MATHEMATICAL MODELS AND POLYHEDRAL STUDIES FOR INTEGRAL SHEET METAL DESIGN

We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.

A Cost-Effectiveness-Assessing Model of Vaccination for Varicella and Zoster

A decision analytical model is presented and analysed to assess the effectiveness and cost-effectiveness of routine vaccination against varicella and herpes-zoster, or shingles. These diseases have as common aetiological agent the varicella-zoster virus (VZV). Zoster can more likely occur in aged people with declining cell-mediated immunity. The general concern is that universal varicella vaccination might lead to more cases of zoster: with more vaccinated children exposure of the general population to varicella infectives become smaller and thus a larger proportion of older people will have weaker immunity to VZV, leading to more cases of reactivation of zoster. Our compartment model shows that only two possible equilibria exist, one without varicella and the other one where varicella arid zoster both thrive. Threshold quantities to distinguish these cases are derived. Cost estimates on a possible herd vaccination program are discussed indicating a possible tradeoff choice.

An in-depth analysis of the HIV-1/AIDS dynamics by comprehensive mathematical modeling

This work presents major results from a novel dynamic model intended to deterministically represent the complex relation between HIV-1 and the human immune system. The novel structure of the model extends previous work by representing different host anatomic compartments under a more in-depth cellular and molecular immunological phenomenology. Recently identified mechanisms related to HIV-1 infection as well as other well known relevant mechanisms typically ignored in mathematical models of HIV-1 pathogenesis and immunology, such as cell-cell transmission, are also addressed. (C) 2011 Elsevier Ltd. All rights reserved.

Biventricular structural and functional responses to aortic constriction in a rabbit model of chronic right ventricular pressure overload

Objectives: Chronic right ventricular (RV) pressure overload results in pathologic RV hypertrophy and diminished RV function. Although aortic constriction has been shown to improve systolic function in acute RV failure, its effect on RV responses to chronic pressure overload is unknown. Methods: Adjustable vascular banding devices were placed on the main pulmonary artery and descending aorta. In 5 animals (sham group), neither band was inflated. In 9 animals (PAB group), only the pulmonary arterial band was inflated, with adjustments on a weekly basis to generate systemic or suprasystemic RV pressure at 28 days. In 9 animals, both pulmonary arterial and aortic devices were inflated (PAB+AO group), the pulmonary arterial band as for the PAB group and the aortic band adjusted to increase proximal systolic blood pressure by approximately 20 mm Hg. Effects on the functional performance were assessed 5 weeks after surgery by conductance catheters, followed by histologic and molecular assessment. Results: Contractile performance was significantly improved in the PAB+AO group versus the PAB group for both ventricles. Relative to sham-operated animals, both banding groups showed significant differences in myocardial histologic and molecular responses. Relative to the PAB group, the PAB+AO group showed significantly decreased RV cardiomyocyte diameter, decreased RV collagen content, and reduced RV expression of endothelin receptor type B, matrix metalloproteinase 9, and transforming growth factor beta genes. Conclusions: Aortic constriction in an experimental model of chronic RV pressure overload not only resulted in improved biventricular systolic function but also improved myocardial remodeling. These data suggest that chronically increased left ventricular afterload leads to a more physiologically hypertrophic response in the pressure-overloaded RV. (J Thorac Cardiovasc Surg 2012;144:1494-501)

Phase Transition for the Ising Model on the Critical Lorentzian Triangulation

The ferromagnetic Ising model without external field on an infinite Lorentzian triangulation sampled from the uniform distribution is considered. We prove uniqueness of the Gibbs measure in the high temperature region and coexistence of at least two Gibbs measures at low temperature. The proofs are based on the disagreement percolation method and on a variant of the Peierls contour method. The critical temperature is shown to be constant a.s.

On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, da parts per thousand yen1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.

