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Topics in the geometry of non Riemannian lie groups
Get PDFThis dissertation consists of an introduction and four papers. The papers deal with several problems of non-Riemannian metric spaces, such as sub-Riemannian Carnot groups and homogeneous metric spaces. The research has been carried out between the University of Trento (Italy) and the University of Jyväskylä (Finland) under the supervision of prof. F. Serra Cassano and E. Le Donne, respectively. In the following we present the abstracts of the four papers.
1) REGULARITY PROPERTIES OF SPHERES IN HOMOGENEOUS GROUPS
E. Le Donne AND S. Nicolussi Golo
We study left-invariant distances on Lie groups for which there exists a one-parameter family of homothetic automorphisms. The main examples are Carnot groups, in particular the Heisenberg group with the standard dilations. We are interested in criteria implying that, locally and away from the diagonal, the distance is Euclidean Lipschitz and, consequently, that the metric spheres are boundaries of Lipschitz domains in the Euclidean sense. In the first part of the paper, we consider geodesic distances. In this case, we actually prove the regularity of the distance in the more general context of sub-Finsler manifolds with no abnormal geodesics. Secondly, for general groups we identify an algebraic criterium in terms of the dilating automorphisms, which for example makes us conclude the regularity of every homogeneous distance on the Heisenberg group. In such a group, we analyze in more details the geometry of metric spheres. We also provide examples of homogeneous groups where spheres present cusps.
2) ASYMPTOTIC BEHAVIOR OF THE RIEMANNIAN HEISENBERG GROUP AND ITS HOROBOUNDARY
E. Le Donne, S. Nicolussi Golo, AND A. Sambusetti
The paper is devoted to the large scale geometry of the Heisenberg group H equipped with left-invariant Riemannian metrics. We prove that two such metrics have bounded difference if and only if they are asymptotic, i.e., their ratio goes to one, at infinity. Moreover, we show that for every left-invariant Riemannian metric d on H there is a unique sub-Riemanniann metric d' for which d − d' goes to zero at infinity, and we estimate the rate of convergence. As a first immediate consequence we get that the Riemannian Heisenberg group is at bounded distance from its asymptotic cone. The second consequence, which was our aim, is the explicit description of the horoboundary of the Riemannian Heisenberg group.
3) FROM HOMOGENEOUS METRIC SPACES TO LIE GROUPS
M. G. Cowling, V. Kivioja, E. Le Donne, S. Nicolussi Golo, AND A. Ottazzi
We study connected, locally compact metric spaces with transitive isometry groups. For all , each such space is - quasi-isometric to a Lie group equipped with a left-invariant metric. Further, every metric Lie group is -quasi-isometric to a solvable Lie group, and every simply connected metric Lie group is -quasi-isometrically homeomorphic to a solvable-by-compact metric Lie group. While any contractible Lie group may be made isometric to a solvable group, only those that are solvable and of type (R) may be made isometric to a nilpotent Lie group, in which case the nilpotent group is the nilshadow of the group. Finally, we give a complete metric characterisation of metric Lie groups for which there exists an automorphic dilation. These coincide with the metric spaces that are locally compact, connected, homogeneous, and admit a metric dilation.
4) SOME REMARKS ON CONTACT VARIATIONS IN THE FIRST HEISENBERG GROUP
S. Nicolussi Golo
We show that in the first sub-Riemannian Heisenberg group there are intrinsic graphs of smooth functions that are both critical and stable points of the sub-Riemannian perimeter under compactly supported variations of contact diffeomorphisms, despite the fact that they are not area-minimizing surfaces. In particular, we show that if is a -intrinsic function, and , then the first contact variation of the sub-Riemannian area of its intrinsic graph is zero and the second contact variation is positive
A two-layered Knowledge Architecture for perceptual and linguistic Knowledge
Get PDFThe lack of generality is a structural weakness of knowledge representation formalisms. Here by lack of generality we mean the inability of any given representation to describe the infinite richness and diversity of the world and also its potentially infinite descriptions which are enabled by language. This lack of generality is the main cause of many of the difficulties encountered so far, just think of the problems which have arisen in the effort of creating reusable ontologies. In this thesis we propose a solution to the problem of generality which is based on the key idea that knowledge should not be modeled a priori, at design time, but it should continuously generated, adapted and evolved, from generation to usage. The thesis provides four main contributions: (i) a shared terminology for the characterization of concepts and for their computational representation; (ii) a formalization of the distinction between substance concepts and classification concepts; (iii) the integration of these two notions of concept into a general representation language that organizes them into a hierarchy of increasing abstraction of what is perceived, and (iv) a two-layered knowledge representation formalism, where the first layer allows to represent concepts, as the main devices for achieving generality, and where the second layer allows to represent concepts as the result of “adapting” a description to the current knowledge representation needs and requirements
The neuro-cognitive representation of word meaning resolved in space and time.
