Statistical analysis of the error associated with the simplification of the stratigraphy in geotechnical models

The uncertainties in the determination of the stratigraphic profile of natural soils is one of the main problems in geotechnics, in particular for landslide characterization and modeling. The study deals with a new approach in geotechnical modeling which relays on a stochastic generation of different soil layers distributions, following a boolean logic – the method has been thus called BoSG (Boolean Stochastic Generation). In this way, it is possible to randomize the presence of a specific material interdigitated in a uniform matrix. In the building of a geotechnical model it is generally common to discard some stratigraphic data in order to simplify the model itself, assuming that the significance of the results of the modeling procedure would not be affected. With the proposed technique it is possible to quantify the error associated with this simplification. Moreover, it could be used to determine the most significant zones where eventual further investigations and surveys would be more effective to build the geotechnical model of the slope. The commercial software FLAC was used for the 2D and 3D geotechnical model. The distribution of the materials was randomized through a specifically coded MatLab program that automatically generates text files, each of them representing a specific soil configuration. Besides, a routine was designed to automate the computation of FLAC with the different data files in order to maximize the sample number. The methodology is applied with reference to a simplified slope in 2D, a simplified slope in 3D and an actual landslide, namely the Mortisa mudslide (Cortina d’Ampezzo, BL, Italy). However, it could be extended to numerous different cases, especially for hydrogeological analysis and landslide stability assessment, in different geological and geomorphological contexts.

Tools and methods for the quality assurance of force platforms in human movement analysis

The human movement analysis (HMA) aims to measure the abilities of a subject to stand or to walk. In the field of HMA, tests are daily performed in research laboratories, hospitals and clinics, aiming to diagnose a disease, distinguish between disease entities, monitor the progress of a treatment and predict the outcome of an intervention [Brand and Crowninshield, 1981; Brand, 1987; Baker, 2006]. To achieve these purposes, clinicians and researchers use measurement devices, like force platforms, stereophotogrammetric systems, accelerometers, baropodometric insoles, etc. This thesis focus on the force platform (FP) and in particular on the quality assessment of the FP data. The principal objective of our work was the design and the experimental validation of a portable system for the in situ calibration of FPs. The thesis is structured as follows: Chapter 1. Description of the physical principles used for the functioning of a FP: how these principles are used to create force transducers, such as strain gauges and piezoelectrics transducers. Then, description of the two category of FPs, three- and six-component, the signals acquisition (hardware structure), and the signals calibration. Finally, a brief description of the use of FPs in HMA, for balance or gait analysis. Chapter 2. Description of the inverse dynamics, the most common method used in the field of HMA. This method uses the signals measured by a FP to estimate kinetic quantities, such as joint forces and moments. The measures of these variables can not be taken directly, unless very invasive techniques; consequently these variables can only be estimated using indirect techniques, as the inverse dynamics. Finally, a brief description of the sources of error, present in the gait analysis. Chapter 3. State of the art in the FP calibration. The selected literature is divided in sections, each section describes: systems for the periodic control of the FP accuracy; systems for the error reduction in the FP signals; systems and procedures for the construction of a FP. In particular is detailed described a calibration system designed by our group, based on the theoretical method proposed by ?. This system was the “starting point” for the new system presented in this thesis. Chapter 4. Description of the new system, divided in its parts: 1) the algorithm; 2) the device; and 3) the calibration procedure, for the correct performing of the calibration process. The algorithm characteristics were optimized by a simulation approach, the results are here presented. In addiction, the different versions of the device are described. Chapter 5. Experimental validation of the new system, achieved by testing it on 4 commercial FPs. The effectiveness of the calibration was verified by measuring, before and after calibration, the accuracy of the FPs in measuring the center of pressure of an applied force. The new system can estimate local and global calibration matrices; by local and global calibration matrices, the non–linearity of the FPs was quantified and locally compensated. Further, a non–linear calibration is proposed. This calibration compensates the non– linear effect in the FP functioning, due to the bending of its upper plate. The experimental results are presented. Chapter 6. Influence of the FP calibration on the estimation of kinetic quantities, with the inverse dynamics approach. Chapter 7. The conclusions of this thesis are presented: need of a calibration of FPs and consequential enhancement in the kinetic data quality. Appendix: Calibration of the LC used in the presented system. Different calibration set–up of a 3D force transducer are presented, and is proposed the optimal set–up, with particular attention to the compensation of non–linearities. The optimal set–up is verified by experimental results.

