One-loop conformal anomaly in an implicit momentum space regularization framework

In this paper we consider matter fields in a gravitational background in order to compute the breaking of the conformal current at one-loop order. Standard perturbative calculations of conformal symmetry breaking expressed by the non-zero trace of the energy-momentum tensor have shown that some violating terms are regularization dependent, which may suggest the existence of spurious breaking terms in the anomaly. Therefore, we perform the calculation in a momentum space regularization framework in which regularization dependent terms are judiciously parametrized. We compare our results with those obtained in the literature and conclude that there is an unavoidable arbitrariness in the anomalous term $\Box R$.Comment: in European Physical Journal C, 201

Existence results for a fourth order partial differential equation arising in condensed matter physics

We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation whose nonlinearity is the determinant of the Hessian matrix of the solution. We consider this model in a bounded domain of the real plane and study its stationary solutions both when the geometry of this domain is arbitrary and when it is the unit ball and the solution is radially symmetric. We also consider the initial-boundary value problem for the full parabolic equation. We summarize our results on existence of solutions in these cases and propose an open problem related to the existence of self-similar solutions.Comment: To appear in Mathematica Bohemic

Evolução da produção e do mercado mundial do feijão.

Realizou-se uma avaliação do mercado internacional de feijão, considerando produção, exportação e importação, mostrando o comportamento e oscilações dos principais países

On Optimal Regularization Parameters via Bilevel Learning

Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information, and is weighted by a regularization parameter. Selection of an appropriate regularization parameter is critical, with various choices leading to very different reconstructions. Existing strategies such as the discrepancy principle and L-curve can be used to determine a suitable parameter value, but in recent years a supervised machine learning approach called bilevel learning has been employed. Bilevel learning is a powerful framework to determine optimal parameters, and involves solving a nested optimisation problem. While previous strategies enjoy various theoretical results, the well-posedness of bilevel learning in this setting is still a developing field. One necessary property is positivity of the determined regularization parameter. In this work, we provide a new condition that better characterises positivity of optimal regularization parameters than the existing theory. Numerical results verify and explore this new condition for both small and large dimensional problems.Comment: 26 pages, 6 figure

Brazil nut almonds: nutritional and market aspects.

The aim of this study was to estimate the annual growth rate in production and exportation of Brazil nut almonds. Presents information related to the composition of different fatty acids from brazil nut almonds and the human daily intake needs, as well as an analysis of its production, its growth rate during the last 20 years and its export. and the human daily intake needs

Sharing Positive Affective States Amongst Rodents

Group living is thought to benefit from the ability to empathize with others. Much attention has been paid to empathy for the pain of others as an inhibitor of aggression. Empathizing with the positive affect of others has received less attention although it could promote helping by making it vicariously rewarding. Here, we review this latter, nascent literature to show that three components of the ability to empathize with positive emotions are already present in rodents, namely, the ability to perceive, share, and prefer actions that promote positive emotional states of conspecifics. While it has often been argued that empathy evolved as a motivation to care for others, we argue that these tendencies may have selfish benefits that could have stabilized their evolution: approaching others in a positive state can provide information about the source of valuable resources; becoming calmer and optimistic around animals in a calm or positive mood can help adapt to the socially sensed safety level in the environment; and preferring actions also benefiting others can optimize foraging, reduce aggression, and trigger reciprocity. Together, these findings illustrate an emerging field shedding light on the emotional world of rodents and on the biology and evolution of our ability to cooperate in groups.</p

Consumo, valor nutritivo e evolução da produção e de mercado mundial de feijão.

Apresentado Painel na 6º Semana de Ensino, Pesquisa e Extensão Universidade Federal de Santa Catarina

On Optimal Regularization Parameters via Bilevel Learning

Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter. Selection of an appropriate regularization parameter is critical, with various choices leading to very different reconstructions. Classical strategies used to determine a suitable parameter value include the discrepancy principle and the L-curve criterion, and in recent years a supervised machine learning approach called bilevel learning has been employed. Bilevel learning is a powerful framework to determine optimal parameters and involves solving a nested optimization problem. While previous strategies enjoy various theoretical results, the well-posedness of bilevel learning inthis setting is still an open question. In particular, a necessary property is positivity of the determined regularization parameter. In this chapter, we provide a new condition that better characterizes positivity of optimal regularization parameters than the existing theory. Numerical results verify and explore this new condition for both small and high-dimensional problems

Nature versus Nurture: The curved spine of the galaxy cluster X-ray luminosity -- temperature relation

The physical processes that define the spine of the galaxy cluster X-ray luminosity -- temperature (L-T) relation are investigated using a large hydrodynamical simulation of the Universe. This simulation models the same volume and phases as the Millennium Simulation and has a linear extent of 500 h^{-1} Mpc. We demonstrate that mergers typically boost a cluster along but also slightly below the L-T relation. Due to this boost we expect that all of the very brightest clusters will be near the peak of a merger. Objects from near the top of the L-T relation tend to have assembled much of their mass earlier than an average halo of similar final mass. Conversely, objects from the bottom of the relation are often experiencing an ongoing or recent merger.Comment: 8 pages, 7 figures, submitted to MNRA