Direct and Inverse Spectral Problems for (2N + 1)-Diagonal, Complex, Symmetric, Non-Hermitian Matrices

2000 Mathematics Subject Classification: 42C05.

The Direct and Inverse Spectral Problems for some Banded Matrices

2000 Mathematics Subject Classification: 15A29.

Beyond pollinator reward: steps forward and knowledge gaps on the role of floral nectar in plant-animal interactions.

The work done within the framework of my PhD project has been carried out between November 2019 and January 2023 at the Department of Biological, Geological and Environmental Sciences of the University of Bologna, under the supervision of Prof. Marta Galloni and PhD Gherardo Bogo. A period of three months was spent at the Natural History Museum of Rijeka, under the supervision of Prof. Boštjan Surina. The main aim of the thesis was to investigate further the so-called pollinator manipulation hypothesis, which states that when a floral visitor gets in contact with a specific nectar chemistry, the latter affects its behavior of visit on flowers, with potential repercussions on the plant reproductive fitness. To the purpose, the topic was tackled by means of three main approaches: field studies, laboratory assessments, and bibliographic reviews. This research project contributes to two main aspects. First, when insects encounter nectar-like concentrations of a plethora of secondary metabolites in their food-environment, various aspects of their behavior relevant to flower visitation can be affected. In addition, the results I gained confirm that the combination of field studies and laboratory assessments allows to get more realistic pictures of a given phenomenon than the single approaches. Second, reviewing the existent literature in the field of nectar ecology has highlighted how crucial is to establish the origin of nectar biogenic amines to either confirm or reject the multiple speculations made on the role of nectar microbes in shaping plant-animal interactions.

Use of neural networks in robot positioning of large flexible redundant manipulators

Deflection compensation of flexible boom structures in robot positioning is usually done using tables containing the magnitude of the deflection with inverse kinematics solutions of a rigid structure. The number of table values increases greatly if the working area of the boom is large and the required positioning accuracy is high. The inverse kinematics problems are very nonlinear, and if the structure is redundant, in some cases it cannot be solved in a closed form. If the structural flexibility of the manipulator arms is taken into account, the problem is almost impossible to solve using analytical methods. Neural networks offer a possibility to approximate any linear or nonlinear function. This study presents four different methods of using neural networks in the static deflection compensation and inverse kinematics solution of a flexible hydraulically driven manipulator. The training information required for training neural networks is obtained by employing a simulation model that includes elasticity characteristics. The functionality of the presented methods is tested based on the simulated and measured results of positioning accuracy. The simulated positioning accuracy is tested in 25 separate coordinate points. For each point, the positioning is tested with five different mass loads. The mean positioning error of a manipulator decreased from 31.9 mm to 4.1 mm in the test points. This accuracy enables the use of flexible manipulators in the positioning of larger objects. The measured positioning accuracy is tested in 9 separate points using three different mass loads. The mean positioning error decreased from 10.6 mm to 4.7 mm and the maximum error from 27.5 mm to 11.0 mm.

Mapeamento da cinemática inversa de um manipulador robótico utilizando redes neurais artificiais configuradas em paralelo

Pós-graduação em Engenharia Elétrica - FEIS

Efficient computation of discrete polynomial transforms

This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2 additions, 2( +1) memory units, and +1multipliers for the +1-point Hermite and binomial transforms. The recursive flow diagram for the +1-point Laguerre transform requires 2 additions, 2( +1) memory units, and 2( +1) multipliers. The transform computation time for all of these transforms is ( )

The DLMT. An alternative to the DCT

In the last recent years, with the popularity of image compression techniques, many architectures have been proposed. Those have been generally based on the Forward and Inverse Discrete Cosine Transform (FDCT, IDCT). Alternatively, compression schemes based on discrete “wavelets” transform (DWT), used, both, in JPEG2000 coding standard and in the next H264-SVC (Scalable Video Coding), do not need to divide the image into non-overlapping blocks or macroblocks. This paper discusses the DLMT (Discrete Lopez-Moreno Transform). It proposes a new scheme intermediate between the DCT and the DWT (Discrete Wavelet Transform). The DLMT is computationally very similar to the DCT and uses quasi-sinusoidal functions, so the emergence of artifact blocks and their effects have a relative low importance. The use of quasi-sinusoidal functions has allowed achieving a multiresolution control quite close to that obtained by a DWT, but without increasing the computational complexity of the transformation. The DLMT can also be applied over a whole image, but this does not involve increasing computational complexity. Simulation results in MATLAB show that the proposed DLMT has significant performance benefits and improvements comparing with the DCT

A contribution on modeling methodologies for multibody systems.

