Compact operators without extended eigenvalues

A complex number lambda is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT = lambda TX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}.

On the Condition Number Distribution of Complex Wishart Matrices

This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading. © 2010 IEEE.

Genomic organization, complex splicing pattern and expression of a human septin gene on chromosome 17q25.3

The Ov/Br septin gene, which is also a fusion partner of MLL in acute myeloid leukaemia, is a member of a family of novel GTP binding proteins that have been implicated in cytokinesis and exocytosis. In this study, we describe the genomic and transcriptional organization of this gene, detailing seventeen exons distributed over 240 kb of sequence. Extensive database analyses identified orthologous rodent cDNAs that corresponded to new, unidentified 5' splice variants of the Ov/Br septin gene, increasing the total number of such variants to six. We report that splicing events, occurring at non-canonical sites within the body of the 3' terminal exon, remove either 1801 bp or 1849 bp of non-coding sequence and facilitate access to a secondary open reading frame of 44 amino acids maintained near the end of the 3' UTR. These events constitute a novel coding arrangement and represent the first report of such a design being implemented by a eukaryotic gene. The various Ov/Br proteins either differ minimally at their amino and carboxy termini or are equivalent to truncated versions of larger isoforms. Northern analysis with an Ov/Br septin 3' UTR probe reveals three transcripts of 4.4, 4 and 3 kb, the latter being restricted to a sub-set of the tissues tested. Investigation of the identified Ov/Br septin isoforms by RT-PCR confirms a complex transcriptional pattern, with several isoforms showing tissue-specific distribution. To date, none of the other human septins have demonstrated such transcriptional complexity.

A complex zinc finger controls the enzymatic activities of nidovirus helicases.

Nidoviruses (Coronaviridae, Arteriviridae, and Roniviridae) encode a nonstructural protein, called nsp10 in arteriviruses and nsp13 in coronaviruses, that is comprised of a C-terminal superfamily 1 helicase domain and an N-terminal, putative zinc-binding domain (ZBD). Previously, mutations in the equine arteritis virus (EAV) nsp10 ZBD were shown to block arterivirus reproduction by disrupting RNA synthesis and possibly virion biogenesis. Here, we characterized the ATPase and helicase activities of bacterially expressed mutant forms of nsp10 and its human coronavirus 229E ortholog, nsp13, and correlated these in vitro activities with specific virus phenotypes. Replacement of conserved Cys or His residues with Ala proved to be more deleterious than Cys-for-His or His-for-Cys replacements. Furthermore, denaturation-renaturation experiments revealed that, during protein refolding, Zn2+ is essential for the rescue of the enzymatic activities of nidovirus helicases. Taken together, the data strongly support the zinc-binding function of the N-terminal domain of nidovirus helicases. nsp10 ATPase/helicase deficiency resulting from single-residue substitutions in the ZBD or deletion of the entire domain could not be complemented in trans by wild-type ZBD, suggesting a critical function of the ZBD in cis. Consistently, no viral RNA synthesis was detected after transfection of EAV full-length RNAs encoding ATPase/helicase-deficient nsp10 into susceptible cells. In contrast, diverse phenotypes were observed for mutants with enzymatically active nsp10, which in a number of cases correlated with the activities measured in vitro. Collectively, our data suggest that the ZBD is critically involved in nidovirus replication and transcription by modulating the enzymatic activities of the helicase domain and other, yet unknown, mechanisms.

Inter-professional working in child protection with families with long-term and complex needs

Within the United Kingdom there is growing awareness of the need to identify and support the small number of children who are living in families experiencing multiple problems. Research indicates that adverse experiences in childhood can result in poor outcomes in adulthood in terms of lack of employment, poorer physical and mental health and increases in social problems experienced. It is acknowledged that most of these children are known to child welfare professionals and that some are referred to social services, subsequently entering the child protection system. This paper reports research conducted with twenty-eight experienced child welfare professionals. It explores their views about families known to the child protection system with long-term and complex needs in relation to the characteristics of children and their families; the process of intervention with families; and the effects of organisational arrangements on practice. The research indicates that these families are characterised by the range and depth of the problems experienced by the adults, such as domestic violence, mental health difficulties and substance misuse problems, and the need for professionals to have good inter-personal skills and access to specialist therapeutic services if families are to be supported to address their problems.

