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

Social Search with Missing Data: Which Ranking Algorithm?

Online social networking tools are extremely popular, but can miss potential discoveries latent in the social 'fabric'. Matchmaking services which can do naive profile matching with old database technology are too brittle in the absence of key data, and even modern ontological markup, though powerful, can be onerous at data-input time. In this paper, we present a system called BuddyFinder which can automatically identify buddies who can best match a user's search requirements specified in a term-based query, even in the absence of stored user-profiles. We deploy and compare five statistical measures, namely, our own CORDER, mutual information (MI), phi-squared, improved MI and Z score, and two TF/IDF based baseline methods to find online users who best match the search requirements based on 'inferred profiles' of these users in the form of scavenged web pages. These measures identify statistically significant relationships between online users and a term-based query. Our user evaluation on two groups of users shows that BuddyFinder can find users highly relevant to search queries, and that CORDER achieved the best average ranking correlations among all seven algorithms and improved the performance of both baseline methods

Spinning Hexagons

We reduce the computation of three point function of three spinning operators with arbitrary polarizations to a statistical mechanics problem via the hexagon formalism. The central building block of these correlation functions is the hexagon partition function. We explore its analytic structure and use it to generate perturbative data for spinning three point functions. For certain polarizations and any coupling, we express the full asymptotic three point function in determinant form. With the integrability approach established we open the ground to study the large spin limit where dualities with null Wilson loops and integrable pentagons must appear.Comment: 40 pages, 14 figure

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 a component of the 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

Educação Física Infantil e seus contornos inclusivos: recortes de observações em uma creche brasileira

O presente trabalho é parte de um projeto mais amplo realizado em Florianópolis/SC/Brasil, no interior do qual foram observadas rotinas de três instituições de educação infantil (0 a 6 anos), com olhar voltado, sobretudo, para as aulas de Educação Física. Especificamente, ele se refere à inclusão de pessoas com histórico de deficiência em aulas regulares daquela disciplina. O tema é da maior atualidade no debate educacional contemporâneo e nele se colocam exageradas esperanças de mudança na educação e na sociedade. Em uma turma com crianças entre 15 e 24 meses de idade, encontramos duas crianças cegas, um menino e uma menina, o que constituiu um contexto repleto de significados que remetem para a busca de práticas inclusivas. A pesquisa incluiu, além de observações sistemáticas das aulas, uma entrevista narrativa com a professora. Os resultados apontam para uma paradoxal relação de produção de menoridade das crianças deficientes, uma inclusão exclusiva demarcada pelas tarefas pedagógicas que não podem por eles ser realizadas, pela relação de condescendência por parte dos pares e mesmo da professora. Reafirma-se a idéia de que a presença no espaço institucional já seria condição suficiente para elas, o que coloca em suspenso a utopia formativa para as crianças com histórico de deficiência, bem como em questão a ênfase nas políticas de inclusão.Ponencia presentada en el Panel "Educación e inclusión social".Departamento de Educación Físic