No full textOne of the core human abilities is that of interpreting symbols. Prompted with a perceptual stimulus devoid of any intrinsic meaning, such as a written word, our brain can access a complex multidimensional representation, called semantic representation, which corresponds to its meaning. Notwithstanding decades of neuropsychological and neuroimaging work on the cognitive and neural substrate of semantic representations, many questions are left unanswered. The research in this dissertation attempts to unravel one of them: are the neural substrates of different components of concrete word meaning dissociated?
In the first part, I review the different theoretical positions and empirical findings on the cognitive and neural correlates of semantic representations. I highlight how recent methodological advances, namely the introduction of multivariate methods for the analysis of distributed patterns of brain activity, broaden the set of hypotheses that can be empirically tested. In particular, they allow the exploration of the representational geometries of different brain areas, which is instrumental to the understanding of where and when the various dimensions of the semantic space are activated in the brain. Crucially, I propose an operational distinction between motor-perceptual dimensions (i.e., those attributes of the objects referred to by the words that are perceived through the senses) and conceptual ones (i.e., the information that is built via a complex integration of multiple perceptual features).
In the second part, I present the results of the studies I conducted in order to investigate the automaticity of retrieval, topographical organization, and temporal dynamics of motor-perceptual and conceptual dimensions of word meaning. First, I show how the representational spaces retrieved with different behavioral and corpora-based methods (i.e., Semantic Distance Judgment, Semantic Feature Listing, WordNet) appear to be highly correlated and overall consistent within and across subjects. Second, I present the results of four priming experiments suggesting that perceptual dimensions of word meaning (such as implied real world size and sound) are recovered in an automatic but task-dependent way during reading. Third, thanks to a functional magnetic resonance imaging experiment, I show a representational shift along the ventral visual path: from perceptual features, preferentially encoded in primary visual areas, to conceptual ones, preferentially encoded in mid and anterior temporal areas. This result indicates that complementary dimensions of the semantic space are encoded in a distributed yet partially dissociated way across the cortex. Fourth, by means of a study conducted with magnetoencephalography, I present evidence of an early (around 200 ms after stimulus onset) simultaneous access to both motor-perceptual and conceptual dimensions of the semantic space thanks to different aspects of the signal: inter-trial phase coherence appears to be key for the encoding of perceptual while spectral power changes appear to support encoding of conceptual dimensions.
These observations suggest that the neural substrates of different components of symbol meaning can be dissociated in terms of localization and of the feature of the signal encoding them, while sharing a similar temporal evolution
Coping and adjustment in children's pain: processes of adaptation to illness and develop effective interventions for pain management
No full textMy PhD project mainly focused on understanding how a child or adolescent copes with pain associated with a disease, intended in a broader sense (i.e. procedures, treatments and disease-related). I tried to prove an innovative perspective that can help understand the wide variation in children’s pain experience, by considering intra-interpersonal influences, contextual factors, and intrapsychic factors that focus on needs, defenses, and self-structure. Overall, the whole project involved three pediatric units in Italy: the pediatric wards of Trento and Rovereto hospitals and the pediatric clinic of San Gerardo hospital, Monza (Milan).
This doctoral thesis has achieved five goals:
1. Providing a selective overview on current relevant topics in the pediatric pain research and state of the art regarding the existing models of pediatric pain.
