Linear identification of nonlinear systems: A lifting technique based on the Koopman operator

We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear identification technique by recasting the problem in the infinite-dimensional space of observables. This technique can be described in two main steps. In the first step, similar to the socalled Extended Dynamic Mode Decomposition algorithm, the data are lifted to the infinite-dimensional space and used for linear identification of the Koopman operator. In the second step, the obtained Koopman operator is "projected back" to the finite-dimensional state space, and identified to the nonlinear vector field through a linear least squares problem. The proposed technique is efficient to recover (polynomial) vector fields of different classes of systems, including unstable, chaotic, and open systems. In addition, it is robust to noise, well-suited to model low sampling rate datasets, and able to infer network topology and dynamics.Comment: 6 page

Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator

In this paper, we further develop a recently proposed control method to switch a bistable system between its steady states using temporal pulses. The motivation for using pulses comes from biomedical and biological applications (e.g. synthetic biology), where it is generally difficult to build feedback control systems due to technical limitations in sensing and actuation. The original framework was derived for monotone systems and all the extensions relied on monotone systems theory. In contrast, we introduce the concept of switching function which is related to eigenfunctions of the so-called Koopman operator subject to a fixed control pulse. Using the level sets of the switching function we can (i) compute the set of all pulses that drive the system toward the steady state in a synchronous way and (ii) estimate the time needed by the flow to reach an epsilon neighborhood of the target steady state. Additionally, we show that for monotone systems the switching function is also monotone in some sense, a property that can yield efficient algorithms to compute it. This observation recovers and further extends the results of the original framework, which we illustrate on numerical examples inspired by biological applications.Comment: 7 page

Global analysis of piecewise linear systems using impact maps and surface Lyapunov functions

This paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems (PLS). This methodology infers global properties of PLS solely by studying the behavior at switching surfaces associated with PLS. The main idea is to analyze impact maps, i.e., maps from one switching surface to the next switching surface. Such maps are known to be "unfriendly" maps in the sense that they are highly nonlinear, multivalued, and not continuous. We found, however, that an impact map induced by an linear time-invariant flow between two switching surfaces can be represented as a linear transformation analytically parametrized by a scalar function of the state. This representation of impact maps allows the search for surface Lyapunov functions (SuLF) to be done by simply solving a semidefinite program, allowing global asymptotic stability, robustness, and performance of limit cycles and equilibrium points of PLS to be efficiently checked. This new analysis methodology has been applied to relay feedback, on/off and saturation systems, where it has shown to be very successful in globally analyzing a large number of examples. In fact, it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology. Examples analyzed include systems of relative degree larger than one and of high dimension, for which no other analysis methodology could be applied. This success in globally analyzing certain classes of PLS has shown the power of this new methodology, and suggests its potential toward the analysis of larger and more complex PLS

Las TIC como TAC y como TEP para realizar experimentos de Ciencias Naturales

Treball Final de Grau en Mestre o Mestra d'Educació Primària. Codi: MP1040. Curs acadèmic: 2016/2017Este trabajo de investigación se ha llevado a cabo en el CEIP Ausiàs March de La Vall d’Uxó, que está considerado un Centro de Acción Educativo Singular debido al contexto de su alumnado. Investigaremos la insuficiencia de horario curricular en la asignatura de Ciencias Naturales para llevar a cabo experimentos. En primer lugar se muestra dicha insuficiencia horaria y a continuación se realiza un proyecto de un experimento en la clase de sexto de primaria del año 2016/2017, dónde realicé mi estancia en prácticas del Practicum II. En este experimento los alumnos estudiarán el sonido y podrán llevar a la práctica lo estudiando mediante el experimento. En este proyecto trataremos de utilizar las TIC (Tecnologías de la Información y la Comunicación) como TAC (Tecnologías para el aprendizaje y el conocimiento) y como TEP (Tecnologías para el Empoderamiento y la Participación), y así, poder paliar la insuficiencia de tiempo en el aula para hacer experimentos que establece el currículo actual

Applicability of semi-supervised learning assumptions for gene ontology terms prediction

Gene Ontology (GO) is one of the most important resources in bioinformatics, aiming to provide a unified framework for the biological annotation of genes and proteins across all species. Predicting GO terms is an essential task for bioinformatics, but the number of available labelled proteins is in several cases insufficient for training reliable machine learning classifiers. Semi-supervised learning methods arise as a powerful solution that explodes the information contained in unlabelled data in order to improve the estimations of traditional supervised approaches. However, semi-supervised learning methods have to make strong assumptions about the nature of the training data and thus, the performance of the predictor is highly dependent on these assumptions. This paper presents an analysis of the applicability of semi-supervised learning assumptions over the specific task of GO terms prediction, focused on providing judgment elements that allow choosing the most suitable tools for specific GO terms. The results show that semi-supervised approaches significantly outperform the traditional supervised methods and that the highest performances are reached when applying the cluster assumption. Besides, it is experimentally demonstrated that cluster and manifold assumptions are complimentary to each other and an analysis of which GO terms can be more prone to be correctly predicted with each assumption, is provided.Postprint (published version

Comunicação para a mudança social e de comportamento na luta contra a malária em Moçambique

Long-lasting insecticide-treated nets and/or indoor residual spraying, associated with case management, are key interventions in the control of malaria in Africa. The objective of this study is to comment on the role of social and behavior change communication as a potential key intervention in the control of malaria in Mozambique.As redes mosquiteiras impregnadas com insecticidade de longa duração e/ou pulverização intra-domiciliária, associada ao manejo de casos são intervenções-chave no controlo da malária em África. O objetivo deste estudo foi comentar o papel da comunicação para a mudança social e de comportamento como intervenção potencialmente chave no controlo da malária em Moçambique

Multi-GPU support on the marrow algorithmic skeleton framework

Dissertação para obtenção do Grau de Mestre em Engenharia InformáticaWith the proliferation of general purpose GPUs, workload parallelization and datatransfer optimization became an increasing concern. The natural evolution from using a single GPU, is multiplying the amount of available processors, presenting new challenges, as tuning the workload decompositions and load balancing, when dealing with heterogeneous systems. Higher-level programming is a very important asset in a multi-GPU environment, due to the complexity inherent to the currently used GPGPU APIs (OpenCL and CUDA), because of their low-level and code overhead. This can be obtained by introducing an abstraction layer, which has the advantage of enabling implicit optimizations and orchestrations such as transparent load balancing mechanism and reduced explicit code overhead. Algorithmic Skeletons, previously used in cluster environments, have recently been adapted to the GPGPU context. Skeletons abstract most sources of code overhead, by defining computation patterns of commonly used algorithms. The Marrow algorithmic skeleton library is one of these, taking advantage of the abstractions to automate the orchestration needed for an efficient GPU execution. This thesis proposes the extension of Marrow to leverage the use of algorithmic skeletons in the modular and efficient programming of multiple heterogeneous GPUs, within a single machine. We were able to achieve a good balance between simplicity of the programming model and performance, obtaining good scalability when using multiple GPUs, with an efficient load distribution, although at the price of some overhead when using a single-GPU.projects PTDC/EIA-EIA/102579/2008 and PTDC/EIA-EIA/111518/200