Testing phenomenological and theoretical models of dark matter density profiles with galaxy clusters

We use the stacked gravitational lensingmass profile of four high-mass (M 1015M ) galaxy clusters around z≈0.3 from Umetsu et al. to fit density profiles of phenomenological [Navarro– Frenk–White (NFW), Einasto, S´ersic, Stadel, Baltz–Marshall–Oguri (BMO) and Hernquist] and theoretical (non-singular Isothermal Sphere, DARKexp and Kang & He) models of the dark matter distribution. We account for large-scale structure effects, including a two-halo term in the analysis.We find that the BMO model provides the best fit to the data as measured by the reduced χ2. It is followed by the Stadel profile, the generalized NFW profile with a free inner slope and by the Einasto profile. The NFW model provides the best fit if we neglect the two-halo term, in agreement with results from Umetsu et al. Among the theoretical profiles, the DARKexp model with a single form parameter has the best performance, very close to that of the BMO profile. This may indicate a connection between this theoretical model and the phenomenology of dark matter haloes, shedding light on the dynamical basis of empirical profiles which emerge from numerical simulations.

Creep and damage models for the service behaviour of structural members

Deformability is often a crucial to the conception of many civil-engineering structural elements. Also, design is all the more burdensome if both long- and short-term deformability has to be considered. In this thesis, long- and short-term deformability has been studied from the material and the structural modelling point of view. Moreover, two materials have been handled: pultruded composites and concrete. A new finite element model for thin-walled beams has been introduced. As a main assumption, cross-sections rigid are considered rigid in their plane; this hypothesis replaces that of the classical beam theory of plane cross-sections in the deformed state. That also allows reducing the total number of degrees of freedom, and therefore making analysis faster compared with twodimensional finite elements. Longitudinal direction warping is left free, allowing describing phenomena such as the shear lag. The new finite-element model has been first applied to concrete thin-walled beams (such as roof high span girders or bridge girders) subject to instantaneous service loadings. Concrete in his cracked state has been considered through a smeared crack model for beams under bending. At a second stage, the FE-model has been extended to the viscoelastic field and applied to pultruded composite beams under sustained loadings. The generalized Maxwell model has been adopted. As far as materials are concerned, long-term creep tests have been carried out on pultruded specimens. Both tension and shear tests have been executed. Some specimen has been strengthened with carbon fibre plies to reduce short- and long- term deformability. Tests have been done in a climate room and specimens kept 2 years under constant load in time. As for concrete, a model for tertiary creep has been proposed. The basic idea is to couple the UMLV linear creep model with a damage model in order to describe nonlinearity. An effective strain tensor, weighting the total and the elasto-damaged strain tensors, controls damage evolution through the damage loading function. Creep strains are related to the effective stresses (defined by damage models) and so associated to the intact material.

Development of Clinical Decision Support Systems based on Mathematical Models of Physiological Systems

