of six topologically distinct backbone loops are critical for folding into the native conformation, and these involve disruption of the embedded ring in the cystine knot. Surprisingly, it is possible to disrupt regions of the p-sheet and still allow folding into native-like structure, provided the cystine knot is intact. Kalata B1 has mild hemolytic activity, but despite the overall structure of the native peptide being retained in all but two cases, none of the acyclic permutants displayed hemolytic activity. This loss of activity is not localized to one particular region and suggests that cyclization is critical for hemolytic activity.

Identifying rate-limiting nodes in large-scale cortical networks for visuospatial processing: an illustration using fMRI

With the advent of functional neuroimaging techniques, in particular functional magnetic resonance imaging (fMRI), we have gained greater insight into the neural correlates of visuospatial function. However, it may not always be easy to identify the cerebral regions most specifically associated with performance on a given task. One approach is to examine the quantitative relationships between regional activation and behavioral performance measures. In the present study, we investigated the functional neuroanatomy of two different visuospatial processing tasks, judgement of line orientation and mental rotation. Twenty-four normal participants were scanned with fMRI using blocked periodic designs for experimental task presentation. Accuracy and reaction time (RT) to each trial of both activation and baseline conditions in each experiment was recorded. Both experiments activated dorsal and ventral visual cortical areas as well as dorsolateral prefrontal cortex. More regionally specific associations with task performance were identified by estimating the association between (sinusoidal) power of functional response and mean RT to the activation condition; a permutation test based on spatial statistics was used for inference. There was significant behavioral-physiological association in right ventral extrastriate cortex for the line orientation task and in bilateral (predominantly right) superior parietal lobule for the mental rotation task. Comparable associations were not found between power of response and RT to the baseline conditions of the tasks. These data suggest that one region in a neurocognitive network may be most strongly associated with behavioral performance and this may be regarded as the computationally least efficient or rate-limiting node of the network.

A family of perfect factorisations of complete bipartite graphs

A 1-factorisation of a graph is perfect if the union of any two of its 1-factors is a Hamiltonian cycle. Let n = p(2) for an odd prime p. We construct a family of (p-1)/2 non-isomorphic perfect 1-factorisations of K-n,K-n. Equivalently, we construct pan-Hamiltonian Latin squares of order n. A Latin square is pan-Hamiltoilian if the permutation defined by any row relative to any other row is a single Cycle. (C) 2002 Elsevier Science (USA).

Overlarge sets of 2-(11, 5, 2) designs and related configurations

We consider the construction of several configurations, including: • overlarge sets of 2-(11,5,2) designs, that is, partitions of the set of all 5-subsets of a 12-set into 72 2-(11,5,2) designs; • an indecomposable doubly overlarge set of 2-(11,5,2) designs, that is, a partition of two copies of the set of all 5-subsets of a 12-set into 144 2-(11,5,2) designs, such that the 144 designs can be arranged into a 12 × 12 square with interesting row and column properties; • a partition of the Steiner system S(5,6,12) into 12 disjoint 2-(11,6,3) designs arising from the diagonal of the square; • bidistant permutation arrays and generalized Room squares arising from the doubly overlarge set, and their relation to some new strongly regular graphs.

On the validity of thermogravimetric determination of carbon gasification kinetics

Thermogravimetric analysis has been widely applied in kinetic studies of carbon gasification, with the associated temporal weight change profiles being used to extract kinetic information and to validate gasification models. However the weight change profiles are not always governed by the intrinsic gasification activity because of the effect of chemisorption and its dynamics. In the present work we theoretically determine the criteria under which weight change profiles can be used to determine intrinsic kinetics for CO2 and O2 gasification by examining the region in which the chemisorption dynamics can be assumed pseudo-steady. It is found that the validity of the pseudo-steady assumption depends on the experimental conditions as well as on the initial surface area of carbon. Based on known mechanisms and rate constants an active surface area region is identified within which the steady state assumption is valid and the effect of chemisorption dynamics is negligible. The size of the permissible region is sensitive to the reaction temperature and gas pressure. The results indicate that in some cases the thermogravimetric data should be used with caution in kinetic studies. A large amount of literature on thermogravimetric analyzer determined char gasification kinetics is examined and the importance of chemisorption dynamics for the data assessed.

