Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

Completeness of certain function spaces

We give an example of a complete locally convex m-topology on the algebra of infinite differentiable functions on [0, 1] which is strictly coarser than the natural Frechet-topology but finer than the topology of pointwise convergence. A similar construction works on the algebra of continuous functions on [0, 1]. Using this examples we can separate different notions of diffotopy and homotopy.

On weak and strong Peano theorems

We say that the Peano theorem holds for a topological vector space $E$ if, for any continuous mapping $f : {\Bbb R}\times E \to E$ and any $(t(0), x(0))$ is an element of ${\Bbb R}\times E$, the Cauchy problem $\dot x(t) = f(t,x(t))$, $x(t(0)) = x(0)$, has a solution in some neighborhood of $t(0)$. We say that the weak version of Peano theorem holds for $E$ if, for any continuous map $f : {\Bbb R}\times E \to E$, the equation $\dot x(t) = f (t, x(t))$ has a solution on some interval. We construct an example (answering a question posed by S. G. Lobanov) of a Hausdorff locally convex topological vector space E for which the weak version of Peano theorem holds and the Peano theorem fails to hold. We also construct a Hausdorff locally convex topological vector space E for which the Peano theorem holds and any barrel in E is neither compact nor sequentially compact.

Gateaux complex differentiability and continuity

As is known, there are everywhere discontinuous infinitely Frechet differentiable functions on the real locally convex spaces D(R) and V(R) of finitely supported infinitely differentiable functions and, respectively, of generalized functions. In this paper the relationship between the complex differentiability and continuity of a function on a complex locally convex space is considered. We describe a class of complex locally convex spaces, which includes the complex space V(R), such that every Gateaux complex-differentiable function on a space of this class is continuous. We also describe another class of locally convex spaces, which includes the complex space D(R), such that on every space of this class there is an everywhere discontinuous infinitely Frechet complex-differentiable function whose derivatives are continuous.

On linear extension operators

We construct a countable-dimensional Hausdorff locally convex topological vector space $E$ and a stratifiable closed linear subspace $F$ subset of $E$ such that any linear extension operator from $C_b(F)$ to $C_b(E)$ is unbounded (here $C_b(X)$ stands for the Banach space of continuous bounded real-valued functions on $X$).

An investigation of possible mechanisms of the water-gas shift reaction over a ZrO2-supported Pt catalyst

The present work investigates the reactivity of the surface species observable by in situ DRIFTS formed over a Pt/ZrO2 during the water-gas shift (WGS) reaction. A DRIFTS cell/mass spectrometer system was operated at the chemical steady state during isotopic transients to yield information about the true nature (i.e., main reaction intermediate or spectators) of adsorbates. Only carbonyl and formate species were observed by DRIFTS under reaction conditions; the surface coverage of carbonate species was negligible. Isotopic transient kinetic analyses revealed that formates exchanged uniformly according to a first-order law, suggesting that most formates observed by DRIFTS were of the same reactivity. In addition, the time scale of the exchange of the reaction product CO2 was significantly shorter than that of the surface formates. Therefore, a formate route based on the formates as detected by DRIFTS can be ruled out as the main reaction pathway in the present case. The number of precursors of the reaction product CO2 was smaller than the number of surface Pt atoms, suggesting that carbonyl species or some \

Model selection approaches for non-linear system identification: a review

The identification of non-linear systems using only observed finite datasets has become a mature research area over the last two decades. A class of linear-in-the-parameter models with universal approximation capabilities have been intensively studied and widely used due to the availability of many linear-learning algorithms and their inherent convergence conditions. This article presents a systematic overview of basic research on model selection approaches for linear-in-the-parameter models. One of the fundamental problems in non-linear system identification is to find the minimal model with the best model generalisation performance from observational data only. The important concepts in achieving good model generalisation used in various non-linear system-identification algorithms are first reviewed, including Bayesian parameter regularisation and models selective criteria based on the cross validation and experimental design. A significant advance in machine learning has been the development of the support vector machine as a means for identifying kernel models based on the structural risk minimisation principle. The developments on the convex optimisation-based model construction algorithms including the support vector regression algorithms are outlined. Input selection algorithms and on-line system identification algorithms are also included in this review. Finally, some industrial applications of non-linear models are discussed.

Adjustment to inflammatory bowel disease: The relative influence of illness perceptions and coping

Background: The Common Sense Model (CSM) of illness representations was used in the current study to examine the relative contribution of illness perceptions and coping strategies in explaining adjustment to inflammatory bowel disease (IBD). Methods: Participants were 80 adults consecutively attending an outpatients' clinic with a diagnosis of either Crohn's disease or ulcerative colitis. Respondents completed and returned a questionnaire booklet that assessed illness perceptions, coping, and adjustment. Adjustment was measured from the perspectives of psychological distress, quality of life, and functional independence. Results: Illness perceptions (particularly perception of consequences of IBD) were uniformly the most consistent variables explaining adjustment to IBD. Coping did not significantly add to predicting adjustment once illness perceptions were controlled for and therefore did not mediate the relationship between illness perceptions and adjustment, as proposed in the CSM. Conclusions: The results suggest the importance of addressing illness perceptions in developing appropriate psychological interventions for IBD.

