Orthogonal polynomials and recurrence equations, operator equations and factorization

This article surveys the classical orthogonal polynomial systems of the Hahn class, which are solutions of second-order differential, difference or q-difference equations. Orthogonal families satisfy three-term recurrence equations. Example applications of an algorithm to determine whether a three-term recurrence equation has solutions in the Hahn class - implemented in the computer algebra system Maple - are given. Modifications of these families, in particular associated orthogonal systems, satisfy fourth-order operator equations. A factorization of these equations leads to a solution basis.

A generic formula for the values at the boundary points of monic classical orthogonal polynomials

In a previous paper we have determined a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type σ(x)y"n(x)+τ(x)y'n(x)-λnyn(x)=0. In this paper, we give another such formula which enables us to present a generic formula for the values of monic classical orthogonal polynomials at their boundary points of definition.

Duplication coefficients via generating functions

In this paper, we solve the duplication problem P_n(ax) = sum_{m=0}^{n}C_m(n,a)P_m(x) where {P_n}_{n>=0} belongs to a wide class of polynomials, including the classical orthogonal polynomials (Hermite, Laguerre, Jacobi) as well as the classical discrete orthogonal polynomials (Charlier, Meixner, Krawtchouk) for the specific case a = −1. We give closed-form expressions as well as recurrence relations satisfied by the duplication coefficients.

Moments of classical orthogonal polynomials

The aim of this work is to find simple formulas for the moments mu_n for all families of classical orthogonal polynomials listed in the book by Koekoek, Lesky and Swarttouw. The generating functions or exponential generating functions for those moments are given.

The psychological, neurochemical and functional neuroanatomical mediators of the effects of positive and negative mood on executive functions

In this review we evaluate the cognitive and neural effects of positive and negative mood on executive function. Mild manipulations of negative mood appear to have little effect on cognitive control processes, whereas positive mood impairs aspects of updating, planning and switching. These cognitive effects may be linked to neurochemistry: with positive mood effects mediated by dopamine while negative mood effects may be mediated by serotonin levels. Current evidence on the effects of mood on regional brain activity during executive functions, indicates that the prefrontal cortex is a recurrent site of integration between mood and cognition. We conclude that there is a disparity between the importance of this topic and awareness of how mood affects, executive functions in the brain. Most behavioural and neuroimaging studies of executive function in normal samples do not explore the potential role of variations in mood, yet the evidence we outline indicates that even mild fluctuations in mood can have a significant influence on neural activation and cognition. (c) 2006 Elsevier Ltd. All rights reserved.

Maturation of limbic corticostriatal activation and connectivity associated with developmental changes in temporal discounting

Temporal discounting (TD) matures with age, alongside other markers of increased impulse control, and coherent, self-regulated behaviour. Discounting paradigms quantify the ability to refrain from preference of immediate rewards, in favour of delayed, larger rewards. As such, they measure temporal foresight and the ability to delay gratification, functions that develop slowly into adulthood. We investigated the neural maturation that accompanies the previously observed age-related behavioural changes in discounting, from early adolescence into mid-adulthood. We used functional magnetic resonance imaging of a hypothetical discounting task with monetary rewards delayed in the week to year range. We show that age-related reductions in choice impulsivity were associated with changes in activation in ventromedial prefrontal cortex (vmPFC), anterior cingulate cortex (ACC), ventral striatum (VS), insula, inferior temporal gyrus, and posterior parietal cortex. Limbic frontostriatal activation changes were specifically associated with age-dependent reductions in impulsive choice, as part of a more extensive network of brain areas showing age-related changes in activation, including dorsolateral PFC, inferior parietal cortex, and subcortical areas. The maturational pattern of functional connectivity included strengthening in activation coupling between ventromedial and dorsolateral PFC, parietal and insular cortices during selection of delayed alternatives, and between vmPFC and VS during selection of immediate alternatives. We conclude that maturational mechanisms within limbic frontostriatal circuitry underlie the observed post-pubertal reductions in impulsive choice with increasing age, and that this effect is dependent on increased activation coherence within a network of areas associated with discounting behaviour and inter-temporal decision-making.