No effect of creatine supplementation on oxidative stress and cardiovascular parameters in spontaneously hypertensive rats

Background: Exacerbated oxidative stress is thought to be a mediator of arterial hypertension. It has been postulated that creatine (Cr) could act as an antioxidant agent preventing increased oxidative stress. The aim of this study was to investigate the effects of nine weeks of Cr or placebo supplementation on oxidative stress and cardiovascular parameters in spontaneously hypertensive rats (SHR). Findings: Lipid hydroperoxidation, one important oxidative stress marker, remained unchanged in the coronary artery (Cr: 12.6 +/- 1.5 vs. Pl: 12.2 +/- 1.7 nmol.mg(-1); p = 0.87), heart (Cr: 11.5 +/- 1.8 vs. Pl: 14.6 +/- 1.1 nmol.mg(-1); p = 0.15), plasma (Cr: 67.7 +/- 9.1 vs. Pl: 56.0 +/- 3.2 nmol.mg(-1); p = 0.19), plantaris (Cr: 10.0 +/- 0.8 vs. Pl: 9.0 +/- 0.8 nmol.mg(-1); p = 0.40), and EDL muscle (Cr: 14.9 +/- 1.4 vs. Pl: 17.2 +/- 1.5 nmol.mg(-1); p = 0.30). Additionally, Cr supplementation affected neither arterial blood pressure nor heart structure in SHR (p > 0.05). Conclusions: Using a well-known experimental model of systemic arterial hypertension, this study did not confirm the possible therapeutic effects of Cr supplementation on oxidative stress and cardiovascular dysfunction associated with arterial hypertension.

Effect of external fields in Axelrod's model of social dynamics

The study of the effects of spatially uniform fields on the steady-state properties of Axelrod's model has yielded plenty of counterintuitive results. Here, we reexamine the impact of this type of field for a selection of parameters such that the field-free steady state of the model is heterogeneous or multicultural. Analyses of both one- and two-dimensional versions of Axelrod's model indicate that the steady state remains heterogeneous regardless of the value of the field strength. Turning on the field leads to a discontinuous decrease on the number of cultural domains, which we argue is due to the instability of zero-field heterogeneous absorbing configurations. We find, however, that spatially nonuniform fields that implement a consensus rule among the neighborhood of the agents enforce homogenization. Although the overall effects of the fields are essentially the same irrespective of the dimensionality of the model, we argue that the dimensionality has a significant impact on the stability of the field-free homogeneous steady state.

A Bayesian destructive weighted Poisson cure rate model and an application to a cutaneous melanoma data

In this article, we propose a new Bayesian flexible cure rate survival model, which generalises the stochastic model of Klebanov et al. [Klebanov LB, Rachev ST and Yakovlev AY. A stochastic-model of radiation carcinogenesis - latent time distributions and their properties. Math Biosci 1993; 113: 51-75], and has much in common with the destructive model formulated by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)]. In our approach, the accumulated number of lesions or altered cells follows a compound weighted Poisson distribution. This model is more flexible than the promotion time cure model in terms of dispersion. Moreover, it possesses an interesting and realistic interpretation of the biological mechanism of the occurrence of the event of interest as it includes a destructive process of tumour cells after an initial treatment or the capacity of an individual exposed to irradiation to repair altered cells that results in cancer induction. In other words, what is recorded is only the damaged portion of the original number of altered cells not eliminated by the treatment or repaired by the repair system of an individual. Markov Chain Monte Carlo (MCMC) methods are then used to develop Bayesian inference for the proposed model. Also, some discussions on the model selection and an illustration with a cutaneous melanoma data set analysed by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)] are presented.

Strategy and model building in the fourth dimension: a null model for genotype × age interaction as a Gaussian stationary stochastic process

Abstract Background Using univariate and multivariate variance components linkage analysis methods, we studied possible genotype × age interaction in cardiovascular phenotypes related to the aging process from the Framingham Heart Study. Results We found evidence for genotype × age interaction for fasting glucose and systolic blood pressure. Conclusions There is polygenic genotype × age interaction for fasting glucose and systolic blood pressure and quantitative trait locus × age interaction for a linkage signal for systolic blood pressure phenotypes located on chromosome 17 at 67 cM.