2. Developing a multi-dimensional protocol with an intra-method design for the assessment of pediatric pain in several chronic illnesses (cystic fibrosis, rheumatic diseases, cancer), by using also a battery of projective tests (drawings) to screen the emotional adjustment.
3. Validating the protocol by extending the methodology of projective drawings’ scoring with a control group and adding other assessment variables on a single cohort of patients (with malignant hematologic cancer) to test the new model that I developed. Quantitative analysis phase preceded qualitative analysis phase within the same framework to yield a parallel mixed analysis.
4. Planning specific training modules about pain management, starting from a bottom-up process concerning the local health professionals’ needs. I investigated these training needs through a series of open-ended questions, analyzed by a thematic analysis method.
5. Evaluate treatment’s feasibility, acceptability, and satisfaction of a problem-solving skills training for parents of children who have received an intensive pain rehabilitation from one pediatric pain rehabilitation program (Seattle Children's Hospital). I provided a methodological contribute within the mixed-method approach (statistical analysis and grounded theory).
The results presented and their implications, are discussed in a clinical perspective since the rationale of this dissertation is that effective pain assessment must be multidimensional, multidisciplinary and at the same time feasible and practical to meet each pediatric patient’s needs
Flash Sintering of Alumina-based Ceramics
No full textFlash sintering is an electrical field-assisted consolidation technology and represents a very novel technique for producing ceramic materials, which allows to decrease sensibly both processing temperature and time. Starting from 2010, when flash sintering was discovered, different ceramic materials with a wide range of electrical properties have been successfully densified. Up to date, the research on flash sintering has been mainly focused on ionic and electronic conductors and on semiconductor ceramics. In the present work, we studied the flash sintering behavior of a resistive technical ceramic like alumina also in the presence of magnesia silicate glass phase typically used for activating liquid phase sintering. The materials were studied by using different combinations of electric field and current density. Physical, structural and microstructural properties of sintered samples were extensively investigated by Archimedes’ method, SEM, XRD, XPS and pholuminescence spectroscopy. Light emission and electrical behavior during the flash process were studied,as well. The results point out the applicability of flash sintering to alumina and glass-containing alumina using electrical-field in excess of 500 V/cm, allowing an almost complete densification at temperatures lower than 1000°C. Different densification mechanisms were pointed out in the two systems, namely “solid state flash sintering” and “liquid phase flash sintering” for pure alumina and glass containing alumina, respectively. The glass addition allows a significant reduction of the current and power dissipation needed for densification, by promoting liquid phase sintering. The results suggest that unconventional mass transport phenomena are activated by the current flow in the ceramic body and they can be very likely attributed to partial reduction of the oxide induced by the electrical current. The hypothesis that the oxide gets partially reduced during DC-flash sintering experiments is supported by several experimental findings.
Finally, strong affinities between flash sintering and other physical processes, like dielectric breakdown, were pointed out
Pionless Effective Field Theory: Building the Bridge Between Lattice Quantum Chromodynamics and Nuclear Physics
Get PDFWe analyze ground state properties of few-nucleons systems and O using \eftnopi (Pionless Effective Field Theory) at \ac{LO}. This is the first time the theory is extended to many-body nuclear systems. The free constants of the interaction are fitted using both experimental data and \ac{LQCD} results. The nuclear many-body Schr\"odinger equation is solved by means of the Auxiliary Field Diffusion Monte Carlo method. A linear optimization procedure has been used to recover the correct structure of the ground state wavefunction. {\eftnopi} as revealed to be an appropriate theory to describe light nuclei both in nature, and in the case where heavier quarks are used in order to make \ac{LQCD} calculation feasible. Our results are in good agreement with experiments and \ac{LQCD} predictions.
In our \ac{LO} calculation, O appears to be unstable against breakup into four He for the quark masses considered
Funzioni e potenzialità dell'analisi statistica di test su larga scala in didattica della matematica
Get PDFQuesta tesi si propone di mettere in luce come l’analisi statistica di prove standardizzate di matematica possa avere importanti ricadute per lo studio di fenomeni didattici.
