Serum α-tocopherol has a nonlinear inverse association with periodontitis among US adults

Background: Previous experimental models suggest that vitamin E may ameliorate periodontitis. However, epidemiologic studies show inconsistent evidence in supporting this plausible association. Objective: We aimed to investigate the association between serum α-tocopherol (αT) and γ-tocopherol (γT) and periodontitis in a large cross-sectional US population. Methods: This study included 4708 participants in the 1999–2001 NHANES. Serum tocopherols were measured by HPLC and values were adjusted by total cholesterol (TC). Periodontal status was assessed by mean clinical attachment loss (CAL) and probing pocket depth (PPD). Total periodontitis (TPD) was defined as the sum of mild, moderate, and severe periodontitis. All measurements were performed by NHANES. Results: Means ± SDs of serum αT:TC ratio from low to high quartiles were 4.0 ± 0.4, 4.8 ± 0.2, 5.7 ± 0.4, and 9.1 ± 2.7 μmol/mmol. In multivariate regression models, αT:TC quartiles were inversely associated with mean CAL (P-trend = 0.06), mean PPD (P-trend < 0.001), and TPD (P-trend < 0.001) overall. Adjusted mean differences (95% CIs) between the first and fourth quartile of αT:TC were 0.12 mm (0.03, 0.20; P-difference = 0.005) for mean CAL and 0.12 mm (0.06, 0.17; P < 0.001) for mean PPD, whereas corresponding OR for TPD was 1.65 (95% CI: 1.26, 2.16; P-difference = 0.001). In a dose-response analysis, a clear inverse association between αT:TC and mean CAL, mean PPD, and TPD was observed among participants with relatively low αT:TC. No differences were seen in participants with higher αT:TC ratios. Participants with γT:TC ratio in the interquartile range showed a significantly lower mean PPD than those in the highest quartile. Conclusions: A nonlinear inverse association was observed between serum αT and severity of periodontitis, which was restricted to adults with normal but relatively low αT status. These findings warrant further confirmation in longitudinal or intervention settings.

Nonlinear inverse synthesis technique for optical links with lumped amplification

The nonlinear inverse synthesis (NIS) method, in which information is encoded directly onto the continuous part of the nonlinear signal spectrum, has been proposed recently as a promising digital signal processing technique for combating fiber nonlinearity impairments. However, because the NIS method is based on the integrability property of the lossless nonlinear Schrödinger equation, the original approach can only be applied directly to optical links with ideal distributed Raman amplification. In this paper, we propose and assess a modified scheme of the NIS method, which can be used effectively in standard optical links with lumped amplifiers, such as, erbium-doped fiber amplifiers (EDFAs). The proposed scheme takes into account the average effect of the fiber loss to obtain an integrable model (lossless path-averaged model) to which the NIS technique is applicable. We found that the error between lossless pathaveraged and lossy models increases linearly with transmission distance and input power (measured in dB). We numerically demonstrate the feasibility of the proposed NIS scheme in a burst mode with orthogonal frequency division multiplexing (OFDM) transmission scheme with advanced modulation formats (e.g., QPSK, 16QAM, and 64QAM), showing a performance improvement up to 3.5 dB; these results are comparable to those achievable with multi-step per span digital backpropagation.

A mixture density network approach to modelling and exploiting uncertainty in nonlinear control problems

In nonlinear and stochastic control problems, learning an efficient feed-forward controller is not amenable to conventional neurocontrol methods. For these approaches, estimating and then incorporating uncertainty in the controller and feed-forward models can produce more robust control results. Here, we introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. A nonlinear multi-variable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non-Gaussian distributions of control signal as well as processes with hysteresis. © 2004 Elsevier Ltd. All rights reserved.

