Weighted Coloring in Trees

A proper coloring of a graph is a partition of its vertex set into stable sets, where each part corresponds to a color. For a vertex-weighted graph, the weight of a color is the maximum weight of its vertices. The weight of a coloring is the sum of the weights of its colors. Guan and Zhu (1997) defined the weighted chromatic number of a vertex-weighted graph G as the smallest weight of a proper coloring of G. If vertices of a graph have weight 1, its weighted chromatic number coincides with its chromatic number. Thus, the problem of computing the weighted chromatic number, a.k.a. Max Coloring Problem, is NP-hard in general graphs. It remains NP-hard in some graph classes as bipartite graphs. Approximation algorithms have been designed in several graph classes, in particular, there exists a PTAS for trees. Surprisingly, the time-complexity of computing this parameter in trees is still open. The Exponential Time Hypothesis (ETH) states that 3-SAT cannot be solved in sub-exponential time. We show that, assuming ETH, the best algorithm to compute the weighted chromatic number of n-node trees has time-complexity n O(log(n)). Our result mainly relies on proving that, when computing an optimal proper weighted coloring of a graph G, it is hard to combine colorings of its connected components

Ensaios em finanças aplicadas : normas contábeis, estrutura de dependência e volatilidade

Nesta pesquisa, composta por três ensaios, buscamos resultados que contribuam com informações sobre três temas relevantes na área de finanças: o impacto de normas internacionais na qualidade da informação contábil; quantidades e estrutura de dependência entre commodities alimentares e o petróleo; e o estudo da relação entre o retorno e a volatilidade implícita de um fundo do mercado do petróleo. Em particular, trabalhamos para sugerir novas estratégias, com formas alternativas para a solução de problemas relacionados a esses temas. No primeiro ensaio, adotamos uma estratégia empírica, em duas etapas, para avaliar o impacto das normas internacionais de contabilidade (IFRS) na qualidade da informação contábil. Na primeira, construímos grupos de controle, por meio de um pareamento por escore de propensão, com a intenção de selecionar um contrafactual para avaliar o impacto das IFRS no Brasil. A busca e o uso de contrafactuais para a avaliação de normas contábeis ainda não foi explorado de forma adequada nos estudos específicos para o país. Na segunda etapa, estimamos modelos de painel para medidas de qualidade da informação. Os resultados apontaram para o efeito positivo da adoção de normas sobre a qualidade da informação contábil para as empresas avaliadas. No ensaio número dois, calculamos medidas de dependência entre as principais commodities alimentares e o petróleo, e testamos a existência de neutralidade entre esses mercados. Além disso, investigamos mudanças na estrutura de dependência ao passar de um período de estabilidade para um de crises. Para tanto, adotamos um procedimento que envolveu a estimação de valores para as marginais com modelos ARMA-GARCH, estimação de cópulas não paramétricas, via kernel, e cálculos aproximados de medidas de dependência. Também construímos intervalos de confi-ança para essas medidas de dependência utilizando técnicas de block bootstrap. De posse dos resultados dos intervalos refutarmos, de maneira geral, a hipótese de neutralidade entre esses mercados. Outro ponto a se destacar foi a mudança da estrutura de dependência observada ao passar de um período de estabilidade para um período de crises. Finalmente, no terceiro ensaio, realizamos a avaliação da relação entre o retorno e a volatilidade de um fundo representativo do mercado de petróleo e seu respectivo índice de volatilidade esperada. Neste ensaio, em particular, nos dedicamos na análise da não linearidade e assimetria entre os diferentes quantis de volatilidade. Com base nos resultados de regressões quantílicas e na análise não paramétrica do método B-splines, encontramos resultados que apontam para respostas de retornos negativos mais intensos do que positivos, em especial nos extremos da distribuição. E ainda, que existe uma relação no formato de "S" inclinado entre as variáveis, em forma de “U” para retornos ne-gativos e “U” invertido para retornos positivos, nos quantis (0.05, 0.90 e 0.95) de volatilidade.In this research, composed of three essays, we seek results that contribute to information on three relevant topics in the finance: the impact of international standards on the accounting information quality; Quantities and structure of dependence between grain commodities and oil; and the study of the relationship between return-volatility of an oil investment fund. In particular, we work to suggest new strategies, with alternative ways to solve problems related to these themes. In the first essay, we adopted a two-stage empirical strategy to assess the impact of international accounting standards (IFRS) on the accounting information quality. In the first stage, we constructed control groups, through a pairing by propensity score macthing, with the intention of selecting a counterfactual to evaluate the impact of IFRS in Brazil. The search and use of counterfactuals for the evaluation of accounting standards has not yet been adequately explored in the specific s tudies f or B razil. In the second s tep, we e stimate panel models for the main measures of information quality. The results pointed to the positive effect of adopting standards on the quality of accounting information for the companies evaluated. In essay number two, we calculated measures of dependence between the main grain commodities and oil, and we tested the existence of neutrality between these markets. In addition, we investigate changes in the dependency structure when moving from a period of stability to one of crisis. For that, we adopted a procedure that involved the estimation of values for the marginal ones with ARMA-GARCH models, estimation of non-parametric copulas, via kernel, and approximate calculations of dependence measures. We also constructed confidence intervals for these dependency measures using blockbootstrap techniques. With the results of the intervals, we refute the hypothesis of neutrality between these markets, in general. Another point to highlight was the change in the structure of dependence observed when changing from one period of stability to another of crises. Finally, in the third essay, we evaluated the relationship between the return and the volatility of a fund representative of the oil market and its expected volatility index. In this essay, in particular, we focus on the analysis of nonlinearity and asymmetry between the different quantile of volatility. Based on the results of quantile regressions and the non-parametric analysis of the B-splines method, we find results that point to responses of negative returns that are more intense than positive, especially at the extremes of the distribution. Also, there is an "S"-shaped relationship between the variables, in the form of "U"-shaped for negative returns and "U"-shaped inverted for positive returns, for the quantis (0.05, 0.90 and 0.95) of volatility

