The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius-Perron operator $U$ of the cusp map $F:[-1,1]\to [-1,1]$, $F(x)=1-2 x^{1/2}$ (which is an approximation of the Poincare section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in (0,1)$ the spectrum of $U$ in the Hardy space in the disk $\{z\in C:|z-q|

Decay spectrum and decay subspace of normal operators

Let A be a self-adjoint operator on a Hilbert space. It is well known that A admits a unique decomposition into a direct sum of three self-adjoint operators A(p), A(ac) and A(sc) such that there exists an orthonormal basis of eigenvectors for the operator A(p) the operator A(ac) has purely absolutely continuous spectrum and the operator A(sc) has purely singular continuous spectrum. We show the existence of a natural further decomposition of the singular continuous component A c into a direct sum of two self-adjoint operators A(sc)(D) and A(sc)(ND). The corresponding subspaces and spectra are called decaying and purely non-decaying singular subspaces and spectra. Similar decompositions are also shown for unitary operators and for general normal operators.

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

Inter-phyla studies on neuropeptides: the potential for broad-spectrum anthelmintic and/or endectocide discovery

Flatworm, nematode and arthropod parasites have proven their ability to develop resistance to currently available chemotherapeutics. The heavy reliance on chemotherapy and the ability of target species to develop resistance has prompted the search for novel drug targets. In view of its importance to parasite/pest survival, the neuromusculature of parasitic helminths and pest arthropod species remains an attractive target for the discovery Of novel endectocide targets. Exploitation of the neuropeptidergic system in helminths and arthropods has been hampered by a limited Understanding of the functional roles of individual peptides and the structure of endogenous targets, such as receptors. Basic research into these systems has the potential to facilitate target characterization and its offshoots (screen development and drug identification). Of particular interest to parasitologists is the fact that selected neuropeptide families are common to metazoan pest species (nematodes, platyhelminths and arthropods) and fulfil specific roles in the modulation of muscle function in each of the three phyla. This article reviews the inter-phyla activity of two peptide families, the FMRFamide-like peptides and allatostatins, on motor function in helminths and arthropods and discusses the potential of neuropeptide signalling as a target system that could uncover novel endectocidal agents.

Dissociation in performance of children with ADHD and high-functioning autism on a task of sustained attention

Attention deficit hyperactivity disorder (ADHD) and autism are two neurodevelopmental disorders associated with prominent executive dysfunction, which may be underpinned by disruption within fronto-striatal and fronto-parietal circuits. We probed executive function in these disorders using a sustained attention task with a validated brain-behaviour basis. Twenty-three children with ADHD, 21 children with high-functioning autism (HFA) and 18 control children were tested on the Sustained Attention to Response Task (SART). In a fixed sequence version of the task, children were required to withhold their response to a predictably occurring no-go target (3) in a 1-9 digit sequence; in the random version the sequence was unpredictable. The ADHD group showed clear deficits in response inhibition and sustained attention, through higher errors of commission and omission on both SART versions. The HFA group showed no sustained attention deficits, through a normal number of omission errors on both SART versions. The HFA group showed dissociation in response inhibition performance, as indexed by commission errors. On the Fixed SART, a normal number of errors was made, however when the stimuli were randomised, the HFA group made as many commission errors as the ADHD group. Greater slow-frequency variability in response time and a slowing in mean response time by the ADHD group suggested impaired arousal processes. The ADHD group showed greater fast-frequency variability in response time, indicative of impaired top-down control, relative to the HFA and control groups. These data imply involvement of fronto-parietal attentional networks and sub-cortical arousal systems in the pathology of ADHD and prefromal cortex dysfunction in children with HFA. (c) 2007 Elsevier Ltd. All rights reserved.

Movement-related potentials in high-functioning autism and Asperger's disorder

Autism and Asperger's disorder (AD) are neurodevelopmental conditions that affect cognitive and social-communicative function. Using a movement-related potential (MRP) paradigm, we investigated the clinical and neurobiological issue of 'disorder separateness' versus 'disorder variance' in autism and AD. This paradigm has been used to assess basal ganglia/supplementary motor functioning in Parkinson's disease. Three groups (high functioning autism [HFA]: 16 males, 1 female; mean age 12y 5mo [SD 4y 4mo]; AD: 11 males, 2 females; mean age 13y 5mo [SD 3y 8mo]; comparison group: 13 males, 8 females; mean age 13y 10mo, [SD 3y 11 mo]) completed a cued motor task during electroencephalogram recording of MRPs. The HFA group showed reduced peak amplitude at Cz, indicating less activity over the supplementary motor area during movement preparation. Although an overall significant between-group effect was found for early slope and peak amplitude, subanalysis revealed that the group with AD did not differ significantly from either group. However, it is suggested that autism and AD may be dissociated on the basis of brain-behaviour correlations of IQ with specific neurobiological measures. The overlap between MRP traces for autism and Parkinson's disease suggests that the neurobiological wiring of motor functioning in autism may bypass the supplementary motor area/primary motor cortex pathway.

Phylloseptin-1 (PSN-1) from Phyllomedusa sauvagei skin secretion: a novel broad-spectrum antimicrobial peptide with antibiofilm activity

Amphibian skin secretions have proven to be rich sources of antimicrobial peptides that are proposed to be fundamental components of the innate immune system. As amphibian skin is a multi-functional organ playing, among other things, a crucial role in respiration, it has been deemed that a core biological role for such peptides is control of microbial flora on this surface. To date, however, antimicrobial efficacy has been universally determined by means of establishing minimum inhibitory concentrations (MICs) using planktonic organisms rather than those within a biofilm such as would occur on this exposed surface. Here we describe the identification and structural characterisation of a novel 19 amino acid residue antimicrobial peptide of the phylloseptin family, named PSN-1, from the skin secretion of the waxy monkey frog, Phyllomedusa sauvagei. PSN-1 displayed broad-spectrum activity against a range of planktonic organisms with a high potency (MIC 5 µM) against Staphylococcus aureus. In a specific bioassay with the same organism grown as a biofilm, the minimal biofilm eradication concentration (MBEC) was found to be of the same high potency (5 µM). The present data would suggest that evaluation of actions and potency of amphibian skin secretion antimicrobial peptides might best be achieved by evaluating MBEC rather than MIC using planktonic organisms and that data arising from such studies may have more biological relevance in reflecting the purpose for which they have evolved through natural selection.