Multiobjective engineering design optimization problems: a sensitivity analysis approach

This paper proposes two new approaches for the sensitivity analysis of multiobjective design optimization problems whose performance functions are highly susceptible to small variations in the design variables and/or design environment parameters. In both methods, the less sensitive design alternatives are preferred over others during the multiobjective optimization process. While taking the first approach, the designer chooses the design variable and/or parameter that causes uncertainties. The designer then associates a robustness index with each design alternative and adds each index as an objective function in the optimization problem. For the second approach, the designer must know, a priori, the interval of variation in the design variables or in the design environment parameters, because the designer will be accepting the interval of variation in the objective functions. The second method does not require any law of probability distribution of uncontrollable variations. Finally, the authors give two illustrative examples to highlight the contributions of the paper.

Quantification of cellular action fibers alignment from confocal microscopic images.

The cellular rheology has recently undergone a rapid development with particular attention to the cytoskeleton mechanical properties and its main components - actin filaments, intermediate filaments, microtubules and crosslinked proteins. However it is not clear what are the cellular structural changes that directly affect the cell mechanical properties. Thus, in this work, we aimed to quantify the structural rearrangement of these fibers that may emerge in changes in the cell mechanics. We created an image analysis platform to study smooth muscle cells from different arteries: aorta, mammary, renal, carotid and coronary and processed respectively 31, 29, 31, 30 and 35 cell image obtained by confocal microscopy. The platform was developed in Matlab (MathWorks) and it uses the Sobel operator to determine the actin fiber image orientation of the cell, labeled with phalloidin. The Sobel operator is used as a filter capable of calculating the pixel brightness gradient, point to point, in the image. The operator uses vertical and horizontal convolution kernels to calculate the magnitude and the angle of the pixel intensity gradient. The image analysis followed the sequence: (1) opens a given cells image set to be processed; (2) sets a fix threshold to eliminate noise, based on Otsu's method; (3) detect the fiber edges in the image using the Sobel operator; and (4) quantify the actin fiber orientation. Our first result is the probability distribution II(Δθ) to find a given fiber angle deviation (Δθ) from the main cell fiber orientation θ0. The II(Δθ) follows an exponential decay II(Δθ) = Aexp(-αΔθ) regarding to its θ0. We defined and determined a misalignment index α of the fibers of each artery kind: coronary αCo = (1.72 ‘+ or =’ 0.36)rad POT -1; renal αRe = (1.43 + or - 0.64)rad POT -1; aorta αAo = (1.42 + or - 0.43)rad POT -1; mammary αMa = (1.12 + or - 0.50)rad POT -1; and carotid αCa = (1.01 + or - 0.39)rad POT -1. The α of coronary and carotid are statistically different (p < 0.05) among all analyzed cells. We discussed our results correlating the misalignment index data with the experimental cell mechanical properties obtained by using Optical Magnetic Twisting Cytometry with the same group of cells.

EoR in alternative cosmological scenarios

The aim of this Thesis is to investigate the possibility that the observations related to the epoch of reionization can probe not only the evolution of the IGM state, but also the cosmological background in which this process occurs. In fact, the history of the IGM ionization is indeed affected by the evolution of the sources of ionizing photons that, under the assumption of a structure formation paradigm determined by the hierarchic growth of the matter uctuations, results strongly dependent on the characteristics of the background universe. For the purpose of our investigation, we have analysed the reionization history in innovative cosmological frameworks, still in agreement with the recent observational tests related to the SNIa and the CMB probes, comparing our results with the reionization scenario predicted by the commonly used LCDM cosmology. In particular, in this Thesis we have considered two different alternative universes. The first one is a at universe dominated at late epochs by a dynamic dark energy component, characterized by an equation of state evolving in time. The second cosmological framework we have assumed is a LCDM characterized by a primordial overdensity field having a non-Gaussian probability distribution. The reionization scenario have been investigated, in this Thesis, through semi-analytic approaches based on the hierarichic growth of the matter uctuations and on suitable assumptions concerning the ionization and the recombination of the IGM. We make predictions for the evolution and the distribution of the HII regions, and for the global features of reionization, that can be constrained by future observations. Finally, we brie y discuss the possible future prospects of this Thesis work.

