On the Explicit Solutions of Separation of Variables Type for the Incompressible 2D Euler Equations

We study explicit solutions to the 2 dimensional Euler equations in the Lagrangian framework. All known solutions have been of the separation of variables type, where time and space dependence are treated separately. The first such solutions were known already in the 19th century. We show that all the solutions known previously belong to two families of solutions and introduce three new families of solutions. It seems likely that these are all the solutions that are of the separation of variables type.

Transition waves for lattice Fisher-KPP equations with time and space dependence

This paper is concerned with the existence results for generalized transition waves of space periodic and time heterogeneous lattice Fisher-KPP equations. By constructing appropriate subsolutions and supersolutions, we show that there is a critical wave speed such that a transition wave solution exists as soon as the least mean of wave speed is above this critical speed. Moreover, the critical speed we construct is proved to be minimal in some particular cases, such as space-time periodic or space independent.

Symbolic Analysis Applied to the Specification of Spatial Trends and Spatial Dependence

This article provides symbolic analysis tools for specifying spatial econometric models. It firstly considers testing spatial dependence in the presence of potential leading deterministic spatial components (similar to time-series tests for unit roots in the presence of temporal drift and/or time-trend) and secondly considers how to econometrically model spatial economic relations that might contain unobserved spatial structure of unknown form. Hypothesis testing is conducted with a symbolic-entropy based non-parametric statistical procedure, recently proposed by Garcia-Cordoba, Matilla-Garcia, and Ruiz (2019), which does not rely on prior weight matrices assumptions. It is shown that the use of geographically restricted semiparametric spatial models is a promising modeling strategy for cross-sectional datasets that are compatible with some types of spatial dependence. The results state that models that merely incorporate space coordinates might be sufficient to capture space dependence. Hedonic models for Baltimore, Boston, and Toledo housing prices datasets are revisited, studied (with the new proposed procedures), and compared with standard spatial econometric methodologies.

A New Technique Based on Voronoi Tessellation to Assess the Space-Dependence of Categorical Variables

Based on a sample of geolocated elements, each of them labeled with a (not necessarily ordered) categorical feature, several indexes for assessing the relationship between the geolocation variables (latitude and longitude) and the categorical variable are evaluated. Among these indexes, a new one based on a Voronoi tessellation presents several advantages since it does not require a variable transformation or a previous discretization; in addition, simulations show that this index is considerably robust when compared with the previously known ones. Finally, the use of the presented indexes is also illustrated by analyzing the geolocation of communities in some communication networks derived from Call Detail Records.

Mitochondrial morphology provides a mechanism for energy buffering at synapses

Mitochondria as the main energy suppliers of eukaryotic cells are highly dynamic organelles that fuse, divide and are transported along the cytoskeleton to ensure cellular energy homeostasis. While these processes are well established, substantial evidence indicates that the internal structure is also highly variable in dependence on metabolic conditions. However, a quantitative mechanistic understanding of how mitochondrial morphology affects energetic states is still elusive. To address this question, we here present an agent-based dynamic model using three-dimensional morphologies from electron microscopy tomography which considers the molecular dynamics of the main ATP production components. We apply our modeling approach to mitochondria at the synapse which is the largest energy consumer within the brain. Interestingly, comparing the spatiotemporal simulations with a corresponding space-independent approach, we find minor space dependence when the system relaxes toward equilibrium but a qualitative difference in fluctuating environments. These results suggest that internal mitochondrial morphology is not only optimized for ATP production but also provides a mechanism for energy buffering and may represent a mechanism for cellular robustness.

SPACE DEPENDENCE OF SOIL MOISTURE AND SOIL ELECTRICAL CONDUCTIVITY IN ALUVIAL REGION1

SPACE DEPENDENCE OF SOIL MOISTURE AND SOIL ELECTRICAL CONDUCTIVITY IN ALUVIAL REGION1 IUG LOPES2 E ABELARDO ANTONIO DE ASSUNÇÃO MONTENEGRO3 1Paper extracted from the doctoral thesis of the first author. 2Department of Agronomy, Instituto Federal de Educação, Ciência e Tecnologia Baiano, BR 349, Km 14 - Zona Rural, CEP: 47600-000, Bom Jesus da Lapa - BA, Brazil; [email protected] - ORCID: 0000-0003-0592-4774. 3Department of Agricultural Engineering, Universidade Federal Rural de Pernambuco, Rua Dom Manoel de Medeiros, Dois Irmão, CEP: 52171-900, Recife - PE, Brazil; [email protected] -ORCID: 0000-0002-5746-8574. 1 ABSTRACT Spatial information on soil characteristics is essential to proper decision-making regarding to the environment and land use management. The objective of this work was the investigation of cross - variance between soil moisture and apparent soil electrical conductivity (CEa), under different land uses in an alluvial valley of Pernambuco. The study was developed at the Advanced Research Unit of Universidade Federal Rural de Pernambuco (UFRPE), located at Brígida River Basin, municipality of Panamirim-PE. Soil samples were collected in a regular mesh of 20 x 10 m, for soil moisture by gravimetric method and, following a regular 10 x 10 m mesh, CEa measurements were performed using EM38® device. Cross-semivariograms were assessed and spatial dependence was verified by geostatistical procedures. It was verified in geostatistical procedures low variation for soil moisture and intermediate variation for CEa. The use of geostatistics allowed identification of covariance between soil moisture and ECa, as well as spatial dependence for both variables, for agricultural areas. It was verified that soil moisture, even at levels close to residual, constitutes a relevant secondary component for increasing soil salinity maps precision, and hence to precision agriculture. Keywords: geostatistics, semi-arid, precision agriculture LOPES, I. E MONTENEGRO, A. A. DE A. DEPENDÊNCIA ESPACIAL DA UMIDADE DO SOLO E CONDUTIVIDADE ELÉTRICA EM REGIÃO ALUVIAL 2 RESUMO Informações espaciais sobre as características do solo são essenciais para uma tomada de decisão adequada em relação ao meio ambiente e ao gerenciamento do uso do solo. O objetivo deste trabalho foi investigar a variância cruzada entre a umidade do solo e a condutividade elétrica aparente do solo (CEa), sob diferentes usos do solo em um vale aluvial de Pernambuco. O estudo foi desenvolvido na Unidade de Pesquisa Avançada da Universidade Federal Rural de Pernambuco (UFRPE), localizada na bacia do rio Brígida, município de Panamirim-PE. As amostras de solo foram coletadas em uma malha regular de 20 x 10 m, para a umidade do solo pelo método gravimétrico e, seguindo uma malha regular de 10 x 10 m, as medidas de CEa foram realizadas usando o dispositivo EM38®. Os semivariogramas cruzados foram avaliados e a dependência espacial foi verificada por procedimentos geoestatísticos. Verificou-se procedimentos geoestatísticos, uma baixa variação da umidade do solo e variação intermediária para CEa. O uso da geoestatística permitiu identificar a covariância entre a umidade do solo e o CEa, bem como a dependência espacial para ambas as variáveis, para as áreas agrícolas. Verificou-se que a umidade do solo, mesmo em níveis próximos ao residual, constitui um componente secundário relevante para o aumento da precisão do mapeamento da salinidade do solo e, consequentemente, para a agricultura de precisão. Palavras-chave: geoestatística, semiárido, agricultura de precisão