Association between UCP2 A55V polymorphism and risk of cardiovascular events in patients with multi-vessel coronary arterial disease

Background UCP2 (uncoupling protein 2) plays an important role in cardiovascular diseases and recent studies have suggested that the A55V polymorphism can cause UCP2 dysfunction. The main aim was to investigate the association of A55V polymorphism with cardiovascular events in a group of 611 patients enrolled in the Medical, Angioplasty or Surgery Study II (MASS II), a randomized trial comparing treatments for patients with coronary artery disease and preserved left ventricular function. Methods The participants of the MASS II were genotyped for the A55V polymorphism using allele-specific PCR assay. Survival curves were calculated with the Kaplan–Meier method and evaluated with the log-rank statistic. The relationship between baseline variables and the composite end-point of cardiac death, acute myocardial infarction (AMI), refractory angina requiring revascularization and cerebrovascular accident were assessed using a Cox proportional hazards survival model. Results There were no significant differences for baseline variables according genotypes. After 2 years of follow-up, dysglycemic patients harboring the VV genotype had higher occurrence of AMI (p=0.026), Death+AMI (p=0.033), new revascularization intervention (p=0.009) and combined events (p=0.037) as compared with patients carrying other genotypes. This association was not evident in normoglycemic patients. Conclusions These findings support the hypothesis that A55V polymorphism is associated with UCP2 functional alterations that increase the risk of cardiovascular events in patients with previous coronary artery disease and dysglycemia.

Metabolic, hemodynamic and structural adjustments to low intensity exercise training in a metabolic syndrome model

Background The increase in fructose consumption is paralleled by a higher incidence of metabolic syndrome, and consequently, cardiovascular disease mortality. We examined the effects of 8 weeks of low intensity exercise training (LET) on metabolic, hemodynamic, ventricular and vascular morphological changes induced by fructose drinking in male rats. Methods Male Wistar rats were divided into (n = 8 each) control (C), sedentary fructose (F) and ET fructose (FT) groups. Fructose-drinking rats received D-fructose (100 g/l). FT rats were assigned to a treadmill training protocol at low intensity (30% of maximal running speed) during 1 h/day, 5 days/week for 8 weeks. Measurements of triglyceride concentrations, white adipose tissue (WAT) and glycemia were carried out together with insulin tolerance test to evaluate metabolic profile. Arterial pressure (AP) signals were directly recorded. Baroreflex sensitivity (BS) was evaluated by the tachycardic and bradycardic responses. Right atria, left ventricle (LV) and ascending aorta were prepared to morphoquantitative analysis. Results LET reduced WAT (−37.7%), triglyceride levels (−33%), systolic AP (−6%), heart weight/body weight (−20.5%), LV (−36%) and aortic (−76%) collagen fibers, aortic intima-media thickness and circumferential wall tension in FT when compared to F rats. Additionally, FT group presented improve of BS, numerical density of atrial natriuretic peptide granules (+42%) and LV capillaries (+25%), as well as the number of elastic lamellae in aorta compared with F group. Conclusions Our data suggest that LET, a widely recommended practice, seems to be particularly effective for preventing metabolic, hemodynamic and morphological disorders triggered by MS.

Numerical simulation of an ethanol turbulent spray flame with RANS and diffusion combustion model

A detailed numerical simulation of ethanol turbulent spray combustion on a rounded jet flame is pre- sented in this article. The focus is to propose a robust mathematical model with relatively low complexity sub- models to reproduce the main characteristics of the cou- pling between both phases, such as the turbulence modulation, turbulent droplets dissipation, and evaporative cooling effect. A RANS turbulent model is implemented. Special features of the model include an Eulerian– Lagrangian procedure under a fully two-way coupling and a modified flame sheet model with a joint mixture fraction– enthalpy b -PDF. Reasonable agreement between measured and computed mean profiles of temperature of the gas phase and droplet size distributions is achieved. Deviations found between measured and predicted mean velocity profiles are attributed to the turbulent combustion modeling adopted

