Model Reduction for Nonlinear Systems by Balanced Truncation of State and Gradient Covariance

Data-driven reduced-order models often fail to make accurate forecasts of high-dimensional nonlinear dynamical systems that are sensitive along coordinates with low-variance because such coordinates are often truncated, e.g., by proper orthogonal decomposition, kernel principal component analysis, and autoencoders. Such systems are encountered frequently in shear-dominated fluid flows where non-normality plays a significant role in the growth of disturbances. In order to address these issues, we employ ideas from active subspaces to find low-dimensional systems of coordinates for model reduction that balance adjoint-based information about the system's sensitivity with the variance of states along trajectories. The resulting method, which we refer to as covariance balancing reduction using adjoint snapshots (CoBRAS), is analogous to balanced truncation with state and adjoint-based gradient covariance matrices replacing the system Gramians and obeying the same key transformation laws. Here, the extracted coordinates are associated with an oblique projection that can be used to construct Petrov-Galerkin reduced-order models. We provide an efficient snapshot-based computational method analogous to balanced proper orthogonal decomposition. This also leads to the observation that the reduced coordinates can be computed relying on inner products of state and gradient samples alone, allowing us to find rich nonlinear coordinates by replacing the inner product with a kernel function. In these coordinates, reduced-order models can be learned using regression. We demonstrate these techniques and compare to a variety of other methods on a simple, yet challenging three-dimensional system and a nonlinear axisymmetric jet flow simulation with $10^5$ state variables

Analysis of amplification mechanisms and cross-frequency interactions in nonlinear flows via the harmonic resolvent

We propose a framework that elucidates the input-output characteristics of flows with complex dynamics arising from nonlinear interactions between different time scales. More specifically, we consider a periodically time-varying base flow, and perform a frequency-domain analysis of periodic perturbations about this base flow; the response of these perturbations is governed by the harmonic resolvent, which is a linear operator similar to the harmonic transfer function introduced by Wereley (1991). This approach makes it possible to explicitly capture the triadic interactions that are responsible for the energy transfer between different time scales in the flow. For instance, perturbations at frequency $\alpha$ are coupled with perturbations at frequency $\omega$ through the base flow at frequency $\omega-\alpha$. We draw a connection with resolvent analsyis, which is a special case of the harmonic resolvent when evaluated about a steady base flow. We show that the left and right singular vectors of the harmonic resolvent are the optimal response and forcing modes, which can be understood as full spatio-temporal signals that reveal space-time amplification characteristics of the flow. We illustrate the method on examples, including a three-dimensional system of ordinary differential equations and the flow over an airfoil at near-stall angle of attack

The thermal state and interior structure of Mars

©2018. American Geophysical UnionThe present‐day thermal state, interior structure, composition, and rheology of Mars can be constrained by comparing the results of thermal history calculations with geophysical, petrological, and geological observations. Using the largest‐to‐date set of 3‐D thermal evolution models, we find that a limited set of models can satisfy all available constraints simultaneously. These models require a core radius strictly larger than 1,800 km, a crust with an average thickness between 48.8 and 87.1 km containing more than half of the planet's bulk abundance of heat producing elements, and a dry mantle rheology. A strong pressure dependence of the viscosity leads to the formation of prominent mantle plumes producing melt underneath Tharsis up to the present time. Heat flow and core size estimates derived from the InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission will increase the set of constraining data and help to confine the range of admissible models.DFG, 280637173, FOR 2440: Materie im Inneren von Planeten - Hochdruck-, Planeten- und Plasmaphysi

Decomposição de adubos verdes perenes consorciados com a bananeira em um sistema sob transição agroecológica em Mato Grosso do Sul.

bitstream/item/68857/1/040-osorio-decomposicao.pdfPublicado também no Cadernos de Agroecologia, v. 7, n.2, 2012

The IARA Model Proved Effective in Emotional Literacy, Characters Strengths Awareness, and Cohesion among Italian Children

Literature highlights how education in the twenty-first century begins to advocate multiple new concepts, such as new technology, new pedagogies, interdisciplinary curricula, open learning, etc. Among these concepts, the recognition and awareness about one’s character strengths are demonstrated to improve emotional management and individual/group’s quality of life. We studied three fifth-grade Italian classes using an emerging educational model called IARA to verify if it can truly improve emotional literacy, characters strengths awareness, and cohesion in ten-years children. To demonstrate its efficacy, we used Bloom’s Taxonomy and Sociogrammatic study. We proved that the IARA could be an efficient model to improve one’s character strengths and class milieu awareness

Desempenho da bananeira consorciada com leguminosas herbáceas perenes em um agroecossistema sob manejo ecológico em Mato Grosso do Sul.

bitstream/item/68901/1/042-sousa-desempenho.pdfPublicado também no Cadernos de Agroecologia, v. 7, n.2, 2012

Solo cultivado com adubos verdes perenes consorciados com a bananeira, em um agroecossistema sob manejo ecológico em Mato Grosso do Sul: efeito sobre atributos químicos.

bitstream/item/69056/1/094-carneiro-solo.pdfPublicado também no Cadernos de Agroecologia, v. 7, n.2, 2012

A Agroecologia na Escola Família Agrícola de Itaquiraí, em Mato Grosso do Sul.

bitstream/item/66246/1/31208.pdfOrganizado por: Alberto Feiden, Milton Parron Padovan, Adalgiza Inês Campolim, Aurélio Vinícius Borsato, Ivo de Sá Motta, João Batista Catto, Tércio Jacques Fehlauer

Variants Within TSC2 Exons 25 and 31 Are Very Unlikely to Cause Clinically Diagnosable Tuberous Sclerosis

Inactivating mutations in TSC1 and TSC2 cause tuberous sclerosis complex (TSC). The 2012 international consensus meeting on TSC diagnosis and management agreed that the identification of a pathogenic TSC1 or TSC2 variant establishes a diagnosis of TSC, even in the absence of clinical signs. However, exons 25 and 31 of TSC2 are subject to alternative splicing. No variants causing clinically diagnosed TSC have been reported in these exons, raising the possibility that such variants would not cause TSC. We present truncating and in‐frame variants in exons 25 and 31 in three individuals unlikely to fulfil TSC diagnostic criteria and examine the importance of these exons in TSC using different approaches. Amino acid conservation analysis suggests significantly less conservation in these exons compared with the majority of TSC2 exons, and TSC2 expression data demonstrates that the majority of TSC2 transcripts lack exons 25 and/or 31 in many human adult tissues. In vitro assay of both exons shows that neither exon is essential for TSC complex function. Our evidence suggests that variants in TSC2 exons 25 or 31 are very unlikely to cause classical TSC, although a role for these exons in tissue/stage specific development cannot be excluded