5 research outputs found

    Time Series Analysis on Satellite Observed Carbon Dioxide Data

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    Carbon dioxide is one of the most important greenhouse gas contributing to global warming [10] and the dramatic increase of carbon dioxide in recent year has been recorded. This paper mainly analyzes the carbon dioxide data from 2011 to 2017 collected by Atmospheric Infrared Sounder (AIRS) on NASA Aqua satellite. We concentrate on the area in Caribbean ocean and northeastern state of Amazonas in Brazil. The statistical models including multiple linear regression, autoregressive–moving-average models, and discrete wavelet transform are employed to study the trends and patterns in the carbon dioxide time series. This results in a partial linear model to find the time dependency, seasonal signals, and significant environmental-factor predictors

    Finding Biclique Partitions of Co-Chordal Graphs

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    The biclique partition number (bp)(\text{bp}) of a graph GG is referred to as the least number of complete bipartite (biclique) subgraphs that are required to cover the edges of the graph exactly once. In this paper, we show that the biclique partition number (bp\text{bp}) of a co-chordal (complementary graph of chordal) graph G=(V,E)G = (V, E) is less than the number of maximal cliques (mc\text{mc}) of its complementary graph: a chordal graph Gc=(V,Ec)G^c = (V, E^c). We first provide a general framework of the ``divide and conquer" heuristic of finding minimum biclique partitions of co-chordal graphs based on clique trees. Furthermore, a heuristic of complexity O[V(V+Ec)]O[|V|(|V|+|E^c|)] is proposed by applying lexicographic breadth-first search to find structures called moplexes. Either heuristic gives us a biclique partition of GG with size mc(Gc)1\text{mc}(G^c)-1. In addition, we prove that both of our heuristics can solve the minimum biclique partition problem on GG exactly if its complement GcG^c is chordal and clique vertex irreducible. We also show that mc(Gc)2bp(G)mc(Gc)1\text{mc}(G^c) - 2 \leq \text{bp}(G) \leq \text{mc}(G^c) - 1 if GG is a split graph

    Modeling Combinatorial Disjunctive Constraints via Junction Trees

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    We introduce techniques to build small ideal mixed-integer programming (MIP) formulations of combinatorial disjunctive constraints (CDCs) via the independent branching scheme. We present a novel pairwise IB-representable class of CDCs, CDCs admitting junction trees, and provide a combinatorial procedure to build MIP formulations for those constraints. Generalized special ordered sets (SOSk\text{SOS} k) can be modeled by CDCs admitting junction trees and we also obtain MIP formulations of SOSk\text{SOS} k. Furthermore, we provide a novel ideal extended formulation of any combinatorial disjunctive constraints with fewer auxiliary binary variables with an application in planar obstacle avoidance