Non-genomic effects of PPARgamma ligands: inhibition of GPVI-stimulated platelet activation

BACKGROUND: Peroxisome proliferator-activated receptor-(gamma) (PPAR(gamma)) is expressed in human platelets although in the absence of genomic regulation in these cells, its functions are unclear. OBJECTIVE: In the present study, we aimed to demonstrate the ability of PPAR(gamma) ligands to modulate collagen-stimulated platelet function and suppress activation of the glycoprotein VI (GPVI) signaling pathway. METHODS: Washed platelets were stimulated with PPAR(gamma) ligands in the presence and absence of PPAR(gamma) antagonist GW9662 and collagen-induced aggregation was measured using optical aggregometry. Calcium levels were measured by spectrofluorimetry in Fura-2AM-loaded platelets and tyrosine phosphorylation levels of receptor-proximal components of the GPVI signaling pathway were measured using immunoblot analysis. The role of PPAR(gamma) agonists in thrombus formation was assessed using an in vitro model of thrombus formation under arterial flow conditions. RESULTS: PPAR(gamma) ligands inhibited collagen-stimulated platelet aggregation that was accompanied by a reduction in intracellular calcium mobilization and P-selectin exposure. PPAR(gamma) ligands inhibited thrombus formation under arterial flow conditions. The incorporation of GW9662 reversed the inhibitory actions of PPAR(gamma) agonists, implicating PPAR(gamma) in the effects observed. Furthermore, PPAR(gamma) ligands were found to inhibit tyrosine phosphorylation levels of multiple components of the GPVI signaling pathway. PPAR(gamma) was found to associate with Syk and LAT after platelet activation. This association was prevented by PPAR(gamma) agonists, indicating a potential mechanism for PPAR(gamma) function in collagen-stimulated platelet activation. CONCLUSIONS: PPAR(gamma) agonists inhibit the activation of collagen-stimulation of platelet function through modulation of early GPVI signalling.

Platelet endothelial cell adhesion molecule-1 regulates collagen-stimulated platelet function by modulating the association of phosphatidylinositol 3-kinase with Grb-2-associated binding protein-1 and linker for activation of T cells

Background: Platelet activation by collagen depends on signals transduced by the glycoprotein (GP)VI–Fc receptor (FcR)-chain collagen receptor complex, which involves recruitment of phosphatidylinositol 3-kinase (PI3K) to phosphorylated tyrosines in the linker for activation of T cells (LAT). An interaction between the p85 regulatory subunit of PI3K and the scaffolding molecule Grb-2-associated binding protein-1 (Gab1), which is regulated by binding of the Src homology 2 domain-containing protein tyrosine phosphatase-2 (SHP-2) to Gab1, has been shown in other cell types to sustain PI3K activity to elicit cellular responses. Platelet endothelial cell adhesion molecule-1 (PECAM-1) functions as a negative regulator of platelet reactivity and thrombosis, at least in part by inhibiting GPVI–FcR-chain signaling via recruitment of SHP-2 to phosphorylated immunoreceptor tyrosine-based inhibitory motifs in PECAM-1. Objective: To investigate the possibility that PECAM-1 regulates the formation of the Gab1–p85 signaling complexes, and the potential effect of such interactions on GPVI-mediated platelet activation in platelets. Methods: The ability of PECAM-1 signaling to modulate the LAT signalosome was investigated with immunoblotting assays on human platelets and knockout mouse platelets. Results: PECAM-1-associated SHP-2 in collagen-stimulated platelets binds to p85, which results in diminished levels of association with both Gab1 and LAT and reduced collagen-stimulated PI3K signaling. We therefore propose that PECAM-1-mediated inhibition of GPVI-dependent platelet responses result, at least in part, from recruitment of SHP-2–p85 complexes to tyrosine-phosphorylated PECAM-1, which diminishes the association of PI3K with activatory signaling molecules, such as Gab1 and LAT.

Dual-orthogonal radial basis function networks for nonlinear time series prediction

A new structure of Radial Basis Function (RBF) neural network called the Dual-orthogonal RBF Network (DRBF) is introduced for nonlinear time series prediction. The hidden nodes of a conventional RBF network compare the Euclidean distance between the network input vector and the centres, and the node responses are radially symmetrical. But in time series prediction where the system input vectors are lagged system outputs, which are usually highly correlated, the Euclidean distance measure may not be appropriate. The DRBF network modifies the distance metric by introducing a classification function which is based on the estimation data set. Training the DRBF networks consists of two stages. Learning the classification related basis functions and the important input nodes, followed by selecting the regressors and learning the weights of the hidden nodes. In both cases, a forward Orthogonal Least Squares (OLS) selection procedure is applied, initially to select the important input nodes and then to select the important centres. Simulation results of single-step and multi-step ahead predictions over a test data set are included to demonstrate the effectiveness of the new approach.

