The edge-flipping group of a graph

Let $X=(V,E)$ be a finite simple connected graph with $n$ vertices and $m$ edges. A configuration is an assignment of one of two colors, black or white, to each edge of $X.$ A move applied to a configuration is to select a black edge $\epsilon\in E$ and change the colors of all adjacent edges of $\epsilon.$ Given an initial configuration and a final configuration, try to find a sequence of moves that transforms the initial configuration into the final configuration. This is the edge-flipping puzzle on $X,$ and it corresponds to a group action. This group is called the edge-flipping group $\mathbf{W}_E(X)$ of $X.$ This paper shows that if $X$ has at least three vertices, $\mathbf{W}_E(X)$ is isomorphic to a semidirect product of $(\mathbb{Z}/2\mathbb{Z})^k$ and the symmetric group $S_n$ of degree $n,$ where $k=(n-1)(m-n+1)$ if $n$ is odd, $k=(n-2)(m-n+1)$ if $n$ is even, and $\mathbb{Z}$ is the additive group of integers.Comment: 19 page

The flipping puzzle on a graph

Let $S$ be a connected graph which contains an induced path of $n-1$ vertices, where $n$ is the order of $S.$ We consider a puzzle on $S$. A configuration of the puzzle is simply an $n$-dimensional column vector over $\{0, 1\}$ with coordinates of the vector indexed by the vertex set $S$. For each configuration $u$ with a coordinate $u_s=1$, there exists a move that sends $u$ to the new configuration which flips the entries of the coordinates adjacent to $s$ in $u.$ We completely determine if one configuration can move to another in a sequence of finite steps.Comment: 18 pages, 1 figure and 1 tabl

Pooling spaces associated with finite geometry

AbstractMotivated by the works of Ngo and Du [H. Ngo, D. Du, A survey on combinatorial group testing algorithms with applications to DNA library screening, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 55 (2000) 171–182], the notion of pooling spaces was introduced [T. Huang, C. Weng, Pooling spaces and non-adaptive pooling designs, Discrete Mathematics 282 (2004) 163–169] for a systematic way of constructing pooling designs; note that geometric lattices are among pooling spaces. This paper attempts to draw possible connections from finite geometry and distance regular graphs to pooling spaces: including the projective spaces, the affine spaces, the attenuated spaces, and a few families of geometric lattices associated with the orbits of subspaces under finite classical groups, and associated with d-bounded distance-regular graphs

A study on the flexibility of enzyme active sites

<p>Abstract</p> <p>Background</p> <p>A common assumption about enzyme active sites is that their structures are highly conserved to specifically distinguish between closely similar compounds. However, with the discovery of distinct enzymes with similar reaction chemistries, more and more studies discussing the structural flexibility of the active site have been conducted.</p> <p>Results</p> <p>Most of the existing works on the flexibility of active sites focuses on a set of pre-selected active sites that were already known to be flexible. This study, on the other hand, proposes an analysis framework composed of a new data collecting strategy, a local structure alignment tool and several physicochemical measures derived from the alignments. The method proposed to identify flexible active sites is highly automated and robust so that more extensive studies will be feasible in the future. The experimental results show the proposed method is (a) consistent with previous works based on manually identified flexible active sites and (b) capable of identifying potentially new flexible active sites.</p> <p>Conclusions</p> <p>This proposed analysis framework and the former analyses on flexibility have their own advantages and disadvantage, depending on the cause of the flexibility. In this regard, this study proposes an alternative that complements previous studies and helps to construct a more comprehensive view of the flexibility of enzyme active sites.</p

Flexible shear stress sensor skin for aerodynamics applications

Packaging for a large distributed sensing system is a challenging topic. Using flexible skin technology solves many of these problems. Combining with the newly developed backside contact technique, sensor packaging is made even easier by completely avoiding the fragile bonding wires. This paper describes the improved flexible MEMS technology and its application to the fabrication and packaging of practical shear stress sensor skins. An airflow separation detection system including these skins, MOSIS bias circuits and a data acquisition unit has been successfully tested in windtunnel and is being used for the aerodynamic study of a MEMS controlled super-maneuverable low-altitude unmanned aerial vehicle (UAV)

Apoptosis signal-regulating kinase 1 mediates denbinobin-induced apoptosis in human lung adenocarcinoma cells

In the present study, we explore the role of apoptosis signal-regulating kinase 1 (ASK1) in denbinobin-induced apoptosis in human lung adenocarcinoma (A549) cells. Denbinobin-induced cell apoptosis was attenuated by an ASK1 dominant-negative mutant (ASK1DN), two antioxidants (N-acetyl-L-cysteine (NAC) and glutathione (GSH)), a c-Jun N-terminal kinase (JNK) inhibitor (SP600125), and an activator protein-1 (AP-1) inhibitor (curcumin). Treatment of A549 cells with denbinobin caused increases in ASK1 activity and reactive oxygen species (ROS) production, and these effects were inhibited by NAC and GSH. Stimulation of A549 cells with denbinobin caused JNK activation; this effect was markedly inhibited by NAC, GSH, and ASK1DN. Denbinobin induced c-Jun phosphorylation, the formation of an AP-1-specific DNA-protein complex, and Bim expression. Bim knockdown using a bim short interfering RNA strategy also reduced denbinobin-induced A549 cell apoptosis. The denbinobin-mediated increases in c-Jun phosphorylation and Bim expression were inhibited by NAC, GSH, SP600125, ASK1DN, JNK1DN, and JNK2DN. These results suggest that denbinobin might activate ASK1 through ROS production to cause JNK/AP-1 activation, which in turn induces Bim expression, and ultimately results in A549 cell apoptosis