Serum α-tocopherol has a nonlinear inverse association with periodontitis among US adults

Previous experimental models suggest that vitamin E may ameliorate periodontitis. However, epidemiologic studies show inconsistent evidence in supporting this plausible association. We aimed to investigate the association between serum α-tocopherol (αT) and γ-tocopherol (γT) and periodontitis in a large cross-sectional US population. This study included 4708 participants in the 1999–2001 NHANES. Serum tocopherols were measured by HPLC and values were adjusted by total cholesterol (TC). Periodontal status was assessed by mean clinical attachment loss (CAL) and probing pocket depth (PPD). Total periodontitis (TPD) was defined as the sum of mild, moderate, and severe periodontitis. All measurements were performed by NHANES. Means ± SDs of serum αT:TC ratio from low to high quartiles were 4.0 ± 0.4, 4.8 ± 0.2, 5.7 ± 0.4, and 9.1 ± 2.7 μmol/mmol. In multivariate regression models, αT:TC quartiles were inversely associated with mean CAL (P-trend = 0.06), mean PPD (P-trend < 0.001), and TPD (P-trend < 0.001) overall. Adjusted mean differences (95% CIs) between the first and fourth quartile of αT:TC were 0.12 mm (0.03, 0.20; P-difference = 0.005) for mean CAL and 0.12 mm (0.06, 0.17; P < 0.001) for mean PPD, whereas corresponding OR for TPD was 1.65 (95% CI: 1.26, 2.16; P-difference = 0.001). In a dose-response analysis, a clear inverse association between αT:TC and mean CAL, mean PPD, and TPD was observed among participants with relatively low αT:TC. No differences were seen in participants with higher αT:TC ratios. Participants with γT:TC ratio in the interquartile range showed a significantly lower mean PPD than those in the highest quartile. A nonlinear inverse association was observed between serum αT and severity of periodontitis, which was restricted to adults with normal but relatively low αT status. These findings warrant further confirmation in longitudinal or intervention settings.

Optimization models for selecting bus stops for accessibility improvements for people with disabilities

Bus stops are key links in the journeys of transit patrons with disabilities. Inaccessible bus stops prevent people with disabilities from using fixed-route bus services, thus limiting their mobility. The Americans with Disabilities Act (ADA) of 1990 prescribes the minimum requirements for bus stop accessibility by riders with disabilities. Due to limited budgets, transit agencies can only select a limited number of bus stop locations for ADA improvements annually. These locations should preferably be selected such that they maximize the overall benefits to patrons with disabilities. In addition, transit agencies may also choose to implement the universal design paradigm, which involves higher design standards than current ADA requirements and can provide amenities that are useful for all riders, like shelters and lighting. Many factors can affect the decision to improve a bus stop, including rider-based aspects like the number of riders with disabilities, total ridership, customer complaints, accidents, deployment costs, as well as locational aspects like the location of employment centers, schools, shopping areas, and so on. These interlacing factors make it difficult to identify optimum improvement locations without the aid of an optimization model. This dissertation proposes two integer programming models to help identify a priority list of bus stops for accessibility improvements. The first is a binary integer programming model designed to identify bus stops that need improvements to meet the minimum ADA requirements. The second involves a multi-objective nonlinear mixed integer programming model that attempts to achieve an optimal compromise among the two accessibility design standards. Geographic Information System (GIS) techniques were used extensively to both prepare the model input and examine the model output. An analytic hierarchy process (AHP) was applied to combine all of the factors affecting the benefits to patrons with disabilities. An extensive sensitivity analysis was performed to assess the reasonableness of the model outputs in response to changes in model constraints. Based on a case study using data from Broward County Transit (BCT) in Florida, the models were found to produce a list of bus stops that upon close examination were determined to be highly logical. Compared to traditional approaches using staff experience, requests from elected officials, customer complaints, etc., these optimization models offer a more objective and efficient platform on which to make bus stop improvement suggestions.

Lump solitons in a higher-order nonlinear equation in 2+1 dimensions

We propose and examine an integrable system of nonlinear equations that generalizes the nonlinear Schrodinger equation to 2 + 1 dimensions. This integrable system of equations is a promising starting point to elaborate more accurate models in nonlinear optics and molecular systems within the continuum limit. The Lax pair for the system is derived after applying the singular manifold method. We also present an iterative procedure to construct the solutions from a seed solution. Solutions with one-, two-, and three-lump solitons are thoroughly discussed.

Coupled transport in rotor models

Acknowledgement One of us (AP) wishes to acknowledge S. Flach for enlightening discussions about the relationship between the DNLS equation and the rotor model.

