Tartaglia-Pascal’s triangle: a historical perspective with applications

The aim of this paper is to provide a historical perspective of Tartaglia-Pascal’s triangle with its relations to physics, finance, and statistical signal processing. We start by introducing Tartaglia’s triangle and its numerous properties. We then consider its relationship with a number of topics: the Newton binomial, probability theory (in particular with the Gaussian probability density function, pdf), the Fibonacci sequence, the heat equation, the Schrödinger equation, the Black–Scholes equation of mathematical finance and stochastic filtering theory. Thus, the main contribution of this paper is to present a systematic review of the triangle properties, its connection to statistical theory, and its numerous applications. The paper has mostly a scientific-educational character and is addressed to a wide circle of readers. Sections 7 and 8 are more technical; thus, they may be of interest to more expert readers.     

Blood Thiol Redox State in Chronic Kidney Disease

Thiols (sulfhydryl groups) are effective antioxidants that can preserve the correct structure of proteins, and can protect cells and tissues from damage induced by oxidative stress. Abnormal levels of thiols have been measured in the blood of patients with moderate-to-severe chronic kidney disease (CKD) compared to healthy subjects, as well as in end-stage renal disease (ESRD) patients on haemodialysis or peritoneal dialysis. The levels of protein thiols (a measure of the endogenous antioxidant capacity inversely related to protein oxidation) and S-thiolated proteins (mixed disulphides of protein thiols and low molecular mass thiols), and the protein thiolation index (the molar ratio of the S-thiolated proteins to free protein thiols in plasma) have been investigated in the plasma or red blood cells of CKD and ESRD patients as possible biomarkers of oxidative stress. This type of minimally invasive analysis provides valuable information on the redox status of the less-easily accessible tissues and organs, and of the whole organism. This review provides an overview of reversible modifications in protein thiols in the setting of CKD and renal replacement therapy. The evidence suggests that protein thiols, S-thiolated proteins, and the protein thiolation index are promising biomarkers of reversible oxidative stress that could be included in the routine monitoring of CKD and ESRD patients.     

Agreeableness, empathy, and helping: A person × situation perspective.

This research program explored links among prosocial motives, empathy, and helping behavior. Preliminary work found significant relations among components of self-reported empathy and personality (N = 223). In Study 1, the authors examined the generality of prosocial behavior across situations and group memberships of victims (N = 622). In Study 2, empathic focus and the victim's outgroup status were experimentally manipulated (N = 87). Study 3 (N = 245) replicated and extended Study 2 by collecting measures of prosocial emotions before helping. In Study 4 (N = 244), empathic focus and cost of helping as predictors of helping behavior were experimentally manipulated. Overall, prosocial motivation is linked to (a) Agreeableness as a dimension of personality, (b) proximal prosocial cognition and motives, and (c) helping behavior across a range of situations and victims. In persons low in prosocial motivation, when costs of helping are high, efforts to induce empathy situationally can undermine prosocial behavior. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Designing parametric linear quadratic regulators for parametric LTI systems via LMIs

This paper addresses the problem of determining parametric linear quadratic regulators (LQRs) for continuous-time linear-time invariant systems affected by parameters through rational functions. Three situations are considered, where the sought controller has to minimise the best cost, average cost, and worst cost, respectively, over the set of admissible parameters. It is shown that candidates for such controllers can be obtained by solving convex optimisation problems with linear matrix inequality (LMI) constraints. These candidates are guaranteed to approximate arbitrarily well the sought controllers by sufficiently increasing the size of the LMIs. In particular, the candidate that minimises the average cost approximates arbitrarily well the true LQR over the set of admissible parameters. Moreover, conditions for establishing the optimality of the found candidates are provided. Some numerical examples illustrate the proposed methodology.     

Bispecific-armed, interferon gamma-primed macrophage-mediated phagocytosis of malignant non-Hodgkin's lymphoma

To show that macrophages can be effectively targeted against malignant B cells, bispecific antibodies (BsAb) were constructed from two antibodies having specificity for the high-affinity Fc receptor for IgG (Fc gamma RI/CD64) and the B-cell differentiation antigens CD19 and CD37. Using a flow cytometry-based assay and confocal imaging, we show that these constructs mediated significant phagocytosis of B lymphocytes by macrophages that could be enhanced with interferon gamma (IFN gamma) and IFN gamma in combination with macrophage colony-stimulating factor. BsAb-dependent phagocytosis was triggered through Fc gamma RI and could be blocked only by using F(ab')2 fragments from the parent molecule or by cross-linking Fc gamma RI. BsAb-dependent phagocytosis was not blocked by antibodies to the other Fc receptors, Fc gamma RII and Fc gamma RIII. Because these antibody constructs bind to an epitope outside the Fc gamma RI ligand binding site, we show that autologous serum, polyclonal IgG, and monomeric IgG1 did not block BsAb-dependent phagocytosis, whereas autologous serum and the IgG fractions blocked parent molecule monoclonal antibody-dependent phagocytosis due to the avid binding of monomeric IgG to Fc gamma RI. Finally, BsAb-mediated phagocytosis was effective against the malignant B cells of patients with mantle cell lymphoma, prolymphocytic leukemia, and chronic lymphocytic leukemia. Based on these studies, we propose that BsAbs may provide an effective means of immunomodulation for patients with B-cell malignancies.     

