Framework development for providing accessibility to qualitative spatial calculi

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Active ageing index and quality of life

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Economics from the NOVA – School of Business and Economics

Designing cnc knit for hybrid membrane and bending active structures

Recent advances in computation allow for the integration of design and simulation of highly interrelated systems, such as hybrids of structural membranes and bending active elements. The engaged complexities of forces and logistics can be mediated through the development of materials with project specific properties and detailing. CNC knitting with high tenacity yarn enables this practice and offers an alternative to current woven membranes. The design and fabrication of an 8m high fabric tower through an interdisciplinary team of architects, structural and textile engineers, allowed to investigate means to design, specify, make and test CNC knit as material for hybrid structures in architectural scale. This paper shares the developed process, identifies challenges, potentials and future work.

Quantum field theory approach to the optical conductivity of strained and deformed graphene

The computation of the optical conductivity of strained and deformed graphene is discussed within the framework of quantum field theory in curved spaces. The analytical solutions of the Dirac equation in an arbitrary static background geometry for one dimensional periodic deformations are computed, together with the corresponding Dirac propagator. Analytical expressions are given for the optical conductivity of strained and deformed graphene associated with both intra and interbrand transitions. The special case of small deformations is discussed and the result compared to the prediction of the tight-binding model.

ADSNARK: Nearly practical and privacy-preserving proofs on authenticated data

We study the problem of privacy-preserving proofs on authenticated data, where a party receives data from a trusted source and is requested to prove computations over the data to third parties in a correct and private way, i.e., the third party learns no information on the data but is still assured that the claimed proof is valid. Our work particularly focuses on the challenging requirement that the third party should be able to verify the validity with respect to the specific data authenticated by the source — even without having access to that source. This problem is motivated by various scenarios emerging from several application areas such as wearable computing, smart metering, or general business-to-business interactions. Furthermore, these applications also demand any meaningful solution to satisfy additional properties related to usability and scalability. In this paper, we formalize the above three-party model, discuss concrete application scenarios, and then we design, build, and evaluate ADSNARK, a nearly practical system for proving arbitrary computations over authenticated data in a privacy-preserving manner. ADSNARK improves significantly over state-of-the-art solutions for this model. For instance, compared to corresponding solutions based on Pinocchio (Oakland’13), ADSNARK achieves up to 25× improvement in proof-computation time and a 20× reduction in prover storage space.

Diophantine approximation on projective varieties I: algebraic distance and metric Bézout theorem

"Vegeu el resum a l'inici del document del fitxer adjunt."

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Computation of an integral basis of a quartic number field

"Vegeu el resum a l'inici del document del fitxer adjunt."

Optimism and commitment: An elementary theory of bargaining and war

We propose an elementary theory of wars fought by fully rational contenders. Two parties play a Markov game that combines stages of bargaining with stages where one side has the ability to impose surrender on the other. Under uncertainty and incomplete information, in the unique equilibrium of the game, long confrontations occur: war arises when reality disappoints initial (rational) optimism, and it persist longer when both agents are optimists but reality proves both wrong. Bargaining proposals that are rejected initially might eventually be accepted after several periods of confrontation. We provide an explicit computation of the equilibrium, evaluating the probability of war, and its expected losses as a function of i) the costs of confrontation, ii) the asymmetry of the split imposed under surrender, and iii) the strengths of contenders at attack and defense. Changes in these parameters display non-monotonic effects.

Computation of an integral basis of quartic number field

"Vegeu el resum a l'inici del document del fitxer ajunt."

A Modulated Closed Form solution for Quantitative Susceptibility Mapping - A thorough evaluation and comparison to iterative methods based on edge prior knowledge.

The aim of this study is to perform a thorough comparison of quantitative susceptibility mapping (QSM) techniques and their dependence on the assumptions made. The compared methodologies were: two iterative single orientation methodologies minimizing the l2, l1TV norm of the prior knowledge of the edges of the object, one over-determined multiple orientation method (COSMOS) and anewly proposed modulated closed-form solution (MCF). The performance of these methods was compared using a numerical phantom and in-vivo high resolution (0.65mm isotropic) brain data acquired at 7T using a new coil combination method. For all QSM methods, the relevant regularization and prior-knowledge parameters were systematically changed in order to evaluate the optimal reconstruction in the presence and absence of a ground truth. Additionally, the QSM contrast was compared to conventional gradient recalled echo (GRE) magnitude and R2* maps obtained from the same dataset. The QSM reconstruction results of the single orientation methods show comparable performance. The MCF method has the highest correlation (corrMCF=0.95, r(2)MCF =0.97) with the state of the art method (COSMOS) with additional advantage of extreme fast computation time. The l-curve method gave the visually most satisfactory balance between reduction of streaking artifacts and over-regularization with the latter being overemphasized when the using the COSMOS susceptibility maps as ground-truth. R2* and susceptibility maps, when calculated from the same datasets, although based on distinct features of the data, have a comparable ability to distinguish deep gray matter structures.

3D gait assessment in young and elderly subjects using foot-worn inertial sensors.

