Composing dynamic programming tree-decomposition-based algorithms

Given two integers $\ell$ and $p$ as well as $\ell$ graph classes $\mathcal{H}_1,\ldots,\mathcal{H}_\ell$, the problems $\mathsf{GraphPart}(\mathcal{H}_1, \ldots, \mathcal{H}_\ell,p)$, $\mathsf{VertPart}(\mathcal{H}_1, \ldots, \mathcal{H}_\ell)$, and $\mathsf{EdgePart}(\mathcal{H}_1, \ldots, \mathcal{H}_\ell)$ ask, given graph $G$ as input, whether $V(G)$, $V(G)$, $E(G)$ respectively can be partitioned into $\ell$ sets $S_1, \ldots, S_\ell$ such that, for each $i$ between $1$ and $\ell$, $G[V_i] \in \mathcal{H}_i$, $G[V_i] \in \mathcal{H}_i$, $(V(G),S_i) \in \mathcal{H}_i$ respectively. Moreover in $\mathsf{GraphPart}(\mathcal{H}_1, \ldots, \mathcal{H}_\ell,p)$, we request that the number of edges with endpoints in different sets of the partition is bounded by $p$. We show that if there exist dynamic programming tree-decomposition-based algorithms for recognizing the graph classes $\mathcal{H}_i$, for each $i$, then we can constructively create a dynamic programming tree-decomposition-based algorithms for $\mathsf{GraphPart}(\mathcal{H}_1, \ldots, \mathcal{H}_\ell,p)$, $\mathsf{VertPart}(\mathcal{H}_1, \ldots, \mathcal{H}_\ell)$, and $\mathsf{EdgePart}(\mathcal{H}_1, \ldots, \mathcal{H}_\ell)$. We show that, in some known cases, the obtained running times are comparable to those of the best know algorithms

Fatigue Damage Evaluation in Ceramic Matrix Composite

Damage is conventionally defined as the progressive deterioration of materials due to nucleation and growth of microcracks. The purpose of the damage concept [1] is to take into account the microscopic deterioration of the material in its macroscopic constitutive law. In composite materials, the microcracks have a preferential orientation and the damage variable depends on the direction of measurement [2]. Non linear analysis of such materials must consider this anisotropy by introducing a tensorial damage variable in the constitutive equations [3]. The main difficulties when dealing with anisotropic description of damage are to be able to identify the introduced parameters [4]

Contraction-Bidimensionality of Geometric Intersection Graphs

Given a graph G, we define bcg(G) as the minimum k for which G can be contracted to the uniformly triangulated grid Gamma_k. A graph class G has the SQGC property if every graph G in G has treewidth O(bcg(G)c) for some 1 <= c < 2. The SQGC property is important for algorithm design as it defines the applicability horizon of a series of meta-algorithmic results, in the framework of bidimensionality theory, related to fast parameterized algorithms, kernelization, and approximation schemes. These results apply to a wide family of problems, namely problems that are contraction-bidimensional. Our main combinatorial result reveals a general family of graph classes that satisfy the SQGC property and includes bounded-degree string graphs. This considerably extends the applicability of bidimensionality theory for several intersection graph classes of 2-dimensional geometrical objects

Seasonality in natural gas prices : an empirical study of Henry Hub Natural Gas Futures Prices

In this thesis we investigate whether seasonality is a significant factor in natural gas futures prices. We test for seasonality by estimating the two-factor model of Schwartz & Smith (2000), using Kalman filtering techniques in Matlab1. Next, we extend the model with a trigonometric seasonality function, following Sørensen (2002), to see if the new factor is significant and leads to better estimation of other parameters in the model2. Our results indicate that Model 1 suffers from an omitted parameter bias, caused by the lack of a seasonal factor. After including seasonality in Model 2, the model improves significantly; leading us to conclude that seasonality is present in natural gas prices. This seasonality causes prices to be higher in winter months and lower in summer months