Acyclic Bidirected and Skew-Symmetric Graphs: Algorithms and Structure

\emph{Bidirected graphs} (a sort of nonstandard graphs introduced by Edmonds and Johnson) provide a natural generalization to the notions of directed and undirected graphs. By a \emph{weakly (node- or edge-) acyclic} bidirected graph we mean such graph having no (node- or edge-) simple cycles. We call a bidirected graph \emph{strongly acyclic} if it has no cycles (even non-simple). Unlike the case of standard graphs, a bidirected graph may be weakly acyclic but still have non-simple cycles. Testing a given bidirected graph for weak acyclicity is a challenging combinatorial problem, which also has a number of applications (e.g. checking a perfect matching in a general graph for uniqueness). We present (generalizing results of Gabow, Kaplan, and Tarjan) a modification of the depth-first search algorithm that checks (in linear time) if a given bidirected graph is weakly acyclic (in case of negative answer a simple cycle is constructed). Our results are best described in terms of \emph{skew-symmetric graphs} (the latter give another, somewhat more convenient graph language which is essentially equivalent to the language of bidirected graphs). We also give structural results for the class of weakly acyclic bidirected and skew-symmetric graphs explaining how one can construct any such graph starting from strongly acyclic instances and, vice versa, how one can decompose a weakly acyclic graph into strongly acyclic ``parts''. Finally, we extend acyclicity test to build (in linear time) such a decomposition.Comment: 22 pages, 11 pictures, CSR 200

Experimental effects of fuselage camber on longitudinal aerodynamic characteristics of a series of wing-fuselage configurations at a Mach number of 1.41

An experimental investigation was conducted to evaluate a method for the integration of a fighter-type fuselage with a theoretical wing to preserve desirable wing aerodynamic characteristics for efficient maneuvering. The investigation was conducted by using semispan wing fuselage models mounted on a splitter plate. The models were tested through an angle of attack range at a Mach number of 1.41. The wing had a leading edge sweep angle of 50 deg and an aspect ratio of 2.76; the wing camber surface was designed for minimum drag due to lift and was to be self trimming at a lift coefficient of 0.2 and at a Mach number of 1.40. A series of five fuselages of various camber was tested on the wing

CT-SRCNN: Cascade Trained and Trimmed Deep Convolutional Neural Networks for Image Super Resolution

We propose methodologies to train highly accurate and efficient deep convolutional neural networks (CNNs) for image super resolution (SR). A cascade training approach to deep learning is proposed to improve the accuracy of the neural networks while gradually increasing the number of network layers. Next, we explore how to improve the SR efficiency by making the network slimmer. Two methodologies, the one-shot trimming and the cascade trimming, are proposed. With the cascade trimming, the network's size is gradually reduced layer by layer, without significant loss on its discriminative ability. Experiments on benchmark image datasets show that our proposed SR network achieves the state-of-the-art super resolution accuracy, while being more than 4 times faster compared to existing deep super resolution networks.Comment: Accepted to IEEE Winter Conf. on Applications of Computer Vision (WACV) 2018, Lake Tahoe, US

On the complements of 3-dimensional convex polyhedra as polynomial images of R3{\mathbb R}^3

We prove that the complement ${\mathcal S}:={\mathbb R}^3\setminus{\mathcal K}$ of a 3-dimensional convex polyhedron ${\mathcal K}\subset{\mathbb R}^3$ and its closure $\overline{{\mathcal S}}$ are polynomial images of ${\mathbb R}^3$. The former techniques cannot be extended in general to represent such semialgebraic sets ${\mathcal S}$ and $\overline{{\mathcal S}}$ as polynomial images of ${\mathbb R}^n$ if $n\geq4$.Comment: 12 pages, 1 figur