Staphylococcal extracellular adherence protein induces platelet activation by stimulation of thiol isomerases

OBJECTIVE: Staphylococcus aureus can induce platelet aggregation. The rapidity and degree of this correlates with the severity of disseminated intravascular coagulation, and depends on platelet peptidoglycans. Surface-located thiol isomerases play an important role in platelet activation. The staphylococcal extracellular adherence protein (Eap) functions as an adhesin for host plasma proteins. Therefore we tested the effect of Eap on platelets. METHODS AND RESULTS: We found a strong stimulation of the platelet-surface thiol isomerases protein disulfide isomerase, endoplasmic reticulum stress proteins 57 and 72 by Eap. Eap induced thiol isomerase-dependent glycoprotein IIb/IIIa activation, granule secretion, and platelet aggregation. Treatment of platelets with thiol blockers, bacitracin, and anti-protein disulfide isomerase antibody inhibited Eap-induced platelet activation. The effect of Eap on platelets and protein disulfide isomerase activity was completely blocked by glycosaminoglycans. Inhibition by the hydrophobic probe bis(1-anilinonaphthalene 8-sulfonate) suggested the involvement of hydrophobic sites in protein disulfide isomerase and platelet activation by Eap. CONCLUSIONS: In the present study, we found an additional and yet unknown mechanism of platelet activation by a bacterial adhesin, involving stimulation of thiol isomerases. The thiol isomerase stimulatory and prothrombotic features of a microbial secreted protein are probably not restricted to S aureus and Eap. Because many microorganisms are coated with amyloidogenic proteins, it is likely that the observed mechanism is a more general one.

Rhinocetin, a venom-derived integrin-specific antagonist inhibits collagen-induced platelet and endothelial cell functions

Snaclecs are small non-enzymatic proteins present in viper venoms reported to modulate haemostasis of victims through effects on platelets, vascular endothelial and smooth muscle cells. In this study, we have isolated and functionally characterised a snaclec which we named rhinocetin from the venom of West African gaboon viper, Bitis gabonica rhinoceros. Rhinocetin was shown to comprise α and β chains with the molecular masses of 13.5 and 13kDa respectively. Sequence and immunoblot analysis of rhinocetin confirmed this to be a novel snaclec. Rhinocetin inhibited collagen-stimulated activation of human platelets in dose dependent manner, but displayed no inhibitory effects on glycoprotein VI (collagen receptor) selective agonist, CRP-XL-, ADP- or thrombin-induced platelet activation. Rhinocetin antagonised the binding of monoclonal antibodies against the α2 subunit of integrin α2β1 to platelets and coimmunoprecipitation analysis confirmed integrin α2β1 as a target for this venom protein. Rhinocetin inhibited a range of collagen induced platelet functions such as fibrinogen binding, calcium mobilisation, granule secretion, aggregation and thrombus formation. It also inhibited integrin α2β1 dependent functions of human endothelial cells. Together, our data suggest rhinocetin to be a modulator of integrin α2β1 function and thus may provide valuable insights into the role of this integrin in physiological and pathophysiological scenarios including haemostasis, thrombosis and envenomation.

Cell activation state influences the modulation of HLA-DR surface expression on human monocytes/macrophages by parenteral fish oil lipid emulsion