Analysis and developments of uncertainty processors for real time flood forecasting

The hydrologic risk (and the hydro-geologic one, closely related to it) is, and has always been, a very relevant issue, due to the severe consequences that may be provoked by a flooding or by waters in general in terms of human and economic losses. Floods are natural phenomena, often catastrophic, and cannot be avoided, but their damages can be reduced if they are predicted sufficiently in advance. For this reason, the flood forecasting plays an essential role in the hydro-geological and hydrological risk prevention. Thanks to the development of sophisticated meteorological, hydrologic and hydraulic models, in recent decades the flood forecasting has made a significant progress, nonetheless, models are imperfect, which means that we are still left with a residual uncertainty on what will actually happen. In this thesis, this type of uncertainty is what will be discussed and analyzed. In operational problems, it is possible to affirm that the ultimate aim of forecasting systems is not to reproduce the river behavior, but this is only a means through which reducing the uncertainty associated to what will happen as a consequence of a precipitation event. In other words, the main objective is to assess whether or not preventive interventions should be adopted and which operational strategy may represent the best option. The main problem for a decision maker is to interpret model results and translate them into an effective intervention strategy. To make this possible, it is necessary to clearly define what is meant by uncertainty, since in the literature confusion is often made on this issue. Therefore, the first objective of this thesis is to clarify this concept, starting with a key question: should be the choice of the intervention strategy to adopt based on the evaluation of the model prediction based on its ability to represent the reality or on the evaluation of what actually will happen on the basis of the information given by the model forecast? Once the previous idea is made unambiguous, the other main concern of this work is to develope a tool that can provide an effective decision support, making possible doing objective and realistic risk evaluations. In particular, such tool should be able to provide an uncertainty assessment as accurate as possible. This means primarily three things: it must be able to correctly combine all the available deterministic forecasts, it must assess the probability distribution of the predicted quantity and it must quantify the flooding probability. Furthermore, given that the time to implement prevention strategies is often limited, the flooding probability will have to be linked to the time of occurrence. For this reason, it is necessary to quantify the flooding probability within a horizon time related to that required to implement the intervention strategy and it is also necessary to assess the probability of the flooding time.

Comparing Different Approaches for Clustering Categorical Data

There are different ways to do cluster analysis of categorical data in the literature and the choice among them is strongly related to the aim of the researcher, if we do not take into account time and economical constraints. Main approaches for clustering are usually distinguished into model-based and distance-based methods: the former assume that objects belonging to the same class are similar in the sense that their observed values come from the same probability distribution, whose parameters are unknown and need to be estimated; the latter evaluate distances among objects by a defined dissimilarity measure and, basing on it, allocate units to the closest group. In clustering, one may be interested in the classification of similar objects into groups, and one may be interested in finding observations that come from the same true homogeneous distribution. But do both of these aims lead to the same clustering? And how good are clustering methods designed to fulfil one of these aims in terms of the other? In order to answer, two approaches, namely a latent class model (mixture of multinomial distributions) and a partition around medoids one, are evaluated and compared by Adjusted Rand Index, Average Silhouette Width and Pearson-Gamma indexes in a fairly wide simulation study. Simulation outcomes are plotted in bi-dimensional graphs via Multidimensional Scaling; size of points is proportional to the number of points that overlap and different colours are used according to the cluster membership.

Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Single polymers at surfaces: adsorption and detachment

This thesis is concerned with the adsorption and detachment of polymers at planar, rigid surfaces. We have carried out a systematic investigation of adsorption of polymers using analytical techniques as well as Monte Carlo simulations with a coarse grained off-lattice bead spring model. The investigation was carried out in three stages. In the first stage the adsorption of a single multiblock AB copolymer on a solid surface was investigated by means of simulations and scaling analysis. It was shown that the problem could be mapped onto an effective homopolymer problem. Our main result was the phase diagram of regular multiblock copolymers which shows an increase in the critical adsorption potential of the substrate with decreasing size of blocks. We also considered the adsorption of random copolymers which was found to be well described within the annealed disorder approximation. In the next phase, we studied the adsorption kinetics of a single polymer on a flat, structureless surface in the regime of strong physisorption. The idea of a ’stem-flower’ polymer conformation and the mechanism of ’zipping’ during the adsorption process were used to derive a Fokker-Planck equation with reflecting boundary conditions for the time dependent probability distribution function (PDF) of the number of adsorbed monomers. The numerical solution of the time-dependent PDF obtained from a discrete set of coupled differential equations were shown to be in perfect agreement with Monte Carlo simulation results. Finally we studied force induced desorption of a polymer chain adsorbed on an attractive surface. We approached the problem within the framework of two different statistical ensembles; (i) by keeping the pulling force fixed while measuring the position of the polymer chain end, and (ii) by measuring the force necessary to keep the chain end at fixed distance above the adsorbing plane. In the first case we treated the problem within the framework of the Grand Canonical Ensemble approach and derived analytic expressions for the various conformational building blocks, characterizing the structure of an adsorbed linear polymer chain, subject to pulling force of fixed strength. The main result was the phase diagram of a polymer chain under pulling. We demonstrated a novel first order phase transformation which is dichotomic i.e. phase coexistence is not possible. In the second case, we carried out our study in the “fixed height” statistical ensemble where one measures the fluctuating force, exerted by the chain on the last monomer when a chain end is kept fixed at height h over the solid plane at different adsorption strength ε. The phase diagram in the h − ε plane was calculated both analytically and by Monte Carlo simulations. We demonstrated that in the vicinity of the polymer desorption transition a number of properties like fluctuations and probability distribution of various quantities behave differently, if h rather than the force, f, is used as an independent control parameter.

