An Algorithmic Test for Diagonalizability of Finite-Dimensional PT-Invariant Systems

A non-Hermitean operator does not necessarily have a complete set of eigenstates, contrary to a Hermitean one. An algorithm is presented which allows one to decide whether the eigenstates of a given PT-invariant operator on a finite-dimensional space are complete or not. In other words, the algorithm checks whether a given PT-symmetric matrix is diagonalizable. The procedure neither requires to calculate any single eigenvalue nor any numerical approximation.Comment: 13 pages, 1 figur

Attracting domains of maps tangent to the identity whose only characteristic direction is non-degenerate

We prove that a holomorphic fixed point germ in two complex variables, tangent to the identity, and whose only characteristic direction is non-degenerate, has a domain of attraction on which the map is conjugate to a translation. In the case of a global automorphism, the corresponding domain of attraction is a Fatou-Bieberbach domain

Heat-killed probiotic bacteria differentially regulate colonic epithelial cell production of human β-defensin-2: dependence on inflammatory cytokines.

The inducible antimicrobial peptide human β-defensin-2 (hBD-2) stimulated by pro-inflammatory cytokines and bacterial products is essential to antipathogen responses of gut epithelial cells. Commensal and probiotic bacteria can augment such mucosal defences. Probiotic use in the treatment of inflammatory bowel disease, however, may have adverse effects, boosting inflammatory responses. The aim of this investigation was to determine the effect of selected probiotic strains on hBD-2 production by epithelial cells induced by pathologically relevant pro-inflammatory cytokines and the role of cytokine modulators in controlling hBD-2. Caco-2 colonic intestinal epithelial cells were pre-incubated with heat-killed probiotics, i.e. Lactobacillus casei strain Shirota (LcS) or Lactobacillus fermentum strain MS15 (LF), followed by stimulation of hBD-2 by interleukin (IL)-1β and tumour necrosis factor alpha (TNF-α) in the absence or presence of exogenous IL-10 or anti-IL-10 neutralising antibody. Cytokines and hBD-2 mRNA and protein were analysed by real-time quantitative polymerase chain reaction and enzyme-linked immunosorbent assay. LcS augmented IL-1β-induced hBD-2, whereas LF enhanced TNF-α- and suppressed IL-1β-induced hBD-2. LF enhanced TNF-α-induced TNF-α and suppressed IL-10, whereas augmented IL-1β-induced IL-10. LcS upregulated IL-1β-induced TNF-α mRNA and suppressed IL-10. Endogenous IL-10 differentially regulated hBD-2; neutralisation of IL-10 augmented TNF-α- and suppressed IL-1β-induced hBD-2. Exogenous IL-10, however, suppressed both TNF-α- and IL-1β-induced hBD-2; LcS partially rescued suppression in TNF-α- and IL-1β-stimulation, whereas LF further suppressed IL-1β-induced hBD-2. It can be concluded that probiotic strains differentially regulate hBD-2 mRNA expression and protein secretion, modulation being dictated by inflammatory stimulus and resulting cytokine environment

Dynamics in Several Complex Variables

In this chapter we shall describe the dynamics of holomorphic self-maps of taut manifolds, and in particular the dynamics of holomorphic self-maps of convex and strongly pseudoconvex domains. A main tool in this exploration will be provided by the Kobayashi distance

Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics

On hyperbolicity of SU(2)-equivariant, punctured disc bundles over the complex affine quadric

Given a holomorphic line bundle over the complex affine quadric $Q^2$, we investigate its Stein, SU(2)-equivariant disc bundles. Up to equivariant biholomorphism, these are all contained in a maximal one, say $\Omega_{max}$. By removing the zero section to $\Omega_{max}$ one obtains the unique Stein, SU(2)-equivariant, punctured disc bundle over $Q^2$ which contains entire curves. All other such punctured disc bundles are shown to be Kobayashi hyperbolic.Comment: 15 pages, v2: minor changes, to appear in Transformation Group

The expression of Toll-like receptor 4, 7 and co-receptors in neurochemical sub-populations of rat trigeminal ganglion sensory neurons.

The recent discovery that mammalian nociceptors express Toll-like receptors (TLRs) has raised the possibility that these cells directly detect and respond to pathogens with implications for either direct nociceptor activation or sensitization. A range of neuronal TLRs have been identified, however a detailed description regarding the distribution of expression of these receptors within sub-populations of sensory neurons is lacking. There is also some debate as to the composition of the TLR4 receptor complex on sensory neurons. Here we use a range of techniques to quantify the expression of TLR4, TLR7 and some associated molecules within neurochemically-identified sub-populations of trigeminal (TG) and dorsal root (DRG) ganglion sensory neurons. We also detail the pattern of expression and co-expression of two isoforms of lysophosphatidylcholine acyltransferase (LPCAT), a phospholipid remodeling enzyme previously shown to be involved in the lipopolysaccharide-dependent TLR4 response in monocytes, within sensory ganglia. Immunohistochemistry shows that both TLR4 and TLR7 preferentially co-localize with transient receptor potential vallinoid 1 (TRPV1) and purinergic receptor P2X ligand-gated ion channel 3 (P2X3), markers of nociceptor populations, within both TG and DRG. A gene expression profile shows that TG sensory neurons express a range of TLR-associated molecules. LPCAT1 is expressed by a proportion of both nociceptors and non-nociceptive neurons. LPCAT2 immunostaining is absent from neuronal profiles within both TG and DRG and is confined to non-neuronal cell types under naïve conditions. Together, our results show that nociceptors express the molecular machinery required to directly respond to pathogenic challenge independently from the innate immune system

Comparative response spectrum analysis on 15- and 50-story reinforced concrete buildings having shear walls with and without openings as per EN1998-1 Seismic Code

Medium-rise reinforced concrete (RC) framed apartment complexes with stories ranging from 15 to 50 are becoming more common in Ethiopia’s main cities. In these RC-framed structures, shear walls are included for lateral load resistance. As apertures are frequently provided in shear walls, it is critical to evaluate their influence on story drift, stiffness, shear and moments, and stress within the shear walls. A 3D study with five different cases was carried out with ETABS version 19.00 software to investigate the influence of apertures in a building’s shear wall. This study looks at the effects of changing the size and location of these apertures. Based on this analysis, extensive data were acquired, and useful conclusions were formed that will be useful to practicing engineers. The seismic parameter utilized for the response spectrum study was Building Code of Ethiopia ES8-15, which conforms to Eurocode 8-2004 seismic code guidelines (based on EN1998-1) with target response spectrum type-I. The following parameters were used: ground acceleration, ag/g = 0.1, spectrum type = I, ground type = B, soil factor, S = 1.35, spectrum period, Tb, = 0.05 s, spectrum period, Tc = 0.25 s, spectrum period, Td = 1.2 s, lower bound factor, beta = 0.2, behavior factor = 1, and damping ratio = 5%. The outcomes are compared using various parameters such as displacement, story drift, story stiffness, story shear, and story moment both with and without shear wall opening cases. This study will give tremendous insight into the effect of shear wall openings on the performance of the structure. The analysis in this work was carried out on a linear model, which may not represent the complete local response of the structure; thus, future researchers should perform nonlinear analysis based on a performance-based design. It was concluded from this investigation that incorporating shear walls considerably enhanced the performance of the building over framed structures. Shear wall openings in a structure have a significant influence on the building’s performance. Due to their significant resistance to earthquake forces, shear wall structures are highly recommended for seismic hazard zones