abstract water deficit and consecutive droughts have lead to drought stress in most parts of the world recently. we need prepare a good program to use better available water. different material can be used to increase water use efficiency. super absorbent is one of the materials used around the world. these materials absorb water in the soil so that reserved water is usable by plant in the time...

a emph{signed graph} (or, in short, emph{sigraph}) $s=(s^u,sigma)$ consists of an underlying graph $s^u :=g=(v,e)$ and a function $sigma:e(s^u)longrightarrow {+,-}$, called the signature of $s$. a emph{marking} of $s$ is a function $mu:v(s)longrightarrow {+,-}$. the emph{canonical marking} of a signed graph $s$, denoted $mu_sigma$, is given as $$mu_sigma(v) := prod_{vwin e(s)}sigma(vw).$$the li...

Estimating a covariance matrix efficiently and discovering its structure are important statistical problems with applications in many fields. This article takes a Bayesian approach to estimate the covariance matrix of Gaussian data. We use ideas from Gaussian graphical models and model selection to construct a prior for the covariance matrix that is a mixture over all decomposable graphs, where...

The purpose of this project is to show observations taken from the Iterative Proportional Scaling algorithm when used with data taken from Hierarchical LogLinear Models. We show with empirical proof that the difference between decomposable and non-decomposable graph models used is not exceedingly different. For the purpose of this project we looked at the properties of the two, three, and four ...

We explore the properties of subgraphs (called Markovian subgraphs) of a decomposable graph under some condition. For a decomposable graph G and a collection γ of its Markovian subgraphs, we show that the set χ(G) of the intersections of all the neighboring cliques of G contains ∪g∈γχ(g). We also show that χ(G) = ∪g∈γχ(g) holds for a certain type of G which we call a maximal Markovian supergrap...

In this work we focus on solving quadratically constrained pseudoboolean optimization problems with quadratic objective as mixed integer linear programs. The standard mixed integer linear formulation of such problems is strengthened using valid inequalities derived from solving Reformulation-Linearization relaxation called partial DRL* relaxation. The proposed PDRL* relaxation features block-de...

Let G = (V,E) be a graph of order n. Let f : V → {1, 2, . . . , n} be a bijection. For any vertex v ∈ V , the neighbor sum ∑u∈N(v) f(u) is called the weight of the vertex v and is denoted by w(v). If w(v) = k, (a constant) for all v ∈ V , then f is called a distance magic labeling with magic constant k. If the set of vertex weights forms an arithmetic progression {a, a+ d, a+2d, . . . , a+ (n− ...