A probabilistic approach to classify the levee reliability

This work aims to evaluate the reliability of these levee systems, calculating the probability of “failure” of determined levee stretches under different loads, using probabilistic methods that take into account the fragility curves obtained through the Monte Carlo Method. For this study overtopping and piping are considered as failure mechanisms (since these are the most frequent) and the major levee system of the Po River with a primary focus on the section between Piacenza and Cremona, in the lower-middle area of the Padana Plain, is analysed. The novelty of this approach is to check the reliability of individual embankment stretches, not just a single section, while taking into account the variability of the levee system geometry from one stretch to another. This work takes also into consideration, for each levee stretch analysed, a probability distribution of the load variables involved in the definition of the fragility curves, where it is influenced by the differences in the topography and morphology of the riverbed along the sectional depth analysed as it pertains to the levee system in its entirety. A type of classification is proposed, for both failure mechanisms, to give an indication of the reliability of the levee system based of the information obtained by the fragility curve analysis. To accomplish this work, an hydraulic model has been developed where a 500-year flood is modelled to determinate the residual hazard value of failure for each stretch of levee near the corresponding water depth, then comparing the results with the obtained classifications. This work has the additional the aim of acting as an interface between the world of Applied Geology and Environmental Hydraulic Engineering where a strong collaboration is needed between the two professions to resolve and improve the estimation of hydraulic risk.

A Cox Model for Biostatistics of the Future

Professor Sir David R. Cox (DRC) is widely acknowledged as among the most important scientists of the second half of the twentieth century. He inherited the mantle of statistical science from Pearson and Fisher, advanced their ideas, and translated statistical theory into practice so as to forever change the application of statistics in many fields, but especially biology and medicine. The logistic and proportional hazards models he substantially developed, are arguably among the most influential biostatistical methods in current practice. This paper looks forward over the period from DRC's 80th to 90th birthdays, to speculate about the future of biostatistics, drawing lessons from DRC's contributions along the way. We consider "Cox's model" of biostatistics, an approach to statistical science that: formulates scientific questions or quantities in terms of parameters gamma in probability models f(y; gamma) that represent in a parsimonious fashion, the underlying scientific mechanisms (Cox, 1997); partition the parameters gamma = theta, eta into a subset of interest theta and other "nuisance parameters" eta necessary to complete the probability distribution (Cox and Hinkley, 1974); develops methods of inference about the scientific quantities that depend as little as possible upon the nuisance parameters (Barndorff-Nielsen and Cox, 1989); and thinks critically about the appropriate conditional distribution on which to base infrences. We briefly review exciting biomedical and public health challenges that are capable of driving statistical developments in the next decade. We discuss the statistical models and model-based inferences central to the CM approach, contrasting them with computationally-intensive strategies for prediction and inference advocated by Breiman and others (e.g. Breiman, 2001) and to more traditional design-based methods of inference (Fisher, 1935). We discuss the hierarchical (multi-level) model as an example of the future challanges and opportunities for model-based inference. We then consider the role of conditional inference, a second key element of the CM. Recent examples from genetics are used to illustrate these ideas. Finally, the paper examines causal inference and statistical computing, two other topics we believe will be central to biostatistics research and practice in the coming decade. Throughout the paper, we attempt to indicate how DRC's work and the "Cox Model" have set a standard of excellence to which all can aspire in the future.

Locally Efficient Estimation in Censored Data Models: Theory and Examples

In many applications the observed data can be viewed as a censored high dimensional full data random variable X. By the curve of dimensionality it is typically not possible to construct estimators that are asymptotically efficient at every probability distribution in a semiparametric censored data model of such a high dimensional censored data structure. We provide a general method for construction of one-step estimators that are efficient at a chosen submodel of the full-data model, are still well behaved off this submodel and can be chosen to always improve on a given initial estimator. These one-step estimators rely on good estimators of the censoring mechanism and thus will require a parametric or semiparametric model for the censoring mechanism. We present a general theorem that provides a template for proving the desired asymptotic results. We illustrate the general one-step estimation methods by constructing locally efficient one-step estimators of marginal distributions and regression parameters with right-censored data, current status data and bivariate right-censored data, in all models allowing the presence of time-dependent covariates. The conditions of the asymptotics theorem are rigorously verified in one of the examples and the key condition of the general theorem is verified for all examples.