Multibody System Dynamics has been responsible for revolutionizing Mechanical Engineering Design by using mathematical models to simulate and optimize the dynamic behavior of a wide range of mechanical systems. These mathematical models not only can provide valuable informations about a system that could otherwise be obtained only by experiments with prototypes, but also have been responsible for the development of many model-based control systems. This work represents a contribution for dynamic modeling of multibody mechanical systems by developing a novel recursive modular methodology that unifies the main contributions of several Classical Mechanics formalisms. The reason for proposing such a methodology is to motivate the implementation of computational routines for modeling complex multibody mechanical systems without being dependent on closed source software and, consequently, to contribute for the teaching of Multibody System Dynamics in undergraduate and graduate levels. All the theoretical developments are based on and motivated by a critical literature review, leading to a general matrix form of the dynamic equations of motion of a multibody mechanical system (that can be expressed in terms of any set of variables adopted for the description of motions performed by the system, even if such a set includes redundant variables) and to a general recursive methodology for obtaining mathematical models of complex systems given a set of equations describing the dynamics of each of its uncoupled subsystems and another set describing the constraints among these subsystems in the assembled system. This work also includes some discussions on the description of motion (using any possible set of motion variables and admitting any kind of constraint that can be expressed by an invariant), and on the conditions for solving forward and inverse dynamics problems given a mathematical model of a multibody system. Finally, some examples of computational packages based on the novel methodology, along with some case studies, are presented, highlighting the contributions that can be achieved by using the proposed methodology.

Improved robust control of nonlinear stochastic systems using uncertain models

We introduce a technique for quantifying and then exploiting uncertainty in nonlinear stochastic control systems. The approach is suboptimal though robust and relies upon the approximation of the forward and inverse plant models by neural networks, which also estimate the intrinsic uncertainty. Sampling from the resulting Gaussian distributions of the inversion based neurocontroller allows us to introduce a control law which is demonstrably more robust than traditional adaptive controllers.

Robust control of nonlinear stochastic systems by modelling conditional distributions of control signals

We introduce a novel inversion-based neuro-controller for solving control problems involving uncertain nonlinear systems that could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. In this work a novel robust inverse control approach is obtained based on importance sampling from these distributions. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The performance of the new algorithm is illustrated through simulations with example systems.

Exploiting uncertainty in nonlinear stochastic control problem

This work introduces a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. Convergence of the output error for the proposed control method is verified by using a Lyapunov function. Several simulation examples are provided to demonstrate the efficiency of the developed control method. The manner in which such a method is extended to nonlinear multi-variable systems with different delays between the input-output pairs is considered and demonstrated through simulation examples.

Probabilistic control for uncertain systems

In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In the absence of reliable plant models, the proposed control algorithm incorporates uncertainties in model parameters, observations, and latent processes. The local stability of the closed loop system has been established. The efficacy of the control algorithm is demonstrated on two nonlinear stochastic control examples with additive and multiplicative noise.