Role of peripheral afference during acquisition of a complex coordination task

It has long been supposed that the interference observed in certain patterns of coordination is mediated, at least in part, by peripheral afference from the moving limbs. We manipulated the level of afferent input, arising from movement of the opposite limb, during the acquisition of a complex coordination task. Participants learned to generate flexion and extension movements of the right wrist, of 75degrees amplitude, that were a quarter cycle out of phase with a 1-Hz sinusoidal visual reference signal. On separate trials, the left wrist either was at rest, or was moved passively by a torque motor through 50degrees, 75degrees or 100degrees, in synchrony with the reference signal. Five acquisition sessions were conducted on successive days. A retention session was conducted I week later. Performance was initially superior when the opposite limb was moved passively than when it was static. The amplitude and frequency of active movement were lower in the static condition than in the driven conditions and the variation in the relative phase relation across trials was greater than in the driven conditions. In addition, the variability of amplitude, frequency and the relative phase relation during each trial was greater when the opposite limb was static than when driven. Similar effects were expressed in electromyograms. The most marked and consistent differences in the accuracy and consistency of performance (defined in terms of relative phase) were between the static condition and the condition in which the left wrist was moved through 50degrees. These outcomes were exhibited most prominently during initial exposure to the task. Increases in task performance during the acquisition period, as assessed by a number of kinematic variables, were generally well described by power functions. In addition, the recruitment of extensor carpi radialis (ECR), and the degree of co-contraction of flexor carpi radialis and ECR, decreased during acquisition. Our results indicate that, in an appropriate task context, afferent feedback from the opposite limb, even when out of phase with the focal movement, may have a positive influence upon the stability of coordination.

Complex molecule formation in grain mantles

Context. Complex molecules such as ethanol and dimethyl ether have been observed in a number of hot molecular cores and hot corinos. Attempts to model the molecular formation process using gas phase only models have so far been unsuccessful. Aims. To demonstrate that grain surface processing is a viable mechanism for complex molecule formation in these environments. Methods. A variable environment parameter computer model has been constructed which includes both gas and surface chemistry. This is used to investigate a variety of cloud collapse scenarios. Results. Comparison between model results and observation shows that by combining grain surface processing with gas phase chemistry complex molecules can be produced in observed abundances in a number of core and corino scenarios. Differences in abundances are due to the initial atomic and molecular composition of the core/corino and varying collapse timescales. Conclusions. Grain surface processing, combined with variation of physical conditions, can be regarded as a viable method for the formation of complex molecules in the environment found in the vicinity of a hot core/corino and produce abundances comparable to those observed.

Distribution of the Demmel Condition Number of Wishart Matrices

This paper studies the Demmel condition number of Wishart matrices, a quantity which has numerous applications to wireless communications, such as adaptive switching between beamforming and diversity coding, link adaptation, and spectrum sensing. For complex Wishart matrices, we give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF), i.e., the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and DoF increases. We further investigate real Wishart matrices, and derive new expressions for the p.d.f. of the smallest eigenvalue, when the difference between the matrix dimension and DoF is odd. Based on these results, we succeed to obtain an exact p.d.f. expression for the Demmel condition number, and simplified expressions for the high tail regime.

Complex fiber bundle model for optimization of heterogeneous materials

We propose a complex fiber bundle model for the optimization of heterogeneous materials, which consists of many simple bundles. We also present an exact and compact recursion relation for the failure probability of a simple fiber bundle model with local load sharing, which is more efficient than the ones reported previously. Using a ''renormalization method'' and the recursion relation developed for the simple bundle, we calculate the failure probabilities of the complex fiber bundle. When the total number of fibers is given, we find that there exists an optimum way to organize the complex bundle, in which one gets a stronger bundle than in other ways.

Molecular dynamics studies of the STAT3 homodimer:DNA complex: relationships between STAT3 mutations and protein-DNA recognition.