Impact of drought on grape yields in the Western Cape, South Africa

Includes bibliographical references.Droughts remain a threat to grape yields in South Africa. Previous studies on the impact of climate variability on grape yield in South Africa have focussed on either the rainfall or the impact of temperature on the grape yields; meanwhile, the grape yields may be more influenced by impacts of drought (which is function of water balance) than that of rainfall or temperature. This study investigates the impact of drought on grape yields in the Western Cape. A drought index that is based on water balance (called, Standardized Precipitation Evapotranspiration Index; hereafter SPEI) was used to analyse drought events at both farm and district scale (Robertson, Olifants River and Stellenbosch districts). Correlation analysis was used to identify the association between drought and grape yield. In addition, the performance of a grape yield model (Agricultural Production Systems sIMulator, APSIM) in simulating the grape yield at farm scale and investigating the sensitivity of yields to drought, with and without irrigation was evaluated

Sobre a complexidade de coloração mista

National audienceGrafos mistos são estruturas matemáticas que mesclam características de grafos direcionados e não-direcionados. Formalmente, um grafo misto pode ser definido por uma tripla GM = (V, A, E), onde V , A e E representam, respectivamente, um conjunto de vértices, de arcos e de arestas. Uma k-coloração mista de GM = (V, A, E) é função c : V → {0, . . . , k − 1} tal que c(u) < c(v), se (u, v) ∈ A, e c(u) = c(v), se [u, v] ∈ E. O problema de Coloração Mista consiste em determinar o número cromático misto de GM , denotado por χM (GM ), que é o menor inteiro k tal que GM admite uma k-coloração mista. Esse problema modela variações de problemas de escalonamento que consideram simultaneamente restrições de precedência e de compartilhamento de recursos. Neste trabalho, mostramos que Coloração Mista é N P -difícil para as classes dos grafos cordais, dos grafos linha de grafos bipartidos e dos grafos linha de grafos periplanares

Renewable energy for sustainable mining

Mining industry is known for requiring energy-intensive processes with significant impacts on the greenhouse gas emissions, which represents a major concern to both economic competitiveness of the sector and climate change. Low carbon sustainable technologies as renewable energy sources (RES) are emerging as key opportunities to sustainable mining in tandem with climate change challenges. However, the use of RES on this sector is still scarce even in countries well known for their mining potential and availability of renewable energy resources, as is the case of Brazil. This research investigates the economic viability of a proposed renewable-mining model for a mining company in the Northeast region of Brazil. The case of photovoltaic is analyzed considering the avoided electricity grid costs as potential benefits. The results showed that this renewable-mining strategy is promising for both PV and storage-PV.Mining industry is known for requiring energy-intensive processes with significant impacts on the greenhouse gas emissions, which represents a major concern to both economic competitiveness of the sector and climate change. Low carbon sustainable technologies as renewable energy sources (RES) are emerging as key opportunities to sustainable mining in tandem with climate change challenges. However, the use of RES on this sector is still scarce even in countries well known for their mining potential and availability of renewable energy resources, as is the case of Brazil. This research investigates the economic viability of a proposed renewable-mining model for a mining company in the Northeast region of Brazil. The case of photovoltaic is analyzed considering the avoided electricity grid costs as potential benefits. The results showed that this renewable-mining strategy is promising for both PV and storage-PV.This work has been supported by FCT - Fundacao para a Ciencia e Tecnologia within the Project Scope: UID/CEC/00319/2019; and CAPES and Science Without Borders scholarship, BEX Process 10.190-13-9