Thomas Decomposition of Algebraic and Differential Systems

In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new algorithm. For algebraic systems simplicity means triangularity, squarefreeness and non-vanishing initials. For differential systems the algorithm provides not only algebraic simplicity but also involutivity. The algorithm has been implemented in Maple

Algorithmic Thomas Decomposition of Algebraic and Differential Systems

In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems, simplicity means triangularity, square-freeness and non-vanishing initials. Differential simplicity extends algebraic simplicity with involutivity. We build upon the constructive ideas of J. M. Thomas and develop them into a new algorithm for disjoint decomposition. The given paper is a revised version of a previous paper and includes the proofs of correctness and termination of our decomposition algorithm. In addition, we illustrate the algorithm with further instructive examples and describe its Maple implementation together with an experimental comparison to some other triangular decomposition algorithms.Comment: arXiv admin note: substantial text overlap with arXiv:1008.376

Parameter optimization by using differential elimination: a general approach for introducing constraints into objective functions

<p>Abstract</p> <p>Background</p> <p>The investigation of network dynamics is a major issue in systems and synthetic biology. One of the essential steps in a dynamics investigation is the parameter estimation in the model that expresses biological phenomena. Indeed, various techniques for parameter optimization have been devised and implemented in both free and commercial software. While the computational time for parameter estimation has been greatly reduced, due to improvements in calculation algorithms and the advent of high performance computers, the accuracy of parameter estimation has not been addressed. </p> <p>Results</p> <p>We propose a new approach for parameter optimization by using differential elimination, to estimate kinetic parameter values with a high degree of accuracy. First, we utilize differential elimination, which is an algebraic approach for rewriting a system of differential equations into another equivalent system, to derive the constraints between kinetic parameters from differential equations. Second, we estimate the kinetic parameters introducing these constraints into an objective function, in addition to the error function of the square difference between the measured and estimated data, in the standard parameter optimization method. To evaluate the ability of our method, we performed a simulation study by using the objective function with and without the newly developed constraints: the parameters in two models of linear and non-linear equations, under the assumption that only one molecule in each model can be measured, were estimated by using a genetic algorithm (GA) and particle swarm optimization (PSO). As a result, the introduction of new constraints was dramatically effective: the GA and PSO with new constraints could successfully estimate the kinetic parameters in the simulated models, with a high degree of accuracy, while the conventional GA and PSO methods without them frequently failed.</p> <p>Conclusions</p> <p>The introduction of new constraints in an objective function by using differential elimination resulted in the drastic improvement of the estimation accuracy in parameter optimization methods. The performance of our approach was illustrated by simulations of the parameter optimization for two models of linear and non-linear equations, which included unmeasured molecules, by two types of optimization techniques. As a result, our method is a promising development in parameter optimization. </p

Correction of a lunar-irradiance model for aerosol optical depth retrieval and comparison with a star photometer

The emergence of Moon photometers is allowing measurements of lunar irradiance over the world and increasing the potential to derive aerosol optical depth (AOD) at night-time, which is very important in polar areas. Actually, new photometers implement the latest technological advances that permit lunar-irradiance measurements together with classical Sun photometry measurements. However, a proper use of these instruments for AOD retrieval requires accurate time-dependent knowledge of the extraterrestrial lunar irradiance over time due to its fast change throughout the Moon's cycle. This paper uses the RIMO (ROLO Implementation for Moon's Observation) model (an implementation of the ROLO – RObotic Lunar Observatory – model) to estimate the AOD at night-time assuming that the calibration of the solar channels can be transferred to the Moon by a vicarious method. However, the obtained AOD values using a Cimel CE318-T Sun–sky–Moon photometer for 98 pristine nights with low and stable AOD at the Izaña Observatory (Tenerife, Spain) are not in agreement with the expected (low and stable) AOD values estimated by linear interpolations from daytime values obtained during the previous evening and the following morning. Actually, AOD calculated using RIMO shows negative values and with a marked cycle dependent on the optical air mass. The differences between the AOD obtained using RIMO and the expected values are assumed to be associated with inaccuracies in the RIMO model, and these differences are used to calculate the RIMO correction factor (RCF). The RCF is a proposed correction factor that, multiplied by the RIMO value, gives an effective extraterrestrial lunar irradiance that provides AOD closer to the expected values. The RCF varies with the Moon phase angle (MPA) and with wavelength, ranging from 1.01 to 1.14, which reveals an overall underestimation of RIMO compared to the lunar irradiance. These obtained RCF values are modelled for each photometer wavelength to a second-order polynomial as a function of MPA. The AOD derived by this proposed method is compared with the independent AOD measurements obtained by a star photometer at Granada (Spain) for 2 years. The mean of the Moon–star AOD differences is between −0.015 and −0.005, and the standard deviation (SD) is between 0.03 and 0.04 (which is reduced to about 0.01 if 1 month of data affected by instrumental issues is not included in the analysis) for 440, 500, 675, and 870 nm; however, for 380 nm, the mean and standard deviation of these differences are higher. The Moon–star AOD differences are also analysed as a function of MPA, showing no significant dependence.This research has been supported by the Spanish Ministry of Science, Innovation and Universities (grant no. RTI2018-097864-b-I00); the Spanish Ministry of Economy and Competitiveness (grant nos. CGL2016-81092-R and CGL2017-90884-REDT); the European Union's Horizon 2020 research and innovation programme (grant no. ACTRIS IMP 871115); and the Andalusia Regional Government (grant no. P18-RT-3820)