Antidepressant specificity of serotonin transporter suggested by three LeuT-SSRI structures.

Sertraline and fluoxetine are selective serotonin re-uptake inhibitors (SSRIs) that are widely prescribed to treat depression. They exert their effects by inhibiting the presynaptic plasma membrane serotonin transporter (SERT). All SSRIs possess halogen atoms at specific positions, which are key determinants for the drugs' specificity for SERT. For the SERT protein, however, the structural basis of its specificity for SSRIs is poorly understood. Here we report the crystal structures of LeuT, a bacterial SERT homolog, in complex with sertraline, R-fluoxetine or S-fluoxetine. The SSRI halogens all bind to exactly the same pocket within LeuT. Mutation at this halogen-binding pocket (HBP) in SERT markedly reduces the transporter's affinity for SSRIs but not for tricyclic antidepressants. Conversely, when the only nonconserved HBP residue in both norepinephrine and dopamine transporters is mutated into that found in SERT, their affinities for all the three SSRIs increase uniformly. Thus, the specificity of SERT for SSRIs is dependent largely on interaction of the drug halogens with the protein's HBP.

Vaginal delivery of the recombinant HIV-1 clade-C trimeric gp140 envelope protein CN54gp140 within novel rheologically structured vehicles elicits specific immune responses

Rheologically structured vehicle (RSV) gels were developed as delivery systems for vaginal mucosal vaccination with an HIV-1 envelope glycoprotein (CN54gp140). RSVs comprised a mucoadhesive matrix forming and vaginal fluid absorbing polymer. The mucoadhesive and rheological properties of the RSVs were evaluated in vitro, and the distribution, antigenicity and release of CN54gp140 were analysed by ELISA. CN54gp140 was uniformly distributed within the RSVs and continuously released in vitro in an antigenically intact form over 24 h. Vaginal administration to rabbits induced specific serum IgG, and IgG and IgA in genital tract secretions. The RSVs are a viable delivery modality for vaginal immunization.

Unconditional constants and polynomial inequalities

If P is a polynomial on Rm of degree at most n then we define the polynomial |P|. Now if B is a convex compact set in Rm, we define the norm ||P||B of P as the maximum of P on B, and then we investigate the inequality || |P| ||B

Convergence of bimodules over maximal abelian selfadjoint algebras

We prove a continuity result for the map sending a masa-bimodule to its support. We characterise the convergence of a net of weakly closed convex hulls of bilattices in terms of the convergence of the corresponding supports, and establish a lower-semicontinuity result for the map sending a support to the corresponding masa-bimodule.

Genetic regulation of the ramA locus and its expression in clinical isolates of Klebsiella pneumoniae

Tigecycline resistance has been attributed to ramA overexpression and subsequent acrA upregulation. The ramA locus, originally identified in Klebsiella pneumoniae, has homologues in Enterobacter and Salmonella spp. In this study, we identify in silico that the ramR binding site is also present in Citrobacter spp. and that Enterobacter, Citrobacter and Klebsiella spp. share key regulatory elements in the control of the romA–ramA locus. RACE (rapid amplification of cDNA ends) mapping indicated that there are two promoters from which romA–ramA expression can be regulated in K. pneumoniae. Correspondingly, electrophoretic binding studies clearly showed that purified RamA and RamR proteins bind to both of these promoters. Hence, there appear to be two RamR binding sites within the Klebsiella romA–ramA locus. Like MarA, RamA binds the promoter region, implying that it might be subject to autoregulation. We have identified changes within ramR in geographically distinct clinical isolates of K. pneumoniae. Intriguingly, levels of romA and ramA expression were not uniformly affected by changes within the ramR gene, thereby supporting the dual promoter finding. Furthermore, a subset of strains sustained no changes within the ramR gene but which still overexpressed the romA–ramA genes, strongly suggesting that a secondary regulator may control ramA expression.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

RUNX3 protein is overexpressed in human basal cell carcinomas

Basal cell carcinomas (BCC), which are the most common form of skin malignancy, are invariably associated with the deregulation of the Sonic Hedgehog (Shh) signalling pathway. As such, BCC represent a unique model for the study of interactions of the Shh pathway with other genes and pathways. We constructed a tissue microarray (TMA) of 75 paired BCC and normal skin and analysed the expression of beta-catenin and RUNX3, nuclear effectors of the wingless-Int (Wnt) and bone morphogenetic protein/transforming growth factor-beta pathways, respectively. In line with previous reports, we observed varying subcellular expression pattern of beta-catenin in BCC, with 31 cases (41%) showing nuclear accumulation. In contrast, all the BCC cases tested by the TMA showed RUNX3 protein uniformly overexpressed in the nuclei of the cancer cells. Analysis by Western blotting and DNA sequencing indicates that the overexpressed protein is normal and full-length, containing no mutation in the coding region, implicating RUNX3 as an oncogene in certain human cancers. Our results indicate that although the deregulation of Wnt signalling could contribute to the pathogenesis of a subset of BCC, RUNX3 appears to be a universal downstream mediator of a constitutively active Shh pathway in BCC.