Source localization of reaction-diffusion models for brain tumors

We propose a mathematically well-founded approach for locating the source (initial state) of density functions evolved within a nonlinear reaction-diffusion model. The reconstruction of the initial source is an ill-posed inverse problem since the solution is highly unstable with respect to measurement noise. To address this instability problem, we introduce a regularization procedure based on the nonlinear Landweber method for the stable determination of the source location. This amounts to solving a sequence of well-posed forward reaction-diffusion problems. The developed framework is general, and as a special instance we consider the problem of source localization of brain tumors. We show numerically that the source of the initial densities of tumor cells are reconstructed well on both imaging data consisting of simple and complex geometric structures.

Dynamic Programming Approaches for Estimating and Applying Large-scale Discrete Choice Models

People go through their life making all kinds of decisions, and some of these decisions affect their demand for transportation, for example, their choices of where to live and where to work, how and when to travel and which route to take. Transport related choices are typically time dependent and characterized by large number of alternatives that can be spatially correlated. This thesis deals with models that can be used to analyze and predict discrete choices in large-scale networks. The proposed models and methods are highly relevant for, but not limited to, transport applications. We model decisions as sequences of choices within the dynamic discrete choice framework, also known as parametric Markov decision processes. Such models are known to be difficult to estimate and to apply to make predictions because dynamic programming problems need to be solved in order to compute choice probabilities. In this thesis we show that it is possible to explore the network structure and the flexibility of dynamic programming so that the dynamic discrete choice modeling approach is not only useful to model time dependent choices, but also makes it easier to model large-scale static choices. The thesis consists of seven articles containing a number of models and methods for estimating, applying and testing large-scale discrete choice models. In the following we group the contributions under three themes: route choice modeling, large-scale multivariate extreme value (MEV) model estimation and nonlinear optimization algorithms. Five articles are related to route choice modeling. We propose different dynamic discrete choice models that allow paths to be correlated based on the MEV and mixed logit models. The resulting route choice models become expensive to estimate and we deal with this challenge by proposing innovative methods that allow to reduce the estimation cost. For example, we propose a decomposition method that not only opens up for possibility of mixing, but also speeds up the estimation for simple logit models, which has implications also for traffic simulation. Moreover, we compare the utility maximization and regret minimization decision rules, and we propose a misspecification test for logit-based route choice models. The second theme is related to the estimation of static discrete choice models with large choice sets. We establish that a class of MEV models can be reformulated as dynamic discrete choice models on the networks of correlation structures. These dynamic models can then be estimated quickly using dynamic programming techniques and an efficient nonlinear optimization algorithm. Finally, the third theme focuses on structured quasi-Newton techniques for estimating discrete choice models by maximum likelihood. We examine and adapt switching methods that can be easily integrated into usual optimization algorithms (line search and trust region) to accelerate the estimation process. The proposed dynamic discrete choice models and estimation methods can be used in various discrete choice applications. In the area of big data analytics, models that can deal with large choice sets and sequential choices are important. Our research can therefore be of interest in various demand analysis applications (predictive analytics) or can be integrated with optimization models (prescriptive analytics). Furthermore, our studies indicate the potential of dynamic programming techniques in this context, even for static models, which opens up a variety of future research directions.

Nonlinear soil-structure interaction for buried pressure pipes under differential ground motion