Two fluid numerical model for coastal applications

Wave breaking is an important coastal process, influencing hydro-morphodynamic processes such as turbulence generation and wave energy dissipation, run-up on the beach and overtopping of coastal defence structures. During breaking, waves are complex mixtures of air and water (“white water”) whose properties affect velocity and pressure fields in the vicinity of the free surface and, depending on the breaker characteristics, different mechanisms for air entrainment are usually observed. Several laboratory experiments have been performed to investigate the role of air bubbles in the wave breaking process (Chanson & Cummings, 1994, among others) and in wave loading on vertical wall (Oumeraci et al., 2001; Peregrine et al., 2006, among others), showing that the air phase is not negligible since the turbulent energy dissipation involves air-water mixture. The recent advancement of numerical models has given valuable insights in the knowledge of wave transformation and interaction with coastal structures. Among these models, some solve the RANS equations coupled with a free-surface tracking algorithm and describe velocity, pressure, turbulence and vorticity fields (Lara et al. 2006 a-b, Clementi et al., 2007). The single-phase numerical model, in which the constitutive equations are solved only for the liquid phase, neglects effects induced by air movement and trapped air bubbles in water. Numerical approximations at the free surface may induce errors in predicting breaking point and wave height and moreover, entrapped air bubbles and water splash in air are not properly represented. The aim of the present thesis is to develop a new two-phase model called COBRAS2 (stands for Cornell Breaking waves And Structures 2 phases), that is the enhancement of the single-phase code COBRAS0, originally developed at Cornell University (Lin & Liu, 1998). In the first part of the work, both fluids are considered as incompressible, while the second part will treat air compressibility modelling. The mathematical formulation and the numerical resolution of the governing equations of COBRAS2 are derived and some model-experiment comparisons are shown. In particular, validation tests are performed in order to prove model stability and accuracy. The simulation of the rising of a large air bubble in an otherwise quiescent water pool reveals the model capability to reproduce the process physics in a realistic way. Analytical solutions for stationary and internal waves are compared with corresponding numerical results, in order to test processes involving wide range of density difference. Waves induced by dam-break in different scenarios (on dry and wet beds, as well as on a ramp) are studied, focusing on the role of air as the medium in which the water wave propagates and on the numerical representation of bubble dynamics. Simulations of solitary and regular waves, characterized by both spilling and plunging breakers, are analyzed with comparisons with experimental data and other numerical model in order to investigate air influence on wave breaking mechanisms and underline model capability and accuracy. Finally, modelling of air compressibility is included in the new developed model and is validated, revealing an accurate reproduction of processes. Some preliminary tests on wave impact on vertical walls are performed: since air flow modelling allows to have a more realistic reproduction of breaking wave propagation, the dependence of wave breaker shapes and aeration characteristics on impact pressure values is studied and, on the basis of a qualitative comparison with experimental observations, the numerical simulations achieve good results.

Bioimaging of animal embryogenesis: mathematical methods and computational algorithms

Some fundamental biological processes such as embryonic development have been preserved during evolution and are common to species belonging to different phylogenetic positions, but are nowadays largely unknown. The understanding of cell morphodynamics leading to the formation of organized spatial distribution of cells such as tissues and organs can be achieved through the reconstruction of cells shape and position during the development of a live animal embryo. We design in this work a chain of image processing methods to automatically segment and track cells nuclei and membranes during the development of a zebrafish embryo, which has been largely validates as model organism to understand vertebrate development, gene function and healingrepair mechanisms in vertebrates. The embryo is previously labeled through the ubiquitous expression of fluorescent proteins addressed to cells nuclei and membranes, and temporal sequences of volumetric images are acquired with laser scanning microscopy. Cells position is detected by processing nuclei images either through the generalized form of the Hough transform or identifying nuclei position with local maxima after a smoothing preprocessing step. Membranes and nuclei shapes are reconstructed by using PDEs based variational techniques such as the Subjective Surfaces and the Chan Vese method. Cells tracking is performed by combining informations previously detected on cells shape and position with biological regularization constraints. Our results are manually validated and reconstruct the formation of zebrafish brain at 7-8 somite stage with all the cells tracked starting from late sphere stage with less than 2% error for at least 6 hours. Our reconstruction opens the way to a systematic investigation of cellular behaviors, of clonal origin and clonal complexity of brain organs, as well as the contribution of cell proliferation modes and cell movements to the formation of local patterns and morphogenetic fields.