Matrix-product codes over Fq

Codes C-1,...,C-M of length it over F-q and an M x N matrix A over F-q define a matrix-product code C = [C-1 (...) C-M] (.) A consisting of all matrix products [c(1) (...) c(M)] (.) A. This generalizes the (u/u + v)-, (u + v + w/2u + v/u)-, (a + x/b + x/a + b + x)-, (u + v/u - v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of /C/, d(C), the minimum Hamming distance of C, and C-perpendicular to. It also reveals an interesting connection with MDS codes. We determine /C/ when A is non-singular. To underbound d(C), we need A to be 'non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary 'Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C-perpendicular to can be described using C-1(perpendicular to),...,C-M(perpendicular to) and a transformation of A. This yields d(C-perpendicular to). Finally we show that an NSC matrix-product code is a generalized concatenated code.

Lower Bounds on the State Complexity of Geometric Goppa Codes

We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg G less than or equal to n-2/2 or deg G greater than or equal to n-2/2 + 2g then the state complexity of C-L(D, G) is equal to the Wolf bound. For deg G is an element of [n-1/2, n-3/2 + 2g], we use Clifford's theorem to give a simple lower bound on the state complexity of C-L(D, G). We then derive two further lower bounds on the state space dimensions of C-L(D, G) in terms of the gonality sequence of F/F-q. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of C-L(D, G) and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes.

Designs for generalized linear models with several variables and model uncertainty

Standard factorial designs sometimes may be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments that uses a criterion allowing for uncertainty in the link function, the linear predictor, or the model parameters, together with a design search. Designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models. Exact designs are investigated for two applications, and their advantages over factorial and central composite designs are demonstrated.

Sampling phylogenetic tree space with the generalized Gibbs sampler

The generalized Gibbs sampler (GGS) is a recently developed Markov chain Monte Carlo (MCMC) technique that enables Gibbs-like sampling of state spaces that lack a convenient representation in terms of a fixed coordinate system. This paper describes a new sampler, called the tree sampler, which uses the GGS to sample from a state space consisting of phylogenetic trees. The tree sampler is useful for a wide range of phylogenetic applications, including Bayesian, maximum likelihood, and maximum parsimony methods. A fast new algorithm to search for a maximum parsimony phylogeny is presented, using the tree sampler in the context of simulated annealing. The mathematics underlying the algorithm is explained and its time complexity is analyzed. The method is tested on two large data sets consisting of 123 sequences and 500 sequences, respectively. The new algorithm is shown to compare very favorably in terms of speed and accuracy to the program DNAPARS from the PHYLIP package.

Cyclic peroxides and related norterpenes from a southern Australian marine sponge, Mycale sp.

Investigation of a southern Australian marine sponge, Mycale sp., resulted in isolation of the known norsesterterpenes 1-3 as well as two new isomeric norsesterterpenes, mycaperoxide C methyl ester (4) and mycaperoxide D methyl ester (5), and six new norterpenes (6-11).

Role of generalized and episode specific memories in the word frequency effect in recognition

Frequency, recency, and type of prior exposure to very low-and high-frequency words were manipulated in a 3-phase (i.e., familiarization training, study, and test) design. Increasing the frequency with which a definition for a very low-frequency word was provided during familiarization facilitated the word's recognition in both yes-no (Experiment 1) and forced-choice paradigms (Experiment 2). Recognition of very low-frequency words not accompanied by a definition during familiarization first increased, then decreased as familiarization frequency increased (Experiment I). Reasons for these differences were investigated in Experiment 3 using judgments of recency and frequency. Results suggested that prior familiarization of a very low-frequency word with its definition may allow a more adequate episodic representation of the word to be formed during a subsequent study trial. Theoretical implications of these results for current models of memory are discussed.

Observation of generalized synchronization of chaos in a driven chaotic system

We report on the experimental observation of the generalized synchronization of chaos in a real physical system. We show that under a nonlinear resonant interaction, the chaotic dynamics of a single mode laser can become functionally related to that of a chaotic driving signal and furthermore as the coupling strength is further increased, the chaotic dynamics of the laser approaches that of the driving signal.

Trunculins G-I: New norsesterterpene cyclic peroxides from a southern Australian marine sponge, Latrunculia sp.

A Latrunculia sp, collected off Port Phillip Bay, Victoria, returned three new norsesterterpene cyclic peroxides. Trunculins G (9), H (10) and I (11) were isolated as their methyl esters (12), (13) and (14) respectively. Gross structures for these new trunculins were assigned on the basis of spectroscopic analysis, while the absolute stereochemistry about the cyclic peroxide terminus was established by application of the Horeau and Mosher procedures.