Pipelines extend thousands of kilometers across wide geographic areas as a network to provide essential services for modern life. It is inevitable that pipelines must pass through unfavorable ground conditions, which are susceptible to natural disasters. This thesis investigates the behaviour of buried pressure pipelines experiencing ground distortions induced by normal faulting. A recent large database of physical modelling observations on buried pipes of different stiffness relative to the surrounding soil subjected to normal faults provided a unique opportunity to calibrate numerical tools. Three-dimensional finite element models were developed to enable the complex soil-structure interaction phenomena to be further understood, especially on the subjects of gap formation beneath the pipe and the trench effect associated with the interaction between backfill and native soils. Benchmarked numerical tools were then used to perform parametric analysis regarding project geometry, backfill material, relative pipe-soil stiffness and pipe diameter. Seismic loading produces a soil displacement profile that can be expressed by isoil, the distance between the peak curvature and the point of contraflexure. A simplified design framework based on this length scale (i.e., the Kappa method) was developed, which features estimates of longitudinal bending moments of buried pipes using a characteristic length, ipipe, the distance from peak to zero curvature. Recent studies indicated that empirical soil springs that were calibrated against rigid pipes are not suitable for analyzing flexible pipes, since they lead to excessive conservatism (for design). A large-scale split-box normal fault simulator was therefore assembled to produce experimental data for flexible PVC pipe responses to a normal fault. Digital image correlation (DIC) was employed to analyze the soil displacement field, and both optical fibres and conventional strain gauges were used to measure pipe strains. A refinement to the Kappa method was introduced to enable the calculation of axial strains as a function of pipe elongation induced by flexure and an approximation of the longitudinal ground deformations. A closed-form Winkler solution of flexural response was also derived to account for the distributed normal fault pattern. Finally, these two analytical solutions were evaluated against the pipe responses observed in the large-scale laboratory tests.

Design, analysis and evaluation of sigma-delta based beamformers for medical ultrasound imaging applications

The inherent analogue nature of medical ultrasound signals in conjunction with the abundant merits provided by digital image acquisition, together with the increasing use of relatively simple front-end circuitries, have created considerable demand for single-bit  beamformers in digital ultrasound imaging systems. Furthermore, the increasing need to design lightweight ultrasound systems with low power consumption and low noise, provide ample justification for development and innovation in the use of single-bit  beamformers in ultrasound imaging systems. The overall aim of this research program is to investigate, establish, develop and confirm through a combination of theoretical analysis and detailed simulations, that utilize raw phantom data sets, suitable techniques for the design of simple-to-implement hardware efficient  digital ultrasound beamformers to address the requirements for 3D scanners with large channel counts, as well as portable and lightweight ultrasound scanners for point-of-care applications and intravascular imaging systems. In addition, the stability boundaries of higher-order High-Pass (HP) and Band-Pass (BP) Σ−Δ modulators for single- and dual- sinusoidal inputs are determined using quasi-linear modeling together with the describing-function method, to more accurately model the  modulator quantizer. The theoretical results are shown to be in good agreement with the simulation results for a variety of input amplitudes, bandwidths, and modulator orders. The proposed mathematical models of the quantizer will immensely help speed up the design of higher order HP and BP Σ−Δ modulators to be applicable for digital ultrasound beamformers. Finally, a user friendly design and performance evaluation tool for LP, BP and HP  modulators is developed. This toolbox, which uses various design methodologies and covers an assortment of  modulators topologies, is intended to accelerate the design process and evaluation of  modulators. This design tool is further developed to enable the design, analysis and evaluation of  beamformer structures including the noise analyses of the final B-scan images. Thus, this tool will allow researchers and practitioners to design and verify different reconstruction filters and analyze the results directly on the B-scan ultrasound images thereby saving considerable time and effort.

Model reduction for nonlinear aerodynamics and aeroelasticity using a Discrete Empirical Interpolation Method

A novel surrogate model is proposed in lieu of Computational Fluid Dynamics (CFD) solvers, for fast nonlinear aerodynamic and aeroelastic modeling. A nonlinear function is identified on selected interpolation points by
a discrete empirical interpolation method (DEIM). The flow field is then reconstructed using a least square approximation of the flow modes extracted
by proper orthogonal decomposition (POD). The aeroelastic reduce order
model (ROM) is completed by introducing a nonlinear mapping function
between displacements and the DEIM points. The proposed model is investigated to predict the aerodynamic forces due to forced motions using
a N ACA 0012 airfoil undergoing a prescribed pitching oscillation. To investigate aeroelastic problems at transonic conditions, a pitch/plunge airfoil
and a cropped delta wing aeroelastic models are built using linear structural models. The presence of shock-waves triggers the appearance of limit
cycle oscillations (LCO), which the model is able to predict. For all cases
tested, the new ROM shows the ability to replicate the nonlinear aerodynamic forces, structural displacements and reconstruct the complete flow
field with sufficient accuracy at a fraction of the cost of full order CFD
model.