In the last years of research, I focused my studies on different physiological problems. Together with my supervisors, I developed/improved different mathematical models in order to create valid tools useful for a better understanding of important clinical issues. The aim of all this work is to develop tools for learning and understanding cardiac and cerebrovascular physiology as well as pathology, generating research questions and developing clinical decision support systems useful for intensive care unit patients. I. ICP-model Designed for Medical Education We developed a comprehensive cerebral blood flow and intracranial pressure model to simulate and study the complex interactions in cerebrovascular dynamics caused by multiple simultaneous alterations, including normal and abnormal functional states of auto-regulation of the brain. Individual published equations (derived from prior animal and human studies) were implemented into a comprehensive simulation program. Included in the normal physiological modelling was: intracranial pressure, cerebral blood flow, blood pressure, and carbon dioxide (CO2) partial pressure. We also added external and pathological perturbations, such as head up position and intracranial haemorrhage. The model performed clinically realistically given inputs of published traumatized patients, and cases encountered by clinicians. The pulsatile nature of the output graphics was easy for clinicians to interpret. The manoeuvres simulated include changes of basic physiological inputs (e.g. blood pressure, central venous pressure, CO2 tension, head up position, and respiratory effects on vascular pressures) as well as pathological inputs (e.g. acute intracranial bleeding, and obstruction of cerebrospinal outflow). Based on the results, we believe the model would be useful to teach complex relationships of brain haemodynamics and study clinical research questions such as the optimal head-up position, the effects of intracranial haemorrhage on cerebral haemodynamics, as well as the best CO2 concentration to reach the optimal compromise between intracranial pressure and perfusion. We believe this model would be useful for both beginners and advanced learners. It could be used by practicing clinicians to model individual patients (entering the effects of needed clinical manipulations, and then running the model to test for optimal combinations of therapeutic manoeuvres). II. A Heterogeneous Cerebrovascular Mathematical Model Cerebrovascular pathologies are extremely complex, due to the multitude of factors acting simultaneously on cerebral haemodynamics. In this work, the mathematical model of cerebral haemodynamics and intracranial pressure dynamics, described in the point I, is extended to account for heterogeneity in cerebral blood flow. The model includes the Circle of Willis, six regional districts independently regulated by autoregulation and CO2 reactivity, distal cortical anastomoses, venous circulation, the cerebrospinal fluid circulation, and the intracranial pressure-volume relationship. Results agree with data in the literature and highlight the existence of a monotonic relationship between transient hyperemic response and the autoregulation gain. During unilateral internal carotid artery stenosis, local blood flow regulation is progressively lost in the ipsilateral territory with the presence of a steal phenomenon, while the anterior communicating artery plays the major role to redistribute the available blood flow. Conversely, distal collateral circulation plays a major role during unilateral occlusion of the middle cerebral artery. In conclusion, the model is able to reproduce several different pathological conditions characterized by heterogeneity in cerebrovascular haemodynamics and can not only explain generalized results in terms of physiological mechanisms involved, but also, by individualizing parameters, may represent a valuable tool to help with difficult clinical decisions. III. Effect of Cushing Response on Systemic Arterial Pressure. During cerebral hypoxic conditions, the sympathetic system causes an increase in arterial pressure (Cushing response), creating a link between the cerebral and the systemic circulation. This work investigates the complex relationships among cerebrovascular dynamics, intracranial pressure, Cushing response, and short-term systemic regulation, during plateau waves, by means of an original mathematical model. The model incorporates the pulsating heart, the pulmonary circulation and the systemic circulation, with an accurate description of the cerebral circulation and the intracranial pressure dynamics (same model as in the first paragraph). Various regulatory mechanisms are included: cerebral autoregulation, local blood flow control by oxygen (O2) and/or CO2 changes, sympathetic and vagal regulation of cardiovascular parameters by several reflex mechanisms (chemoreceptors, lung-stretch receptors, baroreceptors). The Cushing response has been described assuming a dramatic increase in sympathetic activity to vessels during a fall in brain O2 delivery. With this assumption, the model is able to simulate the cardiovascular effects experimentally observed when intracranial pressure is artificially elevated and maintained at constant level (arterial pressure increase and bradicardia). According to the model, these effects arise from the interaction between the Cushing response and the baroreflex response (secondary to arterial pressure increase). Then, patients with severe head injury have been simulated by reducing intracranial compliance and cerebrospinal fluid reabsorption. With these changes, oscillations with plateau waves developed. In these conditions, model results indicate that the Cushing response may have both positive effects, reducing the duration of the plateau phase via an increase in cerebral perfusion pressure, and negative effects, increasing the intracranial pressure plateau level, with a risk of greater compression of the cerebral vessels. This model may be of value to assist clinicians in finding the balance between clinical benefits of the Cushing response and its shortcomings. IV. Comprehensive Cardiopulmonary Simulation Model for the Analysis of Hypercapnic Respiratory Failure We developed a new comprehensive cardiopulmonary model that takes into account the mutual interactions between the cardiovascular and the respiratory systems along with their short-term regulatory mechanisms. The model includes the heart, systemic and pulmonary circulations, lung mechanics, gas exchange and transport equations, and cardio-ventilatory control. Results show good agreement with published patient data in case of normoxic and hyperoxic hypercapnia simulations. In particular, simulations predict a moderate increase in mean systemic arterial pressure and heart rate, with almost no change in cardiac output, paralleled by a relevant increase in minute ventilation, tidal volume and respiratory rate. The model can represent a valid tool for clinical practice and medical research, providing an alternative way to experience-based clinical decisions. In conclusion, models are not only capable of summarizing current knowledge, but also identifying missing knowledge. In the former case they can serve as training aids for teaching the operation of complex systems, especially if the model can be used to demonstrate the outcome of experiments. In the latter case they generate experiments to be performed to gather the missing data.