Methodological improvement of 3D fluoroscopic analysis for the robust quantification of 3D kinematics of human joints

3D video-fluoroscopy is an accurate but cumbersome technique to estimate natural or prosthetic human joint kinematics. This dissertation proposes innovative methodologies to improve the 3D fluoroscopic analysis reliability and usability. Being based on direct radiographic imaging of the joint, and avoiding soft tissue artefact that limits the accuracy of skin marker based techniques, the fluoroscopic analysis has a potential accuracy of the order of mm/deg or better. It can provide fundamental informations for clinical and methodological applications, but, notwithstanding the number of methodological protocols proposed in the literature, time consuming user interaction is exploited to obtain consistent results. The user-dependency prevented a reliable quantification of the actual accuracy and precision of the methods, and, consequently, slowed down the translation to the clinical practice. The objective of the present work was to speed up this process introducing methodological improvements in the analysis. In the thesis, the fluoroscopic analysis was characterized in depth, in order to evaluate its pros and cons, and to provide reliable solutions to overcome its limitations. To this aim, an analytical approach was followed. The major sources of error were isolated with in-silico preliminary studies as: (a) geometric distortion and calibration errors, (b) 2D images and 3D models resolutions, (c) incorrect contour extraction, (d) bone model symmetries, (e) optimization algorithm limitations, (f) user errors. The effect of each criticality was quantified, and verified with an in-vivo preliminary study on the elbow joint. The dominant source of error was identified in the limited extent of the convergence domain for the local optimization algorithms, which forced the user to manually specify the starting pose for the estimating process. To solve this problem, two different approaches were followed: to increase the optimal pose convergence basin, the local approach used sequential alignments of the 6 degrees of freedom in order of sensitivity, or a geometrical feature-based estimation of the initial conditions for the optimization; the global approach used an unsupervised memetic algorithm to optimally explore the search domain. The performances of the technique were evaluated with a series of in-silico studies and validated in-vitro with a phantom based comparison with a radiostereometric gold-standard. The accuracy of the method is joint-dependent, and for the intact knee joint, the new unsupervised algorithm guaranteed a maximum error lower than 0.5 mm for in-plane translations, 10 mm for out-of-plane translation, and of 3 deg for rotations in a mono-planar setup; and lower than 0.5 mm for translations and 1 deg for rotations in a bi-planar setups. The bi-planar setup is best suited when accurate results are needed, such as for methodological research studies. The mono-planar analysis may be enough for clinical application when the analysis time and cost may be an issue. A further reduction of the user interaction was obtained for prosthetic joints kinematics. A mixed region-growing and level-set segmentation method was proposed and halved the analysis time, delegating the computational burden to the machine. In-silico and in-vivo studies demonstrated that the reliability of the new semiautomatic method was comparable to a user defined manual gold-standard. The improved fluoroscopic analysis was finally applied to a first in-vivo methodological study on the foot kinematics. Preliminary evaluations showed that the presented methodology represents a feasible gold-standard for the validation of skin marker based foot kinematics protocols.