Febrile seizures and generalized epilepsy associated with a mutation in the Na+-channel beta 1 subunit gene SCN1B

Febrile seizures affect approximately 3% of all children under six years of age and are by far the most common seizure disorder(1). A small proportion of children with febrile seizures later develop ongoing epilepsy with afebrile seizures(2). Segregation analysis suggests the majority of cases have complex inheritance(3) but rare families show apparent autosomal dominant: inheritance. Two putative loci have been mapped (FEB1 and FEB2), but specific genes have not yet been identified(4,5). We recently described a clinical subset, termed generalized epilepsy with febrile seizures plus (GEFS(+)), in which many family members have seizures with fever that may persist beyond six years of age or be associated with afebrile generalized seizures(6). We now report linkage, in another large GEFS(+) family, to chromosome region 19q13.1 and identification of a mutation in the voltage-gated sodium (Na+)-channel beta 1 subunit gene (SCN1B). The mutation changes a conserved cysteine residue disrupting a putative disulfide bridge which normally maintains an extracellular immunoglobulin-like fold. Go-expression of the mutant pr subunit with a brain Na+-channel alpha subunit in Xenopus laevis oocytes demonstrates that the mutation interferes with the ability of the subunit to modulate channel-gating kinetics consistent with a loss-of-function allele. This observation develops the theme that idiopathic epilepsies are a family of channelopathies and raises the possibility of involvement of other Na+-channel subunit genes in febrile seizures and generalized epilepsies with complex inheritance patterns.

Nitric oxide inhibition of the rat olfactory cyclic nucleotide-gated cation channel

The effects of nitric oxide (NO) and other cysteine modifying agents were examined on cyclic nucleotide-gated (CNG) cation channels from rat olfactory receptor neurons. The NO compounds, S-nitroso-cysteine (SNC) and 3-morpholino-sydnonomine (SIN-1), did not activate the channels when applied for up to 10 min. The cysteine alkylating agent, N-ethylmaleimide (NEM), and the oxidising agent, dithionitrobensoate (DTNB), were also without agonist efficacy. Neither SNC nor DTNB altered the cAMP sensitivity of the channels. However, 2-min applications of SIN-1, SNC and DTNB inhibited the cAMP-gated current to approximately 50% of the control current level. This inhibition showed no spontaneous reversal for 5 min but was completely reversed by a 2-min exposure to DTT. The presence of cAMP protected the channels against NO-induced inhibition. These results indicate that inhibition is caused by S-nitrosylation of neighboring sulfhydryl groups leading to sulfhydryl bond formation. This reaction is favored in the closed channel state. Since recombinantly expressed rat olfactory alpha and beta CNG channel homomers and alpha/beta heteromers are activated and not inhibited by cysteine modification, the results of this study imply the existence of a novel subunit or tightly bound factor which dominates the effect of cysteine modification in the native channels. As CNG channels provide a pathway for calcum influx, the results may also have important implications for the physiological role of NO in mammalian olfactory receptor neurons.

Generalized optimal lattice covering of finite-dimensional Euclidean space

A generalization of the classical problem of optimal lattice covering of R-n is considered. Solutions to this generalized problem are found in two specific classes of lattices. The global optimal solution of the generalization is found for R-2. (C) 1998 Elsevier Science Inc. All rights reserved.

The solution structure of a copper(II) compound of a new cyclic octapeptide by EPR spectroscopy and force field calculations

A new cyclic octapeptide, cyclo(Ile-Ser-(Gly)Thz-Ile-Thr-(Gly)Thz) (PatN), related to patellamide A, has been synthesized and reacted with copper(II) and base to form mono- and dinuclear complexes. The coordination environments around copper(TI) have been characterized by EPR spectroscopy. The solution structure of the thermodynamically most stable product, a purple dicopper(TI) compound, has been examined by simulating weakly dipole-dipole coupled EPR spectra based upon structural parameters obtained from force field (MM and MD) calculations. The MM-EPR method produces a saddle-shaped structure for [Cu-2(PatN)(OH2)(6)] that is similar to the known solution structure of patellamide A and the known solid-state structure of [Cu-2(AscidH(2))CO3(OH2)(2)]. Compared with the latter, [Cu-2(PatN)] has no carbonate bridge and a significantly flatter topology. The MM-EPR approach to solution-structure determination for paramagnetic metallopeptides may find wide applications to other metallopeptides and metalloproteins.

Nuapapuin A and sigmosceptrellins D and E: New norterpene cyclic peroxides from a southern Australian marine sponge, Sigmosceptrella sp.

A Sigmosceptrella sp. from the Great Australian Eight, Australia, has yielded the new norditerpene cyclic peroxide, nuapapuin A (2a), and the norsesterterpene cyclic peroxide sigmosceptrellin D (3a), characterized as the corresponding methyl esters 2b and 3b. The crude methylated sponge extract also yielded the new norsesterterpene cyclic peroxide sigmosceptrellin E methyl ester (4). Relative stereochemistry about C2, C3, and C6 was assigned by established empirical rules and absolute stereochemistry by the advanced Mosher procedure. A plausible biosynthetic pathway has been proposed that rationalizes key transformations in the biosynthesis of all known norterpene cyclic peroxides and related norterpene ketones, dienes and sigmosceptrins.