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.

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.

Three time-based scale formulations for the two-stage lot sizing and scheduling in process industries

In this paper, we propose three novel mathematical models for the two-stage lot-sizing and scheduling problems present in many process industries. The problem shares a continuous or quasi-continuous production feature upstream and a discrete manufacturing feature downstream, which must be synchronized. Different time-based scale representations are discussed. The first formulation encompasses a discrete-time representation. The second one is a hybrid continuous-discrete model. The last formulation is based on a continuous-time model representation. Computational tests with state-of-the-art MIP solver show that the discrete-time representation provides better feasible solutions in short running time. On the other hand, the hybrid model achieves better solutions for longer computational times and was able to prove optimality more often. The continuous-type model is the most flexible of the three for incorporating additional operational requirements, at a cost of having the worst computational performance. Journal of the Operational Research Society (2012) 63, 1613-1630. doi:10.1057/jors.2011.159 published online 7 March 2012

Validation of the Brazilian Portuguese version of the Beck Depression Inventory-II in a community sample

Background: The Beck Depression Inventory (BDI) is used worldwide for detecting depressive symptoms. This questionnaire has been revised (1996) to match the DSM-IV criteria for a major depressive episode. We assessed the reliability and the validity of the Brazilian Portuguese version of the BDI-II for non-clinical adults. Methods: The questionnaire was applied to 60 college students on two occasions. Afterwards, 182 community-dwelling adults completed the BDI-II, the Self-Report Questionnaire, and the K10 Scale. Trained psychiatrists performed face-to-face interviews with the respondents using the Structured Clinical Interview (SCID-I), the Montgomery-angstrom sberg Depression Scale, and the Hamilton Anxiety Scale. Descriptive analysis, signal detection analysis (Receiver Operating Characteristics), correlation analysis, and discriminant function analysis were performed to investigate the psychometric properties of the BDI-II. Results: The intraclass correlation coefficient of the BDI-II was 0.89, and the Cronbach's alpha coefficient of internal consistency was 0.93. Taking the SCID as the gold standard, the cut-off point of 10/11 was the best threshold for detecting depression, yielding a sensitivity of 70% and a specificity of 87%. The concurrent validity (a correlation of 0.63-0.93 with scales applied simultaneously) and the predictive ability of the severity level (over 65% correct classification) were acceptable. Conclusion: The BDI-II is reliable and valid for measuring depressive symptomatology among Portuguese-speaking Brazilian non-clinical populations.

Modeling the Emergence of Circadian Rhythms in a Clock Neuron Network

Circadian rhythms in pacemaker cells persist for weeks in constant darkness, while in other types of cells the molecular oscillations that underlie circadian rhythms damp rapidly under the same conditions. Although much progress has been made in understanding the biochemical and cellular basis of circadian rhythms, the mechanisms leading to damped or self-sustained oscillations remain largely unknown. There exist many mathematical models that reproduce the circadian rhythms in the case of a single cell of the Drosophila fly. However, not much is known about the mechanisms leading to coherent circadian oscillation in clock neuron networks. In this work we have implemented a model for a network of interacting clock neurons to describe the emergence (or damping) of circadian rhythms in Drosophila fly, in the absence of zeitgebers. Our model consists of an array of pacemakers that interact through the modulation of some parameters by a network feedback. The individual pacemakers are described by a well-known biochemical model for circadian oscillation, to which we have added degradation of PER protein by light and multiplicative noise. The network feedback is the PER protein level averaged over the whole network. In particular, we have investigated the effect of modulation of the parameters associated with (i) the control of net entrance of PER into the nucleus and (ii) the non-photic degradation of PER. Our results indicate that the modulation of PER entrance into the nucleus allows the synchronization of clock neurons, leading to coherent circadian oscillations under constant dark condition. On the other hand, the modulation of non-photic degradation cannot reset the phases of individual clocks subjected to intrinsic biochemical noise.

Prominent Effect of Soil Network Heterogeneity on Microbial Invasion

Using a network representation for real soil samples and mathematical models for microbial spread, we show that the structural heterogeneity of the soil habitat may have a very significant influence on the size of microbial invasions of the soil pore space. In particular, neglecting the soil structural heterogeneity may lead to a substantial underestimation of microbial invasion. Such effects are explained in terms of a crucial interplay between heterogeneity in microbial spread and heterogeneity in the topology of soil networks. The main influence of network topology on invasion is linked to the existence of long channels in soil networks that may act as bridges for transmission of microorganisms between distant parts of soil.

The tangential variation of a localized flux-type eigenvalue problem

In this work the differentiability of the principal eigenvalue lambda = lambda(1)(Gamma) to the localized Steklov problem -Delta u + qu = 0 in Omega, partial derivative u/partial derivative nu = lambda chi(Gamma)(x)u on partial derivative Omega, where Gamma subset of partial derivative Omega is a smooth subdomain of partial derivative Omega and chi(Gamma) is its characteristic function relative to partial derivative Omega, is shown. As a key point, the flux subdomain Gamma is regarded here as the variable with respect to which such differentiation is performed. An explicit formula for the derivative of lambda(1) (Gamma) with respect to Gamma is obtained. The lack of regularity up to the boundary of the first derivative of the principal eigenfunctions is a further intrinsic feature of the problem. Therefore, the whole analysis must be done in the weak sense of H(1)(Omega). The study is of interest in mathematical models in morphogenesis. (C) 2011 Elsevier Inc. All rights reserved.