Origin of the Grande Ronde Formation flows, Columbia River flood basalt group

Lavas belonging to the Grande Ronde Formation (GRB) constitute about 63% of the Columbia River Basalt Group (CRBG), a flood basalt province in the NW United States. A puzzling feature is the lack of phenocrysts (< 5%) in these chemically evolved lavas. Based mainly on this observation it has been hypothesized that GRB lavas were nearly primary melts generated by large-scale melting of eclogite. Another recent hypothesis holds that GRB magmas were extremely hydrous and rose rapidly from the mantle such that the dissolved water kept the magmas close to their liquidi. I present new textural and chemical evidence to show that GRB lavas were neither primary nor hydrous melts but were derived from other melts via efficient fractional crystallization and mixing in shallow intrusive systems. Texture and chemical features further suggest that the melt mixing process may have been exothermic, which forced variable melting of some of the existing phenocrysts. ^ Finally, reported here are the results of efforts to simulate the higher pressure histories of GRB using COMAGMAT and MELTS softwares. The intent was to evaluate (1) whether such melts could be derived from primary melts formed by partial melting of a peridotite source as an alternative to the eclogite model, or if bulk melting of eclogite is required; and (2) at what pressure such primary melts could have been in equilibrium with the mantle. I carried out both forward and inverse modeling. The best fit forward model indicates that most primitive parent melts related to GRB could have been multiply saturated at ∼1.5--2.0 GPa. I interpret this result to indicate that the parental melts last equilibrated with a peridotitic mantle at 1.5--2.0 GPa and such partial melts rose to ∼0.2 GPa where they underwent efficient mixing and fractionation before erupting. These models suggest that the source rock was not eclogitic but a fertile spinel lherzolite, and that the melts had ∼0.5% water. ^

Geometrico-static modelling of continuum parallel robots

In this thesis, we explore three methods for the geometrico-static modelling of continuum parallel robots. Inspired by biological trunks, tentacles and snakes, continuum robot designs can reach confined spaces, manipulate objects in complex environments and conform to curvilinear paths in space. In addition, parallel continuum manipulators have the potential to inherit some of the compactness and compliance of continuum robots while retaining some of the precision, stability and strength of rigid-links parallel robots. Subsequently, the foundation of our work is performed on slender beam by applying the Cosserat rod theory, appropriate to model continuum robots. After that, three different approaches are developed on a case study of a planar parallel continuum robot constituted of two connected flexible links. We solve the forward and inverse geometrico-static problem namely by using (a) shooting methods to obtain a numerical solution, (b) an elliptic method to find a quasi-analytical solution, and (c) the Corde model to perform further model analysis. The performances of each of the studied methods are evaluated and their limits are highlighted. This thesis is divided as follows. Chapter one gives the introduction on the field of the continuum robotics and introduce the parallel continuum robots that is studied in this work. Chapter two describe the geometrico-static problem and gives the mathematical description of this problem. Chapter three explains the numerical approach with the shooting method and chapter four introduce the quasi-analytical solution. Then, Chapter five introduce the analytic method inspired by the Corde model and chapter six gives the conclusions of this work.

Development of a subject-specific musculoskeletal shoulder model : inverse and forward dynamics applications

A prevalência de pessoas que referem dor no complexo articular do ombro, com concomitante limitação na capacidade para realizar atividades da vida diária, é elevada. Estes níveis de prevalência sobrecarregam quer os utentes, como a própria sociedade. A evidência científica atual indicia a existência de uma relação entre as alterações da articulação escápulo-torácica e as patologias associadas à articulação gleno-umeral. A capacidade de quantificar, cinemática e cineticamente, as disfunções ao nível das articulações escápulo-torácica e gleno-umeral, é algo de enorme importância, quer para a comunidade biomecânica, como para a clínica. No decorrer dos trabalhos desta tese foi desenvolvido, através do software OpenSim, um modelo tridimensional músculo-esquelético do complexo articular do ombro que inclui a representação do tórax/coluna, clavícula, omoplata, úmero, rádio, cúbito e articulações que permitem os movimentos relativos desses segmentos, assim como, 16 músculos e 4 ligamentos. Com um total de 11 graus de liberdade, incluindo um novo modelo articular escápulo-torácico, os resultados demonstram que este é capaz de reconstruir de forma precisa e rápida os movimentos escápulo-torácicos e glenoumerais, recorrendo para tal, à cinemática inversa, e à dinâmica inversa e direta. Conta ainda com um método de transformação inovador para determinar, com base nas especificidades dos sujeitos, os locais de inserção muscular. As principais motivações subjacentes ao desenvolvimento desta tese foram contribuir para o aprofundar do atual conhecimento sobre as disfunções do complexo articular do ombro e, simultaneamente, proporcionar à comunidade clínica uma ferramenta biomecânica de livre acesso com o intuito de melhor suportar as decisões clínicas e dessa forma concorrer para uma prática mais efetiva.