Signal Transducers and Activators of Transcription (STAT) proteins are a group of latent cytoplasmic transcription factors involved in cytokine signaling. STAT3 is a member of the STAT family and is expressed at elevated levels in a large number of diverse human cancers and is now a validated target for anticancer drug discovery.. Understanding the dynamics of the STAT3 dimer interface, accounting for both protein-DNA and protein-protein interactions, with respect to the dynamics of the latent unphosphorylated STAT3 monomer, is important for designing potential small-molecule inhibitors of the activated dimer. Molecular dynamics (MD) simulations have been used to study the activated STAT3 homodimer:DNA complex and the latent unphosphorylated STAT3 monomer in an explicit water environment. Analysis of the data obtained from MD simulations over a 50 ns time frame has suggested how the transcription factor interacts with DNA, the nature of the conformational changes, and ways in which function may be affected. Examination of the dimer interface, focusing on the protein-DNA interactions, including involvement of water molecules, has revealed the key residues contributing to the recognition events involved in STAT3 protein-DNA interactions. This has shown that the majority of mutations in the DNA-binding domain are found at the protein-DNA interface. These mutations have been mapped in detail and related to specific protein-DNA contacts. Their structural stability is described, together with an analysis of the model as a starting-point for the discovery of novel small-molecule STAT3 inhibitors.

Molecular Dynamics of HIV1-Integrase in Complex with 93del - A Structural Perspective on the Mechanism of Inhibition

HIV1 integrase is an important target for the antiviral therapy. Guanine-rich quadruplex, such as 93del, have been shown to be potent inhibitors of this enzyme and thus representing a new class of antiviral agents. Although X-ray and NMR structures of HIV1 integrase and 93del have been reported, there is no structural information of the complex and the mechanism of inhibition still remains unexplored. A number of computational methods including automated protein-DNA docking and molecular dynamics simulation in explicit solvent were used to model the binding of 93del to HIV1 integrase. Analysis of the dynamic behaviour of the complex using principal components analysis and elastic network modelling techniques allow us to understand how the binding of 93del aptamer and its interactions with key residues affect the intrinsic motions of the catalytic loops by stabilising them in catalytically inactive conformations. Such insights into the structural mechanism of inhibition can aid in improving the design of anti-HIV aptamers.

Can arsenic-phytochelatin complex formation be used as an indicator for toxicity in Helianthus annuus?

The formation of arsenic-phytochelatin (As-PC) complexes is thought to be part of the plant detoxification strategy for arsenic. This work examines (i) the arsenic (As) concentration-dependent formation of As-PC complex formation and (ii) redistribution and metabolism of As after arrested As uptake in Helianthus annuus. HPLC with parallel ICP-MS/ES-MS detection was used to identify and quantify the species present in plant extracts exposed to arsenate (As(V)) (between 0 and 66.7 micromol As l-1 for 24 h). At As concentrations below the EC50 value for root growth (22 micromol As l-1) As uptake is exponential, but it is reduced at concentrations above. Translocation between root and shoot seemed to be limited to the uptake phase of arsenic. No redistribution of As between root and shoot was observed after arresting As exposure. The formation of As-PC complexes was concentration-dependent. The amount and number of As-PC complexes increased exponentially with concentration up to 13.7 micromol As l-1. As(III)-PC3 and GS-As(III)-PC2 complexes were the dominant species in all samples. The ratio of PC-bound As to unbound As increased up to 1.3 micromol As l-1 and decreased at higher concentrations. Methylation of inorganic As was only a minor pathway in H. annuus with about 1% As methylated over a 32 d period. The concentration dependence of As-PC complex formation, amount of unbound reduced and oxidized PC2, and the relative uptake rate showed that As starts to influence the cellular metabolism of H. annuus negatively at As concentrations well below the EC50 value determined by more traditional means. Generally, As-PC complexes and PC-synthesis rate seem to be the more sensitive parameters to be studied when As toxicity values are to be estimated.

TLM2.0 based timing accurate modeling method for complex NoC systems

Scalability and efficiency of on-chip communication of emerging Multiprocessor System-on-Chip (MPSoC) are critical design considerations. Conventional bus based interconnection schemes no longer fit for MPSoC with a large number of cores. Networks-on-Chip (NoC) is widely accepted as the next generation interconnection scheme for large scale MPSoC. The increase of MPSoC complexity requires fast and accurate system-level modeling techniques for rapid modeling and veri-fication of emerging MPSoCs. However, the existing modeling methods are limited in delivering the essentials of timing accuracy and simulation speed. This paper proposes a novel system-level Networks-on-Chip (NoC) modeling method, which is based on SystemC and TLM2.0 and capable of delivering timing accuracy close to cycle accurate modeling techniques at a significantly lower simulation cost. Experimental results are presented to demonstrate the proposed method. ©2010 IEEE.