Analysis of spring break-up and its effects on a biomass feedstock supply chain in northern Michigan

Demand for bio-fuels is expected to increase, due to rising prices of fossil fuels and concerns over greenhouse gas emissions and energy security. The overall cost of biomass energy generation is primarily related to biomass harvesting activity, transportation, and storage. With a commercial-scale cellulosic ethanol processing facility in Kinross Township of Chippewa County, Michigan about to be built, models including a simulation model and an optimization model have been developed to provide decision support for the facility. Both models track cost, emissions and energy consumption. While the optimization model provides guidance for a long-term strategic plan, the simulation model aims to present detailed output for specified operational scenarios over an annual period. Most importantly, the simulation model considers the uncertainty of spring break-up timing, i.e., seasonal road restrictions. Spring break-up timing is important because it will impact the feasibility of harvesting activity and the time duration of transportation restrictions, which significantly changes the availability of feedstock for the processing facility. This thesis focuses on the statistical model of spring break-up used in the simulation model. Spring break-up timing depends on various factors, including temperature, road conditions and soil type, as well as individual decision making processes at the county level. The spring break-up model, based on the historical spring break-up data from 27 counties over the period of 2002-2010, starts by specifying the probability distribution of a particular county’s spring break-up start day and end day, and then relates the spring break-up timing of the other counties in the harvesting zone to the first county. In order to estimate the dependence relationship between counties, regression analyses, including standard linear regression and reduced major axis regression, are conducted. Using realizations (scenarios) of spring break-up generated by the statistical spring breakup model, the simulation model is able to probabilistically evaluate different harvesting and transportation plans to help the bio-fuel facility select the most effective strategy. For early spring break-up, which usually indicates a longer than average break-up period, more log storage is required, total cost increases, and the probability of plant closure increases. The risk of plant closure may be partially offset through increased use of rail transportation, which is not subject to spring break-up restrictions. However, rail availability and rail yard storage may then become limiting factors in the supply chain. Rail use will impact total cost, energy consumption, system-wide CO2 emissions, and the reliability of providing feedstock to the bio-fuel processing facility.

On low-dimensional projections of high-dimensional distributions

Let P be a probability distribution on q -dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension d<distributions. The present paper provides necessary and sufficient conditions for this phenomenon in a suitable asymptotic framework with increasing dimension q . It turns out, that the conditions formulated by Diaconis and Freedman (1984) are not only sufficient but necessary as well. Moreover, letting P ^ be the empirical distribution of n independent random vectors with distribution P , we investigate the behavior of the empirical process n √ (P ^ −P) under random projections, conditional on P ^ .

Good just isn't Good enough. Best System Probabilities and the Foundations of Statistical Mechanics

Statistical physicists assume a probability distribution over micro-states to explain thermodynamic behavior. The question of this paper is whether these probabilities are part of a best system and can thus be interpreted as Humean chances. I consider two strategies, viz. a globalist as suggested by Loewer, and a localist as advocated by Frigg and Hoefer. Both strategies fail because the system they are part of have rivals that are roughly equally good, while ontic probabilities should be part of a clearly winning system. I conclude with the diagnosis that well-defined micro-probabilities under-estimate the robust character of explanations in statistical physics.

Good just isn't Good Enough: Humean Chances and Boltzmannian Statistical Physics

Statistical physicists assume a probability distribution over micro-states to explain thermodynamic behavior. The question of this paper is whether these probabilities are part of a best system and can thus be interpreted as Humean chances. I consider two Boltzmannian accounts of the Second Law, viz.\ a globalist and a localist one. In both cases, the probabilities fail to be chances because they have rivals that are roughly equally good. I conclude with the diagnosis that well-defined micro-probabilities under-estimate the robust character of explanations in statistical physics.

Empirical Analysis of Credit Risk Regime Switching and Temporal Conditional Default Correlation in Credit Default Swap Valuation: The Market liquidity effect

In this paper, we extend the debate concerning Credit Default Swap valuation to include time varying correlation and co-variances. Traditional multi-variate techniques treat the correlations between covariates as constant over time; however, this view is not supported by the data. Secondly, since financial data does not follow a normal distribution because of its heavy tails, modeling the data using a Generalized Linear model (GLM) incorporating copulas emerge as a more robust technique over traditional approaches. This paper also includes an empirical analysis of the regime switching dynamics of credit risk in the presence of liquidity by following the general practice of assuming that credit and market risk follow a Markov process. The study was based on Credit Default Swap data obtained from Bloomberg that spanned the period January 1st 2004 to August 08th 2006. The empirical examination of the regime switching tendencies provided quantitative support to the anecdotal view that liquidity decreases as credit quality deteriorates. The analysis also examined the joint probability distribution of the credit risk determinants across credit quality through the use of a copula function which disaggregates the behavior embedded in the marginal gamma distributions, so as to isolate the level of dependence which is captured in the copula function. The results suggest that the time varying joint correlation matrix performed far superior as compared to the constant correlation matrix; the centerpiece of linear regression models.