5 research outputs found
Time Series Analysis on Satellite Observed Carbon Dioxide Data
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
The biclique partition number of a graph 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 () of a co-chordal (complementary graph of
chordal) graph is less than the number of maximal cliques
() of its complementary graph: a chordal graph . 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 is proposed by
applying lexicographic breadth-first search to find structures called moplexes.
Either heuristic gives us a biclique partition of with size
. In addition, we prove that both of our heuristics can solve
the minimum biclique partition problem on exactly if its complement
is chordal and clique vertex irreducible. We also show that if is a split graph
Modeling Combinatorial Disjunctive Constraints via Junction Trees
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 () can be modeled by CDCs admitting junction trees
and we also obtain MIP formulations of . 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