Correction to Sheese et al. (2004).

Reports an error in the original article by B. Sheese et al (Health Psychology, 2004[Sep], Vol 23 [5], 457-464). On page 459, Table 1 contained errors in the reported values. The corrected table is provided. (The following abstract of this article originally appeared in record 2004-18051-003.) Research has shown that writing about emotional topics can positively influence physical and mental health. The current study tested the efficacy of an e-mail-based writing treatment and shows how such an implementation can aid in the search for moderators. Participants (N = 546) were randomly assigned to either a long- or short-interval traumatic writing condition or to a nonemotional writing control condition. In contrast to previous disclosure research, participants received and submitted their writing responses via e-mail. Health outcomes were assessed weekly for 5 weeks after treatment and were reported at the conclusion of the study. Results supported the effectiveness of an e-mail-based writing treatment in producing positive health outcomes and successfully identified several moderators of the writing treatment effect. The moderators implicated varied depending on the nature of the health outcome assessment. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Restoration of pedicle screw fixation with an in situ setting calcium phosphate cement

STUDY DESIGN: Pedicle screws were pulled out of human cadaveric vertebrae before and after augmentation with polymethylmethacrylate or in situ-setting calcium phosphate cement. The fixation strength of screws augmented with calcium phosphate cement was compared with that of screws augmented with polymethylmethacrylate. OBJECTIVES: To determine whether a new in situ-setting calcium phosphate cement might be suitable for augmenting the fixation of pedicle screws. The principle objective was to compare the pull-out resistance of screws augmented with calcium phosphate cement with the pull-out behavior of screws augmented with polymethylmethacrylate. Polymethylmethacrylate augmentation was chosen as the standard because of its current clinical use. Five types of screws were tested to determine whether screw design had an effect on the efficacy of augmentation. SUMMARY OF BACKGROUND DATA: Although many factors affect the pull-out resistance of pedicle screws, a key determinant of their performance is the strength of their attachment to the spine. In elderly, osteopenic patients, the screw-bone interface is especially at risk for stripping during insertion or pull-out after surgery. In these patients, polymethylmethacrylate has been used to augment pedicle screw fixation, although its use is not without risk. In situ-setting calcium phosphate cements may provide an alternative to polymethylmethacrylate in this application. Like polymethylmethacrylate, calcium phosphate cements can be injected into the prepared screw hole. They have the added advantage of being resorbed and replaced during healing and normal bone remodeling. METHODS: Thirty human lower lumbar vertebrae (L3-L5) were implanted bilaterally with one of five types of pedicle screws (n = 6 for each screw type). The screws were pulled out 3.0 mm at 0.25 mm/sec with a servohydraulic materials testing machine. The 3.0-mm pull-out distance, which was slightly longer than one thread pitch, was designed to strip the screw-bone interface but to leave the pedicle otherwise intact. After the initial testing, the screws in each vertebrae were removed, and the screw tracks were filled with 2.0 cc of polymethylmethacrylate (one side) or calcium phosphate cement (contralateral side). After augmentation, the screws were reinserted, and the cements were allowed to harden for 24 hours. Postaugmentation testing followed the protocols for preaugmentation testing, and the pull-out resistance of screws augmented with calcium phosphate cement was compared with the pull-out resistance of screws augmented with polymethylmethacrylate. RESULTS: Mechanically, calcium phosphate cement compared favorably with polymethylmethacrylate for augmenting pedicle screws. Both restored the strength of the screw-bone interface: across all screw types, the average increase in pull-out strength was 147% with polymethylmethacrylate augmentation and 102% with calcium phosphate cement. There were no significant differences because of screw type with either type of augmentation. CONCLUSIONS: The in situ-setting calcium phosphate cement investigated in this study compared favorably with polymethylmethacrylate in a single-cycle, pull-out test of augmented pedicle screws in senile trabecular bone. With further evaluation, this cement may offer an alternative to polymethylmethacrylate for the enhancement of pedicle screw fixation clinically.     

Local Effects Induced by Longitudinal Forces in Composite Girders

Local effects on the shear connection of composite girders induced by longitudinal actions such as the anchorages of prestressing cables, concrete shrinkage, or a uniform thermal action on the slab are analyzed. Closed-form solutions are obtained by using the simple model of a composite beam with a linearly elastic shear connection. Successively, by considering the limit scheme of an infinitely long beam, very simple formulas are derived permitting evaluation of the peak value and extension of the interface shear force distribution induced by the longitudinal actions. Numerical applications are carried out to show the effectiveness of the proposed formulas for a wide range of the shear connection stiffness and for longitudinal forces applied both along the beam axis and at the beam end.