Algorithms and Models For Combinatorial Optimization Problems

In this thesis we present some combinatorial optimization problems, suggest models and algorithms for their effective solution. For each problem,we give its description, followed by a short literature review, provide methods to solve it and, finally, present computational results and comparisons with previous works to show the effectiveness of the proposed approaches. The considered problems are: the Generalized Traveling Salesman Problem (GTSP), the Bin Packing Problem with Conflicts(BPPC) and the Fair Layout Problem (FLOP).

Refined Gelfand models for some finite complex reflection groups

In 'Involutory reflection groups and their models' (F. Caselli, 2010), a uniform Gelfand model is constructed for all complex reflection groups G(r,p,n) satisfying GCD(p,n)=1,2 and for all their quotients modulo a scalar subgroup. The present work provides a refinement for this model. The final decomposition obtained is compatible with the Robinson-Schensted generalized correspondence.

Fiber beam-columns models with flexure-shear interaction for nonlinear analysis of reinforced concrete structures

The aim of this study was to develop a model capable to capture the different contributions which characterize the nonlinear behaviour of reinforced concrete structures. In particular, especially for non slender structures, the contribution to the nonlinear deformation due to bending may be not sufficient to determine the structural response. Two different models characterized by a fibre beam-column element are here proposed. These models can reproduce the flexure-shear interaction in the nonlinear range, with the purpose to improve the analysis in shear-critical structures. The first element discussed is based on flexibility formulation which is associated with the Modified Compression Field Theory as material constitutive law. The other model described in this thesis is based on a three-field variational formulation which is associated with a 3D generalized plastic-damage model as constitutive relationship. The first model proposed in this thesis was developed trying to combine a fibre beamcolumn element based on the flexibility formulation with the MCFT theory as constitutive relationship. The flexibility formulation, in fact, seems to be particularly effective for analysis in the nonlinear field. Just the coupling between the fibre element to model the structure and the shear panel to model the individual fibres allows to describe the nonlinear response associated to flexure and shear, and especially their interaction in the nonlinear field. The model was implemented in an original matlab® computer code, for describing the response of generic structures. The simulations carried out allowed to verify the field of working of the model. Comparisons with available experimental results related to reinforced concrete shears wall were performed in order to validate the model. These results are characterized by the peculiarity of distinguishing the different contributions due to flexure and shear separately. The presented simulations were carried out, in particular, for monotonic loading. The model was tested also through numerical comparisons with other computer programs. Finally it was applied for performing a numerical study on the influence of the nonlinear shear response for non slender reinforced concrete (RC) members. Another approach to the problem has been studied during a period of research at the University of California Berkeley. The beam formulation follows the assumptions of the Timoshenko shear beam theory for the displacement field, and uses a three-field variational formulation in the derivation of the element response. A generalized plasticity model is implemented for structural steel and a 3D plastic-damage model is used for the simulation of concrete. The transverse normal stress is used to satisfy the transverse equilibrium equations of at each control section, this criterion is also used for the condensation of degrees of freedom from the 3D constitutive material to a beam element. In this thesis is presented the beam formulation and the constitutive relationships, different analysis and comparisons are still carrying out between the two model presented.