Mixed gas equilibrium adsorption on zeolites and energetic heterogeneity of adsorption volume

A model for binary mixture adsorption accounting for energetic heterogeneity and intermolecular interactions is proposed in this paper. The model is based on statistical thermodynamics, and it is able to describe molecular rearrangement of a mixture in a nonuniform adsorption field inside a cavity. The Helmholtz free energy obtained in the framework of this approach has upper and lower limits, which define a permissible range in which all possible solutions will be found. One limit corresponds to a completely chaotic distribution of molecules within a cavity, while the other corresponds to a maximum ordered molecular structure. Comparison of the nearly ideal O-2-N-2-zeolite NaX system at ambient temperature with the system Of O-2-N-2-zeolite CaX at 144 K has shown that a decrease of temperature leads to a molecular rearrangement in the cavity volume, which results from the difference in the fluid-solid interactions. The model is able to describe this behavior and therefore allows predicting mixture adsorption more accurately compared to those assuming energetic uniformity of the adsorption volume. Another feature of the model is its ability to correctly describe the negative deviations from Raoult's law exhibited by the O-2-N-2-CaX system at 144 K. Analysis of the highly nonideal CO2-C2H6-zeolite NaX system has shown that the spatial molecular rearrangement in separate cavities is induced by not only the ion-quadrupole interaction of the CO2 molecule but also the significant difference in molecular size and the difference between the intermolecular interactions of molecules of the same species and those of molecules of different species. This leads to the highly ordered structure of this system.

Functional recycling of C2 domains throughout evolution: A comparative study of synaptotagmin, protein kinase C and phospholipase C by sequence, structural and modelling approaches

The C2 domain is one of the most frequent and widely distributed calcium-binding motifs. Its structure comprises an eight-stranded beta-sandwich with two structural types as if the result of a circular permutation. Combining sequence, structural and modelling information, we have explored, at different levels of granularity, the functional characteristics of several families of C2 domains. At the coarsest level,the similarity correlates with key structural determinants of the C2 domain fold and, at the finest level, with the domain architecture of the proteins containing them, highlighting the functional diversity between the various subfamilies. The functional diversity appears as different conserved surface patches throughout this common fold. In some cases, these patches are related to substrate-binding sites whereas in others they correspond to interfaces of presumably permanent interaction between other domains within the same polypeptide chain. For those related to substrate-binding sites, the predictions overlap with biochemical data in addition to providing some novel observations. For those acting as protein-protein interfaces' our modelling analysis suggests that slight variations between families are a result of not only complementary adaptations in the interfaces involved but also different domain architecture. In the light of the sequence and structural genomic projects, the work presented here shows that modelling approaches along with careful sub-typing of protein families will be a powerful combination for a broader coverage in proteomics. (C) 2003 Elsevier Ltd. All rights reserved.

Genome scan meta-analysis of schizophrenia and bipolar disorder, part II: Schizophrenia

Schizophrenia is a common disorder with high heritability and a 10-fold increase in risk to siblings of probands. Replication has been inconsistent for reports of significant genetic linkage. To assess evidence for linkage across studies, rank-based genome scan meta-analysis (GSMA) was applied to data from 20 schizophrenia genome scans. Each marker for each scan was assigned to 1 of 120 30-cM bins, with the bins ranked by linkage scores (1 = most significant) and the ranks averaged across studies (R-avg) and then weighted for sample size (rootN[affected cases]). A permutation test was used to compute the probability of observing, by chance, each bin's average rank (P-AvgRnk) or of observing it for a bin with the same place (first, second, etc.) in the order of average ranks in each permutation (P-ord). The GSMA produced significant genomewide evidence for linkage on chromosome 2q (P-AvgRnk

Extremal circular permutations with concave functions

Let {a(1), a(2), ..., a(n)} be a set of n distinct real numbers and let alpha(1), alpha(2), ..., alpha(n) an be a permutation of the numbers. We construct the permutation to maximise L-f = Sigma(i=1)(n) f(\alpha(i+1) - alpha(i)\), for any increasing concave function f, where we denote alpha(n+1) equivalent to alpha(1). The optimal permutation depends on the particular numbers {a(1), a(2), ..., a(n)} and the function f, contrary to a postulate by Chao and Liang (European J. Combin. 13 (1992) 325). (C) 2004 Elsevier Ltd. All rights reserved.