This study describes the validation of a new wearable system for assessment of 3D spatial parameters of gait. The new method is based on the detection of temporal parameters, coupled to optimized fusion and de-drifted integration of inertial signals. Composed of two wirelesses inertial modules attached on feet, the system provides stride length, stride velocity, foot clearance, and turning angle parameters at each gait cycle, based on the computation of 3D foot kinematics. Accuracy and precision of the proposed system were compared to an optical motion capture system as reference. Its repeatability across measurements (test-retest reliability) was also evaluated. Measurements were performed in 10 young (mean age 26.1±2.8 years) and 10 elderly volunteers (mean age 71.6±4.6 years) who were asked to perform U-shaped and 8-shaped walking trials, and then a 6-min walking test (6MWT). A total of 974 gait cycles were used to compare gait parameters with the reference system. Mean accuracy±precision was 1.5±6.8cm for stride length, 1.4±5.6cm/s for stride velocity, 1.9±2.0cm for foot clearance, and 1.6±6.1° for turning angle. Difference in gait performance was observed between young and elderly volunteers during the 6MWT particularly in foot clearance. The proposed method allows to analyze various aspects of gait, including turns, gait initiation and termination, or inter-cycle variability. The system is lightweight, easy to wear and use, and suitable for clinical application requiring objective evaluation of gait outside of the lab environment.

THE USE OF SIMULATIONS IN EVOLUTIONARY POPULATION GENETICS: APPLICATIONS ON HUMANS, OWLS AND VIRTUAL ORGANISMS

Summary (in English) Computer simulations provide a practical way to address scientific questions that would be otherwise intractable. In evolutionary biology, and in population genetics in particular, the investigation of evolutionary processes frequently involves the implementation of complex models, making simulations a particularly valuable tool in the area. In this thesis work, I explored three questions involving the geographical range expansion of populations, taking advantage of spatially explicit simulations coupled with approximate Bayesian computation. First, the neutral evolutionary history of the human spread around the world was investigated, leading to a surprisingly simple model: A straightforward diffusion process of migrations from east Africa throughout a world map with homogeneous landmasses replicated to very large extent the complex patterns observed in real human populations, suggesting a more continuous (as opposed to structured) view of the distribution of modern human genetic diversity, which may play a better role as a base model for further studies. Second, the postglacial evolution of the European barn owl, with the formation of a remarkable coat-color cline, was inspected with two rounds of simulations: (i) determine the demographic background history and (ii) test the probability of a phenotypic cline, like the one observed in the natural populations, to appear without natural selection. We verified that the modern barn owl population originated from a single Iberian refugium and that they formed their color cline, not due to neutral evolution, but with the necessary participation of selection. The third and last part of this thesis refers to a simulation-only study inspired by the barn owl case above. In this chapter, we showed that selection is, indeed, effective during range expansions and that it leaves a distinguished signature, which can then be used to detect and measure natural selection in range-expanding populations. Résumé (en français) Les simulations fournissent un moyen pratique pour répondre à des questions scientifiques qui seraient inabordable autrement. En génétique des populations, l'étude des processus évolutifs implique souvent la mise en oeuvre de modèles complexes, et les simulations sont un outil particulièrement précieux dans ce domaine. Dans cette thèse, j'ai exploré trois questions en utilisant des simulations spatialement explicites dans un cadre de calculs Bayésiens approximés (approximate Bayesian computation : ABC). Tout d'abord, l'histoire de la colonisation humaine mondiale et de l'évolution de parties neutres du génome a été étudiée grâce à un modèle étonnement simple. Un processus de diffusion des migrants de l'Afrique orientale à travers un monde avec des masses terrestres homogènes a reproduit, dans une très large mesure, les signatures génétiques complexes observées dans les populations humaines réelles. Un tel modèle continu (opposé à un modèle structuré en populations) pourrait être très utile comme modèle de base dans l'étude de génétique humaine à l'avenir. Deuxièmement, l'évolution postglaciaire d'un gradient de couleur chez l'Effraie des clocher (Tyto alba) Européenne, a été examiné avec deux séries de simulations pour : (i) déterminer l'histoire démographique de base et (ii) tester la probabilité qu'un gradient phénotypique, tel qu'observé dans les populations naturelles puisse apparaître sans sélection naturelle. Nous avons montré que la population actuelle des chouettes est sortie d'un unique refuge ibérique et que le gradient de couleur ne peux pas s'être formé de manière neutre (sans l'action de la sélection naturelle). La troisième partie de cette thèse se réfère à une étude par simulations inspirée par l'étude de l'Effraie. Dans ce dernier chapitre, nous avons montré que la sélection est, en effet, aussi efficace dans les cas d'expansion d'aire de distribution et qu'elle laisse une signature unique, qui peut être utilisée pour la détecter et estimer sa force.

Population genetic structure and demography analysis in palinurus elephas populations from atlantic and mediterranean waters

Report for the scientific sojourn at the University of Reading, United Kingdom, from January until May 2008. The main objectives have been firstly to infer population structure and parameters in demographic models using a total of 13 microsatellite loci for genotyping approximately 30 individuals per population in 10 Palinurus elephas populations both from Mediterranean and Atlantic waters. Secondly, developing statistical methods to identify discrepant loci, possibly under selection and implement those methods using the R software environment. It is important to consider that the calculation of the probability distribution of the demographic and mutational parameters for a full genetic data set is numerically difficult for complex demographic history (Stephens 2003). The Approximate Bayesian Computation (ABC), based on summary statistics to infer posterior distributions of variable parameters without explicit likelihood calculations, can surmount this difficulty. This would allow to gather information on different demographic prior values (i.e. effective population sizes, migration rate, microsatellite mutation rate, mutational processes) and assay the sensitivity of inferences to demographic priors by assuming different priors.