Conditional and transgenic mouse models as tools to study the role of TGFbeta, BMP signaling in skeletal development

Die TGFbeta/BMP Signaltransduktionskaskade ist wichtig für viele Entwicklungsprozesse fast aller embryonaler sowie extraembryonaler Gewebe und sie ist ebenso essentiell bei der Aufrechterhaltung der Homöostase im adulten Organismus. In vielen Mausmodellen und Zellkulturversuchen wurde gezeigt, dass Liganden dieses Signalweges in verschiedene Stadien der Knorpel- und Knochenentwicklung involviert sind. BMPs sind beispielsweise maßgeblich an der frühen Kondensation und Bildung des Knorpels und später an Proliferation und Hypertrophie der Chondrozyten beteiligt. BMPs können ektopisch Knochenbildung auslösen und das Expressionsmuster der Liganden und spezifischen Rezeptoren in der Wachstumsfuge lässt auf eine wichtige Rolle der BMPs in der Wachstumsfuge schließen. Der gezielte knock out der BMP-Rezeptoren Bmpr1a und Bmpr1b in proliferierenden Chondrozyten führt zur Ausbildung einer generellen Chondrodysplasie. Smad1, Smad5 und Smad8 sind die Mediatoren der BMP-Signalkaskade. Im Rahmen der vorliegenden Arbeit sollte die Rolle und Funktion der Smad1- und Smad5-Proteine in der Wachstumsfuge untersucht werden. Hierzu wurden konditionale Smad1-knock out-Mäuse mit einer transgenen Mauslinie gekreuzt, die die Cre-Rekombinase spezifisch in proliferierenden Chondrozyten exprimiert. Diese Mäuse wurden mit und ohne heterozygotem Smad5-Hintergrund charakterisiert. Bei einem knock out von Smad1 allein konnte ein leichte Verkürzung der Wachstumsfuge beobachtet werden, wobei prähypertrophe und hypertrophe Zone gleichermaßen betroffen waren. Dieser Phänotyp war verstärkt in Mäusen mit zusätzlichem heterozygotem Smad5-Hintergrund. Eine Verringerung der Proliferationsrate konnte zusammen mit einer verminderten Ihh-Expression nachgewiesen werden. Zusätzlich konnte anhand von Röntgenaufnahmen eine Dysorganisation der nasalen Region und ein fehlendes nasales Septum beobachtet werden. Produktion und Mineralisation der extrazellulären Matrix waren nicht beeinträchtigt. Um die Rolle der BMP- und TGFbeta-Signalkaskaden während der endochondralen Ossifikation zu vergleichen, wurden transgene Mäuse generiert, in denen die TGFbeta-Signalkaskade spezifisch in proliferierenden Chondrozyten gestört war. Zwei Mauslinien, die ähnliche Phänotypen zeigten, wurden untersucht. Esl1 ist ein TGFbeta-bindendes Protein, von dem man annimmt, dass es die TGFbeta-Signalkaskade inhibieren kann. Esl1-knock out-Mäuse sind kleiner als Wildtypmäuse und die Überexpression von Esl1 in proliferierenden Chondrozyten führt zu einer Verlängerung der Wachstumsfuge und einer verstärkten Proliferationsrate. Knorpelmarker, wie Col2a1 und Sox9 sind in diesen Mäusen herunterreguliert, während Col10a1 und Ihh als Marker für die hypertrophe und prähypertrophe Zone herunterreguliert waren. Dies führt zu der Annahme, dass mehr Zellen in die terminale Differenzierung eintreten. Bei transgenen Mäusen, in denen ein dominant-negativer (dn) TGFbeta-Rezeptor in proliferierenden Chondrozyten überexprimiert wurde, konnte eine verlängerte prähypertrophe Zone, eine erhöhte Ihh-Expression, sowie eine verstärkte Proliferationsrate beobachtet werden. Zusätzlich konnte in homozygoten Tieren ein craniofacialer Phänotyp beschrieben werden, der zu Problemen bei der Nahrungsaufnahme und damit zu einer starken Wachstumsbeeinträchtigung führte. Die BMP- und TGFbeta-Signalkaskaden haben möglicherweise antagonistische Effekte in der Wachstumsfuge. Während der Ausfall von BMP in proliferierenden Chondrozyten aufgrund einer gesunkenen Proliferationsrate zu einer Verkürzung der Wachstumsfuge führte, kann man in Mäusen mit einer Störung der TGFbeta-Signalkaskade eine verstärkte Proliferation in einer daher verlängerten Wachstumsfuge beobachten. Ein weiteres Ziel dieser Arbeit war die Generation einer transgenen Mauslinie, die die Cre-Rekombinase spezifisch in hypertrophen Chondrozyten exprimiert. Promoterstudien mit transgenen Mäusen weisen darauf hin, dass ein putatives AP1-Element, etwa 4 kb vor dem ersten Exon des Col10a1 gelegen, wichtig für die spezifische Expression in hypertrophen Chondrozyten ist. Ein Konstrukt, dass vier Kopien dieses Elements und den basalen Promoter enthält, wurde benutzt, um die Cre-Rekombinase spezifisch zu exprimieren. Diese Mauslinie befindet sich in der Testphase und erste Daten deuten auf eine spezifische Expression der Cre-Rekombinase in hypertrophen Chondrozyten hin.