Nonlinear distortion generation mechanisms in Doherty amplifiers

Nowadays, wireless communications systems demand for greater mobility and higher data rates. Moreover, the need for spectral efficiency requires the use of non-constant envelope modulation schemes. Hence, power amplifier designers have to build highly efficient, broadband and linear amplifiers. In order to fulfil these strict requirements, the practical Doherty amplifier seems to be the most promising technique. However, due to its complex operation, its nonlinear distortion generation mechanisms are not yet fully understood. Currently, only heuristic interpretations are being used to justify the observed phenomena. Therefore, the main objective of this work is to provide a model capable of describing the Doherty power amplifier nonlinear distortion generation mechanisms, allowing the optimization of its design according to linearity and efficiency criteria. Besides that, this approach will allow a bridge between two different worlds: power amplifier design and digital pre-distortion since the knowledge gathered from the Doherty operation will serve to select the most suitable pre-distortion models.

Development and Application of Predictive Models for Survival, Growth, and Death of Enteric Pathogens in Leafy Greens Supply Chain

Leafy greens are essential part of a healthy diet. Because of their health benefits, production and consumption of leafy greens has increased considerably in the U.S. in the last few decades. However, leafy greens are also associated with a large number of foodborne disease outbreaks in the last few years. The overall goal of this dissertation was to use the current knowledge of predictive models and available data to understand the growth, survival, and death of enteric pathogens in leafy greens at pre- and post-harvest levels. Temperature plays a major role in the growth and death of bacteria in foods. A growth-death model was developed for Salmonella and Listeria monocytogenes in leafy greens for varying temperature conditions typically encountered during supply chain. The developed growth-death models were validated using experimental dynamic time-temperature profiles available in the literature. Furthermore, these growth-death models for Salmonella and Listeria monocytogenes and a similar model for E. coli O157:H7 were used to predict the growth of these pathogens in leafy greens during transportation without temperature control. Refrigeration of leafy greens meets the purposes of increasing their shelf-life and mitigating the bacterial growth, but at the same time, storage of foods at lower temperature increases the storage cost. Nonlinear programming was used to optimize the storage temperature of leafy greens during supply chain while minimizing the storage cost and maintaining the desired levels of sensory quality and microbial safety. Most of the outbreaks associated with consumption of leafy greens contaminated with E. coli O157:H7 have occurred during July-November in the U.S. A dynamic system model consisting of subsystems and inputs (soil, irrigation, cattle, wildlife, and rainfall) simulating a farm in a major leafy greens producing area in California was developed. The model was simulated incorporating the events of planting, irrigation, harvesting, ground preparation for the new crop, contamination of soil and plants, and survival of E. coli O157:H7. The predictions of this system model are in agreement with the seasonality of outbreaks. This dissertation utilized the growth, survival, and death models of enteric pathogens in leafy greens during production and supply chain.

Digital nonlinear equalization for optical transmission systems

This thesis focuses on digital equalization of nonlinear fiber impairments for coherent optical transmission systems. Building from well-known physical models of signal propagation in single-mode optical fibers, novel nonlinear equalization techniques are proposed, numerically assessed and experimentally demonstrated. The structure of the proposed algorithms is strongly driven by the optimization of the performance versus complexity tradeoff, envisioning the near-future practical application in commercial real-time transceivers. The work is initially focused on the mitigation of intra-channel nonlinear impairments relying on the concept of digital backpropagation (DBP) associated with Volterra-based filtering. After a comprehensive analysis of the third-order Volterra kernel, a set of critical simplifications are identified, culminating in the development of reduced complexity nonlinear equalization algorithms formulated both in time and frequency domains. The implementation complexity of the proposed techniques is analytically described in terms of computational effort and processing latency, by determining the number of real multiplications per processed sample and the number of serial multiplications, respectively. The equalization performance is numerically and experimentally assessed through bit error rate (BER) measurements. Finally, the problem of inter-channel nonlinear compensation is addressed within the context of 400 Gb/s (400G) superchannels for long-haul and ultra-long-haul transmission. Different superchannel configurations and nonlinear equalization strategies are experimentally assessed, demonstrating that inter-subcarrier nonlinear equalization can provide an enhanced signal reach while requiring only marginal added complexity.