In particolare, le ricerche presentate si riferiranno alle prove INVALSI studiate attraverso il modello di Rasch. Si mostrerà come questo approccio possa far emergere macro-fenomeni già osservati in didattica della matematica, studiandoli anche da un punto di vista quantitativo. In particolare verranno utilizzati per questi casi dei grafici, detti distractor plot, che mostrano l’andamento della risposta corretta e delle altre opzioni di risposta in funzione dell’abilità degli studenti. Questi grafici, applicati all’intera popolazione o a sottoinsiemi della stessa, permetteranno di evidenziare se una determinata risposta degli studenti, legata a un costrutto didattico, abbia una maggiore influenza su particolari livelli di abilità
Harmonizing Actuation and Data Collection in Low-power and Lossy Networks: From Standard Compliance to Rethinking the Stack
No full textTechnology is evolving towards a higher degree of automation and connectivity, with concepts of Pervasive Computing, Smart Factories, Cyber-Physical Systems (CPS) and the Internet of Things (IoT)promising to integrate countless communicating devices into objects around us at home, in the streets, and on industrial sites. These embedded devices are often very small in size, autonomously-powered, and have restricted computational and communicational capabilities.
Low-power and Lossy Networks (LLNs) are multi-hop, typically wireless, self-organising networks aimed at interconnecting hundreds or thousands of such embedded devices. They inherit many techniques from wireless sensor networks, though going beyond their original task of collecting sensor readings. New applications comprising actuators, control loops, user interface devices and requiring connectivity of every ``smart thing'' with the Internet, pose new challenges to the network protocol stacks.
These stacks should not only efficiently support data collection from numerous low-power sensors, but provide scalable data forwarding in the opposite direction, making every single device in the LLN addressable and reachable from a central controller or from the Internet. This type of forwarding is needed to send commands to wireless actuators in the LLN or to enable request-response communication between a low-power device and a remote server.
Control loops additionally require real-time guarantees from the communication system. We demonstrate in this thesis that reconciling the battery lifetime with high reliability and low latency is still a challenge for existing protocols even at the scale of few hundreds of network nodes.
Moreover, current techniques have a significant performance gap between their data collection and actuation forwarding components on memory-constrained platforms.
This gap limits the applicability of the stacks, as the overall performance is determined by the weaker component.
Motivated by two real-life applications, we first study novel techniques that eliminate the performance gap in the
standard IPv6 stack for LLNs, making the actuation traffic forwarding as performant as the data collection one in networks that are five times larger than what the original standard stack is able to support. Second, we demonstrate that the reliability of packet delivery in the standard-compliant solution is limited in practice at around 99% while its routing overhead causes significant inefficiency in energy consumption. Therefore, we change focus to a forwarding mechanism based on the principle of synchronous transmissions, made popular by Glossy. It is a recent and, thus, non-standard technique, known for excellent reliability, speed and energy efficiency of the flooding-based data dissemination service it provides. This service is a perfect match for actuation, but a similarly efficient data collection protocol did not exist. To close this gap, we design Crystal, a novel data collection protocol based on the same core principle of synchronous transmissions.
We show that, depending on the application, Crystal reaches per-mille or even parts-per-million radio duty cycle.
It does that with a packet loss rate lower than 10e-5 under external Wi-Fi interference of a noisy office building, and
provides a much higher reliability and energy efficiency than the state of the art under even stronger interference generated by JamLab. We thoroughly evaluate the proposed solutions both in realistic simulations and two large-scale testbeds. We follow a principled approach based on understanding of the environment and the properties of the network topologies. The latter are acquired by our connectivity assessment tool Trident, which itself is one of the contributions of this thesis.