Multidimensional item response theory models with general and specific latent traits for ordinal data

The aim of the thesis is to propose a Bayesian estimation through Markov chain Monte Carlo of multidimensional item response theory models for graded responses with complex structures and correlated traits. In particular, this work focuses on the multiunidimensional and the additive underlying latent structures, considering that the first one is widely used and represents a classical approach in multidimensional item response analysis, while the second one is able to reflect the complexity of real interactions between items and respondents. A simulation study is conducted to evaluate the parameter recovery for the proposed models under different conditions (sample size, test and subtest length, number of response categories, and correlation structure). The results show that the parameter recovery is particularly sensitive to the sample size, due to the model complexity and the high number of parameters to be estimated. For a sufficiently large sample size the parameters of the multiunidimensional and additive graded response models are well reproduced. The results are also affected by the trade-off between the number of items constituting the test and the number of item categories. An application of the proposed models on response data collected to investigate Romagna and San Marino residents' perceptions and attitudes towards the tourism industry is also presented.

Markers Models in Survival Analysis and Applications to Issues Associated with AIDS

Jewell and Kalbfleisch (1992) consider the use of marker processes for applications related to estimation of the survival distribution of time to failure. Marker processes were assumed to be stochastic processes that, at a given point in time, provide information about the current hazard and consequently on the remaining time to failure. Particular attention was paid to calculations based on a simple additive model for the relationship between the hazard function at time t and the history of the marker process up until time t. Specific applications to the analysis of AIDS data included the use of markers as surrogate responses for onset of AIDS with censored data and as predictors of the time elapsed since infection in prevalent individuals. Here we review recent work on the use of marker data to tackle these kinds of problems with AIDS data. The Poisson marker process with an additive model, introduced in Jewell and Kalbfleisch (1992) may be a useful "test" example for comparison of various procedures.

Fitting ACE Structural Equation Models to Case-Control Family Data

Investigators interested in whether a disease aggregates in families often collect case-control family data, which consist of disease status and covariate information for families selected via case or control probands. Here, we focus on the use of case-control family data to investigate the relative contributions to the disease of additive genetic effects (A), shared family environment (C), and unique environment (E). To this end, we describe a ACE model for binary family data and then introduce an approach to fitting the model to case-control family data. The structural equation model, which has been described previously, combines a general-family extension of the classic ACE twin model with a (possibly covariate-specific) liability-threshold model for binary outcomes. Our likelihood-based approach to fitting involves conditioning on the proband’s disease status, as well as setting prevalence equal to a pre-specified value that can be estimated from the data themselves if necessary. Simulation experiments suggest that our approach to fitting yields approximately unbiased estimates of the A, C, and E variance components, provided that certain commonly-made assumptions hold. These assumptions include: the usual assumptions for the classic ACE and liability-threshold models; assumptions about shared family environment for relative pairs; and assumptions about the case-control family sampling, including single ascertainment. When our approach is used to fit the ACE model to Austrian case-control family data on depression, the resulting estimate of heritability is very similar to those from previous analyses of twin data.