Correction of a lunar-irradiance model for aerosol optical depth retrieval and comparison with a star photometer

Spanish Ministry of Science, Innovation and Universities RTI2018-097864-b-I00Spanish Ministry of Economy and Competitiveness CGL2016-81092-R CGL2017-90884-REDTEuropean Union's Horizon 2020 research and innovation programme ACTRIS IMP 871115Andalusia Regional Government P18-RT-382

Ozone–climate interactions and effects on solar ultraviolet radiation

This report assesses the effects of stratospheric ozone depletion and anticipated ozone recovery on the intensity of ultraviolet (UV) radiation at the Earth's surface. Interactions between changes in ozone and changes in climate, as well as their effects on UV radiation, are also considered. These evaluations focus mainly on new knowledge gained from research conducted during the last four years. Furthermore, drivers of changes in UV radiation other than ozone are discussed and their relative importance is assessed. The most important of these factors, namely clouds, aerosols and surface reflectivity, are related to changes in climate, and some of their effects on short- and long-term variations of UV radiation have already been identified from measurements. Finally, projected future developments in stratospheric ozone, climate, and other factors affecting UV radiation have been used to estimate changes in solar UV radiation from the present to the end of the 21st century. New instruments and methods have been assessed with respect to their ability to provide useful and accurate information for monitoring solar UV radiation at the Earth's surface and for determining relevant exposures of humans. Evidence since the last assessment reconfirms that systematic and accurate long-term measurements of UV radiation and stratospheric ozone are essential for assessing the effectiveness of the Montreal Protocol and its Amendments and adjustments. Finally, we have assessed aspects of UV radiation related to biological effects and human health, as well as implications for UV radiation from possible solar radiation management (geoengineering) methods to mitigate climate change

Courbure discrète : théorie et applications

International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor

Remote sensing of cloud properties and their effects on shortwave radiation

As nuvens são os principais reguladores da quantidade de radiação solar que atinge a superfície terrestre, e esta quantidade de radiação depende das suas propriedades tais como o raio efetivo e a espessura ótica. Por outro lado, as propriedades das nuvens podem sofrer alterações devido a variações nas quantidades de aerossóis levando a alterações dos efeitos radiativos das nuvens. Deste modo, o trabalho desenvolvido nesta tese visa o estudo dos efeitos radiativos das nuvens na radiação solar à superfície, e a determinação das propriedades das nuvens e das interações aerossol-nuvem utilizando diferentes métodos de deteção remota. A variabilidade sazonal dos valores médios diários dos efeitos radiativos das nuvens na radiação solar foi analisada para sete anos (2003 – 2010) de dados medidos em Évora, tendo sido encontrada uma maior variabilidade durante a primavera quando a variabilidade dos períodos de nuvens é também maior. Para o mesmo período (2003 – 2010), a espessura ótica das nuvens de água líquida foi determinada a partir de medições feitas à superfície, e foi relacionada com os efeitos radiativos correspondentes. Posteriormente, estabeleceu-se um método para determinar a espessura ótica e o raio efetivo das nuvens, baseado em reflectâncias medidas pelo SEVIRI no visível e no infravermelho próximo. As propriedades das nuvens obtidas a partir do SEVIRI sobre a região de Évora foram também relacionadas com os efeitos radiativos das nuvens à superfície para o ano 2015, e para um caso de estudo de eventos de efeitos radiativos positivos das nuvens na radiação solar. Finalmente, foi aplicado um método baseado em medições de Lidar para determinar a espessura ótica das nuvens, a qual foi utilizada para estimar a concentração de gotículas de nuvem e o raio efetivo. Estas propriedades das nuvens foram usadas para avaliar as interações aerossol-nuvem de nuvens de água líquida não precipitantes nos Açores; SUMMARY: Clouds are the main controllers of the amount of solar radiation that reaches the Earth’s surface, and this amount of radiation depends on cloud properties such as the cloud effective radius and the cloud optical thickness. On the other hand, cloud properties may change due to changes in aerosol amounts leading to changes in cloud radiative effects. Thus, the work developed in this thesis aims to study the shortwave cloud radiative effects at the surface, and to determine the cloud properties and the aerosol-cloud interactions using different remote sensing methods. The seasonal variability of the daily-mean shortwave cloud radiative effects was analysed for seven years (2003 – 2010) of measured data in Évora, and a greater variability of the radiative effects was found for springtime when the variability of cloud periods is larger. For the same period (2003 – 2010), the cloud optical thickness was retrieved from ground-based measurements and it was related to the corresponding cloud radiative effects. After, a method to retrieve the cloud thickness depth and the effective radius was established using SEVIRI measured reflectances at visible and near infrared wavelengths. The satellite retrievals over Évora region were also related to the shortwave cloud radiative effects for year 2015, and for a case study with events of positive shortwave cloud radiative effects. Finally, a method based on Lidar signals was applied to retrieve the cloud optical thickness, which was used to estimate the cloud droplet number concentration and the effective radius. These cloud properties were used to evaluate the aerosol-cloud interactions of non-precipitating water clouds over Azores