Through these contributions, this thesis pushes forward the applicability of LLNs, by improving their scalability, reliability, latency, energy efficiency and interference resilience, both in the context of an existing standard and in a clean-slate design. Further, by achieving this superior performance via network stacks that natively support both collection and actuation traffic, this thesis provides a stepping stone for applications that strongly rely on both,
notably including the low-power wireless control applications
Correspondence among connectomes as combinatorial optimization
No full textDiffusion magnetic resonance imaging (dMRI) data allows the reconstruction of the neural pathways of the white matter of the brain as a set of 3D polylines, by means of tractography algorithms. The neuronal axons within the white matter form the anatomical links between regions of the brain, which are referred to as anatomical connectivity, or structural connectivity. The complete collection of structural connectivity is referred to the structural connectome, which helps to understand the human brain functionality. The 3D polylines are called streamlines and the set of all streamlines is called tractogram, which represents the structural connectome of the brain. In neurological studies, it is often important to identify the group of streamlines belonging to the same anatomical structure, called tract or bundle, like the cortico-spinal tract or the arcuate fasciculus. The statistical analysis of the diffusion data of tracts is used in multiple applications, for example, to study gender differences, to observe the changes in age and to correlate with diseases. This kind of studies requires the analysis of groups of subjects, which creates two important problems: aligning tractography data across subjects, a problem called tractogram alignment, and the extraction of tracts of interest, named tract segmentation problem. Due to the anatomical variability across subjects, these two problems are difficult to solve. In this thesis, we investigate those two problems and propose a novel approach and efficient algorithms for their solution.
Typically, the alignment of two tractograms is obtained with registration methods. Registration methods transform the tractograms in order to increase their mutual similarity. In the literature, the best practice for tractogram registration is based on finding one global affine transformation that minimizes their differences. Unfortunately, this approach fails to reconcile local differences between the tractograms. In contrast to transformation-based registration methods, we propose the concept of tractogram correspondence, whose aim is to find which streamline of one tractogram corresponds to which streamline in another tractogram, i.e., a map from one tractogram to another. As a further contribution, we propose to use the relational information of each streamline, i.e., its distances from the other streamlines in its own tractogram, as the building block to define the optimal correspondence. We provide an operational procedure to find the optimal correspondence through a combinatorial optimization problem and we discuss its similarity to the graph matching problem. Finally, we adapted an approximate solution of the graph matching to solve the correspondence.
Several automatic tract segmentation methods have been developed over the last years. Segmentation approaches can be categorized into unsupervised and supervised. A common criticism to unsupervised methods, like clustering, is that there is no guarantee to obtain anatomically meaningful tracts. For this reason, in this thesis, we focus on supervised tract segmentation, which is based on prior knowledge. We propose a novel supervised tract segmentation method, that segments the tract of interest, e.g. the arcuate fasciculus, by exploiting a set of example tracts from different subjects. In analogy to tractogram alignment, our proposed supervised segmentation approach is based on the concept of the streamline correspondence, i.e. on finding which streamline in one tractogram corresponds to which streamline in the other tractogram. We showed that streamline correspondence can be a powerful principle to transfer the anatomical knowledge of a given bundle from one subject to another one. In the literature of supervised segmentation, streamline correspondence has been addressed with a nearest neighbour strategy. We observed that segmenting tracts with a nearest neighbour strategy has a number of limitations. Conversely, in this thesis we address the tract segmentation problem as a linear assignment problem (LAP), a cornerstone of combinatorial optimization. With respect to nearest neighbor, the LAP introduces a constraint of one-to-one correspondence that substantially improves the quality of segmentation. We draw from the literature of algorithms for solving the LAP and adopt one of the most efficient solutions available. To this, we add a strategy for merging correspondences coming from different examples, i.e. from different subjects, in order to account for the anatomical variability across the population.
In order to implement graph matching and LAP for alignment and segmentation of tractograms, we needed to address the very large computational cost due to the large number of streamlines involved. To reduce the amounts of computations, in both cases we represented streamlines as vectors through a Euclidean embedding technique called dissimilarity representation. With such representation, we obtained fast nearest neighbor queries through the use of kd-trees, which were instrumental to dramatically reduce the amount of computations: from months to minutes
Social capital and the labour market: essays on trust, inequality and employment
Get PDFAccording to the 2017 World Economic Forum, the factors that pose a serious risk to today’s global economy are rising inequality and the polarization of societies, which in turn threat the social cohesion. This doctoral dissertation contributes to the understanding of these major current challenges, by investigating the ex- tend of unequal access to opportunity in education and in the labour market in the former communist countries; the potential of diversity in the South African multi- cultural society in terms of employment; the formation of interpersonal trust at the individual level in Germany