Classification Using Generalized Partial Least Squares

The advances in computational biology have made simultaneous monitoring of thousands of features possible. The high throughput technologies not only bring about a much richer information context in which to study various aspects of gene functions but they also present challenge of analyzing data with large number of covariates and few samples. As an integral part of machine learning, classification of samples into two or more categories is almost always of interest to scientists. In this paper, we address the question of classification in this setting by extending partial least squares (PLS), a popular dimension reduction tool in chemometrics, in the context of generalized linear regression based on a previous approach, Iteratively ReWeighted Partial Least Squares, i.e. IRWPLS (Marx, 1996). We compare our results with two-stage PLS (Nguyen and Rocke, 2002A; Nguyen and Rocke, 2002B) and other classifiers. We show that by phrasing the problem in a generalized linear model setting and by applying bias correction to the likelihood to avoid (quasi)separation, we often get lower classification error rates.

Error models for microarray intensities

We derive the additive-multiplicative error model for microarray intensities, and describe two applications. For the detection of differentially expressed genes, we obtain a statistic whose variance is approximately independent of the mean intensity. For the post hoc calibration (normalization) of data with respect to experimental factors, we describe a method for parameter estimation.

Posterior Simulation in the Generalized Linear Model with Semiparmetric Random Effects

Generalized linear mixed models with semiparametric random effects are useful in a wide variety of Bayesian applications. When the random effects arise from a mixture of Dirichlet process (MDP) model, normal base measures and Gibbs sampling procedures based on the Pólya urn scheme are often used to simulate posterior draws. These algorithms are applicable in the conjugate case when (for a normal base measure) the likelihood is normal. In the non-conjugate case, the algorithms proposed by MacEachern and Müller (1998) and Neal (2000) are often applied to generate posterior samples. Some common problems associated with simulation algorithms for non-conjugate MDP models include convergence and mixing difficulties. This paper proposes an algorithm based on the Pólya urn scheme that extends the Gibbs sampling algorithms to non-conjugate models with normal base measures and exponential family likelihoods. The algorithm proceeds by making Laplace approximations to the likelihood function, thereby reducing the procedure to that of conjugate normal MDP models. To ensure the validity of the stationary distribution in the non-conjugate case, the proposals are accepted or rejected by a Metropolis-Hastings step. In the special case where the data are normally distributed, the algorithm is identical to the Gibbs sampler.

ON MARGINALIZED MULTILEVEL MODELS AND THEIR COMPUTATION

Clustered data analysis is characterized by the need to describe both systematic variation in a mean model and cluster-dependent random variation in an association model. Marginalized multilevel models embrace the robustness and interpretations of a marginal mean model, while retaining the likelihood inference capabilities and flexible dependence structures of a conditional association model. Although there has been increasing recognition of the attractiveness of marginalized multilevel models, there has been a gap in their practical application arising from a lack of readily available estimation procedures. We extend the marginalized multilevel model to allow for nonlinear functions in both the mean and association aspects. We then formulate marginal models through conditional specifications to facilitate estimation with mixed model computational solutions already in place. We illustrate this approach on a cerebrovascular deficiency crossover trial.

RANDOM EFFECTS MODELS IN A META-ANALYSIS OF THE ACCURACY OF DIAGNOSTIC TESTS WITHIN A GOLD STANDARD IN THE PRESENCE OF MISSING DATA

In evaluating the accuracy of diagnosis tests, it is common to apply two imperfect tests jointly or sequentially to a study population. In a recent meta-analysis of the accuracy of microsatellite instability testing (MSI) and traditional mutation analysis (MUT) in predicting germline mutations of the mismatch repair (MMR) genes, a Bayesian approach (Chen, Watson, and Parmigiani 2005) was proposed to handle missing data resulting from partial testing and the lack of a gold standard. In this paper, we demonstrate an improved estimation of the sensitivities and specificities of MSI and MUT by using a nonlinear mixed model and a Bayesian hierarchical model, both of which account for the heterogeneity across studies through study-specific random effects. The methods can be used to estimate the accuracy of two imperfect diagnostic tests in other meta-analyses when the prevalence of disease, the sensitivities and/or the specificities of diagnostic tests are heterogeneous among studies. Furthermore, simulation studies have demonstrated the importance of carefully selecting appropriate random effects on the estimation of diagnostic accuracy measurements in this scenario.