Methods for Clearance Influence Analysis in Planar and Spatial Mechanisms

This doctoral dissertation presents a new method to asses the influence of clearancein the kinematic pairs on the configuration of planar and spatial mechanisms. The subject has been widely investigated in both past and present scientific literature, and is approached in different ways: a static/kinetostatic way, which looks for the clearance take-up due to the external loads on the mechanism; a probabilistic way, which expresses clearance-due displacements using probability density functions; a dynamic way, which evaluates dynamic effects like the actual forces in the pairs caused by impacts, or the consequent vibrations. This dissertation presents a new method to approach the problem of clearance. The problem is studied from a purely kinematic perspective. With reference to a given mechanism configuration, the pose (position and orientation) error of the mechanism link of interest is expressed as a vector function of the degrees of freedom introduced in each pair by clearance: the presence of clearance in a kinematic pair, in facts, causes the actual pair to have more degrees of freedom than the theoretical clearance-free one. The clearance-due degrees of freedom are bounded by the pair geometry. A proper modelling of clearance-affected pairs allows expressing such bounding through analytical functions. It is then possible to study the problem as a maximization problem, where a continuous function (the pose error of the link of interest) subject to some constraints (the analytical functions bounding clearance- due degrees of freedom) has to be maximize. Revolute, prismatic, cylindrical, and spherical clearance-affected pairs have been analytically modelled; with reference to mechanisms involving such pairs, the solution to the maximization problem has been obtained in a closed form.

Genome characterization through a mathematical model of the genetic code: an analysis of the whole chromosome 1 of A. thaliana

The objective of this work is to characterize the genome of the chromosome 1 of A.thaliana, a small flowering plants used as a model organism in studies of biology and genetics, on the basis of a recent mathematical model of the genetic code. I analyze and compare different portions of the genome: genes, exons, coding sequences (CDS), introns, long introns, intergenes, untranslated regions (UTR) and regulatory sequences. In order to accomplish the task, I transformed nucleotide sequences into binary sequences based on the definition of the three different dichotomic classes. The descriptive analysis of binary strings indicate the presence of regularities in each portion of the genome considered. In particular, there are remarkable differences between coding sequences (CDS and exons) and non-coding sequences, suggesting that the frame is important only for coding sequences and that dichotomic classes can be useful to recognize them. Then, I assessed the existence of short-range dependence between binary sequences computed on the basis of the different dichotomic classes. I used three different measures of dependence: the well-known chi-squared test and two indices derived from the concept of entropy i.e. Mutual Information (MI) and Sρ, a normalized version of the “Bhattacharya Hellinger Matusita distance”. The results show that there is a significant short-range dependence structure only for the coding sequences whose existence is a clue of an underlying error detection and correction mechanism. No doubt, further studies are needed in order to assess how the information carried by dichotomic classes could discriminate between coding and noncoding sequence and, therefore, contribute to unveil the role of the mathematical structure in error detection and correction mechanisms. Still, I have shown the potential of the approach presented for understanding the management of genetic information.

Inverse Static Analysis of Massive Parallel Arrays of Three-State Actuators via Artificial Intelligence

Massive parallel robots (MPRs) driven by discrete actuators are force regulated robots that undergo continuous motions despite being commanded through a finite number of states only. Designing a real-time control of such systems requires fast and efficient methods for solving their inverse static analysis (ISA), which is a challenging problem and the subject of this thesis. In particular, five Artificial intelligence methods are proposed to investigate the on-line computation and the generalization error of ISA problem of a class of MPRs featuring three-state force actuators and one degree of revolute motion.

Differential expression analysis for sequence count data via mixtures of negative binomials

The recent advent of Next-generation sequencing technologies has revolutionized the way of analyzing the genome. This innovation allows to get deeper information at a lower cost and in less time, and provides data that are discrete measurements. One of the most important applications with these data is the differential analysis, that is investigating if one gene exhibit a different expression level in correspondence of two (or more) biological conditions (such as disease states, treatments received and so on). As for the statistical analysis, the final aim will be statistical testing and for modeling these data the Negative Binomial distribution is considered the most adequate one especially because it allows for "over dispersion". However, the estimation of the dispersion parameter is a very delicate issue because few information are usually available for estimating it. Many strategies have been proposed, but they often result in procedures based on plug-in estimates, and in this thesis we show that this discrepancy between the estimation and the testing framework can lead to uncontrolled first-type errors. We propose a mixture model that allows each gene to share information with other genes that exhibit similar variability. Afterwards, three consistent statistical tests are developed for differential expression analysis. We show that the proposed method improves the sensitivity of detecting differentially expressed genes with respect to the common procedures, since it is the best one in reaching the nominal value for the first-type error, while keeping elevate power. The method is finally illustrated on prostate cancer RNA-seq data.