Emergence of sensory selection mechanisms in Artificial Life simulations

Background The evolutionary advantages of selective attention are unclear. Since the study of selective attention began, it has been suggested that the nervous system only processes the most relevant stimuli because of its limited capacity [1]. An alternative proposal is that action planning requires the inhibition of irrelevant stimuli, which forces the nervous system to limit its processing [2]. An evolutionary approach might provide additional clues to clarify the role of selective attention. Methods We developed Artificial Life simulations wherein animals were repeatedly presented two objects, "left" and "right", each of which could be "food" or "non-food." The animals' neural networks (multilayer perceptrons) had two input nodes, one for each object, and two output nodes to determine if the animal ate each of the objects. The neural networks also had a variable number of hidden nodes, which determined whether or not it had enough capacity to process both stimuli (Table 1). The evolutionary relevance of the left and the right food objects could also vary depending on how much the animal's fitness was increased when ingesting them (Table 1). We compared sensory processing in animals with or without limited capacity, which evolved in simulations in which the objects had the same or different relevances. Table 1. Nine sets of simulations were performed, varying the values of food objects and the number of hidden nodes in the neural networks. The values of left and right food were swapped during the second half of the simulations. Non-food objects were always worth -3. The evolution of neural networks was simulated by a simple genetic algorithm. Fitness was a function of the number of food and non-food objects each animal ate and the chromosomes determined the node biases and synaptic weights. During each simulation, 10 populations of 20 individuals each evolved in parallel for 20,000 generations, then the relevance of food objects was swapped and the simulation was run again for another 20,000 generations. The neural networks were evaluated by their ability to identify the two objects correctly. The detectability (d') for the left and the right objects was calculated using Signal Detection Theory [3]. Results and conclusion When both stimuli were equally relevant, networks with two hidden nodes only processed one stimulus and ignored the other. With four or eight hidden nodes, they could correctly identify both stimuli. When the stimuli had different relevances, the d' for the most relevant stimulus was higher than the d' for the least relevant stimulus, even when the networks had four or eight hidden nodes. We conclude that selection mechanisms arose in our simulations depending not only on the size of the neuron networks but also on the stimuli's relevance for action.

Relationship between Vitamin D Receptor gene polymorphisms and the components of metabolic syndrome

Abstract Background The Vitamin D Receptor gene (VDR) is expressed in many tissues and modulates the expression of several other genes. The purpose of this study was to investigate the association between metabolic syndrome (MetSyn) with the presence of VDR 2228570 C > T and VDR 1544410 A > G polymorphisms in Brazilian adults. Methods Two hundred forty three (243) individuals were included in a cross-sectional study. MetSyn was classified using the criteria proposed by National Cholesterol Educational Program - Adult Treatment Panel III. Insulin resistance and β cell secretion were estimated by the mathematical models of HOMA IR and β, respectively. The VDR 2228570 C > T and VDR 1544410 A > G polymorphisms were detected by enzymatic digestion and confirmed by allele specific PCR or amplification of refractory mutation. Results Individuals with MetSyn and heterozygosis for VDR 2228570 C > T have higher concentrations of iPTH and HOMA β than those without this polymorphism, and subjects with recessive homozygosis for the same polymorphisms presented higher insulin resistance than those with the heterozygous genotype. There is no association among VDR 1544410 A > G and components of MetSyn, HOMA IR and β, serum vitamin D (25(OH)D3) and intact parathormone (iPTH) levels in patients with MetSyn. A significant lower concentration of 25(OH)D3 was observed only in individuals without MetSyn in the VDR 1544410 A > G genotype. Additionally, individuals without MetSyn and heterozygosis for VDR 2228570 C > T presented higher concentration of triglycerides and lower HDL than those without this polymorphism. Conclusions Using two common VDR polymorphism data suggests they may influence insulin secretion, insulin resistance an serum HDL-cholesterol in our highly heterogeneous population. Whether VDR polymorphism may influence the severity of MetSyn component disorder, warrants examination in larger cohorts used for genome-wide association studies.

Performance estimation for concretes made with recycled aggregates of construction and demolition waste of some Brazilian cities

The aim of this paper is to verify the influence of composition variability of recycled aggregates (RA) of construction and demolition wastes (CDW) on the performance of concretes. Performance was evaluated building mathematical models for compressive strength, modulus of elasticity and drying shrinkage. To obtain such models, an experimental program comprising 50 concrete mixtures was carried out. Specimens were casted, tested and results for compressive strength, modulus of elasticity and drying shrinkage were statistically analyzed. Models inputs are CDW composition observed at seven Brazilian cities. Results confirm that using RA from CDW for concrete building is quite feasible, independently of its composition, once compressive strength and modulus of elasticity still reached considerable values. We concluded the variability presented by recycled aggregates of CDW does not compromise their use for concrete building. However, this information must be used with caution, and experimental tests should always be performed to certify concrete properties.

Multimodality and flexibility of stochastic gene expression

We consider a general class of mathematical models for stochastic gene expression where the transcription rate is allowed to depend on a promoter state variable that can take an arbitrary (finite) number of values. We provide the solution of the master equations in the stationary limit, based on a factorization of the stochastic transition matrix that separates timescales and relative interaction strengths, and we express its entries in terms of parameters that have a natural physical and/or biological interpretation. The solution illustrates the capacity of multiple states promoters to generate multimodal distributions of gene products, without the need for feedback. Furthermore, using the example of a three states promoter operating at low, high, and intermediate expression levels, we show that using multiple states operons will typically lead to a significant reduction of noise in the system. The underlying mechanism is that a three-states promoter can change its level of expression from low to high by passing through an intermediate state with a much smaller increase of fluctuations than by means of a direct transition.