Abnormal surface expression of HLA-DR by leukocytes is associated with a poor prognosis in critical care patients. Critical care patients often receive total parenteral nutrition with lipid emulsion (LE). In this study we evaluated the influence of fish oil LE (FO) on human monocyte/macrophage (M phi) expression of surface HLA-DR under distinct activation states. Mononuclear leukocytes from the peripheral blood of healthy volunteers (n = 18) were cultured for 24 hours without LE (control) or with 3 different concentrations (0.1, 0.25, and 0.5%) of the follow LE: a) pure FO b) FO in association (1:1 v/v) with LE composed of 50% medium-chain trygliceride and 50% soybean oil (MCTSO), and c) pure MCTSO. The leukocytes were also submitted to different cell activation states, as determinate by INF-gamma addition time: no INF-gamma addition, 18 hours before, or at the time of LE addition. HLA-DR expression on M phi surface was evaluated by flow cytometry using specific monoclonal antibodies. In relation to controls (for 0.1%, 0.25%, and 0.5%: 100) FO decreased the expression of HLA-DR when added alone [in simultaneously-activated M phi, for 0.1%: 70 (59 +/- 73); for 0.25%: 51 (48 +/- 56); and for 0.5%: 52.5(50 +/- 58)] or in association with MCTSO [in simultaneously-activated M phi, for 0.1%: 50.5 (47 +/- 61); for 25%: 49 (45 +/- 52); and for 05 %: 51 (44 +/- 54) and in previously-activated M phi, for 1.0 % : 63 (44 +/- 88); for 0.25%: 70 (41 +/- 88); and for 0.5%: 59.5 (39 +/- 79)] in culture medium (Friedman p<0.05). In relation to controls (for 0.1%, 0.25%, and 0.5%: 100), FO did not influence the expression of these molecules on non-activated M phi [for 0.1 % : 87.5 (75 +/- 93); for 0.25%: 111 (98 +/- 118); and for 0.5%: 101.5 (84 +/- 113)]. Results show that parenteral FO modulates the expression of HLA-DR on human M phi surface accordingly to leukocyte activation state. Further clinical studies evaluating the ideal moment of fish oil LE infusion to modulate leukocyte functions may contribute to a better understanding of its immune modulatory properties.

Orthogonal packing of identical rectangles within isotropic convex regions

A mixed integer continuous nonlinear model and a solution method for the problem of orthogonally packing identical rectangles within an arbitrary convex region are introduced in the present work. The convex region is assumed to be made of an isotropic material in such a way that arbitrary rotations of the items, preserving the orthogonality constraint, are allowed. The solution method is based on a combination of branch and bound and active-set strategies for bound-constrained minimization of smooth functions. Numerical results show the reliability of the presented approach. (C) 2010 Elsevier Ltd. All rights reserved.

Somatostatin modulates G-CSF-induced but not interleukin-3-induced proliferative responses in myeloid 32D cells via activation of somatostatin receptor subtype 2

Somatostatin, originally identified as a peptide involved in neurotransmission, functions as an inhibitor of multiple cellular responses, including hormonal secretion and proliferation. Somatostatin acts through activation of G-protein-coupled receptors of which five subtypes have been identified. We have recently established that human CD34/c-kit expressing hematopoietic progenitors and acute myeloid leukemia (AML) cells exclusively express SSTR2. A major mechanism implicated in the antiproliferative action of somatostatin involves activation of the SH2 domain-containing protein tyrosine phosphatase SHP-1. While 0.1-1 x 10(-9) M of somatostatin, or its synthetic stable analog octreotide, can inhibit G-CSF-induced proliferation of AML cells, little or no effects are seen on GM-CSF- or IL-3-induced responses.
MATERIALS AND METHODS: To study the mechanisms underlying the antiproliferative responses of myeloblasts to somatostatin, clones of the IL-3-dependent murine cell line 32D that stably express SSTR2 and G-CSF receptors were generated. RESULTS: Similar to AML cells, octreotide inhibited G-CSF-induced but not IL-3-induced proliferative responses of 32D[G-CSF-R/SSTR2] cells. Somatostatin induced SHP-1 activity and inhibited G-CSF-induced, but not IL-3-induced, activation of the signal transducer and activator of transcription proteins STAT3 and STAT5.
CONCLUSION: Based on these data and previous results, we propose a model in which recruitment and activation of the tyrosine phosphatase SHP-1 by SSTR2 is involved in the selective negative action of somatostatin on G-CSF-R signaling.

Multi-wavelets from B-spline super-functions with approximation order

Approximation order is an important feature of all wavelets. It implies that polynomials up to degree p−1 are in the space spanned by the scaling function(s). In the scalar case, the scalar sum rules determine the approximation order or the left eigenvectors of the infinite down-sampled convolution matrix H determine the combinations of scaling functions required to produce the desired polynomial. For multi-wavelets the condition for approximation order is similar to the conditions in the scalar case. Generalized left eigenvectors of the matrix H_f; a finite portion of H determines the combinations of scaling functions that produce the desired superfunction from which polynomials of desired degree can be reproduced. The superfunctions in this work are taken to be B-splines. However, any refinable function can serve as the superfunction. The condition of approximation order is derived and new, symmetric, compactly supported and orthogonal multi-wavelets with approximation orders one, two, three and four are constructed.